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On the Benefits of Populations on the Exploitation Speed of Standard Steady-State Genetic AlgorithmsMar 26 2019It is generally accepted that populations are useful for the global exploration of multi-modal optimisation problems. Indeed, several theoretical results are available showing such advantages over single-trajectory search heuristics. In this paper we ... More

Evolving Boolean Functions with Conjunctions and Disjunctions via Genetic ProgrammingMar 28 2019Recently it has been proved that simple GP systems can efficiently evolve the conjunction of $n$ variables if they are equipped with the minimal required components. In this paper, we make a considerable step forward by analysing the behaviour and performance ... More

On the Impact of the Cutoff Time on the Performance of Algorithm ConfiguratorsApr 12 2019Algorithm configurators are automated methods to optimise the parameters of an algorithm for a class of problems. We evaluate the performance of a simple random local search configurator (ParamRLS) for tuning the neighbourhood size $k$ of the RLS$_k$ ... More

Computational Complexity Analysis of Genetic ProgrammingNov 11 2018Genetic Programming (GP) is an evolutionary computation technique to solve problems in an automated, domain-independent way. Rather than identifying the optimum of a function as in more traditional evolutionary optimization, the aim of GP is to evolve ... More

Standard Steady State Genetic Algorithms Can Hillclimb Faster than Mutation-only Evolutionary AlgorithmsAug 04 2017Aug 25 2017Explaining to what extent the real power of genetic algorithms lies in the ability of crossover to recombine individuals into higher quality solutions is an important problem in evolutionary computation. In this paper we show how the interplay between ... More

Erratum: Simplified Drift Analysis for Proving Lower Bounds in Evolutionary ComputationNov 30 2012This erratum points out an error in the simplified drift theorem (SDT) [Algorithmica 59(3), 369-386, 2011]. It is also shown that a minor modification of one of its conditions is sufficient to establish a valid result. In many respects, the new theorem ... More

Artificial Immune Systems Can Find Arbitrarily Good Approximations for the NP-Hard Partition ProblemJun 01 2018Typical Artificial Immune System (AIS) operators such as hypermutations with mutation potential and ageing allow to efficiently overcome local optima from which Evolutionary Algorithms (EAs) struggle to escape. Such behaviour has been shown for artificial ... More

Fast Artificial Immune SystemsJun 01 2018Various studies have shown that characteristic Artificial Immune System (AIS) operators such as hypermutations and ageing can be very efficient at escaping local optima of multimodal optimisation problems. However, this efficiency comes at the expense ... More

When Hypermutations and Ageing Enable Artificial Immune Systems to Outperform Evolutionary AlgorithmsApr 04 2018Mar 15 2019We present a time complexity analysis of the Opt-IA artificial immune system (AIS). We first highlight the power and limitations of its distinguishing operators (i.e., hypermutations with mutation potential and ageing) by analysing them in isolation. ... More

When Hypermutations and Ageing Enable Artificial Immune Systems to Outperform Evolutionary AlgorithmsApr 04 2018We present a time complexity analysis of the Opt-IA artificial immune system (AIS). We first highlight the power and limitations of its distinguishing operators (i.e., hypermutations with mutation potential and ageing) by analysing them in isolation. ... More

Artificial Immune Systems Can Find Arbitrarily Good Approximations for the NP-Hard Number Partitioning ProblemJun 01 2018Mar 15 2019Typical artificial immune system (AIS) operators such as hypermutations with mutation potential and ageing allow to efficiently overcome local optima from which evolutionary algorithms (EAs) struggle to escape. Such behaviour has been shown for artificial ... More

Theoretical Analysis of Stochastic Search AlgorithmsSep 04 2017Theoretical analyses of stochastic search algorithms, albeit few, have always existed since these algorithms became popular. Starting in the nineties a systematic approach to analyse the performance of stochastic search heuristics has been put in place. ... More

On Inversely Proportional Hypermutations with Mutation PotentialMar 27 2019Artificial Immune Systems (AIS) employing hypermutations with linear static mutation potential have recently been shown to be very effective at escaping local optima of combinatorial optimisation problems at the expense of being slower during the exploitation ... More

Simple Hyper-heuristics Optimise LeadingOnes in the Best Runtime Achievable Using Randomised Local Search Low-Level HeuristicsJan 23 2018Dec 06 2018Selection hyper-heuristics are randomised search methodologies which choose and execute heuristics from a set of low-level heuristics. Recent research for the LeadingOnes benchmark function has shown that the standard Simple Random, Permutation, Random ... More

Escaping Local Optima using Crossover with Emergent or Reinforced DiversityAug 10 2016Population diversity is essential for avoiding premature convergence in Genetic Algorithms (GAs) and for the effective use of crossover. Yet the dynamics of how diversity emerges in populations are not well understood. We use rigorous runtime analysis ... More

A general proof system for logics of imperfect informationJan 27 2012We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.

A Short and Elementary Proof of the Two-sidedness of the Matrix-InverseSep 05 2017An elementary proof of the two-sidedness of the matrix-inverse is given using only linear independence and the reduced row-echelon form of a matrix. In addition, it is shown that a matrix is invertible if and only if it is row-equivalent to the identity ... More

A generalized small model property for languages which force the infinityNov 10 2004Dec 30 2004This paper deals with formulas of set theory which force the infinity. For such formulas, we provide a technique to infer satisfiability from a finite assignment.

Indirect constraints on R-parity violating stop couplingsMar 31 2000Aug 04 2000It was recently claimed that single stop production at the Tevatron, occurring via R-parity (and baryon number) violating couplings, could lead to observable signals. In this talk I present some results of a work in progress, showing that rare B decays ... More

A differential extension of Descartes' foundational approach: a new balance between symbolic and analog computationApr 04 2019In La G\'eom\'etrie, Descartes proposed a balance between geometric constructions and symbolic manipulation with the introduction of suitable ideal machines. In modern terms, that is a balance between analog and symbolic computation. Descartes' geometric ... More

Matrix functions that preserve the strong Perron-Frobenius propertyJul 03 2014Jun 03 2015In this note, we characterize matrix functions that preserve the strong Perron-Frobenius property using the real Jordan canonical form of a real matrix.

Realizing Suleimanova Spectra via Permutative MatricesSep 02 2015Dec 24 2015A permutative matrix is a square matrix such that every row is a permutation of the first row. A constructive version of a result attributed to Suleimanova is given via permutative matrices. In addition, we strengthen a well-known result by showing that ... More

Transition Semantics - The Dynamics of Dependence LogicMar 05 2012May 21 2013We examine the relationship between Dependence Logic and game logics. A variant of Dynamic Game Logic, called Transition Logic, is developed, and we show that its relationship with Dependence Logic is comparable to the one between First-Order Logic and ... More

Periodic solutions of fully nonlinear autonomous equations of Benjamin-Ono typeFeb 15 2012Feb 20 2012We prove the existence of time-periodic, small amplitude solutions of autonomous quasilinear or fully nonlinear completely resonant pseudo-PDEs of Benjamin-Ono type in Sobolev class. The result holds for frequencies in a Cantor set that has asymptotically ... More

Rational fixed points for linear group actionsOct 23 2006Aug 16 2007Let $k$ be a finitely generated field, let $X$ be an algebraic variety and $G$ a linear algebraic group, both defined over $k$. Suppose $G$ acts on $X$ and every element of a Zariski-dense semigroup $\Gamma \subset G(k)$ has a rational fixed point in ... More

Eisenstein's criterion, Fermat's last theorem, and a conjecture on powerful numbersApr 05 2017Feb 13 2018Given integers $\ell > m >0$, we define monic polynomials $X_n$, $Y_n$, and $Z_n$ with the property that $\mu$ is a zero of $X_n$ if and only if the triple $(\mu,\mu+m,\mu+\ell)$ satisfies $x^n + y^n = z^n$. It is shown that the irreducibility of these ... More

Applications of pathwise Burkholder-Davis-Gundy inequalitiesJul 05 2015We present several applications of the pathwise Burkholder-Davis-Gundy (BDG) inequalities. Most importantly we prove them for cadlag semimartingales and a general function $\Phi$, and use this to derive BDG inequalities (non-pathwise ones) for the Bessel ... More

The arithmetical rank of a special class of monomial idealsMay 14 2010Jun 08 2010We give an affirmative answer to a question due to J. He and A. Van Tuyl, proving that the arithmetical rank of a special monomial ideal equals to the projective dimension of corresponding quotient module.

On quantizations of complex contact manifoldsNov 20 2012Dec 31 2014A (holomorphic) quantization of a complex contact manifold is a filtered algebroid stack which is locally equivalent to the ring E of microdifferential operators and which has trivial graded. The existence of a canonical quantization has been proved by ... More

Characterizing downwards closed, strongly first order, relativizable dependenciesSep 01 2018Feb 22 2019In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First Order Logic is equivalent to some first order sentence. In this work it is shown that all nontrivial dependency ... More

Periodic solutions of forced Kirchhoff equationsJan 14 2007Jun 14 2007We consider Kirchhoff equations for vibrating bodies in any dimension in presence of a time-periodic external forcing with period 2pi/omega and amplitude epsilon, both for Dirichlet and for space-periodic boundary conditions. We prove existence, regularity ... More

Uniqueness of quantization of complex contact manifoldsDec 21 2005Using the language of algebroid stacks, we will show that Kashiwara's quantization of a complex contact manifold is unique.

An explicit bound for the log-canonical degree of curves on open surfacesJan 08 2019Let $X$, $D$ be a smooth projective surface and a simple normal crossing divisor on $X$, respectively. Suppose $\kappa (X, K_X + D)\ge 0$, let $C$ be an irreducible curve on $X$ whose support is not contained in $D$ and $\alpha$ a rational number in $ ... More

Combinatorial interpretations of particular evaluations of complete and elementary symmetric functionsNov 11 2011The Jacobi-Stirling numbers and the Legendre-Stirling numbers of the first and second kind were first introduced in [6], [7]. In this paper we note that Jacobi-Stirling numbers and Legendre-Stirling numbers are specializations of elementary and complete ... More

Origins of the unidirectional spin Hall magnetoresistance in metallic bilayersJun 13 2018Recent studies evidence the emergence of asymmetric electron transport in layered conductors owing to the interplay between electrical conductivity, magnetization, and the spin Hall or Rashba- Edelstein effects. Here, we investigate the unidirectional ... More

Constraints on R-Parity violating stop couplings from flavor physicsAug 25 2000Nov 22 2000We perform a critical reassessment of the constraints on the R-parity and baryon number violating (s)top couplings coming from flavor physics. In particular, we study K0-K0bar mixing, including QCD corrections and a class of diagrams that were neglected ... More

Comparing the automorphism group of the measure algebra with some groups related to the infinite permutation group of the natural numbersDec 27 2003We prove, by a straight construction, that the automorphism group of the measure algebra and the subgroup of the measure preserving ones cannot be isomorphic to the trivial automorphisms of P(N)/fin.

Representations of Atiyah algebroids and logarithmic connectionsMay 18 2015In this paper, we investigate representations of $\operatorname{At}(N)$, the Atiyah algebroids of a holomorphic line bundles $N$ over a complex manifold $Y$. In particular, we relate $\operatorname{At}(N)$-modules with logarithmic connections through ... More

A Tenth Hilbert Problem-like Result: The Decidability of MLS with Unordered Cartesian ProductFeb 27 2019Using the technique of formative processes, I solve the decidability problem of MLS with unordered cartesian product in the positive. Moreover I give a pure combinatorial description of the satisfiable MLS with unordered cartesian product-formulas for ... More

Relaxation time of anisotropic simple exclusion processes and quantum Heisenberg modelsFeb 04 2002Motivated by an exact mapping between anisotropic half integer spin quantum Heisenberg models and asymmetric diffusions on the lattice, we consider an anisotropic simple exclusion process with $N$ particles in a rectangle of $\bbZ^2$. Every particle at ... More

Teichmüller spaces of Generalized Hyperelliptic ManifoldsMay 03 2017In this paper we achieve a description of the connected components of Teichm\"uller space corresponding to Generalized Hyperelliptic Manifolds $X$. These are the quotients $ X = T/G$ of a complex torus $T$ by the free action of a finite group $G$, and ... More

Infinite dimensional GrassmanniansJul 14 2003Jun 16 2008We study the analytic and homotopy properties of some infinite dimensional Grassmannians, useful for developing a Morse theory for infinite dimensional manifolds. We study the space of Fredholm pairs of a Hilbert space, we determine its homotopy type, ... More

On the greatest prime factor of (ab+1)(ac+1)May 13 2002We prove that for integers a>b>c>0, the greatest prime factor of (ab+1)(ac+1) tends to infinity with a.

Typical entropy of a subsystem: Page curve and its varianceApr 17 2019When an isolated quantum system is in a random pure state, the average entropy of a subsystem is close to maximal. The exact formula for the average $\langle{S_{A}}\rangle$ was conjectured by Page in 1995 and later proved. Here we compute the exact formula ... More

Kondo effect in single atom contacts: the importance of the atomic geometryAug 05 2008Co single atom junctions on copper surfaces are studied by scanning tunneling microscopy and ab-initio calculations. The Kondo temperature of single cobalt atoms on the Cu(111) surface has been measured at various tip-sample distances ranging from tunneling ... More

GenHap: A Novel Computational Method Based on Genetic Algorithms for Haplotype AssemblyDec 18 2018The computational problem of inferring the full haplotype of a cell starting from read sequencing data is known as haplotype assembly, and consists in assigning all heterozygous Single Nucleotide Polymorphisms (SNPs) to exactly one of the two chromosomes. ... More

Quasi-optimal nonconforming methods for symmetric elliptic problems. I -- Abstract theoryOct 09 2017We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of nonconformity on ... More

Modular forms invariant under non-split Cartan subgroupsMay 17 2018In this paper we describe a method for computing a basis for the space of weight $2$ cusp forms invariant under a non-split Cartan subgroup of prime level $p$. As an application we compute, for certain small values of $p$, explicit equations over $\bf ... More

Traces of Sobolev functions on regular surfaces in infinite dimensionsFeb 09 2013In a Banach space $X$ endowed with a nondegenerate Gaussian measure, we consider Sobolev spaces of real functions defined in a sublevel set $O= \{x\in X:\;G(x) <0\}$ of a Sobolev nondegenerate function $G:X\mapsto \R$. We define the traces at $G^{-1}(0)$ ... More

High-frequency market-making for multi-dimensional Markov processesMar 28 2013Apr 02 2013In this paper we complete and extend our previous work on stochastic control applied to high frequency market-making with inventory constraints and directional bets. Our new model admits several state variables (e.g. market spread, stochastic volatility ... More

Asymmetric velocity and tilt angle of domain walls induced by spin-orbit torquesDec 23 2018We present a micromagnetic study of the current-induced domain wall motion in perpendicularly magnetized Pt/Co/AlOx racetracks. We show that the domain wall velocity depends critically on the tilt angle of the wall relative to the current direction, which ... More

On integral points on surfacesJun 10 2002We study integral points on affine surfaces by means of a new method, relying on the Subspace Theorem. Under suitable assumptions on the divisor at infinity, we prove that the integral points are contained in a curve. As a corollary, we prove that there ... More

On the rational approximations to the powers of an algebraic numberMar 30 2004About fifty years ago Mahler proved that if $\alpha>1$ is rational but not an integer and if $0<l<1$ then the fractional part of $\alpha^n$ is $>l^n$ apart from a finite set of integers $n$ depending on $\alpha$ and $l$. Answering completely a question ... More

A lower bound for the height of a rational function at $S$-unit pointsNov 04 2003Apr 22 2004Let $\Gamma$ be a finitely generated subgroup of the multiplicative group $\G_m^2(\bar{Q})$. Let $p(X,Y),q(X,Y)\in\bat{Q}$ be two coprime polynomials not both vanishing at $(0,0)$; let $\epsilon>0$. We prove that, for all $(u,v)\in\Gamma$ outside a proper ... More

A conditional 0-1 law for the symmetric sigma-fieldMay 21 2007Let (\Omega,\mathcal{B},P) be a probability space, \mathcal{A} a sub-sigma-field of \mathcal{B}, and \mu a regular conditional distribution for P given \mathcal{A}. For various, classically interesting, choices of \mathcal{A} (including tail and symmetric) ... More

Quasi-optimal and pressure robust discretizations of the Stokes equations by new augmented Lagrangian formulationsFeb 08 2019We approximate the solution of the stationary Stokes equations with various conforming and nonconforming inf-sup stable pairs of finite element spaces on simplicial meshes. Based on each pair, we design a discretization that is quasi-optimal and pressure ... More

The fate of quarkonia in heavy-ion collisions at LHC energies: a unified description of the sequential suppression patternsSep 27 2018Measurements made at the LHC have shown that the production of the ${\rm J}/\psi$, $\psi$(2S), $\Upsilon$(1S) and $\Upsilon$(2S) quarkonia is suppressed in Pb-Pb collisions, with respect to the extrapolation of the pp production yields. The $\psi$(2S) ... More

Integral points, divisibility between values of polynomials and entire curves on surfacesJul 09 2009Jul 29 2009We prove some new degeneracy results for integral points and entire curves on surfaces; in particular, we provide the first example, to our knowledge, of a simply connected smooth variety whose sets of integral points are never Zariski-dense (and no entire ... More

On the global stable manifoldJun 15 2005Sep 28 2005We give an alternative proof of the stable manifold theorem as an application of the (right and left) inverse mapping theorem on a space of sequences. We investigate the diffeomorphism class of the global stable manifold, a problem which in the general ... More

A Nash-Moser-Hörmander implicit function theorem with applications to control and Cauchy problems for PDEsSep 01 2016Dec 20 2018We prove an abstract Nash-Moser implicit function theorem which, when applied to control and Cauchy problems for PDEs in Sobolev class, is sharp in terms of the loss of regularity of the solution of the problem with respect to the data. The proof is a ... More

Moduli spaces of $Λ$-modules on abelian varietiesFeb 19 2016Sep 04 2017We study the moduli space $\mathbf{M}_X(\Lambda, n)$ of semistable $\Lambda$-modules of vanishing Chern classes over an abelian variety $X$, where $\Lambda$ belongs to a certain subclass of $D$-algebras. In particular, for $\Lambda = \mathcal{D}_X$ (resp. ... More

Modelling trait dependent speciation with Approximate Bayesian ComputationDec 10 2018Phylogeny is the field of modelling the temporal discrete dynamics of speciation. Complex models can nowadays be studied using the Approximate Bayesian Computation approach which avoids likelihood calculations. The field's progression is hampered by the ... More

Universal Minimal Flow in the Theory of Topological GroupoidsSep 19 2016In this paper we investigate some connections between Topological Dynamics, the theory of G-Principal Bundles, and the theory of Locally Trivial Groupoids.

Finite volume approximation of the effective diffusion matrix: The case of independent bond disorderOct 19 2001Consider uniformly elliptic random walk on $\bbZ^d$ with independent jump rates across nearest neighbour bonds of the lattice. We show that the infinite volume effective diffusion matrix can be almost surely recovered as the limit of finite volume periodized ... More

Formative processes with applications to the decision problem in set theory: II. powerset and singleton operators, finiteness predicateNov 10 2004Jun 27 2013In this paper we solve the satisfiability problem of an extended fragment of set computable theory which "forces the infinity" by a fruitful use of the witness small model property and the theory of formative processes.

A fast subsampling method for estimating the distribution of signal-to-noise ratio statistics in nonparametric time series regression modelsNov 06 2017Apr 17 2019Signal-to-noise ratio (SNR) statistics play a central role in many applications. A common situation where SNR is studied is when a continuous time signal is sampled at a fixed frequency with some noise in the background. While estimation methods exist, ... More

Stacks of quantization-deformation modules on complex symplectic manifoldsMay 12 2003Aug 08 2003On a complex symplectic manifold, we construct the stack of quantization-deformation modules, that is, (twisted) modules of microdifferential operators with an extra central parameter, a substitute to the lack of homogeneity. We also quantize involutive ... More

Quasi-optimal nonconforming methods for symmetric elliptic problems. III -- DG and other interior penalty methodsOct 10 2017We devise new variants of the following nonconforming finite element methods: DG methods of fixed arbitrary order for the Poisson problem, the Crouzeix-Raviart interior penalty method for linear elasticity, and the quadratic $C^0$ interior penalty method ... More

Quasi-optimal nonconforming methods for symmetric elliptic problems. II -- Overconsistency and classical nonconforming elementsOct 10 2017We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions into conforming functions before applying the load functional. We derive and ... More

Study of boundary conditions in the Iterative Filtering method for the decomposition of nonstationary signalsNov 19 2018Feb 13 2019Nonstationary and nonlinear signals are ubiquitous in real life. Their decomposition and analysis is an important topic of research in signal processing. Recently a new technique, called Iterative Filtering, has been developed with the goal of decomposing ... More

On a system involving a critically growing nonlinearityAug 02 2011This paper deals with the system \[\{{array}{ll} -\Delta u = \lambda u + q |u|^3 u \phi & \hbox{in} B_R, -\Delta \phi=q |u|^5 & \hbox{in} B_R, u=\phi=0 & \hbox{on} \partial B_R. {array}.\] We prove existence and nonexistence results depending on the value ... More

Air-Gap Convection in a Switched Reluctance MachineFeb 20 2015Switched reluctance machines (SRMs) have recently become popular in the automotive market as they are a good alternative to the permanent magnet machines commonly employed for an electric powertrain. Lumped parameter thermal networks are usually used ... More

A New Definition of Hypercomplex AnalyticityJan 20 1997Complex analyticity is generalized to hypercomplex functions, quaternion or octonion, in such a manner that it includes the standard complex definition and does not reduce analytic functions to a trivial class. A brief comparison with other definitions ... More

Standing waves for a Schrödinger-Chern-Simons-Higgs systemJul 13 2018We consider a system arising from a nonrelativistic Chern-Simon-Higgs model, in which a charged field is coupled with a gauge field. We prove an existence result for small coupling constants.

Vanishing cohomology on a double cover of a very general hyper surfaceJul 07 2018In this paper, we study the irreducibility of the monodromy action on the anti-invariant part of the vanishing cohomology on the double cover of a very general element in an ample hypersurface of a complex smooth projective variety branched at an ample ... More

Superfluid Vortex Dynamics on Planar Sectors and ConesMar 31 2019We study the dynamics of vortices formed in a superfluid film adsorbed on the curved two-dimensional surface of a cone. To this aim, we observe that a cone can be unrolled to a sector on a plane with periodic boundary conditions on the straight sides. ... More

Matrix roots of imprimitive irreducible nonnegative matricesJul 16 2014Jun 03 2015Using matrix function theory, Perron-Frobenius theory, combinatorial matrix theory, and elementary number theory, we characterize, classify, and describe in terms of the Jordan canonical form the matrix pth-roots of imprimitive irreducible nonnegative ... More

Morita classes of microdifferential algebroidsDec 21 2011May 25 2015Projective cotangent bundles of complex manifolds are the local models of complex contact manifolds. Such bundles are quantized by the algebra of microdifferential operators (a localization of the algebra of differential operators on the base manifold). ... More

Minimal subfamilies and the probabilistic interpretation for modulus on graphsMay 26 2016The notion of $p$-modulus of a family of objects on a graph is a measure of the richness of such families. We develop the notion of minimal subfamilies using the method of Lagrangian duality for $p$-modulus. We show that minimal subfamilies have at most ... More

On Persistency of Excitation and Formulas for Data-driven ControlMar 15 2019Mar 19 2019In a paper by Willems and coworkers it was shown that sufficiently excited data could be used to represent the input-output trajectory of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems that paves ... More

Row Cones, Perron Similarities, and Nonnegative SpectraNov 08 2016In further pursuit of the diagonalizable \emph{real nonnegative inverse eigenvalue problem} (RNIEP), we study the relationship between the \emph{row cone} $\mathcal{C}_r(S)$ and the \emph{spectracone} $\mathcal{C}(S)$ of a Perron similarity $S$. In the ... More

Nonlinear Schrödinger equation in the Bopp-Podolsky electrodynamics: solutions in the electrostatic caseFeb 09 2018Jun 26 2018We study the following nonlinear Schr\"odinger-Bopp-Podolsky system \[ \begin{cases} -\Delta u + \omega u + q^{2}\phi u = |u|^{p-2}u -\Delta \phi + a^2 \Delta^2 \phi = 4\pi u^2 \end{cases} \hbox{ in }\mathbb{R}^3 \] with $a,\omega>0$. We prove existence ... More

Deformation-Quantization of Complex Involutive SubmanifoldsJul 13 2004Mar 03 2005The sheaf of rings of WKB operators provides a deformation-quantization of the cotangent bundle to a complex manifold. On a complex symplectic manifold $X$ there may not exist a sheaf of rings locally isomorphic to a ring of WKB operators. The idea is ... More

Ground states for fractional magnetic operatorsJan 16 2016Nov 09 2016We study a class of minimization problems for a nonlocal operator involving an external magnetic potential. The notions are physically justified and consistent with the case of absence of magnetic fields. Existence of solutions is obtained via concentration ... More

On dominant rational maps from products of curves to surfaces of general typeJun 20 2012Jun 11 2013In this paper we investigate the existence of generically finite dominant rational maps from products of curves to surfaces of general type. We prove that the product CxD of two distinct very general curves of genus g>6 and g'>1 does not admit dominant ... More

On the finiteness theorem for rational maps on a variety of general typeJul 18 2008Apr 09 2009The dominant rational maps of finite degree from a fixed variety to varieties of general type, up to birational isomorphisms, form a finite set. This has been known as the Iitaka-Severi conjecture, and is nowdays an established result, in virtue of some ... More

Soliton dynamics for the Schrodinger-Newton systemJan 05 2013We investigate the soliton dynamics for the Schrodinger-Newton system by proving a suitable modulational stability estimates in the spirit of those obtained by Weinstein for local equations.

A matricial view of the Karpelevič TheoremNov 21 2016Dec 01 2016The question of the exact region in the complex plane of the possible single eigenvalues of all $n$-by-$n$ stochastic matrices was raised by Kolmogorov in 1937 and settled by Karpelevi\v{c} in 1951 after a partial result by Dmitriev and Dynkin in 1946. ... More

Perron Spectratopes and the Real Nonnegative Inverse Eigenvalue ProblemAug 29 2015Nov 19 2015Call an $n$-by-$n$ invertible matrix $S$ a \emph{Perron similarity} if there is a real non-scalar diagonal matrix $D$ such that $S D S^{-1}$ is entrywise nonnegative. We give two characterizations of Perron similarities and study the polyhedra $\mathcal{C}(S) ... More

Jordan chains of $h$-cyclic matricesJul 16 2014Feb 24 2015Arising from the classification of the matrix-roots of a nonnegative imprimitive irreducible matrix, we present results concerning the Jordan chains of an $h$-cyclic matrix. We also present ancillary results applicable to nonnegative imprimitive irreducible ... More

Realizing Suleĭmanova spectra via permutative matrices, IIJun 19 2018Dec 21 2018In this work, the real nonnegative inverse eigenvalue problem is solved for a particular class of permutative matrix. The necessary and sufficient condition there is also shown to be sufficient for the symmetric nonnegative inverse eigenvalue problem. ... More

Bifurcation and Secondary Bifurcation of Heavy Periodic Hydroelastic Travelling WavesNov 29 2008The paper deals with a problem of interaction between hydrodynamics and mechanics of nonlinear elastic bodies. The existence question for two-dimensional symmetric steady waves travelling on the surface of a deep ocean beneath a heavy elastic membrane ... More

On rational maps from the product of two general curvesNov 16 2014Jul 06 2015This paper treats the dominant rational maps from the product of two very general curves to nonsingular projective surfaces. Combining the result by Bastianelli and Pirola, we prove that the product of two very general curves of genus $g\geq 7$ and $g'\geq ... More

On subfields of the function field of a general surface in ${\mathbb P}^3$Sep 03 2014Mar 25 2015In this paper we study birational immersions from a very general smooth plane curve to a non-rational surface with $p_g=q=0$ to treat dominant rational maps from a very general surface $X$ of degree$\geq 5$ in ${\mathbb P}^3$ to smooth projective surfaces ... More

On homaloidal polynomial functions of degree 3 and prehomogeneous vector spacesNov 27 2010In this paper we consider homaloidal polynomial functions $f$ such that their multiplicative Legendre transform $f_*$, defined as in \cite[Section3.2]{MR1890194}, is again polynomial. Following Dolgachev \cite{MR1786486}, we call such polynomials EKP-homaloidal. ... More

Steady periodic water waves under nonlinear elastic membranesMay 05 2008This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and the pressure ... More

Infinitesimal invariant and vector bundlesDec 28 2006We study the Saito-Ikeda infinitesimal invariant of the ccle defined by curves in their jacobians using rank (k+1) vector bundles and we give a criterion for which the higher cycle class map is not trivial. When k=2, this turns out to be strictly linked ... More

$W^{s,p}$-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray-Lions problemsJun 09 2016Jan 30 2017In this work we prove optimal $W^{s,p}$-approximation estimates (with $p\in[1,+\infty]$) for elliptic projectors on local polynomial spaces. The proof hinges on the classical Dupont--Scott approximation theory together with two novel abstract lemmas: ... More

Congruences of lines in $\mathbb{P}^5$, quadratic normality, and completely exceptional Monge-Ampère equationsOct 26 2007The existence is proved of two new families of locally Cohen-Macaulay sextic threefolds in $\mathbb{P}^5$, which are not quadratically normal. These threefolds arise naturally in the realm of first order congruences of lines as focal loci and in the study ... More

Virtualization Technologies and Cloud Security: advantages, issues, and perspectivesJul 29 2018Aug 02 2018Virtualization technologies allow multiple tenants to share physical resources with a degree of security and isolation that cannot be guaranteed by mere containerization. Further, virtualization allows protected transparent introspection of Virtual Machine ... More