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Rotate your Networks: Better Weight Consolidation and Less Catastrophic ForgettingFeb 08 2018In this paper we propose an approach to avoiding catastrophic forgetting in sequential task learning scenarios. Our technique is based on a network reparameterization that approximately diagonalizes the Fisher Information Matrix of the network parameters. ... More

On quantum algebra symmetries of discrete Schrödinger equationsAug 10 1998Two non-standard quantum deformations of the (1+1) Schr\"odinger algebra are identified with the symmetry algebras of either a space or time uniform lattice discretization of the Schr\"odinger equation. For both cases, the deformation parameter of the ... More

The Evans-Krylov theorem for non local fully non linear equationsMay 08 2009We prove an interior regularity result for solutions of a purely integro-differential Bellman equation. This regularity is enough for the solutions to be understood in the classical sense. If we let the order of the equation approach two, we recover the ... More

Bloch-Like Quantum Multiple Reflections of AtomsNov 14 1998We show that under certain circumstances an atom can follow an oscillatory motion in a periodic laser profile with a Gaussian envelope. These oscillations can be well explained by using a model of energetically forbidden spatial regions. The similarities ... More

On the Evans-Krylov theoremMay 08 2009Sep 08 2010In this note, motivated by our work on integral fully nonlinear equations, we provide a variation of the proof of Evans-Krylov theorem about the interior $C^{2,\alpha}$ a priori estimate for concave fully nonlinear elliptic equations. The proof we present ... More

A non local Monge-Ampere equationOct 01 2014Jun 26 2015We introduce a non local analog to the Monge-Ampere operator and show some of its properties. We prove that a global problem involving this operator has C 1,1 solutions in the full space.

An extension problem related to the fractional LaplacianAug 25 2006Feb 13 2007The operator square root of the Laplacian $(-\lap)^{1/2}$ can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition. In this paper we obtain similar ... More

A curved Henon-Heiles system and its integrable perturbationsMar 31 2015Apr 13 2015The constant curvature analogue on the two-dimensional sphere and the hyperbolic space of the integrable H\'enon-Heiles Hamiltonian $\mathcal{H}$ given by $$ \mathcal{H}=\dfrac{1}{2}(p_{1}^{2}+p_{2}^{2})+ \Omega \left(q_{1}^{2}+ 4 q_{2}^{2}\right) +\alpha ... More

On the rationality and holomorphy of Langlands-Shahidi L-functions over function fieldsMay 22 2015Sep 01 2015We prove three main results: all Langlands-Shahidi automorphic $L$-functions over function fields are rational; after twists by highly ramified characters our automorphic $L$-functions become polynomials; and, if $\pi$ is a globally generic cuspidal automorphic ... More

On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusionNov 26 2009Sep 08 2010We prove that the Hamilton Jacobi equation for an arbitrary Hamiltonian $H$ (locally Lipschitz but not necessarily convex) and fractional diffusion of order one (critical) has classical $C^{1,\alpha}$ solutions. The proof is achieved using a new H\"older ... More

Finite-temperature properties of the two-orbital Anderson modelSep 20 1999The metallic phase of the two-orbital Anderson lattice is study in the limit of infinite spatial dimensions, where a second order perturbation treatment is used to solve the single-site problem. Using this approximation, in the Kondo regime, we find that ... More

Some examples of F and D-term SUSY breaking modelsOct 02 2009Oct 10 2009In this paper we investigate the possibility of finding models that, in the global minimum, break SUSY by a combined F and D-term effect. We find that if the superpotential is a cubic polynomial in the fields and the Kahler potential is canonical this ... More

Electronic Phase Separation in Manganite/Insulator InterfacesNov 22 2006By using a realist microscopic model, we study the electric and magnetic properties of the interface between a half metallic manganite and an insulator. We find that the lack of carriers at the interface debilitates the double exchange mechanism, weakening ... More

Effect of the Equivalence Between Topological and Electric Charge on the Magnetization of the Hall FerromagnetJul 01 1999The dependence on temperature of the spin magnetization of a two-dimensional electron gas at filling factor unity is studied. Using classical Monte Carlo simulations we analyze the effect that the equivalence between topological and electrical charge ... More

Magnetic Domain Walls in Double Exchange MaterialsMay 14 1999We study magnetic domain walls in double exchange materials. The domain wall width is proportional to the square root of the stiffness. In the double exchange model the stiffness has two terms: the kinetic energy and the Hartree term. The kinetic energy ... More

Phase Diagram of Half Doped ManganitesJan 03 2005Jan 04 2005An analysis of the properties of half-doped manganites is presented. We build up the phase diagram of the system combining a realistic calculation of the electronic properties and a mean field treatment of the temperature effects. The electronic structure ... More

Anomalous massless modesDec 04 2014Some years ago Anton Yu. Alekseev et al. conjectured the existence of massless modes in the spectrum of excitations ("anomalous massless modes") building upon certain similarities between a spontaneous symmetry breaking and the interplay of axial and ... More

The Lagrangian cobordism group of $T^2$Oct 30 2013Nov 25 2014We compute the Lagrangian cobordism group of the standard symplectic 2-torus and prove that it is isomorphic to the Grothendieck group of its derived Fukaya category. The proofs use homological mirror symmetry for the 2-torus.

On the question of embedding a semigroup into an idempotent generated oneMay 15 2012In this paper we present a new embedding of a semigroup into a semiband (idempotent-generated semigroup) of depth 4 (every element is the product of 4 idempotents) using a semidirect product construction. Our embedding does not assume that S is a monoid ... More

Leptogenesis in a prompt decay scenarioOct 20 2002Dec 15 2003Leptogenesis is studied within the seesaw neutrino mass model in a regime where all sterile neutrinos have prompt rather than delayed decays. It is shown that during neutrino thermal production lepton asymmetries are generated in both active lepton and ... More

Upper bounds for parabolic equations and the Landau equationNov 10 2015Aug 22 2016We consider a parabolic equation in nondivergence form, defined in the full space $[0,\infty) \times \mathbb R^d$, with a power nonlinearity as the right hand side. We obtain an upper bound for the solution in terms of a weighted control in $L^p$. This ... More

Spectral methods for orthogonal rational functionsApr 25 2007An operator theoretic approach to orthogonal rational functions on the unit circle with poles in its exterior is presented in this paper. This approach is based on the identification of a suitable matrix representation of the multiplication operator associated ... More

Solving diophantine equations x^4 + y^4 = q z^pApr 27 2003We give a method to solve generalized Fermat equations of type $x^4 + y^4 = q z^p$, for some prime values of $q$ and every prime $p$ bigger than 13. We illustrate the method by proving that there are no solutions for $q= 73, 89$ and 113.

$K(π,1)$ conjecture for Artin groupsNov 30 2012The purpose of this paper is to put together a large amount of results on the $K(\pi,1)$ conjecture for Artin groups, and to make them accessible to non-experts. Firstly, this is a survey, containing basic definitions, the main results, examples and an ... More

Numerical Relativity: Status and ProspectsFeb 15 2002Feb 19 2002We are entering an era where the numerical construction of generic spacetimes is becoming a reality. The use of computer simulations, in principle, allows us to solve Einstein equations in their full generality and unravel important messages so far hidden ... More

Matching characteristic codes: exploiting two directionsNov 09 1999Combining incoming and outgoing characteristic formulations can provide numerical relativists with a natural implementation of Einstein's equations that better exploits the causal properties of the spacetime and gives access to both null infinity and ... More

A dissipative algorithm for wave-like equations in the characteristic formulationNov 30 1998We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the highly nonlinear ... More

Insulator-to-metal crossover induced by local spin fluctuations in strongly correlated systemsNov 24 2000We study the simplified Hubbard (SH) model in the presence of a transverse field in the infinite dimension limit. The relevant one-particle Green's functions of the model are obtained by means a perturbative treatment of the hopping and of the transverse ... More

From potential modularity to modularity for integral Galois representations and rigid Calabi-Yau threefoldsSep 07 2004We prove modularity for any irreducible crystalline $\ell$-adic odd 2-dimensional Galois representation (with finite ramification set) unramified at 3 verifying an "ordinarity at 3" easy to check condition, with Hodge-Tate weights $\{0, w \}$ such that ... More

Galois characterization of Endoscopy for rational Siegel modular formsOct 16 2003We establish a relation between Galois reducibility and Endoscopy for genus 2 Siegel cusp forms which have rational eigenvalues and are unramified at 3

A Bayesian Statistical Approach for Inference on Static Origin-Destination MatricesDec 05 2010Nov 30 2011We address the problem of static OD matrix estimation from a formal statistical viewpoint. We adopt a novel Bayesian framework to develop a class of models that explicitly cast trip configurations in the study region as random variables. As a consequence, ... More

Asymptotically optimum estimation of a probability in inverse binomial sampling under general loss functionsJan 18 2010Apr 30 2012The optimum quality that can be asymptotically achieved in the estimation of a probability p using inverse binomial sampling is addressed. A general definition of quality is used in terms of the risk associated with a loss function that satisfies certain ... More

A variation on the homological nerve theoremSep 12 2016An equivalent but useful version on the Homological Nerve Theorem is proved.

Does the velocity of light depend on the source movement?Jun 10 2016Jul 05 2016Data from spacecrafts tracking exhibit many anomalies that suggest the dependence of the speed of electromagnetic radiation with the motion of its source. This dependence is different from that predicted from emission theories that long ago have been ... More

To Teach Modal Logic: An Opinionated SurveyJul 16 2015I aim to promote an alternative agenda for teaching modal logic chiefly inspired by the relationships between modal logic and philosophy. The guiding idea for this proposal is a reappraisal of the interest of modal logic in philosophy, which do not stem ... More

Lagrangian antisurgeryNov 16 2015We describe an operation which, under certain conditions, modifies a Lagrangian submanifold $L$ such as to produce a new immersed Lagrangian submanifold $L'$, which as a smooth manifold is obtained by surgery along a framed sphere in $L$. Intuitively, ... More

Spin Orbit Coupling in Graphene Induced by Heavy Adatoms with Electrons in the Outer-Shell $p$ OrbitalsSep 14 2015Many of the exotic properties proposed to occur in graphene rely on the possibility of increasing the spin orbit coupling (SOC). By combining analytical and numerical tight binding calculations, in this work we study the SOC induced by heavy adatoms with ... More

Nonclassical states from the joint statistics of simultaneous measurementsJun 25 2015Nonclassicality cannot be a single-observable property since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior from the joint measurement of multiple observables. ... More

The proof of Birman's conjecture on singular braid monoidsJun 30 2003Sep 29 2004Let B_n be the Artin braid group on n strings with standard generators sigma_1, ..., sigma_{n-1}, and let SB_n be the singular braid monoid with generators sigma_1^{+-1}, ..., sigma_{n-1}^{+-1}, tau_1, ..., tau_{n-1}. The desingularization map is the ... More

Concealed Quantum InformationAug 29 2007We study the teleportation scheme performed by means of a partially entangled pure state. We found that the information belonging to the quantum channel can be distributed into both the system of the transmitter and the system of the receiver. Thus, in ... More

HOMFLYPT Skein module of singular linksAug 27 2009This paper is a presentation, where we compute the HOMFLYPT Skein module of singular links in the 3-sphere. This calculation is based on some results previously proved by Rabenda and the author on Markov traces on singular Hecke algebras, as well as on ... More

Spinless Two-Band Model in Infinite DimensionsMar 26 1999A spinless two-band model is studied in infinite dimension limit. Starting from the atomic limit, the formal exact solution of the model is obtained by means a perturbative treatment of the hopping and hybridisation terms. The model is solved in closed ... More

Interlayer Magnetic Coupling and the Quantum Hall Effect in Multilayer Electron SystemsApr 28 1998We study the effect that the electron-electron interaction has on the properties of a multilayer electron system. We consider the case corresponding to filling factor unity in each layer. We find that as a function of the sample parameters the system ... More

Coherent tunneling and negative differential conductivity in graphene-hBN-graphene heterostructureMar 24 2014Mar 27 2014We address the tunneling current in a graphene-hBN-graphene heterostructure as function of the twisting between the crystals. The twisting induces a modulation of the hopping amplitude between the graphene layers, that provides the extra momentum necessary ... More

Classification of Elliptic Line ScrollsSep 06 2000The classification of projective elliptic line scrolls with the description of their singular loci is given. In particular we recover Atiyah Theorem by using classical methods.

On the rationality and holomorphy of Langlands-Shahidi L-functions over function fieldsMay 22 2015Nov 14 2016We prove three main results: all Langlands-Shahidi automorphic $L$-functions over function fields are rational; after twists by highly ramified characters our automorphic $L$-functions become polynomials; and, if $\pi$ is a globally generic cuspidal automorphic ... More

A new regularization mechanism for the Boltzmann equation without cut-offDec 15 2014Mar 31 2016We apply recent results on regularity for general integro-differential equations to derive a priori estimates in H\"older spaces for the space homogeneous Boltzmann equation in the non cut-off case. We also show an a priori estimate in $L^\infty$ which ... More

From braid groups to mapping class groupsDec 01 2004Mar 24 2005This paper is a survey of some properties of the braid groups and related groups that lead to questions on mapping class groups.

Using Barriers to Reduce the Sensitivity to Edge Miscalculations of Casting-Based Object Projection Feature EstimationMar 01 20123D motion tracking is a critical task in many computer vision applications. Unsupervised markerless 3D motion tracking systems determine the most relevant object in the screen and then track it by continuously estimating its projection features (center ... More

A control theorem for the images of Galois actions on certain infinite families of modular formsJan 18 2007In this letter we show that for certain infinite families of modular forms of growing level it is possible to have a control result for the exceptional primes of the attached Galois representations. As an application, a uniform version of a result of ... More

The level 1 weight 2 case of Serre's conjectureDec 05 2004Apr 02 2007We give a proof of some small weight and level cases of Serre's conjecture.

Existence of families of Galois representations and new cases of the Fontaine-Mazur conjectureApr 27 2003In a previous article, we have proved a result asserting the existence of a compatible family of Galois representations containing a given crystalline irreducible odd two-dimensional representation. We apply this result to establish new cases of the Fontaine-Mazur ... More

Remarks on Serre's modularity conjectureMar 17 2006Apr 24 2011In this article we give a proof of Serre's conjecture for the case of odd level and arbitrary weight. Our proof does not depend on any generalization of Kisin's modularity lifting results to characteristic 2 (moreover, we will not consider at all characteristic ... More

Modularity of abelian surfaces with Quaternionic MultiplicationApr 27 2003We prove that any abelian surface defined over $\Q$ of $GL_2$-type having quaternionic multiplication and good reduction at 3 is modular. We generalize the result to higher dimensional abelian varieties with ``sufficiently many endomorphisms".

Commensurators of parabolic subgroups of Coxeter groupsJan 11 1996Let $(W,S)$ be a Coxeter system, and let $X$ be a subset of $S$. The subgroup of $W$ generated by $X$ is denoted by $W_X$ and is called a parabolic subgroup. We give the precise definition of the commensurator of a subgroup in a group. In particular, ... More

Residual $p$ properties of mapping class groups and surface groupsMar 23 2007Let $\mathcal M (\Sigma, \mathcal P)$ be the mapping class group of a punctured oriented surface $(\Sigma, \mathcal P)$ (where $\mathcal P$ may be empty), and let $\mathcal T_p(\Sigma,\mathcal P)$ be the kernel of the action of $\mathcal M (\Sigma, \mathcal ... More

Gauge Mediation with Gauge Messengers in SU(5)Jul 21 2010Nov 18 2010The inclusion of gauge messengers in models of gauge mediation allows for more general predictions that those described by the framework of general gauge mediation. Motivated by this, we explore some models of gauge mediation with gauge messengers in ... More

Advanced Programming Platform for efficient use of Data Parallel HardwareMar 22 2012Mar 23 2012Graphics processing units (GPU) had evolved from a specialized hardware capable to render high quality graphics in games to a commodity hardware for effective processing blocks of data in a parallel schema. This evolution is particularly interesting for ... More

Holder estimates for advection fractional-diffusion equationsSep 29 2010Apr 22 2011We analyse conditions for an evolution equation with a drift and fractional diffusion to have a Holder continuous solution. In case the diffusion is of order one or more, we obtain Holder estimates for the solution for any bounded drift. In the case when ... More

Small index subgroups of the mapping class groupDec 13 2007We prove that the mapping class group of a closed oriented surface of genus $\rho \ge 3$ has no proper subgroup of index $\le 4 \rho +4$.

Euclidean Jordan Algebras and Generalized Krein parameters of a strongly regular graphSep 23 2007Mar 26 2008Let $\tau$ be a strongly $(n,p;a,c)$ regular graph,such that $0<c<p<n-1,$ $A$ his matrix of adjacency and let ${\cal V}_{n}$ be the Euclidean space spanned by the powers of $A$ over the reals where the scallar product $\bullet|\bullet$ is defined by $x|y={trace}(x ... More

Maps preserving common zeros between subspaces of vector-valued continuous functionsOct 13 2009For metric spaces $X$ and $Y$, normed spaces $E$ and $F$, and certain subspaces $A(X,E)$ and $A(Y,F)$ of vector-valued continuous functions, we obtain a complete characterization of linear and bijective maps $T:A(X,E)\to A(Y,F)$ preserving common zeros, ... More

Separating maps between spaces of vector-valued absolutely continuous functionsJun 09 2009In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vector-valued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and biseparating ... More

On the level p weight 2 case of Serre's conjectureAug 27 2005Aug 30 2005This brief note only contains a modest contribution: we just fix some inaccuracies in the proof of the prime level weight 2 case of Serre's conjecture given in Khare's preprint "On Serre's modularity conjecture for 2-dimensional mod p representations ... More

Elliptic mod \ell Galois representations which are not minimally ellipticSep 07 2004Feb 01 2005In a recent preprint, F. Calegari has shown that for $\ell = 2, 3, 5$ and 7 there exist 2-dimensional surjective representations $\rho$ of $\Gal(\bar{\Q}/\Q)$ with values in $\F_\ell$ coming from the $\ell$-torsion points of an elliptic curve defined ... More

Computing the level of a modular rigid Calabi-Yau threefoldMar 30 2004In a previous article (a joint work with J. Manoharmayum) the modularity of a large class of rigid Calabi-Yau threefolds was established. To make that result more explicit, we recall (and re-prove) a result of Serre giving a bound for the conductor of ... More

Langlands Base Change for GL(2)Dec 10 2009Jun 16 2011Let F be a totally real Galois number field. We prove the existence of base change relative to the extension F/Q for every classical newform of odd level, under simple local assumptions on the field F.

How to facet a gemstone: from potential modularity to the proof of Serre's modularity conjectureDec 09 2007In this survey paper we present recent results obtained by Khare, Wintenberger and the author that have led to a proof of Serre's conjecture, such as existence of compatible families, modular upper bounds for universal deformation rings and existence ... More

Numerical Relativity: A reviewJun 22 2001Jun 29 2001Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of strong field ... More

Continuous Charge Modulated Diagonal Phase in ManganitesOct 15 2003We present a novel ground state that explain the continuous modulated charge diagonal order recently observed in manganese oxides, at hole densities $x$ larger than one half. In this diagonal phase the charge is modulated with a predominant Fourier component ... More

Signal detection without finite-energy limits to quantum resolutionMar 20 2012Jan 16 2013We show that there are extremely simple signal detection schemes where the finiteness of energy resources places no limit to the resolution. On the contrary, larger resolution can be obtained with lower energy. To this end the generator of the signal-dependent ... More

Contradictory uncertainty relationsApr 12 2011We show within a very simple framework that different measures of fluctuations lead to uncertainty relations resulting in contradictory conclusions. More specifically we focus on Tsallis and Renyi entropic uncertainty relations and we get that the minimum ... More

Contradictory entropic joint uncertainty relations for complementary observables in two-level systemsJun 21 2013We show that different entropic measures of fluctuations lead to contradictory uncertainty relations for two complementary observables. We apply Tsallis and R\'{e}nyi entropies to the joint distribution emerging from a noisy simultaneous measurement of ... More

On the Quantum Homology of Real Lagrangians in Fano Toric ManifoldsAug 29 2011Oct 30 2013We study the Lagrangian quantum homology of real parts of Fano toric manifolds of minimal Chern number at least 2, using coefficients in a ring of Laurent polynomials over Z/2Z. We show that these Lagrangians are wide, in the sense that their quantum ... More

Hermitian structures on six dimensional nilmanifoldsNov 11 2004Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant complex structure J and compatible metric g, which is not required to be invariant. We give classifications of 6-dimensional nilmanifolds M admitting strong K\"ahler with torsion, ... More

EntropyWalker, a Fast Algorithm for Small Community Detection in Large GraphsMay 10 2015This report presents a very simple algorithm for overlaping community-detection in large graphs under constraints such as the minimum and maximum number of members allowed. The algorithm is based on the simulation of random walks and measures the entropy ... More

Optical Properties Chern-Simons (3+1)D $θ$-systemsDec 17 2014Chern-Simons (CS) $\theta$-systems are described by a $\theta \int F\wedge F$ term in the action ($\theta$ is an adimensional parameter), which does not change field equations in the bulk, but affects the system behaviour when it is bounded. When two ... More

The covariant action of higher spin black holes in three dimensionsNov 04 2015May 18 2016We propose a set of boundary terms for higher spin theories in AdS$_3$ that lead to a well-defined variational principle compatible with Dirichlet boundary conditions for the metric and higher spin fields. These boundary terms are valid for higher spin ... More

All states are nonclassical: entanglement of joint statisticsJun 05 2016Nov 21 2016Joint measurements of two observables reveal that every state is nonclassical, with the only trivial exception of the state with density matrix proportional to the identity. This naturally includes states considered universally as classical-like, such ... More

Crossed product by actions of finite groups with the Rokhlin PropertyJan 27 2014We introduce and study a Rokhlin-type property for actions of finite groups on (not necessarily unital) C*-algebras. We show that the corresponding crossed product C*-algebras can be locally approximated by C*-algebras that are stably isomorphic to closed ... More

The level 1 case of Serre's conjecture revisitedMay 03 2007Feb 26 2008We prove existence of conjugate Galois representations, and we use it to derive a simple method of weight reduction. As a consequence, an alternative proof of the level 1 case of Serre's conjecture follows.

Braid groups and Artin groupsNov 15 2007This article is a survey on the braid groups, the Artin groups, and the Garside groups. It is a presentation, accessible to non-experts, of various topological and algebraic aspects of these groups. It is also a report on three points of the theory: the ... More

Birman's conjecture for singular braids on closed surfacesJul 17 2003Let $M$ be a closed oriented surface of genus $g\ge 1$, let $B_n(M)$ be the braid group of $M$ on $n$ strings, and let $SB_n(M)$ be the corresponding singular braid monoid. Our purpose in this paper is to prove that the desingularization map $\eta: SB_n(M) ... More

Asymptotic behaviour of a porous medium equation with fractional diffusionApr 07 2010We consider a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. In a previous paper we have found mass-preserving, nonnegative weak solutions of the equation satisfying energy estimates. The equation ... More

Regularity of solutions of the fractional porous medium flow with exponent 1/2Sep 29 2014We study the regularity of a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. The precise model is $u_t=\nabla\cdot(u\nabla (-\Delta)^{-1/2}u).$ For definiteness, the problem is posed in $\{x\in\mathbb{R}^N, ... More

Twitter as a Source of Global Mobility Patterns for Social GoodJun 20 2016Data on human spatial distribution and movement is essential for understanding and analyzing social systems. However existing sources for this data are lacking in various ways; difficult to access, biased, have poor geographical or temporal resolution, ... More

A new integrable anisotropic oscillator on the two-dimensional sphere and the hyperbolic planeMar 07 2014Oct 27 2014A new integrable generalization to the 2D sphere $S^2$ and to the hyperbolic space $H^2$ of the 2D Euclidean anisotropic oscillator Hamiltonian with Rosochatius (centrifugal) terms is presented, and its curved integral of the motion is shown to be quadratic ... More

Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separabilityJan 20 2017The Eisenhart geometric formalism, which transforms an Euclidean natural Hamiltonian $H=T+V$ into a geodesic Hamiltonian ${\cal T}$ with one additional degree of freedom, is applied to the four families of quadratically superintegrable systems with multiple ... More

High mobility conduction at (110) and (111) LaAlO3/SrTiO3 interfacesOct 30 2012In recent years, striking discoveries have revealed that two-dimensional electron liquids (2DEL) confined at the interface between oxide band-insulators can be engineered to display a high mobility transport. The recognition that only few interfaces appear ... More

Fermion localization on branes with generalized dynamicsNov 26 2010Mar 28 2013In this letter we consider a specific model of braneworld with nonstandard dynamics diffused in the literature, specifically we focus our attention on the matter energy density, the energy of system, the Ricci scalar and the thin brane limit. As the model ... More

Effect of the variation of mass on fermion localization on thick branesApr 28 2011In a recent paper published in this journal, Zhao and collaborators [Phys. Rev. D \textbf{82}, 084030 (2010)] analyze a toy model of thick branes generated by a real scalar field with the potential $V(\phi)=a\phi^{2}-b\phi^{4}+c\phi^{6}$, and investigate ... More

Extended Dualization: a method for the Bosonization of Anomalous Fermion Systems in Arbitrary DimensionMar 28 1995Mar 28 1996The technique of extended dualization developed in this paper is used to bosonize quantized fermion systems in arbitrary dimension $D$ in the low energy regime. In its original (minimal) form, dualization is restricted to models wherein it is possible ... More

Why we observe an almost classical spacetimeApr 21 1997We argue that, in order to obtain decoherence of spacetime, we should consider quantum conformal metric fluctuations of spacetime. This could be the required environment in the problem of selfmeasurement of spacetime in quantum gravity.

Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional LaplacianFeb 13 2007We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able ... More

A Nambu-Jona-Lasinio like model from QCD at low energiesDec 01 1997May 28 1998A generalization to any dimension of the fermion field transformation which allows to derive the solution of the massless Schwinger model in the path integral framework is identified. New arguments based on this transformation for a Nambu-Jona-Lasinio ... More

Lithium Ionization by a Strong Laser FieldAug 31 2004We study ab initio computations of the interaction of Lithium with a strong laser field. Numerical solutions of the time-dependent fully-correlated three-particle Schroedinger equation restricted to the one-dimensional soft-core approximation are presented. ... More

Regularity of solutions of the fractional porous medium flowJan 29 2012We study a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. More precisely, $$ u_t=\nabla\cdot(u\nabla (-\Delta)^{-s}u), \quad \ 0<s<1. $$ The problem is posed in $\{x\in\ren, t\in \re\}$ with nonnegative ... More

The "Pioneer effect" as a manifestation of the cosmic expansion in the solar systemOct 28 1998May 24 1999It is proposed that the recently reported anomalous acceleration acting on the Pioneers spacecrafts should be a consequence of the existence of some local curvature in light geodesics when using the coordinate speed of light in an expanding spacetime. ... More

Strong field approximation to the relativistic channeling of electrons in the presence of electromagnetic wavesFeb 20 2002We present a study of the interaction of a relativistically planar channeled electron with an intense electromagnetic field. Using a S-Matrix approach in the Strong Field Approximation, it is shown that the crystal periodicity affects drastically the ... More

Submetries, Souls, and Second Fundamental FormsJun 13 2016We give an optimal estimate for the norm of any submanifold's second fundamental form in terms of its focal radius and the lower sectional curvature bound of the ambient manifold. This is a special case of a similar theorem for intermediate Ricci curvature, ... More