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Retraining-Based Iterative Weight Quantization for Deep Neural NetworksMay 29 2018Model compression has gained a lot of attention due to its ability to reduce hardware resource requirements significantly while maintaining accuracy of DNNs. Model compression is especially useful for memory-intensive recurrent neural networks because ... More

DeepTwist: Learning Model Compression via Occasional Weight DistortionOct 30 2018Model compression has been introduced to reduce the required hardware resources while maintaining the model accuracy. Lots of techniques for model compression, such as pruning, quantization, and low-rank approximation, have been suggested along with different ... More

Learning Low-Rank Approximation for CNNsMay 24 2019Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation methods, such as ... More

Network Pruning for Low-Rank Binary IndexingMay 14 2019Pruning is an efficient model compression technique to remove redundancy in the connectivity of deep neural networks (DNNs). Computations using sparse matrices obtained by pruning parameters, however, exhibit vastly different parallelism depending on ... More

Structured Compression by Unstructured Pruning for Sparse Quantized Neural NetworksMay 24 2019Model compression techniques, such as pruning and quantization, are becoming increasingly important to reduce the memory footprints and the amount of computations. Despite model size reduction, achieving performance enhancement on devices is, however, ... 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

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

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

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.

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

Invariant imbedding theory of wave propagation in arbitrarily inhomogeneous stratified bi-isotropic mediaApr 02 2016Bi-isotropic media, which include isotropic chiral media and Tellegen media as special cases, are the most general form of linear isotropic media where the electric displacement and the magnetic induction are related to both the electric field and the ... 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

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

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

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

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

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

Anderson localization and Brewster anomaly of electromagnetic waves in randomly-stratified anisotropic mediaOct 27 2017May 16 2019Anderson localization of $p$-polarized waves and the Brewster anomaly phenomenon, which is the delocalization of $p$-polarized waves at a special incident angle, in randomly-stratified anisotropic media are studied theoretically for two different random ... 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

A characterization of quaternionic Kleinian groups in dimension 2 with complex trace fieldsDec 26 2016Let $G$ be a non-elementary discrete subgroup of $\mathrm{Sp}(2,1)$. We show that if the sum of diagonal entries of each element of $G$ is a complex number, then $G$ is conjugate to a subgroup of $\mathrm{U}(2,1)$.

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

Primitive stable representations in higher rank semisimple Lie groupsApr 30 2015Jan 25 2016We define primitive stable representations of free groups into higher rank semisimple Lie groups and study their properties. Then we show that the positive representations of a compact surface with one boundary component are primitive stable.

Primitive stable representations in higher rank semisimple Lie groupsApr 30 2015Nov 11 2016We define primitive stable representations of free groups into higher rank semisimple Lie groups and study their properties. Let {\Sigma} be a compact surface with one boundary component. Then we show that the holonomies of convex projective structures ... More

Sequential Learning of Visual Tracking and Mapping Using Unsupervised Deep Neural NetworksFeb 26 2019May 09 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

A Case Study: Exploiting Neural Machine Translation to Translate CUDA to OpenCLMay 18 2019The sequence-to-sequence (seq2seq) model for neural machine translation has significantly improved the accuracy of language translation. There have been new efforts to use this seq2seq model for program language translation or program comparisons. In ... More

Constraints on Flows in Horava-Lifshitz Gravity by Classical SolutionsSep 07 2010Nov 19 2010We find exact static stringy solutions of Horava-Lifshitz gravity with the projectability condition but imposing the detailed balance condition near the UV fixed point, and propose a method on constraining the possible pattern of flows in Horava-Lifshitz ... More

Noncommutative Riemann ConditionsOct 11 2004In this paper we study the holomorphic bundles over a noncommutative complex torus. We define a noncommutative abelian variety as a kind of deformation of abelian variety and we show that for a restricted deformation parameter, one can define a noncommutative ... More

Complex and Quaternionic hyperbolic Kleinian groups with real trace fieldsDec 26 2014Jan 29 2015Let $\Gamma$ be a nonelementary discrete subgroup of SU(n,1) or Sp(n,1). We show that if the trace field of $\Gamma$ is contained in $\mathbb R$, $\Gamma$ preserves a totally geodesic submanifold of constant negative sectional curvature. Furthermore if ... More

Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter FieldsFeb 29 2012May 09 2012The localization formula of Chern-Simons quiver gauge theory on $S^3$ nicely reproduces the geometric data such as volume of Sasaki-Einstein manifolds in the large-$N$ limit, at least for vector-like models. The validity of chiral-like models is not established ... More

Simplicial volume, Barycenter method, and Bounded cohomologyMar 09 2015Mar 12 2015We show that codimension one dimensional Jacobian of the barycentric straightening map is uniformly bounded for most of the higher rank symmetric spaces. As a consequence, we prove that the locally finite simplicial volume of most $\mathbb Q$-rank $1$ ... More

Bounded cohomology and negatively curved manifoldsNov 28 2011We study the bounded fundamental class in the top dimensional bounded cohomology of negatively curved manifolds with infinite volume. We prove that the bounded fundamental class of $M$ vanishes if $M$ is geometrically finite. Furthermore, when $M$ is ... More

Quaternionic hyperbolic Kleinian groups with commutative trace skew-fieldsOct 08 2018Let $\Gamma$ be a nonelementary discrete subgroup of $\mathrm{Sp}(n,1)$. We show that if the trace skew-field of $\Gamma$ is commutative, then $\Gamma$ stabilizes a copy of complex hyperbolic subspace of quaternionic hyperbolic $n$-space.

Anderson localization and delocalization of massless two-dimensional Dirac electrons in random one-dimensional scalar and vector potentialsJan 12 2019We study Anderson localization of massless Dirac electrons in two dimensions in one-dimensional random scalar and vector potentials theoretically for two different cases, in which the scalar and vector potentials are either uncorrelated or correlated. ... More

On the limit set of Anosov representationsDec 04 2012We study the limit set of discrete subgroups arising from Anosov representations. Specially we study the limit set of discrete groups arising from strictly convex real projective structures and Anosov representations from a finitely generated word hyperbolic ... More

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

Resonant absorption and amplification of circularly-polarized waves in inhomogeneous chiral mediaFeb 19 2016It has been found that in the media where the dielectric permittivity $\epsilon$ or the magnetic permeability $\mu$ is near zero and in transition metamaterials where $\epsilon$ or $\mu$ changes from positive to negative values, there occur a strong absorption ... 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

Effect of disorder correlation on Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a random one-dimensional scalar potentialJul 16 2019We study theoretically Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a random one-dimensional scalar potential. We focus explicitly on the effect of disorder correlations, considering a short-range correlated dichotomous ... More

Excitation of surface waves on the interfaces of general bi-isotropic mediaMay 20 2016Jun 30 2016We study theoretically the characteristics of surface waves excited at the interface between a metal and a general bi-isotropic medium, which includes isotropic chiral media and Tellegen media as special cases. We derive an analytical dispersion relation ... More

Black holes with baryonic charge and $\mathcal{I}$-extremizationApr 10 2019Jun 04 2019Recently it was discovered that twisted superconformal index ${\mathcal{I}}$ can be used to understand the Bekenstein-Hawking entropy of magnetically charged black holes in AdS spacetime. In this paper we apply the so-called $\mathcal{I}$-extremization ... More

Learning Not to Learn: Training Deep Neural Networks with Biased DataDec 26 2018We 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

Concurrence of the Blandford-Payne Process and the Bardeen-Petterson Effect: Theoretical Prediction and its Observational EvidencesAug 21 2015Although the Blandford-Payne process, the standard model for the production of AGN jet outflow, has been fully acknowledged and long-known in both the theoretical Astrophysics and observational Astronomy communities, subsequent research works to gain ... 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

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

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

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

The role of Coulomb correlation in charge density wave of CuTeMay 29 2019A quasi one-dimensional layered material, CuTe undergoes a charge density wave (CDW) transition in Te chains with a modulation vector of $q_{CDW}=(0.4, 0.0, 0.5)$. Despite the clear experimental evidence for the CDW, the theoretical understanding especially ... 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

Abstractive Summarization of Reddit Posts with Multi-level Memory NetworksNov 02 2018We 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

1/4-BPS M-theory bubbles with SO(3) x SO(4) symmetryJun 14 2007Jul 06 2007In this paper we generalize the work of Lin, Lunin and Maldacena on the classification of 1/2-BPS M-theory solutions to a specific class of 1/4-BPS configurations. We are interested in the solutions of 11 dimensional supergravity with $SO(3)\times SO(4)$ ... More

Neural Network-Hardware Co-design for Scalable RRAM-based BNN AcceleratorsNov 06 2018Recently, 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

An $L_p$-theory for diffusion equations related to stochastic processes with non-stationary independent incrementMay 03 2017Oct 27 2017Let $X=(X_t)_{t \ge 0}$ be a stochastic process which has an (not necessarily stationary) independent increment on a probability space $(\Omega, \mathbb{P})$. In this paper, we study the following Cauchy problem related to the stochastic process $X$: ... 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

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

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

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

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

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

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

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

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

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

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.

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

Understanding the Impact of Pythia Hadronization in Top Quark Mass Determinations at the LHCJan 12 2018Most of the methods to measure the top quark mass suffer from the jet energy scaling in achieving better precision. As a way to circumvent this issue, the study of $B$-hadron observables is motivated. While they do not involve such an issue, understanding ... More

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

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

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

On the Second Moment Estimate Involving the $λ$-Primitive Roots Modulo $n$Mar 01 2016Artin's Conjecture on Primitive Roots states that a non-square nonunit integer $a$ is a primitive root modulo $p$ for the positive proportion of $p$. This conjecture remains open, but on average, there are many results due to P. J. Stephens (see ~\cite{S}, ... More

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

On a classification of 4-d gradient Ricci solitons with harmonic Weyl curvatureApr 11 2016We study a characterization of 4-dimensional (not necessarily complete) gradient Ricci solitons $(M, g, f)$ which have harmonic Weyl curvature, i.e. $\delta W=0$. Roughly speaking, we prove that the soliton metric $g$ is locally isometric to one of the ... 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

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

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

A classification of links of the flat plumbing basket numbers 4 or lessDec 25 2014Flat plumbing basket surfaces of links were introduced to study the geometry of the complement of the links. In present article, we study links of the flat plumbing basket numbers $4$ or less using a special presentation of the flat plumbing basket surfaces. ... More