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Scaling Behaviour of Quiver Quantum MechanicsMar 09 2015Sep 28 2015We explore vacuum degeneracy of Kronecker quiver with large ranks, by computing Witten index of corresponding 1d gauged linear sigma model. For $(d-1,d)_k$ quivers with the intersection number $k$, we actually counted index of its mutation equivalent, ... More

Comments on twisted indices in 3d supersymmetric gauge theoriesMay 20 2016Jun 21 2016We study three-dimensional ${\mathcal N}=2$ supersymmetric gauge theories on ${\Sigma_g \times S^1}$ with a topological twist along $\Sigma_g$, a genus-$g$ Riemann surface. The twisted supersymmetric index at genus $g$ and the correlation functions of ... More

D-brane anomaly inflow revisitedJan 03 2012Feb 07 2012Axial and gravitational anomaly of field theories, when embedded in string theory, must be accompanied by canceling inflow. We give a self-contained overview for various world-volume theories, and clarify the role of smeared magnetic sources in I-brane/D-brane ... More

Exact Partition Functions on RP2 and OrientifoldsOct 16 2013Feb 06 2014We consider gauged linear sigma models (GLSM) on $\mathbb{RP}^2$, obtained from a parity projection of $S^2$. The theories admit squashing deformation, much like GLSM on $S^2$, which allows us to interpret the partition function as the overlap amplitude ... More

't Hooft anomalies and the holomorphy of supersymmetric partition functionsMay 14 2019We study the dependence of supersymmetric partition functions on continuous parameters for the flavor symmetry group, $G_F$, for 2d $\mathcal{N} = (0,2)$ and 4d $\mathcal{N}=1$ supersymmetric quantum field theories. In any diffeomorphism-invariant scheme ... More

Witten Index and Wall CrossingJul 09 2014Dec 22 2014We compute the Witten index of one-dimensional gauged linear sigma models with at least ${\mathcal N}=2$ supersymmetry. In the phase where the gauge group is broken to a finite group, the index is expressed as a certain residue integral. It is subject ... More

$\mathcal{N}{=}1$ supersymmetric indices and the four-dimensional A-modelJul 18 2017Aug 14 2017We compute the supersymmetric partition function of $\mathcal{N}{=}1$ supersymmetric gauge theories with an $R$-symmetry on $\mathcal{M}_4 \cong \mathcal{M}_{g,p}\times S^1$, a principal elliptic fiber bundle of degree $p$ over a genus-$g$ Riemann surface, ... More

Mutation, Witten Index, and Quiver InvariantApr 01 2015Apr 16 2015We explore Seiberg-like dualities, or mutations, for ${\cal N}=4$ quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed Fayet-Iliopoulos constants, ... More

Seifert fibering operators in 3d $\mathcal{N}=2$ theoriesJul 06 2018Oct 12 2018We study 3d $\mathcal{N}=2$ supersymmetric gauge theories on closed oriented Seifert manifold---circle bundles over an orbifold Riemann surface---, with a gauge group G given by a product of simply-connected and/or unitary Lie groups. Our main result ... More

Supersymmetric partition functions and the three-dimensional A-twistJan 11 2017Jan 19 2017We study three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories on $\mathcal{M}_{g,p}$, an oriented circle bundle of degree $p$ over a closed Riemann surface, $\Sigma_g$. We compute the $\mathcal{M}_{g,p}$ supersymmetric partition function and ... More

Twisted Indices of 3d ${\mathcal N} = 4$ Gauge Theories and Enumerative Geometry of Quasi-MapsDec 13 2018Mar 26 2019We explore the geometric interpretation of the twisted index of 3d ${\mathcal N} =4$ gauge theories on $S^1\times \Sigma$ where $\Sigma$ is a closed genus $g$ Riemann surface. We focus on a rich class of supersymmetric quiver gauge theories that have ... More

Ab Initio Wall-CrossingJul 04 2011Sep 05 2011We derive supersymmetric quantum mechanics of n BPS objects with 3n position degrees of freedom and 4n fermionic partners with SO(4) R-symmetry. The potential terms, essential and sufficient for the index problem for non-threshold BPS states, are universal, ... More

Twisted Indices of 3d ${\mathcal N} = 4$ Gauge Theories and Enumerative Geometry of Quasi-MapsDec 13 2018We explore the geometric interpretation of the twisted index of 3d ${\mathcal N} =4$ gauge theories on $S^1\times \Sigma$ where $\Sigma$ is a closed genus $g$ Riemann surface. We focus on a rich class of supersymmetric quiver gauge theories that have ... More

Moduli Spaces of Standard Holomorphic Bundles on a Noncommutative Complex TorusDec 11 2003In this paper we study the moduli space of standard holomorphic structures on a noncommutative complex two torus. It will be shown that the moduli space is naturally identified with the moduli space of stable bundles on an elliptic curve. We also propose ... More

Comments on the symmetry of AdS$_6$ solutions in String/M-theory and Killing spinor equationsApr 27 2016Aug 22 2016It was recently pointed out in \cite{Kim:2015hya} that AdS$_6$ solutions in IIB theory enjoy an extended symmetry structure and the consistent truncation to $D=4$ internal space leads to a nonlinear sigma model with target $SL(3,\mathbb{R})/SO(2,1)$. ... More

Sequential Learning of Visual Tracking and Mapping Using Unsupervised Deep Neural NetworksFeb 26 2019We proposed an end-to-end deep learning-based simultaneous localization and mapping (SLAM) system following conventional visual odometry (VO) pipelines. The proposed method completes the SLAM framework by including tracking, mapping, and sequential optimization ... More

Giant enhancement of reflectance due to the interplay between surface confined wave modes and nonlinear gain in dielectric mediaDec 04 2017We study theoretically the interplay between the surface confined wave modes and the linear and nonlinear gain of the dielectric layer in the Otto configuration. The surface confined wave modes such as surface plasmons or waveguide modes are excited in ... More

Unavoidable Subtournaments in Tournaments with Large Chromatic NumberApr 13 2018For a set H of tournaments, we say H is heroic if every tournament, not containing any member of H as a subtournament, has bounded chromatic number. Berger et al. explicitly characterized all heroic sets containing one tournament. Motivated by this result, ... More

Primitive stable representations in higher rank semisimple Lie groupsApr 30 2015Jan 10 2019We study primitive stable representations of free groups into higher rank semisimple Lie groups and their properties. Let $\Sigma$ be a compact, connected, orientable surface (possibly with boundary) of negative Euler characteristic. We first verify the ... More

Simplicial volume of Q-rank one locally symmetric manifolds covered by the product of R-rank one symmetric spacesApr 24 2011Jan 10 2012In this paper, we show that the simplicial volume of Q-rank one locally symmetric spaces covered by the product of R-rank one symmetric spaces is strictly positive.

Phase transition of quantum corrected Schwarzschild black holeJul 23 2012Nov 07 2012We study the thermodynamic phase transition of a quantum-corrected Schwarzschild black hole. The modified metric affects the critical temperature which is slightly less than the conventional one. The space without black holes is not the hot flat space ... More

A Novel Statistical Diagnosis of Clinical DataSep 02 2002In this paper, we present a diagnosis method of diseases from clinical data. The data are routine test such as urine test, hematology, chemistries etc. Though those tests have been done for people who check in medical institutes, how each item of the ... More

2D Electrophoresis Gel Image and Diagnosis of a DiseaseMay 28 2003The process of diagnosing a disease from the 2D gel electrophoresis image is a challenging problem. This is due to technical difficulties of generating reproducible images with a normalized form and the effect of negative stain. In this paper, we will ... More

A Representation of Changes of Images and its Application for Developmental BiolologyMay 13 2003In this paper, we consider a series of events observed at spaced time intervals and present a method of representation of the series. To explain an idea, by dealing with a set of gene expression data, which could be obtained from developmental biology, ... More

Learning Not to Learn: Training Deep Neural Networks with Biased DataDec 26 2018Apr 15 2019We propose a novel regularization algorithm to train deep neural networks, in which data at training time is severely biased. Since a neural network efficiently learns data distribution, a network is likely to learn the bias information to categorize ... More

An lp-boundedness of stochastic singular integral operators and its application to spdesAug 31 2016In this article we introduce a stochastic counterpart of the H\"ormander condtion on the kernel $K(r,t,x,y)$: there exists a pseudo-metric $\rho$ on $(0,\infty)\times R^d$ and a positive constant $C_0$ such that for $X=(t,x), Y=(s,y), Z=(r,z) \in (0,\infty) ... More

Geometrical Interpretation of Electromagnetism in 5-Dimensional ManifoldJul 12 2015Sep 21 2016In this paper Kaluza-Klein theory is revisited and its implications are elaborated. We show that electromagnetic 4-potential can be considered as a shearing-like deformation of a 5-dimensional (5D) manifold along the fifth (5th) axis. The charge-to-mass ... More

Spin filtering in a magnetic barrier structure: in-plane spin orientationMar 01 2014We investigate ballistic spin transport in a two dimensional electron gas system through magnetic barriers of various geometries using the transfer matrix method. While most of the previous studies have focused on the effect of magnetic barriers perpendicular ... More

On deformation spaces of nonuniform hyperbolic latticesOct 04 2013Let $\Gamma$ be a nonuniform lattice acting on real hyperbolic n-space. We show that in dimension greater than or equal to 4, the volume of a representation is constant on each connected component of the representation variety of $\Gamma$ in SO(n,1). ... More

On variation of gradients of deep neural networksDec 02 2018We provide a theoretical explanation of the role of the number of nodes at each layer in deep neural networks. We prove that the largest variation of a deep neural network with ReLU activation function arises when the layer with the fewest nodes changes ... More

Jordan Plane and Numerical Range of Operators Involving Two ProjectionsNov 26 2018We use principal angles between two subspaces to define Jordan planes. Jordan planes provide an optimal way to decompose $\mathbb{C}^n$ in relation to given two subspaces. We apply Jordan planes to show that two pairs of of subspaces $(M,N)$ and $(M^{\perp},N^{\perp})$ ... More

Projective Normality Of Algebraic Curves And Its Application To SurfacesJan 09 2006Let $L$ be a very ample line bundle on a smooth curve $C$ of genus $g$ with $\frac{3g+3}{2}<\deg L\le 2g-5$. Then $L$ is normally generated if $\deg L>\max\{2g+2-4h^1(C,L), 2g-\frac{g-1}{6}-2h^1(C,L)\}$. Let $C$ be a triple covering of genus $p$ curve ... More

$J^+$-like invariants of periodic orbits of the second kind in the restricted three body problemAug 28 2017Sep 05 2018We determine three invariants: Arnold's $J^+$-invariant as well as $\mathcal{J}_1$ and $\mathcal{J}_2$ invariants, which were introduced by Cieliebak-Frauenfelder-van Koert, of periodic orbits of the second kind near the heavier primary in the restricted ... More

Mirror duality and noncommutative toriOct 06 2007In this paper, we study a mirror duality on a generalized complex torus and a noncommutative complex torus. First, we derive a symplectic version of Riemann condition using mirror duality on ordinary complex tori. Based on this we will find a mirror correspondence ... More

Application of Support Vector Machine to detect an association between a disease or trait and multiple SNP variationsApr 17 2001May 22 2001After the completion of human genome sequence was anounced, it is evident that interpretation of DNA sequences is an immediate task to work on. For understanding their signals, improvement of present sequence analysis tools and developing new ones become ... More

Geometrical Interpretation of Electromagnetism in a 5-Dimensional ManifoldJul 12 2015Aug 13 2017In this paper, Kaluza-Klein theory is revisited and its implications are elaborated. We show that electromagnetic 4-potential can be considered as a shearing-like deformation of a 5-dimensional (5D) manifold along the fifth (5th) axis. The charge-to-mass ... More

Direct calculation of the strong Goos-Hänchen effect of a Gaussian light beam due to the excitation of surface plasmon polaritons in the Otto configurationJan 12 2019We study theoretically the influence of the surface plasmon excitation on the Goos-H\"{a}nchen lateral shift of a $p$-polarized Gaussian beam incident obliquely on a dielectric-metal bilayer in the Otto configuration. We find that the lateral shift depends ... More

Black holes with baryonic charge and $\mathcal{I}$-extremizationApr 10 2019We study $\mathcal{I}$-extremization of three-dimensional gauge field theories and its geometric dual, focusing in particular on a seven-dimensional Sasaki-Einstein manifold $M^{1,1,1}$. We generalize recent studies on relations among toric geometry, ... More

An lp-boundedness of stochastic singular integral operators and its application to spdesAug 31 2016Jun 08 2017In this article we introduce a stochastic counterpart of the H\"ormander condtion on the kernel $K(r,t,x,y)$: there exists a pseudo-metric $\rho$ on $(0,\infty)\times R^d$ and a positive constant $C_0$ such that for $X=(t,x), Y=(s,y), Z=(r,z) \in (0,\infty) ... More

Volume invariant and maximal representations of discrete subgroups of Lie groupsMay 22 2012Sep 21 2012Let $\Gamma$ be a lattice in a connected semisimple Lie group $G$ with trivial center and no compact factors. We introduce a volume invariant for representations of $\Gamma$ into $G$, which generalizes the volume invariant for representations of uniform ... More

Memorization Precedes Generation: Learning Unsupervised GANs with Memory NetworksMar 05 2018Mar 10 2018We propose an approach to address two issues that commonly occur during training of unsupervised GANs. First, since GANs use only a continuous latent distribution to embed multiple classes or clusters of data, they often do not correctly handle the structural ... More

Neural Network-Hardware Co-design for Scalable RRAM-based BNN AcceleratorsNov 06 2018Apr 15 2019Recently, RRAM-based Binary Neural Network (BNN) hardware has been gaining interests as it requires 1-bit sense-amp only and eliminates the need for high-resolution ADC and DAC. However, RRAM-based BNN hardware still requires high-resolution ADC for partial ... More

Abstractive Summarization of Reddit Posts with Multi-level Memory NetworksNov 02 2018Apr 09 2019We address the problem of abstractive summarization in two directions: proposing a novel dataset and a new model. First, we collect Reddit TIFU dataset, consisting of 120K posts from the online discussion forum Reddit. We use such informal crowd-generated ... More

Parabolic Littlewood-Paley inequality for $φ(-Δ)$-type operators and applications to Stochastic integro-differential equationsFeb 20 2013In this paper we prove a parabolic version of the Littlewood-Paley inequality for the operators of the type $\phi(-\Delta)$, where $\phi$ is a Bernstein function. As an application, we construct an $L_p$-theory for the stochastic integro-differential ... More

Surplus Solid Angle as an Imprint of Horava-Lifshitz GravityJul 17 2009Dec 08 2009We consider the electrostatic field of a point charge coupled to Horava-Lifshitz gravity and find an exact solution describing the space with a surplus (or deficit) solid angle. Although, theoretically in general relativity, a surplus angle is hardly ... More

On the q-Euler numbers related to modified q-Bernstein polynomialsJul 20 2010In this paper we investigate some interesting formulae of q-Euler numbers and polynomials related to the modified q-Bernstein polynomials.

Higher Resonance Contamination of pi NN Couplings Obtained Via the Three-Point Function Method in QCD Sum RulesJul 03 1997We investigate the size of potential higher pseudoscalar resonance contaminations of the estimates of isospin-conserving and isospin-violating $\pi NN$ couplings obtained using the 3-point function method in QCD sum rules. For the isospin-conserving case ... More

The Mixed Vector Current Correlator <0|T(V^3_μV^8_ν)|0> To Two Loops in Chiral Perturbation TheoryApr 27 1995The isospin-breaking correlator of the product of flavor octet vector currents, $V^3_\mu$ and $V^8_\nu$, $\Pi^{38}_{\mu\nu}(q^2)$ is computed to next-to-next- to-leading (two-loop) order in Chiral Perturbation Theory. Large corrections to both the magnitude ... More

alpha_s From the Lattice and Hadronic Tau DecaysJun 26 2009Until recently, determinations of alpha_s(M_Z) from hadronic tau decays and the analysis of short-distance-sensitive lattice observables yielded results which, though precise, were not in good agreement. I review new analyses that bring these into good ... More

A Mixed Tau-Electroproduction Sum Rule for V_usNov 10 2008Jun 07 2009The interpretation of results of recent tau decay determinations of |V_us|, which yield values ~3 sigma low compared to 3-family unitarity expectations, is complicated by the slow convergence of the relevant integrated D=2 OPE series. We introduce a class ... More

$q^2$-Dependence of Meson Mixing in Few-Body Charge Symmetry Breaking: $π^o-η$ Mixing to One Loop in Chiral Perturbation TheoryNov 10 1992It is pointed out that the meson mixing matrix elements usually considered responsible for the bulk of the observed few-body charge symmetry breaking are naturally $q^2$-dependent in QCD. For $\pi^o-\eta$ mixing, using the usual representation of the ... More

Hadronic Tau Decay Based Determinations of |V_us|Jan 10 2011I review sum rule determinations of |V_us| employing hadronic tau decay data, taking into account recent HFAG updates of exclusive tau branching fractions and paying special attention to the impact of the slow convergence of the relevant integrated D=2 ... More

Quark Model Perspectives on Pentaquark ExoticsAug 11 2004Expectations and predictions for pentaquark exotics based on the quark model perspective are presented. Recent quark model scenarios, and calculations performed in different realizations of the quark model approach, up to the end of March 2004, are also ... More

On commutative $p$-schemes of order $p^4$Feb 22 2016In this article, we consider the existence and schurity problem on commutative $p$-schemes of order $p^4$. Using the thin radical and thin residue, we give sufficient conditions for such $p$-schemes to be schurian. We also give questions related to our ... More

Obstructed and unobstructed Poisson deformationsApr 16 2016In this paper, we study obstructed and unobstructed (holomorphic) Poisson deformations with classical examples in deformation theory.

Photomapping Using Aerial VehicleOct 30 2014Nov 10 2014Creating a photomap plays a critical role in navigation. Therefore, flying vehicles are usually used to create topdown maps of the environment. In this report we used two different aerial vehicles to create a map in a simulated environment

Stochastic Processes Driven by Deterministic Scale InteractionsMar 25 2010May 17 2011We study various solution behaviors of scale equations which are recently proposed in \cite{Kim}. On the contrary to conventional mathematical tools, scale equations are capable to accommodate various behaviors at different scale levels into one integrated ... More

Endpoint bounds for a class of spectral multipliers on compact manifoldsFeb 18 2016Aug 29 2016It is well known that the Stein-Tomas $L^2$ Fourier restriction theorem can be used to derive sharp $L^p$ bounds for radial Fourier multipliers such as the Bochner-Riesz means. In a similar manner, $L^p \to L^2$ estimates for spectral projection operators ... More

Random lattice vectors in a set of size O(n)Nov 09 2016We adopt the sieve ideas of Schmidt and S\"odergren in order to study the statistics of vectors of a random lattice of dimension n contained in a set of volume O(n). We also give some sporadic applications of our results to number theory.

Non-vanishing $U_{e3}$ under $S_3$ symmetryMar 07 2012Aug 13 2012This work proposes two models of neutrino masses that predict non-zero $\theta_{13}$ under the non-Abelian discrete flavor symmetry $\mathbb{S}_3\otimes\mathbb{Z}_2$. We advocate that the size of $\theta_{13}$ is understood as a group theoretical consequence ... More

Amenable signatures, algebraic solutions, and filtrations of the knot concordance groupJun 22 2016Jun 27 2016It is known that each of the successive quotient groups of the grope and solvable filtrations of the knot concordance group has an infinite rank subgroup. The generating knots of these subgroups are constructed using iterated doubling operators. In this ... More

On the largest integer that is not a sum of distinct nth powers of positive integersOct 07 2016Oct 29 2016It is known that for an arbitrary positive integer \(n\) the sequence \(S(x^n)=(1^n, 2^n, \ldots)\) is complete, meaning that every sufficiently large integer is a sum of distinct \(n\)th powers of positive integers. We prove that every integer \(m\geq ... More

Betti numbers of Springer fibers of classical typesNov 30 2016For a Weyl group of classical type, we present formulas to calculate the restriction of Springer representations to a maximal parabolic subgroup of the same type. As a result, we obtain closed formulas for Betti numbers of Springer fibers in two-row cases. ... More

On Shell Renormalization Scheme From the Loopwise Expansion of the Pole MassMar 17 2019We introduce an on shell renormalization scheme in which the mass parameter of minimal MS scheme is replaced with the pole mass obtained from the loop order expansion of the pole mass in the MS scheme. As a consequence, the quartic coupling constant remains ... More

Well-posedness for constrained Hamilton-Jacobi equationsApr 12 2018The goal of this paper is to study a Hamilton-Jacobi equation \begin{equation*} \begin{cases} u_t=H(Du)+R(x,I(t)) &\text{in }\mathbb{R}^n \times (0,\infty), \sup_{\mathbb{R}^n} u(\cdot,t)=0 &\text{on }[0,\infty), \end{cases} \end{equation*} with initial ... More

Quiver Chern-Simons theories and 3-algebra orbifoldsDec 30 2009We attempt to derive quiver Chern-Simons-matter theories from the Bagger-Lambert theory with Nambu bracket, through an orbifold prescription which effectively induces a dimensional reduction of the internal space for 3-algebra. We consider M2-branes on ... More

Remarks on type IIB pp waves with Ramond-Ramond fluxes and massive two dimensional nonlinear sigma modelsDec 02 2002Feb 28 2003We continue the study of supersymmetric type IIB pp wave solutions by Maldacena and Maoz (hep-th/0207284), who showed Ramond-Ramond five-forms can induce potential terms in the light cone string actions which are nonlinear sigma models with special holonomy ... More

Supersymmetric Wilson loops with general contours in ABJM theoryApr 29 2013May 01 2013We consider general supersymmetric Wilson loops in ABJM model, i.e. Chern-Simons-matter theory in 2+1 dimensions with N=6 supersymmetry. They are so-called Zarembo-type: the Wilson loops of our interest have generic contours in spacetime, but the scalar ... More

Bagger-Lambert theory on an orbifold and its relation to Chern-Simons-matter theoriesJul 09 2008Mar 31 2010We consider how to take an orbifold reduction for the multiple M2-brane theory recently proposed by Bagger and Lambert, and discuss its relation to Chern-Simons theories. Starting from the infinite dimensional 3-algebra realized as the Nambu bracket on ... More

AdS(3) Solutions of IIB Supergravity from D3-branesNov 03 2005Nov 08 2006We consider pure D3-brane configurations of IIB string theory which lead to supersymmetric solutions containing an AdS$_3$ factor. They can provide new examples of AdS$_3$/CFT$_2$ examples on D3-branes whose worldvolume is partially compactified. When ... More

Orientifolds of Matrix theory and Noncommutative GeometryJan 04 1999Mar 15 1999We study explicit solutions for orientifolds of Matrix theory compactified on noncommutative torus. As quotients of torus, cylinder, Klein bottle and M\"obius strip are applicable as orientifolds. We calculate the solutions using Connes, Douglas and Schwarz's ... More

More on Membranes in Matrix TheoryAug 27 1998Dec 01 1998We study noncompact and static membrane solutions in Matrix theory. Demanding axial symmetry on a membrane embedded in three spatial dimensions, we obtain a wormhole solution whose shape is the same with the catenoidal solution of Born-Infeld theory. ... More

Distributive Lattices, Affine Semigroups, and Branching Rules of the Classical GroupsApr 01 2010Jul 02 2011We study algebras encoding stable range branching rules for the pairs of complex classical groups of the same type in the context of toric degenerations of spherical varieties. By lifting affine semigroup algebras constructed from combinatorial data of ... More

Local times for continuous paths of arbitrary regularityApr 15 2019We study a pathwise continuous local time of order p for functions with finite p-th variation along a sequence of time partitions, for even integers p greater than or equal to 2. With this notion, we establish a Tanaka-type change of variable formula, ... More

The Lie algebra cohomology of jetsAug 01 2002Jun 10 2003Let g be a finite-dimensional complex semi simple Lie algebra. We present a new calculation of the continuous cohomology of the Lie algebra z g[[z]]. In particular, we shall give an explicit formula for the Laplacian on the Lie algebra cochains, from ... More

Relative Fatou's Theorem for $(-Δ)^{α/2}$-harmonic Functions in Bounded $κ$-fat Open SetJan 23 2004Dec 07 2005We give a probabilistic proof of relative Fatou's theorem for $(-\Delta)^{\alpha/2}$-harmonic functions (equivalently for symmetric $\alpha$-stable processes) in bounded $\kappa$-fat open set where $\alpha \in (0,2)$. That is, if $u$ is positive $(-\Delta)^{\alpha/2}$-harmonic ... More

Multiple Hilbert transform associated with polynomialsFeb 07 2013We study conditions determining the $L^p$ boundedness of multiple Hilbert transforms associated with polynomials.

Renyi-alpha entropies of quantum states in closed form: Gaussian states and a class of non-Gaussian statesApr 16 2018Jun 07 2018In this work, we study the Renyi-alpha entropies S_{alpha}(\hat{rho}) = (1 - alpha)^{-1} \ln{Tr(\hat{rho}^{alpha})} of quantum states for N bosons in the phase-space representation. With the help of the Bopp rule, we derive the entropies of Gaussian states ... More

Systole on locally symmetric spacesMay 10 2019Here we survey on the growth of systoles of arithmetic locally symmetric spaces under the congruence covering and give simple proofs for the best possible constants of Gromov for several important classes of symmetric spaces.

Non-negative Wigner-like distributions and Renyi-Wigner entropies of arbitrary non-Gaussian quantum states: The thermal state of the one-dimensional box problemApr 05 2019In this work, we consider the phase-space picture of quantum mechanics. We then introduce non-negative Wigner-like distributions \widetilde{W}_{\rho;\alpha}(x,p)'s corresponding to the density operator \hat{\rho} and being proportional to {W_{\rho^{\alpha/2}}(x,p)\}^2, ... More

Electrostatic-field-induced dynamics in an ultrathin quantum wellMay 10 2012We consider the time evolution of a particle subjected to both a uniform electrostatic field F and a one-dimensional delta-function potential well. We derive the propagator K_F(x,t|x',0) of this system, directly leading to the wavefunction psi_F(x,t), ... More

Counting, Mixing and Equidistribution of horospheres in geometrically finite rank one locally symmetric manifoldsMar 25 2011Jan 04 2012In this paper we study the equidistribution of expanding horospheres in infinite volume geometrically finite rank one locally symmetric manifolds and apply it to the orbital counting problem in apollonian sphere packing.

Non-equilibrium dynamics in the quantum Brownian oscillator and the second law of thermodynamicsJan 14 2011Oct 01 2011We initially prepare a quantum linear oscillator weakly coupled to a bath in equilibrium at an arbitrary temperature. We disturb this system by varying a Hamiltonian parameter of the coupled oscillator, namely, either its spring constant or mass according ... More

Rank one symmetric spaces and RigidityAug 14 1995In this paper we show that if the limit set is not small ,marked length spectrum determines geometric structure of rank one locally symmetric manifolds.

Existence of boundary flex control for the systems governed by Boussinesq equation with the press boundary condition and mixed boundary conditionJul 13 2012In this paper, the boundary flex control problem of non stationary equation governing the coupled mass and heat flow of a viscous incompressible fluid in a generalized Boussinesq approximation by assuming that viscosity and heat conductivity are dependent ... More

A topological characterization of toroidally alternating knotsAug 01 2016We extend Howie's characterization of alternating knots to give a topological characterization of toroidally alternating knots, which were defined by Adams. We provide necessary and sufficient conditions for a knot to be toroidally alternating. We also ... More

A vanishing theorem for Fano varieties in positive characteristicJan 20 2002Jul 05 2002We prove a Kodaira-type vanishing theorem for the Witt vector sheaf on a Fano variety over a perfect field of characteristic p. As a corollary, we deduce that the number of rational points on a Fano variety over a finite field with q=p^n elements is congruent ... More

Stable quasimapsJun 04 2011The moduli spaces of stable quasimaps unify various moduli appearing in the study of Gromov-Witten Theory. This note is a survey article on the moduli of stable quasimaps, based on joint papers with Ciocan-Fontanine and Maulik as well as the author's ... More

Flag enumerations of matroid base polytopesJan 22 2009Jan 30 2009In this paper, we study flag structures of matroid base polytopes. We describe faces of matroid base polytopes in terms of matroid data, and give conditions for hyperplane splits of matroid base polytopes. Also, we show how the cd-index of a polytope ... More

Arithmetic Chern-Simons Theory IOct 20 2015Nov 11 2016In this paper, we apply ideas of Dijkgraaf and Witten on 2+1 dimensional topological quantum field theory to arithmetic curves, that is, the spectra of rings of integers in algebraic number fields. In the first three sections, we define classical Chern-Simons ... More

Arithmetic Gauge Theory: A Brief IntroductionDec 20 2017Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular, the geometry ... More

Chow Stability of Curves of Genus 4 in P^3Jun 04 2008Aug 30 2010In the paper, we study the GIT construction of the moduli space of Chow semistable curves of genus 4 in P^3. By using the GIT method developed by Mumford and a deformation theoretic argument, we give a modular description of this moduli space. We classify ... More

American Sign Language fingerspelling recognition from video: Methods for unrestricted recognition and signer-independenceAug 30 2016In this thesis, we study the problem of recognizing video sequences of fingerspelled letters in American Sign Language (ASL). Fingerspelling comprises a significant but relatively understudied part of ASL, and recognizing it is challenging for a number ... More

Some properties on the integral of the product of several Euler polynomialsNov 18 2012In this paper, we study the formulae for a product of two product Euler polynomials. From this study, we derive some formulae for the integral of the product of two or more Ruler polynomials.

Infinite family of non-concordant knots having the same Seifert formFeb 26 2004By a recent result of Livingston, it is known that if a knot has a prime power branched cyclic cover that is not a homology sphere, then there is an infinite family of non-concordant knots having the same Seifert form as the knot. In this paper, we extend ... More

Symmetry properties of the generalized higher-order Euler polynomialsOct 06 2009The purpose of this paper is to generalize this relation of symmetry between the power sum polynomials and the generalized Euler polynomials to the relation between the power sum polynomials and the generalized higher-order Euler polynomials.

On the Euler Numbers and its ApplicationsAug 07 2008Recently the new q-Euler numbers are defined. In this paper we derive the the Kummer type congruence related to q-Euler numbers and we introduce some interesting formulae related to these q-Euler numbers.

The linear flows in the space of Krichever-Lax matrices over an algebraic curveJan 14 2008In \cite{kri02}, I. M. Krichever invented the space of matrices parametrizing the cotangent bundle of moduli space of stable vector bundles over a compact Riemann surface, which is named as the Hitchin system after the investigation \cite{hit87}. We study ... More

A note on q-Bernstein polynomialsSep 01 2010In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.

Note on multiple q-zeta functionsDec 30 2009In this paper, we construct the alternating multiple q-zeta function(= Multiple Euler q-zeta function) and investigate their properties. Finally, we give some interesting functional eauations related to q-Euler polynomials.