Singular perturbation models in phase transitions for second order materials - Milena Chermisi; Gianni Dal Maso; Irene Fonseca; Giovanni Leoni (Indiana Univ. Math. J. 60 (2011) 367-409, 2011)
A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of Fe is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained.

Solving PVI by Isomonodromy Deformations - Davide Guzzetti (Painlevé equations and related topics : proceedings of the international conference, Saint Petersburg, Russia, June 17-23, 2011 / Aleksandr Dmitrievich Briuno; Alexander B Batkhin. - Berlin : De Gruyter, [2012]. - p. 101-105, 2011)
The critical and asymptotic behaviors of solutions of the sixth Painlev\\\'e\r\nequation, an their parametrization in terms of monodromy data, are\r\nsynthetically reviewed. The explicit formulas are given. This paper has been\r\nwithdrawn by the author himself, because some improvements are necessary.\r\nThis is a proceedings of the international conference \"Painlevé Equations and Related Topics\" which was taking place at the Euler International Mathematical Institute, a branch of the Saint Petersburg Department of the SteklovInstitute of Mathematicsof theRussian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011.
Keywords: Painlevé Equations

On the Space of Symmetric Operators with Multiple Ground States - Andrei A. Agrachev (Functional Analysis and its Applications, Volume 45, Issue 4, December 2011, Pages 241-251, 2011)
We study homological structure of the filtrations of the spaces of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite dimensional generalizations are easily guessed.
Keywords: Multiple eigenvalue

The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry - Bernard Bonnard; Grégoire Charlot; Roberta Ghezzi; Gabriel Janin (Journal of Dynamical and Control Systems, 2011)
We study the tangential case in 2-dimensional almost-Riemannian geometry. We\\r\\nanalyse the connection with the Martinet case in sub-Riemannian geometry. We\\r\\ncompute estimations of the exponential map which allow us to describe the\\r\\nconjugate locus and the cut locus at a tangency point. We prove that this last\\r\\none generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

Structure of level sets and Sard-type properties of Lipschitz maps - Giovanni Alberti; Stefano Bianchini; Gianluca Crippa (SISSA, 2011)

Subharmonic solutions of planar Hamiltonian systems: a rotation number approach - Alberto Boscaggin (Advanced Nonlinear Studies, 2011)

Subharmonic solutions of planar Hamiltonian systems via the Poincaré́-Birkhoff theorem - Alberto Boscaggin (Le Matematiche, 2011)
We revisit some recent results obtained in [1] about the existence of subharmonic solutions for a class of (nonautonomous) planar Hamiltonian systems, and we compare them with the existing literature. New applications to undamped second order equations are discussed, as well.

Supercritical conformal metrics on surfaces with conical singularities - Mauro Bardelloni; Francesca De Marchis; Andrea Malchiodi (Int Math Res Notices (2011) 2011 (24): 5625-5643, 2011)
We study the problem of prescribing the Gaussian curvature on surfaces with conical singularities in supercritical regimes. Using a Morse-theoretical approach we prove a general existence theorem on surfaces with positive genus, with a generic multiplicity result.

A system-level approach for deciphering the transcriptional response to prion infection - Mattia Zampieri; Giuseppe Legname; Daniel Segrè; Claudio Altafini (Bioinformatics (Oxford, England). 2011 Dec; 27(24):3407-14, 2011)
MOTIVATION: Deciphering the response of a complex biological system to an insulting event, at the gene expression level, requires adopting theoretical models that are more sophisticated than a one-to-one comparison (i.e. t-test). Here, we investigate the ability of a novel reverse engineering approach (System Response Inference) to unveil non-obvious transcriptional signatures of the system response induced by prion infection.\\r\\nRESULTS: To this end, we analyze previously published gene expression data, from which we extrapolate a putative full-scale model of transcriptional gene-gene dependencies in the mouse central nervous system. Then, we use this nominal model to interpret the gene expression changes caused by prion replication, aiming at selecting the genes primarily influenced by this perturbation. Our method sheds light on the mode of action of prions by identifying key transcripts that are the most likely to be responsible for the overall transcriptional rearrangement from a nominal regulatory network. As a first result of our inference, we have been able to predict known targets of prions (i.e. PrP(C)) and to unveil the potential role of previously unsuspected genes.\\r\\nCONTACT: altafini@sissa.it\\r\\nSUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Thin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity - Elisa Davoli (2011)
The subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and δ_h, respectively, the diameter and the thickness of the cross-section, we analyse the case where the scaling factor of the elastic energy is of order ε_h^2, with ε_h/δ_h^2 \rightarrow l \in [0, +\infty). Different linearized models are deduced according to the relative order of magnitude of δ_h with respect to h.

The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity - Helmut Abels; Maria Giovanna Mora; Stefan Müller (Calculus of Variations and Partial Differential Equations 41 (2011) 241-259, 2011)
The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation.

The Transition between the Gap Probabilities from the Pearcey to the Airy Process–a Riemann-Hilbert Approach - Marco Bertola; Mattia Cafasso (International Mathematics Research Notices, 2011)

Uniqueness and nondegeneracy of the ground state for a quasilinear Schrödinger equation with a small parameter - Alessandro Selvitella (Nonlinear Analysis: Theory, Methods & Applications, 2011)
We study least energy solutions of a quasilinear Schrödinger equation with a small parameter. We prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory.
Keywords: Bifurcation theory; Nonlinear Schrödinger equations; Stationary solutions

A uniqueness result for the continuity equation in two dimensions - Giovanni Alberti; Stefano Bianchini; Gianluca Crippa (SISSA, 2011)

The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces - Raphaël Danchin; Francesco Fanelli (Journal de Mathématiques Pures et Appliquées, 2011)
This work is the continuation of the recent paper (Danchin, 2010) [9] devoted to the density-dependent incompressible Euler equations. Here we concentrate on the well-posedness issue in Besov spaces of type B∞,rs embedded in the set of Lipschitz continuous functions, a functional framework which contains the particular case of Hölder spaces C1,α and of the endpoint Besov space B∞,11. For such data and under the non-vacuum assumption, we establish the local well-posedness and a continuation criterion in the spirit of that of Beale, Kato and Majda (1984) [2]. In the last part of the paper, we give lower bounds for the lifespan of a solution. In dimension two, we point out that the lifespan tends to infinity when the initial density tends to be a constant. This is, to our knowledge, the first result of this kind for the density-dependent incompressible Euler equations. Résumé Ce travail complète lʼarticle récent (Danchin, 2010) [9] consacré au système dʼEuler incompressible à densité variable. Lorsque lʼétat initial ne comporte pas de vide, on montre ici que le système est bien posé dans tous les espaces de Besov B∞,rs inclus dans lʼensemble des fonctions lipschitziennes. Ce cadre fonctionnel contient en particulier les espaces de Hölder C1,α et lʼespace de Besov limite B∞,11. On établit également un critère de prolongement dans lʼesprit de celui de Beale, Kato et Majda (1984) [2] pour le cas homogène. Dans la dernière partie de lʼarticle, on donne des minorations pour le temps de vie des solutions du système. En dimension deux, on montre que ce temps de vie tend vers lʼinfini lorsque la densité tend à être homogène. À notre connaissance, il sʼagit du premier résultat de ce type pour le système dʼEuler incompressible à densité variable.
Keywords: Blow-up criterion; Critical regularity; Incompressible Euler equations; Lifespan; Nonhomogeneous inviscid fluids

An abstract Nash-Moser theorem with parameters and applications to PDEs - Massimiliano Berti; Philippe Bolle; Michela Procesi (Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis, 2010)
We prove an abstract Nash-Moser implicit function theorem with parameters which covers the applications to the existence of finite dimensional, differentiable, invariant tori of Hamiltonian PDEs with merely differentiable nonlinearities. The main new feature of the abstract iterative scheme is that the linearized operators, in a neighborhood of the expected solution, are invertible, and satisfy the "tame" estimates, only for proper subsets of the parameters. As an application we show the existence of periodic solutions of nonlinear wave equations on Riemannian Zoll manifolds. A point of interest is that, in presence of possibly very large "clusters of small divisors", due to resonance phenomena, it is more natural to expect solutions with only Sobolev regularity. © 2009 Elsevier Masson SAS. All rights reserved.
Keywords: Abstracting; Aircraft engines; Finite dimensional; Hamiltonian PDEs; Implicit function theorem; Invariant tori; Iterative schemes; Linearized operators; Mathematical operators; Moser theorem; Non-Linearity; Nonlinear equations; Nonlinear wave equation; Periodic solution; Point of interest; Resonance phenomena; Small divisors; Sobolev; Wave equations

Almost-Riemannian Geometry from a Control Theoretical Viewpoint - Roberta Ghezzi (SISSA, 2010)

Aspects of Quantum Field Theory on Quantum Spacetime - Gherardo Piacitelli (PoS CNCFG2010:027,2010, 2010)
We provide a minimal, self-contained introduction to the covariant DFR flat\\r\\nquantum spacetime, and to some partial results for the corresponding quantum field theory. Explicit equations are given in the Dirac notation.

Canonical k-Minkowski Spacetime - Gherardo Piacitelli; Ludwik Dabrowski (2010)
A complete classification of the regular representations of the relations [T,X_j] = (i/k)X_j, j=1,...,d, is given. The quantisation of RxR^d canonically (in the sense of Weyl) associated with the universal representation of the above relations is intrinsically \\\"radial\\\", this meaning that it only involves the time variable and the distance from the origin; angle variables remain classical. The time axis through the origin is a spectral singularity of the model: in the large scale limit it is topologically disjoint from the rest. The symbolic calculus is developed; in particular there is a trace functional on symbols. For suitable choices of states localised very close to the origin, the uncertainties of all spacetime coordinates can be made simultaneously small at wish. On the contrary, uncertainty relations become important at \\\"large\\\" distances: Planck scale effects should be visible at LHC energies, if processes are spread in a region of size 1mm (order of peak nominal beam size) around the origin of spacetime.

Cauchy biorthogonal polynomials - Marco Bertola; Gekhtman, M.; Szmigielski, J. (J. Approx. Theory, 2010)

Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality - Andrea Brini; Luca Griguolo; Domenico Seminara; Alessandro Tanzini (J. Geom. Phys. 60 (2010) 417-429, 2010)
We consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS partition function in a generic flat background for the whole L(p,q) family and provide a solution for its large N dynamics; on the other, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and briefly discuss how it could be restored in a non-perturbative setting.

Cohomology of Skew-holomorphic lie algebroids - Ugo Bruzzo; Vladimir Rubtsov (2010)
We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.

Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions - Jesus Garcia Azorero; Andrea Malchiodi; Luigi Montoro; Ireneo Peral (Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56, 2010)
In this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in.

Concentration of solutions for some singularly perturbed mixed problems. Part I: existence results - Jesus Garcia Azorero; Andrea Malchiodi; Luigi Montoro; Ireneo Peral (Arch. Ration. Mech. Anal. 196 (2010) 907-950, 2010)
In this paper we study the asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions. We prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.

Continuity of optimal control costs and its application to weak KAM theory - Andrei A. Agrachev; Paul Lee (Calculus of Variations and Partial Differential Equations. Volume 39, Issue 1, 2010, Pages 213-232, 2010)
We prove continuity of certain cost functions arising from optimal control of\\r\\naffine control systems. We give sharp sufficient conditions for this\\r\\ncontinuity. As an application, we prove a version of weak KAM theorem and\\r\\nconsider the Aubry-Mather problems corresponding to these systems.

Convergence of equilibria of thin elastic rods under physical growth conditions for the energy density - Elisa Davoli; Maria Giovanna Mora (2010)
The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von Kármán plate theory for rods, and the linear theory.

The dependence on the monodromy data of the isomonodromic tau function - Marco Bertola (Comm. Math. Phys., 2010)

Dirac Operators on Quantum Projective Spaces - Francesco D'Andrea; Ludwik Dabrowski (Comm. Math. Phys. 295 (2010) 731-790, 2010)
We construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0<q<1. They provide 0^+ dimensional equivariant even spectral triples. If l is odd and N=(l+1)/2, the spectral triple is real with KO-dimension 2l mod 8.

The disintegration of the Lebesgue measure on the faces of a convex function - Laura Caravenna; Sara Daneri (J. Funct. Anal. 258 (2010) 3604-3661, 2010)
We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets.

Dynamics control by a time-varying feedback - Andrei A. Agrachev; Marco Caponigro (Journal of Dynamical and Control Systems. Volume 16, Issue 2, April 2010, Pages :149-162, 2010)
We consider a smooth bracket generating control-affine system in R^d and show that any orientation preserving diffeomorphism of R^d can be approximated, in the very strong sense, by a diffeomorphism included in the flow generated by a time-varying feedback control which is polynomial with respect to the state variables and trigonometric-polynomial with respect to the time variable.
Keywords: Discrete-time dynamics

Effective Schroedinger dynamics on $ ε$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs - Gianfausto Dell'Antonio; Emanuele Costa (J. Phys. A 43 (2010) 474014, 2010)
We describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric graph.

Estimates on path functionals over Wasserstein Spaces - Stefano Bianchini; Alessio Brancolini (SIAM J. Math. Anal. 42 (2010) 1179-1217, 2010)
In this paper we consider the class a functionals (introduced in [Brancolini, Buttazzo, and Santambrogio, J. Eur. Math. Soc. (JEMS), 8 (2006), pp. 415-434] $\\\\mathcal{G}_{r,p}$ defined on Lipschitz curves $\\\\gamma$ valued in the $p$-Wasserstein space. The problem considered is the following: given a measure $\\\\mu$, give conditions in order to assure the existence of a curve $\\\\gamma$ such that $\\\\gamma(0)=\\\\mu$, $\\\\gamma(1)=\\\\delta_{x_0}$, and $\\\\mathcal{G}_{r,p}(\\\\gamma)<+\\\\infty$. To this end, new estimates on $\\\\mathcal{G}_{r,p}(\\\\mu)$ are given, and a notion of dimension of a measure (called path dimension) is introduced: the path dimension specifies the values of the parameters $(r,p)$ for which the answer to the previous reachability problem is positive. Finally, we compare the path dimension with other known dimensions.

On the Euler-Lagrange equation for a variational problem : the general case II - Stefano Bianchini; Matteo Gloyer (Math. Z. 265 (2010) 889-923, 2010)

Exact reconstruction of damaged color images using a total variation model - Irene Fonseca; Giovanni Leoni; Francesco Maggi; Massimiliano Morini (Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331, 2010)
In this paper the reconstruction of damaged piecewice constant color images is studied using a RGB total variation based model for colorization/inpainting. In particular, it is shown that when color is known in a uniformly distributed region, then reconstruction is possible with maximal fidelity.

Existence of planar curves minimizing length and curvature - Ugo Boscain; Grégoire Charlot; Francesco Rossi (Proc. Steklov Inst. Math. 270 (2010) 43-56, 2010)
In this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional $\\\\int \\\\sqrt{1+K_\\\\gamma^2} ds$, depending both on length and curvature $K$. We fix starting and ending points as well as initial and final directions.\\nFor this functional we discuss the problem of existence of minimizers on various functional spaces. We find non-existence of minimizers in cases in which initial and final directions are considered with orientation. In this case, minimizing sequences of trajectories can converge to curves with angles.\\nWe instead prove existence of minimizers for the \\\"time-reparameterized\\\" functional $$\\\\int \\\\| \\\\dot\\\\gamma(t) \\\\|\\\\sqrt{1+K_\\\\ga^2} dt$$ for all boundary conditions if initial and final directions are considered regardless to orientation. In this case, minimizers can present cusps (at most two) but not angles.

Feedback schemes for radiation damping suppression in NMR: a control-theoretical perspective - Claudio Altafini; Paola Cappellaro; David Cory (Systems and Control Letters, 59 (12):782-786, 2010, 2010)
In NMR spectroscopy, the collective measurement is weakly invasive and its back-action is called radiation damping. The aim of this paper is to provide a control-theoretical analysis of the problem of suppressing this radiation damping. It is shown that the two feedback schemes commonly used in the NMR practice correspond one to a high gain oputput feedback for the simple case of maintaining the spin 1/2 in its inverted state, and the second to a 2-degree of freedom control design with a prefeedback that exactly cancels the radiation damping field. A general high gain feedback stabilization design not requiring the knowledge of the radiation damping time constant is also investigated.

First colonization of a hard-edge in random matrix theory - Marco Bertola; Lee, S. Y. (Constr. Approx., 2010)

Gauge theory: from physics to geometry - Ugo Bruzzo (Rend. Istit. Mat. Univ. Trieste 42 (2010) 103-128, 2010)
Maxwell theory may be regarded as a prototype of gauge theory and generalized to nonabelian gauge theory. We briey sketch the history of the gauge theories, from Maxwell to Yang-Mills theory, and the identification of gauge fields with connections on fibre bundles. We introduce the notion of instanton and consider the moduli spaces of such objects. Finally, we discuss some modern techniques for studying the topology of these moduli spaces.

Gene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus. - Dario Motti; Caroline Le Duigou; Nicole Chemaly; Lucia Wittner; Dejan Lazarevic; Helena Krmac; Troels Torben Marstrand; Eivind Valen; Remo Sanges; Elia Stupka; Albin Sandelin; Enrico Cherubini; et al. (The European journal of neuroscience. 2010 Oct; 32(8):1364-79, 2010)
We report gene profiling data on genomic processes underlying the progression towards recurrent seizures after injection of kainic acid (KA) into the mouse hippocampus. Focal injection enabled us to separate the effects of proepileptic stimuli initiated by KA injection. Both the injected and contralateral hippocampus participated in the status epilepticus. However, neuronal death induced by KA treatment was restricted to the injected hippocampus, although there was some contralateral axonal degeneration. We profiled gene expression changes in dorsal and ventral regions of both the injected and contralateral hippocampus. Changes were detected in the expression of 1526 transcripts in samples from three time-points: (i) during the KA-induced status epilepticus, (ii) at 2 weeks, before recurrent seizures emerged, and (iii) at 6 months after seizures emerged. Grouping genes with similar spatio-temporal changes revealed an early transcriptional response, strong immune, cell death and growth responses at 2 weeks and an activation of immune and extracellular matrix genes persisting at 6 months. Immunostaining for proteins coded by genes identified from array studies provided evidence for gliogenesis and suggested that the proteoglycan biglycan is synthesized by astrocytes and contributes to a glial scar. Gene changes at 6 months after KA injection were largely restricted to tissue from the injection site. This suggests that either recurrent seizures might depend on maintained processes including immune responses and changes in extracellular matrix proteins near the injection site or alternatively might result from processes, such as growth, distant from the injection site and terminated while seizures are maintained.

Generic multiplicity for a scalar field equation on compact surfaces - Francesca De Marchis (Journal of Functional Analysis, 2010)
We prove generic multiplicity of solutions for a scalar field equation on compact surfaces via Morse inequalities. In particular our result improves significantly the multiplicity estimate which can be deduced from the degree-counting formula in Chen and Lin (2003) [12]. Related results are derived for the prescribed Q-curvature equation.
Keywords: Generic multiplicity; Geometric PDE's; Morse inequalities; Scalar field equations

On the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system - Claudio Bartocci; Gregorio Falqui; Igor Mencattini; Giovanni Ortenzi; Marco Pedroni (Int. Math. Res. Not. (2010) 2010:279-296, 2010)
We show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson pair on the cotangent bundle of gl(n,R). The relation with the Lax formalism is also discussed.

The geometry emerging from the symmetries of a quantum system - Giuseppe De Nittis; Gianluca Panati (2010)
We investigate the relation between the symmetries of a quantum system and its topological quantum numbers, in a general C*-algebraic framework. We prove that, under suitable assumptions on the symmetry algebra, there exists a generalization of the Bloch-Floquet transform which induces a direct-integral decomposition of the algebra of observables. Such generalized transform selects uniquely the set of \\\"continuous sections\\\" in the direct integral, thus yielding a Hilbert bundle. The emerging geometric structure provides some topological invariants of the quantum system. Two running examples provide an Ariadne\\\'s thread through the paper. For the sake of completeness, we review two related theorems by von Neumann and Maurin and compare them with our result.

A global compactness result for the p-Laplacian involving critical nonlinearities - Mercuri, Carlo; Willem, Michel (Discrete & Continuous Dynamical Systems-A, 2010)
We prove a representation theorem for Palais-Smale sequences involving the p-Laplacian and critical nonlinearities. Applications are given to a critical problem.

Hamiltonian PDEs: deformations, integrability, solutions - Boris Dubrovin (Journal of Physics A: Mathematical and Theoretical. Volume 43, Issue 43, 29 October 2010, Article number 434002, 2010)
We review recent classification results on the theory of systems of nonlinear\\r\\nHamiltonian partial differential equations with one spatial dimension, including\\r\\na perturbative approach to the integrability theory of such systems, and discuss\\r\\nuniversality conjectures describing critical behaviour of solutions to such\\r\\nsystems.

Hitchin systems, N=2 gauge theories and W-gravity - Giulio Bonelli; Alessandro Tanzini (Phys. Lett. B 691 (2010) 111-115, 2010)
We propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional conformal field theories and N=2 superconformal gauge theories in four dimensions. We find that A_{N-1} Toda field theory is the simplest two-dimensional conformal field theory quantizing the moduli of N M5-branes wrapped on a Riemann surface. This leads us to identify chiral operators of the N=2 gauge theories with W-algebra currents. As a check of this correspondence we study some relevant OPE\\\'s obtaining that Nekrasov\\\'s partition function satisfies W-geometry constraints.

Homogeneous binary trees as ground states of quantum critical Hamiltonians - Pietro Silvi; Vittorio Giovannetti; Simone Montangero; Matteo Rizzi; J. Ignacio Cirac; Rosario Fazio (Phys. Rev. A 81 (2010) 062335, 2010)
Many-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems - Matteo Rizzi; Simone Montangero; Pietro Silvi; Vittorio Giovannetti; Rosario Fazio (New J. Phys. 12 (2010) 075018, 2010)
In this paper, we review the properties of homogeneous multiscale entanglement renormalization ansatz (MERA) to describe quantum critical systems.We discuss in more detail our results for one-dimensional (1D) systems (the Ising and Heisenberg models) and present new data for the 2D Ising model. Together with the results for the critical exponents, we provide a detailed description of the numerical algorithm and a discussion of new optimization\\nstrategies. The relation between the critical properties of the system and the tensor structure of the MERA is expressed using the formalism of quantum channels, which we review and extend.

Homogenization of fiber reinforced brittle material: the intermediate case - Gianni Dal Maso; Caterina Ida Zeppieri (Adv. Calc. Var. 3 (2010) 345-370, 2010)
We derive a cohesive fracture model by homogenizing a periodic composite material whose microstructure is characterized by the presence of brittle inclusions in a reticulated unbreakable elastic structure.

Invariant Lagrange submanifolds of dissipative systems - Andrei A. Agrachev (Russian Mathematical Surveys. Volume 65, Issue 5, 2010, Pages: 977-978, 2010)
We study solutions of modified Hamilton-Jacobi equations H(du/dq,q) + cu(q) =\\r\\n0, q \\\\in M, on a compact manifold M .

A kinetic mechanism inducing oscillations in simple chemical reactions networks - Julien Coatleven; Claudio Altafini (Mathematical Biosciences and Engineering 7(2):301-312, 2010, 2010)
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.

Lorentz Covariant k-Minkowski Spacetime - Ludwik Dabrowski; Michal Godlinski; Gherardo Piacitelli (Phys. Rev. D 81 (2010) 125024, 2010)
In recent years, different views on the interpretation of Lorentz covariance of non commuting coordinates were discussed. Here, by a general procedure, we construct the minimal canonical central covariantisation of the k-Minkowski spacetime. We then show that, though the usual k-Minkowski spacetime is covariant under deformed (or twisted) Lorentz action, the resulting framework is equivalent to taking a non covariant restriction of the covariantised model. We conclude with some general comments on the approach of deformed covariance.

Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks - Giovanni Iacono; Claudio Altafini (BMC Systems Biology 2010, 4:83, 2010)
Background. \\nFor large-scale biological networks represented as signed graphs, the index of frustration measures how far a network is from a monotone system, i.e., how incoherently the system responds to perturbations.\\nResults. \\nIn this paper we find that the frustration is systematically lower in transcriptional networks (modeled at functional level) than in signaling and metabolic networks (modeled at stoichiometric level). A possible interpretation of this result is in terms of energetic cost of an interaction: an erroneous or contradictory transcriptional action costs much more than a signaling/metabolic error, and therefore must be avoided as much as possible. Averaging over all possible perturbations, however, we also find that unlike for transcriptional networks, in the signaling/metabolic networks the probability of finding the system in its least frustrated configuration tends to be high also in correspondence of a moderate energetic regime, meaning that, in spite of the higher frustration, these networks can achieve a globally ordered response to perturbations even for moderate values of the strength of the interactions. Furthermore, an analysis of the energy landscape shows that signaling and metabolic networks lack energetic barriers around their global optima, a property also favouring global order.\\nConclusion. \\nIn conclusion, transcriptional and signaling/metabolic networks appear to have systematic differences in both the index of frustration and the transition to global order. These differences are interpretable in terms of the different functions of the various classes of networks.

Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories - Raoul Santachiara; Alessandro Tanzini (2010)
We identify Moore-Read wavefunctions, describing non-abelian statistics in fractional quantum Hall systems, with the instanton partition of N=2 superconformal quiver gauge theories at suitable values of masses and \\\\Omega-background parameters. This is obtained by extending to rational conformal field theories the SU(2) gauge quiver/Liouville field theory duality recently found by Alday-Gaiotto-Tachikawa. A direct link between the Moore-Read Hall $n$-body wavefunctions and Z_n-equivariant Donaldson polynomials is pointed out.

New approximation results for free discontinuity problems - Flaviana Iurlano (Università degli Studi di Trieste and SISSA, 2010)

Nonlocal character of the reduced theory of thin films with higher order perturbations - Gianni Dal Maso; Irene Fonseca; Giovanni Leoni (Adv. Calc. Var. 3 (2010) 287-319, 2010)

A normal form for generic 2-dimensional almost-Riemannian structures at a tangency point - Ugo Boscain; Grégoire Charlot; Roberta Ghezzi (arXiv preprint arXiv:1008.5036, 2010)

On the number of positive solutions of some semilinear elliptic problems - Antonio Ambrosetti (2010)

Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions - Simonetta Abenda; Tamara Grava; Christian Klein (2010)
The small dispersion limit of solutions to the Camassa-Holm (CH) equation is characterized by the appearance of a zone of rapid modulated oscillations. An asymptotic description of these oscillations is given, for short times, by the one-phase solution to the CH equation, where the branch points of the corresponding elliptic curve depend on the physical coordinates via the Whitham equations. We present a conjecture for the phase of the asymptotic solution. A numerical study of this limit for smooth hump-like initial data provides strong evidence for the validity of this conjecture....

On optimality of c-cyclically monotone transference plans - Stefano Bianchini; Laura Caravenna (Comptes Rendus Mathematique 348 (2010) 613-618, 2010)
Abstract. This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder, applied also to extremality and uniqueness problems. Resume. Dans la presente note nous decrivons brievement la construction introduite dans [7] a propos de l\\\'equivalence entre l\\\'optimalite d\\\'un plan de transport pour le probleme de Monge-Kantorovich et la condition de monotonie c-cyclique ainsi que d\\\'autres sujets que cela nous amene a aborder. Nous souhaitons mettre en evidence l\\\'hypothese de mesurabilite sur la structure sous-jacente de pre-ordre lineaire.

Optimally swimming Stokesian Robots - François Alouges; Antonio DeSimone; Luca Heltai; Aline Lefebvre; Benoit Merlet (2010)
We study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.

Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit - Tom Claeys; Tamara Grava (Comm. Pure Appl. Math. 63 (2010) 203-232, 2010)
In the small dispersion limit, solutions to the Korteweg-de Vries equation develop an interval of fast oscillations after a certain time. We obtain a universal asymptotic expansion for the Korteweg-de Vries solution near the leading edge of the oscillatory zone up to second order corrections. This expansion involves the Hastings-McLeod solution of the Painlev\\\\\\\'e II equation. We prove our results using the Riemann-Hilbert approach.

A Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena - Antonio DeSimone; Livio Fedeli; Turco, Alessandro (IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, 2010)
We discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

Picard group of hypersurfaces in toric varieties - Ugo Bruzzo; Antonella Grassi (2010)
We show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties. This sufficient condition is always satisfied by generic K3 surfaces embedded in Fano toric 3-folds.

Poles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis - Davide Masoero (Nonlinearity. vol. 23, (2010), page 2501-2507, 2010)
Poles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We show that the poles lie near the solutions of a pair of Bohr-Sommerfeld quantization conditions (the Bohr-Sommerfeld-Boutroux system): the distance between a pole and the corresponding solution of the Bohr-Sommerfeld-Boutroux system vanishes asymptotically.

Positive solutions for some non-autonomous Schrödinger–Poisson systems - Giovanna Cerami; Giusi Vaira (Journal of Differential Equations, 2010)

Projective Reeds-Shepp car on $S^2$ with quadratic cost - Ugo Boscain; Francesco Rossi (ESAIM COCV 16 (2010) 275-297, 2010)
Fix two points $x,\\\\bar{x}\\\\in S^2$ and two directions (without orientation) $\\\\eta,\\\\bar\\\\eta$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $$ J[\\\\gamma]=\\\\int_0^T g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t))+\\nK^2_{\\\\gamma(t)}g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t)) ~dt$$ along all smooth curves starting from $x$ with direction $\\\\eta$ and ending in $\\\\bar{x}$ with direction $\\\\bar\\\\eta$. Here $g$ is the standard Riemannian metric on $S^2$ and $K_\\\\gamma$ is the corresponding geodesic curvature.\\nThe interest of this problem comes from mechanics and geometry of vision. It can be formulated as a sub-Riemannian problem on the lens space L(4,1).\\nWe compute the global solution for this problem: an interesting feature is that some optimal geodesics present cusps. The cut locus is a stratification with non trivial topology.

Quantum Spacetime: a Disambiguation - Gherardo Piacitelli (2010)
We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular irreducible component is often referred to as the \\\"canonical quantum spacetime\\\". The aim is to distinguish and compare the approaches under various points of view, including motivations, prescriptions for quantisation, the choice of mathematical objects and concepts, approaches to dynamics and to covariance. Some incorrect statements as \\\"universality of Planck scale conflicts with Lorentz-Fitzgerald contraction and requires a modification of covariance\\\", or \\\"stability of the geometric background requires an absolute lower bound of (\\\\Delta x^\\\\mu)\\\", or \\\"violations of unitarity are due to time/space non-commutativity\\\" are put in context, and discussed.

Quasistatic crack growth in elasto-plastic materials: the two-dimensional case - Gianni Dal Maso; Rodica Toader (Arch. Ration. Mech. Anal. 196 (2010) 867-906, 2010)
We study a variational model for the quasistatic evolution of elasto-plastic materials with cracks in the case of planar small strain associative elasto-plasticity.

Quasistatic crack growth in finite elasticity with non-interpenetration - Gianni Dal Maso; Giuliano Lazzaroni (Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 257-290, 2010)
We present a variational model to study the quasistatic growth of brittle cracks in hyperelastic materials, in the framework of finite elasticity, taking\\ninto account the non-interpenetration condition.

Quasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case - Gianni Dal Maso; Francesco Solombrino (Netw. Heterog. Media 5 (2010) 97-132, 2010)
We study the spatially uniform case of the problem of quasistatic evolution in small strain nonassociative elastoplasticity (Cam-Clay model). Through the introdution of a viscous approximation, the problem reduces to determine the limit behavior of the solutions of a singularly perturbed system of ODE\\\'s in a finite dimensional Banach space. Depending on the sign of two explicit scalar indicators, we see that the limit dynamics presents, under quite generic assumptions, the alternation of three possible regimes: the elastic regime, when the limit equation is just the equation of linearized elasticity, the slow dynamics, when the strain evolves smoothly on the yield surface and plastic flow is produced, and the fast dynamics, which may happen only in the softening regime, where\\nviscous solutions exhibit a jump across a heteroclinic orbit of an auxiliary system.
Keywords: Cam-Clay plasticity

Quasistatic evolution for plasticity with softening: The spatially homogeneous case - Francesco Solombrino (Discrete & Continuous Dynamical Systems - A, 2010)
The spatially uniform case of the problem of quasistatic evolution in small strain associative elastoplasticity with softening is studied. Through the introdution of a viscous approximation, the problem reduces to determine the limit behaviour of the solutions of a singularly perturbed system of ODE's in a finite dimensional Banach space. We see that the limit dynamics presents, for a generic choice of the initial data, the alternation of three possible regimes (elastic regime, slow dynamics, fast dynamics), which is determined by the sign of two scalar indicators, whose explicit expression is given.
Keywords: plasticity with softening; rate independent processes

The reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures - Guido Carlet; Paolo Lorenzoni; Andrea Raimondo (J. Phys. A 43 (2010) 045201, 2010)
We study finite-dimensional reductions of the dispersionless 2D Toda hierarchy showing that the consistency conditions for such reductions are given by a system of radial Loewner equations. We then construct their Hamiltonian structures, following an approach proposed by Ferapontov.

Riemann-Roch theorems and elliptic genus for virtually smooth schemes - Barbara Fantechi; Lothar Göttsche (Geom. Topol. 14 (2010) 83-115, 2010)
For a proper scheme X with a fixed 1-perfect obstruction theory, we define virtual versions of holomorphic Euler characteristic, chi y-genus, and elliptic genus; they are deformation invariant, and extend the usual definition in the smooth case. We prove virtual versions of the Grothendieck-Riemann-Roch and Hirzebruch-Riemann-Roch theorems. We show that the virtual chi y-genus is a polynomial, and use this to define a virtual topological Euler characteristic. We prove that the virtual elliptic genus satisfies a Jacobi modularity property; we state and prove a localization theorem in the toric equivariant case. We show how some of our results apply to moduli spaces of stable sheaves.

The role of membrane viscosity in the dynamics of fluid membranes - Marino Arroyo; Antonio DeSimone; Luca Heltai (2010)
Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3.

Semiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential - Alessandro Selvitella (Adv. Differential Equations, 2010)

On semistable principal bundles over complex projective manifolds, II - Indranil Biswas; Ugo Bruzzo (Geom. Dedicata 146 (2010) 27-41, 2010)
Let (X, \\\\omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero.

Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials - Mouhamed Moustapha Fall; Roberta Musina (2010)
In this paper we deal with nonnegative distributional supersolutions for a class of linear\\nelliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results.

Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity - Marta Lewicka; Maria Giovanna Mora; Mohammad Reza Pakzad (Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295, 2010)
We discuss the limiting behavior (using the notion of gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Karman theory for plates.

Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions - Massimiliano Berti; Philippe Bolle (Archive for Rational Mechanics and Analysis, 2010)
We prove the existence of Cantor families of periodic solutions for nonlinear wave equations in higher spatial dimensions with periodic boundary conditions. We study both forced and autonomous PDEs. In the latter case our theorems generalize previous results of Bourgain to more general nonlinearities of class C k and assuming weaker non-resonance conditions. Our solutions have Sobolev regularity both in time and space. The proofs are based on a differentiable Nash-Moser iteration scheme, where it is sufficient to get estimates of interpolation-type for the inverse linearized operators. Our approach works also in presence of very large "clusters of small divisors". © Springer-Verlag (2009).

Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit - Tamara Grava; Tom Claeys (SIAM J. Math. Anal. 42 (2010) 2132-2154, 2010)
We study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\\\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to sharp pulses near the trailing edge. Locally those pulses resemble soliton solutions of the KdV equation.

A spatial model of cellular molecular trafficking including active transport along microtubules - Andrea Cangiani; Natalini, R. (J. Theoret. Biol., 2010)

Stable determination of an immersed body in a stationary Stokes fluid - Andrea Ballerini (Inverse Problems, 2010)
We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of the stability of log–log type.

Taming open/closed string duality with a Losev trick - Giulio Bonelli; Andrea Prudenziati; Alessandro Tanzini (JHEP 06(2010)063, 2010)
A target space string field theory formulation for open and closed B-model is provided by giving a Batalin-Vilkovisky quantization of the holomorphic Chern-Simons theory with off-shell gravity background. The target space expression for the coefficients of the holomorphic anomaly equation for open strings are obtained. Furthermore, open/closed string duality is proved from a judicious integration over the open string fields. In particular, by restriction to the case of independence on continuous open moduli, the shift formulas of [7] are reproduced and shown therefore to encode the data of a closed string dual.

A three-dimensional model for the dynamics and hydrodynamics of rowing boats - L. Formaggia; Andrea Mola; N Parolini; M Pischiutta (Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, 2010)
This paper proposes a new model describing the dynamics of a rowing boat for general three-dimensional motions. The complex interaction between the different components of the rowers–-oars–-boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action.

A time-dependent perturbative analysis for a quantum particle in a cloud chamber - Gianfausto Dell'Antonio; Rodolfo Figari; Alessandro Teta (Annales Henri Poincare 11 (2010) 539-564, 2010)
We consider a simple model of a cloud chamber consisting of a test particle (the alpha-particle) interacting with two other particles (the atoms of the vapour) subject to attractive potentials centered in $a_1, a_2 \\\\in \\\\mathbb{R}^3$. At time zero the alpha-particle is described by an outgoing spherical wave centered in the origin and the atoms are in their ground state. We show that, under suitable assumptions on the physical parameters of the system and up to second order in perturbation theory, the probability that both atoms are ionized is negligible unless $a_2$ lies on the line joining the origin with $a_1$. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929.

Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model - Gherardo Piacitelli (Comm. Math. Phys. 295 (2010) 701-729, 2010)
We discuss twisted covariance over the noncommutative spacetime algebra generated by the relations [q_theta^mu,q_theta^nu]=i theta^{mu nu}, where the matrix theta is treated as fixed (not a tensor), and we refrain from using the asymptotic Moyal expansion of the twists. We show that the tensor nature of theta is only hidden in the formalism: in particular if theta fulfils the DFR conditions, the twisted Lorentz covariant model of the flat quantum spacetime may be equivalently described in terms of the DFR model, if we agree to discard a huge non invariant set of localisation states; it is only this last step which, if taken as a basic assumption, severely breaks the relativity principle. We also will show that the above mentioned, relativity breaking, ad hoc rejection of localisation states is an independent, unnecessary assumption, as far as some popular approaches to quantum field theory on the quantum Minkowski spacetime are concerned. The above should raise some concerns about speculations on possible observable consequences of arbitrary choices of theta in arbitrarily selected privileged frames.

Two-dimensional almost-Riemannian structures with tangency points - Andrei A. Agrachev; Ugo Boscain; Grégoire Charlot; Roberta Ghezzi; Mario Sigalotti (Ann. Inst. H. Poincare Anal. Non Lineaire, 2010)
Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss-Bonnet formula for almost-Riemannian structures with tangency points.

Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces - Ugo Bruzzo; Dimitri Markushevich; Alexander Tikhomirov (2010)
We construct a compactification $M^{\\\\mu ss}$ of the Uhlenbeck-Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\\\\gamma \\\\colon M^s \\\\to M^{\\\\mu ss}$, where $M^s$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\\\\mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.

Universality in the profile of the semiclassical limit solutions to the focusing nonlinear Schrödinger equation at the first breaking curve - Marco Bertola; Alexander Tovbis (Int. Math. Res. Not. IMRN, 2010)

Well-posed infinite horizon variational problems on a compact manifold - Andrei A. Agrachev (Proceedings of the Steklov Institute of Mathematics. Volume 268, Issue 1, 2010, Pages 17-31, 2010)
We give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e., a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis, we construct an invariant Lagrangian submanifold (well-projected to M) of the flow of extremals in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics

1D periodic potentials with gaps vanishing at k=0 - Alessandro Michelangeli; Osvaldo Zagordi (Mem. Differential Equations Math. Phys. 47 (2009) 133-158, 2009)
Appearance of energy bands and gaps in the dispersion relations of a periodic potential is a standard feature of Quantum Mechanics. We investigate the class of one-dimensional periodic potentials for which all gaps vanish at the center of the Brillouin zone. We characterise themthrough a necessary and sufficient condition. Potentials of the form we focus on arise in different fields of Physics, from supersymmetric Quantum Mechanics, to Korteweg-de Vries equation theory and classical diffusion problems. The O.D.E. counterpart to this problem is the characterisation of periodic potentials for which coexistence occurs of linearly independent solutions of the corresponding Schrödinger equation (Hill\\\'s equation). This result is placed in the perspective of the previous related results available in the literature.

Biological Fluid Dynamics, Non-linear Partial Differential Equations - Antonio DeSimone; François Alouges; Aline Lefebvre (Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554, 2009)

The boundary Riemann solver coming from the real vanishing viscosity approximation - Stefano Bianchini; Laura Spinolo (Arch. Ration. Mech. Anal. 191 (2009) 1-96, 2009)
We study the limit of the hyperbolic-parabolic approximation $$ \\\\begin{array}{lll} v_t + \\\\tilde{A} ( v, \\\\, \\\\varepsilon v_x ) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in R^N\\\\\\\\ \\\\tilde \\\\beta (v (t, \\\\, 0)) = \\\\bar g \\\\\\\\ v (0, \\\\, x) = \\\\bar v_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nThe function $\\\\tilde \\\\beta$ is defined in such a way to guarantee that the initial boundary value problem is well posed even if $\\\\tilde \\\\beta$ is not invertible.\\nThe data $\\\\bar g$ and $\\\\bar v_0$ are constant. When $\\\\tilde B$ is invertible, the previous problem takes the simpler form $$ \\\\left\\\\{ \\\\begin{array}{lll} v_t + \\\\tilde{A} \\\\big( v, \\\\, \\\\varepsilon v_x \\\\big) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in \\\\mathbb{R}^N\\\\\\\\ v (t, \\\\, 0) \\\\equiv \\\\bar v_b \\\\\\\\ v (0, \\\\, x) \\\\equiv \\\\bar{v}_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nAgain, the data $\\\\bar v_b$ and $\\\\bar v_0$ are constant. The conservative case is included in the previous formulations. It is assumed convergence of the v, smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $\\\\tilde A$ can be 0.\\n Second, as pointed out before we take into account the possibility that $\\\\tilde B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.

Bubbles with prescribed mean curvature: the variational approach - Paolo Caldiroli; Roberta Musina (2009)

The Cauchy two–matrix model - Marco Bertola; M Gekhtman; J Szmigielski (Comm. Math. Phys., 2009)

Characterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity - Frederic D. Broccard; Silvia Pegoraro; Maria Elisabetta Ruaro; Claudio Altafini; Vincent Torre (BMC Research Notes (2009) 2:13, 2009)
BACKGROUND: Neuronal plasticity is initiated by transient elevations of neuronal networks activity leading to changes of synaptic properties and providing the basis for memory and learning 1. An increase of electrical activity can be caused by electrical stimulation 2 or by pharmacological manipulations: elevation of extracellular K+ 3, blockage of inhibitory pathways 4 or by an increase of second messengers intracellular concentrations 5. Neuronal plasticity is mediated by several biochemical pathways leading to the modulation of synaptic strength, density of ionic channels and morphological changes of neuronal arborisation 6. On a time scale of a few minutes, neuronal plasticity is mediated by local protein trafficking 7 while, in order to sustain modifications beyond 2-3 h, changes of gene expression are required 8. FINDINGS: In the present manuscript we analysed the time course of changes of the evoked electrical activity during neuronal plasticity and we correlated it with a transcriptional analysis of the underlying changes of gene expression. Our investigation shows that treatment for 30 min. with the GABAA receptor antagonist gabazine (GabT) causes a potentiation of the evoked electrical activity occurring 2-4 hours after GabT and the concomitant up-regulation of 342 genes. Inhibition of the ERK1/2 pathway reduced but did not abolish the potentiation of the evoked response caused by GabT. In fact not all the genes analysed were blocked by ERK1/2 inhibitors. CONCLUSION: These results are in agreement with the notion that neuronal plasticity is mediated by several distinct pathways working in unison.

Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights - Marco Bertola; Mo, M. Y. (Adv. Math., 2009)

A connection between viscous profiles and singular ODEs - Stefano Bianchini; Laura Spinolo (Rend. Istit. Mat. Univ. Trieste 41 (2009) 35-41, 2009)

Controllability and simultaneous controllability of isospectral bilinear control systems on complex flag manifolds - Claudio Altafini (Systems Control Lett. 58 (2009) 213-216, 2009)
For isospectral bilinear control systems evolving on the so-called complex flag manifolds (i.e., on the orbits of the Hermitian matrices under unitary conjugation action) it is shown that controllability is almost always verified. Easy and generic sufficient conditions are provided. The result applies to the problem of density operator controllability of finite dimensional quantum mechanical systems. In addition, we show that systems having different drifts (corresponding for example to different Larmor frequencies) are simultaneously controllable by the same control field.

Controllability of the discrete-spectrum Schrodinger equation driven by an external field - Thomas Chambrion; Paolo Mason; Mario Sigalotti; Ugo Boscain (Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349, 2009)
We prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials.

Controllability on the group of diffeomorphisms - Andrei A. Agrachev; Marco Caponigro (Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 2503-2509, 2009)
Given a compact manifold M, we prove that any bracket generating family of vector fields on M, which is invariant under multiplication by smooth functions, generates the connected component of identity of the group of diffeomorphisms of M.

Convergence analysis of the mimetic finite difference method for elliptic problems - Andrea Cangiani; Manzini, Gianmarco; Russo, Alessandro (SIAM J. Numer. Anal., 2009)

On the convergence of viscous approximations after shock interactions - Alberto Bressan; Carlotta Donadello (Discrete Contin. Dyn. Syst. 23 (2009) 29-48, 2009)
We consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient.

Cubic string boundary value problems and Cauchy biorthogonal polynomials - Marco Bertola; Gekhtman, M.; Szmigielski, J. (J. Phys. A, 2009)

Decoupling A and B model in open string theory: topological adventures in the world of tadpoles - Giulio Bonelli; Andrea Prudenziati; Alessandro Tanzini; Yang Jie (JHEP 06 (2009) 046, 2009)
In this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the worldsheet then guarantees the decoupling at all loops. The holomorphic anomaly equations for open topological strings at one loop are also obtained and compared with the results of the Quillen formula.

Differential geometry of curves in Lagrange Grassmannians with given Young diagram - Igor Zelenko; Li Chengbo (Differential Geom. Appl. 27 (2009) 723-742, 2009)
Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure. The Pontryagin extremals of this optimal problem are integral curves of certain Hamiltonian system in the cotangent bundle. The dynamics of the fibers of the cotangent bundle w.r.t. this system along an extremal is described by certain curve in a Lagrange Grassmannian, called Jacobi curve of the extremal. Any symplectic invariant of the Jacobi curves produces the invariant of the original geometric structure. The basic characteristic of a curve in a Lagrange Grassmannian is its Young diagram. The number of boxes in its kth column is equal to the rank of the kth derivative of the curve (which is an appropriately defined linear mapping) at a generic point. We will describe the construction of the complete system of symplectic invariants for parameterized curves in a Lagrange Grassmannian with given Young diagram. It allows to develop in a unified way local differential geometry of very wide classes of geometric structures on manifolds, including both classical geometric structures such as Riemannian and Finslerian structures and less classical ones such as sub-Riemannian and sub-Finslerian structures, defined on nonholonomic distributions.

Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers - Marco Cicalese; Antonio DeSimone; Caterina Ida Zeppieri (Netw. Heterog. Media 4 (2009) 667-708, 2009)
In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields.

The Disintegration Theorem and Applications to Optimal Mass Transportation - Laura Caravenna (SISSA, 2009)

Equivariant cohomology and localization for Lie algebroids - Ugo Bruzzo; Lucio Cirio; Paolo Rossi; Vladimir Rubtsov (Funct. Anal. Appl. 43 (2009) 18-29, 2009)
Let M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related localization formula. As an application we prove a Bott-type formula.

ERNEST: a toolbox for chemical reaction network theory - Nicola Soranzo; Claudio Altafini (Bioinformatics 25 (2009) 2853-2854, 2009)
Summary: ERNEST Reaction Network Equilibria Study Toolbox is a MATLAB package which, by checking various different criteria on the structure of a chemical reaction network, can exclude the multistationarity of the corresponding reaction system. The results obtained are independent of the rate constants of the reactions, and can be used for model discrimination.\\nAvailability and Implementation: The software, implemented in MATLAB, is available under the GNU GPL free software license from http://people.sissa.it/~altafini/papers/SoAl09/. It requires the MATLAB Optimization Toolbox.

Exact results for topological strings on resolved Yp,q singularities - Andrea Brini; Alessandro Tanzini (Comm. Math. Phys. 289 (2009) 205-252, 2009)

Existence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities - Roberta Musina (Nonlinear Anal. 70 (2009) 3002-3007, 2009)
This paper deals with some Sobolev-type inequalities with weights that were proved by Maz\\\'ya in 1980 and by Caffarelli-Kohn-Nirenberg in 1984.

An existence result for the Monge problem in R^n with norm cost - Laura Caravenna (2009)

On the extremality, uniqueness and optimality of transference plans - Stefano Bianchini; Laura Caravenna (Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458, 2009)
We consider the following standard problems appearing in optimal mass transportation theory: when a transference plan is extremal; when a transference plan is the unique transference plan concentrated on a set A,; when a transference plan is optimal.

Families of Monads and Instantons from a Noncommutative ADHM Construction - Simon Brain; Giovanni Landi (2009)
We give a \\\\theta-deformed version of the ADHM construction of SU(2) instantons with arbitrary topological charge on the sphere S^4. Classically the instanton gauge fields are constructed from suitable monad data; we show that in the deformed case the set of monads is itself a noncommutative space. We use these monads to construct noncommutative `families\\\' of SU(2) instantons on the deformed sphere S^4_\\\\theta. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent.

First colonization of a spectral outpost in random matrix theory - Marco Bertola; Lee, S. Y. (Constr. Approx., 2009)

Foliations of small tubes in Riemannian manifolds by capillary minimal discs - Fall, Mouhamed Moustapha; Mercuri, Carlo (Nonlinear Analysis: Theory, Methods & Applications, 2009)
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font-size: 18px;"><span id="MathJax-Element-3-Frame" class="MathJax_SVG" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" data-mathml="Γ"><span class="MJX_Assistive_MathML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px 0px !important; top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); user-select: none; position: absolute !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important; transition: none 0s ease 0s;">Γ<span style="color: #2e2e2e; font-family: NexusSerif, Georgia, 'Times New Roman', Times, STIXGeneral, 'Cambria Math', 'Lucida Sans Unicode', 'Microsoft Sans Serif', 'Segoe UI Symbol', 'Arial Unicode MS', serif; font-size: 18px;">inside the surface of revolution of <span class="math" style="box-sizing: border-box; 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font-family: NexusSerif, Georgia, 'Times New Roman', Times, STIXGeneral, 'Cambria Math', 'Lucida Sans Unicode', 'Microsoft Sans Serif', 'Segoe UI Symbol', 'Arial Unicode MS', serif; font-size: 18px;"> around <span class="math" style="box-sizing: border-box; margin: 0px; padding: 0px; color: #2e2e2e; font-family: NexusSerif, Georgia, 'Times New Roman', Times, STIXGeneral, 'Cambria Math', 'Lucida Sans Unicode', 'Microsoft Sans Serif', 'Segoe UI Symbol', 'Arial Unicode MS', serif; font-size: 18px;"><span id="MathJax-Element-5-Frame" class="MathJax_SVG" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" data-mathml="Γ"><span class="MJX_Assistive_MathML" style="box-sizing: border-box; margin: 0px; padding: 1px 0px 0px !important; top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); user-select: none; position: absolute !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important; transition: none 0s ease 0s;">Γ<span style="color: #2e2e2e; font-family: NexusSerif, Georgia, 'Times New Roman', Times, STIXGeneral, 'Cambria Math', 'Lucida Sans Unicode', 'Microsoft Sans Serif', 'Segoe UI Symbol', 'Arial Unicode MS', serif; font-size: 18px;">, having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs.

Gauged Laplacians on quantum Hopf bundles - Giovanni Landi; Cesare Reina; Alessandro Zampini (Comm. Math. Phys. 287 (2009) 179-209, 2009)
We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe `excitations moving on the quantum sphere\\\' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.

Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions - Boris Dubrovin (New Trends in Mathematical Physics : Selected contributions of the XVth International Congress on Mathematical Physics, Springer Netherlands, 2009, pp. 231-276., 2009)
We begin with presentation of classi cation results in the theory of Hamiltonian\\r\\nPDEs with one spatial dimension depending on a small parameter. Special\\r\\nattention is paid to the deformation theory of integrable hierarchies, including an\\r\\nimportant subclass of the so-called integrable hierarchies of the topological type\\r\\nassociated with semisimple Frobenius manifolds. Many well known equations of\\r\\nmathematical physics, such as KdV, NLS, Toda, Boussinesq etc., belong to this\\r\\nsubclass, but there are many new integrable PDEs, some of them being of interest\\r\\nfor applications. Connections with the theory of Gromov{Witten invariants\\r\\nand random matrices are outlined. We then address the problem of comparative\\r\\nstudy of singularities of solutions to the systems of first order quasilinear\\r\\nPDEs and their Hamiltonian perturbations containing higher derivatives. We\\r\\nformulate Universality Conjectures describing different types of critical behavior\\r\\nof perturbed solutions near the point of gradient catastrophe of the unperturbed\\r\\none.

Hardy-Sobolev-Maz\\\'ja inequalities: symmetry and breaking symmetry of extremal functions - Marita Gazzini; Roberta Musina (Commun. Contemp. Math. 11 (2009) 993-1007, 2009)

A higher order model for image restoration: the one dimensional case - Gianni Dal Maso; Irene Fonseca; Giovanni Leoni; Massimiliano Morini (SIAM J. Math. Anal. 40 (2009) 2351-2391, 2009)
The higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals.

Holomorphic equivariant cohomology of Atiyah algebroids and localization - Ugo Bruzzo; Vladimir Rubtsov (2009)

Homogenization of fiber reinforced brittle materials: the extremal cases - Marco Barchiesi; Gianni Dal Maso (SIAM J. Math. Anal. 41 (2009) 1874-1889, 2009)
We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period $\\\\varepsilon$ of the grid and the ratio $\\\\delta$ between the thickness of the fibers and the period $\\\\varepsilon$. We show that the asymptotic behavior as $\\\\varepsilon\\\\to0^+$ and $\\\\delta\\\\to0^+$ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., $\\\\varepsilon\\\\ll\\\\delta$ and $\\\\varepsilon\\\\gg\\\\delta$, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively.

Initial value problem of the Whitham equations for the Camassa-Holm equation - Tamara Grava; Virgil U. Pierce; Fei-Ran Tian (Physica D 238 (2009) 55-66, 2009)
We study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the initial value problem of the Whitham equations. When the initial values are given by a step function, the Whitham solution is self-similar. When the initial values are given by a smooth function, the Whitham solution exists within a cusp in the x-t plane. On the boundary of the cusp, the Whitham equation matches the Burgers solution, which exists outside the cusp.

The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups - Andrei A. Agrachev; Ugo Boscain; Jean-Paul Gauthier; Francesco Rossi (J. Funct. Anal. 256 (2009) 2621-2655, 2009)
We present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp\\\'s volume form introduced by Montgomery. This definition generalizes the one of the Laplace-Beltrami operator in Riemannian geometry. In the case of left-invariant problems on unimodular Lie groups we prove that it coincides with the usual sum of squares.\\nWe then extend a method (first used by Hulanicki on the Heisenberg group) to compute explicitly the kernel of the hypoelliptic heat equation on any unimodular Lie group of type I. The main tool is the noncommutative Fourier transform. We then study some relevant cases: SU(2), SO(3), SL(2) (with the metrics inherited by the Killing form), and the group SE(2) of rototranslations of the plane.\\nOur study is motivated by some recent results about the cut and conjugate loci on these sub-Riemannian manifolds. The perspective is to understand how singularities of the sub-Riemannian distance reflect on the kernel of the corresponding hypoelliptic heat equation.

Investigating the Conformational Stability of Prion Strains through a Kinetic Replication Model - Mattia Zampieri; Giuseppe Legname; Claudio Altafini (PLoS Comput Biol 2009;5(7): e1000420, 2009)
Prion proteins are known to misfold into a range of different aggregated forms, showing different phenotypic and pathological states. Understanding strain specificities is an important problem in the field of prion disease. Little is known about which PrPSc structural properties and molecular mechanisms determine prion replication, disease progression and strain phenotype. The aim of this work is to investigate, through a mathematical model, how the structural stability of different aggregated forms can influence the kinetics of prion replication. The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage. A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows). The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils\\\' mean length) and is coherent with all experimental observations concerning strain-specific behavior.

Jacobi Equations and Comparison Theorems for Corank 1 Sub-Riemannian structures with symmetries - Li Chengbo; Igor Zelenko (2009)
The Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about the solutions of the Jacobi equations along this extremal. In our previous works we constructed the canonical\\nbundle of moving frames and the complete system of symplectic invariants, called curvature maps, for\\nparametrized curves in Lagrange Grassmannians satisfying very general assumptions. The structural\\nequation for a canonical moving frame of the Jacobi curve of an extremal can be interpreted as the\\nnormal form for the Jacobi equation along this extremal and the curvature maps can be seen as the\\n\\\"coefficients\\\"of this normal form. In the case of a Riemannian metric there is only one curvature map and it is naturally related to the Riemannian sectional curvature. In the present paper we study the curvature maps for a sub-Riemannian structure on a corank 1 distribution having an additional transversal infinitesimal symmetry. After the factorization by the integral foliation of this symmetry, such sub-Riemannian structure can be reduced to a Riemannian manifold equipped with a closed 2-form(a magnetic field). We obtain explicit expressions for the curvature maps of the original sub-Riemannian structure in terms of the curvature tensor of this Riemannian manifold and the magnetic field. We also estimate the number of conjugate points along the sub-Riemannian extremals in terms of the bounds for the curvature tensor of this Riemannian manifold and the magnetic field in the case of an uniform magnetic field. The language developed for the calculation of the curvature maps can be applied to more general sub-Riemannian structures with symmetries, including sub-Riemmannian structures appearing naturally in Yang-Mills fields.

Low-Frequency Variations of Force Coefficients on Square Cylinders with Sharp and Rounded Corners - Andrea Mola; Giancarlo Bordonaro; Muhammad R. Hajj (Journal of Structural Engineering, 2009)

Mesoscopic colonization in a spectral band - Marco Bertola; Lee, S. Y.; Mo, M. Y. (J. Phys. A, 2009)

Minimal disc-type surfaces embedded in a perturbed cylinder - Fall, Mouhamed Moustapha; Mercuri, Carlo (Differential and Integral Equations, 2009)
In the present note we deal with small perturbations of an infinite cylinder in the 3D euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration.

A model for the dynamics of rowing boats - L. Formaggia; Edie Miglio; Andrea Mola; Antonio Montano (International Journal for Numerical Methods in Fluids, 2009)

A model for the orbifold Chow ring of weighted projective spaces - Samuel Boissiere; Etienne Mann; Fabio Perroni (Comm. Algebra 37 (2009) 503-514, 2009)
We construct an isomorphism of graded Frobenius algebras between the orbifold Chow ring of weighted projective spaces and graded algebras of groups of roots of the unity.

Moment determinants as isomonodromic tau functions - Marco Bertola (Nonlinearity, 2009)

mRNA stability and the unfolding of gene expression in the long-period yeast metabolic cycle - Nicola Soranzo; Mattia Zampieri; Lorenzo Farina; Claudio Altafini (BMC Systems Biology (2009) 3:18, 2009)
Background: In yeast, genome-wide periodic patterns associated with energy-metabolic oscillations have been shown recently for both short (approx. 40 min) and long (approx. 300 min) periods.\\nResults: The dynamical regulation due to mRNA stability is found to be an important aspect of the genome-wide coordination of the long-period yeast metabolic cycle. It is shown that for periodic genes, arranged in classes according either to expression profile or to function, the pulses of mRNA abundance have phase and width which are directly proportional to the corresponding turnover rates.\\nConclusion: The cascade of events occurring during the yeast metabolic cycle (and their correlation with mRNA turnover) reflects to a large extent the gene expression program observable in other dynamical contexts such as the response to stresses/stimuli.

A nonlinear theory for shells with slowly varying thickness - Marta Lewicka; Maria Giovanna Mora; Mohammad Reza Pakzad (C. R. Math. 347 (2009) 211-216, 2009)
We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.

A note on the paper \\\"Optimizing improved Hardy inequalities\\\" by S. Filippas and A. Tertikas - Roberta Musina (J. Funct. Anal. 256 (2009) 2741-2745, 2009)

Optimal transportation under nonholonomic constraints - Andrei A. Agrachev; Paul Lee (Trans. Amer. Math. Soc. 361 (2009) 6019-6047, 2009)
We study the Monge\\\'s optimal transportation problem where the cost is given by optimal control cost. We prove the existence and uniqueness of optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures and most importantly the absent of sharp abnormal minimizers. In particular, this result is applicable in the case of subriemannian manifolds with a 2-generating distribution and cost given by d2, where d is the subriemannian distance. Also, we discuss some properties of the optimal plan when abnormal minimizers are present. Finally, we consider some examples of displacement interpolation in the case of Grushin plane.

The partition function of the two-matrix model as an isomonodromic τ function - Marco Bertola; Marchal, O. (J. Math. Phys., 2009)

Quasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions - Gianni Dal Maso; Antonio DeSimone (Math. Models Methods Appl. Sci. 19 (2009) 1643-1711, 2009)
We study a quasistatic evolution problem for Cam-Clay plasticity under a special loading program which leads to spatially homogeneous solutions. Under some initial conditions, the solutions exhibit a softening behaviour and time discontinuities.\\nThe behavior of the solutions at the jump times is studied by a viscous approximation.

Quasistatic evolution problems for nonhomogeneous elastic plastic materials - Francesco Solombrino (J. Convex Anal., 2009)
The paper studies the quasistatic evolution for elastoplastic materials when the yield surface depends on the position in the reference configuration. The main results are obtained when the yield surface is continuous with respect to the space variable. The case of piecewise constant dependence is also considered. The evolution is studied in the framework of the variational formulation for rate independent problems developed by Mielke. The results are proved by adapting the arguments introduced for a constant yield surface, using some properties of convex valued semicontinuous multifunctions. A strong formulation of the problem is also obtained, which includes a pointwise version of the plastic flow rule. Some examples are considered, which show that strain concentration may occur as a consequence of a nonconstant yield surface.

Regularity of a vector potential problem and its spectral curve - Ferenc Balogh; Marco Bertola (J. Approx. Theory, 2009)

Relaxation dynamics of fluid membranes - Marino Arroyo; Antonio DeSimone (Phys. Rev. E 79 (2009) 031915, 2009)
We study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest.

On a Sobolev type inequality related to the weighted p-Laplace operator - Marita Gazzini; Roberta Musina (J. Math. Anal. Appl. 352 (2009) 99-111, 2009)

Solutions of the Schrödinger–Poisson problem concentrating on spheres, part I: necessary conditions - Ianni, Isabella; Giusi Vaira (Mathematical Models and Methods in Applied Sciences, 2009)
In this paper we study a coupled nonlinear Schrödinger–Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schrödinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

Some new entire solutions of semilinear elliptic equations on Rn - Andrea Malchiodi (Adv. Math. 221 (2009) 1843-1909, 2009)

Strain-order coupling in nematic elastomers: equilibrium configurations - Pierluigi Cesana; Antonio DeSimone (Math. Models Methods Appl. Sci. 19 (2009) 601-630, 2009)
We consider models that describe liquid crystal elastomers either in a biaxial or in a uniaxial phase and in the framework of Frank\\\'s director theory. We prove existence of static equilibrium solutions in the presence of frustrations due to electro-mechanical boundary conditions and to applied loads and fields. We find explicit solutions arising in connection with special boundary conditions and the corresponding phase diagrams, leading to significant implications on possible experimental observations.

Stratos: a code for 3D free surface flows with floating constraints - Antonio DeSimone; B. Bianchi; Luca Heltai (2009)
This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers......

Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II - Antonio DeSimone; Luca Heltai; Cataldo Manigrasso (2009)
The deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations.

Topological branes, p-algebras and generalized Nahm equations - Giulio Bonelli; Alessandro Tanzini; Maxim Zabzine (Phys. Lett. B 672 (2009) 390-395, 2009)
Inspired by the recent advances in multiple M2-brane theory, we consider the generalizations of Nahm equations for arbitrary p-algebras. We construct the topological p-algebra quantum mechanics associated to them and we show that this can be obtained as a truncation of the topological p-brane theory previously studied by the authors. The resulting topological p-algebra quantum mechanics is discussed in detail and the relation with the M2-M5 system is pointed out in the p=3 case, providing a geometrical argument for the emergence of the 3-algebra structure in the Bagger-Lambert-Gustavsson theory

Topological expansion for the Cauchy two-matrix model - Marco Bertola; Ferrer, A. Prats (J. Phys. A, 2009)

Twisted Covariance vs Weyl Quantisation - Gherardo Piacitelli (2009)
In this letter we wish to clarify in which sense the tensor nature of the commutation relations [x^mu,x^nu]=i theta ^{mu nu} underlying Minkowski spacetime quantisation cannot be suppressed even in the twisted approach to Lorentz covariance. We then address the vexata quaestio \\\"why theta\\\"?

On universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the \\\\it tritronquée solution to the Painlevé-I equation - Boris Dubrovin; Tamara Grava; Christian Klein (J. Nonlinear Sci. 19 (2009) 57-94, 2009)
We argue that the critical behaviour near the point of ``gradient catastrophe\\\" of the solution to the Cauchy problem for the focusing nonlinear Schr\\\\\\\"odinger equation $ i\\\\epsilon \\\\psi_t +\\\\frac{\\\\epsilon^2}2\\\\psi_{xx}+ |\\\\psi|^2 \\\\psi =0$ with analytic initial data of the form $\\\\psi(x,0;\\\\epsilon) =A(x) e^{\\\\frac{i}{\\\\epsilon} S(x)}$ is approximately described by a particular solution to the Painlev\\\\\\\'e-I equation.

Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach - Tamara Grava; Tom Claeys (Comm. Math. Phys. 286 (2009) 979-1009, 2009)
We obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation in the small dispersion limit near the point of gradient catastrophe (x_c,t_c) for the solution of the dispersionless equation.\\nThe sub-leading term in this expansion is described by the smooth solution of a fourth order ODE, which is a higher order analogue to the Painleve I equation. This is in accordance with a conjecture of Dubrovin, suggesting that this is a universal phenomenon for any Hamiltonian perturbation of a hyperbolic equation. Using the Deift/Zhou steepest descent method applied on the Riemann-Hilbert problem for the KdV equation, we are able to prove the asymptotic expansion rigorously in a double scaling limit.

A variational model for quasistatic crack growth in nonlinear elasticity: some qualitative properties of the solutions - Gianni Dal Maso; Alessandro Giacomini; Marcello Ponsiglione (Boll. Unione Mat. Ital. (9) 2 (2009) 371-390, 2009)

On viscosity solutions of Hamilton-Jacobi equations - Sandro Zagatti (Trans. Amer. Math. Soc. 361 (2009) 41-59, 2009)
We consider the Dirichlet problem for Hamilton-Jacobi equations and prove existence, uniqueness and continuous dependence on boundary data of Lipschitz continuous maximal viscosity solutions.

Asymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields - Alessandro Selvitella (Journal of Differential Equations, 2008)
In this paper we study the semiclassical limit for the solutions of a subcritical focusing NLS with electric and magnetic potentials. We consider in particular the Cauchy problem for initial data close to solitons and show that, when the Planck constant goes to zero, the motion shadows that of a classical particle. Several works were devoted to the case of standing waves: differently from these we show that, in the dynamic version, the Lorentz force appears crucially.

Cantor families of periodic solutions for completely resonant wave equations - Massimiliano Berti; Philippe Bolle (Frontiers of Mathematics in China, 2008)
We present recent existence results of Cantor families of small amplitude periodic solutions for completely resonant nonlinear wave equations. The proofs rely on the Nash-Moser implicit function theory and variational methods. © 2008 Higher Education Press.

Cantor families of periodic solutions for wave equations via a variational principle - Massimiliano Berti; Philippe Bolle (Advances in Mathematics, 2008)
We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation-variational in nature-defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to "small divisors" phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical "Arnold non-degeneracy condition" of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities. © 2007 Elsevier Inc. All rights reserved.

Cantor families of periodic solutions of wave equations with C k nonlinearities - Massimiliano Berti; Philippe Bolle (Nonlinear Differential Equations and Applications, 2008)
We prove bifurcation of Cantor families of periodic solutions for wave equations with nonlinearities of class C k . It requires a modified Nash-Moser iteration scheme with interpolation estimates for the inverse of the linearized operators and for the composition operators. © 2008 Birkhaueser.

Concentrating solutions of some singularly perturbed elliptic equations - Andrea Malchiodi (Front. Math. China 3 (2008) 239-252, 2008)
We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry.

On concentration of positive bound states for the Schrödinger-Poisson problem with potentials - Ianni, Isabella; Giusi Vaira (Advanced nonlinear studies, 2008)
We study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

Convergence of equilibria of three-dimensional thin elastic beams - Maria Giovanna Mora; Stefan Müller (Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896, 2008)
A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and Müller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument.

Decomposition results for functions with bounded variation - Gianni Dal Maso; Rodica Toader (Boll. Unione Mat. Ital. (9) 1 (2008) 497-505, 2008)

Discerning static and causal interactions in genome-wide reverse engineering problems - Mattia Zampieri; Nicola Soranzo; Claudio Altafini (Bioinformatics 24 (2008) 1510-1515, 2008)
Background. In the past years devicing methods for discovering gene regulatory mechanisms at a genome-wide level has become a fundamental topic in the field of system biology. The aim is to infer gene-gene interactions in a more sophisticated and reliable way through the continuously improvement of reverse engineering algorithms exploiting microarray technologies. Motivation. This work is inspired by the several studies suggesting that co-expression is mostly related to \\\"static\\\" stable binding relationships, like belonging to the same protein complex, rather than other types of interactions more of a \\\"causal\\\" and transient nature (metabolic pathway or transcription factor-binding site interaction). Discerning static relationships from causal ones on the basis of their characteristic regulatory structures and in particular identifing \\\"dense modules\\\" with protein complex, and \\\"sparse modules\\\" with causal interactions such as those between transcription factor and corresponding binding site, the performances of different network inference algorithms in artificial and real networks (derived from E.coli and S.cerevisiae) can be tested and compared. Results. Our study shows that methods that try to prune indirect interactions from the inferred gene networks may fail to retrieve genes co-participating in a protein complex. On the other hand they are more robust in the identification of transcription factor-binding sites dependences when multiple transcription factors regulate the expression of the same gene. In the end we confirm the stronger co-expression regarding genes belonging to a protein complex than transcription factor-binding site, according, also, to the effect of multiple transcription factors and a low expression variance.

Entire solutions of autonomous equations on Rn with nontrivial asymptotics - Andrea Malchiodi (Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72, 2008)
We prove existence of a new type of solutions for the semilinear equation $- \\\\D u + u = u^p$ on $\\\\R^n$, with $1 < p < \\\\frac{n+2}{n-2}$. These solutions are positive, bounded, decay exponentially to zero away from three half-lines with a common origin, and at infinity are asymptotically periodic.

An entropy based Glimm-type functional - Laura Caravenna (J. Hyperbolic Differ. Equ. 5 (2008) 643-662, 2008)

Equivalent definitions of asymptotic 100% B.E.C. - Alessandro Michelangeli (Nuovo Cimento B 123 (2008) 181-192, 2008)
In the mathematical analysis Bose-Einstein condensates, in particular in the study of the quantum dynamics, some kind of factorisation property has been recently proposed as a convenient technical assumption of condensation. After having surveyed both the standard definition of complete Bose-Einstein condensation in the limit of infinitely many particles and some forms of asymptotic factorisation, we prove that these characterisations are equivalent.

Eulerian calculus for the displacement convexity in the Wasserstein distance - Sara Daneri; Giuseppe Savarè (SIAM J. Math. Anal. 40 (2008) 1104-1122, 2008)
In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space.

Existence of conformal metrics with constant $Q$-curvature - Zindine Djadli; Andrea Malchiodi (Ann. of Math. 168 (2008) 813-858, 2008)
Given a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author.

Fluid–structure interaction problems in free surface flows: Application to boat dynamics - L. Formaggia; Edie Miglio; Andrea Mola; N Parolini (International Journal for Numerical Methods in Fluids, 2008)

Flux reconstruction and solution post-processing in mimetic finite difference methods - Andrea Cangiani; Manzini, Gianmarco (Comput. Methods Appl. Mech. Engrg., 2008)

Forced Vibrations of a Nonhomogeneous String - P Baldi; Massimiliano Berti (SIAM J. Math. Anal. 40 (2008) 382-412, 2008)
We prove existence of vibrations of a nonhomogeneous string under a nonlinear time periodic forcing term in the case in which the forcing frequency avoids resonances with the vibration modes of the string (nonresonant case). The proof relies on a Lyapunov-Schmidt reduction and a Nash-Moser iteration scheme.

Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures - Boris Dubrovin; Liu Si-Qi; Zhang Youjin (Adv. Math. 219 (2008) 780-837, 2008)
The Drinfeld - Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete set of invariants of the related bihamiltonian structures with respect to the group of Miura type transformations.

Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices - Matteo Rizzi; Marco Polini; Miguel A. Cazalilla; M.R. Bakhtiari; Mario P. Tosi; Rosario Fazio (Phys. Rev. B 77 (2008) 245105, 2008)
Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.

A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds - Andrei A. Agrachev; Ugo Boscain; Mario Sigalotti (Discrete Contin. Dyn. Syst. 20 (2008) 801-822, 2008)
We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$. If $X$ and $Y$ are everywhere linearly independent, then they define a classical Riemannian metric on $M$ (the metric for which they are orthonormal) and they give to $M$ the structure of metric space. If $X$ and $Y$ become linearly dependent somewhere on $M$, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. They are special cases of rank-varying sub-Riemannian structures, which are naturally defined in terms of submodules of the space of smooth vector fields on $M$. Almost-Riemannian structures show interesting phenomena, in particular for what concerns the relation between curvature, presence of conjugate points, and topology of the manifold. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula.

Globally stable quasistatic evolution in plasticity with softening - Gianni Dal Maso; Antonio DeSimone; Maria Giovanna Mora; Massimiliano Morini (Netw. Heterog. Media 3 (2008) 567-614, 2008)
We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.

Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics - Gianni Dal Maso; Adriana Garroni (Calc. Var. Partial Differential Equations 31 (2008) 137-145, 2008)
In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem.

Hamiltonian partial differential equations and Frobenius manifolds - Boris Dubrovin (Russian Mathematical Surveys. Volume 63, Issue 6, 2008, Pages 999-1010, 2008)
In the first part of this paper the theory of Frobenius manifolds\\r\\nis applied to the problem of classification of Hamiltonian systems of partial\\r\\ndifferential equations depending on a small parameter. Also developed is\\r\\na deformation theory of integrable hierarchies including the subclass of\\r\\nintegrable hierarchies of topological type. Many well-known examples\\r\\nof integrable hierarchies, such as the Korteweg–de Vries, non-linear\\r\\nSchr¨odinger, Toda, Boussinesq equations, and so on, belong to this\\r\\nsubclass that also contains new integrable hierarchies. Some of these new\\r\\nintegrable hierarchies may be important for applications. Properties of the\\r\\nsolutions to these equations are studied in the second part. Consideration\\r\\nis given to the comparative study of the local properties of perturbed and\\r\\nunperturbed solutions near a point of gradient catastrophe. A Universality\\r\\nConjecture is formulated describing the various types of critical behaviour\\r\\nof solutions to perturbed Hamiltonian systems near the point of gradient\\r\\ncatastrophe of the unperturbed solution.

Harish-Chandra integrals as nilpotent integrals - Marco Bertola; Ferrer, Aleix Prats (Int. Math. Res. Not. IMRN, 2008)

Instanton counting on Hirzebruch surfaces - Ugo Bruzzo; Rubik Poghossian; Alessandro Tanzini (2008)
We perform a study of the moduli space of framed torsion free sheaves on Hirzebruch surfaces by using localization techniques. After discussing general properties of this moduli space, we classify its fixed points under the appropriate toric action and compute its Poincare\\\' polynomial. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on Hirzebruch surfaces, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.

Invariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces - Ugo Boscain; Francesco Rossi (SIAM J. Control Optim. 47 (2008) 1851-1878, 2008)
In this paper we study the invariant Carnot-Caratheodory metrics on SU(2) \\\' S3,\\nSO(3) and SL(2) induced by their Cartan decomposition. Beside computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the Carnot-Caratheodory distance as the inverse of an elementary function. We then prove that the metric\\ngiven on SU(2) projects on the so called Lens Spaces L(p; q). Also for Lens Spaces, we compute\\nthe cut loci (globally).

Invariant Manifolds for Viscous Profiles of a Class of Mixed Hyperbolic-Parabolic Systems - Stefano Bianchini; Laura Spinolo (2008)

The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere - Francesco D'Andrea; Ludwik Dabrowski; Giovanni Landi (Comm. Math. Phys. 279 (2008) 77-116, 2008)
Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the quantum Euclidean 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one of the spin structure of the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an `instanton\\\' projection. A real structure which satisfies all required properties modulo a suitable ideal of `infinitesimals\\\' is also introduced.

Limit Time Optimal Syntheses for a control-affine system on S² - Paolo Mason; Rebecca Salmoni; Ugo Boscain; Yacine Chitour (SIAM J. Control Optim. 47 (2008) 111-143, 2008)
For $\\\\alpha \\\\in ]0,\\\\pi/2[$, let $(\\\\Sigma)_\\\\alpha$ be the control system $\\\\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\\\\in [-1,1]$, and $F,G$ are $3\\\\times3$ skew-symmetric matrices generating rotations with perpendicular axes and of respective norms $\\\\cos(\\\\alpha)$ and $\\\\sin(\\\\alpha)$. In this paper, we study the time optimal synthesis (TOS) from the north pole $(0,0,1)^T$ associated to $(\\\\Sigma)_\\\\alpha$, as the parameter $\\\\alpha$ tends to zero; this problem is motivated by specific issues in the control of quantum systems. We first prove that the TOS is characterized by a \\\"two-snakes\\\" configuration on the whole $S^2$, except for a neighborhood $U_\\\\alpha$ of the south pole $(0,0,-1)^T$ of diameter at most ${\\\\cal O}(\\\\alpha)$. We next show that, inside $U_\\\\alpha$, the TOS depends on the relationship between $r(\\\\alpha):=\\\\pi/2\\\\alpha-[\\\\pi/2\\\\alpha]$ and $\\\\alpha$. More precisely, we characterize three main relationships by considering sequences $(\\\\alpha_k)_{k\\\\geq 0}$ satisfying (a) $r(\\\\alpha_k)=\\\\bar{r}$, (b) $r(\\\\alpha_k)=C\\\\alpha_k$, and (c) $r(\\\\alpha_k)=0$, where $\\\\bar{r}\\\\in (0,1)$ and $C>0$. In each case, we describe the TOS and provide, after a suitable rescaling, the limiting behavior, as $\\\\alpha$ tends to zero, of the corresponding TOS inside $U_\\\\alpha$.

On the Logarithmic Asymptotics of the Sixth Painleve\' Equation (Summer 2007) - Davide Guzzetti (J.Phys.A: Math.Theor. 41,(2008), 205201-205247, 2008)
We study the solutions of the sixth Painlev\'e equation with a logarithmic\r\nasymptotic behavior at a critical point. We compute the monodromy group\r\nassociated to the solutions by the method of monodromy preserving deformations\r\nand we characterize the asymptotic behavior in terms of the monodromy itself.

Minimization of non quasiconvex functionals by integro-extremization method - Sandro Zagatti (Discrete Contin. Dyn. Syst. 21 (2008) 625-641, 2008)

Minimizers of non convex scalar functionals and viscosity solutions of Hamilton-Jacobi equations - Sandro Zagatti (Calc. Var. Partial Differential Equations 31 (2008) 511-519, 2008)

Morse theory and a scalar field equation on compact surfaces - Andrea Malchiodi (Adv. Differential Equations 13 (2008) 1109-1129, 2008)

Multiple bound states for the Schroedinger-Poisson problem - Antonio Ambrosetti; David Ruiz (Commun. Contemp. Math. 10 (2008) 391-404, 2008)

Noncommutative families of instantons - Giovanni Landi; Chiara Pagani; Cesare Reina; Walter van Suijlekom (Int. Math. Res. Not. vol. 2008, Article ID rnn038, 2008)
We construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$.

The Noncommutative Geometry of the Quantum Projective Plane - Francesco D'Andrea; Ludwik Dabrowski; Giovanni Landi (Rev. Math. Phys. 20 (2008) 979-1006, 2008)
We study the spectral geometry of the quantum projective plane CP^2_q. In particular, we construct a Dirac operator which gives a 0^+ summable triple, equivariant under U_q(su(3)).

A note on the differentiability of Lipschitz functions and the chain rule in Sobolev spaces - Massimiliano Morini (2008)

Numerical study of a multiscale expansion of the Korteweg-de Vries equation and Painlevé-II equation - Tamara Grava; Christian Klein (Proc. R. Soc. A 464 (2008) 733-757, 2008)
The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\\\\e^2$, $\\\\e\\\\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference between the KdV and the asymptotic solution decreases as $\\\\epsilon$ in the interior of the Whitham oscillatory zone, it is known to be only of order $\\\\epsilon^{1/3}$ near the leading edge of this zone. To obtain a more accurate description near the leading edge of the oscillatory zone we present a multiscale expansion of the solution of KdV in terms of the Hastings-McLeod solution of the Painlev\\\\\\\'e-II equation. We show numerically that the resulting multiscale solution approximates the KdV solution, in the small dispersion limit, to the order $\\\\epsilon^{2/3}$.

Optimal Strokes for Low Reynolds Number Swimmers: An Example - François Alouges; Antonio DeSimone; Aline Lefebvre (J. Nonlinear Sci. 18 (2008) 277-302, 2008)
Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901-062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics).

Origin of Co-Expression Patterns in E.coli and S.cerevisiae Emerging from Reverse Engineering Algorithms - Mattia Zampieri; Nicola Soranzo; Daniele Bianchini; Claudio Altafini (PLoS ONE 3 (2008) e2981, 2008)
Background: The concept of reverse engineering a gene network, i.e., of inferring a genome-wide graph of putative genegene interactions from compendia of high throughput microarray data has been extensively used in the last few years to deduce/integrate/validate various types of \\\"physical\\\" networks of interactions among genes or gene products. Results: This paper gives a comprehensive overview of which of these networks emerge significantly when reverse engineering large collections of gene expression data for two model organisms, E.coli and S.cerevisiae, without any prior information. For the first organism the pattern of co-expression is shown to reflect in fine detail both the operonal structure of the DNA and the regulatory effects exerted by the gene products when co-participating in a protein complex. For the second organism we find that direct transcriptional control (e.g., transcription factor-binding site interactions) has little statistical significance in comparison to the other regulatory mechanisms (such as co-sharing a protein complex, colocalization on a metabolic pathway or compartment), which are however resolved at a lower level of detail than in E.coli. Conclusion: The gene co-expression patterns deduced from compendia of profiling experiments tend to unveil functional categories that are mainly associated to stable bindings rather than transient interactions. The inference power of this systematic analysis is substantially reduced when passing from E.coli to S.cerevisiae. This extensive analysis provides a way to describe the different complexity between the two organisms and discusses the critical limitations affecting this type of methodologies.

On periodic elliptic equations with gradient dependence - Massimiliano Berti; Matzeu, M; Enrico Valdinoci (Communications on Pure and Applied Analysis, 2008)
We construct entire solutions of Δu = f(x, u, ∇u) which are superpositions of odd, periodic functions and linear ones, with prescribed integer or rational slope.

Positive solutions of nonlinear Schrödinger-Poisson systems with radial potentials vanishing at infinity - Mercuri, Carlo (Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl, 2008)
We deal with a weighted nonlinear Schr¨odinger-Poisson system, allowing the potentials to vanish at infinity.

Relaxation of some transversally isotropic energies and applications to smectic A elastomers - James Adams; Sergio Conti; Antonio DeSimone; Georg Dolzmann (Math. Models Methods Appl. Sci. 18 (2008) 1-20, 2008)

A second order minimality condition for the Mumford-Shah functional - Filippo Cagnetti; Maria Giovanna Mora; Massimiliano Morini (Calc. Var. Partial Differential Equations 33 (2008) 37-74, 2008)
A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\\\\Gamma)$, $\\\\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\\\\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.

On semistable principal bundles over a complex projective manifold - Indranil Biswas; Ugo Bruzzo (Int. Math. Res. Not. vol. 2008, article ID rnn035, 2008)
Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \\\\chi of P. We prove that a holomorphic principal G-bundle E over a connected complex projective manifold M is semistable and the second Chern class of its adjoint bundle vanishes in rational cohomology if and only if the line bundle over E/P defined by \\\\chi is numerically effective. Similar results remain valid for principal bundles with a reductive linear algebraic group as the structure group. These generalize an earlier work of Y. Miyaoka where he gave a characterization of semistable vector bundles over a smooth projective curve. Using these characterizations one can also produce similar criteria for the semistability of parabolic principal bundles over a compact Riemann surface.