We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of a given inverse problem, together with a series of model examples and numerical experiments.

VL - 56 ER - TY - JOUR T1 - Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes JF - Proceedings of the National Academy of Sciences Y1 - 2017 A1 - Massimiliano Rossi A1 - Giancarlo Cicconofri A1 - Alfred Beran A1 - Giovanni Noselli A1 - Antonio DeSimone AB - Active flagella provide the propulsion mechanism for a large variety of swimming eukaryotic microorganisms, from protists to sperm cells. Planar and helical beating patterns of these structures are recurrent and widely studied. The fast spinning motion of the locomotory flagellum of the alga Euglena gracilis constitutes a remarkable exception to these patterns. We report a quantitative description of the 3D flagellar beating in swimming E. gracilis. Given their complexity, these shapes cannot be directly imaged with current microscopy techniques. We show how to overcome these limitations by developing a method to reconstruct in full the 3D kinematics of the cell from conventional 2D microscopy images, based on the exact characterization of the helical motion of the cell body.The flagellar swimming of euglenids, which are propelled by a single anterior flagellum, is characterized by a generalized helical motion. The 3D nature of this swimming motion, which lacks some of the symmetries enjoyed by more common model systems, and the complex flagellar beating shapes that power it make its quantitative description challenging. In this work, we provide a quantitative, 3D, highly resolved reconstruction of the swimming trajectories and flagellar shapes of specimens of Euglena gracilis. We achieved this task by using high-speed 2D image recordings taken with a conventional inverted microscope combined with a precise characterization of the helical motion of the cell body to lift the 2D data to 3D trajectories. The propulsion mechanism is discussed. Our results constitute a basis for future biophysical research on a relatively unexplored type of eukaryotic flagellar movement. VL - 114 UR - https://www.pnas.org/content/114/50/13085 ER - TY - JOUR T1 - The Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes' phenomenon JF - Comm. Math. Phys Y1 - 2017 A1 - Marco Bertola A1 - Mattia Cafasso VL - DOI 10.1007/s00220-017-2856-3 UR - http://arxiv.org/abs/1603.06420 ER - TY - RPRT T1 - Krein-Visik-Birman self-adjoint extension theory revisited Y1 - 2017 A1 - Matteo Gallone A1 - Alessandro Michelangeli A1 - Andrea Ottolini AB - The core results of the so-called KreIn-Visik-Birman theory of self-adjoint extensions of semi-bounded symmetric operators are reproduced, both in their original and in a more modern formulation, within a comprehensive discussion that includes missing details, elucidative steps, and intermediate results of independent interest. UR - http://preprints.sissa.it/handle/1963/35286 U1 - 35591 U2 - Mathematics ER - TY - JOUR T1 - KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation JF - Mathematische Annalen Y1 - 2014 A1 - P Baldi A1 - Massimiliano Berti A1 - Riccardo Montalto AB - We prove the existence of small amplitude quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of the linear Airy equation. For Hamiltonian or reversible nonlinearities we also prove their linear stability. The key analysis concerns the reducibility of the linearized operator at an approximate solution, which provides a sharp asymptotic expansion of its eigenvalues. For quasi-linear perturbations this cannot be directly obtained by a KAM iteration. Hence we first perform a regularization procedure, which conjugates the linearized operator to an operator with constant coefficients plus a bounded remainder. These transformations are obtained by changes of variables induced by diffeomorphisms of the torus and pseudo-differential operators. At this point we implement a Nash-Moser iteration (with second order Melnikov non-resonance conditions) which completes the reduction to constant coefficients. © 2014 Springer-Verlag Berlin Heidelberg. N1 - cited By (since 1996)0; Article in Press ER - TY - THES T1 - KAM for quasi-linear and fully nonlinear perturbations of Airy and KdV equations Y1 - 2014 A1 - Riccardo Montalto PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7476 U1 - 7571 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - KAM for quasi-linear KdV JF - C. R. Math. Acad. Sci. Paris Y1 - 2014 A1 - P Baldi A1 - Massimiliano Berti A1 - Riccardo Montalto AB -We prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

PB - Elsevier VL - 352 UR - http://urania.sissa.it/xmlui/handle/1963/35067 IS - 7-8 U1 - 35302 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - KAM for Reversible Derivative Wave Equations JF - Arch. Ration. Mech. Anal. Y1 - 2014 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Michela Procesi AB -We prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

PB - Springer VL - 212 UR - http://urania.sissa.it/xmlui/handle/1963/34646 IS - 3 U1 - 34850 U2 - Mathematics ER - TY - JOUR T1 - KAM theory for the Hamiltonian derivative wave equation JF - Annales Scientifiques de l'Ecole Normale Superieure Y1 - 2013 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Michela Procesi AB -We prove an infinite dimensional KAM theorem which implies the existence of Can- tor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. © 2013 Société Mathématique de France.

VL - 46 N1 - cited By (since 1996)4 ER - TY - JOUR T1 - The KdV hierarchy: universality and a Painleve transcendent JF - International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099 Y1 - 2012 A1 - Tom Claeys A1 - Tamara Grava KW - Small-Dispersion limit AB - We study the Cauchy problem for the Korteweg-de Vries (KdV) hierarchy in the small dispersion limit where $\e\to 0$. For negative analytic initial data with a single negative hump, we prove that for small times, the solution is approximated by the solution to the hyperbolic transport equation which corresponds to $\e=0$. Near the time of gradient catastrophe for the transport equation, we show that the solution to the KdV hierarchy is approximated by a particular Painlev\'e transcendent. This supports Dubrovins universality conjecture concerning the critical behavior of Hamiltonian perturbations of hyperbolic equations. We use the Riemann-Hilbert approach to prove our results. PB - Oxford University Press UR - http://hdl.handle.net/1963/6921 N1 - This article was published in "International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099 U1 - 6902 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A kinetic mechanism inducing oscillations in simple chemical reactions networks JF - Mathematical Biosciences and Engineering 7(2):301-312, 2010 Y1 - 2010 A1 - Julien Coatleven A1 - Claudio Altafini AB - It is known that a kinetic reaction network in which one or more secondary substrates are acting as cofactors may exhibit an oscillatory behavior. The aim of this work is to provide a description of the functional form of such a cofactor action guaranteeing the\\r\\nonset of oscillations in sufficiently simple reaction networks. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/2393 U1 - 2304 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the K+P problem for a three-level quantum system: optimality implies resonance JF - J.Dynam. Control Systems 8 (2002),no.4, 547 Y1 - 2002 A1 - Ugo Boscain A1 - Thomas Chambrion A1 - Jean-Paul Gauthier PB - SISSA Library UR - http://hdl.handle.net/1963/1601 U1 - 2517 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Kam theorem for generic analytic perturbations of the Guler system JF - Z. Angew. Math. Phys. 48 (1997), no. 2, 193-219 Y1 - 1997 A1 - Marta Mazzocco AB - We apply here KAM theory to the fast rotations of a rigid body with a fixed point, subject to a purely positional potential. The problem is equivalent to a small perturbation of the Euler system. The difficulty is that the unperturbed system is properly degenerate, namely the unperturbed Hamiltonian depends only on two actions. Following the scheme used by Arnol\\\'d for the N-body problem, we use part of the perturbation to remove the degeneracy: precisely, we construct Birkhoff normal form up to a suitable finite order, thus eliminating the two fast angles; the resulting system is nearly integrable and (generically) no more degenerate, so KAM theorem applies. The resulting description of the motion is that, if the initial kinetic energy is sufficiently large, then for most initial data the angular momentum has nearly constant module, and moves slowly in the space, practically following the level curves of the initial potential averaged on the two fast angles; on the same time the body precesses around the instantaneous direction of the angular momentum, essentially as in the Euler-Poinsot motion. We also provide two simple physical examples, where the procedure does apply. PB - Springer UR - http://hdl.handle.net/1963/1038 U1 - 2818 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Krichever maps, Faà di Bruno polynomials, and cohomology in KP theory JF - Lett. Math. Phys. 42 (1997) 349-361 Y1 - 1997 A1 - Gregorio Falqui A1 - Cesare Reina A1 - Alessandro Zampa AB - We study the geometrical meaning of the Faa\\\' di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faa\\\' di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning. PB - Springer UR - http://hdl.handle.net/1963/3539 U1 - 1162 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A Kellogg property for µ-capacities JF - Boll. Un. Mat. Ital. A (7) 2, 1988, no. 1, 127-135 Y1 - 1988 A1 - Gianni Dal Maso A1 - Anneliese Defranceschi PB - SISSA Library UR - http://hdl.handle.net/1963/492 U1 - 3412 U2 - Mathematics U3 - Functional Analysis and Applications ER -