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Elementary abelian regular subgroups as hidden sums for cryptographic trapdoorsFeb 02 2017We study special subgroups of the affine general linear group acting on a vector space. To be more precise, we study elementary abelian regular sub- groups. It turns out that these have a strong cryptographic significance, since they can be exploited ... More

Abelian regular subgroups of the affine group and radical ringsOct 08 2005Apr 20 2006We establish a link between abelian regular subgroup of the affine group, and commutative, associative algebra structures on the underlying vector space that are (Jacobson) radical rings. As an application, we show that if the underlying field has positive ... More

Several Proofs of Security for a Tokenization AlgorithmSep 01 2016In this paper we propose a tokenization algorithm of the Reversible Hybrid type, based on a block cipher with a secret key and (possibly public) additional input. We provide some formal proofs of security for it.

A generalization of bounds for cyclic codes, including the HT and BS boundsJun 20 2013We use the algebraic structure of cyclic codes and some properties of the discrete Fourier transform to give a reformulation of several classical bounds for the distance of cyclic codes, by extending techniques of linear algebra. We propose a bound, whose ... More

On differential uniformity of maps that may hide an algebraic trapdoorJan 17 2015Jun 11 2015We investigate some differential properties for permutations in the affine group, of a vector space V over the binary field, with respect to a new group operation $\circ$, inducing an alternative vector space structure on $V$ .

Public Ledger for Sensitive DataJun 17 2019Satoshi Nakamoto's Blockchain allows to build publicly verifiable and almost immutable ledgers, but sometimes privacy has to be factored in. In this work an original protocol is presented that allows sensitive data to be stored on a ledger where its integrity ... More

Generalized AG codes as evaluation codesDec 23 2012We extend the construction of GAG codes to the case of evaluation codes. We estimate the minimum distance of these extended evaluation codes and we describe the connection to the one-point GAG codes.

A deterministic algorithm for the distance and weight distribution of binary nonlinear codesMay 04 2015May 05 2015Given a binary nonlinear code, we provide a deterministic algorithm to compute its weight and distance distribution, and in particular its minimum weight and its minimum distance, which takes advantage of fast Fourier techniques. This algorithm's performance ... More

A bound on the size of linear codesFeb 10 2009Jun 27 2012We present a bound on the size of linear codes. This bound is independent of other known bounds, e.g. the Griesmer bound.

Intersections between the norm-trace curve and some low degree curvesDec 20 2018In this paper we analyze the intersection between the norm-trace curve over $\mathbb{F}_{q^3}$ and the curves of the form $y=ax^3+bx^2+cx+d$, giving a complete characterization of the intersection between the curve and the parabolas, as well as sharp ... More

Code generator matrices as entropy extractorsFeb 05 2015We show the connection between the Walsh spectrum of the output of a binary random number generator (RNG) and the bias of individual bits, and use this to show how previously known bounds on the performance of linear binary codes as entropy extractors ... More

A note on an infeasible linearization of some block ciphersNov 07 2015Nov 20 2015A block cipher can be easily broken if its encryption functions can be seen as linear maps on a small vector space. Even more so, if its round functions can be seen as linear maps on a small vector space. We show that this cannot happen for the AES. More ... More

Some bounds on the size of codesJun 26 2012Dec 27 2012We present some upper bounds on the size of non-linear codes and their restriction to systematic codes and linear codes. These bounds are independent of other known theoretical bounds, e.g. the Griesmer bound, the Johnson bound or the Plotkin bound, and ... More

On optimal nonlinear systematic codesJun 10 2015Feb 11 2016Most bounds on the size of codes hold for any code, whether linear or not. Notably, the Griesmer bound holds only in the linear case and so optimal linear codes are not necessarily optimal codes. In this paper we identify code parameters $(q,d,k)$, namely ... More

A possible intrinsic weakness of AES and other cryptosystemsJun 30 2010Nov 11 2010It has been suggested that the algebraic structure of AES (and other similar block ciphers) could lead to a weakness exploitable in new attacks. In this paper, we use the algebraic structure of AES-like ciphers to construct a cipher embedding where the ... More

Computing the distance distribution of systematic non-linear codesSep 09 2009The most important families of non-linear codes are systematic. A brute-force check is the only known method to compute their weight distribution and distance distribution. On the other hand, it outputs also all closest word pairs in the code. In the ... More

Key-Policy Multi-Authority Attribute-Based EncryptionDec 13 2014Feb 04 2016Bilinear groups are often used to create Attribute-Based Encryption (ABE) algorithms. In particular, they have been used to create an ABE system with multi authorities, but limited to the ciphertext-policy instance. Here, for the first time, we propose ... More

Hilbert quasi-polynomial for order domain codesJul 25 2016We present an application of Hilbert quasi-polynomials to order domain codes, allowing the effective computation of the order domain condition in a direct way. We also provide an improved and specialized algorithm for the computation of the related Hilbert ... More

A weight-distribution bound for entropy extractors using linear binary codesMay 12 2014We consider a bound on the bias reduction of a random number generator by processing based on binary linear codes. We introduce a new bound on the total variation distance of the processed output based on the weight distribution of the code generated ... More

Improved decoding of affine-variety codesFeb 21 2011Dec 20 2011General error locator polynomials are polynomials able to decode any correctable syndrome for a given linear code. Such polynomials are known to exist for all cyclic codes and for a large class of linear codes. We provide some decoding techniques for ... More

Do AES encryptions act randomly?Nov 11 2010The Advanced Encryption Standard (AES) is widely recognized as the most important block cipher in common use nowadays. This high assurance in AES is given by its resistance to ten years of extensive cryptanalysis, that has shown no weakness, not even ... More

An algorithmic approach using multivariate polynomials for the nonlinearity of Boolean functionsOct 19 2016The nonlinearity of a Boolean function is a key property in deciding its suitability for cryptographic purposes, e.g. as a combining function in stream ciphers, and so the nonlinearity computation is an important problem for applications. Traditional ... More

Permutation equivalent maximal irreducible Goppa codesJun 10 2008We consider the problem of finding the number of permutation non-equivalent classical irreducible maximal Goppa codes having fixed parameters q, n and r from a group theory point of view.

Complexity of multivariate polynomial evaluationJun 14 2011We describe a method to evaluate multivariate polynomials over a finite field and discuss its multiplicative complexity.

A proof of security for a key-policy RS-ABE schemeMar 21 2016A revocable-storage attribute-based encryption (RS-ABE) scheme is an encryption scheme which extends attribute-based encryption by intro- ducing user revocation. A key-policy RS-ABE scheme links each key to an access structure. We propose a new key-policy ... More

Several Proofs of Security for a Tokenization AlgorithmSep 01 2016Oct 13 2016In this paper we propose a tokenization algorithm of Reversible Hybrid type, as defined in PCI DSS guidelines for designing a tokenization solution, based on a block cipher with a secret key and (possibly public) additional input. We provide some formal ... More

On the Hermitian curve, its intersections with some conics and their applications to affine-variety codes and Hermitian codesAug 08 2012Sep 12 2012For any affine-variety code we show how to construct an ideal whose solutions correspond to codewords with any assigned weight. We classify completely the intersections of the Hermitian curve with lines and parabolas (in the $\mathbb{F}_{q^2}$ affine ... More

On the Hermitian curve and its intersections with some conicsFeb 16 2014We classify completely the intersections of the Hermitian curve with parabolas in the affine plane. To obtain our results we employ well-known algebraic methods for finite fields and geometric properties of the curve automorphisms. In particular, we provide ... More

Several Proofs of Security for a Tokenization AlgorithmSep 01 2016Feb 01 2017In this paper we propose a tokenization algorithm of Reversible Hybrid type, as defined in PCI DSS guidelines for designing a tokenization solution, based on a block cipher with a secret key and (possibly public) additional input. We provide some formal ... More

Code generator matrices as RNG conditionersFeb 05 2015Mar 02 2017We quantify precisely the distribution of the output of a binary random number generator (RNG) after conditioning with a binary linear code generator matrix by showing the connection between the Walsh spectrum of the resulting random variable and the ... More

Hilbert quasi-polynomial for order domains and application to coding theoryJul 25 2016Feb 02 2018We present an application of Hilbert quasi-polynomials to order domains, allowing the effective check of the second order-domain condition in a direct way. We also provide an improved algorithm for the computation of the related Hilbert quasi-polynomials. ... More

Quasi-cyclic LDPC codes with high girthJun 18 2009We study a class of quasi-cyclic LDPC codes. We provide precise conditions guaranteeing high girth in their Tanner graph. Experimentally, the codes we propose perform no worse than random LDPC codes with their same parameters, which is a significant achievement ... More

On Hidden Sums Compatible with A Given Block Cipher Diffusion LayerFeb 27 2017Oct 03 2018Sometimes it is possible to embed an algebraic trapdoor into a block cipher. Building on previous research, in this paper we investigate an especially dangerous algebraic structure, which is called a hidden sum and which is related to some regular subgroups ... More

The role of Boolean functions in hiding sums as trapdoors for some block ciphersNov 27 2014Jan 16 2015Most modern block ciphers are built using components whose cryptographic strength is evaluated in terms of their resistance to attacks on the whole cipher. In particular, differential properties of vectorial Boolean functions are studied for the S-Boxes ... More

A note on an infeasible linearization of some block ciphersNov 07 2015Feb 02 2017A block cipher can be easily broken if its encryption functions can be seen as linear maps on a small vector space. Even more so, if its round functions can be seen as linear maps on a small vector space. We show that this cannot happen for the AES. More ... More

First-Degree Prime Ideals of Biquadratic Fields dividing prescribed Principal IdealsAug 01 2019We describe first-degree prime ideals of biquadratic extensions in terms of first-degree prime ideals of two underlying quadratic fields. The identification of the prime divisors is given by numerical conditions involving their ideal norms. Interestingly, ... More

Study of the transition from the hard to the soft Pomeron in the small x region using optimal renormalizationDec 04 2012We show that it is possible to describe the effective Pomeron intercept using NLO BFKL evolution together with collinear improvements. In order to obtain a good description over the whole range of Q^2 we use a non-Abelian physical renormalization scheme ... More

Some exact solutions for the Caudrey-Dodd-Gibbon equationMay 19 2008May 21 2008In this paper we show some exact solutions for the Caudrey-Dodd-Gibbon equation (CDG equation). These solutions are obtained via \circledR \emph{Mathematica} 6.0 by the projective Riccati equation method.

On Prime Reciprocals in the Cantor SetJun 02 2009Nov 11 2011The middle-third Cantor set C_3 is a fractal consisting of all the points in [0, 1] which have non-terminating base-3 representations involving only the digits 0 and 2. It is easily shown that the reciprocals of all prime numbers p > 3 satisfying an equation ... More

Chiral symmetry and the axial nucleon to Delta(1232) transition form factorsMar 29 2008We study the momentum and the quark mass dependence of the axial nucleon to Delta(1232) transition form factors in the framework of non-relativistic chiral effective field theory to leading-one-loop order. The outcome of our analysis provides a theoretical ... More

Existence of good divisors on Mukai varietiesMay 09 1997A Mukai variety is a Fano n-fold of index n-2. In this paper we study the fundamental divisor of a Mukai variety with at worst log terminal singularities. The main result is a complete classification of log terminal Mukai varieties which have not good ... More

Particle production and transplanckian problem on the non-commutative planeMar 11 2010Aug 02 2010We consider the coherent state approach to non-commutativity, and we derive from it an effective quantum scalar field theory. We show how the non-commutativity can be taken in account by a suitable modification of the Klein-Gordon product, and of the ... More

Brane-worlds in T-dual BulksNov 17 2003Nov 20 2003We consider brane-world models with a Schwarzschild-AdS black hole bulk. In the particular case of a flat black hole horizon geometry, we study the behaviour of the brane cosmological equations when T-duality transformations act on the bulk. We find that ... More

The entropy of an acoustic black hole in Bose-Einstein condensates: transverse modes as a cure for divergencesDec 15 2011Jan 21 2013We consider the entropy associated to the phonons generated via the Hawking mechanism in a sonic hole in a Bose-Einsten condensate. In a previous paper, we looked at the (1+1)-dimensional case both in the hydrodynamic limit and in the case when high-frequency ... More

Observational signatures of pre-inflationary and lower-dimensional effective gravityNov 02 2010Mar 02 2012Several alternative ways to quantize gravitational interactions seem to indicate that gravity at short distances is effectively two-dimensional. If this were true, and the energy scale at which the dimensional transition occurs is of the order of the ... More

Unified ab initio formulation of flexoelectricity and strain-gradient elasticityApr 27 2016The theories of flexoelectricity and that of nonlocal elasticity are closely related, and are often considered together when modeling strain-gradient effects in solids. Here I show, based on a first-principles lattice-dynamical analysis, that their relationship ... More

Birational geometry of rational quartic surfacesMay 10 2019Two birational subvarieties of P^n are called Cremona equivalent if there is a Cremona modification of P^n mapping one to the other. If the codimension of the varieties is at least 2 then they are always Cremona Equivalent. For divisors the question is ... More

Singularities of linear systems and the Waring ProblemJun 15 2004Waring problem for homogeneus forms asks for additive decomposition of a form $f$ into powers of linear forms. A classical problem is to determine when such a decomposition is unique. In this paper I answer this question when the degree of $f$ is greater ... More

Approximation of the first passage time density of a Wiener process to an exponentially decaying threshold by two-piecewise linear threshold. Application to neuronal spiking activityJul 04 2015Feb 17 2016The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here we consider a Brownian motion in presence of an exponentially decaying threshold to model the neuronal spiking activity. ... More

A survey on efficient parallelization of blockchain-based smart contractsFeb 08 2019The main problem faced by smart contract platforms is the amount of time and computational power required to reach consensus. In a classical blockchain model, each operation is in fact performed by each node, both to update the status and to validate ... More

Flavour and Higgs physics near the Fermi scaleDec 05 2013After a discussion of the hierarchy problem of the Fermi scale, we study the flavour and Higgs boson(s) phenomenology of new physics close to it, both in general and in the specific cases of Supersymmetry and composite Higgs models. First, we promote ... More

Acerca del Algoritmo de DijkstraOct 01 2008In this paper we prove the correctness of Dijkstra's algorithm. We also discuss it and at the end we show an application.

Two-tier blockchain timestamped notarization with incremental securityFeb 08 2019Digital notarization is one of the most promising services offered by modern blockchain-based solutions. We present a digital notary design with incremental security and cost reduced with respect to current solutions. A client of the service receives ... More

Wave-Shaped Round Functions and Primitive GroupsAug 29 2017Sep 21 2018Round functions used as building blocks for iterated block ciphers, both in the case of Substitution-Permutation Networks and Feistel Networks, are often obtained as the composition of different layers which provide confusion and diffusion, and key additions. ... More

Postulation of general quintuple fat point schemes in P^3Mar 28 2011We study the postulation of a general union Y of double, triple, quartuple and quintuple points of P^3. In characteristic 0, we prove that Y has good postulation in degree $d\ge 11$. The proof is based on the combination of the Horace differential lemma ... More

Measurement of airborne 131I, 134Cs, and 137Cs nuclides due to the Fukushima reactors accident in air particulate in Milan (Italy)Jun 21 2011After the earthquake and the tsunami occurred in Japan on 11th March 2011, four of the Fukushima reactors had released in air a large amount of radioactive isotopes that had been diffused all over the world. The presence of airborne 131I, 134Cs, and 137Cs ... More

On the shape of the general error locator polynomial for cyclic codesFeb 10 2015Dec 24 2015A general result on the explicit form of the general error locator polynomial for all cyclic codes is given, along with several results for infinite classes of cyclic codes with $t=2$ and $t=3$. From these, a theoretically justification of the sparsity ... More

On the provable security of BEAR and LION schemesMay 02 2011BEAR, LION and LIONESS are block ciphers presented by Biham and Anderson (1996), inspired by the famous Luby-Rackoff constructions of block ciphers from other cryptographic primitives (1988). The ciphers proposed by Biham and Anderson are based on one ... More

On the Griesmer bound for nonlinear codesJan 18 2015Most bounds on the size of codes hold for any code, whether linear or nonlinear. Notably, the Griesmer bound, holds only in the linear case. In this paper we characterize a family of systematic nonlinear codes for which the Griesmer bound holds. Moreover, ... More

On causality of extreme eventsJan 26 2016May 19 2016Multiple metrics have been developed to detect causality relations between data describing the elements constituting complex systems, all of them considering their evolution through time. Here we propose a metric able to detect causality within static ... More

Flexoelectricity from density-functional perturbation theoryJun 18 2013Sep 20 2013We derive the complete flexoelectric tensor, including electronic and lattice-mediated effects, of an arbitrary insulator in terms of the microscopic linear response of the crystal to atomic displacements. The basic ingredient, which can be readily calculated ... More

Tripartite information of highly entangled statesDec 11 2015Apr 14 2016Holographic systems require monogamous mutual information for validity of semiclassical geometry. This is encoded by the sign of the tripartite information ($I3$). We investigate the behaviour of $I3$ for all partitionings of systems in states which are ... More

Controlling Rough PathsJun 30 2003Oct 28 2003We formulate indefinite integration with respect to an irregular function as an algebraic problem and provide a criterion for the existence and uniqueness of a solution. This allows us to define a good notion of integral with respect to irregular paths ... More

On weakly APN functions and 4-bit S-BoxesFeb 17 2011Aug 02 2011S-Boxes are important security components of block ciphers. We provide theoretical results on necessary or sufficient criteria for an (invertible) 4-bit S-Box to be weakly APN. Thanks to a classification of 4-bit invertible S-Boxes achieved independently ... More

On the security of the Blockchain Bix Protocol and CertificatesJul 28 2016The BIX protocol is a blockchain-based protocol that allows distribution of certificates linking a subject with his public key, hence providing a service similar to that of a PKI but without the need of a CA. In this paper we analyze the security of the ... More

Existence of good divisors on Mukai manifoldsNov 20 1996A normal projective variety X is called Fano if a multiple of the anticanonical Weil divisor, -K_X, is an ample Cartier divisor, the index of a Fano variety is the number i(X):=sup{t: -K_X= tH, for some ample Cartier divisor H}. Mukai announced, the classification ... More

The dark aftermath of Higgs inflationSep 27 2013Mar 11 2014In this letter we study the dynamics of the late Universe when a nonminimally coupled Higgs field is present. In general, the nonminimal coupling leads to a nontrivial mixing between the gravitational degrees of freedom and the Goldstone massless bosons. ... More

Black holes with non-minimal derivative couplingAug 01 2012Nov 06 2012We study the gravitational field equations in the presence of a coupling between the derivative of a massless scalar field and the Einstein tensor. This configuration is motivated by Galileon gravity as it preserves shift invariance in the scalar sector. ... More

Aspects of Quantum Gravity in CosmologyJan 22 2012Feb 13 2012We review some aspects of quantum gravity in the context of cosmology. In particular, we focus on models with a phenomenology accessible to current and near-future observations, as the early Universe might be our only chance to peep through the quantum ... More

Modified Dispersion Relations and trans-Planckian PhysicsNov 06 2007Nov 08 2007We consider modified dispersion relations in quantum field theory on curved space-time. Such relations, despite breaking the local Lorentz invariance at high energy, are considered in several phenomenological approaches to quantum gravity. Their existence ... More

A momentum-space representation of Green's functions with modified dispersion on ultra-static space-timeSep 17 2007Oct 05 2007We consider the Green's functions associated to a scalar field propagating on a curved, ultra-static background, in the presence of modified dispersion relations. The usual proper-time deWitt-Schwinger procedure to obtain a series representation of the ... More

Can we neglect the multi-layer structure of functional networks?Mar 14 2015Functional networks, i.e. networks representing dynamic relationships between the components of a complex system, have been instrumental for our understanding of, among others, the human brain. Due to limited data availability, the multi-layer nature ... More

On alternative formulations of the small-world metric in complex networksMay 14 2015Small-world networks, i.e. networks displaying both a high clustering coefficient and a small characteristic path length, are obliquitous in nature. Since their identification, the "small-worldness" metric, as proposed by Humphries and Gurney, has frequently ... More

WWW Spiders: an introductionOct 26 2007In recent years, the study of complex networks has received a lot of attention. Real systems have gained importance in scientific publications, despite of an important drawback: the difficulty of retrieving and manage such great quantity of information. ... More

Free loop space and the cyclic bar constructionFeb 29 2016Aug 29 2016Using the $E_\infty-$structure on singular cochains, we construct a homotopy coherent map from the cyclic bar construction of the differential graded algebra of cochains on a space to a model for the cochains on its free loop space. This fills a gap in ... More

Free loop spaces and dihedral homologyAug 29 2016We prove an $O(2)$-equivariant version of the Jones isomorphism relating the Borel $O(2)$-equivariant cohomology of the free loop space to the dihedral homology of the cochain algebra. We discuss polynomial forms and a variation of the de Rham isomorphism ... More

A momentum-space representation of Green's functions with modified dispersion relations on general backgroundsMar 26 2008Jun 04 2008We consider the problem of calculating the Green's functions associated to a massive scalar field with modified dispersion relations. We analyze the case when dispersion is modified by higher derivative spatial operators acting on the field orthogonally ... More

Mimicking dark matter in Horndeski gravityAug 12 2016Since the rediscovery of Horndeski gravity, a lot of work has been devoted to the exploration of its properties, especially in the context of dark energy. However, one sector of this theory, namely the one containing the coupling of the Einstein tensor ... More

Higgs Dark EnergyApr 02 2014Jan 20 2015We study the classical dynamics of a non-abelian Higgs theory coupled to gravity in an isotropic and homogeneous Universe. For non-minimal coupling, this theory leads to a model of cosmic inflation that is very attractive due to its simplicity and consistency ... More

Self-T-Dual Brane CosmologyOct 23 2006Oct 24 2006We show how T-duality can be implemented with brane cosmology. As a result, we obtain a smooth bouncing cosmology with features similar to the ones of the pre-Big Bang scenario. Also, by allowing T-duality transformations along the time-like direction, ... More

The entropy of an acoustic black hole in Bose-Einstein condensatesJun 23 2011Nov 11 2011We compute the entanglement entropy associated to the Hawking emission of a $(1+1)$-dimensional acoustic black hole in a Bose-Einstein condensate. We use the brick wall model proposed by 't Hooft, adapted to the momentum space, in order to tackle the ... More

Optical steering of mutual capacitance in nematic liquid crystal cellJul 19 2017In this study a variable capacitor made of Nematic Liquid Crystal cell is proposed and analyzed theoretically. The mutual capacitance is steered with an optical beam of a Gaussian shape launched into the cell. The optical field changes the orientation ... More

Codes Correcting Two DeletionsDec 19 2017Apr 30 2018In this work, we investigate the problem of constructing codes capable of correcting two deletions. In particular, we construct a code that requires redundancy approximately 8 log n + O(log log n) bits of redundancy, where n is the length of the code. ... More

On the approximation of dynamical indicators in systems with nonuniformly hyperbolic behaviorMay 11 2015Oct 20 2015Let $f$ be a $C^{1+\alpha}$ diffeomorphism of a compact Riemannian manifold and $\mu$ an ergodic hyperbolic measure with positive entropy. We prove that for every continuous potential $\phi$ there exists a sequence of basic sets $\Omega_n$ such that the ... More

Framed sheaves on projective stacksNov 12 2013Nov 05 2014Given a normal projective irreducible stack $\mathscr X$ over an algebraically closed field of characteristic zero we consider framed sheaves on $\mathscr X$, i.e., pairs $(\mathcal E,\phi_{\mathcal E})$, where $\mathcal E$ is a coherent sheaf on $\mathscr ... More

Ringed Finite SpacesSep 16 2014Oct 10 2014A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed space, endowed ... More

Exact solutions for the Generalized Modified Degasperis-Procesi equationSep 17 2008this paper we show some new exact solutions for the generalized modified Degasperis$-$Procesi equation (mDP equation)

Variational principles and approximation of dynamical indicators for systems with nonuniformly hyperbolic behaviorMar 20 2013Nov 20 2013This note is concerned with approximation of dynamical indicators as pressures, Lyapunov exponents and dimension-like quantities, in systems with nonuniformly hyperbolic behavior. For this we let $P^*(\Phi) := \sup_{\mu}\{h(\mu) + \mu(\Phi)\}$ be a variational ... More

Models for the soft X-ray emission of post-outburst classical novaeApr 15 2005A hydrostatic and stationary white dwarf envelope model has been developed for the study of the post-outburst phases of classical novae and their soft X-ray emission. Several white dwarf masses and chemical compositions typical for classical novae have ... More

Epistemological approach in immersive virtual environments and the neurophysiology learning processAug 04 2019Currently virtual reality (VR) usage in training processes is increasing due to their usefulness in the learning processes based on visual information empowered. The information in virtual environments is perceived by sight, sound and touch, but the relationship ... More

Stable regular critical points of the Mumford-Shah functional are local minimizersJul 25 2013In this paper it is shown that any regular critical point of the Mumford-Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the L^1-topology.

Empirical Bernstein Bounds and Sample Variance PenalizationJul 21 2009We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the sample size ... More

Comment on "Molecular Transport Junctions: Clearing Mists"May 22 2008May 26 2008This is a comment to a review article by Lindsay and Ratner titled "Molecular Transport Junctions: Clearing Mists".

KPZ reloadedAug 16 2015We analyze the one-dimensional periodic Kardar-Parisi-Zhang equation in the language of paracontrolled distributions, giving an alternative viewpoint on the seminal results of Hairer. Apart from deriving a basic existence and uniqueness result for paracontrolled ... More

Evolution of the tangent vectors and localization of the stable and unstable manifolds of hyperbolic orbits by Fast Lyapunov IndicatorsJul 25 2013The Fast Lyapunov Indicators are functions defined on the tangent fiber of the phase-space of a discrete (or continuous) dynamical system, by using a finite number of iterations of the dynamics. In the last decade, they have been largely used in numerical ... More

Approximate solutions of quasiequilibrium problems in Banach spacesApr 06 2015In this note we show that a recent existence result on quasiequilibrium problems, which seems to improve deeply some well-known results, is not correct. We exhibit a counterexample and we furnish a generalization of a lemma about continuous "-minimizers ... More

Quasi-periodic standing wave solutions of gravity-capillary water wavesFeb 07 2016We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity ... More

Thermodynamics of Quantum Information FlowsJan 04 2019Mar 26 2019We report two results complementing the second law of thermodynamics for Markovian open quantum systems coupled to multiple reservoirs with different temperatures and chemical potentials. First, we derive a nonequilibrium free energy inequality providing ... More

Quasi-periodic solutions with Sobolev regularity of NLS on T^d with a multiplicative potentialDec 07 2010We prove the existence of quasi-periodic solutions for Schroedinger equations with a multiplicative potential on T^d, d \geq 1, merely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions ... More

Weak universality for a class of 3d stochastic reaction-diffusion modelsAug 10 2017Jan 26 2018We establish the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on a three dimensional periodic domain to the dynamic $\Phi^4_3$ model within the framework of paracontrolled distributions. Our work extends ... More