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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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

$J^+$-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

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

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

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

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

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

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

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

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

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

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

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

On the largest integer that is not a sum of distinct nth powers of positive integersOct 07 2016Oct 12 2016It is known that for an arbitrary positive integer n the sequence S(x^n)=(1^n, 2^n, ...) is complete, meaning that every sufficiently large integer is a sum of distinct nth powers of positive integers. We prove that the upper bound of an integer that ... More

Quantum cohomology of flag manifolds G/B and quantum Toda latticesJul 02 1996Jan 01 1999We prove the Givental conjecture that the (equivariant) quantum cohomology of flag manifolds G/B are governed by the conservation law of Toda lattices. In addition, we find the quantum differential module structure of the flag manifolds.

A critical look at V_us determinations from hadronic tau decay dataNov 29 2010Jan 07 2011A critical review of hadronic tau decay data based determinations of |V_{us}| is given, focussing on the impact of the slow convergence of the integrated D=2 OPE series for the conventional flavor-breaking sum rule determination and the potential role ... More

A-type Supergiant Abundances in the SMC: Probes of EvolutionJan 21 1999New abundances of N, O, Na, Mg, Si, Ca, Sc, Ti, Cr, Fe, Sr, Zr, and Ba are presented for 10 A-type supergiants in the SMC, plus upper limits for C. In interpreting the CNO results for constraints on stellar evolution theories, careful attention has been ... More

Solitons of the Self-dual Chern-Simons Theory on a CylinderMay 30 2001We study the self-dual Chern-Simons Higgs theory on an asymptotically flat cylinder. A topological multivortex solution is constructed and the fast decaying property of solutions is proved

Ulrich bundles on blowupsJul 11 2016We construct an Ulrich bundle on the blowup at a point when the original variety is embedded by a sufficiently positive linear system and carries an Ulrich bundle. In particular, we describe the relation between special Ulrich bundles on the blown-up ... More

Langlands-Shahidi $L$-functions for $GSpin$ groups and the generic Arthur packet conjectureJul 26 2015Dec 09 2015We prove that $L$-functions from Langlands-Shahidi method in the case of $GSpin$ groups over a non-Archimedean local field of characteristic zero are Artin $L$-functions through the local Langlands correspondence. It has an application on the proof of ... More

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

Towards Predictable Real-Time Performance on Multi-Core PlatformsJul 28 2016Cyber-physical systems (CPS) integrate sensing, computing, communication and actuation capabilities to monitor and control operations in the physical environment. A key requirement of such systems is the need to provide predictable real-time performance: ... More

Distributed agent-based automated theorem proving in order-sorted first-order logicSep 08 2016This paper presents a distributed agent-based automated theorem proving framework based on order-sorted first-order logic. Each agent in our framework has its own knowledge base, communicating to its neighboring agent(s) using message-passing algorithms. ... More

The group $G_{n}^{2}$ with a parity and with pointsApr 30 2016In~\cite{Ma} Manturov studied groups $G_{n}^{k}$ for fixed integers $n$ and $k$ such that $k<n$. In particular, $G_{n}^{2}$ is isomorphic to the group of free braids of $n$-stands. In~\cite{KiMa} Manturov and the author studied an invariant valued in ... More

On the recurrence formula of the Euler zeta functionsDec 23 2015In this paper, we find a new recurrence formula fo the Euler zeta functions.

A Nonconvex Unconstrained Method for Eigenvalue Problems and A Nonsingular System for Eigenvector EstimationNov 28 2016We propose a nonconvex unconstrained minimization problem for eigenvalue problems. In this framework, given a symmetric matrix $A$, it turns out that any nonzero critical point is an eigenvector of $A$ and any local minimizer is a global minimizer, an ... More

Seesaw Scale and CP Phases in a Minimal Model of LeptogenesisNov 14 2016The seesaw mechanism to derive the light masses of left-handed neutrinos using heavy masses of right-handed neutrinos gives rise to a connection between low-energy measurables and GUT-scale mechanism. We expresses the neutrino mixing angles in terms of ... More

The Particle- and Astro-Physics of Dark MatterNov 09 1994We review some recent determinations of the amount of dark matter on galactic, cluster, and large scales, noting some puzzles and their possible resolutions. We discuss the interpretation of big bang nucleosynthesis for dark matter, and then review the ... More

On a quadratic Waring's problem with congruence conditionsJan 16 2019Jan 17 2019We say a quadratic polynomial is represented by a sum of $r$ odd squares if it is represented by $\Delta_r(y_1,...,y_r)=\sum_{i=1}^r (y_i+\frac{1}{2})^2$. For each positive integer $n$, let $g_\Delta(n)$ be the smallest positive integer $g$ such that ... More

Galois deformation theory for norm fields and flat deformation ringsMay 18 2010Let $K$ be a finite extension of $\mathbb{Q}_p$, and choose a uniformizer $\pi\in K$, and put $K_\infty:=K(\sqrt[p^\infty]{\pi})$. We introduce a new technique using restriction to $\Gal(\ol K/K_\infty)$ to study flat deformation rings. We show the existence ... More

Origin of Hawking Radiation: Firewall or Atmosphere?Apr 02 2016Apr 14 2016The Unruh vacuum not admitting any outgoing flux at the horizon implies that the origin of the outgoing Hawking radiation would be the atmosphere of a near-horizon quantum region without resort to the firewall; however, the existence of the firewall of ... More

Character design for soccer commmentaryJul 31 1998In this paper we present early work on an animated talking head commentary system called {\bf Byrne}\footnote{David Byrne is the lead singer of the Talking Heads.}. The goal of this project is to develop a system which can take the output from the RoboCup ... More

Group-theoretical vector space modelSep 20 2015This paper presents a group-theoretical vector space model (VSM) that extends the VSM with a group action on a vector space of the VSM. We use group and its representation theory to represent a dynamic transformation of information objects, in which each ... More

Origin of Hawking Radiation: Firewall or Atmosphere?Apr 02 2016Jan 16 2017The Unruh vacuum not admitting any outgoing flux at the horizon implies that the origin of the outgoing Hawking radiation is the atmosphere of a near-horizon quantum region without resort to the firewall; however, the existence of the firewall of superplanckian ... More

Motivic L-FunctionsOct 27 2007This is the text of an introductory lecture delivered at the IHES summer school on motives in July, 2006.

p-adic L-functions and Selmer varieties associated to elliptic curves with complex multiplicationOct 28 2007We show how non-vanishing of p-adic L functions controls the dimensions of Selmer varieties associated to the complement of the origin in an elliptic curve with CM. As a corollary, one obtains a \pi_1-proof of the theorem of Siegel for such curves.

Diophantine geometry and non-abelian reciprocity laws IDec 25 2013May 15 2015We use non-abelian fundamental groups to define a sequence of higher reciprocity maps on the adelic points of a variety over a number field satisfying certain conditions in Galois cohomology. The non-abelian reciprocity law then states that the global ... More

Comments on $AdS_2$ solutions from M2-branes on complex curves and the backreacted Kähler geometryNov 28 2013Jan 31 2014We consider $AdS_2$ solutions of M-theory which are obtained by twisted compactifications of M2-branes on a complex curve. They are of a generalized class, in the sense that the non-abelian part of the connection for the holomorphic bundle over the supersymmetric ... More

Link diagrams with low Turaev genusJul 10 2015Nov 30 2015We classify link diagrams with Turaev genus one and two in terms of an alternating tangle structure of the link diagram. The proof involves surgery along simple closed curves on the Turaev surface, called cutting loops, which have corresponding cutting ... More

The Causal Effect of Answer Changing on Multiple-Choice ItemsAug 31 2018Mar 12 2019Whether examinees' answer changing behavior on multiple-choice exams is beneficial or harmful is a long-standing puzzle in the educational and psychological measurement literature. This article unravels the problem by formalizing it using the potential ... More

The nullcone in the multi-vector representation of the symplectic group and related combinatoricsApr 25 2009Mar 18 2010We study the nullcone in the multi-vector representation of the symplectic group with respect to a joint action of the general linear group and the symplectic group. By extracting an algebra over a distributive lattice structure from the coordinate ring ... More

Rapoport-Zink spaces of Hodge typeAug 26 2013Jan 29 2018When $p>2$, we construct a Hodge-type analogue of Rapoport-Zink spaces under the unramifiedness assumption, as formal schemes parametrising "deformations" (up to quasi-isogeny) of $p$-divisible groups with certain crystalline Tate tensors. We also define ... More

Optimal condition 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

Separated Rows structure of vortex streets behind triangular objectsJun 30 2018Aug 09 2018We discuss two distinct spatial structures of vortex streets. The `conventional mushroom' structure is commonly discuss in many experimental studies, but the exotic `separated rows' structure is characterized by a thin irrotational fluid between two rows ... More

An $L_p$-Lipschitz theory for parabolic equations with time measurable pseudo-differential operatorsJul 15 2017In this article we prove the existence and uniqueness of a (weak) solution $u$ in $L_p\left((0,T) , \Lambda_{\gamma+m}\right)$ to the Cauchy problem \begin{align} \notag &\frac{\partial u}{\partial t}(t,x)=\psi(t,i\nabla)u(t,x)+f(t,x),\quad (t,x) \in ... More

Deformation space of a non-uniform 3-dimensional real hyperbolic lattice in quaternionic hyperbolic planeFeb 29 2012In this note, we study deformations of a non-uniform real hyperbolic lattice in quaternionic hyperbolic spaces. Specially we show that the representations of the fundamental group of the figure eight knot complement into PU(2,1) cannot be deformed in ... More

Handlebody-preserving finite group actions on Haken manifolds with Heegaard genus two - IIFeb 07 2009May 25 2009Let $M$ be a closed orientable 3-manifold with a genus two Heegaard splitting $(V_1, V_2; F)$ and a non-trivial JSJ-decomposition, where all components of the intersection of the JSJ-tori and $V_i$ are not $\partial$-parallel in $V_i$ for $i=1,2$. If ... More

Welfare Maximization with Deferred Acceptance Auctions in Reallocation ProblemsJul 06 2015Sep 20 2015We design approximate weakly group strategy-proof mechanisms for resource reallocation problems using Milgrom and Segal's deferred acceptance auction framework: the radio spectrum and network bandwidth reallocation problems in the procurement auction ... More

On a quadratic Waring's problem with congruence conditionsJan 16 2019Feb 12 2019For each positive integer $n$, let $g_\Delta(n)$ be the smallest positive integer $g$ such that every complete quadratic polynomial in $n$ variables which can be represented by a sum of odd squares is represented by a sum of at most $g$ odd squares. In ... More

A note on a system of cubic nonlinear Klein-Gordon equations in one space dimensionJul 24 2014Feb 15 2015We study the Cauchy problem for a system of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the order $O(t^{-1/2})$ ... More

Generalized Heegaard splittings and the disk complexJul 02 2016Oct 08 2016Let $M$ be an orientable, irreducible $3$-manifold and $(\mathcal{V},\mathcal{W};F)$ a weakly reducible, unstabilized Heegaard splitting of $M$ of genus at least three. In this article, we define an equivalent relation $\sim$ on the set of the generalized ... More

On critical Heegaard splittings of tunnel number two composite knot exteriorsOct 11 2012Oct 15 2012In this article, we prove that a tunnel number two knot induces a critical Heegaard splitting in its exterior if there are two weak reducing pairs such that each weak reducing pair contains the cocore disk of each tunnel. Moreover, we prove that a connected ... More

Langlands-Shahidi $L$-functions for $GSpin$ groups and the generic Arthur packet conjectureJul 26 2015Dec 26 2017We prove that $L$-functions from Langlands-Shahidi method in the case of $GSpin$ groups over a non-Archimedean local field of characteristic zero are Artin $L$-functions through the local Langlands correspondence. It has an application on the proof of ... More

On a gradient maximum principle for some quasilinear parabolic equations on convex domainsMay 16 2016We establish a spatial gradient maximum principle for classical solutions to the initial and Neumann boundary value problem of some quasilinear parabolic equations on smooth convex domains.

A splitting theorem for holomorphic Banach bundlesMay 14 2008This paper is motivated by Grothendieck's splitting theorem. In the 1960s, Gohberg generalized this to a class of Banach bundles. We consider a compact complex manifold $X$ and a holomorphic Banach bundle $E \to X$ that is a compact perturbation of a ... More

Fast AutoAugmentMay 01 2019Data augmentation is an indispensable technique to improve generalization and also to deal with imbalanced datasets. Recently, AutoAugment has been proposed to automatically search augmentation policies from a dataset and has significantly improved performances ... More

Parameterized Wasserstein mean with its propertiesApr 20 2019A new least squares mean of positive definite matrices for the divergence associated with the sandwiched quasi-relative entropy has been introduced. It generalizes the well-known Wasserstein mean for covariance matrices of Gaussian distributions with ... More

Normal all pseudo-Anosov subgroups of mapping class groupsJun 20 1999Oct 14 2000We construct the first known examples of nontrivial, normal, all pseudo-Anosov subgroups of mapping class groups of surfaces. Specifically, we construct such subgroups for the closed genus two surface and for the sphere with five or more punctures. Using ... More

Minimal volume of complete uniform visibility manifolds with finite volumeApr 10 2012We show that complete uniform visibility manifolds of finite volume with sectional curvature $-1 \leq K \leq 0$ have positive simplicial volumes. This implies that their minimal volumes are non-zero.

Deep Neural Network Optimized to Resistive Memory with Nonlinear Current-Voltage CharacteristicsMar 30 2017Artificial Neural Network computation relies on intensive vector-matrix multiplications. Recently, the emerging nonvolatile memory (NVM) crossbar array showed a feasibility of implementing such operations with high energy efficiency, thus there are many ... More

Hyperelliptic curves and Hitchin tangential coversAug 30 2011Oct 11 2011In \cite{kim11} we have generalized a tangency condition in the Treibich-Verdier theory \cite{trei89,tv90,trei97} about elliptic solitons to a Hitchin system. As an application of this generalization, we will define, so-called, Hitchin hyperelliptic tangential ... More

A study on the q-Euler numbers and the fermionic q-integrals of the product of several type $q$-Bernstein polynomials on ZpOct 19 2010In this paper, we investigate some interesting properties of q-Berstein polynomials realted to q-Euler numbers by using the fermionic q-integral on Zp.

Some identities of symmetry for the generalized Bernoulli numbers and polynomialsMar 17 2009In this paper, by the properties of p-adic invariant integral on Zp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. From the symmetric properties of p-adic invariant integral on Zp, we give some interesting ... More

On the weighted q-Bernoulli numbers and polynomialsNov 24 2010In this paper we consider the weighted q-Bernoulli numbers and polynomials which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From these numbers and polynomials, we derive some interesting formulaes and identities.

Euler number and polynomials of higher orderJan 11 2010In this paper we study the higher-order Euler numbers and polynomials and we introduce the mutiple zeta functions which interpolate higher-order Euler polynomials and numbers at negative integers