total 338took 0.12s

Analysis of a free boundary at contact points with Lipschitz dataMay 22 2012Sep 23 2013In this paper we consider a minimization problem for the functional $$ J(u)=\int_{B_1^+}|\nabla u|\sp 2+\lambda_{+}^2\chi_{\{u>0\}}+\lambda_{-}^2\chi_{\{u\leq0\}}, $$ in the upper half ball $B_1^+\subset\R^n, n\geq 2$ subject to a Lipschitz continuous ... More

$K$-surfaces with free boundariesMay 13 2017Jun 10 2017A well-known question in classical differential geometry and geometric analysis asks for a description of possible boundaries of $K$-surfaces, which are smooth, compact hypersurfaces in $\mathbb{R}^d$ having constant Gauss curvature equal to $K \geq 0$. ... More

Regularity for a quasilinear continuous casting problemDec 27 2015In this paper study the regularity of continuous casting problem \begin{equation} \hbox{div}(|\nabla u|^{p-2}\nabla u-{\bf v} \beta(u))=0\tag{$\sharp$} \end{equation} for prescribed constant velocity $\bf v$ and enthalpy $\beta(u)$ with jump discontinuity ... More

An inverse problem for the refractive surfaces with parallel lightingMar 11 2014Dec 27 2015In this article we examine the regularity of two types of weak solutions to a Monge-Amp\`ere type equation which emerges in a problem of finding surfaces that refract coaxial light rays emitted from source domain and striking a given target after refraction. ... More

A nonlocal free boundary problem with Wasserstein distanceApr 12 2019May 21 2019We study the probability measures $\rho\in \mathcal M(\mathbb R^2)$ minimizing the functional \[ J[\rho]=\iint \log\frac1{|x-y|}d\rho(x)d\rho(y)+d^2(\rho, \rho_0), \] where $\rho_0$ is a given probability measure and $d(\rho, \rho_0)$ is the 2-Wasserstein ... More

Structure of singularities in the nonlinear nerve conduction problemJun 12 2019Jun 28 2019We give a characterisation of the singular points of the free boundary $\partial \{u>0\}$ for viscosity solutions of the nonlinear equation \begin{equation}F(D^2 u)=-\chi_{\{u>0\}},\tag{0.1} \end{equation} where $F$ is a fully nonlinear elliptic operator ... More

Log-gas equilibria with free boundary and optimal transportApr 12 2019We study the probability measures $\rho\in \mathcal M(\mathbb R^2)$ minimizing the functional \[ J[\rho]=\iint \log\frac1{|x-y|}d\rho(x)d\rho(y)+d^2(\rho, \rho_0), \] where $\rho_0$ is a given probability measure and $d(\rho, \rho_0)$ is the 2-Wasserstein ... More

Structure of singularities in the nonlinear nerve conduction problemJun 12 2019We give a characterisation of the singular points of the free boundary $\partial \{u>0\}$ for viscosity solutions of the nonlinear equation \begin{equation}F(D^2 u)=-\chi_{\{u>0\}},\tag{0.1} \end{equation} where $F$ is a fully nonlinear elliptic operator ... More

Log-gas equilibria with free boundary and optimal transportApr 12 2019Apr 17 2019We study the probability measures $\rho\in \mathcal M(\mathbb R^2)$ minimizing the functional \[ J[\rho]=\iint \log\frac1{|x-y|}d\rho(x)d\rho(y)+d^2(\rho, \rho_0), \] where $\rho_0$ is a given probability measure and $d(\rho, \rho_0)$ is the 2-Wasserstein ... More

Blaschke's rolling ball theorem and the Trudinger-Wang monotone bendingDec 27 2015We revisit the classical rolling ball theorem of Blaschke for convex surfaces with positive curvature and show that it is linked to another inclusion principle in the optimal mass transportation theory due to Trudinger and Wang. We also discuss an application ... More

Refractor surfaces determined by near-field dataOct 16 2018In this paper we study the near-field refractor problem with point source at the origin and prescribed target on the given receiver surface $\Sigma$. This nonvariational problem can be studied in the framework of prescribed Jacobian equations. We construct ... More

A new discrete monotonicity formula with application to a two-phase free boundary problem in dimension twoSep 01 2015We continue the analysis of the two-phase free boundary problems initiated in \cite{DK}, where we studied the linear growth of minimizers in a Bernoulli type free boundary problem at the non-flat points and the related regularity of free boundary. There, ... More

On a conjecture of De Giorgi related to homogenizationSep 20 2014Dec 29 2015For a periodic vector field $\bf F$, let ${\bf X}^\epsilon$ solve the dynamical system \begin{equation*} \frac{d{\bf X}^\epsilon}{dt} = {\bf F}\left(\frac {{\bf X}^\epsilon}\epsilon\right) . \end{equation*} In \cite{DeGiorgi} Ennio De Giorgi enquiers ... More

On a conjecture of De Giorgi related to homogenizationSep 20 2014Apr 25 2017For a periodic vector field $\bf F$, let ${\bf X}^\epsilon$ solve the dynamical system \begin{equation*} \frac{d{\bf X}^\epsilon}{dt} = {\bf F}\left(\frac {{\bf X}^\epsilon}\epsilon\right) . \end{equation*} In \cite{DeGiorgi} Ennio De Giorgi enquiers ... More

On derivation of Euler-Lagrange Equations for incompressible energy-minimizersJul 24 2008We prove that any distribution $q$ satisfying the equation $\nabla q=\div{\bf f}$ for some tensor ${\bf f}=(f^i_j), f^i_j\in h^r(U)$ ($1\leq r<\infty$) -the {\it local Hardy space}, $q$ is in $h^r$, and is locally represented by the sum of singular integrals ... More

Estimates for capacity and discrepancy of convex surfaces in sieve-like domains with an application to homogenizationMay 08 2015We consider the intersection of a convex surface $\Ga$ with a periodic perforation of $\R^d$, which looks like a sieve, given by $T_\e = \bigcup_{k\in \Z^d}\{\e k+a_\e T\}$ where $T$ is a given compact set and $a_\e\ll \e$ is the size of the perforation ... More

Potential theoretic approach to Schauder estimates for the fractional LaplacianFeb 17 2016Jun 30 2016We present an elementary approach for the proof of Schauder estimates for the equation $(-\Delta)^s u(x)=f(x), \,0<s<1$, with $f$ having a modulus of continuity $\omega_f$, based on the Poisson representation formula and dyadic ball approximation argument. ... More

Stratification of free boundary points for a two-phase variational problemAug 29 2015Dec 10 2015In this paper we study the two-phase Bernoulli type free boundary problem arising from the minimization of the functional $$ J(u):=\int_{\Omega}|\nabla u|^p +\lambda_+^p\,\chi_{\{u>0\}} +\lambda_-^p\,\chi_{\{u\le 0\}}, \quad 1<p<\infty. $$ Here $\Omega ... More

A nonlinear free boundary problem with a self-driven Bernoulli conditionNov 01 2016We study a Bernoulli type free boundary problem with two phases $$J[u]=\int_{\Omega}|\nabla u(x)|^2\,dx+\Phi\big({\mathcal M}_-(u), {\mathcal{M}}_+(u)\big), \quad u-\bar u\in W^{1,2}_0(\Omega), $$ where $\bar u\in W^{1,2}(\Omega)$ is a given boundary ... More

A class of unstable free boundary problemsDec 09 2015We consider the free boundary problem arising from an energy functional which is the sum of a Dirichlet energy and a nonlinear function of either the classical or the fractional perimeter. The main difference with the existing literature is that the total ... More

Limit behaviour of a singular perturbation problem for the biharmonic operatorFeb 18 2019We study here a singular perturbation problem of biLaplacian type, which can be seen as the biharmonic counterpart of classical combustion models. We provide different results, that include the convergence to a free boundary problem driven by a biharmonic ... More

The non-local action for the induced 2d supergravityJun 19 1997The two-dimensional simple supergravity is reexamined from the point of view of super-Weyl group cohomologies. The non-local form of the effective action of 2d supergravity which generalise the famous $R 1/\Box R$ is obtained.

Zero-curvature condition in Calogero modelSep 19 2013Sep 21 2013We consider the mutual commutativity of Dunkl operators of the rational Calogero model as zero-curvature condition and calculate the non-local operator, related to these flat connections. This operator has physical meaning of particular scattering matrix ... More

Solutions to the Yang-Baxter equations with $osp_q(1|2)$ symmetry: Lax operatorsJun 17 2008Jun 28 2008We find a new $4\times4$ solution to the $osp_q(1|2)$-invariant Yang-Baxter equation with simple dependence on the spectral parameter and propose $2\times 2$ matrix expressions for the corresponding Lax operator. The general inhomogeneous universal spectral-parameter ... More

New solutions to the $s\ell_q(2)$-invariant Yang-Baxter equations at roots of unityDec 29 2010May 23 2011We find new solutions to the Yang-Baxter equations with the $R$-matrices possessing $sl_q(2)$ symmetry at roots of unity, using indecomposable representations. The corresponding quantum one-dimensional chain models, which can be treated as extensions ... More

Conserved currents of the three-reggeon interactionFeb 22 1999We consider an extension of Lipatov's conjecture about the deep relation between amplitudes in the high-energy limit of QCD and XXX Heisenberg chains with non-compact spins.

Jordan-Schwinger Representations and Factorised Yang-Baxter OperatorsOct 27 2009Apr 07 2010The construction elements of the factorised form of the Yang-Baxter R operator acting on generic representations of q-deformed sl(n+1) are studied. We rely on the iterative construction of such representations by the restricted class of Jordan-Schwinger ... More

Fusion Rules of the Lowest Weight Representations of osp_q(1|2) at Roots of Unity: Polynomial Realization and Degeneration at Roots of UnityFeb 08 2006Aug 27 2009The degeneracy of the lowest weight representations of the quantum superalgebra $osp_q(1|2)$ and their tensor products at exceptional values of %when deformation parameter $q$ takes exceptional values is studied. The main features of the structures of ... More

The effective action of W_3-gravityOct 07 1996Apr 29 1998A new method for integrating anomalous Ward identities and finding the effective action is proposed. Two-dimensional supergravity and $W_3$-gravity are used as examples to demonstrate its potential. An operator is introduced that associates each physical ... More

Polynomial Realization of $s\ell_q(2)$ and Fusion Rules at Exceptional Values of $q$Feb 09 2005Representations of the $s\ell_q(2)$ algebra are constructed in the space of polynomials of real (complex) variable for $q^N=1$. The spin addition rule based on eigenvalues of Casimir operator is illustrated on few simplest cases and conjecture for general ... More

High-energy scattering in gauge theories and integrable spin chainsFeb 03 1999In the leading log approximation and at large $N_C$ the interaction of two fermionic and one gluonic reggeons is described by an integrable system corresponding to an open spin chain.

Beyond Collins and Sivers: further measurements of the target transverse spin-dependent azimuthal asymmetries in semi-inclusive DIS from COMPASSMay 16 2007In semi-inclusive DIS of polarized leptons on a transversely polarized target eight azimuthal modulations appear in the cross-section. Within QCD parton model four azimuthal asymmetries can be interpreted at leading order, two of them being the already ... More

Cahn and Sivers effects in the target fragmentation region of SIDISApr 11 2005LEPTO event generator is modified to describe the azimuthal modulations arising from Cahn and Sivers effects. The comparisons with some existing data in the current fragmentation region of SIDIS are presented. The predictions for Cahn and Sivers asymmetries ... More

Isospin and isospin/strangeness correlations in relativistic heavy ion collisionsDec 11 2007A fundamental symmetry of nuclear and particle physics is isospin whose third component is the Gell-Mann/Nishijima expression I(z)=Q-(B+S)/2 . The role of isospin symmetry in relativistic heavy ion collisions is studied. An isospin I(z), strangeness S ... More

New Quark Distributions and Semi-Inclusive Electroproduction on Polarized NucleonsDec 13 1994Jan 10 1995The quark-parton model calculation including the effects of intrinsic transverse momentum and of all six twist-two distribution functions of quarks in polarized nucleons is performed. It is demonstrated that new twist-two quark distribution functions ... More

Azimuthal Correlations in the Structure Functions of polarized Dihadron Semi-Inclusive Deep Inelastic ScatteringAug 28 2014Mar 24 2015Azimuthal correlations in two hadron production in deep inelastic scattering of unpolarized leptons off transversely polarized nucleon are discussed. Specifically, a simple approach for accessing ratios of structure functions corresponding to Sivers effect ... More

Continuous Strategy Replicator Dynamics for Multi--Agent LearningApr 29 2009Sep 22 2011The problem of multi-agent learning and adaptation has attracted a great deal of attention in recent years. It has been suggested that the dynamics of multi agent learning can be studied using replicator equations from population biology. Most existing ... More

Baxter Q-operators of the XXZ chain and R-matrix factorizationNov 02 2005Nov 14 2005We construct Baxter operators as generalized transfer matrices being traces of products of generic $R$ matrices. The latter are shown to factorize into simpler operators allowing for explicit expressions in terms of functions of a Weyl pair of basic operators. ... More

The structure of invariants in conformal mechanicsFeb 10 2014We investigate the integrals of motion of general conformal mechanical systems with and without confining harmonic potential as well as of the related angular subsystems, by employing the SL(2,R) algebra and its representations. In particular, via the ... More

Heisenberg spin chains based on sl(2|1) symmetryMar 10 2000We find solutions of the Yang-Baxter equation acting on tensor product of arbitrary representations of the superalgebra sl(2|1). Based on these solutions we construct the local Hamiltonians for integrable homogeneous periodic chains and open chains.

Yang-Baxter R operators and parameter permutationsMar 08 2007Jun 01 2007We present an uniform construction of the solution to the Yang- Baxter equation with the symmetry algebra $s\ell(2)$ and its deformations: the q-deformation and the elliptic deformation or Sklyanin algebra. The R-operator acting in the tensor product ... More

Universal R operator with Jordanian deformation of conformal symmetryOct 15 2003Oct 24 2003The Jordanian deformation of $sl(2)$ bi-algebra structure is studied in view of physical applications to breaking of conformal symmetry in the high energy asymptotics of scattering. Representations are formulated in terms of polynomials, generators in ... More

Universal R-matrix as integral operatorFeb 20 2001We derive the integral operator form for the general rational solution of the Yang-Baxter equation with $s\ell(2|1)$ symmetry. Considering the defining relations for the kernel of the R-operator as a system of second order differential equations we observe ... More

Universal R operator with deformed conformal symmetryNov 14 2001May 28 2002We study the general solution of the Yang-Baxter equation with deformed $sl(2)$ symmetry. The universal R operator acting on tensor products of arbitrary representations is obtained in spectral decomposition and in integral forms. The results for eigenvalues, ... More

Casimir effect with non-local boundary conditionsDec 05 2005Mar 16 2006Non-local boundary conditions have been considered in theoretical high-energy physics with emphasis on one-loop quantum cosmology, one-loop conformal anomalies, Bose-Einstein condensation models and spectral branes. In the present paper, for the first ... More

Search for top partners with charge 5e/3Sep 09 2013May 01 2014A feasibility study of searches for top partners with charge 5e/3 at the upgraded Large Hadron Collider is performed. The discovery potential and exclusion limits are presented using integrated luminosities of 300 fb$^{-1}$ and 3000 fb$^{-1}$ at center-of-mass ... More

Analysis of Social Voting Patterns on DiggJun 11 2008The social Web is transforming the way information is created and distributed. Blog authoring tools enable users to publish content, while sites such as Digg and Del.icio.us are used to distribute content to a wider audience. With content fast becoming ... More

Coherent Communication of Classical MessagesJul 12 2003Jan 09 2004We define "coherent communication" in terms of a simple primitive, show it is equivalent to the ability to send a classical message with a unitary or isometric operation, and use it to relate other resources in quantum information theory. Using coherent ... More

Applications of coherent classical communication and the Schur transform to quantum information theoryDec 30 2005Quantum mechanics has led not only to new physical theories, but also a new understanding of information and computation. Quantum information began by yielding new methods for achieving classical tasks such as factoring and key distribution but also suggests ... More

Scalar Casimir effect with non-local boundary conditionsApr 13 2006Apr 18 2006Non-local boundary conditions have been considered in theoretical high-energy physics with emphasis on one-loop quantum cosmology, one-loop conformal anomalies, Bose-Einstein condensation models and spectral branes. We have therefore studied the Wightman ... More

Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithmsJan 16 2019A broad class of hybrid quantum-classical algorithms known as "variational algorithms" have been proposed in the context of quantum simulation, machine learning, and combinatorial optimization as a means of potentially achieving a quantum speedup on a ... More

Determinants Containing Powers of Generalized Fibonacci NumbersDec 22 2015Jul 30 2016We study determinants of matrices whose entries are powers of Fibonacci numbers. We then extend the results to include entries that are powers of generalized Fibonacci numbers defined as a second-order linear recurrence relation. These studies have led ... More

An analogue of the Robinson-Schensted-Knuth correspondence and non-symmetric Cauchy kernels for truncated staircasesOct 01 2013Nov 26 2014We prove a restriction of an analogue of the Robinson--Schensted--Knuth correspondence for semi-skyline augmented fillings, due to Mason, to multisets of cells of a staircase possibly truncated by a smaller staircase at the upper left end corner, or at ... More

Enhanced Rashba effect for hole states in a quantum dotSep 17 2009Sep 21 2009The effect of Rashba spin-orbit (SO) interaction on the hole states in a quantum dot is studied in the presence of an external magnetic field. We demonstrate here that the Rashba SO coupling has a profound effect on the energy spectrum of the holes revealing ... More

Phase Transformation in Self-Organized Carbon TribolayersMar 11 2016The simplest way to obtain thin carbon layers is to draw or rub with a graphite rod. During rubbing, forces of friction acting in graphite/substrate tribological system cause drastic changes in the structure of the interface stratum developing thereby ... More

Coevolutionary networks of reinforcement-learning agentsAug 05 2013This paper presents a model of network formation in repeated games where the players adapt their strategies and network ties simultaneously using a simple reinforcement-learning scheme. It is demonstrated that the coevolutionary dynamics of such systems ... More

Convergence of Alternating Least Squares Optimisation for Rank-One Approximation to High Order TensorsMar 18 2015The approximation of tensors has important applications in various disciplines, but it remains an extremely challenging task. It is well known that tensors of higher order can fail to have best low-rank approximations, but with an important exception ... More

Exact universality from any entangling gate without inversesJun 03 2008This note proves that arbitrary local gates together with any entangling bipartite gate V are universal. Previously this was known only when access to both V and V^{-1} was given, or when approximate universality was demanded.

Why now is the right time to study quantum computingDec 30 2014Quantum computing is a good way to justify difficult physics experiments. But until quantum computers are built, do computer scientists need to know anything about quantum information? In fact, quantum computing is not merely a recipe for new computing ... More

A study of Feshbach resonances and the unitary limit in a model of strongly correlated nucleonsMar 05 2010A model of strongly interacting and correlated hadrons is developed. The interaction used contains a long range attraction and short range repulsive hard core. Using this interaction and various limiting situations of it, a study of the effect of bound ... More

Polarization of the Fulling-Rindler vacuum by uniformly accelerated mirrorOct 03 2001Positive frequency Wightman function and vacuum expectation values of the energy-momentum tensor are computed for a massive scalar field with general curvature coupling parameter and satisfying Robin boundary condition on a uniformly accelerated infinite ... More

Cascading Dynamics in Modular NetworksMar 13 2008In this paper we study a simple cascading process in a structured heterogeneous population, namely, a network composed of two loosely coupled communities. We demonstrate that under certain conditions the cascading dynamics in such a network has a two--tiered ... More

On Maximum a Posteriori Estimation of Hidden Markov ProcessesJun 10 2009We present a theoretical analysis of Maximum a Posteriori (MAP) sequence estimation for binary symmetric hidden Markov processes. We reduce the MAP estimation to the energy minimization of an appropriately defined Ising spin model, and focus on the performance ... More

NW-SE expansions of non-symmetric Cauchy kernels on near staircases and growth diagramsDec 01 2014Lascoux has given a triangular version of the Cauchy identity where Schur polynomials are replaced by Demazure characters and Demazure atoms. He has then used the staircase expansion to recover expansions for all Ferrers shapes, where the Demazure characters ... More

Approximate unitary $t$-designs by short random quantum circuits using nearest-neighbor and long-range gatesSep 18 2018We prove that $poly(t) \cdot n^{1/D}$-depth local random quantum circuits with two qudit nearest-neighbor gates on a $D$-dimensional lattice with n qudits are approximate $t$-designs in various measures. These include the "monomial" measure, meaning that ... More

Sects and lattice paths over the Lagrangian GrassmannianMar 18 2019We examine Borel subgroup orbits in the classical symmetric space of type CI, which are parametrized by skew symmetric (n, n)-clans. We describe bijections between such clans, certain weighted lattice paths, and pattern-avoiding signed involutions, and ... More

The Church of the Symmetric SubspaceAug 29 2013The symmetric subpace has many applications in quantum information theory. This review article begins by explaining key background facts about the symmetric subspace from a quantum information perspective. Then we review, and in some places extend, work ... More

Review of Quantum Algorithms for Systems of Linear EquationsDec 30 2014This article reviews the 2008 quantum algorithm for linear systems of equations due to Harrow, Hassidim and Lloyd, as well as some of the followup and related work. It was submitted to the Springer Encyclopedia of Algorithms.

Entanglement spread and clean resource inequalitiesSep 08 2009Oct 27 2013This article will examine states that superpose different amounts of entanglement and protocols that run in superposition but generate or consume different amounts of entanglement. In both cases we find a uniquely quantum difficulty: entanglement cannot ... More

Quantum expanders from any classical Cayley graph expanderSep 07 2007Oct 09 2007We give a simple recipe for translating walks on Cayley graphs of a group G into a quantum operation on any irrep of G. Most properties of the classical walk carry over to the quantum operation: degree becomes the number of Kraus operators, the spectral ... More

Spin interactions in a quantum dot containing a magnetic impurityJul 22 2010The electron and hole states in a CdTe quantum dot containing a single magnetic impurity in an external magnetic field are investigated, using the multiband approximation which includes the heavy hole-light hole coupling effects. The electron-hole spin ... More

Dynamics of Boltzmann Q-Learning in Two-Player Two-Action GamesSep 07 2011Mar 01 2012We consider the dynamics of Q-learning in two-player two-action games with a Boltzmann exploration mechanism. For any non-zero exploration rate the dynamics is dissipative, which guarantees that agent strategies converge to rest points that are generally ... More

Adaptive Boolean Networks and Minority Games with Time--Dependent CapacitiesJul 16 2004In this paper we consider a network of boolean agents that compete for a limited resource. The agents play the so called Generalized Minority Game where the capacity level is allowed to vary externally. We study the properties of such a system for different ... More

Baxter operators with deformed symmetryNov 13 2012Baxter operators are constructed for quantum spin chains with deformed $s\ell_2$ symmetry. The parallel treatment of Yang-Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier and relying ... More

Eigenvalues and eigenstates of the s ell_q(2)-invariant Universal R-operator defined for cyclic representations at roots of unityAug 13 2002Sep 03 2002The s ell_q(2) representations are realized in the space of polynomials for general and exceptional values of deformation parameter q and on finite set of theta-functions for cyclic representation corresponding to q^N = +/- 1, which are a natural extension ... More

Iterative construction of $U_q (s\ell (n+1)) $ representations and Lax matrix factorisationMay 30 2008Jun 06 2008The construction of a generic representation of $g\ell(n+1)$ or of the trigonomentric deformation of its enveloping algebra known as algebraic induction is conveniently formulated in term of Lax matrices. The Lax matrix of the constructed representation ... More

Baxter operators for arbitrary spinJun 24 2011Sep 16 2011We construct Baxter operators for the homogeneous closed $\mathrm{XXX}$ spin chain with the quantum space carrying infinite or finite dimensional $s\ell_2$ representations. All algebraic relations of Baxter operators and transfer matrices are deduced ... More

Local Hamiltonians Whose Ground States are Hard to ApproximateOct 07 2015Nov 21 2016Ground states of local Hamiltonians can be generally highly entangled: any quantum circuit that generates them (even approximately) must be sufficiently deep to allow coupling (entanglement) between any pair of qubits. Until now this property was not ... More

Integrable XYZ Model with Staggered Anisotropy ParameterNov 26 2001We apply to the XYZ model the technique of construction of integrable models with staggered parameters, presented recently for the XXZ case. The solution of modified Yang-Baxter equations is found and the corresponding integrable zig-zag ladder Hamiltonian ... More

Fermionisation of the Spin-S Uimin-Lai-Sutherland Model: Generalisation of Supersymmetric t-J Model to Spin-SSep 29 1999The spin-1 Uimin-Lai-Sutherland (ULS) isotropic chain model is expressed in terms of fermions and the equivalence of the fermionic representation to the supersymmetric t-J model is established directly at the level of Hamiltonians.The spin-S ULS model ... More

Quantum Supremacy through the Quantum Approximate Optimization AlgorithmFeb 24 2016The Quantum Approximate Optimization Algorithm (QAOA) is designed to run on a gate model quantum computer and has shallow depth. It takes as input a combinatorial optimization problem and outputs a string that satisfies a high fraction of the maximum ... More

Testing product states, quantum Merlin-Arthur games and tensor optimisationJan 04 2010Nov 04 2012We give a test that can distinguish efficiently between product states of n quantum systems and states which are far from product. If applied to a state psi whose maximum overlap with a product state is 1-epsilon, the test passes with probability 1-Theta(epsilon), ... More

Efficient Analysis of Confined Guided Modes in Phoxonic Crystal SlabsMar 24 2017Jun 28 2017Today's standard fabrication processes are just capable of manufacturing slab of photonic and phononic crystals, so an efficient method for analysis of these crystals is indispensable. Plane wave expansion (PWE) as a widely used method in studying photonic ... More

Emergence of Leadership in CommunicationOct 25 2017We study a neuro-inspired model that mimics a discussion (or information dissemination) process in a network of agents. During their interaction, agents redistribute activity and network weights, resulting in emergence of leader(s). The model is able ... More

Le Chatelier principle in replicator dynamicsOct 26 2011The Le Chatelier principle states that physical equilibria are not only stable, but they also resist external perturbations via short-time negative-feedback mechanisms: a perturbation induces processes tending to diminish its results. The principle has ... More

Opinion Dynamics with Confirmation BiasNov 16 2014Background: Confirmation bias is the tendency to acquire or evaluate new information in a way that is consistent with one's preexisting beliefs. It is omnipresent in psychology, economics, and even scientific practices. Prior theoretical research of this ... More

Convergence of a Recombination-Based Elitist Evolutionary Algorithm on the Royal Roads Test FunctionAug 20 2011Aug 24 2011We present an analysis of the performance of an elitist Evolutionary algorithm using a recombination operator known as 1-Bit-Swap on the Royal Roads test function based on a population. We derive complete, approximate and asymptotic convergence rates ... More

Convergence Properties of Two (μ + λ) Evolutionary Algorithms On OneMax and Royal Roads Test FunctionsAug 20 2011We present a number of bounds on convergence time for two elitist population-based Evolutionary Algorithms using a recombination operator k-Bit-Swap and a mainstream Randomized Local Search algorithm. We study the effect of distribution of elite species ... More

SectsOct 31 2018By explicitly describing a cellular decomposition we determine the Borel invariant cycles that generate the Chow groups of the quotient of a reductive group by a Levi subgroup. For illustrations we consider the variety of polarizations $\mbf{SL}_n / \mbf{S}(\mbf{GL}_p\times ... More

Universality of EPR pairs in Entanglement-Assisted Communication Complexity, and the Communication Cost of State ConversionFeb 20 2019Entanglement assistance is known to reduce the quantum communication complexity of evaluating functions with distributed inputs. But does the type of entanglement matter, or are EPR pairs always sufficient? This is a natural question because in several ... More

How many copies are needed for state discrimination?Jun 15 2006Given a collection of states (rho_1, ..., rho_N) with pairwise fidelities F(rho_i, rho_j) <= F < 1, we show the existence of a POVM that, given rho_i^{otimes n}, will identify i with probability >= 1-epsilon, as long as n>=2(log N/eps)/log (1/F). This ... More

The Information SieveJul 08 2015Jun 09 2016We introduce a new framework for unsupervised learning of representations based on a novel hierarchical decomposition of information. Intuitively, data is passed through a series of progressively fine-grained sieves. Each layer of the sieve recovers a ... More

Low Complexity Gaussian Latent Factor Models and a Blessing of DimensionalityJun 11 2017Jan 19 2018Learning the structure of graphical models from data usually incurs a heavy curse of dimensionality that renders this problem intractable in many real-world situations. The rare cases where the curse becomes a blessing provide insight into the limits ... More

Active Inference for Binary Symmetric Hidden Markov ModelsNov 03 2014We consider active maximum a posteriori (MAP) inference problem for Hidden Markov Models (HMM), where, given an initial MAP estimate of the hidden sequence, we select to label certain states in the sequence to improve the estimation accuracy of the remaining ... More

Discovering Structure in High-Dimensional Data Through Correlation ExplanationJun 04 2014Oct 31 2014We introduce a method to learn a hierarchy of successively more abstract representations of complex data based on optimizing an information-theoretic objective. Intuitively, the optimization searches for a set of latent factors that best explain the correlations ... More

Novel variational approach for analysis of photonic crystal slabsFeb 12 2015Apr 04 2015We propose a new method based on variational principle for analysis of photonic crystal (PC) slabs. Most of the methods used today treat PC slab as a three-dimensional (3D) crystal and this makes them very time and/or memory consuming. In this method ... More

Scalable cavity quantum electrodynamics system for quantum computingJul 18 2015We introduce a new scalable cavity quantum electrodynamics platform which can be used for quantum computing. This system is composed of coupled photonic crystal (PC) cavities which their modes lie on a Dirac cone in the whole super crystal band structure. ... More

Baxter operators for arbitrary spin IIJul 04 2011Sep 07 2011This paper presents the second part of our study devoted to the construction of Baxter operators for the homogeneous closed XXX spin chain with the quantum space carrying infinite or finite-dimensional $s\ell_2$ representations. We consider the Baxter ... More

Trace Anomalies and Cocycles of Weyl and Diffeomorphisms GroupsNov 08 1994The general structure of trace anomaly, suggested recently by Deser and Shwimmer, is argued to be the consequence of the Wess-Zumino consistency condition. The response of partition function on a finite Weyl transformation, which is connected with the ... More

Area-preserving structure of 2d-gravityJan 10 1994The effective action for 2d-gravity with manifest area-preserving invariance is obtained in the flat and in the general gravitational background. The cocyclic properties of the last action are proved, and generalizations on higher dimensions are discussed. ... More