%0 Journal Article %J International Journal for Numerical Methods in Engineering %D 2022 %T Kernel-based active subspaces with application to computational fluid dynamics parametric problems using discontinuous Galerkin method %A Francesco Romor %A Marco Tezzele %A Andrea Lario %A Gianluigi Rozza %B International Journal for Numerical Methods in Engineering %V 123 %P 6000-6027 %G eng %R 10.1002/nme.7099 %0 Book %D 2020 %T Kernel-based Active Subspaces with application to CFD parametric problems using Discontinuous Galerkin method %A Francesco Romor %A Marco Tezzele %A Lario, Andrea %A Gianluigi Rozza %G eng %0 Journal Article %J Calcolo %D 2019 %T On Krylov solutions to infinite-dimensional inverse linear problems %A Noe Caruso %A Alessandro Michelangeli %A Paolo Novati %X

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.

%B Calcolo %V 56 %P 1–25 %G eng %0 Journal Article %J Proceedings of the National Academy of Sciences %D 2017 %T Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes %A Massimiliano Rossi %A Giancarlo Cicconofri %A Alfred Beran %A Giovanni Noselli %A Antonio DeSimone %X 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. %B Proceedings of the National Academy of Sciences %V 114 %P 13085-13090 %G eng %U https://www.pnas.org/content/114/50/13085 %R 10.1073/pnas.1708064114 %0 Journal Article %J Comm. Math. Phys %D 2017 %T The Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes' phenomenon %A Marco Bertola %A Mattia Cafasso %B Comm. Math. Phys %V DOI 10.1007/s00220-017-2856-3 %G eng %U http://arxiv.org/abs/1603.06420 %0 Report %D 2017 %T Krein-Visik-Birman self-adjoint extension theory revisited %A Matteo Gallone %A Alessandro Michelangeli %A Andrea Ottolini %X 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. %G en %U http://preprints.sissa.it/handle/1963/35286 %1 35591 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-05-31T08:18:47Z No. of bitstreams: 1 Gallone-Michelangeli-Ottolini-KVB.pdf: 675862 bytes, checksum: 325168fcaae89a9faedde0e5c32e69a7 (MD5) %0 Journal Article %J Mathematische Annalen %D 2014 %T KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation %A P Baldi %A Massimiliano Berti %A Riccardo Montalto %X 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. %B Mathematische Annalen %P 1-66 %G eng %R 10.1007/s00208-013-1001-7 %0 Thesis %D 2014 %T KAM for quasi-linear and fully nonlinear perturbations of Airy and KdV equations %A Riccardo Montalto %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7476 %1 7571 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by rmontalt@sissa.it (rmontalt@sissa.it) on 2014-10-27T10:15:33Z No. of bitstreams: 1 Tesi-Phd-Montalto-Riccardo.pdf: 1843377 bytes, checksum: b4e504e6ad1860c3d3580beb4e24efff (MD5) %0 Journal Article %J C. R. Math. Acad. Sci. Paris %D 2014 %T KAM for quasi-linear KdV %A P Baldi %A Massimiliano Berti %A Riccardo Montalto %X

We prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

%B C. R. Math. Acad. Sci. Paris %I Elsevier %V 352 %P 603-607 %G en %U http://urania.sissa.it/xmlui/handle/1963/35067 %N 7-8 %1 35302 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-11-30T15:30:40Z (GMT) No. of bitstreams: 0 %R 10.1016/j.crma.2014.04.012 %0 Journal Article %J Arch. Ration. Mech. Anal. %D 2014 %T KAM for Reversible Derivative Wave Equations %A Massimiliano Berti %A Luca Biasco %A Michela Procesi %X

We prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

%B Arch. Ration. Mech. Anal. %I Springer %V 212 %P 905-955 %G en %U http://urania.sissa.it/xmlui/handle/1963/34646 %N 3 %1 34850 %2 Mathematics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-14T16:55:00Z No. of bitstreams: 1 preprint2014.pdf: 620515 bytes, checksum: d1d981f350e63c9906f793bcfe66e972 (MD5) %R 10.1007/s00205-014-0726-0 %0 Journal Article %J Annales Scientifiques de l'Ecole Normale Superieure %D 2013 %T KAM theory for the Hamiltonian derivative wave equation %A Massimiliano Berti %A Luca Biasco %A Michela Procesi %X

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.

%B Annales Scientifiques de l'Ecole Normale Superieure %V 46 %P 301-373 %G eng %0 Journal Article %J International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099 %D 2012 %T The KdV hierarchy: universality and a Painleve transcendent %A Tom Claeys %A Tamara Grava %K Small-Dispersion limit %X 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. %B International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099 %I Oxford University Press %G en %U http://hdl.handle.net/1963/6921 %1 6902 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-05-29T08:08:55Z No. of bitstreams: 1 1101.2602v1.pdf: 327994 bytes, checksum: 5b5bbc9f9b74ce97c2bf5ae794698819 (MD5) %0 Journal Article %J Mathematical Biosciences and Engineering 7(2):301-312, 2010 %D 2010 %T A kinetic mechanism inducing oscillations in simple chemical reactions networks %A Julien Coatleven %A Claudio Altafini %X 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. %B Mathematical Biosciences and Engineering 7(2):301-312, 2010 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/2393 %1 2304 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-12T13:08:42Z\\r\\nNo. of bitstreams: 1\\r\\nCoAl07.pdf: 254781 bytes, checksum: 0906fef8209903070cd78781f52b13b1 (MD5) %R 10.3934/mbe.2010.7.301 %0 Journal Article %J J.Dynam. Control Systems 8 (2002),no.4, 547 %D 2002 %T On the K+P problem for a three-level quantum system: optimality implies resonance %A Ugo Boscain %A Thomas Chambrion %A Jean-Paul Gauthier %B J.Dynam. Control Systems 8 (2002),no.4, 547 %I SISSA Library %G en %U http://hdl.handle.net/1963/1601 %1 2517 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:08Z (GMT). No. of bitstreams: 1\\nmath.OC0204233.pdf: 252630 bytes, checksum: 14283368a7848e46caf6447b4bad85d4 (MD5)\\n Previous issue date: 2002 %R 10.1023/A:1020767419671 %0 Journal Article %J Z. Angew. Math. Phys. 48 (1997), no. 2, 193-219 %D 1997 %T Kam theorem for generic analytic perturbations of the Guler system %A Marta Mazzocco %X 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. %B Z. Angew. Math. Phys. 48 (1997), no. 2, 193-219 %I Springer %G en %U http://hdl.handle.net/1963/1038 %1 2818 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:42:01Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %R 10.1007/PL00001474 %0 Journal Article %J Lett. Math. Phys. 42 (1997) 349-361 %D 1997 %T Krichever maps, Faà di Bruno polynomials, and cohomology in KP theory %A Gregorio Falqui %A Cesare Reina %A Alessandro Zampa %X 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. %B Lett. Math. Phys. 42 (1997) 349-361 %I Springer %G en_US %U http://hdl.handle.net/1963/3539 %1 1162 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-23T17:16:39Z\\nNo. of bitstreams: 1\\n9704010v1.pdf: 180279 bytes, checksum: c51b95b568001428607e6092a798cce5 (MD5) %R 10.1023/A:1007323118991 %0 Journal Article %J Boll. Un. Mat. Ital. A (7) 2, 1988, no. 1, 127-135 %D 1988 %T A Kellogg property for µ-capacities %A Gianni Dal Maso %A Anneliese Defranceschi %B Boll. Un. Mat. Ital. A (7) 2, 1988, no. 1, 127-135 %I SISSA Library %G en %U http://hdl.handle.net/1963/492 %1 3412 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:33:34Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987