Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.

}, keywords = {active matter, adhesive locomotion, cell motility, cell sheet folding, knotted DNA, topological defects, unicellular swimmers, unjamming transition}, issn = {2640-3501}, doi = {10.3934/mine.2020011}, url = {http://dx.doi.org/10.3934/mine.2020011}, author = {Daniele Agostinelli and Roberto Cerbino and Del Alamo, Juan C and Antonio DeSimone and Stephanie H{\"o}hn and Cristian Micheletti and Giovanni Noselli and Eran Sharon and Julia Yeomans} } @article {AlzettaHeltai-2020-a, title = {Multiscale modeling of fiber reinforced materials via non-matching immersed methods}, journal = {Computers \& Structures}, year = {2020}, note = {To appear}, url = {https://arxiv.org/abs/1906.03881}, author = {Giovanni Alzetta and Luca Heltai} } @article {Agostinelli2020.07.06.188987, title = {Nutations in plant shoots: endogenous and exogenous factors in the presence of mechanical deformations}, year = {2020}, institution = {Cold Spring Harbor Laboratory}, type = {preprint}, abstract = {We present a three-dimensional morphoelastic rod model capable to describe the morphogenesis of growing plant shoots, as driven by differential growth at the tip. We discuss the evolution laws for endogenous oscillators, straightening mechanisms and reorientations to directional cues, such as phototropic responses to a far light source and gravitropic reactions governed by the statoliths avalanche dynamics. We use this model to investigate the role of elastic deflections due to gravity loading in circumnutating plant shoots. We show that, in the absence of endogenous cues, pendular and circular oscillations arise as a critical length is attained, thus suggesting the occurrence of a Hopf bifurcation reminiscent of flutter instabilities exhibited by structural systems under nonconservative loads. When also oscillations due to endogenous cues are present, their weight relative to those associated with the Hopf instability varies in time as the shoot length and other biomechanical properties change. Thanks to the simultaneous occurrence of these two oscillatory mechanisms, we are able to reproduce a variety of complex behaviors, including trochoid-like patterns, which evolve into circular orbits as the shoot length increases, and the amplitude of the flutter induced oscillations becomes dominant. Our findings suggest that the relative importance of the two mechanisms is an emergent property of the system that is affected by the amplitude of elastic deformations, and highlight the crucial role of elasticity in the analysis of circumnutations.Competing Interest StatementThe authors have declared no competing interest.

}, doi = {10.1101/2020.07.06.188987}, url = {https://www.biorxiv.org/content/early/2020/07/06/2020.07.06.188987}, author = {Daniele Agostinelli and Antonio DeSimone and Giovanni Noselli} } @conference {2020, title = {A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries}, booktitle = {IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22{\textendash}25, 2018}, year = {2020}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, abstract = {A model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat transfer problems and we rely on a sufficiently refined shape-regular background mesh to account for parametrized geometries. In particular, the employed embedded boundary element method is the Shifted Boundary Method (SBM) recently proposed. This approach is based on the idea of shifting the location of true boundary conditions to a surrogate boundary, with the goal of avoiding cut cells near the boundary of the computational domain. This combination of methodologies has multiple advantages. In the first place, since the Shifted Boundary Method always relies on the same background mesh, there is no need to update the discretized parametric domain. Secondly, we avoid the treatment of cut cell elements, which usually need particular attention. Thirdly, since the whole background mesh is considered in the reduced basis construction, the SBM allows for a smooth transition of the reduced modes across the immersed domain boundary. The performances of the method are verified in two dimensional heat transfer numerical examples.

}, doi = {10.1007/978-3-030-21013-7_8}, url = {https://arxiv.org/abs/1807.07753}, author = {Efthymios N. Karatzas and Giovanni Stabile and Nabib Atallah and Guglielmo Scovazzi and Gianluigi Rozza}, editor = {Fehr, J{\"o}rg and Haasdonk, Bernard} } @article {riccobelli2018activation, title = {Activation of a muscle as a mapping of stress{\textendash}strain curves}, journal = {Extreme Mech. Lett.}, volume = {28}, year = {2019}, pages = {37{\textendash}42}, publisher = {Elsevier BV}, author = {Davide Riccobelli and D. Ambrosi} } @article {ArndtBangerthClevenger-2019-a, title = {The deal.II Library, Version 9.1}, journal = {Journal of Numerical Mathematics}, year = {2019}, abstract = {This paper provides an overview of the new features of the finite element library deal.II, version 9.1.}, issn = {15702820}, doi = {10.1515/jnma-2019-0064}, author = {Arndt, Daniel and Bangerth, Wolfgang and Clevenger, Thomas C. and Davydov, Denis and Fehling, Marc and Garcia-Sanchez, Daniel and Harper, Graham and Heister, Timo and Heltai, Luca and Kronbichler, Martin and Maguire Kynch, Ross and Maier, Matthias and Pelteret, Jean Paul and Turcksin, Bruno and Wells, David} } @article {riccobelli2018constitutive, title = {On the existence of elastic minimizers for initially stressed materials}, journal = {Phil. Trans. R. Soc. A}, volume = {377}, number = {2144}, year = {2019}, publisher = {The Royal Society}, author = {Davide Riccobelli and A. Agosti and Pasquale Ciarletta} } @article {2019, title = {A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {351}, year = {2019}, pages = {379-403}, abstract = {Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional discretizations of partial differential equations (PDEs) that can be used to more efficiently treat problems in control and optimization, uncertainty quantification, and other settings that require multiple approximate PDE solutions. In this work, a ROM is developed and tested for the treatment of nonlinear PDEs whose solutions bifurcate as input parameter values change. In such cases, the parameter domain can be subdivided into subregions, each of which corresponds to a different branch of solutions. Popular ROM approaches such as proper orthogonal decomposition (POD), results in a global low-dimensional basis that does no respect not take advantage of the often large differences in the PDE solutions corresponding to different subregions. Instead, in the new method, the k-means algorithm is used to cluster snapshots so that within cluster snapshots are similar to each other and are dissimilar to those in other clusters. This is followed by the construction of local POD bases, one for each cluster. The method also can detect which cluster a new parameter point belongs to, after which the local basis corresponding to that cluster is used to determine a ROM approximation. Numerical experiments show the effectiveness of the method both for problems for which bifurcation cause continuous and discontinuous changes in the solution of the PDE.

}, doi = {10.1016/j.cma.2019.03.050}, url = {https://arxiv.org/abs/1807.08851}, author = {Hess, Martin and Alla, Alessandro and Quaini, Annalisa and Rozza, Gianluigi and Gunzburger, Max} } @article {AGOSTINELLI2019103702, title = {Nutations in growing plant shoots: The role of elastic deformations due to gravity loading}, journal = {Journal of the Mechanics and Physics of Solids}, year = {2019}, pages = {103702}, abstract = {The effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin{\textquoteright}s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.

}, keywords = {Circumnutations, Flutter instability, Gravitropism, Hopf bifurcation}, issn = {0022-5096}, doi = {10.1016/j.jmps.2019.103702}, url = {https://doi.org/10.1016/j.jmps.2019.103702}, author = {Daniele Agostinelli and Alessandro Lucantonio and Giovanni Noselli and Antonio DeSimone} } @article {2019, title = {Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras}, journal = {arXiv e-prints}, year = {2019}, month = {May}, pages = {arXiv:1905.07730}, abstract = {We strengthen a result of Hanke{\textendash}Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group $C^*$-algebra even holds for the reduced group $C^*$-algebra. To achieve this we provide a Fell absorption principle for certain exotic crossed product functors.

}, keywords = {Mathematics - K-Theory and Homology, Mathematics - Operator Algebras}, author = {Paolo Antonini and Buss, Alcides and Engel, Alexander and Siebenand , Timo} } @article {2018arXiv180705892A, title = {The Baum{\textendash}Connes conjecture localised at the unit element of a discrete group}, journal = {ArXiv e-prints}, year = {2018}, keywords = {19K35, 46L80, 46L85, 58J22, Mathematics - K-Theory and Homology, Mathematics - Operator Algebras}, author = {Paolo Antonini and Azzali, S. and Skandalis, G.} } @inbook {AuricchioContiLefieuxMorgantiRealiRozzaVeneziani2018, title = {Computational methods in cardiovascular mechanics}, booktitle = {Cardiovascular Mechanics}, year = {2018}, pages = {54}, publisher = {CRC Press}, organization = {CRC Press}, chapter = {Computational methods in cardiovascular mechanics}, abstract = {The introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.

}, url = {https://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201\%2Fb21917-5}, author = {Auricchio, Ferdinando and Conti, Michele and Lefieux, Adrian and Morganti, Simone and Alessandro Reali and Gianluigi Rozza and Veneziani, Alessandro}, editor = {Michel F. Labrosse} } @article {20.500.11767_81694, title = {The deal.II Library, Version 9.0}, journal = {JOURNAL OF NUMERICAL MATHEMATICS}, year = {2018}, doi = {10.1515/jnma-2018-0054}, url = {https://doi.org/10.1515/jnma-2018-0054}, author = {Giovanni Alzetta and Arndt, Daniel and W. Bangerth and Boddu, Vishal and Brands, Benjamin and Denis Davydov and Gassm{\"o}ller, Rene and Timo Heister and Luca Heltai and Kormann, Katharina and Martin Kronbichler and Matthias Maier and Pelteret, Jean-Paul and B. Turcksin and David Wells} } @booklet {1807.11370, title = {The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows}, year = {2018}, author = {Saddam Hijazi and Shafqat Ali and Giovanni Stabile and Francesco Ballarin and Gianluigi Rozza} } @article {agostiniani2018foldable, title = {Foldable structures made of hydrogel bilayers}, year = {2018}, author = {Virginia Agostiniani and Antonio DeSimone and Alessandro Lucantonio and Danka Lu{\v c}i{\'c}} } @article {Antonelli2018, title = {Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials}, journal = {Zeitschrift f{\"u}r angewandte Mathematik und Physik}, volume = {69}, number = {2}, year = {2018}, month = {Mar}, pages = {46}, abstract = {We prove the existence of weak solutions in the space of energy for a class of nonlinear Schr{\"o}dinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

}, issn = {1420-9039}, doi = {10.1007/s00033-018-0938-5}, url = {https://doi.org/10.1007/s00033-018-0938-5}, author = {Paolo Antonelli and Alessandro Michelangeli and Raffaele Scandone} } @article {agostiniani2018heterogeneous, title = {Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, year = {2018}, publisher = {EDP Sciences}, doi = {https://doi.org/10.1051/cocv/2018046}, author = {Virginia Agostiniani and Alessandro Lucantonio and Danka Lu{\v c}i{\'c}} } @article {2018, title = {Peristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots}, journal = {Frontiers in Robotics and AI}, volume = {5}, year = {2018}, month = {09/2018}, abstract = {*Peristalsis*, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a {\textquotedblleft}phase coordination{\textquotedblright} principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed.

In the setting of planar linearized elasticity, we study a fracture model depending on the crack opening. Assuming that the crack path is known a priori and sufficiently smooth, we prove that the energy release rate is well defined. Then, we consider the problem of quasi-static evolution for our model. Thanks to a vanishing viscosity approach, we show the existence of such an evolution satisfying a weak Griffith{\textquoteright}s criterion.

}, doi = {10.1051/cocv/2016014}, url = {https://www.esaim-cocv.org/component/article?access=doi\&doi=10.1051/cocv/2016014}, author = {Stefano Almi} } @article {2017, title = {Friedrichs systems in a Hilbert space framework: solvability and multiplicity}, number = {SISSA;16/2017/MATE}, year = {2017}, abstract = {The Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antoni{\'c} and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide suffcient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.}, url = {http://preprints.sissa.it/handle/1963/35280}, author = {Nenad Antoni{\'c} and Marko Erceg and Alessandro Michelangeli} } @article {Agrachev2017, title = {Homotopically invisible singular curves}, journal = {Calculus of Variations and Partial Differential Equations}, volume = {56}, number = {4}, year = {2017}, month = {Jul}, pages = {105}, issn = {1432-0835}, doi = {10.1007/s00526-017-1203-z}, url = {https://doi.org/10.1007/s00526-017-1203-z}, author = {Andrei A. Agrachev and Francesco Boarotto and Antonio Lerario} } @article {2017arXiv170707595A, title = {The injectivity radius of Lie manifolds}, journal = {ArXiv e-prints}, year = {2017}, abstract = {We prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive

}, keywords = {(58J40), 53C21, Mathematics - Differential Geometry}, url = {https://arxiv.org/pdf/1707.07595.pdf}, author = {Paolo Antonini and Guido De Philippis and Nicola Gigli} } @article {2017arXiv170704855A, title = {Integrable lifts for transitive Lie algebroids}, journal = {ArXiv e-prints}, year = {2017}, abstract = {Inspired by the work of Molino, we show that the integrability obstruction for transitive Lie algebroids can be made to vanish by adding extra dimensions. In particular, we prove that the Weinstein groupoid of a non-integrable transitive and abelian Lie algebroid, is the quotient of a finite dimensional Lie groupoid. Two constructions as such are given: First, explaining the counterexample to integrability given by Almeida and Molino, we see that it can be generalized to the construction of an "Almeida-Molino" integrable lift when the base manifold is simply connected. On the other hand, we notice that the classical de Rham isomorphism provides a universal integrable algebroid. Using it we construct a "de Rham" integrable lift for any given transitive Abelian Lie algebroid.

}, keywords = {14F40, 58H05, Mathematics - Differential Geometry}, url = {https://arxiv.org/pdf/1707.04855.pdf}, author = {Androulidakis, I. and Paolo Antonini} } @article {2017, title = {Linearisation of multiwell energies}, number = {SISSA;31/2017/MATE}, year = {2017}, abstract = {Linear elasticity can be rigorously derived from finite elasticity under the assumption of small loadings in terms of Gamma-convergence. This was first done in the case of one-well energies with super-quadratic growth and later generalised to different settings, in particular to the case of multi-well energies where the distance between the wells is very small (comparable to the size of the load). In this paper we study the case when the distance between the wells is independent of the size of the load. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions whose optimality is shown in most of the cases. Finally, the derivation of linear elasticty from a two-well discrete model is provided, showing that the role of the singular perturbation term is played in this setting by interactions beyond nearest neighbours.}, url = {http://preprints.sissa.it/handle/1963/35288}, author = {Roberto Alicandro and Gianni Dal Maso and Giuliano Lazzaroni and Mariapia Palombaro} } @article {2015, title = {A lower semicontinuity result for a free discontinuity functional with a boundary term}, journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es}, volume = {108}, year = {2017}, pages = {952-990}, chapter = {952}, abstract = {We study the lower semicontinuity in $GSBV^{p}(\Omega;\mathbb{R}^{m})$ of a free discontinuity functional $\mathcal{F}(u)$ that can be written as the sum of a crack term, depending only on the jump set $S_{u}$, and of a boundary term, depending on the trace of $u$ on $\partial\Omega$. We give sufficient conditions on the integrands for the lower semicontinuity of $\mathcal{F}$. Moreover, we prove a relaxation result, which shows that, if these conditions are not satisfied, the lower semicontinuous envelope of $\mathcal{F}$ can be represented by the sum of two integrals on $S_{u}$ and $\partial\Omega$, respectively.

}, doi = {10.1016/j.matpur.2017.05.018}, url = {http://hdl.handle.net/20.500.11767/15979}, author = {Stefano Almi and Gianni Dal Maso and Rodica Toader} } @article {ambrosi2017solid, title = {Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth}, journal = {J. Elast.}, volume = {129}, number = {1-2}, year = {2017}, pages = {107{\textendash}124}, publisher = {Springer Netherlands}, author = {D. Ambrosi and Pezzuto, S. and Davide Riccobelli and Stylianopoulos, T. and Pasquale Ciarletta} } @article {2016, title = {Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II}, number = {SISSA;32/2016/MATE}, year = {2016}, url = {http://urania.sissa.it/xmlui/handle/1963/35197}, author = {Giovanni Alberti and Stefano Bianchini and Laura Caravenna} } @article {2016, title = {Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I}, journal = {Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337}, number = {Journal of Differential Equations;261}, year = {2016}, publisher = {Elsevier}, doi = {10.1016/j.jde.2016.06.026}, url = {http://urania.sissa.it/xmlui/handle/1963/35207}, author = {Giovanni Alberti and Stefano Bianchini and Laura Caravenna} } @article {2016, title = {A fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts}, year = {2016}, institution = {Submitted}, abstract = {A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases.}, url = {http://urania.sissa.it/xmlui/handle/1963/35240}, author = {Francesco Ballarin and Elena Faggiano and Andrea Manzoni and Gianluigi Rozza and Alfio Quarteroni and Sonia Ippolito and Roberto Scrofani and Carlo Antona} } @article {arici2016gysin, title = {The Gysin sequence for quantum lens spaces}, journal = {Journal of Noncommutative Geometry}, volume = {9}, number = {4}, year = {2016}, pages = {1077{\textendash}1111}, abstract = {We define quantum lens spaces as {\textquoteleft}direct sums of line bundles{\textquoteright} and exhibit them as {\textquoteleft}total spaces{\textquoteright} of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as {\textquoteleft}line bundles{\textquoteright} over quantum lens spaces and generically define {\textquoteleft}torsion classes{\textquoteright}. We work out explicit examples of these classes.

}, doi = {10.4171/JNCG/216}, author = {Francesca Arici and Simon Brain and Giovanni Landi} } @inbook {Arici2016, title = {Pimsner Algebras and Circle Bundles}, booktitle = {Noncommutative Analysis, Operator Theory and Applications}, year = {2016}, pages = {1{\textendash}25}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {We report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with examples of quantum weighted projective and lens spaces and θ-deformations.

}, isbn = {978-3-319-29116-1}, doi = {10.1007/978-3-319-29116-1_1}, url = {https://doi.org/10.1007/978-3-319-29116-1_1}, author = {Francesca Arici and Francesco D{\textquoteright}Andrea and Giovanni Landi}, editor = {Alpay, Daniel and Cipriani, Fabio and Colombo, Fabrizio and Guido, Daniele and Sabadini, Irene and Sauvageot, Jean-Luc} } @article {arici2016pimsner, title = {Pimsner algebras and Gysin sequences from principal circle actions}, journal = {Journal of Noncommutative Geometry}, volume = {10}, year = {2016}, pages = {29{\textendash}64}, issn = {1661-6952}, doi = {10.4171/jncg/228}, url = {http://hdl.handle.net/2066/162951}, author = {Francesca Arici and Jens Kaad and Giovanni Landi} } @article {2016, title = {Quasi-static hydraulic crack growth driven by Darcy{\textquoteright}s law}, number = {SISSA;29/2016/MATE}, year = {2016}, abstract = {In the framework of rate independent processes, we present a variational model of quasi-static crack growth in hydraulic fracture. We first introduce the energy functional and study the equilibrium conditions of an unbounded linearly elastic body subject to a remote strain ε ∈ R and with a sufficiently regular crack Γ filled by a volume V of incompressible fluid. In particular, we are able to find the pressure p of the fluid inside the crack as a function of Γ, V , and ε. Then, we study the problem of quasi-static evolution for our model, imposing that the fluid volume V and the fluid pressure p are related by Darcy{\textquoteright}s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith{\textquoteright}s criterion.

}, url = {http://urania.sissa.it/xmlui/handle/1963/35198}, author = {Stefano Almi} } @mastersthesis {2016, title = {Some results on the mathematical analysis of crack problems with forces applied on the fracture lips}, year = {2016}, school = {SISSA}, abstract = {This thesis is devoted to the study of some models of fracture growth in elastic materials, characterized by the presence of forces acting on the crack lips. Working in the general framework of rate-independent processes, we first discuss a variational formulation of the problem of quasi-static crack evolution in hydraulic fracture. Then, we investigate the crack growth process in a cohesive fracture model, showing the existence of an evolution satisfying a weak Griffith{\textquoteright}s criterion. Finally, in the last chapter of this work we investigate, in the static case, the interaction between the energy spent in order to create a new fracture and the energy spent by the applied surface forces. This leads us to study the lower semicontinuity properties of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending on the jump set of u, and of a boundary term, depending on the trace of u.}, keywords = {Fracture mechanics}, author = {Stefano Almi} } @article {agrachev2016volume, title = {Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics}, journal = {arXiv preprint arXiv:1602.08745}, year = {2016}, author = {Andrei A. Agrachev and Davide Barilari and Elisa Paoli} } @article {2015, title = {Anisotropic mean curvature on facets and relations with capillarity}, number = {Geometric Flows;1}, year = {2015}, publisher = {de Gruyter}, abstract = {We discuss the relations between the anisotropic calibrability of a facet F of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet of the Wulff shape, calibrability is equivalent to show the existence of an anisotropic subunitary vector field in $F, with suitable normal trace on the boundary of the facet, and with constant divergence equal to the anisotropic mean curvature of F. When the Wulff shape is a cylynder, assuming E convex at F, and F (strictly) calibrable, such a vector field is obtained by solving the capillary problem on F in absence of gravity and with zero contact angle. We show some examples of facets for which it is possible, even without the strict calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C^{1,1}, the solution of the total variation flow starting at 1_F.

}, doi = {10.1515/geofl-2015-0005}, url = {http://urania.sissa.it/xmlui/handle/1963/34481}, author = {Stefano Amato and Lucia Tealdi and Giovanni Bellettini} } @article {2014, title = {Constrained BV functions on double coverings for Plateau{\textquoteright}s type problems}, journal = {Adv. Calc. Var.}, year = {2015}, abstract = {We link Brakke{\textquoteright}s "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau{\textquoteright}s problem without fixing a priori the topology of the solution. The minimization is set up in the class of $BV$ functions defined on a double covering space of the complement of an $(n - 2)$-dimensional smooth compact manifold $S$ without boundary. The main novelty of our approach stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. The model allows to avoid all issues concerning the presence of the boundary $S$. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on $Γ$-convergence theory.

}, author = {Stefano Amato and Giovanni Bellettini and Maurizio Paolini} } @article {agrachev2015geodesics, title = {Geodesics and horizontal-path spaces in Carnot groups}, journal = {Geometry \& Topology}, volume = {19}, number = {3}, year = {2015}, pages = {1569{\textendash}1630}, publisher = {Mathematical Sciences Publishers}, abstract = {We study properties of the space of horizontal paths joining the origin with a vertical point on a generic two-step Carnot group. The energy is a Morse-Bott functional on paths and its critical points (sub-Riemannian geodesics) appear in families (compact critical manifolds) with controlled topology. We study the asymptotic of the number of critical manifolds as the energy grows. The topology of the horizontal-path space is also investigated, and we find asymptotic results for the total Betti number of the sublevels of the energy as it goes to infinity. We interpret these results as local invariants of the sub-Riemannian structure.

}, doi = {10.2140/gt.2015.19.1569}, author = {Andrei A. Agrachev and Alessandro Gentile and Antonio Lerario} } @article {2015, title = {The phototransduction machinery in the rod outer segment has a strong efficacy gradient}, number = {Proceedings of the National Academy of Sciences of the United States of America;Volume 112, issue 20; pp. E2715-E2724}, year = {2015}, note = {Open Access article}, publisher = {National Academy of Sciences}, doi = {10.1073/pnas.1423162112}, url = {http://urania.sissa.it/xmlui/handle/1963/35157}, author = {Monica Mazzolini and Giuseppe Facchetti and L. Andolfi and R. Proietti Zaccaria and S. Tuccio and J. Treud and Claudio Altafini and Enzo M. Di Fabrizio and Marco Lazzarino and G. Rapp and Vincent Torre} } @mastersthesis {2015, title = {Principal circle bundles, Pimsner algebras and Gysin sequences}, year = {2015}, school = {SISSA}, abstract = {Principal circle bundles and Gysin sequences play a crucial role in mathematical physics, in particular in Chern-Simons theories and T-duality. This works focuses on the noncommutative topology of principal circle bundles: we investigate the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. At the C*-algebraic level, we start from a self-Morita equivalence bimodule E for a C*-algebra B which we think of as a non commutative line bundle over the {\textquoteleft}base space{\textquoteright} algebra B. The corresponding Pimsner algebra O_E, is then the total space algebra of an associated circle bundle. A natural six term exact sequence, an analogue of the Gysin sequence for circle bundles, relates the KK-theories of O_E and of the base space B. We illustrate several results with the examples of quantum weighted projective and lens spaces.}, author = {Francesca Arici} } @mastersthesis {2015, title = {Some results on anisotropic mean curvature and other phase-transition problems}, year = {2015}, school = {SISSA}, abstract = {The present thesis is divided into three parts. In the first part, we analyze a suitable regularization {\textemdash} which we call nonlinear multidomain model {\textemdash} of the motion of a hypersurface under smooth anisotropic mean curvature flow. The second part of the thesis deals with crystalline mean curvature of facets of a solid set of R^3 . Finally, in the third part we study a phase-transition model for Plateau{\textquoteright}s type problems based on the theory of coverings and of BV functions.}, keywords = {Anisotropic mean curvature}, author = {Stefano Amato} } @article {2014, title = {Achieving unanimous opinions in signed social networks}, number = {2014 European Control Conference;article number 6862161; pages 184-189;}, year = {2014}, publisher = {Institute of Electrical and Electronics Engineers Inc.}, abstract = {Being able to predict the outcome of an opinion forming process is an important problem in social network theory. However, even for linear dynamics, this becomes a difficult task as soon as non-cooperative interactions are taken into account. Such interactions are naturally modeled as negative weights on the adjacency matrix of the social network. In this paper we show how the Perron-Frobenius theorem can be used for this task also beyond its standard formulation for cooperative systems. In particular we show how it is possible to associate the achievement of unanimous opinions with the existence of invariant cones properly contained in the positive orthant. These cases correspond to signed adjacency matrices having the eventual positivity property, i.e., such that in sufficiently high powers all negative entries have disappeared. More generally, we show how for social networks the achievement of a, possibily non-unanimous, opinion can be associated to the existence of an invariant cone fully contained in one of the orthants of n.}, doi = {10.1109/ECC.2014.6862161}, url = {http://urania.sissa.it/xmlui/handle/1963/34935}, author = {Claudio Altafini and Gabriele Lini} } @article {2013, title = {On conjugate times of LQ optimal control problems}, number = {Journal of Dynamical and Control Systems}, year = {2014}, note = {14 pages, 1 figure}, publisher = {Springer}, abstract = {Motivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if $\vec{H}$ has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we obtain bounds from below on the number of conjugate times contained in an interval in terms of the spectrum of $\vec{H}$.}, keywords = {Optimal control, Lagrange Grassmannian, Conjugate point}, doi = {10.1007/s10883-014-9251-6}, url = {http://hdl.handle.net/1963/7227}, author = {Andrei A. Agrachev and Luca Rizzi and Pavel Silveira} } @article {2014, title = {On the Lp-differentiability of certain classes of functions}, number = {Revista Matematica Iberoamericana;Volume 30; issue 1; pp. 349-367;}, year = {2014}, publisher = {European Mathematical Society}, abstract = {We prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation.}, doi = {10.4171/rmi/782}, url = {http://urania.sissa.it/xmlui/handle/1963/34695}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @article {2012, title = {New results on Gamma-limits of integral functionals}, number = {Annales de l{\textquoteright}Institut Henri Poincare. Analyse Non Lineaire}, year = {2014}, publisher = {Elsevier}, keywords = {Gamma-convergence}, doi = {10.1016/j.anihpc.2013.02.005}, url = {http://hdl.handle.net/1963/5880}, author = {Nadia Ansini and Gianni Dal Maso and Caterina Ida Zeppieri} } @article {2012, title = {Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D}, number = {Computer Methods in Applied Mechanics and Engineering}, year = {2014}, publisher = {Elsevier}, abstract = {Isogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM.}, keywords = {Isogeometric Analysis}, doi = {10.1016/j.cma.2013.09.017}, url = {http://hdl.handle.net/1963/6326}, author = {Luca Heltai and Marino Arroyo and Antonio DeSimone} } @article {2014, title = {Quasi-static crack growth in hydraulic fracture}, journal = {Nonlinear Analysis}, volume = {109}, number = {Nonlinear Analysis, Theory, Methods and Applications;109}, year = {2014}, pages = {301-318}, publisher = {Elsevier}, type = {Journal article}, chapter = {301}, abstract = {We present a variational model for the quasi-static crack growth in hydraulic fracture in the framework of the energy formulation of rate-independent processes. The cracks are assumed to lie on a prescribed plane and to satisfy a very weak regularity assumption.

}, doi = {10.1016/j.na.2014.07.009}, url = {http://hdl.handle.net/20.500.11767/17350}, author = {Stefano Almi and Gianni Dal Maso and Rodica Toader} } @inbook {2013, title = {Reduction on characteristics for continuous of a scalar balance law}, booktitle = {AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406}, number = {AIMS Series on Applied Mathematics}, year = {2014}, publisher = {SISSA}, organization = {SISSA}, keywords = {Method of characteristics}, url = {http://hdl.handle.net/1963/6562}, author = {Giovanni Alberti and Stefano Bianchini and Laura Caravenna} } @article {2014, title = {Shape control of active surfaces inspired by the movement of euglenids}, number = {Journal of the Mechanics and Physics of Solids;volume 62; issue 1; pages 99-112;}, year = {2014}, publisher = {Elsevier}, abstract = {We examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines.}, doi = {10.1016/j.jmps.2013.09.017}, url = {http://urania.sissa.it/xmlui/handle/1963/35118}, author = {Marino Arroyo and Antonio DeSimone} } @article {2014, title = {A uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday}, number = {Journal of the European Mathematical Society;Volume 16; issue 2; pp. 201-234;}, year = {2014}, publisher = {European Mathematical Society; Springer Verlag}, abstract = {We characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation ∂tu +div(bu) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b. As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain nonautonomous vector fields b with bounded divergence.}, doi = {10.4171/JEMS/431}, url = {http://urania.sissa.it/xmlui/handle/1963/34692}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @article {2013, title = {Attainment results for nematic elastomers}, year = {2013}, institution = {SISSA}, abstract = {We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids.}, url = {http://hdl.handle.net/1963/7174}, author = {Virginia Agostiniani and Gianni Dal Maso and Antonio DeSimone} } @article {2013, title = {Common dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons.}, journal = {Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013}, year = {2013}, publisher = {SISSA}, abstract = {Sensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

}, doi = {10.1038/srep01251}, author = {Giovanna De Palo and Giuseppe Facchetti and Monica Mazzolini and Anna Menini and Vincent Torre and Claudio Altafini} } @article {2013, title = {The curvature: a variational approach}, number = {arXiv:1306.5318;}, year = {2013}, note = {88 pages, 10 figures, (v2) minor typos corrected, (v3) added sections on Finsler manifolds, slow growth distributions, Heisenberg group}, institution = {SISSA}, abstract = {The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.}, keywords = {Crurvature, subriemannian metric, optimal control problem}, url = {http://hdl.handle.net/1963/7226}, author = {Andrei A. Agrachev and Davide Barilari and Luca Rizzi} } @article {2013, title = {Early phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus}, journal = {PloS one. Volume 8, Issue 7, July 2013 : e68078}, number = {PMID:23935853;}, year = {2013}, note = {The article is composed of 15 pages}, publisher = {Public Library of Science}, abstract = {Hippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 {\textmu}M gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10:90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box.}, doi = {10.1371/journal.pone.0068078}, url = {http://hdl.handle.net/1963/7287}, author = {Giovanni Iacono and Claudio Altafini and Vincent Torre} } @article {2013, title = {Expanded degenerations and pairs}, journal = {Communications in Algebra. Volume 41, Issue 6, May 2013, Pages 2346-2386}, number = {arXiv:1110.2976v1;}, year = {2013}, note = {This article is composed of 41 pages and is recorded in PDF format}, publisher = {Taylor and Francis}, abstract = {Since Jun Li{\textquoteright}s original definition, several other definitions of expanded pairs and expanded degenerations have appeared in the literature. We explain how these definitions are related and introduce several new variants and perspectives. Among these are the twisted expansions used by Abramovich and Fantechi as a basis for orbifold techniques in degeneation formulas.}, keywords = {Expanded pairs}, doi = {10.1080/00927872.2012.658589}, url = {http://hdl.handle.net/1963/7383}, author = {Dan Abramovich and Charles Cadman and Barbara Fantechi and Jonathan Wise} } @article {2013, title = {Minimal partitions and image classification using a gradient-free perimeter approximation}, year = {2013}, institution = {SISSA}, abstract = {In this paper a new mathematically-founded method for the optimal partitioning of domains, with applications to the classification of greyscale and color images, is proposed. Since optimal partition problems are in general ill-posed, some regularization strategy is required. Here we regularize by a non-standard approximation of the total interface length, which does not involve the gradient of approximate characteristic functions, in contrast to the classical Modica-Mortola approximation. Instead, it involves a system of uncoupled linear partial differential equations and nevertheless shows $\Gamma$-convergence properties in appropriate function spaces. This approach leads to an alternating algorithm that ensures a decrease of the objective function at each iteration, and which always provides a partition, even during the iterations. The efficiency of this algorithm is illustrated by various numerical examples. Among them we consider binary and multilabel minimal partition problems including supervised or automatic image classification, inpainting, texture pattern identification and deblurring.}, keywords = {Image classification, deblurring, optimal partitions, perimeter approximation}, url = {http://hdl.handle.net/1963/6976}, author = {Samuel Amstutz and Nicolas Van Goethem and Antonio Andr{\'e} Novotny} } @article {2013, title = {The nonlinear multidomain model: a new formal asymptotic analysis.}, journal = {Geometry Partial Differential Equations {\textendash} proceedings, CRM Series (15), 2013.}, number = {SISSA preprint;SISSA 54/2013/MATE}, year = {2013}, abstract = {We study the asymptotic analysis of a singularly perturbed weakly parabolic system of m- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

}, keywords = {bidomain model, anisotropic mean curvature, star-shaped combination}, isbn = {8876424724}, author = {Stefano Amato and Giovanni Bellettini and Maurizio Paolini} } @article {2013, title = {Quadratic cohomology}, year = {2013}, note = {24 pages}, publisher = {SISSA}, abstract = {We study homological invariants of smooth families of real quadratic forms as\r\na step towards a \"Lagrange multipliers rule in the large\" that intends to\r\ndescribe topology of smooth vector functions in terms of scalar Lagrange\r\nfunctions.}, author = {Andrei A. Agrachev} } @article {2013, title = {Some open problems}, number = {arXiv:1304.2590;}, year = {2013}, publisher = {SISSA}, abstract = {We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry.}, keywords = {Geometry}, url = {http://hdl.handle.net/1963/7070}, author = {Andrei A. Agrachev} } @article {2013, title = {Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control}, journal = {IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85}, year = {2013}, abstract = {In this paper, we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement, and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment, or by non-Hermitian measurements, there is no need for feedback, as open-loop time-invariant control is sufficient to achieve stabilization of the target set in probability. Constructive necessary and sufficient conditions on the form of the control Hamiltonian can be provided in this case. When time-invariant control is not sufficient, state stabilization can be attained by the addition of filtering-based feedback control}, doi = {10.1109/TAC.2012.2206713}, url = {http://hdl.handle.net/1963/6503}, author = {Claudio Altafini and Francesco Ticozzi and K. Nishio} } @mastersthesis {2013, title = {Topology of moduli spaces of framed sheaves}, year = {2013}, school = {SISSA}, keywords = {Moduli spaces, framed sheaves, instantons}, url = {http://hdl.handle.net/1963/7152}, author = {Gharchia Abdellaoui} } @inbook {9897, title = {Computing optimal strokes for low reynolds number swimmers}, booktitle = {Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors,}, number = {The IMA volumes in mathematics and its applications;155}, year = {2012}, publisher = {Springer}, organization = {Springer}, abstract = {We discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

}, keywords = {Numerical analysis.}, isbn = {9781461439967}, doi = {10.1007/978-1-4614-3997-4_13}, url = {http://hdl.handle.net/1963/6445}, author = {Antonio DeSimone and Luca Heltai and Fran{\c c}ois Alouges and Lefebvre-Lepot Aline} } @article {2012, title = {Decompositions of large-scale biological systems based on dynamical properties}, journal = {Bioinformatics (Oxford, England). 2012 Jan; 28(1):76-83}, number = {PMID:22072388;}, year = {2012}, publisher = {Oxford University Press}, abstract = {MOTIVATION: Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties.\\r\\nRESULTS: The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsystem of the given system. Another dynamical property investigated is strong monotonicity. We propose two methods to deal with this property, both aimed at decomposing the system into strongly monotone subsystems, but with different structural characteristics: one method tends to produce a single large strongly monotone component, while the other typically generates a set of smaller disjoint strongly monotone subsystems.\\r\\nAVAILABILITY: Original heuristics for the methods investigated are described in the article.}, doi = {10.1093/bioinformatics/btr620}, url = {http://hdl.handle.net/1963/5226}, author = {Nicola Soranzo and Fahimeh Ramezani and Giovanni Iacono and Claudio Altafini} } @article {2012, title = {Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime}, journal = {Phys. Rev. D 86 (2012) 124035}, number = {arXiv:1206.5315;}, year = {2012}, note = {12 pages, 5 figures}, publisher = {American Physical Society}, abstract = {The interest of part of the quantum-gravity community in the possibility of\r\nPlanck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective, of observations of bursts of particles from cosmological distances. In this respect the fact that so far the implications of deformed Lorentz symmetry have been investigated only for flat (Minkowskian) spacetimes represents a very significant limitation, since for propagation over cosmological distances the curvature/expansion of spacetime is evidently tangible. We here provide a significant step toward filling this gap by exhibiting an explicit example of Planck-scale-deformed relativistic symmetries of a spacetime with constant rate of expansion (deSitterian). Technically we obtain the first ever example of a relativistic theory of worldlines of particles with 3 nontrivial relativistic invariants: a large speed scale (\"speed-of-light scale\"), a large distance scale (inverse of the \"expansion-rate scale\"), and a large momentum scale (\"Planck scale\"). We address some of the challenges that had obstructed success for previous attempts by exploiting the recent understanding of the connection between deformed Lorentz symmetry and relativity of spacetime locality. We also offer a preliminary analysis of the differences between the scenario we here propose and the most studied scenario for broken (rather than deformed) Lorentz symmetry in expanding spacetimes.}, keywords = {Doubly special relativity}, doi = {10.1103/PhysRevD.86.124035}, author = {Giovanni Amelino-Camelia and Antonino Marciano and Marco Matassa and Giacomo Rosati} } @article {2012, title = {Detection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis}, journal = {Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149}, year = {2012}, publisher = {SISSA}, abstract = {The capacity of microorganisms to respond to variable external conditions requires a coordination of environment-sensing mechanisms and decisionmaking regulatory circuits. Here, we seek to understand the interplay between these two processes by combining high-throughput measurement of time-dependent mRNA profiles with a novel computational approach that searches for key genetic triggers of transcriptional changes. Our approach helped us understand the regulatory strategies of a respiratorily versatile bacterium with promising bioenergy and bioremediation applications, Shewanella oneidensis, in minimal and rich media. By comparing expression profiles across these two conditions, we unveiled components of the transcriptional program that depend mainly on the growth phase. Conversely, by integrating our time-dependent data with a previously available large compendium of static perturbation responses, we identified transcriptional changes that cannot be explained solely by internal network dynamics, but are rather triggered by specific genes acting as key mediators of an environment-dependent response. These transcriptional triggers include known and novel regulators that respond to carbon, nitrogen and oxygen limitation. Our analysis suggests a sequence of physiological responses, including a coupling between nitrogen depletion and glycogen storage, partially recapitulated through dynamic flux balance analysis, and experimentally confirmed by metabolite measurements. Our approach is broadly applicable to other systems}, doi = {10.1093/nar/gks467}, url = {http://hdl.handle.net/1963/6506}, author = {Q Beg and Mattia Zampieri and N Klitgord and S Collins and M Serres and Daniel Segr{\`e} and Claudio Altafini} } @article {2012, title = {A dynamical feedback model for adaptation in the olfactory transduction pathway}, journal = {Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686}, number = {PMID:22735517;}, year = {2012}, publisher = {Biophysical Society, Elsevier}, abstract = {Olfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species.}, doi = {10.1016/j.bpj.2012.04.040}, url = {http://hdl.handle.net/1963/7019}, author = {Giovanna De Palo and Anna Boccaccio and Andrew Miri and Anna Menini and Claudio Altafini} } @article {2012, title = {Dynamics of opinion forming in structurally balanced social networks}, journal = {PloS one. 2012 ; 7(6):e38135}, number = {PMID:22761667;}, year = {2012}, publisher = {PLoS}, abstract = {A structurally balanced social network is a social community that splits into two antagonistic factions (typical example being a two-party political system). The process of opinion forming on such a community is most often highly predictable, with polarized opinions reflecting the bipartition of the network. The aim of this paper is to suggest a class of dynamical systems, called monotone systems, as natural models for the dynamics of opinion forming on structurally balanced social networks. The high predictability of the outcome of a decision process is explained in terms of the order-preserving character of the solutions of this class of dynamical systems. If we represent a social network as a signed graph in which individuals are the nodes and the signs of the edges represent friendly or hostile relationships, then the property of structural balance corresponds to the social community being splittable into two antagonistic factions, each containing only friends.}, doi = {10.1371/journal.pone.0038135}, url = {http://hdl.handle.net/1963/6051}, author = {Claudio Altafini} } @article {2012, title = {Exploring the low-energy landscape of large-scale signed social networks}, journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Volume 86, Issue 3, 26 September 2012, Article number036116}, year = {2012}, publisher = {SISSA}, abstract = {Analogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers.}, doi = {10.1103/PhysRevE.86.036116}, url = {http://hdl.handle.net/1963/6504}, author = {Giuseppe Facchetti and Giovanni Iacono and Claudio Altafini} } @article {2012, title = {Gamma-convergence and H-convergence of linear elliptic operators}, journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es, Available online 12 September 2012}, number = {SISSA;04/2012/M}, year = {2012}, publisher = {Elsevier}, keywords = {Linear elliptic operators}, doi = {10.1016/j.matpur.2012.09.004}, url = {http://hdl.handle.net/1963/5878}, author = {Nadia Ansini and Gianni Dal Maso and Caterina Ida Zeppieri} } @article {2012, title = {On the Hausdorff volume in sub-Riemannian geometry}, journal = {Calculus of Variations and Partial Differential Equations. Volume 43, Issue 3-4, March 2012, Pages 355-388}, number = {arXiv:1005.0540;}, year = {2012}, publisher = {SISSA}, abstract = {For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative\r\nof the spherical Hausdorff measure with respect to a smooth volume. We prove\r\nthat this is the volume of the unit ball in the nilpotent approximation and it\r\nis always a continuous function. We then prove that up to dimension 4 it is\r\nsmooth, while starting from dimension 5, in corank 1 case, it is C^3 (and C^4\r\non every smooth curve) but in general not C^5. These results answer to a\r\nquestion addressed by Montgomery about the relation between two intrinsic\r\nvolumes that can be defined in a sub-Riemannian manifold, namely the Popp and\r\nthe Hausdorff volume. If the nilpotent approximation depends on the point (that\r\nmay happen starting from dimension 5), then they are not proportional, in\r\ngeneral.}, doi = {10.1007/s00526-011-0414-y}, url = {http://hdl.handle.net/1963/6454}, author = {Andrei A. Agrachev and Davide Barilari and Ugo Boscain} } @article {2012, title = {Introduction to Riemannian and sub-Riemannian geometry}, number = {SISSA;09/2012/M}, year = {2012}, institution = {SISSA}, url = {http://hdl.handle.net/1963/5877}, author = {Andrei A. Agrachev and Davide Barilari and Ugo Boscain} } @article {2012, title = {Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire}, volume = {29}, number = {SISSA;30/2011/M}, year = {2012}, pages = {715-735}, publisher = {Gauthier-Villars;Elsevier}, abstract = {The energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

}, keywords = {Nonlinear elasticity}, doi = {10.1016/j.anihpc.2012.04.001}, url = {http://hdl.handle.net/1963/4267}, author = {Virginia Agostiniani and Gianni Dal Maso and Antonio DeSimone} } @article {2012, title = {Modeling and control of quantum systems: An introduction}, journal = {IEEE Transactions on Automatic Control. Volume 57, Issue 8, 2012, Article number6189035, Pages 1898-1917}, year = {2012}, publisher = {Institute of Electrical and Electronics Engineers}, abstract = {The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis. While part of the existing theory, especially in the open-loop setting, stems directly from classical control theory (most notably geometric control and optimal control), a number of tools specifically tailored for quantum systems have been developed since the 1980s, in order to take into account their distinctive features: the probabilistic nature of atomic-scale physical systems, the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback-design problems. The relevant dynamical models for both closed and open quantum systems are presented, along with the main results on their controllability and stability. A brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies}, doi = {10.1109/TAC.2012.2195830}, url = {http://hdl.handle.net/1963/6505}, author = {Claudio Altafini and Francesco Ticozzi} } @article {2012, title = {Ogden-type energies for nematic elastomers}, journal = {International Journal of Non-Linear mechanics }, volume = {47}, year = {2012}, pages = {402-412}, publisher = {Elsevier}, abstract = {Ogden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).

}, keywords = {Nonlinear elasticity}, doi = {10.1016/j.ijnonlinmec.2011.10.001}, author = {Virginia Agostiniani and Antonio DeSimone} } @article {2012, title = {Predicting and characterizing selective multiple drug treatments for metabolic diseases and cancer.}, journal = {BMC Systems Biology. 29 August 2012, Page 115}, year = {2012}, publisher = {BioMed Central}, abstract = {Background: In the field of drug discovery, assessing the potential of multidrug therapies is a difficult task because of the combinatorial complexity (both theoretical and experimental) and because of the requirements on the selectivity of the therapy. To cope with this problem, we have developed a novel method for the systematic in silico investigation of synergistic effects of currently available drugs on genome-scale metabolic networks. The algorithm finds the optimal combination of drugs which guarantees the inhibition of an objective function, while minimizing the side effect on the overall network. Results: Two different applications are considered: finding drug synergisms for human metabolic diseases (like diabetes, obesity and hypertension) and finding antitumoral drug combinations with minimal side effect on the normal human metabolism.The results we obtain are consistent with some of the available therapeutic indications and predict some new multiple drug treatments.A cluster analysis on all possible interactions among the currently available drugs indicates a limited variety on the metabolic targets for the approved drugs. Conclusion: The in silico prediction of drug synergism can represent an important tool for the repurposing of drug in a realistic perspective which considers also the selectivty of the therapy. Moreover, for a more profitable exploitation of drug-drug interactions, also drugs which show a too low efficacy but which have a non-common mechanism of action, can be reconsider as potential ingredients of new multicompound therapeutic indications.Needless to say the clues provided by a computational study like ours need in any case to be thoroughly evaluated experimentally.}, doi = {doi:10.1186/1752-0509-6-115}, url = {http://hdl.handle.net/1963/6515}, author = {Giuseppe Facchetti and Claudio Altafini and Mattia Zampieri} } @article {2012, title = {Reverse engineering the euglenoid movement}, journal = {Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879}, year = {2012}, abstract = {Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20\% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340\%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.}, keywords = {microswimmers}, doi = {10.1073/pnas.1213977109}, url = {http://hdl.handle.net/1963/6444}, author = {Marino Arroyo and Luca Heltai and Daniel Mill{\'a}n and Antonio DeSimone} } @article {2012, title = {On robust Lie-algebraic stability conditions for switched linear systems}, journal = {Systems and Control Letters. Volume 61, Issue 2, February 2012, Pages 347-353}, year = {2012}, abstract = {This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novelty feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters.}, doi = {10.1016/j.sysconle.2011.11.016}, url = {http://hdl.handle.net/1963/6455}, author = {Andrei A. Agrachev and Yurij Baryshnikov and Daniel Liberzon} } @article {1078-0947_2012_4_1125, title = {Second order approximations of quasistatic evolution problems in finite dimension}, journal = {Discrete \& Continuous Dynamical Systems - A}, volume = {32}, number = {1078-0947_2012_4_112}, year = {2012}, pages = {1125}, abstract = {In this paper, we study the limit, as ε goes to zero, of a particular solution of the equation $\epsilon^2A\ddot u^ε(t)+εB\dot u^ε(t)+\nabla_xf(t,u^ε(t))=0$, where $f(t,x)$ is a potential satisfying suitable coerciveness conditions. The limit $u(t)$ of $u^ε(t)$ is piece-wise continuous and verifies $\nabla_xf(t,u(t))=0$. Moreover, certain jump conditions characterize the behaviour of $u(t)$ at the discontinuity times. The same limit behaviour is obtained by considering a different approximation scheme based on time discretization and on the solutions of suitable autonomous systems.

}, keywords = {discrete approximations, perturbation methods, saddle-node bifurcation, Singular perturbations, vanishing viscosity}, issn = {1078-0947}, doi = {10.3934/dcds.2012.32.1125}, url = {http://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f8}, author = {Virginia Agostiniani} } @article {2012, title = {Sub-Riemannian structures on 3D Lie groups}, journal = {Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44}, number = {arXiv:1007.4970;}, year = {2012}, publisher = {SISSA}, abstract = {We give a complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. As a corollary we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups $SL(2)$ and $A^+(\mathbb{R})\times S^1$, where $A^+(\mathbb{R})$ denotes the group of orientation preserving affine maps on the real line.

}, doi = {10.1007/s10883-012-9133-8}, url = {http://hdl.handle.net/1963/6453}, author = {Andrei A. Agrachev and Davide Barilari} } @article {2012, title = {Systems of Quadratic Inequalities}, journal = {Proceedings of the London Mathematical Society, Volume 105, Issue 3, September 2012, Pages 622-660}, number = {arXiv:1012.5731;}, year = {2012}, publisher = {SISSA}, abstract = {We present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of RP^n defined by a system of quadratic inequalities and the image of the homology homomorphism induced by the inclusion of this subset in RP^n. We do not restrict ourselves to the term E_2 of the spectral sequence and give a simple explicit formula for the differential d_2.}, doi = {DOI: 10.1112/plms/pds010}, url = {http://hdl.handle.net/1963/7072}, author = {Andrei A. Agrachev and Antonio Lerario} } @article {2012, title = {Topological sensitivity analysis for high order elliptic operators}, number = {SISSA;36/2012/M}, year = {2012}, institution = {SISSA}, abstract = {The topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. The topological derivative has been fully developed for a wide range of second order differential operators. In this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m, m>=1. The general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced. We provide full mathematical justifications for the derived formulas, including precise estimates of remainders.}, keywords = {Topological derivative, Elliptic operators, Polarization tensor}, url = {http://hdl.handle.net/1963/6343}, author = {Samuel Amstutz and Antonio Andr{\'e} Novotny and Nicolas Van Goethem} } @article {2011, title = {Adaptation as a genome-wide autoregulatory principle in the stress response of yeast.}, journal = {IET systems biology. 2011 Jul; 5(4):269-79}, number = {PMID:21823758;}, year = {2011}, publisher = {The Institution of Engineering and Technology}, abstract = {The gene expression response of yeast to various types of stresses/perturbations shows a common functional and dynamical pattern for the vast majority of genes, characterised by a quick transient peak (affecting primarily short genes) followed by a return to the pre-stimulus level. Kinetically, this process of adaptation following the transient excursion can be modelled using a genome-wide autoregulatory mechanism by means of which yeast aims at maintaining a preferential concentration in its mRNA levels. The resulting feedback system explains well the different time constants observable in the transient response, while being in agreement with all the known experimental dynamical features. For example, it suggests that a very rapid transient can be induced also by a slowly varying concentration of the gene products.}, doi = {10.1049/iet-syb.2009.0050}, url = {http://hdl.handle.net/1963/5106}, author = {F Eduati and B Di Camillo and G Toffolo and Claudio Altafini and Giovanna De Palo and Mattia Zampieri} } @article {2011, title = {Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry}, year = {2011}, note = {25 pages}, publisher = {SISSA}, abstract = {We prove a Bishop volume comparison theorem and a Laplacian comparison\r\ntheorem for three dimensional contact subriemannian manifolds with symmetry.}, url = {http://hdl.handle.net/1963/6508}, author = {Andrei A. Agrachev and Paul Lee} } @article {2011, title = {Computing global structural balance in large-scale signed social networks.}, journal = {Proceedings of the National Academy of Sciences of the United States of America. Volume 108, Issue 52, 27 December 2011, Pages 20953-20958}, number = {PMID:22167802;}, year = {2011}, note = {Free fulltext article in Pubmed Central}, publisher = {National Academy of Sciences}, abstract = {Structural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly \\\"apparent disorder,\\\" rather than true \\\"frustration.\\\"}, keywords = {Combinatorial optimization}, doi = {10.1073/pnas.1109521108}, url = {http://hdl.handle.net/1963/6426}, author = {Giuseppe Facchetti and Giovanni Iacono and Claudio Altafini} } @article {2011, title = {Gamma-convergence of energies for nematic elastomers in the small strain limit}, journal = {Continuum. Mech. Therm.}, volume = { 23}, number = {SISSA;07/2011/M}, year = {2011}, publisher = {Springer}, chapter = {257}, abstract = {We study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

}, keywords = {Liquid crystals}, doi = {10.1007/s00161-011-0180-2}, url = {http://hdl.handle.net/1963/4141}, author = {Virginia Agostiniani and Antonio DeSimone} } @article {2011, title = {Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds}, number = {arXiv:0903.2550;}, year = {2011}, note = {This is a revised extended version that contains new results.}, publisher = {SISSA}, url = {http://hdl.handle.net/1963/6507}, author = {Andrei A. Agrachev and Paul Lee} } @article {2011, title = {The geometry of Maximum Principle}, journal = {Proceedings of the Steklov Institute of mathematics. vol. 273 (2011), page: 5-27 ; ISSN: 0081-5438}, number = {Proceedings of the Steklov Institute of mathematics;v.273}, year = {2011}, abstract = {An invariant formulation of the maximum principle in optimal control is presented, and some second-order invariants are discussed.}, url = {http://hdl.handle.net/1963/6456}, author = {Andrei A. Agrachev and Revaz Gamkrelidze} } @article {2011, title = {Large Time Existence for Thin Vibrating Plates}, journal = {Communication in Partial Differential Equations 36 (2011) 2062-2102}, number = {SISSA;59/2009/M}, year = {2011}, publisher = {Taylor \& Francis}, abstract = {We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large\\r\\ntimes under appropriate scaling of the initial values such that the limit system as h --> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange equation. In the case of the\\r\\nlinear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.}, doi = {10.1080/03605302.2011.618209}, url = {http://hdl.handle.net/1963/3755}, author = {Helmut Abels and Maria Giovanna Mora and Stefan M{\"u}ller} } @article {2011, title = {Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers}, journal = {Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387}, number = {SISSA;33/2009/M}, year = {2011}, publisher = {World Scientific}, abstract = {We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms.}, keywords = {Optimal swimming}, doi = {10.1142/S0218202511005088}, url = {http://hdl.handle.net/1963/3657}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Luca Heltai} } @article {2011, title = {Osservazioni sui teoremi di inversione globale}, journal = {Rendiconti Lincei - Matematica e Applicazioni 22 (2011) 3-15}, number = {SISSA;64/2010/M}, year = {2011}, publisher = {European Mathematical Society}, abstract = {Some global inversion theorems with applications to semilinear elliptic equation are discussed.}, doi = {10.4171/RLM/584}, url = {http://hdl.handle.net/1963/4068}, author = {Antonio Ambrosetti} } @article {2011, title = {Quasistatic evolution of sessile drops and contact angle hysteresis}, journal = {Arch. Rational Mech. Anal. 202 (2011) 295-348}, year = {2011}, publisher = {Springer}, abstract = {We consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of quasistatic evolutions with prescribed initial configuration. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations.}, doi = {10.1007/s00205-011-0427-x}, url = {http://hdl.handle.net/1963/4912}, author = {Giovanni Alberti and Antonio DeSimone} } @article {2011, title = {On the Space of Symmetric Operators with Multiple Ground States}, journal = {Functional Analysis and its Applications, Volume 45, Issue 4, December 2011, Pages 241-251}, number = {arXiv:1107.3010;}, year = {2011}, publisher = {SISSA}, abstract = {We study homological structure of the filtrations of the spaces of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite dimensional generalizations are easily guessed.}, keywords = {Multiple eigenvalue}, doi = {DOI: 10.1007/s10688-011-0026-5}, url = {http://hdl.handle.net/1963/7069}, author = {Andrei A. Agrachev} } @article {2011, title = {Structure of level sets and Sard-type properties of Lipschitz maps}, number = {SISSA;51/2011/M}, year = {2011}, institution = {SISSA}, url = {http://hdl.handle.net/1963/4657}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @article {2011, title = {A system-level approach for deciphering the transcriptional response to prion infection}, journal = {Bioinformatics (Oxford, England). 2011 Dec; 27(24):3407-14}, number = {PMID:22016408;}, year = {2011}, publisher = {Oxford University Press}, abstract = {MOTIVATION: Deciphering the response of a complex biological system to an insulting event, at the gene expression level, requires adopting theoretical models that are more sophisticated than a one-to-one comparison (i.e. t-test). Here, we investigate the ability of a novel reverse engineering approach (System Response Inference) to unveil non-obvious transcriptional signatures of the system response induced by prion infection.\\r\\nRESULTS: To this end, we analyze previously published gene expression data, from which we extrapolate a putative full-scale model of transcriptional gene-gene dependencies in the mouse central nervous system. Then, we use this nominal model to interpret the gene expression changes caused by prion replication, aiming at selecting the genes primarily influenced by this perturbation. Our method sheds light on the mode of action of prions by identifying key transcripts that are the most likely to be responsible for the overall transcriptional rearrangement from a nominal regulatory network. As a first result of our inference, we have been able to predict known targets of prions (i.e. PrP(C)) and to unveil the potential role of previously unsuspected genes.\\r\\nCONTACT: altafini@sissa.it\\r\\nSUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.}, doi = {10.1093/bioinformatics/btr580}, url = {http://hdl.handle.net/1963/5745}, author = {Mattia Zampieri and Giuseppe Legname and Daniel Segr{\`e} and Claudio Altafini} } @article {2011, title = {The time-dependent von K{\'a}rm{\'a}n plate equation as a limit of 3d nonlinear elasticity}, journal = {Calculus of Variations and Partial Differential Equations 41 (2011) 241-259}, number = {SISSA;74/2009/M}, year = {2011}, publisher = {Springer}, abstract = {The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation.}, doi = {10.1007/s00526-010-0360-0}, url = {http://hdl.handle.net/1963/3835}, author = {Helmut Abels and Maria Giovanna Mora and Stefan M{\"u}ller} } @article {2011, title = {A uniqueness result for the continuity equation in two dimensions}, number = {SISSA;52/2011/M}, year = {2011}, institution = {SISSA}, url = {http://hdl.handle.net/1963/4663}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @article {2010, title = {Continuity of optimal control costs and its application to weak KAM theory}, journal = {Calculus of Variations and Partial Differential Equations. Volume 39, Issue 1, 2010, Pages 213-232}, number = {arXiv:0909.3826;}, year = {2010}, note = {23 pages, 1 figures}, publisher = {SISSA}, abstract = {We prove continuity of certain cost functions arising from optimal control of\\r\\naffine control systems. We give sharp sufficient conditions for this\\r\\ncontinuity. As an application, we prove a version of weak KAM theorem and\\r\\nconsider the Aubry-Mather problems corresponding to these systems.}, doi = {10.1007/s00526-010-0308-4}, url = {http://hdl.handle.net/1963/6459}, author = {Andrei A. Agrachev and Paul Lee} } @article {2010, title = {Dynamics control by a time-varying feedback}, journal = {Journal of Dynamical and Control Systems. Volume 16, Issue 2, April 2010, Pages :149-162}, year = {2010}, publisher = {SISSA}, abstract = {We consider a smooth bracket generating control-affine system in R^d and show that any orientation preserving diffeomorphism of R^d can be approximated, in the very strong sense, by a diffeomorphism included in the flow generated by a time-varying feedback control which is polynomial with respect to the state variables and trigonometric-polynomial with respect to the time variable.}, keywords = {Discrete-time dynamics}, doi = {10.1007/s10883-010-9087-7}, url = {http://hdl.handle.net/1963/6461}, author = {Andrei A. Agrachev and Marco Caponigro} } @article {2010, title = {Feedback schemes for radiation damping suppression in NMR: a control-theoretical perspective}, journal = {Systems and Control Letters, 59 (12):782-786, 2010}, year = {2010}, publisher = {Elsevier}, abstract = {In NMR spectroscopy, the collective measurement is weakly invasive and its back-action is called radiation damping. The aim of this paper is to provide a control-theoretical analysis of the problem of suppressing this radiation damping. It is shown that the two feedback schemes commonly used in the NMR practice correspond one to a high gain oputput feedback for the simple case of maintaining the spin 1/2 in its inverted state, and the second to a 2-degree of freedom control design with a prefeedback that exactly cancels the radiation damping field. A general high gain feedback stabilization design not requiring the knowledge of the radiation damping time constant is also investigated.}, doi = {10.1016/j.sysconle.2010.09.004}, url = {http://hdl.handle.net/1963/4384}, author = {Claudio Altafini and Paola Cappellaro and David Cory} } @article {2010, title = {Invariant Lagrange submanifolds of dissipative systems}, journal = {Russian Mathematical Surveys. Volume 65, Issue 5, 2010, Pages: 977-978}, number = {arXiv:0912.2248;}, year = {2010}, publisher = {SISSA}, abstract = {We study solutions of modified Hamilton-Jacobi equations H(du/dq,q) + cu(q) =\\r\\n0, q \\\\in M, on a compact manifold M .}, doi = {10.1070/RM2010v065n05ABEH004707}, url = {http://hdl.handle.net/1963/6457}, author = {Andrei A. Agrachev} } @article {2010, title = {A kinetic mechanism inducing oscillations in simple chemical reactions networks}, journal = {Mathematical Biosciences and Engineering 7(2):301-312, 2010}, number = {SISSA;82/2007/M}, year = {2010}, publisher = {American Institute of Mathematical Sciences}, abstract = {It is known that a kinetic reaction network in which one or more secondary substrates are acting as cofactors may exhibit an oscillatory behavior. The aim of this work is to provide a description of the functional form of such a cofactor action guaranteeing the\\r\\nonset of oscillations in sufficiently simple reaction networks.}, doi = {10.3934/mbe.2010.7.301}, url = {http://hdl.handle.net/1963/2393}, author = {Julien Coatleven and Claudio Altafini} } @article {2010, title = {Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks}, journal = {BMC Systems Biology 2010, 4:83}, year = {2010}, publisher = {BioMed Central}, abstract = {Background. \\nFor large-scale biological networks represented as signed graphs, the index of frustration measures how far a network is from a monotone system, i.e., how incoherently the system responds to perturbations.\\nResults. \\nIn this paper we find that the frustration is systematically lower in transcriptional networks (modeled at functional level) than in signaling and metabolic networks (modeled at stoichiometric level). A possible interpretation of this result is in terms of energetic cost of an interaction: an erroneous or contradictory transcriptional action costs much more than a signaling/metabolic error, and therefore must be avoided as much as possible. Averaging over all possible perturbations, however, we also find that unlike for transcriptional networks, in the signaling/metabolic networks the probability of finding the system in its least frustrated configuration tends to be high also in correspondence of a moderate energetic regime, meaning that, in spite of the higher frustration, these networks can achieve a globally ordered response to perturbations even for moderate values of the strength of the interactions. Furthermore, an analysis of the energy landscape shows that signaling and metabolic networks lack energetic barriers around their global optima, a property also favouring global order.\\nConclusion. \\nIn conclusion, transcriptional and signaling/metabolic networks appear to have systematic differences in both the index of frustration and the transition to global order. These differences are interpretable in terms of the different functions of the various classes of networks.}, doi = {10.1186/1752-0509-4-83}, url = {http://hdl.handle.net/1963/4055}, author = {Giovanni Iacono and Claudio Altafini} } @article {2010, title = {On the number of positive solutions of some semilinear elliptic problems}, number = {SISSA;66/2010/M}, year = {2010}, url = {http://hdl.handle.net/1963/4083}, author = {Antonio Ambrosetti} } @article {2010, title = {Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions}, number = {SISSA;10/2010/FM}, year = {2010}, abstract = {The small dispersion limit of solutions to the Camassa-Holm (CH) equation is characterized by the appearance of a zone of rapid modulated oscillations. An asymptotic description of these oscillations is given, for short times, by the one-phase solution to the CH equation, where the branch points of the corresponding elliptic curve depend on the physical coordinates via the Whitham equations. We present a conjecture for the phase of the asymptotic solution. A numerical study of this limit for smooth hump-like initial data provides strong evidence for the validity of this conjecture....}, url = {http://hdl.handle.net/1963/3840}, author = {Simonetta Abenda and Tamara Grava and Christian Klein} } @article {2010, title = {Optimally swimming Stokesian Robots}, number = {SISSA;54/2010/M}, year = {2010}, abstract = {We study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.}, url = {http://hdl.handle.net/1963/3929}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Luca Heltai and Aline Lefebvre and Benoit Merlet} } @article {2010, title = {The role of membrane viscosity in the dynamics of fluid membranes}, number = {SISSA;55/2010/M}, year = {2010}, abstract = {Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3.}, url = {http://hdl.handle.net/1963/3930}, author = {Marino Arroyo and Antonio DeSimone and Luca Heltai} } @article {2010, title = {Two-dimensional almost-Riemannian structures with tangency points}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire }, volume = {27}, number = {arXiv.org;0908.2564v1}, year = {2010}, pages = {793-807}, publisher = {Elsevier}, abstract = {Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss-Bonnet formula for almost-Riemannian structures with tangency points.

}, doi = {10.1016/j.anihpc.2009.11.011}, url = {http://hdl.handle.net/1963/3870}, author = {Andrei A. Agrachev and Ugo Boscain and Gr{\'e}goire Charlot and Roberta Ghezzi and Mario Sigalotti} } @article {2010, title = {Well-posed infinite horizon variational problems on a compact manifold}, journal = {Proceedings of the Steklov Institute of Mathematics. Volume 268, Issue 1, 2010, Pages 17-31}, number = {arXiv:0906.4433;}, year = {2010}, publisher = {SISSA}, abstract = {We give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e., a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis, we construct an invariant Lagrangian submanifold (well-projected to M) of the flow of extremals in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics}, doi = {10.1134/S0081543810010037}, url = {http://hdl.handle.net/1963/6458}, author = {Andrei A. Agrachev} } @inbook {2009, title = {Biological Fluid Dynamics, Non-linear Partial Differential Equations}, booktitle = {Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554}, number = {SISSA;21/2008/M}, year = {2009}, url = {http://hdl.handle.net/1963/2630}, author = {Antonio DeSimone and Fran{\c c}ois Alouges and Aline Lefebvre} } @article {2009, title = {Characterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity}, journal = {BMC Research Notes (2009) 2:13}, year = {2009}, publisher = {BioMed Central}, abstract = {BACKGROUND: Neuronal plasticity is initiated by transient elevations of neuronal networks activity leading to changes of synaptic properties and providing the basis for memory and learning 1. An increase of electrical activity can be caused by electrical stimulation 2 or by pharmacological manipulations: elevation of extracellular K+ 3, blockage of inhibitory pathways 4 or by an increase of second messengers intracellular concentrations 5. Neuronal plasticity is mediated by several biochemical pathways leading to the modulation of synaptic strength, density of ionic channels and morphological changes of neuronal arborisation 6. On a time scale of a few minutes, neuronal plasticity is mediated by local protein trafficking 7 while, in order to sustain modifications beyond 2-3 h, changes of gene expression are required 8. FINDINGS: In the present manuscript we analysed the time course of changes of the evoked electrical activity during neuronal plasticity and we correlated it with a transcriptional analysis of the underlying changes of gene expression. Our investigation shows that treatment for 30 min. with the GABAA receptor antagonist gabazine (GabT) causes a potentiation of the evoked electrical activity occurring 2-4 hours after GabT and the concomitant up-regulation of 342 genes. Inhibition of the ERK1/2 pathway reduced but did not abolish the potentiation of the evoked response caused by GabT. In fact not all the genes analysed were blocked by ERK1/2 inhibitors. CONCLUSION: These results are in agreement with the notion that neuronal plasticity is mediated by several distinct pathways working in unison.}, doi = {10.1186/1756-0500-2-13}, url = {http://hdl.handle.net/1963/3706}, author = {Frederic D. Broccard and Silvia Pegoraro and Maria Elisabetta Ruaro and Claudio Altafini and Vincent Torre} } @article {2009, title = {Controllability and simultaneous controllability of isospectral bilinear control systems on complex flag manifolds}, journal = {Systems Control Lett. 58 (2009) 213-216}, year = {2009}, publisher = {Elsevier}, abstract = {For isospectral bilinear control systems evolving on the so-called complex flag manifolds (i.e., on the orbits of the Hermitian matrices under unitary conjugation action) it is shown that controllability is almost always verified. Easy and generic sufficient conditions are provided. The result applies to the problem of density operator controllability of finite dimensional quantum mechanical systems. In addition, we show that systems having different drifts (corresponding for example to different Larmor frequencies) are simultaneously controllable by the same control field.}, doi = {10.1016/j.sysconle.2008.10.008}, url = {http://hdl.handle.net/1963/3523}, author = {Claudio Altafini} } @article {2009, title = {Controllability on the group of diffeomorphisms}, journal = {Ann. Inst. H. Poincar{\'e} Anal. Non Lin{\'e}aire 26 (2009) 2503-2509}, number = {SISSA;79/2008/M}, year = {2009}, abstract = {Given a compact manifold M, we prove that any bracket generating family of vector fields on M, which is invariant under multiplication by smooth functions, generates the connected component of identity of the group of diffeomorphisms of M.}, doi = {10.1016/j.anihpc.2009.07.003}, url = {http://hdl.handle.net/1963/3396}, author = {Andrei A. Agrachev and Marco Caponigro} } @article {2009, title = {ERNEST: a toolbox for chemical reaction network theory}, journal = {Bioinformatics 25 (2009) 2853-2854}, year = {2009}, publisher = {Oxford University Press}, abstract = {Summary: ERNEST Reaction Network Equilibria Study Toolbox is a MATLAB package which, by checking various different criteria on the structure of a chemical reaction network, can exclude the multistationarity of the corresponding reaction system. The results obtained are independent of the rate constants of the reactions, and can be used for model discrimination.\\nAvailability and Implementation: The software, implemented in MATLAB, is available under the GNU GPL free software license from http://people.sissa.it/~altafini/papers/SoAl09/. It requires the MATLAB Optimization Toolbox.}, doi = {10.1093/bioinformatics/btp513}, url = {http://hdl.handle.net/1963/3826}, author = {Nicola Soranzo and Claudio Altafini} } @article {2009, title = {The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups}, journal = {J. Funct. Anal. 256 (2009) 2621-2655}, number = {SISSA;33/2008/M}, year = {2009}, abstract = {We present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp\\\'s volume form introduced by Montgomery. This definition generalizes the one of the Laplace-Beltrami operator in Riemannian geometry. In the case of left-invariant problems on unimodular Lie groups we prove that it coincides with the usual sum of squares.\\nWe then extend a method (first used by Hulanicki on the Heisenberg group) to compute explicitly the kernel of the hypoelliptic heat equation on any unimodular Lie group of type I. The main tool is the noncommutative Fourier transform. We then study some relevant cases: SU(2), SO(3), SL(2) (with the metrics inherited by the Killing form), and the group SE(2) of rototranslations of the plane.\\nOur study is motivated by some recent results about the cut and conjugate loci on these sub-Riemannian manifolds. The perspective is to understand how singularities of the sub-Riemannian distance reflect on the kernel of the corresponding hypoelliptic heat equation.}, doi = {10.1016/j.jfa.2009.01.006}, url = {http://hdl.handle.net/1963/2669}, author = {Andrei A. Agrachev and Ugo Boscain and Jean-Paul Gauthier and Francesco Rossi} } @article {2009, title = {Investigating the Conformational Stability of Prion Strains through a Kinetic Replication Model}, journal = {PLoS Comput Biol 2009;5(7): e1000420}, year = {2009}, publisher = {PLoS}, abstract = {Prion proteins are known to misfold into a range of different aggregated forms, showing different phenotypic and pathological states. Understanding strain specificities is an important problem in the field of prion disease. Little is known about which PrPSc structural properties and molecular mechanisms determine prion replication, disease progression and strain phenotype. The aim of this work is to investigate, through a mathematical model, how the structural stability of different aggregated forms can influence the kinetics of prion replication. The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage. A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows). The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils\\\' mean length) and is coherent with all experimental observations concerning strain-specific behavior.}, doi = {10.1371/journal.pcbi.1000420}, url = {http://hdl.handle.net/1963/3989}, author = {Mattia Zampieri and Giuseppe Legname and Claudio Altafini} } @article {2009, title = {mRNA stability and the unfolding of gene expression in the long-period yeast metabolic cycle}, journal = {BMC Systems Biology (2009) 3:18}, year = {2009}, publisher = {BioMed Central}, abstract = {Background: In yeast, genome-wide periodic patterns associated with energy-metabolic oscillations have been shown recently for both short (approx. 40 min) and long (approx. 300 min) periods.\\nResults: The dynamical regulation due to mRNA stability is found to be an important aspect of the genome-wide coordination of the long-period yeast metabolic cycle. It is shown that for periodic genes, arranged in classes according either to expression profile or to function, the pulses of mRNA abundance have phase and width which are directly proportional to the corresponding turnover rates.\\nConclusion: The cascade of events occurring during the yeast metabolic cycle (and their correlation with mRNA turnover) reflects to a large extent the gene expression program observable in other dynamical contexts such as the response to stresses/stimuli.}, doi = {10.1186/1752-0509-3-18}, url = {http://hdl.handle.net/1963/3630}, author = {Nicola Soranzo and Mattia Zampieri and Lorenzo Farina and Claudio Altafini} } @article {2009, title = {Optimal transportation under nonholonomic constraints}, journal = {Trans. Amer. Math. Soc. 361 (2009) 6019-6047}, number = {SISSA;68/2007/M}, year = {2009}, abstract = {We study the Monge\\\'s optimal transportation problem where the cost is given by optimal control cost. We prove the existence and uniqueness of optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures and most importantly the absent of sharp abnormal minimizers. In particular, this result is applicable in the case of subriemannian manifolds with a 2-generating distribution and cost given by d2, where d is the subriemannian distance. Also, we discuss some properties of the optimal plan when abnormal minimizers are present. Finally, we consider some examples of displacement interpolation in the case of Grushin plane.}, doi = {10.1090/S0002-9947-09-04813-2}, url = {http://hdl.handle.net/1963/2176}, author = {Andrei A. Agrachev and Paul Lee} } @article {2009, title = {Relaxation dynamics of fluid membranes}, journal = {Phys. Rev. E 79 (2009) 031915}, year = {2009}, publisher = {American Physical Society}, abstract = {We study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest.}, doi = {10.1103/PhysRevE.79.031915}, url = {http://hdl.handle.net/1963/3618}, author = {Marino Arroyo and Antonio DeSimone} } @article {2008, title = {Discerning static and causal interactions in genome-wide reverse engineering problems}, journal = {Bioinformatics 24 (2008) 1510-1515}, year = {2008}, abstract = {Background. In the past years devicing methods for discovering gene regulatory mechanisms at a genome-wide level has become a fundamental topic in the field of system biology. The aim is to infer gene-gene interactions in a more sophisticated and reliable way through the continuously improvement of reverse engineering algorithms exploiting microarray technologies. Motivation. This work is inspired by the several studies suggesting that co-expression is mostly related to \\\"static\\\" stable binding relationships, like belonging to the same protein complex, rather than other types of interactions more of a \\\"causal\\\" and transient nature (metabolic pathway or transcription factor-binding site interaction). Discerning static relationships from causal ones on the basis of their characteristic regulatory structures and in particular identifing \\\"dense modules\\\" with protein complex, and \\\"sparse modules\\\" with causal interactions such as those between transcription factor and corresponding binding site, the performances of different network inference algorithms in artificial and real networks (derived from E.coli and S.cerevisiae) can be tested and compared. Results. Our study shows that methods that try to prune indirect interactions from the inferred gene networks may fail to retrieve genes co-participating in a protein complex. On the other hand they are more robust in the identification of transcription factor-binding sites dependences when multiple transcription factors regulate the expression of the same gene. In the end we confirm the stronger co-expression regarding genes belonging to a protein complex than transcription factor-binding site, according, also, to the effect of multiple transcription factors and a low expression variance.}, doi = {10.1093/bioinformatics/btn220}, url = {http://hdl.handle.net/1963/2757}, author = {Mattia Zampieri and Nicola Soranzo and Claudio Altafini} } @article {2008, title = {A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds}, journal = {Discrete Contin. Dyn. Syst. 20 (2008) 801-822}, number = {SISSA;55/2006/M}, year = {2008}, abstract = {We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$. If $X$ and $Y$ are everywhere linearly independent, then they define a classical Riemannian metric on $M$ (the metric for which they are orthonormal) and they give to $M$ the structure of metric space. If $X$ and $Y$ become linearly dependent somewhere on $M$, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. They are special cases of rank-varying sub-Riemannian structures, which are naturally defined in terms of submodules of the space of smooth vector fields on $M$. Almost-Riemannian structures show interesting phenomena, in particular for what concerns the relation between curvature, presence of conjugate points, and topology of the manifold. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula.}, doi = {10.3934/dcds.2008.20.801}, url = {http://hdl.handle.net/1963/1869}, author = {Andrei A. Agrachev and Ugo Boscain and Mario Sigalotti} } @article {2008, title = {Multiple bound states for the Schroedinger-Poisson problem}, journal = {Commun. Contemp. Math. 10 (2008) 391-404}, year = {2008}, doi = {10.1142/S021919970800282X}, url = {http://hdl.handle.net/1963/2679}, author = {Antonio Ambrosetti and David Ruiz} } @article {2008, title = {Optimal Strokes for Low Reynolds Number Swimmers: An Example}, journal = {J. Nonlinear Sci. 18 (2008) 277-302}, year = {2008}, publisher = {Springer}, abstract = {Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901-062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics).}, doi = {10.1007/s00332-007-9013-7}, url = {http://hdl.handle.net/1963/4006}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Aline Lefebvre} } @article {2008, title = {Origin of Co-Expression Patterns in E.coli and S.cerevisiae Emerging from Reverse Engineering Algorithms}, journal = {PLoS ONE 3 (2008) e2981}, year = {2008}, abstract = {Background: The concept of reverse engineering a gene network, i.e., of inferring a genome-wide graph of putative genegene interactions from compendia of high throughput microarray data has been extensively used in the last few years to deduce/integrate/validate various types of \\\"physical\\\" networks of interactions among genes or gene products. Results: This paper gives a comprehensive overview of which of these networks emerge significantly when reverse engineering large collections of gene expression data for two model organisms, E.coli and S.cerevisiae, without any prior information. For the first organism the pattern of co-expression is shown to reflect in fine detail both the operonal structure of the DNA and the regulatory effects exerted by the gene products when co-participating in a protein complex. For the second organism we find that direct transcriptional control (e.g., transcription factor-binding site interactions) has little statistical significance in comparison to the other regulatory mechanisms (such as co-sharing a protein complex, colocalization on a metabolic pathway or compartment), which are however resolved at a lower level of detail than in E.coli. Conclusion: The gene co-expression patterns deduced from compendia of profiling experiments tend to unveil functional categories that are mainly associated to stable bindings rather than transient interactions. The inference power of this systematic analysis is substantially reduced when passing from E.coli to S.cerevisiae. This extensive analysis provides a way to describe the different complexity between the two organisms and discusses the critical limitations affecting this type of methodologies.}, doi = {10.1371/journal.pone.0002981}, url = {http://hdl.handle.net/1963/2722}, author = {Mattia Zampieri and Nicola Soranzo and Daniele Bianchini and Claudio Altafini} } @article {2008, title = {Relaxation of some transversally isotropic energies and applications to smectic A elastomers}, journal = {Math. Models Methods Appl. Sci. 18 (2008) 1-20}, number = {SISSA;01/2007/M}, year = {2008}, doi = {10.1142/S0218202508002693}, url = {http://hdl.handle.net/1963/1912}, author = {James Adams and Sergio Conti and Antonio DeSimone and Georg Dolzmann} } @article {2008, title = {Solitons of linearly coupled systems of semilinear non-autonomous equations on Rn}, journal = {J. Funct. Anal. 254 (2008) 2816-2845}, number = {SISSA;73/2007/M}, year = {2008}, abstract = {Using concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schr{\"o}dinger equations.}, doi = {10.1016/j.jfa.2007.11.013}, url = {http://hdl.handle.net/1963/2175}, author = {Antonio Ambrosetti and Giovanna Cerami and David Ruiz} } @article {2007, title = {Comparing association network algorithms for reverse engineering of large scale gene regulatory networks: synthetic vs real data}, journal = {Bioinformatics 23 (2007) 1640-1647}, year = {2007}, abstract = {Motivation: Inferring a gene regulatory network exclusively from microarray expression profiles is a difficult but important task. The aim of this work is to compare the predictive power of some of the most popular algorithms in different conditions (like data taken at equilibrium or time courses) and on both synthetic and real microarray data. We are in particular interested in comparing similarity measures both of linear type (like correlations and partial correlations) and of nonlinear type (mutual information and conditional mutual information), and in investigating the underdetermined case (less samples than genes). Results: In our simulations we see that all network inference algorithms obtain better performances from data produced with \\\"structural\\\" perturbations, like gene knockouts at steady state, than with any dynamical perturbation. The predictive power of all algorithms is confirmed on a reverse engineering problem from E. coli gene profiling data: the edges of the \\\"physical\\\" network of transcription factor-binding sites are significantly overrepresented among the highest weighting edges of the graph that we infer directly from the data without any structure supervision. Comparing synthetic and in vivo data on the same network graph allows us to give an indication of how much more complex a real transcriptional regulation program is with respect to an artificial model. Availability: Software and supplementary material are freely available at the URL http://people.sissa.it/~altafini/papers/SoBiAl07/}, doi = {10.1093/bioinformatics/btm163}, url = {http://hdl.handle.net/1963/2028}, author = {Nicola Soranzo and Ginestra Bianconi and Claudio Altafini} } @inbook {2007, title = {Concentration phenomena for nonlinear Schr{\"o}dinger equations: Recent results and new perspectives}, booktitle = {Perspectives in Nonlinear Partial Differential Equations: In Honor of Ha{\"\i}m Brezis / ed. by Henri Beresticky [et al.]. - Providence : American Mathematical Society, 2007. - (Contemporary mathematics ; 446). - p. 19-30}, year = {2007}, publisher = {American Mathematical Society}, organization = {American Mathematical Society}, abstract = {We survey some results on (NLSepsilon), discussing also new perspectives and open problems.}, url = {http://hdl.handle.net/1963/3516}, author = {Antonio Ambrosetti and Andrea Malchiodi} } @article {2007, title = {On feedback classification of control-affine systems with one and two-dimensional inputs}, journal = {SIAM J. Control Optim. 46 (2007) 1431-1460}, number = {arXiv.org;math/050231v2}, year = {2007}, abstract = {The paper is devoted to the local classification of generic control-affine systems on an n-dimensional manifold with scalar input for any n>3 or with two inputs for n=4 and n=5, up to state-feedback transformations, preserving the affine structure. First using the Poincare series of moduli numbers we introduce the intrinsic numbers of functional moduli of each prescribed number of variables on which a classification problem depends. In order to classify affine systems with scalar input we associate with such a system the canonical frame by normalizing some structural functions in a commutative relation of the vector fields, which define our control system. Then, using this canonical frame, we introduce the canonical coordinates and find a complete system of state-feedback invariants of the system. It also gives automatically the micro-local (i.e. local in state-input space) classification of the generic non-affine n-dimensional control system with scalar input for n>2. Further we show how the problem of feedback-equivalence of affine systems with two-dimensional input in state space of dimensions 4 and 5 can be reduced to the same problem for affine systems with scalar input. In order to make this reduction we distinguish the subsystem of our control system, consisting of the directions of all extremals in dimension 4 and all abnormal extremals in dimension 5 of the time optimal problem, defined by the original control system. In each classification problem under consideration we find the intrinsic numbers of functional moduli of each prescribed number of variables according to its Poincare series.}, doi = {10.1137/050623711}, url = {http://hdl.handle.net/1963/2186}, author = {Andrei A. Agrachev and Igor Zelenko} } @article {2007, title = {Feedback control of spin systems}, number = {SISSA;01/2006/M}, year = {2007}, note = {Proc. of the 44th IEEE Conf. on Decision and Control,. Seville, Spain, December 2005 (to appear).}, abstract = {The feedback stabilization problem for ensembles of coupled spin 1/2 systems is discussed from a control theoretic perspective. The noninvasive nature of the bulk measurement allows for a fully unitary and deterministic closed loop. The Lyapunov-based feedback design presented does not require spins that are selectively addressable. With this method, it is possible to obtain control inputs also for difficult tasks, like suppressing undesired couplings in identical spin systems.}, doi = {10.1007/s11128-006-0038-x}, url = {http://hdl.handle.net/1963/1808}, author = {Claudio Altafini} } @article {2007, title = {Feedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds}, journal = {45th IEEE Conference on Decision and Control (2007) 2471-2476}, number = {SISSA;65/2005/M}, year = {2007}, abstract = {In an N-level quantum mechanical system, the problem of unitary feedback stabilization of mixed density operators to periodic orbits admits a natural Lyapunov-based time-varying feedback design. A global description of the domain of attraction of the closed-loop system can be provided based on a \\\"root-space\\\"-like structure of the space of density operators. This convex set foliates as a complex flag manifold where each leaf is identified with the coadjoint orbit of the eigenvalues of the density operator. The converging conditions are time-independent but depend from the topology of the flag manifold: it is shown that the closed loop must have a number of equilibria at least equal to the Euler characteristic of the manifold, thus imposing obstructions of topological nature to global stabilizability.}, doi = {10.1109/CDC.2006.377774}, url = {http://hdl.handle.net/1963/1729}, author = {Claudio Altafini} } @article {2007, title = {On finite-dimensional projections of distributions for solutions of randomly forced PDE\\\'s}, journal = {Ann. Inst. Henri Poincare-Prob. Stat. 43 (2007) 399-415}, number = {arXiv.org;math/0603295}, year = {2007}, abstract = {The paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue measure and continuously depends on the map. The results obtained are applied to the 2D Navier-Stokes equations perturbed by various random forces of low dimension.}, doi = {10.1016/j.anihpb.2006.06.001}, url = {http://hdl.handle.net/1963/2012}, author = {Andrei A. Agrachev and Sergei Kuksin and Andrey Sarychev and Armen Shirikyan} } @article {2007, title = {Multi-bump solitons to linearly coupled systems of nonlinear Schr{\"o}dinger equations}, number = {SISSA;29/2006/M}, year = {2007}, doi = {10.1007/s00526-006-0079-0}, url = {http://hdl.handle.net/1963/1835}, author = {Antonio Ambrosetti and Eduardo Colorado and David Ruiz} } @article {2007, title = {Nearly time optimal stabilizing patchy feedbacks}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 279-310}, number = {arXiv.org;math/0512531v1}, year = {2007}, abstract = {We consider the time optimal stabilization problem for a nonlinear control system $\\\\dot x=f(x,u)$. Let $\\\\tau(y)$ be the minimum time needed to steer the system from the state $y\\\\in\\\\R^n$ to the origin, and call $\\\\A(T)$ the set of initial states that can be steered to the origin in time $\\\\tau(y)\\\\leq T$. Given any $\\\\ve>0$, in this paper we construct a patchy feedback $u=U(x)$ such that every solution of $\\\\dot x=f(x, U(x))$, $x(0)=y\\\\in \\\\A(T)$ reaches an $\\\\ve$-neighborhood of the origin within time $\\\\tau(y)+\\\\ve$.}, doi = {10.1016/j.anihpc.2006.03.010}, url = {http://hdl.handle.net/1963/2185}, author = {Fabio Ancona and Alberto Bressan} } @article {2007, title = {The number of eigenvalues of three-particle Schr{\"o}dinger operators on lattices}, journal = {J. Phys. A 40 (2007) 14819-14842}, number = {arXiv.org;math/0703191v1}, year = {2007}, abstract = {We consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\\\\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location and structure of the essential spectrum of the three-particle discrete Schr\\\\\\\"{o}dinger operator $H_{\\\\gamma}(K),$ $K$ being the total quasi-momentum and $\\\\gamma>0$ the ratio of the mass of fermion and boson.\\nWe choose for $\\\\gamma>0$ the interaction $v(\\\\gamma)$ in such a way the system consisting of one fermion and one boson has a zero energy resonance.\\nWe prove for any $\\\\gamma> 0$ the existence infinitely many eigenvalues of the operator $H_{\\\\gamma}(0).$ We establish for the number $N(0,\\\\gamma; z;)$ of eigenvalues lying below $z<0$ the following asymptotics $$ \\\\lim_{z\\\\to 0-}\\\\frac{N(0,\\\\gamma;z)}{\\\\mid \\\\log \\\\mid z\\\\mid \\\\mid}={U} (\\\\gamma) .$$ Moreover, for all nonzero values of the quasi-momentum $K \\\\in T^3 $ we establish the finiteness of the number $ N(K,\\\\gamma;\\\\tau_{ess}(K))$ of eigenvalues of $H(K)$ below the bottom of the essential spectrum and we give an asymptotics for the number $N(K,\\\\gamma;0)$ of eigenvalues below zero.}, doi = {10.1088/1751-8113/40/49/015}, url = {http://hdl.handle.net/1963/2576}, author = {Sergio Albeverio and Gianfausto Dell{\textquoteright}Antonio and Saidakhmat N. Lakaev} } @article {2007, title = {Reciprocal transformations and flat metrics on Hurwitz spaces}, journal = {J. Phys. A 40 (2007) 10769-10790}, number = {arXiv.org;0704.1779v2}, year = {2007}, abstract = {We consider hydrodynamic systems which possess a local Hamiltonian structure of Dubrovin-Novikov type. To such a system there are also associated an infinite number of nonlocal Hamiltonian structures. We give necessary and sufficient conditions so that, after a nonlinear transformation of the independent variables, the reciprocal system still possesses a local Hamiltonian structure of Dubrovin-Novikov type. We show that, under our hypotheses, bi-hamiltonicity is preserved by the reciprocal transformation. Finally we apply such results to reciprocal systems of genus g Whitham-KdV modulation equations.}, doi = {10.1088/1751-8113/40/35/004}, url = {http://hdl.handle.net/1963/2210}, author = {Simonetta Abenda and Tamara Grava} } @article {2007, title = {Soft elasticity and microstructure in smectic C elastomers}, number = {SISSA;05/2006/M}, year = {2007}, abstract = {Smectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable.}, doi = {10.1007/s00161-006-0031-8}, url = {http://hdl.handle.net/1963/1811}, author = {Antonio DeSimone and James Adams and Sergio Conti} } @article {2007, title = {Standing waves of some coupled Nonlinear Schr{\"o}dinger Equations}, number = {SISSA;02/2006/M}, year = {2007}, abstract = {We deal with a class of systems of NLS equations, proving the existence of bound and ground states provided the coupling parameter is small, respectively, large.}, doi = {10.1112/jlms/jdl020}, url = {http://hdl.handle.net/1963/1821}, author = {Antonio Ambrosetti and Eduardo Colorado} } @article {2006, title = {Almost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics}, number = {SISSA;80/2005/M}, year = {2006}, abstract = {We propose several parametrization-free solutions to the problem of quantum state reduction control by means of continuous measurement and smooth quantum feedback. In particular, we design a feedback law for which almost global stochastic feedback stabilization can be proved analytically by means of Lyapunov techinques. This synthesis arises very naturally from the physics of the problem, as it relies on the variance associated with the quantum filtering process.}, url = {http://hdl.handle.net/1963/1727}, author = {Claudio Altafini and Francesco Ticozzi} } @article {2006, title = {Bound and ground states of coupled nonlinear Schr{\"o}dinger equations}, journal = {C. R. Acad. Sci. Paris, Ser. I 342 (2006) 453-458}, year = {2006}, abstract = {We prove existence of bound and ground states of some systems of coupled nonlinear Schrodinger equations.}, doi = {10.1016/j.crma.2006.01.024}, url = {http://hdl.handle.net/1963/2149}, author = {Antonio Ambrosetti and Eduardo Colorado} } @article {2006, title = {Bound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity}, journal = {J. Anal. Math. 98 (2006) 317-348}, number = {SISSA;18/2005/M}, year = {2006}, doi = {10.1007/BF02790279}, url = {http://hdl.handle.net/1963/1756}, author = {Antonio Ambrosetti and Andrea Malchiodi and David Ruiz} } @article {2006, title = {A cyclic integral on k-Minkowski noncommutative space-time}, journal = {Int. J. Mod. Phys. A 21 (2006) 3133-3150}, number = {arXiv.org;hep-th/0407227v1}, year = {2006}, abstract = {We examine some alternative possibilities for an action functional for $\\\\kappa$-Minkowski noncommutative spacetime, with an approach which should be applicable to other spacetimes with coordinate-dependent commutators of the spacetime coordinates ($[x_\\\\mu,x_\\\\nu]=f_{\\\\mu,\\\\nu}(x)$). Early works on $\\\\kappa$-Minkowski focused on $\\\\kappa$-Poincar\\\\\\\'e covariance and the dependence of the action functional on the choice of Weyl map, renouncing to invariance under cyclic permutations of the factors composing the argument of the action functional. A recent paper (hep-th/0307149), by Dimitrijevic, Jonke, Moller, Tsouchnika, Wess and Wohlgenannt, focused on a specific choice of Weyl map and, setting aside the issue of $\\\\kappa$-Poincar\\\\\\\'e covariance of the action functional, introduced in implicit form a cyclicity-inducing measure. We provide an explicit formula for (and derivation of) a choice of measure which indeed ensures cyclicity of the action functional, and we show that the same choice of measure is applicable to all the most used choices of Weyl map. We find that this {\textquoteleft}{\textquoteleft}cyclicity-inducing measure\\\'\\\' is not covariant under $\\\\kappa$-Poincar\\\\\\\'e transformations. We also notice that the cyclicity-inducing measure can be straightforwardly derived using a map which connects the $\\\\kappa$-Minkowski spacetime coordinates and the spacetime coordinates of a {\textquoteleft}{\textquoteleft}canonical\\\'\\\' noncommutative spacetime, with coordinate-independent commutators.}, doi = {10.1142/S0217751X06031077}, url = {http://hdl.handle.net/1963/2158}, author = {Alessandra Agostini and Giovanni Amelino-Camelia and Michele Arzano and Francesco D{\textquoteright}Andrea} } @article {2006, title = {An estimation of the controllability time for single-input systems on compact Lie Groups}, journal = {ESAIM Control Optim. Calc. Var. 12 (2006) 409-441}, year = {2006}, abstract = {Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper.}, doi = {10.1051/cocv:2006007}, url = {http://hdl.handle.net/1963/2135}, author = {Andrei A. Agrachev and Thomas Chambrion} } @article {2006, title = {Experimental and modeling studies of desensitization of P2X3 receptors.}, journal = {Molecular pharmacology. 2006 Jul; 70(1):373-82}, number = {PMID:16627751;}, year = {2006}, publisher = {the American Society for Pharmacology and Experimental Therapeutics}, abstract = {The function of ATP-activated P2X3 receptors involved in pain sensation is modulated by desensitization, a phenomenon poorly understood. The present study used patch-clamp recording from cultured rat or mouse sensory neurons and kinetic modeling to clarify the properties of P2X3 receptor desensitization. Two types of desensitization were observed, a fast process (t1/2 = 50 ms; 10 microM ATP) following the inward current evoked by micromolar agonist concentrations, and a slow process (t1/2 = 35 s; 10 nM ATP) that inhibited receptors without activating them. We termed the latter high-affinity desensitization (HAD). Recovery from fast desensitization or HAD was slow and agonist-dependent. When comparing several agonists, there was analogous ranking order for agonist potency, rate of desensitization and HAD effectiveness, with 2-methylthioadenosine triphosphate the strongest and beta,gamma-methylene-ATP the weakest. HAD was less developed with recombinant (ATP IC50 = 390 nM) than native P2X3 receptors (IC50 = 2.3 nM). HAD could also be induced by nanomolar ATP when receptors seemed to be nondesensitized, indicating that resting receptors could express high-affinity binding sites. Desensitization properties were well accounted for by a cyclic model in which receptors could be desensitized from either open or closed states. Recovery was assumed to be a multistate process with distinct kinetics dependent on the agonist-dependent dissociation rate from desensitized receptors. Thus, the combination of agonist-specific mechanisms such as desensitization onset, HAD, and resensitization could shape responsiveness of sensory neurons to P2X3 receptor agonists. By using subthreshold concentrations of an HAD-potent agonist, it might be possible to generate sustained inhibition of P2X3 receptors for controlling chronic pain.}, doi = {10.1124/mol.106.023564}, url = {http://hdl.handle.net/1963/4974}, author = {Elena Sokolova and Andrei Skorinkin and Igor Moiseev and Andrei A. Agrachev and Andrea Nistri and Rashid Giniatullin} } @article {2006, title = {Homogeneous polynomial forms for simultaneous stabilizability of families of linear control systems: a tensor product approach}, journal = {IEEE Trans. Automat. Control 51 (2006) 1566-1571}, year = {2006}, abstract = {The paper uses the formalism of tensor products in order to deal with the problem of simultaneous\\nstabilizability of a family of linear control systems by means of Lyapunov functions which are homogeneous polynomial forms. While the feedback synthesis seems to be nonconvex, the simultaneous stability by means of homogeneous polynomial forms of the uncontrollable modes yields (convex) necessary but not sufficient conditions for simultaneous stabilizability.}, doi = {10.1109/TAC.2006.880811}, url = {http://hdl.handle.net/1963/2226}, author = {Claudio Altafini} } @article {2006, title = {Radial solutions concentrating on spheres of nonlinear Schr{\"o}dinger equations with vanishing potentials}, journal = {Proc. Roy. Soc. Edinburgh Sect. A 136 (2006) 889-907}, number = {SISSA;38/2005/M}, year = {2006}, abstract = {We prove the existence of radial solutions of 1.2) concentrating at a sphere for potentials which might be zero and might decay to zero at\\r\\ninfinity. The proofs use a perturbation technique in a variational setting, through a Lyapunov-Schmidt reduction.}, doi = {10.1017/S0308210500004789}, url = {http://hdl.handle.net/1963/1755}, author = {Antonio Ambrosetti and David Ruiz} } @article {2006, title = {Reflection symmetries for multiqubit density operators}, journal = {J. Math. Phys. 47 (2006) 032104}, number = {arXiv.org;quant-ph/0405123v2}, year = {2006}, abstract = {For multiqubit density operators in a suitable tensorial basis, we show that a number of nonunitary operations used in the detection and synthesis of entanglement are classifiable as reflection symmetries, i.e., orientation changing rotations. While one-qubit reflections correspond to antiunitary symmetries, as is known for example from the partial transposition criterion, reflections on the joint density of two or more qubits are not accounted for by the Wigner Theorem and are well-posed only for sufficiently mixed states. One example of such nonlocal reflections is the unconditional NOT operation on a multiparty density, i.e., an operation yelding another density and such that the sum of the two is the identity operator. This nonphysical operation is admissible only for sufficiently mixed states.}, doi = {10.1063/1.2181827}, url = {http://hdl.handle.net/1963/2121}, author = {Claudio Altafini and Timothy F. Havel} } @article {2005, title = {On the attainable set for Temple class systems with boundary controls}, journal = {SIAM J. Control Optim. 43 (2005) 2166-2190}, number = {SISSA;10/2002/M}, year = {2005}, publisher = {SISSA Library}, abstract = {Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws \% $$ u_t+f(u)_x=0, \\\\qquad u(0,x)=\\\\ov u(x), \\\\qquad {{array}{ll} \&u(t,a)=\\\\widetilde u_a(t), \\\\noalign{\\\\smallskip} \&u(t,b)=\\\\widetilde u_b(t), {array}. \\\\eqno(1) $$ on the domain $\\\\Omega =\\\\{(t,x)\\\\in\\\\R^2 : t\\\\geq 0, a \\\\le x\\\\leq b\\\\}.$ We study the mixed problem (1) from the point of view of control theory, taking the initial data $\\\\bar u$ fixed, and regarding the boundary data $\\\\widetilde u_a, \\\\widetilde u_b$ as control functions that vary in prescribed sets $\\\\U_a, \\\\U_b$, of $\\\\li$ boundary controls. In particular, we consider the family of configurations $$ \\\\A(T) \\\\doteq \\\\big\\\\{u(T,\\\\cdot); ~ u {\\\\rm is a sol. to} (1), \\\\quad \\\\widetilde u_a\\\\in \\\\U_a, \\\\widetilde u_b \\\\in \\\\U_b \\\\big\\\\} $$ that can be attained by the system at a given time $T>0$, and we give a description of the attainable set $\\\\A(T)$ in terms of suitable Oleinik-type conditions. We also establish closure and compactness of the set $\\\\A(T)$ in the $lu$ topology.}, doi = {10.1137/S0363012902407776}, url = {http://hdl.handle.net/1963/1581}, author = {Fabio Ancona and Giuseppe Maria Coclite} } @article {2005, title = {Commuting multiparty quantum observables and local compatibility}, journal = {Phys. Rev. A 72 (2005) 012112}, number = {SISSA;93/2004/M}, year = {2005}, abstract = {A formula for the commutator of tensor product matrices is used to shows that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site and to predict when this happens/does not happen in a concise manner. In particular, it is shown that two {\textquoteleft}{\textquoteleft}fully nontrivial\\\'\\\' $n$-qubit observables are compatible locally and globally if and only if they are equal up to sign. In addition, the formula gives insight into the construction of new paradoxes of the type of the Kochen-Specker Theorem, which can then be easily rephrased into proposals for new no hidden variable experiments of the type of the {\textquoteleft}{\textquoteleft}Bell Theorem without inequalities\\\'\\\'.}, doi = {10.1103/PhysRevA.72.012112}, url = {http://hdl.handle.net/1963/2228}, author = {Claudio Altafini} } @article {2005, title = {On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals}, journal = {J. Dyn. Control Syst. 11 (2005) 297-327}, number = {SISSA;58/2004/M}, year = {2005}, abstract = {Pairs (Hamiltonian system, Lagrangian distribution), called dynamical Lagrangian distributions, appear naturally in Differential Geometry, Calculus of Variations and Rational Mechanics. The basic differential invariants of a dynamical Lagrangian distribution w.r.t. the action of the group of symplectomorphisms of the ambient symplectic manifold are the curvature operator and the curvature form. These invariants can be seen as generalizations of the classical curvature tensor in Riemannian Geometry. In particular, in terms of these invariants one can localize the focal points along extremals of the corresponding variational problems. In the present paper we study the behavior of the curvature operator, the curvature form and the focal points of a dynamical Lagrangian distribution after its reduction by arbitrary first integrals in involution. The interesting phenomenon is that the curvature form of so-called monotone increasing Lagrangian dynamical distributions, which appear naturally in mechanical systems, does not decrease after reduction. It also turns out that the set of focal points to the given point w.r.t. the monotone increasing dynamical Lagrangian distribution and the corresponding set of focal points w.r.t. its reduction by one integral are alternating sets on the corresponding integral curve of the Hamiltonian system of the considered dynamical distributions. Moreover, the first focal point corresponding to the reduced Lagrangian distribution comes before any focal point related to the original dynamical distribution. We illustrate our results on the classical $N$-body problem.}, doi = {10.1007/s10883-005-6581-4}, url = {http://hdl.handle.net/1963/2254}, author = {Andrei A. Agrachev and Natalia N. Chtcherbakova and Igor Zelenko} } @article {2005, title = {Explicit Wei{\textendash}Norman formulae for matrix Lie groups via Putzer\\\'s method}, journal = {Systems and Control Letters, 54 (11):1121-1130, 2005}, year = {2005}, publisher = {Elsevier}, abstract = {The Wei{\textendash}Norman formula locally relates the Magnus solution of a system of linear time-varying ODEs with the solution expressed in terms of products of exponentials by means of a set of nonlinear differential equations in the parameters of the two types of solutions. A closed form expression of such formula is proposed based on the use of Putzer\\\'s method.}, doi = {10.1016/j.sysconle.2005.03.006}, url = {http://hdl.handle.net/1963/4538}, author = {Claudio Altafini} } @article {2005, title = {Ground states of nonlinear Schroedinger equations with potentials vanishing at infinity}, journal = {J. Eur. Math. Soc. 7 (2005) 117-144}, number = {SISSA;16/2004/M}, year = {2005}, abstract = {We deal with a class on nonlinear Schr\\\\\\\"odinger equations \\\\eqref{eq:1} with potentials $V(x)\\\\sim |x|^{-\\\\a}$, $0<\\\\a<2$, and $K(x)\\\\sim |x|^{-\\\\b}$, $\\\\b>0$. Working in weighted Sobolev spaces, the existence of ground states $v_{\\\\e}$ belonging to $W^{1,2}(\\\\Rn)$ is proved under the assumption that $p$ satisfies \\\\eqref{eq:p}. Furthermore, it is shown that $v_{\\\\e}$ are {\\\\em spikes} concentrating at a minimum of ${\\\\cal A}=V^{\\\\theta}K^{-2/(p-1)}$, where $\\\\theta= (p+1)/(p-1)-1/2$.}, url = {http://hdl.handle.net/1963/2352}, author = {Antonio Ambrosetti and Veronica Felli and Andrea Malchiodi} } @article {2005, title = {Modulation of the Camassa-Holm equation and reciprocal transformations}, journal = {Ann. Inst. Fourier (Grenoble) 55 (2005) 1803-1834}, number = {SISSA;107/2004/FM}, year = {2005}, abstract = {We derive the modulation equations or Whitham equations for the Camassa-Holm (CH) equation. We show that the modulation equations are hyperbolic and admit bi-Hamiltonian structure. Furthermore they are connected by a reciprocal transformation to the modulation equations of the first negative flow of the Korteweg de Vries (KdV) equation. The reciprocal transformation is generated by the Casimir of the second Poisson bracket of the KdV averaged flow. We show that the geometry of the bi-Hamiltonian structure of the KdV and CH modulation equations is quite different: indeed the KdV averaged bi-Hamiltonian structure can always be related to a semisimple Frobenius manifold while the CH one cannot.}, url = {http://hdl.handle.net/1963/2305}, author = {Simonetta Abenda and Tamara Grava} } @article {2005, title = {Nonlinear Schr{\"o}dinger Equations with vanishing and decaying potentials}, number = {SISSA;52/2005/M}, year = {2005}, url = {http://hdl.handle.net/1963/1760}, author = {Antonio Ambrosetti and Wang Zhi-Qiang} } @article {2005, title = {Wetting of rough surfaces: a homogenization approach}, journal = {Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97}, number = {SISSA;75/2004/M}, year = {2005}, abstract = {The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational\\napproach: the classical laws of Wenzel and Cassie-Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case.}, doi = {10.1098/rspa.2004.1364}, url = {http://hdl.handle.net/1963/2253}, author = {Antonio DeSimone and Giovanni Alberti} } @article {2004, title = {Blow-up solutions for the Schr{\"o}dinger equation in dimension three with a concentrated nonlinearity}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137}, year = {2004}, publisher = {Elsevier}, abstract = {We present some results on the blow-up phenomenon for the Schroedinger equation in dimension three with a nonlinear term supported in a fixed point. We find sufficient conditions for the blow up exploiting the moment of inertia of the solution and the uncertainty principle. In the critical case, we discuss the additional symmetry of the equation and construct a family of explicit blow up solutions.}, doi = {10.1016/j.anihpc.2003.01.002}, url = {http://hdl.handle.net/1963/2998}, author = {Riccardo Adami and Gianfausto Dell{\textquoteright}Antonio and Rodolfo Figari and Alessandro Teta} } @article {2004, title = {Coherent control of open quantum dynamical systems}, journal = {Phys. Rev. A 70 (2004) 062321}, number = {SISSA;90/2004/M}, year = {2004}, abstract = {A systematic analysis of the behavior of the quantum Markovian master equation driven by coherent control fields is proposed. Its irreversible character is formalized using control-theoretic notions and the sets of states that can be reached via cohere nt controls are described. The analysis suggests to which extent (and how) it is possible to counteract the effect of dissipation.}, doi = {10.1103/PhysRevA.70.062321}, url = {http://hdl.handle.net/1963/2227}, author = {Claudio Altafini} } @article {2004, title = {Energetics and switching of quasi-uniform states in small ferromagnetic particles}, journal = {M2AN Math. Model. Numer. Anal. 38 (2004) 235-248}, year = {2004}, publisher = {EDP Sciences}, abstract = {We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size.}, doi = {10.1051/m2an:2004011}, url = {http://hdl.handle.net/1963/2999}, author = {Fran{\c c}ois Alouges and Sergio Conti and Antonio DeSimone and Ivo Pokern} } @article {2004, title = {Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric}, journal = {ESAIM: COCV 10 (2004) 526-548}, year = {2004}, publisher = {EDP Sciences}, abstract = {For a Riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the Riemannian exponential map and the Lie group exponential map do not coincide. The consequence is that the reduced equations look more complicated than the original ones. The main scope of this paper is to treat the reduction of second order variational problems (corresponding to geometric splines) on such semidirect products of Lie groups. Due to the semidirect structure, a number of extra terms appears in the reduction, terms that are calculated explicitely. The result is used to compute the necessary conditions of an optimal control problem for a simple mechanical control system having invariant Lagrangian equal to the kinetic energy corresponding to the metric tensor. As an example, the case of a rigid body on the Special Euclidean group is considered in detail.}, doi = {10.1051/cocv:2004018}, url = {http://hdl.handle.net/1963/3521}, author = {Claudio Altafini} } @article {2004, title = {Representing multiqubit unitary evolutions via Stokes tensors}, journal = {Phys. Rev. A 70 (2004) 032331}, number = {SISSA;91/2004/M}, year = {2004}, abstract = {For the Stokes tensor parametrization of a multiqubit density operator, we provide an explicit formulation of the corresponding unitary dynamics at the infinitesimal level. The main advantage of this formalism (clearly reminiscent of the ideas of {\textquoteleft}{\textquoteleft}coherences\\\'\\\' and {\textquoteleft}{\textquoteleft}coupling Hamiltonians\\\'\\\' of spin systems) is that the pattern of correlation between qubits and the pattern of infinitesimal correlation are highlighted simultaneously and can be used constructively for qubit manipulation. For example, it allows to compute explicitly a Rodrigues\\\' formula for the one-parameter orbits of nonlocal Hamiltonians. The result is easily generalizable to orbits of Cartan subalgebras and allows to express the Cartan decomposition of unitary propagators as a linear action directly in terms of the infinitesimal generators.}, doi = {10.1103/PhysRevA.70.032331}, url = {http://hdl.handle.net/1963/2307}, author = {Claudio Altafini} } @article {2004, title = {Singularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II}, journal = {Indiana Univ. Math. J. 53 (2004) 297-392}, number = {SISSA;93/2002/M}, year = {2004}, publisher = {Indiana University Mathematics Journal}, doi = {10.1512/iumj.2004.53.2400}, url = {http://hdl.handle.net/1963/1663}, author = {Antonio Ambrosetti and Andrea Malchiodi and Wei-Ming Ni} } @article {2004, title = {Stability rates for patchy vector fields}, journal = {ESAIM COCV 10 (2004) 168-200}, number = {arXiv.org;math/0111109v1}, year = {2004}, publisher = {EDP Sciences}, abstract = {This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude as the impulsive forcing term.}, doi = {10.1051/cocv:2004003}, url = {http://hdl.handle.net/1963/2959}, author = {Fabio Ancona and Alberto Bressan} } @article {2004, title = {Tensor of coherences parametrization of multiqubit density operators for entanglement characterization}, journal = {Phys. Rev. A 69 (2004) 012311}, number = {arXiv.org;quant-ph/0308019v1}, year = {2004}, publisher = {American Physical Society}, abstract = {For multiqubit densities, the tensor of coherences (or Stokes tensor) is a real parameterization obtained by the juxtaposition of the affine Bloch vectors of each qubit. While it maintains the tensorial structure of the underlying space, it highlights the pattern of correlations, both classical and quantum, between the subsystems and, due to the affine parameterization, it contains in its components all reduced densities of all orders. The main purpose of our use of this formalism is to deal with entanglement. For example, the detection of bipartite entanglement is straightforward, as it is the synthesis of densities having positive partial transposes between desired qubits. In addition, finding explicit mixtures for families of separable states becomes a feasible issue for few qubit symmetric densities (we compute it for Werner states) and, more important, it provides some insight on the possible origin of entanglement for such densities.}, doi = {10.1103/PhysRevA.69.012311}, url = {http://hdl.handle.net/1963/2845}, author = {Claudio Altafini} } @article {2004, title = {Well-posedness for general 2x2 systems of conservation laws}, journal = {Mem. Amer. Math. Soc. 169 (2004), no. 801, x+170 pp.}, number = {SISSA;27/99/M}, year = {2004}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1241}, author = {Fabio Ancona and Andrea Marson} } @article {2003, title = {The calibration method for the Mumford-Shah functional and free-discontinuity problems}, journal = {Calc. Var. Partial Differential Equations 16 (2003) 299-333}, number = {SISSA;35/2001/M}, year = {2003}, publisher = {Springer}, abstract = {We present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results.}, doi = {10.1007/s005260100152}, url = {http://hdl.handle.net/1963/3051}, author = {Giovanni Alberti and Guy Bouchitte and Gianni Dal Maso} } @article {2003, title = {Controllability properties for finite dimensional quantum Markovian master equations}, journal = {J. Math. Phys. 44 (2003) 2357-2372}, number = {SISSA;7/2003/M}, year = {2003}, publisher = {American Institute of Physics}, abstract = {Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states. It is shown that the system can be accessible but neither small-time controllable nor controllable in finite time. In particular, if the generators of quantum dynamical semigroups are unital, then the reachable sets admit easy characterizations as they monotonically grow in time. The two level case is treated in detail.}, doi = {10.1063/1.1571221}, url = {http://hdl.handle.net/1963/2909}, author = {Claudio Altafini} } @article {2003, title = {Geometric motion control for a kinematically redundant robotic chain: application to a holonomic mobile manipulator}, journal = {J. Robotic Syst. 20 (2003) 211-227}, year = {2003}, publisher = {Wiley}, abstract = {For kinematically redundant robotic manipulators, the extra degrees of freedom available allows freedom in the generation of the trajectories of the end-effector. In this paper, for this scope, we use techniques for motion control of rigid bodies on Riemannian manifolds (and Lie groups in particular) to design workspace control algorithms for the end-effector of the robotic chain and then to pull them back to joint space, all respecting the different geometric structures of the two underlying model spaces. The trajectory planner makes use of geometric splines. Examples of the different kinds of curves that are obtained via the De Casteljau algorithm in correspondence of different metric structures in SE(3) are reported. The feedback module, instead, consists of a Lyapunov based PD controller defined from a suitable notion of error distance on the Lie group. The motivating application of our work is a holonomic mobile manipulator for which simulation results are described in detail.}, doi = {10.1002/rob.10084}, url = {http://hdl.handle.net/1963/3019}, author = {Claudio Altafini} } @article {2003, title = {On the local structure of optimal trajectories in R3}, journal = {SIAM J. Control Optim. 42 (2003) 513-531}, number = {SISSA;41/2002/M}, year = {2003}, publisher = {SISSA Library}, abstract = {We analyze the structure of a control function u(t) corresponding to an optimal trajectory for the system $\\\\dot q =f(q)+u\\\\, g(q)$ in a three-dimensional manifold, near a point where some nondegeneracy conditions are satisfied. The kind of optimality which is studied includes time-optimality. The control turns out to be the concatenation of some bang and some singular arcs. Studying the index of the second variation of the switching times, the number of such arcs is bounded by four.}, doi = {10.1137/S0363012902409246}, url = {http://hdl.handle.net/1963/1612}, author = {Andrei A. Agrachev and Mario Sigalotti} } @article {2003, title = {Motion on submanifolds of noninvariant holonomic constraints for a kinematic control system evolving on a matrix Lie group}, journal = {Syst. Control Lett. 50 (2003) 241-250}, year = {2003}, publisher = {Elsevier}, abstract = {For a control system on a matrix Lie group with one or more configuration constraints that are not left/right invariant, finding the combinations of (kinematic) control inputs satisfying the motion constraints is not a trivial problem. Two methods, one coordinate-dependent and the other coordinate-free are suggested. The first is based on the Wei-Norman formula; the second on the calculation of the annihilator of the coadjoint action of the constraint one-form at each point of the group manifold. The results are applied to a control system on SE(3) with a holonomic inertial constraint involving the noncommutative part in a nontrivial way. The difference in terms of compactness of the result between the two methods is considerable.}, doi = {10.1016/S0167-6911(03)00168-3}, url = {http://hdl.handle.net/1963/3018}, author = {Claudio Altafini and Ruggero Frezza} } @article {2003, title = {Parameter differentiation and quantum state decomposition for time varying Schr{\"o}dinger equations}, journal = {Rep. Math. Phys. 52 (2003) 381-400}, number = {arXiv.org;quant-ph/0201034v2}, year = {2003}, publisher = {Elsevier}, abstract = {For the unitary operator, solution of the Schroedinger equation corresponding to a time-varying Hamiltonian, the relation between the Magnus and the product of exponentials expansions can be expressed in terms of a system of first order differential equations in the parameters of the two expansions. A method is proposed to compute such differential equations explicitly and in a closed form.}, doi = {10.1016/S0034-4877(03)80037-X}, url = {http://hdl.handle.net/1963/3017}, author = {Claudio Altafini} } @article {2003, title = {Positive solutions to a class of quasilinear elliptic equations on R}, journal = {Discrete Contin.Dyn.Syst. 9 (2003), no.1, 55-68}, number = {SISSA;58/2002/M}, year = {2003}, publisher = {American Institute of Mathematical Sciences}, abstract = {We discuss the existence of positive solutions of perturbation to a class of quasilinear elliptic equations on R.}, doi = {10.3934/dcds.2003.9.55}, url = {http://hdl.handle.net/1963/1628}, author = {Antonio Ambrosetti and Wang Zhi-Qiang} } @article {2003, title = {Prescribing scalar and boundary mean curvature on the three dimensional half sphere}, journal = {J. Geom. Anal. 13 (2003) 255-289}, number = {SISSA;36/2001/M}, year = {2003}, publisher = {Springer}, abstract = {We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove some existence and compactness results.}, doi = {10.1007/BF02930697}, url = {http://hdl.handle.net/1963/3086}, author = {Zindine Djadli and Andrea Malchiodi and Mohameden Ould Ahmedou} } @article {2003, title = {Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I}, journal = {Comm. Math. Phys. 235 (2003) no.3, 427-466}, number = {SISSA;63/2002/M}, year = {2003}, publisher = {Springer}, doi = {10.1007/s00220-003-0811-y}, url = {http://hdl.handle.net/1963/1633}, author = {Antonio Ambrosetti and Andrea Malchiodi and Wei-Ming Ni} } @article {2003, title = {Some results on the boundary control of systems of conservation laws}, journal = {SIAM J.Control Optim. 41 (2003),no.2, 607}, number = {SISSA;44/2002/M}, year = {2003}, publisher = {SISSA Library}, doi = {10.1137/S0363012901392529}, url = {http://hdl.handle.net/1963/1615}, author = {Alberto Bressan and Fabio Ancona and Giuseppe Maria Coclite} } @article {2002, title = {Controllability of quantum mechanical systems by root space decomposition of su(N)}, journal = {J.Math.Phys. 43(2002), no.5, 2051}, number = {SISSA;42/2002/M}, year = {2002}, publisher = {SISSA Library}, doi = {10.1063/1.1467611}, url = {http://hdl.handle.net/1963/1613}, author = {Claudio Altafini} } @article {2002, title = {Flow Stability of Patchy Vector Fields and Robust Feedback Stabilization}, journal = {SIAM J. Control Optim. 41 (2002) 1455-1476}, number = {SISSA;71/2001/M}, year = {2002}, publisher = {SIAM}, abstract = {The paper is concerned with patchy vector fields, a class of discontinuous, piecewise smooth vector fields that were introduced in AB to study feedback stabilization problems. We prove the stability of the corresponding solution set w.r.t. a wide class of impulsive perturbations. These results yield the robusteness of patchy feedback controls in the presence of measurement errors and external disturbances.}, doi = {10.1137/S0363012901391676}, url = {http://hdl.handle.net/1963/3073}, author = {Fabio Ancona and Alberto Bressan} } @article {2002, title = {Following a path of varying curvature as an output regulation problem}, journal = {IEEE Trans. Automatic Control 47 (2002) 1551-1556}, year = {2002}, publisher = {IEEE}, abstract = {Given a path of nonconstant curvature, local asymptotic stability can be proven for the general n trailer whenever the curvature can be considered as the output of an exogenous dynamical system. The controllers that provide convergence to zero of the tracking error chosen for the path-following problem are composed of a prefeedback that input-output linearizes the system, plus a linear controller.}, doi = {10.1109/TAC.2002.802750}, url = {http://hdl.handle.net/1963/3143}, author = {Claudio Altafini} } @article {2002, title = {On the generation of sequential unitary gates from continuous time Schrodinger equations driven by external fields}, journal = {Quantum Inf.Process. 1 (2002),no.3,207}, number = {SISSA;43/2002/M}, year = {2002}, publisher = {SISSA Library}, doi = {10.1023/A:1019825109040}, url = {http://hdl.handle.net/1963/1614}, author = {Claudio Altafini} } @article {2002, title = {Geometry of Jacobi Curves I}, journal = {J. Dynam. Control Systems 8 (2002) 93-140}, number = {SISSA;75/2001/M}, year = {2002}, publisher = {Springer}, abstract = {Jacobi curves are deep generalizations of the spaces of \\\"Jacobi fields\\\" along Riemannian geodesics. Actually, Jacobi curves are curves in the Lagrange Grassmannians. In our paper we develop differential geometry of these curves which provides basic feedback or gauge invariants for a wide class of smooth control systems and geometric structures. Two principal invariants are the generalized Ricci curvature, which is an invariant of the parametrized curve in the Lagrange Grassmannian endowing the curve with a natural projective structure, and a fundamental form, which is a fourth-order differential on the curve. The so-called rank 1 curves are studied in more detail. Jacobi curves of this class are associated with systems with scalar controls and with rank 2 vector distributions.\\nIn the forthcoming second part of the paper we will present the comparison theorems (i.e., the estimates for the conjugate points in terms of our invariants( for rank 1 curves an introduce an important class of \\\"flat curves\\\".}, doi = {10.1023/A:1013904801414}, url = {http://hdl.handle.net/1963/3110}, author = {Andrei A. Agrachev and Igor Zelenko} } @article {2002, title = {Geometry of Jacobi curves II}, journal = {J. Dynam. Control Systems 8 (2002), no. 2, 167--215}, number = {SISSA;18/2002/M}, year = {2002}, publisher = {SISSA Library}, doi = {10.1023/A:1015317426164}, url = {http://hdl.handle.net/1963/1589}, author = {Andrei A. Agrachev and Igor Zelenko} } @article {2002, title = {Multiplicity results for the Yamabe problem on Sn}, journal = {Proceedings of the National Academy of Sciences of the United States of America. 2002 Nov; 99(24):15252-6}, number = {PMID:12399546;}, year = {2002}, publisher = {National Academy of Sciences}, abstract = {We discuss some results related to the existence of multiple solutions for the Yamabe problem.}, doi = {10.1073/pnas.222494199}, url = {http://hdl.handle.net/1963/5885}, author = {Antonio Ambrosetti} } @article {2002, title = {Prescribing a fourth oder conformal invariant on the standard sphere - Part I: a perturbation result}, journal = {Commun. Contemp. Math., 2002, 4, 375}, number = {SISSA;82/00/M}, year = {2002}, publisher = {SISSA Library}, doi = {10.1142/S0219199702000695}, url = {http://hdl.handle.net/1963/1539}, author = {Zindine Djadli and Mohameden Ould Ahmedou and Andrea Malchiodi} } @article {2002, title = {Prescribing a fourth oder conformal invariant on the standard sphere - Part II: blow up analysis and applications}, journal = {Ann. Sc. Norm. Super. Pisa Cl. Sci., 2002, 1, 387}, number = {SISSA;83/00/M}, year = {2002}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1540}, author = {Zindine Djadli and Andrea Malchiodi and Mohameden Ould Ahmedou} } @article {2002, title = {The reachable set of a linear endogenous switching system}, journal = {Systems Control Lett. 47 (2002) 343-353}, year = {2002}, publisher = {Elsevier}, abstract = {In this work, switching systems are named endogenous when their switching pattern is controllable. Linear endogenous switching systems can be considered as a particular class of bilinear control systems. The key idea is that both types of systems are equivalent to polysystems, i.e. to systems whose flow is piecewise smooth. The reachable set of a linear endogenous switching system can be studied consequently. The main result is that, in general, it has the structure of a semigroup, even when the Lie algebra rank condition is satisfied since the logic inputs cannot reverse the direction of the flow. The adaptation of existing controllability criteria for bilinear systems is straightforward.}, doi = {10.1016/S0167-6911(02)00228-1}, url = {http://hdl.handle.net/1963/3142}, author = {Claudio Altafini} } @article {2002, title = {Solutions concentrating on spheres to symmetric singularly perturbed problems}, journal = {C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150}, number = {SISSA;23/2002/M}, year = {2002}, publisher = {SISSA Library}, abstract = {We discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere.}, doi = {10.1016/S1631-073X(02)02414-7}, url = {http://hdl.handle.net/1963/1594}, author = {Antonio Ambrosetti and Andrea Malchiodi and Wei-Ming Ni} } @article {2002, title = {On the Yamabe problem and the scalar curvature problems under boundary conditions}, journal = {Math. Ann., 2002, 322, 667}, number = {SISSA;52/00/M}, year = {2002}, publisher = {SISSA Library}, doi = {10.1007/s002080100267}, url = {http://hdl.handle.net/1963/1510}, author = {Antonio Ambrosetti and Li YanYan and Andrea Malchiodi} } @article {2001, title = {Multiplicity results for some nonlinear Schrodinger equations with potentials}, journal = {Arch. Ration. Mech. An., 2001, 159, 253}, number = {SISSA;108/00/AF}, year = {2001}, publisher = {SISSA Library}, doi = {10.1007/s002050100152}, url = {http://hdl.handle.net/1963/1564}, author = {Antonio Ambrosetti and Andrea Malchiodi and Simone Secchi} } @article {2001, title = {On the subanalyticity of Carnot-Caratheodory distances}, journal = {Ann. I. H. Poincare - An., 2001, 18, 359}, number = {SISSA;25/00/M}, year = {2001}, publisher = {SISSA Library}, doi = {10.1016/S0294-1449(00)00064-0}, url = {http://hdl.handle.net/1963/1483}, author = {Andrei A. Agrachev and Jean-Paul Gauthier} } @article {2001, title = {On the symmetric scalar curvature problem on S\\\\sp n}, journal = {J. Differential Equations 170 (2001) 228-245}, year = {2001}, publisher = {Elsevier}, abstract = {We discuss some existence results dealing with the scalar curvature problem on S\\\\sp n in the presence of various symmetries.}, doi = {10.1006/jdeq.2000.3816}, url = {http://hdl.handle.net/1963/3095}, author = {Antonio Ambrosetti and Andrea Malchiodi} } @article {2000, title = {Elliptic variational problems in $ R\\\\sp N$ with critical growth}, journal = {J. Differential Equations 168 (2000), no. 1, 10--32}, number = {SISSA;44/99/M}, year = {2000}, publisher = {SISSA Library}, doi = {10.1006/jdeq.2000.3875}, url = {http://hdl.handle.net/1963/1258}, author = {Antonio Ambrosetti and Jesus Garcia Azorero and Ireneo Peral} } @article {2000, title = {Existence and multiplicity results for some nonlinear elliptic equations: a survey.}, journal = {Rend. Mat. Appl., 2000, 20, 167}, number = {SISSA;4/00/M}, year = {2000}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1462}, author = {Antonio Ambrosetti and Jesus Garcia Azorero and Ireneo Peral} } @article {2000, title = {A note on the scalar curvature problem in the presence of symmetries}, journal = {Ricerche Mat. 49 (2000), suppl., 169-176}, number = {SISSA;150/99/M}, year = {2000}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1365}, author = {Antonio Ambrosetti and Li YanYan and Andrea Malchiodi} } @inbook {2000, title = {Principal invariants of Jacobi curves}, booktitle = {Nonlinear control in the Year 2000 / Alberto Isidori, Francoise Lamnabhi-Lagarrigue, Witold Respondek (eds.) - Springer : Berlin, 2001. - (Lecture notes in control and information sciences ; 258). - ISBN 1-85233-363-4 (v. 1). - p. 9-22.}, year = {2000}, publisher = {Springer}, organization = {Springer}, abstract = {Jacobi curves are far going generalizations of the spaces of \\\"Jacobi fields\\\" along Riemannian geodesics. Actually, Jacobi curves are curves in the Lagrange Grassmannians. Differential geometry of these curves provides basic feedback or gauge invariants for a wide class of smooth control systems and geometric structures. In the present paper we mainly discuss two principal invariants: the generalized Ricci curvature, which is an invariant of the parametrized curve in the Lagrange Grassmanian providing the curve with a natural projective structure, and a fundamental form, which is a 4-oder differential on the curve.}, doi = {10.1007/BFb0110204}, url = {http://hdl.handle.net/1963/3825}, author = {Andrei A. Agrachev and Igor Zelenko} } @article {2000, title = {A Remark on One-Dimensional Many-Body Problems with Point Interactions}, journal = {Int. J. Mod. Phys. B 14 (2000) 721-727}, number = {arXiv.org;quant-ph/0001089v1}, year = {2000}, publisher = {World Scientific}, abstract = {The integrability of one dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) $\\\\delta$-function interaction there is another singular point interactions which gives rise to a new one-parameter family of integrable quantum mechanical many-body systems. The bound states and scattering matrices are calculated for both bosonic and fermionic statistics.}, doi = {10.1142/S0217979200000601}, url = {http://hdl.handle.net/1963/3214}, author = {Sergio Albeverio and Ludwik Dabrowski and Shao-Ming Fei} } @article {2000, title = {Scalar curvature under boundary conditions}, journal = {Cr. Acad. Sci. I-Math, 2000, 330, 1013}, number = {SISSA;48/00/M}, year = {2000}, publisher = {SISSA Library}, doi = {10.1016/S0764-4442(00)00312-8}, url = {http://hdl.handle.net/1963/1506}, author = {Antonio Ambrosetti and Li YanYan and Andrea Malchiodi} } @article {1999, title = {The calibration method for the Mumford-Shah functional}, journal = {C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254}, number = {SISSA;21/99/M}, year = {1999}, publisher = {Elsevier}, abstract = {In this Note we adapt the calibration method to functionals of Mumford-Shah type, and provide a criterion (Theorem 1) to verify that a given function is energy minimizing. Among other applications, we use this criterion to show that certain triple-junction configurations are minimizing (Example 3).}, doi = {10.1016/S0764-4442(00)88602-4}, url = {http://hdl.handle.net/1963/1235}, author = {Giovanni Alberti and Guy Bouchitte and Gianni Dal Maso} } @article {1999, title = {A multiplicity result for the Yamabe problem on $S\\\\sp n$}, journal = {J. Funct. Anal. 168 (1999), no. 2, 529-561}, number = {SISSA;50/99/M}, year = {1999}, publisher = {Elsevier}, abstract = {We prove a multiplicity result for the Yamabe problem on the manifold (S, g), where g is a perturbation of the standard metric g0 of Sn. Solutions are found by variational methods via an abstract perturbation result.}, doi = {10.1006/jfan.1999.3458}, url = {http://hdl.handle.net/1963/1264}, author = {Antonio Ambrosetti and Andrea Malchiodi} } @article {1999, title = {Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws}, journal = {J. Differential Equations 151 (1999) 345-372}, number = {SISSA;139/97/M}, year = {1999}, publisher = {Elsevier}, abstract = {The Riemann problem for a conservation law with a nonconvex (cubic) flux can be solved in a class of admissible nonclassical solutions that may violate the Oleinik entropy condition but satisfy a single entropy inequality and a kinetic relation. We use such a nonclassical Riemann solver in a front tracking algorithm, and prove that the approximate solutions remain bounded in the total variation norm. The nonclassical shocks induce an increase of the total variation and, therefore, the classical measure of total variation must be modified accordingly. We prove that the front tracking scheme converges strongly to a weak solution satisfying the entropy inequality.}, doi = {10.1006/jdeq.1998.3513}, url = {http://hdl.handle.net/1963/3312}, author = {Debora Amadori and Paolo Baiti and Philippe G. LeFloch and Benedetto Piccoli} } @article {1999, title = {Perturbation of $\Delta u+u^{(N+2)/(N-2)}=0$, the scalar curvature problem in $R^N$, and related topics}, journal = {J. Funct. Anal. 165 (1999) 117-149}, number = {SISSA;141/98/M}, year = {1999}, publisher = {Elsevier}, abstract = {Some nonlinear elliptic equations on $R^N$ which arise perturbing the problem with the critical Sobolev exponent are studied. In particular, some results dealing with the scalar curvature problem in $R^N$ are given.

}, doi = {10.1006/jfan.1999.3390}, url = {http://hdl.handle.net/1963/3255}, author = {Antonio Ambrosetti and Jesus Garcia Azorero and Ireneo Peral} } @article {1999, title = {On the scalar curvature problem under symmetry}, number = {SISSA;73/99/M}, year = {1999}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1287}, author = {Antonio Ambrosetti and Andrea Malchiodi} } @article {1998, title = {Branching points for a class of variational operators}, journal = {J. Anal. Math. 76 (1998) 321-335}, year = {1998}, publisher = {Springer}, doi = {10.1007/BF02786940}, url = {http://hdl.handle.net/1963/3314}, author = {Antonio Ambrosetti} } @article {1998, title = {Special functions with bounded variation and with weakly differentiable traces on the jump set}, journal = {NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243}, number = {SISSA;123/95/M}, year = {1998}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1025}, author = {Luigi Ambrosio and Andrea Braides and Adriana Garroni} } @article {1997, title = {Homogeneous tangent vectors and high order necessary conditions for optimal controls}, journal = {J. Dynam. Control Systems 3 (1997), no. 2, 205--240}, number = {SISSA;113/95/M}, year = {1997}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1015}, author = {Fabio Ancona} } @mastersthesis {1994, title = {Analysis of Singularity Structures for Quasi-Integrable Hamiltonian Systems}, year = {1994}, school = {SISSA}, keywords = {Hamiltonian systems}, url = {http://hdl.handle.net/1963/5685}, author = {Simonetta Abenda} } @article {1990, title = {Existence of solutions for a class of non-convex differential inclusions}, journal = {Rend.Sem.Mat.Univ. Padova, 83 (1990), 71-76}, number = {SISSA;31/89/M}, year = {1990}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/792}, author = {Fabio Ancona and Giovanni Colombo} } @article {1990, title = {A general chain rule for distributional derivatives}, journal = {Proc. Amer. Math. Soc. 108 (1990), no. 3, 691-702}, number = {SISSA;54/88/M}, year = {1990}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/650}, author = {Luigi Ambrosio and Gianni Dal Maso} } @article {1987, title = {Solutions with minimal period for Hamiltonian systems in a potential well.}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 4 (1987), no. 3, 275-296}, number = {SISSA;79/85/M}, year = {1987}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/466}, author = {Antonio Ambrosetti and Vittorio Coti Zelati} } @article {1987, title = {Symmetry breaking in Hamiltonian systems}, journal = {J. Differential Equations 67 (1987), no. 2, 165-184}, number = {SISSA;22/85/M}, year = {1987}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/409}, author = {Antonio Ambrosetti and Vittorio Coti Zelati and Ivar Ekeland} } @article {1986, title = {Dirichlet problems for demicoercive functionals}, journal = {Nonlinear anal. 10(1986), no.6, 603-613}, number = {SISSA;03/85/M}, year = {1986}, publisher = {SISSA Library}, doi = {10.1016/0362-546X(86)90145-8}, url = {http://hdl.handle.net/1963/390}, author = {Gabriele Anzellotti and Giuseppe Buttazzo and Gianni Dal Maso} } @article {1982, title = {Differential equations with multiple solutions and nonlinear functional analysis}, journal = {Equadiff 82 (Wurzburg, 1982), 10--37, Lecture Notes in Math., 1017, Springer, Berlin, 1983}, number = {SISSA;71/82/M}, year = {1982}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/222}, author = {Antonio Ambrosetti} } @article {1981, title = {Recent advances in the study of the existence of periodic orbits of Hamiltonian systems}, journal = {Advances in Hamiltonian systems (Rome, 1981), 1--22, Ann. CEREMADE, Birkhauser Boston, Boston, MA, 1983.}, number = {SISSA;8/82/M}, year = {1981}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/159}, author = {Antonio Ambrosetti} }