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.

10aactive matter10aadhesive locomotion10acell motility10acell sheet folding10aknotted DNA10atopological defects10aunicellular swimmers10aunjamming transition1 aAgostinelli, Daniele1 aCerbino, Roberto1 aDel Alamo, Juan, C1 aDeSimone, Antonio1 aHöhn, Stephanie1 aMicheletti, Cristian1 aNoselli, Giovanni1 aSharon, Eran1 aYeomans, Julia uhttp://dx.doi.org/10.3934/mine.202001100478nas a2200133 4500008004100000245006600041210006600107260001600173300001200189490000700201100002300208700001600231856009700247 2019 eng d00aActivation of a muscle as a mapping of stress–strain curves0 aActivation of a muscle as a mapping of stress–strain curves bElsevier BV a37–420 v281 aRiccobelli, Davide1 aAmbrosi, D. uhttps://www.math.sissa.it/publication/activation-muscle-mapping-stress%E2%80%93strain-curves00512nas a2200133 4500008004100000245007600041210006900117260002200186490000800208100002300216700001500239700002400254856010000278 2019 eng d00aOn the existence of elastic minimizers for initially stressed materials0 aexistence of elastic minimizers for initially stressed materials bThe Royal Society0 v3771 aRiccobelli, Davide1 aAgosti, A.1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/existence-elastic-minimizers-initially-stressed-materials02026nas a2200205 4500008004100000022001400041245009500055210006900150300001100219520136500230653002001595653002401615653001701639653002101656100002501677700002701702700002201729700002201751856004701773 2019 eng d a0022-509600aNutations in growing plant shoots: The role of elastic deformations due to gravity loading0 aNutations in growing plant shoots The role of elastic deformatio a1037023 aThe 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’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.

10aCircumnutations10aFlutter instability10aGravitropism10aHopf bifurcation1 aAgostinelli, Daniele1 aLucantonio, Alessandro1 aNoselli, Giovanni1 aDeSimone, Antonio uhttps://doi.org/10.1016/j.jmps.2019.10370201020nas a2200181 4500008004100000245008500041210006900126260000800195300002100203520034100224653004000565653003600605100002000641700001800661700002100679700002000700856011800720 2019 eng d00aStrong Novikov conjecture for low degree cohomology and exotic group C*-algebras0 aStrong Novikov conjecture for low degree cohomology and exotic g cMay aarXiv:1905.077303 aWe strengthen a result of Hanke–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.

10aMathematics - K-Theory and Homology10aMathematics - Operator Algebras1 aAntonini, Paolo1 aBuss, Alcides1 aEngel, Alexander1 aSiebenand, Timo uhttps://www.math.sissa.it/publication/strong-novikov-conjecture-low-degree-cohomology-and-exotic-group-c-algebras00657nas a2200181 4500008004100000245008300041210007100124653001000195653001000205653001000215653001000225653004000235653003600275100002000311700001500331700001800346856011100364 2018 eng d00aThe Baum–Connes conjecture localised at the unit element of a discrete group0 aBaum–Connes conjecture localised at the unit element of a discre10a19K3510a46L8010a46L8510a58J2210aMathematics - K-Theory and Homology10aMathematics - Operator Algebras1 aAntonini, Paolo1 aAzzali, S.1 aSkandalis, G. uhttps://www.math.sissa.it/publication/baum%E2%80%93connes-conjecture-localised-unit-element-discrete-group01813nas a2200205 4500008004100000245005400041210005400095260001400149300000700163520117300170100002601343700001901369700002001388700002101408700002201429700002101451700002601472700002501498856008401523 2018 eng d00aComputational methods in cardiovascular mechanics0 aComputational methods in cardiovascular mechanics bCRC Press a543 aThe 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.

1 aAuricchio, Ferdinando1 aConti, Michele1 aLefieux, Adrian1 aMorganti, Simone1 aReali, Alessandro1 aRozza, Gianluigi1 aVeneziani, Alessandro1 aLabrosse, Michel, F. uhttps://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201%2Fb21917-500702nas a2200253 4500008004100000245003700041210003000078100002200108700001800130700001700148700001800165700002100183700001900204700002200223700001800245700001700263700002300280700002400303700002000327700002400347700001700371700001700388856004300405 2018 eng d00aThe deal.II Library, Version 9.00 adealII Library Version 901 aAlzetta, Giovanni1 aArndt, Daniel1 aBangerth, W.1 aBoddu, Vishal1 aBrands, Benjamin1 aDavydov, Denis1 aGassmöller, Rene1 aHeister, Timo1 aHeltai, Luca1 aKormann, Katharina1 aKronbichler, Martin1 aMaier, Matthias1 aPelteret, Jean-Paul1 aTurcksin, B.1 aWells, David uhttps://doi.org/10.1515/jnma-2018-005400590nas a2200133 4500008004100000245012000041210006900161100001900230700001700249700002200266700002400288700002100312856012300333 2018 eng d00aThe Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows0 aEffort of Increasing Reynolds Number in ProjectionBased Reduced 1 aHijazi, Saddam1 aAli, Shafqat1 aStabile, Giovanni1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/effort-increasing-reynolds-number-projection-based-reduced-order-methods-laminar00442nas a2200121 4500008004100000245005000041210005000091100002600141700002200167700002700189700001900216856008500235 2018 eng d00aFoldable structures made of hydrogel bilayers0 aFoldable structures made of hydrogel bilayers1 aAgostiniani, Virginia1 aDeSimone, Antonio1 aLucantonio, Alessandro1 aLučić, Danka uhttps://www.math.sissa.it/publication/foldable-structures-made-hydrogel-bilayers01283nas a2200169 4500008004100000022001400041245010100055210006900156260000800225300000700233490000700240520074700247100002100994700002901015700002301044856004601067 2018 eng d a1420-903900aGlobal, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials0 aGlobal finite energy weak solutions for the NLS with rough timed cMar a460 v693 aWe prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger 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.

1 aAntonelli, Paolo1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttps://doi.org/10.1007/s00033-018-0938-500570nas a2200121 4500008004100000245011800041210006900159260001700228100002600245700002700271700001900298856013100317 2018 eng d00aHeterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets0 aHeterogeneous elastic plates with inplane modulation of the targ bEDP Sciences1 aAgostiniani, Virginia1 aLucantonio, Alessandro1 aLučić, Danka uhttps://www.math.sissa.it/publication/heterogeneous-elastic-plates-plane-modulation-target-curvature-and-applications-thin-gel00583nas a2200145 4500008004100000245008400041210006900125653003700194100002100231700001300252700002100265700002100286700001900307856011100326 2018 eng d00aA Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions0 aLocalized ReducedOrder Modeling Approach for PDEs with Bifurcati10aMathematics - Numerical Analysis1 aHess, Martin, W.1 aAlla, A.1 aQuaini, Annalisa1 aRozza, Gianluigi1 aGunzburger, M. uhttps://www.math.sissa.it/publication/localized-reduced-order-modeling-approach-pdes-bifurcating-solutions02205nas a2200253 4500008004100000022001400041245007200055210006900127260001200196490000600208520146100214653002201675653002201697653002501719653002101744653001701765653001601782653002001798653001801818100002501836700002301861700002201884856004501906 2018 eng d a2296-914400aPeristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots0 aPeristaltic Waves as Optimal Gaits in Metameric BioInspired Robo c09/20180 v53 a*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 “phase coordination” 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’s criterion.

1 aAlmi, Stefano uhttps://www.esaim-cocv.org/component/article?access=doi&doi=10.1051/cocv/201601401281nas a2200121 4500008004100000245008200041210006900123520085300192100002001045700001701065700002901082856004801111 2017 en d00aFriedrichs systems in a Hilbert space framework: solvability and multiplicity0 aFriedrichs systems in a Hilbert space framework solvability and 3 aThe 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 Antonić 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.1 aAntonić, Nenad1 aErceg, Marko1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/3528000440nas a2200157 4500008004100000022001400041245004400055210004400099260000800143300000800151490000700159100002500166700002400191700002100215856004600236 2017 eng d a1432-083500aHomotopically invisible singular curves0 aHomotopically invisible singular curves cJul a1050 v561 aAgrachev, Andrei, A.1 aBoarotto, Francesco1 aLerario, Antonio uhttps://doi.org/10.1007/s00526-017-1203-z00713nas a2200157 4500008004100000245004400041210004000085520026500125653001200390653001000402653004000412100002000452700002400472700001800496856004100514 2017 eng d00aThe injectivity radius of Lie manifolds0 ainjectivity radius of Lie manifolds3 aWe prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive

10a(58J40)10a53C2110aMathematics - Differential Geometry1 aAntonini, Paolo1 aDe Philippis, Guido1 aGigli, Nicola uhttps://arxiv.org/pdf/1707.07595.pdf01299nas a2200145 4500008004100000245005100041210005100092520086700143653001001010653001001020653004001030100002201070700002001092856004101112 2017 eng d00aIntegrable lifts for transitive Lie algebroids0 aIntegrable lifts for transitive Lie algebroids3 aInspired 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.

10a14F4010a58H0510aMathematics - Differential Geometry1 aAndroulidakis, I.1 aAntonini, Paolo uhttps://arxiv.org/pdf/1707.04855.pdf01406nas a2200133 4500008004100000245004000041210004000081520101100121100002301132700002101155700002401176700002401200856004801224 2017 en d00aLinearisation of multiwell energies0 aLinearisation of multiwell energies3 aLinear 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.1 aAlicandro, Roberto1 aDal Maso, Gianni1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://preprints.sissa.it/handle/1963/3528801104nas a2200145 4500008004100000245009100041210006900132300001200201490000800213520063400221100001800855700002100873700001900894856004500913 2017 en d00aA lower semicontinuity result for a free discontinuity functional with a boundary term0 alower semicontinuity result for a free discontinuity functional a952-9900 v1083 aWe 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.

1 aAlmi, Stefano1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/20.500.11767/1597900623nas a2200169 4500008004100000245008300041210006900124260002500193300001400218490000800232100001600240700001600256700002300272700002300295700002400318856011100342 2017 eng d00aSolid tumors are poroelastic solids with a chemo-mechanical feedback on growth0 aSolid tumors are poroelastic solids with a chemomechanical feedb bSpringer Netherlands a107–1240 v1291 aAmbrosi, D.1 aPezzuto, S.1 aRiccobelli, Davide1 aStylianopoulos, T.1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/solid-tumors-are-poroelastic-solids-chemo-mechanical-feedback-growth00434nas a2200109 4500008004100000245009700041210006900138100002200207700002300229700002100252856005100273 2016 en d00aEulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II0 aEulerian Lagrangian and Broad continuous solutions to a balance 1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://urania.sissa.it/xmlui/handle/1963/3519700458nas a2200121 4500008004100000245009600041210006900137260001300206100002200219700002300241700002100264856005100285 2016 en d00aEulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I0 aEulerian Lagrangian and Broad continuous solutions to a balance bElsevier1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://urania.sissa.it/xmlui/handle/1963/3520701717nas a2200193 4500008004100000245011900041210006900160260001400229520106200243100002401305700002001329700002001349700002101369700002201390700002001412700002201432700001801454856005101472 2016 en d00aA fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts0 afast virtual surgery platform for many scenarios haemodynamics o bSubmitted3 aA 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.1 aBallarin, Francesco1 aFaggiano, Elena1 aManzoni, Andrea1 aRozza, Gianluigi1 aQuarteroni, Alfio1 aIppolito, Sonia1 aScrofani, Roberto1 aAntona, Carlo uhttp://urania.sissa.it/xmlui/handle/1963/3524001057nas a2200145 4500008004100000245004700041210004300088300001600131490000600147520062100153100002100774700001700795700002000812856007900832 2016 eng d00aThe Gysin sequence for quantum lens spaces0 aGysin sequence for quantum lens spaces a1077–11110 v93 aWe define quantum lens spaces as ‘direct sums of line bundles’ and exhibit them as ‘total spaces’ 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 ‘line bundles’ over quantum lens spaces and generically define ‘torsion classes’. We work out explicit examples of these classes.

1 aArici, Francesca1 aBrain, Simon1 aLandi, Giovanni uhttps://www.math.sissa.it/publication/gysin-sequence-quantum-lens-spaces-000912nas a2200229 4500008004100000020002200041245004000063210004000103260004400143300001100187520024800198100002100446700002400467700002000491700001800511700002000529700002200549700001900571700002000590700002400610856004800634 2016 eng d a978-3-319-29116-100aPimsner Algebras and Circle Bundles0 aPimsner Algebras and Circle Bundles aChambSpringer International Publishing a1–253 aWe 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.

1 aArici, Francesca1 aD'Andrea, Francesco1 aLandi, Giovanni1 aAlpay, Daniel1 aCipriani, Fabio1 aColombo, Fabrizio1 aGuido, Daniele1 aSabadini, Irene1 aSauvageot, Jean-Luc uhttps://doi.org/10.1007/978-3-319-29116-1_100454nas a2200145 4500008004100000022001400041245007100055210006900126300001200195490000700207100002100214700001500235700002000250856003800270 2016 eng d a1661-695200aPimsner algebras and Gysin sequences from principal circle actions0 aPimsner algebras and Gysin sequences from principal circle actio a29–640 v101 aArici, Francesca1 aKaad, Jens1 aLandi, Giovanni uhttp://hdl.handle.net/2066/16295101110nas a2200097 4500008004100000245006200041210006000103520078000163100001800943856005100961 2016 en d00aQuasi-static hydraulic crack growth driven by Darcy's law0 aQuasistatic hydraulic crack growth driven by Darcys law3 aIn 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’s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith’s criterion.

1 aAlmi, Stefano uhttp://urania.sissa.it/xmlui/handle/1963/3519801439nas a2200121 4500008004100000245010500041210006900146260001000215520093000225653002301155100001801178856012101196 2016 en d00aSome results on the mathematical analysis of crack problems with forces applied on the fracture lips0 aSome results on the mathematical analysis of crack problems with bSISSA3 aThis 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'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.10aFracture mechanics1 aAlmi, Stefano uhttps://www.math.sissa.it/publication/some-results-mathematical-analysis-crack-problems-forces-applied-fracture-lips00469nas a2200109 4500008004100000245007600041210006900117100002500186700002100211700001700232856011000249 2016 eng d00aVolume geodesic distortion and Ricci curvature for Hamiltonian dynamics0 aVolume geodesic distortion and Ricci curvature for Hamiltonian d1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aPaoli, Elisa uhttps://www.math.sissa.it/publication/volume-geodesic-distortion-and-ricci-curvature-hamiltonian-dynamics01380nas a2200133 4500008004300000245007200043210006900115260001500184520093400199100001901133700001801152700002501170856005101195 2015 en_Ud 00aAnisotropic mean curvature on facets and relations with capillarity0 aAnisotropic mean curvature on facets and relations with capillar bde Gruyter3 aWe 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.

1 aAmato, Stefano1 aTealdi, Lucia1 aBellettini, Giovanni uhttp://urania.sissa.it/xmlui/handle/1963/3448101209nas a2200121 4500008004300000245007700043210006900120520072500189100001900914700002500933700002200958856010700980 2015 en_Ud 00aConstrained BV functions on double coverings for Plateau's type problems0 aConstrained BV functions on double coverings for Plateaus type p3 aWe link Brakke's "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau'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.

1 aAmato, Stefano1 aBellettini, Giovanni1 aPaolini, Maurizio uhttps://www.math.sissa.it/publication/constrained-bv-functions-double-coverings-plateaus-type-problems01188nas a2200157 4500008004100000245005800041210005700099260003700156300001600193490000700209520065100216100002500867700002400892700002100916856009300937 2015 eng d00aGeodesics and horizontal-path spaces in Carnot groups0 aGeodesics and horizontalpath spaces in Carnot groups bMathematical Sciences Publishers a1569–16300 v193 aWe 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.

1 aAgrachev, Andrei, A.1 aGentile, Alessandro1 aLerario, Antonio uhttps://www.math.sissa.it/publication/geodesics-and-horizontal-path-spaces-carnot-groups00719nas a2200217 4500008004100000245009200041210006900133260003300202100002200235700002400257700001600281700002300297700001500320700001400335700002200349700002600371700002100397700001300418700001900431856005100450 2015 en d00aThe phototransduction machinery in the rod outer segment has a strong efficacy gradient0 aphototransduction machinery in the rod outer segment has a stron bNational Academy of Sciences1 aMazzolini, Monica1 aFacchetti, Giuseppe1 aAndolfi, L.1 aZaccaria, Proietti1 aTuccio, S.1 aTreud, J.1 aAltafini, Claudio1 aDi Fabrizio, Enzo, M.1 aLazzarino, Marco1 aRapp, G.1 aTorre, Vincent uhttp://urania.sissa.it/xmlui/handle/1963/3515701307nas a2200109 4500008004100000245006700041210006600108260001000174520088800184100002101072856010401093 2015 en d00aPrincipal circle bundles, Pimsner algebras and Gysin sequences0 aPrincipal circle bundles Pimsner algebras and Gysin sequences bSISSA3 aPrincipal 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 `base space’ 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.1 aArici, Francesca uhttps://www.math.sissa.it/publication/principal-circle-bundles-pimsner-algebras-and-gysin-sequences00981nas a2200121 4500008004100000245008300041210006900124260001000193520048800203653003100691100001900722856011800741 2015 en d00aSome results on anisotropic mean curvature and other phase-transition problems0 aSome results on anisotropic mean curvature and other phasetransi bSISSA3 aThe present thesis is divided into three parts. In the first part, we analyze a suitable regularization — which we call nonlinear multidomain model — 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’s type problems based on the theory of coverings and of BV functions.10aAnisotropic mean curvature1 aAmato, Stefano uhttps://www.math.sissa.it/publication/some-results-anisotropic-mean-curvature-and-other-phase-transition-problems01483nas a2200121 4500008004100000245005900041210005900100260005900159520105100218100002201269700001901291856005101310 2014 en d00aAchieving unanimous opinions in signed social networks0 aAchieving unanimous opinions in signed social networks bInstitute of Electrical and Electronics Engineers Inc.3 aBeing 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.1 aAltafini, Claudio1 aLini, Gabriele uhttp://urania.sissa.it/xmlui/handle/1963/3493501122nas a2200145 4500008004100000245005400041210005100095260001300146520066000159653006000819100002500879700001600904700002000920856003600940 2014 en d00aOn conjugate times of LQ optimal control problems0 aconjugate times of LQ optimal control problems bSpringer3 aMotivated 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 $\vec{H}$.10aOptimal control, Lagrange Grassmannian, Conjugate point1 aAgrachev, Andrei, A.1 aRizzi, Luca1 aSilveira, Pavel uhttp://hdl.handle.net/1963/722700800nas a2200133 4500008004100000245006400041210005600105260003400161520035400195100002200549700002300571700002100594856005100615 2014 en d00aOn the Lp-differentiability of certain classes of functions0 aLpdifferentiability of certain classes of functions bEuropean Mathematical Society3 aWe 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.1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://urania.sissa.it/xmlui/handle/1963/3469500423nas a2200133 4500008004100000245005600041210005500097260001300152653002200165100001800187700002100205700002700226856003600253 2014 en d00aNew results on Gamma-limits of integral functionals0 aNew results on Gammalimits of integral functionals bElsevier10aGamma-convergence1 aAnsini, Nadia1 aDal Maso, Gianni1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/588002051nas a2200145 4500008004100000245007600041210006900117260001300186520158600199653002601785100001701811700001901828700002201847856003601869 2014 en d00aNonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D0 aNonsingular Isogeometric Boundary Element Method for Stokes Flow bElsevier3 aIsogeometric 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.10aIsogeometric Analysis1 aHeltai, Luca1 aArroyo, Marino1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/632600712nas a2200157 4500008004100000245005200041210005100093260001300144300001200157490000800169520027400177100001800451700002100469700001900490856004500509 2014 en d00aQuasi-static crack growth in hydraulic fracture0 aQuasistatic crack growth in hydraulic fracture bElsevier a301-3180 v1093 aWe 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.

1 aAlmi, Stefano1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/20.500.11767/1735000458nas a2200133 4500008004100000245007200041210006900113260001000182653003000192100002200222700002300244700002100267856003600288 2014 en d00aReduction on characteristics for continuous of a scalar balance law0 aReduction on characteristics for continuous of a scalar balance bSISSA10aMethod of characteristics1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/656201649nas a2200121 4500008004100000245007500041210006900116260001300185520123700198100001901435700002201454856005101476 2014 en d00aShape control of active surfaces inspired by the movement of euglenids0 aShape control of active surfaces inspired by the movement of eug bElsevier3 aWe 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.1 aArroyo, Marino1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3511801084nas a2200133 4500008004100000245014200041210006900183260005100252520053000303100002200833700002300855700002100878856005100899 2014 en d00aA uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday0 auniqueness result for the continuity equation in two dimensions bEuropean Mathematical Society; Springer Verlag3 aWe 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.1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://urania.sissa.it/xmlui/handle/1963/3469200882nas a2200133 4500008004100000245004600041210004600087260001000133520050000143100002600643700002100669700002200690856003600712 2013 en d00aAttainment results for nematic elastomers0 aAttainment results for nematic elastomers bSISSA3 aWe 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.1 aAgostiniani, Virginia1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/717401565nas a2200169 4500008004100000245010100041210006900142260001000211520092400221100002201145700002401167700002201191700001701213700001901230700002201249856012401271 2013 en d00aCommon dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons.0 aCommon dynamical features of sensory adaptation in photoreceptor bSISSA3 aSensory 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.

1 aDe Palo, Giovanna1 aFacchetti, Giuseppe1 aMazzolini, Monica1 aMenini, Anna1 aTorre, Vincent1 aAltafini, Claudio uhttps://www.math.sissa.it/publication/common-dynamical-features-sensory-adaptation-photoreceptors-and-olfactory-sensory01043nas a2200145 4500008004100000245004200041210003700083260001000120520060700130653006200737100002500799700002100824700001600845856003600861 2013 en d00aThe curvature: a variational approach0 acurvature a variational approach bSISSA3 aThe 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.10aCrurvature, subriemannian metric, optimal control problem1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aRizzi, Luca uhttp://hdl.handle.net/1963/722601988nas a2200133 4500008004100000245010500041210006900146260003000215520151100245100002101756700002201777700001901799856003601818 2013 en d00aEarly phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus0 aEarly phase of plasticityrelated gene regulation and SRF depende bPublic Library of Science3 aHippocampal 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 µM 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.1 aIacono, Giovanni1 aAltafini, Claudio1 aTorre, Vincent uhttp://hdl.handle.net/1963/728700809nas a2200157 4500008004100000245003700041210003700078260002300115520037700138653001900515100002000534700002000554700002200574700001900596856003600615 2013 en d00aExpanded degenerations and pairs0 aExpanded degenerations and pairs bTaylor and Francis3 aSince Jun Li'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.10aExpanded pairs1 aAbramovich, Dan1 aCadman, Charles1 aFantechi, Barbara1 aWise, Jonathan uhttp://hdl.handle.net/1963/738301676nas a2200145 4500008004100000245009400041210006900135260001000204520112400214653008201338100002001420700002501440700002901465856003601494 2013 en d00aMinimal partitions and image classification using a gradient-free perimeter approximation0 aMinimal partitions and image classification using a gradientfree bSISSA3 aIn 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.10aImage classification, deblurring, optimal partitions, perimeter approximation1 aAmstutz, Samuel1 aVan Goethem, Nicolas1 aNovotny, Antonio, André uhttp://hdl.handle.net/1963/697601020nas a2200145 4500008004100000020001500041245007100056210006500127520044300192653007200635100001900707700002500726700002200751856010100773 2013 en d a887642472400aThe nonlinear multidomain model: a new formal asymptotic analysis.0 anonlinear multidomain model a new formal asymptotic analysis3 aWe 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.

10abidomain model, anisotropic mean curvature, star-shaped combination1 aAmato, Stefano1 aBellettini, Giovanni1 aPaolini, Maurizio uhttps://www.math.sissa.it/publication/nonlinear-multidomain-model-new-formal-asymptotic-analysis00550nas a2200109 4500008004100000245002500041210002500066260001000091520025100101100002500352856006300377 2013 en d00aQuadratic cohomology0 aQuadratic cohomology bSISSA3 aWe 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.1 aAgrachev, Andrei, A. uhttps://www.math.sissa.it/publication/quadratic-cohomology00401nas a2200121 4500008004100000245002300041210002300064260001000087520010800097653001300205100002500218856003600243 2013 en d00aSome open problems0 aSome open problems bSISSA3 aWe discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry.10aGeometry1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/707001218nas a2200121 4500008004100000245008200041210006900123520080800192100002201000700002301022700001501045856003601060 2013 en d00aStabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control0 aStabilization of Stochastic Quantum Dynamics via Open and Closed3 aIn 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 control1 aAltafini, Claudio1 aTicozzi, Francesco1 aNishio, K. uhttp://hdl.handle.net/1963/650300364nas a2200109 4500008004100000245004800041210004800089260001000137653004600147100002500193856003600218 2013 en d00aTopology of moduli spaces of framed sheaves0 aTopology of moduli spaces of framed sheaves bSISSA10aModuli spaces, framed sheaves, instantons1 aAbdellaoui, Gharchia uhttp://hdl.handle.net/1963/715200824nas a2200169 4500008004100000020001800041245006300059210006300122260001300185520030800198653002400506100002200530700001700552700002300569700002600592856003600618 2012 en d a978146143996700aComputing optimal strokes for low reynolds number swimmers0 aComputing optimal strokes for low reynolds number swimmers bSpringer3 aWe 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.

10aNumerical analysis.1 aDeSimone, Antonio1 aHeltai, Luca1 aAlouges, François1 aAline, Lefebvre-Lepot uhttp://hdl.handle.net/1963/644501414nas a2200145 4500008004100000245008300041210006900124260002800193520092600221100002001147700002201167700002101189700002201210856003601232 2012 en d00aDecompositions of large-scale biological systems based on dynamical properties0 aDecompositions of largescale biological systems based on dynamic bOxford University Press3 aMOTIVATION: 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.1 aSoranzo, Nicola1 aRamezani, Fahimeh1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/522602150nas a2200157 4500008004100000245008500041210006900126260003000195520152900225653003001754100003001784700002301814700001901837700002001856856011601876 2012 en d00aDeformed Lorentz symmetry and relative locality in a curved/expanding spacetime0 aDeformed Lorentz symmetry and relative locality in a curvedexpan bAmerican Physical Society3 aThe 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.10aDoubly special relativity1 aAmelino-Camelia, Giovanni1 aMarciano, Antonino1 aMatassa, Marco1 aRosati, Giacomo uhttps://www.math.sissa.it/publication/deformed-lorentz-symmetry-and-relative-locality-curvedexpanding-spacetime02153nas a2200181 4500008004100000245015200041210006900193260001000262520154500272100001101817700002101828700001601849700001501865700001401880700001901894700002201913856003601935 2012 en d00aDetection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis0 aDetection of transcriptional triggers in the dynamics of microbi bSISSA3 aThe 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 systems1 aBeg, Q1 aZampieri, Mattia1 aKlitgord, N1 aCollins, S1 aSerres, M1 aSegrè, Daniel1 aAltafini, Claudio uhttp://hdl.handle.net/1963/650601693nas a2200157 4500008004100000245008400041210006900125260003400194520117300228100002201401700002001423700001701443700001701460700002201477856003601499 2012 en d00aA dynamical feedback model for adaptation in the olfactory transduction pathway0 adynamical feedback model for adaptation in the olfactory transdu bBiophysical Society, Elsevier3 aOlfactory 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.1 aDe Palo, Giovanna1 aBoccaccio, Anna1 aMiri, Andrew1 aMenini, Anna1 aAltafini, Claudio uhttp://hdl.handle.net/1963/701901344nas a2200109 4500008004100000245007300041210006900114260000900183520098400192100002201176856003601198 2012 en d00aDynamics of opinion forming in structurally balanced social networks0 aDynamics of opinion forming in structurally balanced social netw bPLoS3 aA 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/605101741nas a2200133 4500008004100000245007700041210006900118260001000187520130700197100002401504700002101528700002201549856003601571 2012 en d00aExploring the low-energy landscape of large-scale signed social networks0 aExploring the lowenergy landscape of largescale signed social ne bSISSA3 aAnalogously 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.1 aFacchetti, Giuseppe1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/650400456nas a2200133 4500008004100000245006900041210006700110260001300177653003000190100001800220700002100238700002700259856003600286 2012 en d00aGamma-convergence and H-convergence of linear elliptic operators0 aGammaconvergence and Hconvergence of linear elliptic operators bElsevier10aLinear elliptic operators1 aAnsini, Nadia1 aDal Maso, Gianni1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/587801194nas a2200133 4500008004100000245005500041210004700096260001000143520080800153100002500961700002100986700001701007856003601024 2012 en d00aOn the Hausdorff volume in sub-Riemannian geometry0 aHausdorff volume in subRiemannian geometry bSISSA3 aFor 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.1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aBoscain, Ugo uhttp://hdl.handle.net/1963/645400389nas a2200121 4500008004100000245005900041210005800100260001000158100002500168700002100193700001700214856003600231 2012 en d00aIntroduction to Riemannian and sub-Riemannian geometry0 aIntroduction to Riemannian and subRiemannian geometry bSISSA1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aBoscain, Ugo uhttp://hdl.handle.net/1963/587700709nas a2200169 4500008004100000245011000041210006900151260003000220300001200250490000700262520014000269653002500409100002600434700002100460700002200481856003600503 2012 en d00aLinear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions0 aLinear elasticity obtained from finite elasticity by Gammaconver bGauthier-Villars;Elsevier a715-7350 v293 aThe energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

10aNonlinear elasticity1 aAgostiniani, Virginia1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/426701486nas a2200121 4500008004100000245006100041210006000102260005400162520106700216100002201283700002301305856003601328 2012 en d00aModeling and control of quantum systems: An introduction0 aModeling and control of quantum systems An introduction bInstitute of Electrical and Electronics Engineers3 aThe 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 studies1 aAltafini, Claudio1 aTicozzi, Francesco uhttp://hdl.handle.net/1963/650501684nas a2200157 4500008004100000245004700041210004600088260001300134300001200147490000700159520120600166653002501372100002601397700002201423856008101445 2012 en d00aOgden-type energies for nematic elastomers0 aOgdentype energies for nematic elastomers bElsevier a402-4120 v473 aOgden-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).

10aNonlinear elasticity1 aAgostiniani, Virginia1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/ogden-type-energies-nematic-elastomers02201nas a2200133 4500008004100000245010400041210006900145260001900214520173100233100002401964700002201988700002102010856003602031 2012 en d00aPredicting and characterizing selective multiple drug treatments for metabolic diseases and cancer.0 aPredicting and characterizing selective multiple drug treatments bBioMed Central3 aBackground: 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.1 aFacchetti, Giuseppe1 aAltafini, Claudio1 aZampieri, Mattia uhttp://hdl.handle.net/1963/651502076nas a2200145 4500008004100000245004700041210004700088520166300135653001801798100001901816700001701835700002001852700002201872856003601894 2012 en d00aReverse engineering the euglenoid movement0 aReverse engineering the euglenoid movement3 aEuglenids 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.10amicroswimmers1 aArroyo, Marino1 aHeltai, Luca1 aMillán, Daniel1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/644400821nas a2200121 4500008004100000245007700041210006900118520040700187100002500594700002300619700002100642856003600663 2012 en d00aOn robust Lie-algebraic stability conditions for switched linear systems0 arobust Liealgebraic stability conditions for switched linear sys3 aThis 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.1 aAgrachev, Andrei, A.1 aBaryshnikov, Yurij1 aLiberzon, Daniel uhttp://hdl.handle.net/1963/645501260nas a2200193 4500008004100000022001400041245008600055210006900141300000900210490000700219520060600226653002800832653002500860653002800885653002700913653002400940100002600964856007600990 2012 eng d a1078-094700aSecond order approximations of quasistatic evolution problems in finite dimension0 aSecond order approximations of quasistatic evolution problems in a11250 v323 aIn 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.

10adiscrete approximations10aperturbation methods10asaddle-node bifurcation10aSingular perturbations10avanishing viscosity1 aAgostiniani, Virginia uhttp://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f800752nas a2200121 4500008004100000245004700041210004600088260001000134520040400144100002500548700002100573856003600594 2012 en d00aSub-Riemannian structures on 3D Lie groups0 aSubRiemannian structures on 3D Lie groups bSISSA3 aWe 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.

1 aAgrachev, Andrei, A.1 aBarilari, Davide uhttp://hdl.handle.net/1963/645300723nas a2200121 4500008004100000245003800041210003800079260001000117520039200127100002500519700002100544856003600565 2012 en d00aSystems of Quadratic Inequalities0 aSystems of Quadratic Inequalities bSISSA3 aWe 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_2.1 aAgrachev, Andrei, A.1 aLerario, Antonio uhttp://hdl.handle.net/1963/707201511nas a2200145 4500008004100000245007100041210006900112260001000181520099600191653006801187100002001255700002901275700002501304856003601329 2012 en d00aTopological sensitivity analysis for high order elliptic operators0 aTopological sensitivity analysis for high order elliptic operato bSISSA3 aThe 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.10aTopological derivative, Elliptic operators, Polarization tensor1 aAmstutz, Samuel1 aNovotny, Antonio, André1 aVan Goethem, Nicolas uhttp://hdl.handle.net/1963/634301400nas a2200169 4500008004100000245009000041210006900131260005000200520083200250100001401082700001801096700001501114700002201129700002201151700002101173856003601194 2011 en d00aAdaptation as a genome-wide autoregulatory principle in the stress response of yeast.0 aAdaptation as a genomewide autoregulatory principle in the stres bThe Institution of Engineering and Technology3 aThe 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.1 aEduati, F1 aDi Camillo, B1 aToffolo, G1 aAltafini, Claudio1 aDe Palo, Giovanna1 aZampieri, Mattia uhttp://hdl.handle.net/1963/510600585nas a2200121 4500008004100000245011300041210006900154260001000223520015500233100002500388700001400413856003600427 2011 en d00aBishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry0 aBishop and Laplacian Comparison Theorems on Three Dimensional Co bSISSA3 aWe prove a Bishop volume comparison theorem and a Laplacian comparison\r\ntheorem for three dimensional contact subriemannian manifolds with symmetry.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/650801286nas a2200145 4500008004100000245007900041210006900120260003300189520078400222653003101006100002401037700002101061700002201082856003601104 2011 en d00aComputing global structural balance in large-scale signed social networks.0 aComputing global structural balance in largescale signed social bNational Academy of Sciences3 aStructural 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.\\\"10aCombinatorial optimization1 aFacchetti, Giuseppe1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/642600898nas a2200145 4500008004100000245008300041210006900124260001300193490000800206520043400214653002000648100002600668700002200694856003600716 2011 en d00aGamma-convergence of energies for nematic elastomers in the small strain limit0 aGammaconvergence of energies for nematic elastomers in the small bSpringer0 v 233 aWe 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.

10aLiquid crystals1 aAgostiniani, Virginia1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/414100398nas a2200109 4500008004100000245009300041210006900134260001000203100002500213700001400238856003600252 2011 en d00aGeneralized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds0 aGeneralized Ricci Curvature Bounds for Three Dimensional Contact bSISSA1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/650700442nas a2200109 4500008004100000245003800041210003400079520013500113100002500248700002300273856003600296 2011 en d00aThe geometry of Maximum Principle0 ageometry of Maximum Principle3 aAn invariant formulation of the maximum principle in optimal control is presented, and some second-order invariants are discussed.1 aAgrachev, Andrei, A.1 aGamkrelidze, Revaz uhttp://hdl.handle.net/1963/645601000nas a2200133 4500008004300000245005100043210005100094260002100145520060100166100001800767700002500785700002000810856003600830 2011 en_Ud 00aLarge Time Existence for Thin Vibrating Plates0 aLarge Time Existence for Thin Vibrating Plates bTaylor & Francis3 aWe 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.1 aAbels, Helmut1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/375500977nas a2200145 4500008004300000245007900043210006900122260002100191520050000212653002100712100002300733700002200756700001700778856003600795 2011 en_Ud 00aNumerical Strategies for Stroke Optimization of Axisymmetric Microswimmers0 aNumerical Strategies for Stroke Optimization of Axisymmetric Mic bWorld Scientific3 aWe 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.10aOptimal swimming1 aAlouges, François1 aDeSimone, Antonio1 aHeltai, Luca uhttp://hdl.handle.net/1963/365700449nas a2200109 4500008004300000245005100043210005100094260003400145520010000179100002400279856003600303 2011 en_Ud 00aOsservazioni sui teoremi di inversione globale0 aOsservazioni sui teoremi di inversione globale bEuropean Mathematical Society3 aSome global inversion theorems with applications to semilinear elliptic equation are discussed.1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/406800823nas a2200121 4500008004100000245007200041210006900113260001300182520042600195100002200621700002200643856003600665 2011 en d00aQuasistatic evolution of sessile drops and contact angle hysteresis0 aQuasistatic evolution of sessile drops and contact angle hystere bSpringer3 aWe 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.1 aAlberti, Giovanni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/491200674nas a2200121 4500008004100000245006800041210006100109260001000170520028700180653002400467100002500491856003600516 2011 en d00aOn the Space of Symmetric Operators with Multiple Ground States0 aSpace of Symmetric Operators with Multiple Ground States bSISSA3 aWe 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.10aMultiple eigenvalue1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/706900415nas a2200121 4500008004100000245007100041210006900112260001000181100002200191700002300213700002100236856003600257 2011 en d00aStructure of level sets and Sard-type properties of Lipschitz maps0 aStructure of level sets and Sardtype properties of Lipschitz map bSISSA1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://hdl.handle.net/1963/465701822nas a2200145 4500008004100000245009200041210006900133260002800202520132600230100002101556700002201577700001901599700002201618856003601640 2011 en d00aA system-level approach for deciphering the transcriptional response to prion infection0 asystemlevel approach for deciphering the transcriptional respons bOxford University Press3 aMOTIVATION: 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.1 aZampieri, Mattia1 aLegname, Giuseppe1 aSegrè, Daniel1 aAltafini, Claudio uhttp://hdl.handle.net/1963/574500881nas a2200133 4500008004300000245008900043210007100132260001300203520043200216100001800648700002500666700002000691856003600711 2011 en_Ud 00aThe time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity0 atimedependent von Kármán plate equation as a limit of 3d nonline bSpringer3 aThe 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.1 aAbels, Helmut1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/383500413nas a2200121 4500008004100000245007000041210006800111260001000179100002200189700002300211700002100234856003600255 2011 en d00aA uniqueness result for the continuity equation in two dimensions0 auniqueness result for the continuity equation in two dimensions bSISSA1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://hdl.handle.net/1963/466300703nas a2200121 4500008004100000245007900041210006900120260001000189520030700199100002500506700001400531856003600545 2010 en d00aContinuity of optimal control costs and its application to weak KAM theory0 aContinuity of optimal control costs and its application to weak bSISSA3 aWe 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.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/645900778nas a2200133 4500008004100000245004800041210004700089260001000136520038900146653002700535100002500562700002100587856003600608 2010 en d00aDynamics control by a time-varying feedback0 aDynamics control by a timevarying feedback bSISSA3 aWe 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.10aDiscrete-time dynamics1 aAgrachev, Andrei, A.1 aCaponigro, Marco uhttp://hdl.handle.net/1963/646101148nas a2200133 4500008004100000245009700041210006900138260001300207520069800220100002200918700002200940700001600962856003600978 2010 en d00aFeedback schemes for radiation damping suppression in NMR: a control-theoretical perspective0 aFeedback schemes for radiation damping suppression in NMR a cont bElsevier3 aIn 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.1 aAltafini, Claudio1 aCappellaro, Paola1 aCory, David uhttp://hdl.handle.net/1963/438400468nas a2200109 4500008004100000245005900041210005900100260001000159520012800169100002500297856003600322 2010 en d00aInvariant Lagrange submanifolds of dissipative systems0 aInvariant Lagrange submanifolds of dissipative systems bSISSA3 aWe study solutions of modified Hamilton-Jacobi equations H(du/dq,q) + cu(q) =\\r\\n0, q \\\\in M, on a compact manifold M .1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/645700781nas a2200121 4500008004300000245008400043210006900127260004800196520033500244100002200579700002200601856003600623 2010 en_Ud 00aA kinetic mechanism inducing oscillations in simple chemical reactions networks0 akinetic mechanism inducing oscillations in simple chemical react bAmerican Institute of Mathematical Sciences3 aIt 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.1 aCoatleven, Julien1 aAltafini, Claudio uhttp://hdl.handle.net/1963/239302106nas a2200121 4500008004300000245013400043210006900177260001900246520164000265100002101905700002201926856003601948 2010 en_Ud 00aMonotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks0 aMonotonicity frustration and ordered response an analysis of the bBioMed Central3 aBackground. \\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.1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/405500335nas a2200085 4500008004300000245007700043210006900120100002400189856003600213 2010 en_Ud 00aOn the number of positive solutions of some semilinear elliptic problems0 anumber of positive solutions of some semilinear elliptic problem1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/408301048nas a2200121 4500008004300000245012100043210006900164520059600233100002200829700001800851700002100869856003600890 2010 en_Ud 00aNumerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions0 aNumerical Solution of the Small Dispersion Limit of the CamassaH3 aThe 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....1 aAbenda, Simonetta1 aGrava, Tamara1 aKlein, Christian uhttp://hdl.handle.net/1963/384001187nas a2200145 4500008004300000245004000043210004000083520078100123100002300904700002200927700001700949700002000966700001900986856003601005 2010 en_Ud 00aOptimally swimming Stokesian Robots0 aOptimally swimming Stokesian Robots3 aWe 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.1 aAlouges, François1 aDeSimone, Antonio1 aHeltai, Luca1 aLefebvre, Aline1 aMerlet, Benoit uhttp://hdl.handle.net/1963/392901810nas a2200121 4500008004300000245007000043210006600113520141500179100001901594700002201613700001701635856003601652 2010 en_Ud 00aThe role of membrane viscosity in the dynamics of fluid membranes0 arole of membrane viscosity in the dynamics of fluid membranes3 aFluid 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 3.1 aArroyo, Marino1 aDeSimone, Antonio1 aHeltai, Luca uhttp://hdl.handle.net/1963/393001439nas a2200181 4500008004300000245007000043210006800113260001300181300001200194490000700206520090200213100002501115700001701140700002301157700002001180700002101200856003601221 2010 en_Ud 00aTwo-dimensional almost-Riemannian structures with tangency points0 aTwodimensional almostRiemannian structures with tangency points bElsevier a793-8070 v273 aTwo-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.

1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aCharlot, Grégoire1 aGhezzi, Roberta1 aSigalotti, Mario uhttp://hdl.handle.net/1963/387000894nas a2200109 4500008004100000245007500041210006900116260001000185520052800195100002500723856003600748 2010 en d00aWell-posed infinite horizon variational problems on a compact manifold0 aWellposed infinite horizon variational problems on a compact man bSISSA3 aWe 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 dynamics1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/645800396nas a2200109 4500008004300000245007300043210006900116100002200185700002300207700002000230856003600250 2009 en_Ud 00aBiological Fluid Dynamics, Non-linear Partial Differential Equations0 aBiological Fluid Dynamics Nonlinear Partial Differential Equatio1 aDeSimone, Antonio1 aAlouges, François1 aLefebvre, Aline uhttp://hdl.handle.net/1963/263002219nas a2200157 4500008004300000245014000043210006900183260001900252520163800271100002601909700002101935700002801956700002201984700001902006856003602025 2009 en_Ud 00aCharacterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity0 aCharacterization of the time course of changes of the evoked ele bBioMed Central3 aBACKGROUND: 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.1 aBroccard, Frederic D.1 aPegoraro, Silvia1 aRuaro, Maria Elisabetta1 aAltafini, Claudio1 aTorre, Vincent uhttp://hdl.handle.net/1963/370600997nas a2200109 4500008004300000245011900043210006900162260001300231520058500244100002200829856003600851 2009 en_Ud 00aControllability and simultaneous controllability of isospectral bilinear control systems on complex flag manifolds0 aControllability and simultaneous controllability of isospectral bElsevier3 aFor 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/352300583nas a2200109 4500008004300000245005200043210005200095520024400147100002500391700002100416856003600437 2009 en_Ud 00aControllability on the group of diffeomorphisms0 aControllability on the group of diffeomorphisms3 aGiven 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.1 aAgrachev, Andrei, A.1 aCaponigro, Marco uhttp://hdl.handle.net/1963/339600980nas a2200121 4500008004300000245005900043210005800102260002800160520059200188100002000780700002200800856003600822 2009 en_Ud 00aERNEST: a toolbox for chemical reaction network theory0 aERNEST a toolbox for chemical reaction network theory bOxford University Press3 aSummary: 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.1 aSoranzo, Nicola1 aAltafini, Claudio uhttp://hdl.handle.net/1963/382601520nas a2200133 4500008004300000245008600043210006900129520106500198100002501263700001701288700002401305700002101329856003601350 2009 en_Ud 00aThe intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups0 aintrinsic hypoelliptic Laplacian and its heat kernel on unimodul3 aWe 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.1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aGauthier, Jean-Paul1 aRossi, Francesco uhttp://hdl.handle.net/1963/266901588nas a2200133 4500008004300000245010000043210006900143260000900212520113200221100002101353700002201374700002201396856003601418 2009 en_Ud 00aInvestigating the Conformational Stability of Prion Strains through a Kinetic Replication Model0 aInvestigating the Conformational Stability of Prion Strains thro bPLoS3 aPrion 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.1 aZampieri, Mattia1 aLegname, Giuseppe1 aAltafini, Claudio uhttp://hdl.handle.net/1963/398901344nas a2200145 4500008004300000245009700043210006900140260001900209520085100228100002001079700002101099700002001120700002201140856003601162 2009 en_Ud 00amRNA stability and the unfolding of gene expression in the long-period yeast metabolic cycle0 amRNA stability and the unfolding of gene expression in the longp bBioMed Central3 aBackground: 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.1 aSoranzo, Nicola1 aZampieri, Mattia1 aFarina, Lorenzo1 aAltafini, Claudio uhttp://hdl.handle.net/1963/363001018nas a2200109 4500008004300000245005800043210005800101520067400159100002500833700001400858856003600872 2009 en_Ud 00aOptimal transportation under nonholonomic constraints0 aOptimal transportation under nonholonomic constraints3 aWe 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.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/217601411nas a2200121 4500008004300000245004300043210004300086260003000129520105300159100001901212700002201231856003601253 2009 en_Ud 00aRelaxation dynamics of fluid membranes0 aRelaxation dynamics of fluid membranes bAmerican Physical Society3 aWe 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.1 aArroyo, Marino1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/361802210nas a2200121 4500008004300000245009000043210006900133520178700202100002101989700002002010700002202030856003602052 2008 en_Ud 00aDiscerning static and causal interactions in genome-wide reverse engineering problems0 aDiscerning static and causal interactions in genomewide reverse 3 aBackground. 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.1 aZampieri, Mattia1 aSoranzo, Nicola1 aAltafini, Claudio uhttp://hdl.handle.net/1963/275701551nas a2200121 4500008004300000245007900043210006900122520113900191100002501330700001701355700002101372856003601393 2008 en_Ud 00aA Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds0 aGaussBonnetlike formula on twodimensional almostRiemannian manif3 aWe 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.1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aSigalotti, Mario uhttp://hdl.handle.net/1963/186900342nas a2200097 4500008004300000245006300043210006200106100002400168700001600192856003600208 2008 en_Ud 00aMultiple bound states for the Schroedinger-Poisson problem0 aMultiple bound states for the SchroedingerPoisson problem1 aAmbrosetti, Antonio1 aRuiz, David uhttp://hdl.handle.net/1963/267901131nas a2200133 4500008004300000245006500043210006400108260001300172520071100185100002300896700002200919700002000941856003600961 2008 en_Ud 00aOptimal Strokes for Low Reynolds Number Swimmers: An Example0 aOptimal Strokes for Low Reynolds Number Swimmers An Example bSpringer3 aSwimming, 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).1 aAlouges, François1 aDeSimone, Antonio1 aLefebvre, Aline uhttp://hdl.handle.net/1963/400602183nas a2200133 4500008004300000245010900043210006900152520170600221100002101927700002001948700002301968700002201991856003602013 2008 en_Ud 00aOrigin of Co-Expression Patterns in E.coli and S.cerevisiae Emerging from Reverse Engineering Algorithms0 aOrigin of CoExpression Patterns in Ecoli and Scerevisiae Emergin3 aBackground: 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.1 aZampieri, Mattia1 aSoranzo, Nicola1 aBianchini, Daniele1 aAltafini, Claudio uhttp://hdl.handle.net/1963/272200444nas a2200121 4500008004300000245009700043210006900140100001700209700001800226700002200244700002000266856003600286 2008 en_Ud 00aRelaxation of some transversally isotropic energies and applications to smectic A elastomers0 aRelaxation of some transversally isotropic energies and applicat1 aAdams, James1 aConti, Sergio1 aDeSimone, Antonio1 aDolzmann, Georg uhttp://hdl.handle.net/1963/191200611nas a2200121 4500008004300000245008600043210006900129520019400198100002400392700002100416700001600437856003600453 2008 en_Ud 00aSolitons of linearly coupled systems of semilinear non-autonomous equations on Rn0 aSolitons of linearly coupled systems of semilinear nonautonomous3 aUsing concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schrödinger equations.1 aAmbrosetti, Antonio1 aCerami, Giovanna1 aRuiz, David uhttp://hdl.handle.net/1963/217502020nas a2200121 4500008004300000245013300043210006900176520155200245100002001797700002301817700002201840856003601862 2007 en_Ud 00aComparing association network algorithms for reverse engineering of large scale gene regulatory networks: synthetic vs real data0 aComparing association network algorithms for reverse engineering3 aMotivation: 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/SoBiAl07/1 aSoranzo, Nicola1 aBianconi, Ginestra1 aAltafini, Claudio uhttp://hdl.handle.net/1963/202800549nas a2200121 4500008004300000245010200043210007000145260003400215520009600249100002400345700002200369856003600391 2007 en_Ud 00aConcentration phenomena for nonlinear Schrödinger equations: Recent results and new perspectives0 aConcentration phenomena for nonlinear Schrödinger equations Rece bAmerican Mathematical Society3 aWe survey some results on (NLSepsilon), discussing also new perspectives and open problems.1 aAmbrosetti, Antonio1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/351602024nas a2200109 4500008004300000245009300043210006900136520163000205100002501835700001801860856003601878 2007 en_Ud 00aOn feedback classification of control-affine systems with one and two-dimensional inputs0 afeedback classification of controlaffine systems with one and tw3 aThe 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.1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/218600760nas a2200097 4500008004300000245003700043210003700080520048700117100002200604856003600626 2007 en_Ud 00aFeedback control of spin systems0 aFeedback control of spin systems3 aThe 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/180801194nas a2200097 4500008004300000245010500043210006900148520082100217100002201038856003601060 2007 en_Ud 00aFeedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds0 aFeedback stabilization of quantum ensembles a global convergence3 aIn 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/172900873nas a2200133 4500008004300000245009700043210006900140520040800209100002500617700001900642700002100661700002100682856003600703 2007 en_Ud 00aOn finite-dimensional projections of distributions for solutions of randomly forced PDE\\\'s0 afinitedimensional projections of distributions for solutions of 3 aThe 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.1 aAgrachev, Andrei, A.1 aKuksin, Sergei1 aSarychev, Andrey1 aShirikyan, Armen uhttp://hdl.handle.net/1963/201200408nas a2200109 4500008004300000245008800043210006900131100002400200700002200224700001600246856003600262 2007 en_Ud 00aMulti-bump solitons to linearly coupled systems of nonlinear Schrödinger equations0 aMultibump solitons to linearly coupled systems of nonlinear Schr1 aAmbrosetti, Antonio1 aColorado, Eduardo1 aRuiz, David uhttp://hdl.handle.net/1963/183500894nas a2200109 4500008004300000245005300043210005300096520056000149100001800709700002100727856003600748 2007 en_Ud 00aNearly time optimal stabilizing patchy feedbacks0 aNearly time optimal stabilizing patchy feedbacks3 aWe 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 $\\\\tau(y)+\\\\ve$.1 aAncona, Fabio1 aBressan, Alberto uhttp://hdl.handle.net/1963/218501687nas a2200121 4500008004300000245008300043210007000126520125600196100002201452700002901474700002601503856003601529 2007 en_Ud 00aThe number of eigenvalues of three-particle Schrödinger operators on lattices0 anumber of eigenvalues of threeparticle Schrödinger operators on 3 aWe 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.1 aAlbeverio, Sergio1 aDell'Antonio, Gianfausto1 aLakaev, Saidakhmat N. uhttp://hdl.handle.net/1963/257600973nas a2200109 4500008004300000245006600043210006600109520061200175100002200787700001800809856003600827 2007 en_Ud 00aReciprocal transformations and flat metrics on Hurwitz spaces0 aReciprocal transformations and flat metrics on Hurwitz spaces3 aWe 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.1 aAbenda, Simonetta1 aGrava, Tamara uhttp://hdl.handle.net/1963/221000945nas a2200121 4500008004300000245006300043210006300106520056100169100002200730700001700752700001800769856003600787 2007 en_Ud 00aSoft elasticity and microstructure in smectic C elastomers0 aSoft elasticity and microstructure in smectic C elastomers3 aSmectic 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.1 aDeSimone, Antonio1 aAdams, James1 aConti, Sergio uhttp://hdl.handle.net/1963/181100537nas a2200109 4500008004300000245006800043210006800111520016600179100002400345700002200369856003600391 2007 en_Ud 00aStanding waves of some coupled Nonlinear Schrödinger Equations0 aStanding waves of some coupled Nonlinear Schrödinger Equations3 aWe 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.1 aAmbrosetti, Antonio1 aColorado, Eduardo uhttp://hdl.handle.net/1963/182100859nas a2200109 4500008004300000245008400043210006900127520047200196100002200668700002300690856003600713 2006 en_Ud 00aAlmost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics0 aAlmost Global Stochastic Feedback Stabilization of Conditional Q3 aWe 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.1 aAltafini, Claudio1 aTicozzi, Francesco uhttp://hdl.handle.net/1963/172700487nas a2200109 4500008004300000245007200043210007000115520011000185100002400295700002200319856003600341 2006 en_Ud 00aBound and ground states of coupled nonlinear Schrödinger equations0 aBound and ground states of coupled nonlinear Schrödinger equatio3 aWe prove existence of bound and ground states of some systems of coupled nonlinear Schrodinger equations.1 aAmbrosetti, Antonio1 aColorado, Eduardo uhttp://hdl.handle.net/1963/214900412nas a2200109 4500008004300000245009200043210006900135100002400204700002200228700001600250856003600266 2006 en_Ud 00aBound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity0 aBound states of Nonlinear Schroedinger Equations with Potentials1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aRuiz, David uhttp://hdl.handle.net/1963/175601941nas a2200133 4500008004300000245006300043210005900106520150700165100002501672700003001697700002001727700002401747856003601771 2006 en_Ud 00aA cyclic integral on k-Minkowski noncommutative space-time0 acyclic integral on kMinkowski noncommutative spacetime3 aWe 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 ``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 ``canonical\\\'\\\' noncommutative spacetime, with coordinate-independent commutators.1 aAgostini, Alessandra1 aAmelino-Camelia, Giovanni1 aArzano, Michele1 aD'Andrea, Francesco uhttp://hdl.handle.net/1963/215800974nas a2200109 4500008004300000245009300043210006900136520057600205100002500781700002200806856003600828 2006 en_Ud 00aAn estimation of the controllability time for single-input systems on compact Lie Groups0 aestimation of the controllability time for singleinput systems o3 aGeometric 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.1 aAgrachev, Andrei, A.1 aChambrion, Thomas uhttp://hdl.handle.net/1963/213502436nas a2200169 4500008004100000245007600041210006900117260007200186520184400258100002002102700002202122700001802144700002502162700001902187700002402206856003602230 2006 en d00aExperimental and modeling studies of desensitization of P2X3 receptors.0 aExperimental and modeling studies of desensitization of P2X3 rec bthe American Society for Pharmacology and Experimental Therapeutics3 aThe 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.1 aSokolova, Elena1 aSkorinkin, Andrei1 aMoiseev, Igor1 aAgrachev, Andrei, A.1 aNistri, Andrea1 aGiniatullin, Rashid uhttp://hdl.handle.net/1963/497400866nas a2200097 4500008004300000245013100043210006900174520046700243100002200710856003600732 2006 en_Ud 00aHomogeneous polynomial forms for simultaneous stabilizability of families of linear control systems: a tensor product approach0 aHomogeneous polynomial forms for simultaneous stabilizability of3 aThe 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/222600669nas a2200109 4500008004300000245010800043210007000151520026200221100002400483700001600507856003600523 2006 en_Ud 00aRadial solutions concentrating on spheres of nonlinear Schrödinger equations with vanishing potentials0 aRadial solutions concentrating on spheres of nonlinear Schröding3 aWe 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.1 aAmbrosetti, Antonio1 aRuiz, David uhttp://hdl.handle.net/1963/175501165nas a2200109 4500008004300000245005900043210005900102520081400161100002200975700002200997856003601019 2006 en_Ud 00aReflection symmetries for multiqubit density operators0 aReflection symmetries for multiqubit density operators3 aFor 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.1 aAltafini, Claudio1 aHavel, Timothy F. uhttp://hdl.handle.net/1963/212101579nas a2200121 4500008004100000245007400041210006700115260001800182520117500200100001801375700002801393856003601421 2005 en d00aOn the attainable set for Temple class systems with boundary controls0 aattainable set for Temple class systems with boundary controls bSISSA Library3 aConsider 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.1 aAncona, Fabio1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/158101041nas a2200097 4500008004300000245006900043210006900112520070400181100002200885856003600907 2005 en_Ud 00aCommuting multiparty quantum observables and local compatibility0 aCommuting multiparty quantum observables and local compatibility3 aA 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 ``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 ``Bell Theorem without inequalities\\\'\\\'.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/222802094nas a2200121 4500008004300000245013000043210006900173520162100242100002501863700003001888700001801918856003601936 2005 en_Ud 00aOn curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals0 acurvatures and focal points of distributions of dynamical Lagran3 aPairs (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.1 aAgrachev, Andrei, A.1 aChtcherbakova, Natalia N.1 aZelenko, Igor uhttp://hdl.handle.net/1963/225400739nas a2200109 4500008004100000245008000041210007100121260001300192520036600205100002200571856003600593 2005 en d00aExplicit Wei–Norman formulae for matrix Lie groups via Putzer\\\'s method0 aExplicit Wei–Norman formulae for matrix Lie groups via Putzers m bElsevier3 aThe Wei–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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/453800958nas a2200121 4500008004300000245009200043210006900135520053000204100002400734700002000758700002200778856003600800 2005 en_Ud 00aGround states of nonlinear Schroedinger equations with potentials vanishing at infinity0 aGround states of nonlinear Schroedinger equations with potential3 aWe 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 $\\\\theta= (p+1)/(p-1)-1/2$.1 aAmbrosetti, Antonio1 aFelli, Veronica1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/235201078nas a2200109 4500008004300000245007500043210006900118520070500187100002200892700001800914856003600932 2005 en_Ud 00aModulation of the Camassa-Holm equation and reciprocal transformations0 aModulation of the CamassaHolm equation and reciprocal transforma3 aWe 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.1 aAbenda, Simonetta1 aGrava, Tamara uhttp://hdl.handle.net/1963/230500367nas a2200097 4500008004300000245007600043210007000119100002400189700002000213856003600233 2005 en_Ud 00aNonlinear Schrödinger Equations with vanishing and decaying potentials0 aNonlinear Schrödinger Equations with vanishing and decaying pote1 aAmbrosetti, Antonio1 aZhi-Qiang, Wang uhttp://hdl.handle.net/1963/176001324nas a2200109 4500008004300000245005700043210005600100520097800156100002201134700002201156856003601178 2005 en_Ud 00aWetting of rough surfaces: a homogenization approach0 aWetting of rough surfaces a homogenization approach3 aThe 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.1 aDeSimone, Antonio1 aAlberti, Giovanni uhttp://hdl.handle.net/1963/225300908nas a2200145 4500008004300000245010400043210007000147260001300217520040600230100002000636700002900656700002000685700002100705856003600726 2004 en_Ud 00aBlow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity0 aBlowup solutions for the Schrödinger equation in dimension three bElsevier3 aWe 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.1 aAdami, Riccardo1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/299800697nas a2200097 4500008004300000245005500043210005500098520038800153100002200541856003600563 2004 en_Ud 00aCoherent control of open quantum dynamical systems0 aCoherent control of open quantum dynamical systems3 aA 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/222701258nas a2200145 4500008004300000245008600043210006900129260001700198520078200215100002300997700001801020700002201038700001601060856003601076 2004 en_Ud 00aEnergetics and switching of quasi-uniform states in small ferromagnetic particles0 aEnergetics and switching of quasiuniform states in small ferroma bEDP Sciences3 aWe 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.1 aAlouges, François1 aConti, Sergio1 aDeSimone, Antonio1 aPokern, Ivo uhttp://hdl.handle.net/1963/299901711nas a2200109 4500008004300000245014800043210006900191260001700260520126600277100002201543856003601565 2004 en_Ud 00aReduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric0 aReduction by group symmetry of second order variational problems bEDP Sciences3 aFor 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/352101168nas a2200097 4500008004300000245006600043210006600109520083700175100002201012856003601034 2004 en_Ud 00aRepresenting multiqubit unitary evolutions via Stokes tensors0 aRepresenting multiqubit unitary evolutions via Stokes tensors3 aFor 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 ``coherences\\\'\\\' and ``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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/230700490nas a2200121 4500008004100000245011600041210006900157260004300226100002400269700002200293700001700315856003600332 2004 en d00aSingularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II0 aSingularity perturbed elliptic equations with symmetry existence bIndiana University Mathematics Journal1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aNi, Wei-Ming uhttp://hdl.handle.net/1963/166300882nas a2200121 4500008004300000245004500043210004500088260001700133520053500150100001800685700002100703856003600724 2004 en_Ud 00aStability rates for patchy vector fields0 aStability rates for patchy vector fields bEDP Sciences3 aThis 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.1 aAncona, Fabio1 aBressan, Alberto uhttp://hdl.handle.net/1963/295901375nas a2200109 4500008004300000245010700043210006900150260003000219520095800249100002201207856003601229 2004 en_Ud 00aTensor of coherences parametrization of multiqubit density operators for entanglement characterization0 aTensor of coherences parametrization of multiqubit density opera bAmerican Physical Society3 aFor 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/284500369nas a2200109 4500008004100000245006400041210006300105260001800168100001800186700001900204856003600223 2004 en d00aWell-posedness for general 2x2 systems of conservation laws0 aWellposedness for general 2x2 systems of conservation laws bSISSA Library1 aAncona, Fabio1 aMarson, Andrea uhttp://hdl.handle.net/1963/124100697nas a2200133 4500008004300000245009100043210006900134260001300203520024900216100002200465700001900487700002100506856003600527 2003 en_Ud 00aThe calibration method for the Mumford-Shah functional and free-discontinuity problems0 acalibration method for the MumfordShah functional and freediscon bSpringer3 aWe 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.1 aAlberti, Giovanni1 aBouchitte, Guy1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/305100974nas a2200109 4500008004300000245008900043210006900132260003400201520057100235100002200806856003600828 2003 en_Ud 00aControllability properties for finite dimensional quantum Markovian master equations0 aControllability properties for finite dimensional quantum Markov bAmerican Institute of Physics3 aVarious 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/290901411nas a2200109 4500008004300000245012000043210006900163260001000232520100100242100002201243856003601265 2003 en_Ud 00aGeometric motion control for a kinematically redundant robotic chain: application to a holonomic mobile manipulator0 aGeometric motion control for a kinematically redundant robotic c bWiley3 aFor 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/301900867nas a2200121 4500008004100000245005700041210005000098260001800148520049700166100002500663700002100688856003600709 2003 en d00aOn the local structure of optimal trajectories in R30 alocal structure of optimal trajectories in R3 bSISSA Library3 aWe 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.1 aAgrachev, Andrei, A.1 aSigalotti, Mario uhttp://hdl.handle.net/1963/161201197nas a2200121 4500008004300000245012700043210006900170260001300239520074500252100002200997700002001019856003601039 2003 en_Ud 00aMotion on submanifolds of noninvariant holonomic constraints for a kinematic control system evolving on a matrix Lie group0 aMotion on submanifolds of noninvariant holonomic constraints for bElsevier3 aFor 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.1 aAltafini, Claudio1 aFrezza, Ruggero uhttp://hdl.handle.net/1963/301800793nas a2200109 4500008004300000245010200043210006900145260001300214520039800227100002200625856003600647 2003 en_Ud 00aParameter differentiation and quantum state decomposition for time varying Schrödinger equations0 aParameter differentiation and quantum state decomposition for ti bElsevier3 aFor 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/301700551nas a2200121 4500008004100000245007300041210006900114260004800183520011800231100002400349700002000373856003600393 2003 en d00aPositive solutions to a class of quasilinear elliptic equations on R0 aPositive solutions to a class of quasilinear elliptic equations bAmerican Institute of Mathematical Sciences3 aWe discuss the existence of positive solutions of perturbation to a class of quasilinear elliptic equations on R.1 aAmbrosetti, Antonio1 aZhi-Qiang, Wang uhttp://hdl.handle.net/1963/162800736nas a2200133 4500008004300000245008800043210006900131260001300200520028300213100002000496700002200516700002800538856003600566 2003 en_Ud 00aPrescribing scalar and boundary mean curvature on the three dimensional half sphere0 aPrescribing scalar and boundary mean curvature on the three dime bSpringer3 aWe 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.1 aDjadli, Zindine1 aMalchiodi, Andrea1 aAhmedou, Mohameden Ould uhttp://hdl.handle.net/1963/308600459nas a2200121 4500008004100000245011500041210006900156260001300225100002400238700002200262700001700284856003600301 2003 en d00aSingularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I0 aSingularly perturbed elliptic equations with symmetry existence bSpringer1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aNi, Wei-Ming uhttp://hdl.handle.net/1963/163300426nas a2200121 4500008004100000245007300041210006900114260001800183100002100201700001800222700002800240856003600268 2003 en d00aSome results on the boundary control of systems of conservation laws0 aSome results on the boundary control of systems of conservation bSISSA Library1 aBressan, Alberto1 aAncona, Fabio1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/161500371nas a2200097 4500008004100000245008700041210006900128260001800197100002200215856003600237 2002 en d00aControllability of quantum mechanical systems by root space decomposition of su(N)0 aControllability of quantum mechanical systems by root space deco bSISSA Library1 aAltafini, Claudio uhttp://hdl.handle.net/1963/161300809nas a2200121 4500008004300000245007700043210006900120260000900189520041400198100001800612700002100630856003600651 2002 en_Ud 00aFlow Stability of Patchy Vector Fields and Robust Feedback Stabilization0 aFlow Stability of Patchy Vector Fields and Robust Feedback Stabi bSIAM3 aThe 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.1 aAncona, Fabio1 aBressan, Alberto uhttp://hdl.handle.net/1963/307300768nas a2200109 4500008004300000245007400043210006900117260000900186520040500195100002200600856003600622 2002 en_Ud 00aFollowing a path of varying curvature as an output regulation problem0 aFollowing a path of varying curvature as an output regulation pr bIEEE3 aGiven 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/314300403nas a2200097 4500008004100000245011900041210006900160260001800229100002200247856003600269 2002 en d00aOn the generation of sequential unitary gates from continuous time Schrodinger equations driven by external fields0 ageneration of sequential unitary gates from continuous time Schr bSISSA Library1 aAltafini, Claudio uhttp://hdl.handle.net/1963/161401353nas a2200121 4500008004300000245003200043210003200075260001300107520103200120100002501152700001801177856003601195 2002 en_Ud 00aGeometry of Jacobi Curves I0 aGeometry of Jacobi Curves I bSpringer3 aJacobi 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\\\".1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/311000314nas a2200109 4500008004100000245003300041210003300074260001800107100002500125700001800150856003600168 2002 en d00aGeometry of Jacobi curves II0 aGeometry of Jacobi curves II bSISSA Library1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/158900451nas a2200109 4500008004100000245005400041210005400095260003300149520009900182100002400281856003600305 2002 en d00aMultiplicity results for the Yamabe problem on Sn0 aMultiplicity results for the Yamabe problem on Sn bNational Academy of Sciences3 aWe discuss some results related to the existence of multiple solutions for the Yamabe problem.1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/588500461nas a2200121 4500008004100000245010500041210006900146260001800215100002000233700002800253700002200281856003600303 2002 en d00aPrescribing a fourth oder conformal invariant on the standard sphere - Part I: a perturbation result0 aPrescribing a fourth oder conformal invariant on the standard sp bSISSA Library1 aDjadli, Zindine1 aAhmedou, Mohameden Ould1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/153900474nas a2200121 4500008004100000245011800041210006900159260001800228100002000246700002200266700002800288856003600316 2002 en d00aPrescribing a fourth oder conformal invariant on the standard sphere - Part II: blow up analysis and applications0 aPrescribing a fourth oder conformal invariant on the standard sp bSISSA Library1 aDjadli, Zindine1 aMalchiodi, Andrea1 aAhmedou, Mohameden Ould uhttp://hdl.handle.net/1963/154001047nas a2200109 4500008004300000245006200043210005800105260001300163520070300176100002200879856003600901 2002 en_Ud 00aThe reachable set of a linear endogenous switching system0 areachable set of a linear endogenous switching system bElsevier3 aIn 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/314200585nas a2200133 4500008004100000245008200041210006900123260001800192520014200210100002400352700002200376700001700398856003600415 2002 en d00aSolutions concentrating on spheres to symmetric singularly perturbed problems0 aSolutions concentrating on spheres to symmetric singularly pertu bSISSA Library3 aWe discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere.1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aNi, Wei-Ming uhttp://hdl.handle.net/1963/159400433nas a2200121 4500008004100000245008600041210006900127260001800196100002400214700001500238700002200253856003600275 2002 en d00aOn the Yamabe problem and the scalar curvature problems under boundary conditions0 aYamabe problem and the scalar curvature problems under boundary bSISSA Library1 aAmbrosetti, Antonio1 aYanYan, Li1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/151000433nas a2200121 4500008004100000245008200041210006900123260001800192100002400210700002200234700001900256856003600275 2001 en d00aMultiplicity results for some nonlinear Schrodinger equations with potentials0 aMultiplicity results for some nonlinear Schrodinger equations wi bSISSA Library1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aSecchi, Simone uhttp://hdl.handle.net/1963/156400364nas a2200109 4500008004100000245005900041210005100100260001800151100002500169700002400194856003600218 2001 en d00aOn the subanalyticity of Carnot-Caratheodory distances0 asubanalyticity of CarnotCaratheodory distances bSISSA Library1 aAgrachev, Andrei, A.1 aGauthier, Jean-Paul uhttp://hdl.handle.net/1963/148300499nas a2200121 4500008004300000245005900043210004800102260001300150520013200163100002400295700002200319856003600341 2001 en_Ud 00aOn the symmetric scalar curvature problem on S\\\\sp n0 asymmetric scalar curvature problem on Ssp n bElsevier3 aWe discuss some existence results dealing with the scalar curvature problem on S\\\\sp n in the presence of various symmetries.1 aAmbrosetti, Antonio1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/309500420nas a2200121 4500008004100000245007100041210006400112260001800176100002400194700002600218700001800244856003600262 2000 en d00aElliptic variational problems in $ R\\\\sp N$ with critical growth0 aElliptic variational problems in Rsp N with critical growth bSISSA Library1 aAmbrosetti, Antonio1 aGarcia Azorero, Jesus1 aPeral, Ireneo uhttp://hdl.handle.net/1963/125800442nas a2200121 4500008004100000245008800041210006900129260001800198100002400216700002600240700001800266856003600284 2000 en d00aExistence and multiplicity results for some nonlinear elliptic equations: a survey.0 aExistence and multiplicity results for some nonlinear elliptic e bSISSA Library1 aAmbrosetti, Antonio1 aGarcia Azorero, Jesus1 aPeral, Ireneo uhttp://hdl.handle.net/1963/146200420nas a2200121 4500008004100000245007300041210006900114260001800183100002400201700001500225700002200240856003600262 2000 en d00aA note on the scalar curvature problem in the presence of symmetries0 anote on the scalar curvature problem in the presence of symmetri bSISSA Library1 aAmbrosetti, Antonio1 aYanYan, Li1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/136500974nas a2200121 4500008004300000245004200043210004200085260001300127520063300140100002500773700001800798856003600816 2000 en_Ud 00aPrincipal invariants of Jacobi curves0 aPrincipal invariants of Jacobi curves bSpringer3 aJacobi 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.1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/382500914nas a2200133 4500008004300000245007500043210006900118260002100187520047300208100002200681700002200703700001900725856003600744 2000 en_Ud 00aA Remark on One-Dimensional Many-Body Problems with Point Interactions0 aRemark on OneDimensional ManyBody Problems with Point Interactio bWorld Scientific3 aThe 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.1 aAlbeverio, Sergio1 aDabrowski, Ludwik1 aFei, Shao-Ming uhttp://hdl.handle.net/1963/321400372nas a2200121 4500008004100000245004700041210004700088260001800135100002400153700001500177700002200192856003600214 2000 en d00aScalar curvature under boundary conditions0 aScalar curvature under boundary conditions bSISSA Library1 aAmbrosetti, Antonio1 aYanYan, Li1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/150600703nas a2200133 4500008004100000245005900041210005400100260001300154520030400167100002200471700001900493700002100512856003600533 1999 en d00aThe calibration method for the Mumford-Shah functional0 acalibration method for the MumfordShah functional bElsevier3 aIn 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).1 aAlberti, Giovanni1 aBouchitte, Guy1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/123500599nas a2200121 4500008004100000245006400041210005600105260001300161520022100174100002400395700002200419856003600441 1999 en d00aA multiplicity result for the Yamabe problem on $S\\\\sp n$0 amultiplicity result for the Yamabe problem on Ssp n bElsevier3 aWe 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.1 aAmbrosetti, Antonio1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/126401145nas a2200145 4500008004300000245007900043210006900122260001300191520067400204100002000878700001700898700002500915700002300940856003600963 1999 en_Ud 00aNonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws0 aNonclassical Shocks and the Cauchy Problem for Nonconvex Conserv bElsevier3 aThe 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.1 aAmadori, Debora1 aBaiti, Paolo1 aLeFloch, Philippe G.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/331200698nas a2200133 4500008004300000245010800043210006900151260001300220520022700233100002400460700002600484700001800510856003600528 1999 en_Ud 00aPerturbation of $\Delta u+u^{(N+2)/(N-2)}=0$, the scalar curvature problem in $R^N$, and related topics0 aPerturbation of Delta uu N2N2 0 the scalar curvature problem in bElsevier3 aSome 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.

1 aAmbrosetti, Antonio1 aGarcia Azorero, Jesus1 aPeral, Ireneo uhttp://hdl.handle.net/1963/325500346nas a2200109 4500008004100000245005100041210004400092260001800136100002400154700002200178856003600200 1999 en d00aOn the scalar curvature problem under symmetry0 ascalar curvature problem under symmetry bSISSA Library1 aAmbrosetti, Antonio1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/128700330nas a2200097 4500008004300000245005800043210005800101260001300159100002400172856003600196 1998 en_Ud 00aBranching points for a class of variational operators0 aBranching points for a class of variational operators bSpringer1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/331400446nas a2200121 4500008004100000245009900041210006900140260001800209100002000227700002000247700002100267856003600288 1998 en d00aSpecial functions with bounded variation and with weakly differentiable traces on the jump set0 aSpecial functions with bounded variation and with weakly differe bSISSA Library1 aAmbrosio, Luigi1 aBraides, Andrea1 aGarroni, Adriana uhttp://hdl.handle.net/1963/102500369nas a2200097 4500008004100000245008900041210006900130260001800199100001800217856003600235 1997 en d00aHomogeneous tangent vectors and high order necessary conditions for optimal controls0 aHomogeneous tangent vectors and high order necessary conditions bSISSA Library1 aAncona, Fabio uhttp://hdl.handle.net/1963/101500392nas a2200109 4500008004100000245008000041210006900121260001000190653002400200100002200224856003600246 1994 en d00aAnalysis of Singularity Structures for Quasi-Integrable Hamiltonian Systems0 aAnalysis of Singularity Structures for QuasiIntegrable Hamiltoni bSISSA10aHamiltonian systems1 aAbenda, Simonetta uhttp://hdl.handle.net/1963/568500390nas a2200109 4500008004100000245007700041210006900118260001800187100001800205700002200223856003500245 1990 en d00aExistence of solutions for a class of non-convex differential inclusions0 aExistence of solutions for a class of nonconvex differential inc bSISSA Library1 aAncona, Fabio1 aColombo, Giovanni uhttp://hdl.handle.net/1963/79200355nas a2200109 4500008004100000245005600041210005400097260001800151100002000169700002100189856003500210 1990 en d00aA general chain rule for distributional derivatives0 ageneral chain rule for distributional derivatives bSISSA Library1 aAmbrosio, Luigi1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/65000402nas a2200109 4500008004100000245007900041210006900120260001800189100002400207700002600231856003500257 1987 en d00aSolutions with minimal period for Hamiltonian systems in a potential well.0 aSolutions with minimal period for Hamiltonian systems in a poten bSISSA Library1 aAmbrosetti, Antonio1 aCoti Zelati, Vittorio uhttp://hdl.handle.net/1963/46600374nas a2200121 4500008004100000245004500041210004500086260001800131100002400149700002600173700001800199856003500217 1987 en d00aSymmetry breaking in Hamiltonian systems0 aSymmetry breaking in Hamiltonian systems bSISSA Library1 aAmbrosetti, Antonio1 aCoti Zelati, Vittorio1 aEkeland, Ivar uhttp://hdl.handle.net/1963/40900389nas a2200121 4500008004100000245005200041210005200093260001800145100002500163700002300188700002100211856003500232 1986 en d00aDirichlet problems for demicoercive functionals0 aDirichlet problems for demicoercive functionals bSISSA Library1 aAnzellotti, Gabriele1 aButtazzo, Giuseppe1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/39000370nas a2200097 4500008004100000245008500041210006900126260001800195100002400213856003500237 1982 en d00aDifferential equations with multiple solutions and nonlinear functional analysis0 aDifferential equations with multiple solutions and nonlinear fun bSISSA Library1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/22200377nas a2200097 4500008004100000245009200041210006900133260001800202100002400220856003500244 1981 en d00aRecent advances in the study of the existence of periodic orbits of Hamiltonian systems0 aRecent advances in the study of the existence of periodic orbits bSISSA Library1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/159