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Particle-Hole Duality in the Lowest Landau LevelDec 22 2016We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various ... More

Random Lindblad DynamicsFeb 04 2019We study the mixing behavior of random Lindblad generators with no symmetries, using the dynamical map or propagator of the dissipative evolution. In particular, we determine the long-time behavior of a dissipative form factor, which is the trace of the ... More

Central charge from adiabatic transport of cusp singularities in the quantum Hall effectNov 17 2016We study quantum Hall (QH) states on a punctured Riemann sphere. We compute the Berry curvature under adiabatic motion in the moduli space in the large N limit. The Berry curvature is shown to be finite in the large N limit and controlled by the conformal ... More

Atomic Resolution Imaging of Currents in Nanoscopic Quantum Networks via Scanning Tunneling MicroscopySep 18 2012We propose a new method for atomic-scale imaging of spatial current patterns in nanoscopic quantum networks by using scanning tunneling microscopy (STM). By measuring the current flowing from the STM tip into one of the leads attached to the network as ... More

Spatial Current Patterns, Dephasing and Current Imaging in Graphene NanoribbonsFeb 06 2014Using the non-equilibrium Keldysh Green's function formalism, we investigate the local, non-equilibrium charge transport in graphene nanoribbons (GNRs). In particular, we demonstrate that the spatial current patterns associated with discrete transmission ... More

Odd surface waves in two-dimensional incompressible fluidsJan 30 2018Jun 18 2018We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken. For the case ... More

Current Eigenmodes and Dephasing in Nanoscopic Quantum NetworksMar 14 2012Using the non-equilibrium Keldysh Green's function formalism, we show that the non-equilibrium charge transport in nanoscopic quantum networks takes place via {\it current eigenmodes} that possess characteristic spatial patterns. We identify the microscopic ... More

Spectral gaps and mid-gap states in random quantum master equationsFeb 04 2019We discuss the decay rates of chaotic quantum systems coupled to noise. We model both the Hamiltonian and the system-noise coupling by random $N \times N$ Hermitian matrices, and study the spectral properties of the resulting Lindblad superoperator. We ... More

Measuring Electromagnetic and Gravitational Responses of Photonic Landau LevelsFeb 13 2018The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it changes its ... More

Homotopies in Classical and Paraconsistent Modal LogicsJul 25 2011Topological semantics for modal logics has recently gained new momentum in many different branches of logic. In this paper, we will consider the topological semantics of both classical and paraconsistent modal logics. This work is a new step in the research ... More

Some Non-Classical Approaches to the Branderburger-Keisler ParadoxJul 25 2011In this paper, we discuss a well-known self-referential paradox in foundational game theory, the Brandenburger - Keisler paradox. We approach the paradox from two different perspectives: non-well-founded set theory and paraconsistent logic. We show that ... More

The time optimal control problem with control constraints of the rectangular type for a class of ODEsNov 28 2011Apr 26 2012This paper studies a time optimal control problem with control constraints of the rectangular type for the linear multi-input time-varying ordinary differential equations. The aims of this study are to establish certain necessary and sufficient conditions ... More

Public Announcement Logic in Geometric FrameworksJul 25 2011Aug 18 2011In this paper we introduce public announcement logic in different geometric frameworks. First, we consider topological models, and then extend our discussion to a more expressive model, namely, subset space models. Furthermore, we prove the completeness ... More

On the stability of exact ABCs for the reaction-subdiffusion equation on unbounded domainOct 29 2015Oct 30 2015In this note we propose the exact artificial boundary conditions formula to the fractional reaction-subdiffusion equation on an unbounded domain. With the application of Laplace transformation, the exact artificial boundary conditions (ABCs) are derived ... More

Stable torsion theories and the injective hulls of simple modulesFeb 13 2014A torsion theoretical characterization of left Noetherian rings $R$ over which injective hulls of simple left modules are locally Artinian is given. Sufficient conditions for a left Noetherian ring to satisfy this finiteness condition are obtained in ... More

Dawn of Cavity SpintronicsAug 08 2015Merging the progress of spintronics with the advancement in cavity quantum electrodynamics and cavity polaritons, a new field of Cavity Spintronics is forming, which connects some of the most exciting modern physics, such as quantum information and quantum ... More

Enhancing Multiuser MIMO Through Opportunistic D2D CooperationApr 21 2016Sep 30 2016We propose a cellular architecture that combines multiuser MIMO (MU-MIMO) downlink with opportunistic use of unlicensed ISM bands to establish device-to-device (D2D) cooperation. The architecture consists of a physical-layer cooperation scheme based on ... More

A remarkable representation on nilpotent file placementsJun 04 2015Exploiting the interplay between the rook theory, graph theory, and semigroup theory, we define and study a remarkable representation of the symmetric group on labeled rooted forests. We compute various character formulas and multiplicities.

Metastability for the contact process on the preferential attachment graphFeb 19 2015Mar 02 2015We consider the contact process on the preferential attachment graph. The work of Berger, Borgs, Chayes and Saberi [BBCS1] confirmed physicists predictions that the contact process starting from a typical vertex becomes endemic for an arbitrarily small ... More

Universal Sound Attenuation in Amorphous Solids at Low-TemperaturesMar 06 2012Disordered solids are known to exhibit quantitative universalities at low temperatures, the most striking of which is the ultrasonic attenuation coefficient Q. The established theory of tunneling two state systems (TTLS) in its original form (i.e. without ... More

Toroidal affine Nash groupsSep 22 2015Apr 07 2016A toroidal affine Nash group is the affine Nash group analogue of an anti-affine algebraic group. In this note, we prove analogues of Rosenlicht's structure and decomposition theorems: (1) Every affine Nash group $G$ has a smallest normal affine Nash ... More

Second order WSGD operators II: A new family of difference schemes for space fractional advection diffusion equationOct 29 2013The second order weighted and shifted Gr\"{u}nwald difference (WSGD) operators are developed in [Tian et al., arXiv:1201.5949] to solve space fractional partial differential equations. Along this direction, we further design a new family of second order ... More

High order schemes for the tempered fractional diffusion equationsFeb 01 2014Sep 25 2014L\'{e}vy flight models whose jumps have infinite moments are mathematically used to describe the superdiffusion in complex systems. Exponentially tempering the Levy measure of L\'{e}vy flights leads to the tempered stable L\'{e}vy processes which combine ... More

Emergence of cosmological Friedmann equations from quantum entanglementSep 11 2017Jul 11 2018We study the deep connections between the concepts of quantum information theory and cosmology. Employing Fermi normal coordinates and conformal Fermi coordinates, we construct a relation between Friedmann equations of Friedmann-Lemaitre-Robertson-Walker ... More

Refined Topological Strings and Toric Calabi-Yau ThreefoldsOct 10 2012The refined topological vertex formulation computes the refined topological string partition function for non-compact toric Calabi-Yau threefolds which engineer N=2 supersymmetric gauge theories. For geometries such as the local P^2, which do not give ... More

Computing Periods of HypersurfacesMar 21 2018We give an algorithm to compute the periods of smooth projective hypersurfaces of any dimension. This is an improvement over existing algorithms which could only compute the periods of plane curves. Our algorithm reduces the evaluation of period integrals ... More

Sales Forecast in E-commerce using Convolutional Neural NetworkAug 26 2017Sales forecast is an essential task in E-commerce and has a crucial impact on making informed business decisions. It can help us to manage the workforce, cash flow and resources such as optimizing the supply chain of manufacturers etc. Sales forecast ... More

Critical behavior of the annealed ising model on random regular graphsJan 30 2017Sep 19 2017In [17], the authors have defined an annealed Ising model on random graphs and proved limit theorems for the magnetization of this model on some random graphs including random 2-regular graphs. Then in [11], we generalized their results to the class of ... More

Fusing image representations for classification using support vector machinesJul 16 2012In order to improve classification accuracy different image representations are usually combined. This can be done by using two different fusing schemes. In feature level fusion schemes, image representations are combined before the classification process. ... More

Unique Continuation and Observability Estimates for 2-D Stokes Equations with the Navier Slip Boundary ConditionMay 27 2012This paper presents a unique continuation estimate for 2-D Stokes equations with the Naiver slip boundary condition in a bounded and simply connected domain. Consequently, an observability estimate for this equation from a subset of positive measure in ... More

The Rook Monoid is Lexicographically ShellableJan 28 2010Aug 16 2018We prove that the Bruhat-Chevalley-Renner order on the rook monoid is EL-shellable. We determine the homeomorphism type of the associated order complex.

Building Morphological Chains for Agglutinative LanguagesMay 05 2017In this paper, we build morphological chains for agglutinative languages by using a log-linear model for the morphological segmentation task. The model is based on the unsupervised morphological segmentation system called MorphoChains. We extend MorphoChains ... More

Nondestructive testing of grating imperfections using grating-based X-ray phase-contrast imagingAug 23 2017We reported the usage of grating-based X-ray phase-contrast imaging in nondestructive testing of grating imperfections. It was found that electroplating flaws could be easily detected by conventional absorption signal, and in particular, we observed that ... More

Sampling for approximating $R$-limited functionsSep 07 2017$R$-limited functions are multivariate generalization of band-limited functions whose Fourier transforms are supported within a compact region $R\subset\mathbb{R}^{n}$. In this work, we generalize sampling and interpolation theorems for band-limited functions ... More

Interpolation inequality at one time point for parabolic equations with time-independent coefficients and applicationsDec 04 2017In this paper, we study the H\"older-type interpolation inequality and observability inequality from measurable sets in time for parabolic equations either with L^p unbounded potentials or with electric potentials. The parabolic equations under consideration ... More

Optimal polynomial blow up range for critical wave mapsMar 28 2014We prove that the critical Wave Maps equation with target $S^2$ and origin $\mathbb{R}^{2+1}$ admits energy class blow up solutions of the form $$u(t,r)=Q(\lambda(t)r)+\epsilon(t,r)$$where $Q: \mathbb{R}^2 \to S^2$ is the ground state harmonic map and ... More

Nested Hilbert schemes and the nested q,t-Catalan seriesNov 05 2007In this paper we study the tangent spaces of the smooth nested Hilbert scheme $ Hil{n,n-1}$ of points in the plane, and give a general formula for computing the Euler characteristic of a $\TT^2$-equivariant locally free sheaf on $\Hil{n,n-1}$. Applying ... More

A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivativeSep 11 2011A one dimensional fractional diffusion model with the Riemann-Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite difference method ... More

Signatures of Resonant Super-Partner Production with Charged-Current DecaysApr 06 2011Sep 15 2011Hadron collider signatures of new physics are investigated in which a primary resonance is produced that decays to a secondary resonance by emitting a W-boson, with the secondary resonance decaying to two jets. This topology can arise in supersymmetric ... More

Complexity $c$ Pairs in Simple Algebraic GroupsMar 15 2017Dec 25 2018We call a pair of closed subgroups $(G_1,G_2)$ from a connected reductive algebraic group $G$ a {\it complexity $c$ pair} if the multiplication action of the pair on $G$ is of complexity $c$. The main focus of this article is on the cases where $G$ is ... More

Exponential extinction time of the contact process on rank-one inhomogeneous random graphsFeb 05 2016Sep 19 2017We show that the contact process on the rank-one inhomogeneous random graphs and Erdos-R{\'e}nyi graphs with mean degree large enough survives a time exponential in the size of these graphs for any positive infection rate. In addition, a metastable result ... More

Metastability for the contact process on the preferential attachment graphFeb 19 2015Feb 22 2017We consider the contact process on the preferential attachment graph. The work of Berger, Borgs, Chayes and Saberi [BBCS1] confirmed physicists predictions that the contact process starting from a typical vertex becomes endemic for an arbitrarily small ... More

The Complete Weight Enumerator of A Class of Linear CodesMay 25 2015May 26 2015Linear codes can be employed to construct authentication codes, which is an interesting area of cryptography. The parameters of the authentication codes depend on the complete weight enumerator of the underlying linear codes. In order to obtain an authentication ... More

Observability inequalities from measurable sets for some evolution equationsJun 13 2014In this paper, we build up two observability inequalities from measurable sets in time for some evolution equations in Hilbert spaces from two different settings. The equation reads: $u'=Au,\; t>0$, and the observation operator is denoted by $B$. In the ... More

Refined Hopf Link RevisitedNov 02 2011We establish a relation between the refined Hopf link invariant and the S-matrix of the refined Chern-Simons theory. We show that the refined open string partition function corresponding to the Hopf link, calculated using the refined topological vertex, ... More

Magnetized Quark and Strange Quark Matter in the Spherical Symmetric Space-Time Admitting Conformal MotionMay 21 2007Aug 22 2007This paper has been removed by arXiv administrators because it plagiarizes astro-ph/0611537, astro-ph/0506256, astro-ph/0203033, astro-ph/0311128, gr-qc/0505144, astro-ph/0611460, and astro-ph/0610840.

Precision Electroweak Observables in the Minimal Moose Little Higgs ModelDec 03 2003Aug 04 2004Little Higgs theories, in which the Higgs particle is realized as the pseudo-Goldstone boson of an approximate global chiral symmetry have generated much interest as possible alternatives to weak scale supersymmetry. In this paper we analyze precision ... More

Nonextensive Thermostatistical Approach to the Thermoluminescence DecayMay 31 2003In this study, thermoluminescence decay is investigated within Tsallis thermostatistics (TT). We belive that this is the first attempt to handle themoluminescence decay process within TT.

A compactification of the moduli space of multiple-spin curvesJan 07 2017Apr 09 2019Using line bundles on quasi-stable curves, we construct a smooth Deligne-Mumford compactification for the moduli space of curves with an m-tuple of spin structures. This compactification normalizes the m-fold product of Cornalba's compactification of ... More

A New Descent Algebra for Standard Parabolic Subgroups of $W(A_n)$Aug 13 2014A new descent algebra $\sum_{W}(A_{n})$ of Weyl groups of type $A_n$, constructed by present authors in [1], is generated by equivalence classes $[x_J]$ arising from the equivalence relation defined on the set of all $x_J$. In this paper, we introduce ... More

Generalized Burnside Algebra of type $B_{n}$Oct 30 2014We define the generalized Burnside algebra $HB(W_{n})$ for $B_{n}$-type Coxeter group $W_{n}$ and construct an surjective algebra morphism between Mantaci-Reutenauer algebra ${\sum}'(W_{n})$ and $HB(W_{n})$. Then, by obtaining the primitive idempotents ... More

Edge sampling using network local informationOct 13 2017Edge sampling is an important topic in network analysis. It provides a natural way to reduce network size while retaining desired features of the original network. Sampling methods that only use local information are common in practice as they do not ... More

Character analogues of certain Hardy-Berndt sumsJun 05 2015In this paper we consider transformation formulas for \[ B\left( z,s:\chi\right) =\sum\limits_{m=1}^{\infty}\sum\limits_{n=0} ^{\infty}\chi(m)\chi(2n+1)\left( 2n+1\right) ^{s-1}e^{\pi im(2n+1)z/k}. \] We derive reciprocity theorems for the sums arising ... More

Joint PoS Tagging and Stemming for Agglutinative LanguagesMay 24 2017The number of word forms in agglutinative languages is theoretically infinite and this variety in word forms introduces sparsity in many natural language processing tasks. Part-of-speech tagging (PoS tagging) is one of these tasks that often suffers from ... More

Computing Periods of HypersurfacesMar 21 2018Apr 23 2019We give an algorithm to compute the periods of smooth projective hypersurfaces of any dimension. This is an improvement over existing algorithms which could only compute the periods of plane curves. Our algorithm reduces the evaluation of period integrals ... More

A New Descent Algebra of Weyl Groups of Type AnApr 18 2014In this paper we define an equivalence relation on the set of all $x_{J}$ in order to form a basis for a new descent algebra of Weyl groups of type $A_{n}$. By means of this, we construct a new commutative and semi-simple descent algebra of Weyl groups ... More

Integral and measure-turnpike properties for infinite-dimensional optimal control systemsMay 08 2017We first derive a general integral-turnpike property around a set for infinite-dimensional non-autonomous optimal control problems with any possible terminal state constraints, under some appropriate assumptions. Roughly speaking, the integral-turnpike ... More

Approximating fractional derivative of the Gaussian function and Dawson's integralSep 07 2017A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial or discrete ... More

Early Diagnosis of Pneumonia with Deep LearningApr 01 2019Pneumonia has been one of the fatal diseases and has the potential to result in severe consequences within a short period of time, due to the flow of fluid in lungs, which leads to drowning. If not acted upon by drugs at the right time, pneumonia may ... More

Cavity Spintronics: An Early Review of Recent Progress in the Study of Magnon-Photon Level RepulsionNov 26 2018Light-matter interactions lie at the heart of condensed matter physics, providing physical insight into material behaviour while enabling the design of new devices. Perhaps this is most evident in the push to develop quantum information and spintronic ... More

Ordered Bell numbers, Hermite polynomials, Skew Young Tableaux, and Borel orbitsNov 29 2011Jun 07 2012We give three interpretations of the number $b$ of orbits of the Borel subgroup of upper triangular matrices on the variety $\ms{X}$ of complete quadrics. First, we show that $b$ is equal to the number of standard Young tableaux on skew-diagrams. Then, ... More

SL(2)-regular Subvarieties of Complete QuadricsOct 29 2011We determine SL(n)-stable, SL(2)-regular subvarieties of the variety of complete quadrics. We extend the results of Aky{\i}ld{\i}z and Carrell on Kostant-Macdonald identity by computing the Poincar{\'e} polynomials of these regular subvarieties.

Basic Performance Limits and Tradeoffs in Energy Harvesting Sensor Nodes with Finite Data and Energy StorageSep 03 2010Sep 05 2012As many sensor network applications require deployment in remote and hard-to-reach areas, it is critical to ensure that such networks are capable of operating unattended for long durations. Consequently, the concept of using nodes with energy replenishment ... More

Extended Bernoulli and Stirling matrices and related combinatorial identitiesJun 25 2013Dec 04 2013In this paper we establish plenty of number theoretic and combinatoric identities involving generalized Bernoulli and Stirling numbers of both kinds. These formulas are deduced from Pascal type matrix representations of Bernoulli and Stirling numbers. ... More

Diagonal Orbits in a Double Flag Variety of Complexity One, Type AOct 15 2018We continue our study of the inclusion posets of diagonal $SL(n)$-orbit closures in a product of two partial flag varieties. We prove that, if the diagonal action is of complexity one, then the poset is isomorphic to one of the 28 lattices that we determine ... More

Smooth Schubert Varieties are SphericalMar 14 2018Sep 18 2018We prove the statement in the title of this paper: a smooth Schubert variety $X$ is spherical with respect to the induced action of any Levi subgroup of the parabolic subgroup which stabilizes $X$.

A numerical transcendental method in algebraic geometryNov 26 2018Based on high precision computation of periods and lattice reduction techniques, we compute the Picard group of smooth surfaces. We also study the lattice reduction technique that is employed in order to quantify the possibility of numerical error in ... More

Temperature as a quantum observableAug 30 2017Jul 18 2018In this article, we address the problem of how temperature of a quantum system is observed. By proposing a thought experiment, we argue that temperature must be conceived as an operator and its measurement must necessarily accompany a collapse in the ... More

Mathematical and numerical validation of the simplified spherical harmonics approach for time-dependent anisotropic-scattering transport problems in homogeneous mediaJan 02 2017In this work, we extend the solid harmonics derivation, which was used by Ackroyd et al to derive the steady-state SP$_N$ equations, to transient problems. The derivation expands the angular flux in ordinary surface harmonics but uses harmonic polynomials ... More

Omitting parentheses from the cyclic notationAug 05 2013Aug 28 2013The purpose of this article is to initiate a combinatorial study of the Bruhat-Chevalley ordering on certain sets of permutations obtained by omitting the parentheses from their standard cyclic notation. In particular, we show that these sets form a bounded, ... More

Weak Order on Complete QuadricsJan 10 2012Mar 08 2012Using an action of the Richardson-Springer monoid on involutions, we study the weak order on the variety of complete quadrics. Maximal chains in the poset are explicitly determined. Applying results of Brion, our calculations describe certain cohomology ... More

Some anisotropic universes in the presence of imperfect fluid coupling with spatial curvatureAug 15 2010Feb 17 2011We consider Bianchi VI spacetime, which also can be reduced to Bianchi types VI0-V-III-I. We initially consider the most general form of the energy-momentum tensor which yields anisotropic stress and heat flow. We then derive an energy-momentum tensor ... More

Bianchi type III models with anisotropic dark energySep 07 2009The general form of the anisotropy parameter of the expansion for Bianchi type-III metric is obtained in the presence of a single diagonal imperfect fluid with a dynamically anisotropic equation of state parameter and a dynamical energy density in general ... More

On the integral of products of higher-order Bernoulli and Euler polynomialsSep 29 2016In this paper, we derive a formula on the integral of products of the higher-order Euler polynomials. By the same way, similar relations are obtained for $l$ higher-order Bernoulli polynomials and $r$ higher-order Euler polynomials. Moreover, we establish ... More

Passage time of the frog model has a sublinear varianceApr 07 2019In this paper, we show that the passage time in the frog model on $\mathbb{Z}^d$ with $d\geq 2$ has a sublinear variance. The proof is based on the method introduced in \cite{DHS} combining with tessellation arguments to estimate the martingale difference. ... More

Prym varieties of genus four curvesAug 23 2018May 02 2019Double covers of a generic genus four curve C are in bijection with Cayley cubics containing the canonical model of C. The Prym variety associated to a double cover is a quadratic twist of the Jacobian of a genus three curve X. The curve X can be obtained ... More

Trace of the twisted Heisenberg CategoryFeb 26 2017Oct 23 2017We show that the trace decategorification, or zeroth Hochschild homology, of the twisted Heisenberg category defined by Cautis and Sussan is isomorphic to a quotient of $W^-$, a subalgebra of $W_{1+\infty}$ defined by Kac, Wang, and Yan. Our result is ... More

Character analogue of the Boole summation formula with applicationsOct 04 2016In this paper, we present the character analogue of the Boole summation formula. Using this formula, an integral representation is derived for the alternating Dirichlet $L-$function and its derivative is evaluated at $s=0$. Some applications of the character ... More

Inferring Network Structure from CascadesNov 15 2016Many physical, biological and social phenomena can be described by cascades taking place on a network. Often, the activity can be empirically observed, but not the underlying network of interactions. In this paper we solve the dynamics of general cascade ... More

Equivariant $K$-theory of smooth projective spherical varietiesMar 16 2016We provide a GKM-type description of the equivariant $K$-theory of a smooth projective spherical variety. This provides an integral $K$-theory version of Brion's calculation of equivariant Chow-cohomology of such varieties. We then analyze the torus equivariant ... More

Prym varieties of genus four curvesAug 23 2018Double covers of a generic genus four curve C are in bijection with Cayley cubics containing the canonical model of C. The dual of one such cubic intersected with the dual of the quadric containing C yields the genus three Prym curve corresponding to ... More

Scheme for preparation of mulipartite entanglement of atomic ensemblesMay 28 2002Oct 27 2003We describe an experimental scheme of preparing multipartite W class of maximally entangled states between many atomic ensembles. The scheme is based on laser manipulation of atomic ensembles and single-photon detection, and well fits the status of the ... More

On generalized Eisenstein series and Ramanujan's formula for periodic zeta-functionsFeb 22 2016In this paper, transformation formulas for a large class of Eisenstein series defined by \[ G(z,s;A_{\alpha},B_{\beta};r_{1},r_{2})=\sum\limits_{m,n=-\infty}^{\infty }\ \hspace{-0.19in}^{^{\prime}}\frac{f(\alpha m)f^{\ast}(\beta n)} {((m+r_{1})z+n+r_{2})^{s}},\text{ ... More

Monodromy of torus fiber bundles and decomposability problemJul 25 2016Mar 20 2017The notion of a (stably) decomposable fiber bundle is introduced. In low dimensions, for torus fiber bundles over a circle the notion translates into a property of elements of the special linear group of integral matrices. We give a complete characterization ... More

On the cohomology rings of Grassmann varieties and Hilbert schemesJun 08 2017Jul 24 2017By using vector field techniques, we compute the ordinary and equivariant cohomology rings of Hilbert scheme of points in the projective plane in relation with that of a Grassmann variety.

Equivariant $K$-theory of smooth projective spherical varietiesMar 16 2016Feb 13 2017We present a description of the equivariant $K$-theory of a smooth projective spherical variety. This provides an integral $K$-theory version of Brion's calculation of equivariant Chow-cohomology of such varieties. We consider the equivariant $K$-theory ... More

Metastability for the contact process on the configuration model with infinite mean degreeOct 12 2014Jul 17 2015We study the contact process on the configuration model with a power law degree distribution, when the exponent is smaller than or equal to two. We prove that the extinction time grows exponentially fast with the size of the graph and prove two metastability ... More

Generators of the Hecke algebra of $(S_{2n},B_n)$Sep 27 2010May 04 2012A set of ring generators for the Hecke algebra of the Gel'fand pair $(S_{2n},B_n)$, where $B_n$ is the hyperoctahedral subgroup of the symmetric group $S_{2n}$ is presented. Various corollaries are given. A conjecture of Sho Matsumoto is proven.

de Sitter expansion with anisotropic fluid in Bianchi type-I space-timeJan 04 2010Jan 25 2010Some features of the Bianchi type-I universes in the presence of a fluid that wields an anisotropic equation of state (EoS) parameter are discussed in the context of general relativity. The models that exhibit de Sitter volumetric expansion due to the ... More

Almost automorphic solutions of discrete delayed neutral systemDec 26 2014Nov 05 2015We study almost automorphic solutions of the discrete delayed neutral dynamic system% \[ x(t+1)=A(t)x(t)+\Delta Q(t,x(t-g(t)))+G(t,x(t),x(t-g(t))) \] by means of a fixed point theorem due to Krasnoselskii. Using discrete variant of exponential dichotomy ... More

Complex $\text{G}_2$ and associative grassmannianDec 10 2015By using techniques from calibrated geometries, we investigate the parametrizing variety of quaternion subalgebras of the complex octonions. This variety is the unique smooth spherical compactification of $G_2/SO(4)$ with Picard number 1. We describe ... More

Transformation formulas of a character analogue of $\logθ_{2}(z)$Oct 13 2017In this paper, transformation formulas for the function \[ A_{1}\left(z,s:\chi\right)=\sum\limits_{n=1}^{\infty}\sum\limits_{m=1}^{\infty}\chi\left(n\right)\chi\left(m\right)\left(-1\right)^{m}n^{s-1}e^{2\pi imnz/k} \] are obtained. Sums that appear in ... More

On reciprocity formula of character Dedekind sums and the integral of products of Bernoulli polynomialsDec 23 2014Feb 09 2015We give a simple proof for the reciprocity formulas of character Dedekind sums associated with two primitive characters, whose modulus need not to be same, by utilizing the character analogue of the Euler-MacLaurin summation formula. Moreover, we extend ... More

Floquet theory based on new periodicity concept for hybrid systems involving $q$-difference equationsMay 30 2013Nov 06 2015Using the new periodicity concept based on shifts, we construct a unified Floquet theory for homogeneous and nonhomogeneous hybrid periodic systems on domains having continuous, discrete or hybrid structure. New periodicity concept based on shifts enables ... More

Adjoint Representations of the Symmetric GroupMar 29 2018We study the restriction to the symmetric group, $\mc{S}_n$ of the adjoint representation of $\mt{GL}_n(\C)$. We determine the irreducible constituents of the space of symmetric as well as the space of skew-symmetric $n\times n$ matrices as $\mc{S}_n$-modules. ... More

Monodromy of torus fibrations and decomposability problemJul 25 2016The notion of a (stably) decomposable fiber bundle is introduced. For torus fibrations over the circle, the notion translates into a property of matrices from special linear group of integral matrices. We give a complete characterization of the stably ... More

Scheme for preparation of nonmaximal entanglement between two atomic ensemblesJul 03 2002Jul 08 2002We propose an experimentally feasible scheme to generate nonmaximal entanglement between two atomic ensembles. The degree of entanglement is readily tunable. The scheme involves laser manipulation of atomic ensembles, adjustable quarter- and half-wave ... More

Periodic analogues of Dedekind sums and transformation formulas of Eisenstein seriesJun 05 2015Jan 06 2016In this paper, a transformation formula under modular substitutions is derived for a large class of generalized Eisenstein series. Appearing in the transformation formulae are generalizations of Dedekind sums involving the periodic Bernoulli function. ... More

UDFNet: Unsupervised Disparity Fusion with Adversarial NetworksApr 22 2019Existing disparity fusion methods based on deep learning achieve state-of-the-art performance, but they require ground truth disparity data to train. As far as I know, this is the first time an unsupervised disparity fusion not using ground truth disparity ... More

Calculating Heegaard-Floer Homology by Counting Lattice Points in TetrahedraNov 21 2012Feb 21 2013We introduce a notion of complexity for Sefiert homology spheres by establishing a correspondence between lattice point counting in tethrahedra and the Heegaard-Floer homology. This complexity turns out to be equivalent to a version of Casson invariant ... More