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Metamorphic Detection of Adversarial Examples in Deep Learning Models With Affine TransformationsJul 10 2019Adversarial attacks are small, carefully crafted perturbations, imperceptible to the naked eye; that when added to an image cause deep learning models to misclassify the image with potentially detrimental outcomes. With the rise of artificial intelligence ... More

Conjugacy growth series for finitary wreath productsNov 19 2016We examine the conjugacy growth series of all wreath products of the finitary permutation groups $\text{Sym}(X)$ and $\text{Alt}(X)$ for an infinite set $X$. We determine their asymptotics, and we characterize the limiting behavior between the $\text{Alt}(X)$ ... More

Quadratic Packing Polynomials on Sectors of $\mathbb{R}^2$Aug 29 2014A polynomial $p(x,y)$ on a region $S$ in the plane is called a packing polynomial if the restriction of $p(x,y)$ to $S\cap \mathbb{Z}^2$ yields a bijection to $\mathbb{N}$. In this paper, we determine all quadratic packing polynomials on rational sectors ... More

Matroids and their DressiansFeb 14 2019We study Dressians of matroids using the initial matroids of Dress and Wenzel. These correspond to cells in regular matroid subdivisions of matroid polytopes. We characterize matroids that do not admit any proper matroid subdivisions. An efficient algorithm ... More

The slack realization space of a matroidApr 14 2018We introduce a new model for the realization space of a matroid, which is obtained from a variety defined by a saturated determinantal ideal, called the slack ideal, coming from the vertex-hyperplane incidence matrix of the matroid. This is inspired by ... More

Deconvolution of dust mixtures by latent Dirichlet allocation in forensic scienceMay 16 2018Jan 31 2019Dust particles recovered from the soles of shoes may be indicative of the sites recently visited by an individual, and, in particular, of the presence of an individual at a particular site of interest, e.g., the scene of a crime. By describing the dust ... More

A new formula for Chebotarev densitiesMar 23 2017Aug 13 2017We give a new formula for the Chebotarev densities of Frobenius elements in Galois groups. This formula is given in terms of smallest prime factors $p_{\mathrm{min}}(n)$ of integers $n\geq2$. More precisely, let $C$ be a conjugacy class of the Galois ... More

Voronoi Cells in Metric Algebraic Geometry of Plane CurvesJun 26 2019Voronoi cells of varieties encode many features of their metric geometry. We prove that each Voronoi or Delaunay cell of a plane curve appears as the limit of a sequence of cells obtained from point samples of the curve. We then use this result to study ... More

Congruences for powers of the partition functionApr 26 2016Let $p_{-t}(n)$ denote the number of partitions of $n$ into $t$ colors. In analogy with Ramanujan's work on the partition function, Lin recently proved in \cite{Lin} that $p_{-3}(11n+7)\equiv0\pmod{11}$ for every integer $n$. Such congruences, those of ... More

Divisorial motivic zeta functions for marked stable curvesJul 11 2019We define a divisorial motivic zeta function for stable curves with marked points which agrees with Kapranov's motivic zeta function when the curve is smooth and unmarked. We show that this zeta function is rational, and give a formula in terms of the ... More

CM Evaluations of the Goswami-Sun SeriesMay 09 2018In recent work, Sun constructed two $q$-series, and he showed that their limits as $q\rightarrow1$ give new derivations of the Riemann-zeta values $\zeta(2)=\pi^2/6$ and $\zeta(4)=\pi^4/90$. Goswami extended these series to an infinite family of $q$-series, ... More

Category of Noncommutative CW complexes. IIINov 04 2002Jul 03 2007We prove in this paper a noncommutative version of Leray Spectral Sequence Theorem and then Leray-Serre Spectral Theorem for noncommutative Serre fibrations: for NC Serre fibration there are converging spectral sequences with $\E^2$ terms as $\E^2_{p,q} ... More

Jeffrey-Kirwan-Witten Localization Formula for Reductions at Regular Co-adjoint OrbitsJul 21 1998For Marsden-Weinstein reductions at the point 0 in the vector space dual to the Lie algebra, the well-known Jeffrey-Kirwan-Witten localization formula was proven and lastly modified by M. Vergne. We prove in this paper the same kind formula for the reductions ... More

Theoretical methods for understanding advanced magnetic materials: the case of frustrated thin filmsApr 22 2016Materials science has been intensively developed during the last 30 years. This is due, on the one hand, to an increasing demand of new materials for new applications and, on the other hand, to technological progress which allows for the synthesis of ... More

Riemann-Roch Theorem and Index Theorem in Non-commutative GeometryNov 05 2002In this lecture we review apprearance of the Riemann-Roch Theorem in classical function theory, Algebraic topology, in theory of pseudo-differential operators and finally in noncommutative geometry. We show also it usefulness in many problem of quantization ... More

Quantum Strata of Coadjoint OrbitsMar 16 2000May 18 2000In this paper we construct quantum analogs of strata of coadjoint orbits and describe their representations. This kind objects play an important role in describing quantum groups as repeated extensions of quantum strata.

Inequalities satisfied by the Andrews spt-functionJun 06 2017Aug 27 2017In a recent paper, W. Y. Chen conjectured a number of inequalities involving the partition function $p(n)$ and the Andrews smallest parts partition function $\mathrm{spt}(n)$. Here we prove these conjectures. Further, we strengthen one of the conjectures, ... More

A Survey of Noncommutative Chern CharactersMar 17 2000We report in this survey some new results concerning noncommutative Chern characters: construction and the cases when they are exactly computed. The major result indicates some clear relation of these noncommutative objects and their commutative counterparts. ... More

On the Structure of Lie Group C*-Algebras and Compact Quantum GroupsAug 06 1998We expose a K-theoretic approach to study group C*-algebras and C*-algebraic compact quantum groups: 1. The conception of multidimensional geometric quantization and the index of group C*-algebras; 2. the entire homology of noncommutative de Rham currents ... More

Discrete Series for Loop Groups.I. An algebraic Realization of Standard ModulesSep 23 1998In this paper we consider the category $C (\tilde k, \tilde H)$ of the $(\tilde k, \tilde H)$-modules, including all the Verma modules, where $k$ is some compact Lie algebra and H some Cartan subgroup, $\tilde k$ and $\tilde H$ are the corresponding affine ... More

Noncommutative Spherical Tight Frames in finitely generated Hilbert C*-modulesSep 28 2004In the paper we describe the C*-algebras of noncommutative spherical tight frames over some C*-algebras and then apply to study the noncommutative version of the universal classifying space.

Category of Noncommutative CW Complexes. IINov 04 2002Jul 02 2007We introduce in this paper the notion of noncommutative Serre fibration (shortly, NCSF) and show that up to homotopy, every NCCW complex morphism is some noncommutative Serre fibration. We then deduce a six-term exact sequence for the periodic cyclic ... More

Quantized Algebras of Functions on Affine Hecke AlgebrasJan 02 2001The so called quantized algebras of functions on affine Hecke algebras of type A and the corresponding q-Schur algebras are defined and their irreducible unitarizable representations are classified.

Quantization of Fields and Automorphic RepresentationsApr 05 2017In this paper we use the quantization of fields based on Geometric Langlands Correspondence \cite{diep1} to realize the automorphic representations of some concrete series of groups: for the affine Heisenberg (loop) groups it is reduced to the construction ... More

$\ell$-adic Poisson Formula and Endoscopy for $p$-Adic Reductive GroupsOct 06 2016For two distinguished prime $\ell$ and $p$, we prove a $\ell$-adic version of the Poisson formula for reductive $p$-adic groups. In order to do this we write an identity for the trace of regular representation and orbital integrals. Next we reduce them ... More

Effective Bounds for the Andrews spt-functionJun 06 2017May 28 2019In this paper, we establish an asymptotic formula with an effective bound on the error term for the Andrews smallest parts function $\mathrm{spt}(n)$. We use this formula to prove recent conjectures of Chen concerning inequalities which involve the partition ... More

Higher Width MoonshineJul 19 2018$\textit{Weak moonshine}$ for a finite group $G$ is the phenomenon where an infinite dimensional graded $G$-module $$V_G=\bigoplus_{n\gg-\infty}V_G(n)$$ has the property that its trace functions, known as McKay-Thompson series, are modular functions. ... More

Quantum Theory of Helimagnetic Thin FilmsNov 30 2014We study properties of a helimagnetic thin film with quantum Heisenberg spin model by using the Green's function method. Surface spin configuration is calculated by minimizing the spin interaction energy. It is shown that the angles between spins near ... More

The Noncommutative Chern-Connes Character of the Locally Compact Quantum Normalizer of SU(1,1) in SL(2,C)Sep 12 2003We observe that the von Neumann envelope of the quantum algebra of functions on the normalizer of thegroup $\SU(1,1)\cong \SL(2,\mathbb R)$ in $\SL(2,\mathbb C)$ via deformation quantization contains the von Neumann algebraic quantum normalizer of $\SU(1,1)$ ... More

Category of Noncommutative CW ComplexesJul 02 2007We expose the notion of noncommutative CW (NCCW) complexes, define noncommutative (NC) mapping cylinder and NC mapping cone, and prove the noncommutative Approximation Theorem. The long exact homotopy sequences associated with arbitrary morphisms are ... More

On the Twisted KK-Theory and Positive Scalar Curvature ProblemFeb 05 2016Positiveness of scalar curvature and Ricci curvature requires vanishing the obstruction $\theta(M)$ which is computed in some KK-theory of C*-algebras index as a pairing of spin Dirac operator and Mishchenko bundle associated to the manifold. U. Pennig ... More

$\mathbf Z_2$-graded Cech Cohomology in Noncommutative GeometrySep 10 2004Sep 24 2004The Z_2-graded Cech cohomology theory is considered in the framework of noncommutative geometry over complex number field and in particular the homotopy invariance and Morita invariance are proven.

Temperature Dependence of the Spin Resistivity in Ferromagnetic Thin FilmsJan 29 2008The magnetic phase transition is experimentally known to give rise to an anomalous temperature-dependence of the electron resistivity in ferromagnetic crystals. Phenomenological theories based on the interaction between itinerant electron spins and lattice ... More

Potts-Percolation-Gauss Model of a SolidNov 14 2007We study a statistical mechanics model of a solid. Neighboring atoms are connected by Hookian springs. If the energy is larger than a threshold the "spring" is more likely to fail, while if the energy is lower than the threshold the spring is more likely ... More

Extended Defects in the Potts-Percolation Model of a Solid: Renormalization Group and Monte Carlo AnalysisMay 17 2009We extend the model of a 2$d$ solid to include a line of defects. Neighboring atoms on the defect line are connected by ?springs? of different strength and different cohesive energy with respect to the rest of the system. Using the Migdal-Kadanoff renormalization ... More

Equation of State from Potts-Percolation Model of a SolidJul 06 2011Nov 07 2011We expand the Potts-percolation model of a solid to include stress and strain. Neighboring atoms are connected by bonds. We set the energy of a bond to be given by the Lennard-Jones potential. If the energy is larger than a threshold the bond is more ... More

Monte Carlo Study of Magnetic Resistivity in Semiconducting MnTeNov 07 2011We investigate in this paper properties of the spin resistivity in the magnetic semiconducting MnTe of NiAs structure. MnTe is a crossroad semiconductor with a large band gap. It is an antiferromagnet with the N\'eel temperature around 310K. Due to this ... More

Fast Flat-Histogram Method for Generalized Spin ModelsApr 14 2005Oct 07 2005We present a Monte Carlo method that efficiently computes the density of states for spin models having any number of interaction per spin. By combining a random-walk in the energy space with collective updates controlled by the microcanonical temperature, ... More

Multiquadratic fields generated by characters of $A_n$Apr 24 2019For a finite group $G$, let $K(G)$ denote the field generated over $\mathbb{Q}$ by its character values. For $n>24$, G. R. Robinson and J. G. Thompson proved that $$K(A_n)=\mathbb{Q}\left (\{ \sqrt{p^*} \ : \ p\leq n \ {\text{ an odd prime with } p\neq ... More

On the energy landscape of the mixed even $p$-spin modelSep 14 2016Mar 24 2017We investigate the energy landscape of the mixed even $p$-spin model with Ising spin configurations. We show that for any given energy level between zero and the maximal energy, with overwhelming probability there exist exponentially many distinct spin ... More

Melting of Rare-Gas Crystals: Monte Carlo Simulation versus ExperimentsOct 04 2012We study the melting transition in crystals of rare gas Ar, Xe, and Kr by the use of extensive Monte Carlo simulations with the Lennard-Jones potential. The parameters of this potential have been deduced by Bernardes in 1958 from experiments of rare gas ... More

Integer Generalized Splines on CyclesSep 04 2014Let G be a graph whose edges are labeled by positive integers. Label each vertex with an integer and suppose if two vertices are joined by an edge, the vertex labels are congruent to each other modulo the edge label. The set of vertex labels satisfying ... More

Phase transition in random tensors with multiple spikesSep 18 2018Dec 15 2018Consider a spiked random tensor obtained as a mixture of two components: noise in the form of a symmetric Gaussian $p$-tensor and signal in the form of a symmetric low-rank random tensor. The latter low-rank tensor is formed as a linear combination of ... More

Effects of Ferromagnetic Magnetic Ordering and Phase Transition on the Resistivity of Spin CurrentNov 02 2007It has been shown experimentally a long time ago that the magnetic ordering causes an anomalous behavior of the electron resistivity in ferromagnetic crystals. Phenomenological explanations based on the interaction between itinerant electron spins and ... More

Simulation of Spin Models in Multicanonical Ensemble with Collective UpdatesSep 21 2004We propose a Monte Carlo method which performs a random walk in energy space using cluster-like collective updates. By imposing that bond probabilities depend continuously on the microcanonical temperature, we obtain dynamic exponents close to their ideal ... More

On the energy landscape of the mixed even $p$-spin modelSep 14 2016Sep 19 2016We investigate the energy landscape of the mixed even $p$-spin model with Ising spin configurations. We show that for any given energy level between zero and the maximal energy, with overwhelming probability there exist exponentially many distinct spin ... More

Multiquadratic fields generated by characters of $A_n$Apr 24 2019May 02 2019For a finite group $G$, let $K(G)$ denote the field generated over $\mathbb{Q}$ by its character values. For $n>24$, G. R. Robinson and J. G. Thompson proved that $$K(A_n)=\mathbb{Q}\left (\{ \sqrt{p^*} \ : \ p\leq n \ {\text{ an odd prime with } p\neq ... More

Review of several false positive error rate estimates for latent fingerprint examination proposed based on the 2014 Miami Dade Police Department studySep 11 2018Oct 22 2018During the past decade, several studies have been conducted to estimate the false positive error rate (FPR) associated with latent fingerprint examination. The so-called Black-box study by Ulery et al. is regularly used to support the claim that the FPR ... More

From Curves to Tropical Jacobians and BackJan 12 2017Given a curve defined over an algebraically closed field which is complete with respect to a nontrivial valuation, we study its tropical Jacobian. This is done by first tropicalizing the curve, and then computing the Jacobian of the resulting weighted ... More

Reexamination of the long-range Potts model: a multicanonical approachJun 19 2003Apr 17 2004We investigate the critical behavior of the one-dimensional q-state Potts model with long-range (LR) interaction $1/r^{d+\sigma}$, using a multicanonical algorithm. The recursion scheme initially proposed by Berg is improved so as to make it suitable ... More

Magnetic Properties of (La0.56Ce0.14)Sr0.30MnO3 PerovskiteJul 01 2016We investigate in this paper magnetic properties of the perovskite compound (La0.56Ce0.14)Sr0.30MnO3. The method we use here is Monte Carlo simulation, in which we take into account different kinds of interactions between nearest and between next-nearest ... More

Monte Carlo Simulation of Melting and Lattice Relaxation of the (111) Surface of SilverJan 15 2013It is experimentally observed and theoretically proved that the distance between topmost layers of a metal surface has a contraction. However, well-known potentials such as Lennard-Jones and Morse potentials lead to an expansion of the surface inter-layer ... More

Tricriticality of the Blume-Emery-Griffiths Model In Thin Films of Stacked Triangular LatticesApr 06 2015Oct 24 2015We study in this paper the Blume-Emery-Griffiths model in a thin film of stacked triangular lattices.The model is described by three parameters: bilinear exchange interaction between spins $J$, quadratic exchange interaction $K$ and single-ion anisotropy ... More

Phase Transition in Heisenberg Stacked Triangular Antiferromagnets: End of a ControversyAug 04 2008By using the Wang-Landau flat-histogram Monte Carlo (MC) method for very large lattice sizes never simulated before, we show that the phase transition in the frustrated Heisenberg stacked triangular antiferromagnet is of first-order, contrary to results ... More

Frustration Effects in Antiferromagnetic FCC Heisenberg FilmsMay 08 2007We study the effects of frustration in an antiferromagnetic film of FCC lattice with Heisenberg spin model including an Ising-like anisotropy. Monte Carlo (MC) simulations have been used to study thermodynamic properties of the film. We show that the ... More

Stacked Triangular XY Antiferromagnets: End of a Controversial Issue on the Phase TransitionNov 02 2007We show in this paper by using the Wang-Landau flat-histogram Monte Carlo method that the phase transition in the XY stacked triangular antiferromagnet is clearly of first-order, confirming results from latest Monte Carlo simulation and from a nonperturbative ... More

Quantum Communication and Quantum Multivariate Polynomial InterpolationApr 05 2017The paper is devoted to the problem of multivariate polynomial interpolation and its application to quantum secret sharing. We show that using quantum Fourier transform one can produce the protocol for quantum secret sharing distribution.

Poisson Summation and Endoscopy for $SL(3,\mathbb R)$Jul 13 2014The group is interesting as the first example of split rank 2 semisimple group, all the irreducible unitary representations of which are known. We make a precise realization of the discrete series representations (in Section 2) by using the Orbit Method ... More

Quantum Co-Adjoint Orbits of the Group of Affine Transformations of the Complex Straight LineAug 11 1999We construct start-products on the co-adjoint orbit of Lie group $\Aff({\bf C})$ of affine transformations of the complex straight line and apply them to obtain the irreducible unitary representations of this group. These results show effectiveness of ... More

Effect of Dipolar Interaction in Molecular CrystalsDec 20 2011We investigate in this paper the ground state and the nature of the transition from an orientational ordered phase at low temperature to the disordered state at high temperature in a molecular crystal. Our model is a Potts model which takes into account ... More

Quantum Gauss Jordan EliminationNov 07 2005Jul 04 2007In this paper we construct the Quantum Gau\ss Jordan Elimination (QGJE) Algorithm and estimate the complexity time of computation of Reduced Row Echelon Form (RREF) of an $N\times N$ matrix using QGJE procedure. The main theorem asserts that QGJE has ... More

Automorphic Representations of $\SL(2,\mathbb R)$ and Quantization of FieldsJun 11 2014In this paper we make a clear relationship between the automorphic representations and the quantization through the Geometric Langlands Correspondence. We observe that the discrete series representation are realized in the sum of eigenspaces of Cartan ... More

Quantum E-ChequesMay 29 2017We analyze the procedure providing quantum cheques of S. R. Moulick and P. K. Panigrahi to produce quantum e-cheques, based on multiparty quantum telecommunication between customer and cooperated branches of bank.

Poisson Summation and Endoscopy for SU(2,1)Jul 23 2014May 14 2016In this paper we analyze the endoscopy for $SU(2,1)$. The new results are a precise realization of the discrete series representations (in Section 2), a computation of their traces (Section 3) and an exact formula for the Poisson summation and endoscopy ... More

Magnetic properties of perovskites La$_{0.7}$Sr$_{0.3}$Mn$_{0.7}^{3+}$Mn$_{0.3-x}^{4+}$Ti$_x$O$_3$:Monte Carlo simulation versus experimentsMay 17 2016This work presents a Monte Carlo study of the phase transition in the perovskites La$_{0.7}$Sr$_{0.3}$Mn$_{0.7}^{3+}$Mn$_{0.3-x}^{4+}$Ti$_x$O$_3$ ($x$= 0.1, 0.2, and 0.25). We take into accountnearest-neighbor (NN) interactions between magnetic ions Mn$^{3+}$($S=2$) ... More

Helimagnetic thin films: surface reconstruction, surface spin-waves and magnetizationAug 06 2015Quantum properties of a helimagnetic thin film of simple cubic lattice with Heisenberg spin model are studied using the Green's function method. We find that the spin configuration across the film is strongly non uniform. Using the exactly determined ... More

Spin transport in magnetic multilayersMay 07 2007We study by extensive Monte Carlo simulations the transport of itinerant spins travelling inside a multilayer composed of three ferromagnetic films antiferromagnetically coupled to each other in a sandwich structure. The two exterior films interact with ... More

First-order transition of tethered membranes in 3d spaceJul 02 2002We study a model of phantom tethered membranes, embedded in three-dimensional space, by extensive Monte Carlo simulations. The membranes have hexagonal lattice structure where each monomer is interacting with six nearest-neighbors (NN). Tethering interaction ... More

Phase Transition in Dimer LiquidsSep 05 2013We study the phase transition in a system composed of dimers interacting with each other via a nearest-neighbor (NN) exchange $J$ and competing interactions taken from a truncated dipolar coupling. Each dimer occupies a link between two nearest sites ... More

Montecarlo simulation of the role of defects as the melting mechanismJun 21 2000Mar 06 2001We study in this paper the melting transition of a crystal of fcc structure with the Lennard-Jones potential, by using isobaric-isothermal Monte Carlo simulations. Local and collective updates are sequentially used to optimize the convergence. We show ... More

Secure Transmissions Using Artificial Noise in MIMO Wiretap Interference Channel: A Game Theoretic ApproachDec 23 2016We consider joint optimization of artificial noise (AN) and information signals in a MIMO wiretap interference network, wherein the transmission of each link may be overheard by several MIMO-capable eavesdroppers. Each information signal is accompanied ... More

A Geometric Realization of Degenerate Principal Series Representations of Symplectic GroupsSep 15 1998The multidimensional quantization procedure, proposed by the first author and its modifications (reduction to radicals and lifting on U(1)-coverings) give us a almost universal theoretical tools to find irreducible representations of Lie groups. By using ... More

Quantum Half-Planes via Deformation QuantizationMay 02 1999May 07 1999We demonstrate the main idea of constructing irreducible unitary representations of Lie groups by using Fedosov deformation quantization in the concrete case of the group Aff(R) of affine transformations of the real straight line. By an exact computation ... More

Optimal Packings of Two to Four Equal Circles on Any Flat TorusAug 17 2017May 14 2019We find explicit formulas for the radii and locations of the circles in all the optimally dense packings of two, three or four equal circles on any flat torus, defined to be the quotient of the Euclidean plane by the lattice generated by two independent ... More

Optimal Packings of Two to Four Equal Circles on Any Flat TorusAug 17 2017We find explicit formulas for the radii and locations of the circles in all the optimally dense packings of two, three or four equal circles on any flat torus, defined to be the quotient of the Euclidean plane by the lattice generated by two independent ... More

Two-stage approach for the inference of the source of high-dimension and complex chemical data in forensic scienceApr 03 2018Jan 11 2019Forensic scientists are often criticised for the lack of quantitative support for the conclusions of their examinations. While scholars advocate for the use of a Bayes factor to quantify the weight of forensic evidence, it is often impossible to assign ... More

Quickly fading afterimages: hierarchical adaptations in human perceptionJun 10 2019Afterimages result from a prolonged exposure to still visual stimuli. They are best detectable when viewed against uniform backgrounds and can persist for multiple seconds. Consequently, the dynamics of afterimages appears to be slow by their very nature. ... More

Performance Boundary Identification for the Evaluation of Automated Vehicles using Gaussian Process ClassificationJul 11 2019Safety is an essential aspect in the facilitation of automated vehicle deployment. Current testing practices are not enough, and going beyond them leads to infeasible testing requirements, such as needing to drive billions of kilometres on public roads. ... More

The degree of $\text{SO}(n)$Jan 12 2017Jan 13 2017We provide a closed formula for the degree of $\text{SO}(n)$ over an algebraically closed field of characteristic zero. In addition, we describe symbolic and numerical techniques which can also be used to compute the degree of $\text{SO}(n)$ for small ... More

Expansion of permutations as products of transpositionsFeb 20 2017We compute the number of ways a given permutation can be written as a product of exactly $k$ transpositions. We express this number as a linear combination of explicit geometric sequences, with coefficients which can be computed in many particular cases. ... More

Spin Resistivity in Frustrated AntiferromagnetsJun 06 2010Dec 29 2010In this paper we study the spin transport in frustrated antiferromagnetic FCC films by Monte Carlo simulation. In the case of Ising spin model, we show that the spin resistivity versus temperature exhibits a discontinuity at the phase transition temperature: ... More

Hexagonal-Close-Packed Lattice: Phase Transition and Spin TransportDec 24 2011We study the ground state (GS) and the phase transition in a hexagonal-close-packed lattice with both XY and Ising models by using extensive Monte Carlo simulation. We suppose the in-plane interaction $J_1$ and inter-plane interaction $J_2$, both antiferromagnetic. ... More

Accounting Principles are Simulated on Quantum ComputersNov 07 2005Jul 04 2007The paper is devoted to a new idea of simulation of accounting by quantum computing. We expose the actual accounting principles in a pure mathematics language. After that we simulated the accounting principles on quantum computers. We show that all arbitrary ... More

K-Theory and peiodic cyclic homology of some noncompact quantum algebrasSep 06 2001Jul 14 2003We prove in this paper that the periodic cyclic homology of the quantized algebras of functions on coadjoint orbits of connected and simply connected Lie group, are isomorphic to the periodic cyclic homology of the quantized algebras of functions on coadjoint ... More

Effects of Frustrated Surface in Heisenberg Thin FilmsSep 21 2004Nov 29 2006We study by extensive Monte Carlo (MC) simulations and analytical Green function (GF) method effects of frustrated surfaces on the properties of thin films made of stacked triangular layers of atoms bearing Heisenberg spins with an Ising-like interaction ... More

A building block for hardware belief networksJun 01 2016Belief networks represent a powerful approach to problems involving probabilistic inference, but much of the work in this area is software based utilizing standard deterministic hardware based on the transistor which provides the gain and directionality ... More

Poisson Summation and Endoscopy for $Sp(4,\mathbb R)$Jul 25 2014In this paper we analyze the endoscopy for $\Sp(4,\mathbb R)$. The new results are a precise realization of the discrete series representations (in Section 2), a computation of their traces (Section 3) and an exact formula for the noncommutative Poisson ... More

Algebraic structure representations for latticesNov 30 2018For an arbitrary group, the subgroups form a lattice with order determined by set inclusion. Not every lattice is isomorphic to the subgroup lattice for a group. However, Birkhoff and Frink proved that any compactly generated lattice is isomorphic to ... More

Focal onset seizure prediction using convolutional networksMay 29 2018Objective: This work investigates the hypothesis that focal seizures can be predicted using scalp electroencephalogram (EEG) data. Our first aim is to learn features that distinguish between the interictal and preictal regions. The second aim is to define ... More

Unitary equivalence to a complex symmetric matrix: a modulus criterionMar 14 2010We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. Our approach has several advantages over existing methods. We discuss these differences and present a ... More

Conjugacy growth series for finitary wreath productsNov 19 2016Mar 23 2017We examine the conjugacy growth series of all wreath products of the finitary permutation groups $\text{Sym}(X)$ and $\text{Alt}(X)$ for an infinite set $X$. We determine their asymptotics, and we characterize the limiting behavior between the $\text{Alt}(X)$ ... More

Moral attitudes and willingness to induce cognitive enhancement and repair with brain stimulationJan 27 2018Feb 01 2018The availability of technological means to enhance and repair human cognitive function raises questions about the perceived morality of their use. In this study, we administered a survey to the public in which subjects were asked to report how willing ... More

Monte Carlo Study of the Spin Transport in Magnetic MaterialsOct 24 2009Dec 29 2010The resistivity in magnetic materials has been theoretically shown to depend on the spin-spin correlation function which in turn depends on the magnetic-field, the density of conduction electron, the magnetic ordering stability, etc. However, these theories ... More

Genus one factors of curves defined by separated variable polynomialsSep 08 2014We give some sufficient conditions on complex polynomials P and Q to assure that the algebraic plane curve P(x)-Q(y)=0 has no irreducible component of genus 0 or 1. Moreover, if deg (P)=deg (Q) and if both P, Q satisfy Hypothesis I introduced by H. Fujimoto, ... More

Spin transport in magnetically ordered systems: effect of the lattice relaxation timeJan 30 2011Spin resistivity $R$ has been shown to result mainly from the scattering of itinerant spins with magnetic impurities and lattice spins. $R$ is proportional to the spin-spin correlation so that its behavior is very complicated near and at the magnetic ... More

Flat Energy-Histogram Simulation of the Phase Transition in an Ising Fully Frustrated LatticeDec 27 2010Jan 03 2011We show in this paper the results on the phase transition of the so-called fully frustrated simple cubic lattice with the Ising spin model. We use here the Monte Carlo method with the flat energy-histogram Wang-Landau technique which is very powerful ... More

Nature of phase transition in magnetic thin filmsMay 28 2007We study the critical behavior of magnetic thin films as a function of the film thickness. We use the ferromagnetic Ising model with the high-resolution multiple histogram Monte Carlo (MC) simulation. We show that though the 2D behavior remains dominant ... More

Optical determination and magnetic manipulation of single nitrogen-vacancy color center in diamond nanocrystalFeb 15 2010The controlled and coherent manipulation of individual quantum systems is a fundamental key for the development of quantum information processing. The nitrogen-vacancy (NV) color center in diamond is a promising system since its photoluminescence is perfectly ... More

Descent methods for Nonnegative Matrix FactorizationJan 21 2008Aug 24 2009In this paper, we present several descent methods that can be applied to nonnegative matrix factorization and we analyze a recently developped fast block coordinate method called Rank-one Residue Iteration (RRI). We also give a comparison of these different ... More

Critical behavior of magnetic thin films as a function of thicknessDec 19 2007We study the critical behavior of magnetic thin films as a function of the film thickness. We use the ferromagnetic Ising model with the high-resolution multiple histogram Monte Carlo (MC) simulation. We show that though the 2D behavior remains dominant ... More