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Ubiquitous Talker: Spoken Language Interaction with Real World ObjectsMay 23 1995Augmented reality is a research area that tries to embody an electronic information space within the real world, through computational devices. A crucial issue within this area, is the recognition of real world objects or situations. In natural language ... More

wavEMS: Improving Signal Variation Freedom of Electrical Muscle StimulationFeb 08 2019There has been a long history in electrical muscle stimulation (EMS), which has been used for medical and interaction purposes. Human-computer interaction (HCI) researchers are now working on various applications, including virtual reality (VR), notification, ... More

Post-Data Augmentation to Improve Deep Pose Estimation of Extreme and Wild MotionsFeb 12 2019Contributions of recent deep-neural-network (DNN) based techniques have been playing a significant role in human-computer interaction (HCI) and user interface (UI) domains. One of the commonly used DNNs is human pose estimation. This kind of technique ... More

Fairy Lights in Femtoseconds: Aerial and Volumetric Graphics Rendered by Focused Femtosecond Laser Combined with Computational Holographic FieldsJun 22 2015We present a method of rendering aerial and volumetric graphics using femtosecond lasers. A high-intensity laser excites a physical matter to emit light at an arbitrary 3D position. Popular applications can then be explored especially since plasma induced ... More

Ishikawa iteration process on CAT(K) spacesMar 26 2013In this paper, we establish $\Delta$-convergence results for Ishikawa iterations in complete CAT(K) spaces.

On a generalization of Dipper--James--Murphy's ConjectureFeb 14 2009Jan 16 2010Let $K$ be a field and $q\in K^{\times}$. Let $e$ be the multiplicative order of $q$; or 0 if $q$ is not a root of unity. Let $\bQ:=(q^{v_1},...,q^{v_r})$. Let ${K}_r(n)$ be the set of Kleshchev $r$-multipartitions with respect to $(e;\bQ)$. In this paper, ... More

The first two Betti numbers of the moduli spaces of vector bundles on surfacesApr 16 1995We determined the first two Betti numbers of the moduli of rank two stable sheaves on an arbitrary algebraic surface

Duality in interacting particle systems and boson representationSep 29 2009Dec 10 2009In the context of Markov processes, we show a new scheme to derive dual processes and a duality function based on a boson representation. This scheme is applicable to a case in which a generator is expressed by boson creation and annihilation operators. ... More

Algebraic probability, classical stochastic processes, and counting statisticsOct 25 2012We study a connection between the algebraic probability and classical stochastic processes described by master equations. Introducing a definition of a state which has not been used for quantum cases, the classical stochastic processes can be reformulated ... More

Counting statistics for genetic switches based on effective interaction approximationSep 11 2012Applicability of counting statistics for a system with an infinite number of states is investigated. The counting statistics has been studied a lot for a system with a finite number of states. While it is possible to use the scheme in order to count specific ... More

p-cyclic persistent homology and Hofer distanceMay 24 2016In this paper, we generalize the result from L. Polterovich and E. Shelukhin's paper stating that Hofer distance from time-dependent Hamiltonian diffeomorphism to the set of p-th power Hamiltonian diffeomorphism can be arbitrarily large to hold in the ... More

Zero dimensional Donaldson-Thomas invariants of threefoldsApr 23 2006Mar 03 2009Using a homotopy approach, we prove in this paper a conjecture of Maulik, Nekrasov, Okounkov and Pandharipande on the dimension zero Donaldson-Thomas invariants of all smooth complex threefolds.

Differentiating the production mechanisms of the Higgs-like resonance using inclusive observables at hadron collidersAug 25 2013Feb 20 2014We present a study on differentiating direct production mechanisms of the newly discovered Higgs-like boson at the LHC based on several inclusive observables. The ratios introduced reveal the parton constituents or initial state radiations involved in ... More

The Ground State Energy of Dilute Bose Gas in Potentials with Positive Scattering LengthAug 29 2008The leading term of the ground state energy/particle of a dilute gas of bosons with mass $m$ in the thermodynamic limit is $2\pi \hbar^2 a \rho/m$ when the density of the gas is $\rho$, the interaction potential is non-negative and the scattering length ... More

Parameter estimation of qubit states with unknown phase parameterNov 15 2014Feb 24 2015We discuss a problem of parameter estimation for quantum two-level system, qubit system, in presence of unknown phase parameter. We analyze trade-off relations for mean-square errors when estimating relevant parameters with separable measurements based ... More

Note on Nonlinear Schrödinger Equation, KdV Equation and 2D Topological Yang-Mills-Higgs TheoryNov 14 2016In this paper we discuss the relation between the (1+1)D nonlinear Schr\"odinger equation and the KdV equation. By applying the boson/vortex duality, we can map the classical nonlinear Schr\"odinger equation into the classical KdV equation in the small ... More

Colour Dependence of the Distribution of IRAS Galaxies revealed by Multifractal MeasuresApr 11 2006Jul 04 2006Multifractal measures are applied to three IRAS galaxy subsamples selected by colour from the PSCz catalogue. As shown by generalised dimension spectrum, hot IRAS galaxies are found less clustered than cold galaxies, but the difference is very weak. An ... More

From colored Jones invariants to logarithmic invariantsJun 05 2014Mar 16 2015In this work, we give a formula for the logarithmic invariant of knots in terms of certain derivatives of the colored Jones invariant. This invariant is related to the logarithmic conformal field theory, and was defined by using the centers in the radical ... More

(-2,3,7)-pretzel knot and Reebless foliationMar 26 2003If p/q > 18, p is odd, and $p/q \ne 37/2$, (p,q)-Dehn surgery for the (-2,3,7)-pretzel knot produces a 3-manifold without Reebless foliation.

On the decomposition numbers of the Hecke algebra of type $D_n$ when $n$ is evenSep 09 2008Dec 17 2008Let $n\geq 4$ be an even integer. Let $K$ be a field with $\cha K\neq 2$ and $q$ an invertible element in $K$ such that $\prod_{i=1}^{n-1}(1+q^i)\neq 0$. In this paper, we study the decomposition numbers over $K$ of the Iwahori--Hecke algebra $\HH_q(D_n)$ ... More

Maximal abelian subgroups of compact simple Lie groups of type EMar 11 2014We classify closed abelian subgroups of a compact simple Lie group of adjoint type and of type E having centralizer of the same dimension as the dimension of the subgroup and describe Weyl groups of maximal abelian subgroups.

On the Iwasawa invariants for links and Kida's formulaMay 29 2016Aug 12 2016Analogues of Iwasawa invariants in the context of 3-dimensional topology have been studied by M.~Morishita and others. In this paper, following the dictionary of arithmetic topology, we formulate an analogue of Kida's formula on $\lambda$-invariants in ... More

Acceptable compact Lie groupsJun 17 2018Jul 31 2018This paper contributes to the goal of classifying acceptable groups. We show that for a connected compact semisimple Lie group to be acceptable it is necessary and sufficient that it is isomorphic to a direct product of the groups $SU(n)$, $Sp(n)$, $SO(2n+1)$, ... More

Twisted root system of a (*)-subgroupMay 16 2018Jul 20 2018We classify (*)-subgroups of compact Lie groups of adjoint type, and associate a twisted root system to every (*)-subgroup. We study the structure of twisted root system in several aspects: properties of the small Weyl group W_{small} and its normal subgroups ... More

2MASS photometry and age estimate of globular clusters in the outer halo of M31Nov 11 2011We present the first photometric results in J, H, and K_s from 2MASS imaging of 10 classical globular clusters in the far outer regions of M31. Combined with the V and I photometric data from previous literature, we constructed the color-color diagram ... More

Learning to imitate stochastic time series in a compositional way by chaosMay 13 2008This study shows that a mixture of RNN experts model can acquire the ability to generate sequences combining multiple primitive patterns by means of self-organizing chaos. By training of the model, each expert learns a primitive sequence pattern, and ... More

A model for learning to segment temporal sequences, utilizing a mixture of RNN experts together with adaptive varianceJun 09 2007Jun 17 2008This paper proposes a novel learning method for a mixture of recurrent neural network (RNN) experts model, which can acquire the ability to generate desired sequences by dynamically switching between experts. Our method is based on maximum likelihood ... More

A note on closed subgroups of compact Lie groupsDec 22 2009Mar 27 2012We reduce the classification of finite subgroups in compact Lie groups to that of quasi-simple ones, prove the number of conjugacy classes is finite and each cojugacy class is Zariski closed in mapping space, and classify "strongly controlling fusions" ... More

Two decay paths for calculation of nuclear matrix element of neutrinoless double-beta decay using quasiparticle random-phase approximationDec 24 2015It is possible to employ virtual decay paths, including two-particle transfer, to calculate the nuclear matrix element of neutrinoless double-beta decay under the closure approximation, in addition to the true double-beta path. In the quasiparticle random-phase ... More

On an Inclusion of the Essential Spectrum of Laplacians under Non-Compact Change of MetricMar 10 2011It is shown the stability of the essential self-adjointness, and an inclusion of the essential spectra of Laplacians under the change of Riemannian metric on a subset K of M. The set K may have infinite volume measured with the new metric and its completion ... More

An isomorphism between the completion of an Algebra and its Caratheodory ExtensionMar 12 2008Let $\Omega$ denote an algebra of sets and $\mu$ a $\sigma$-finite measure. We then prove that the completion of $\Omega$ under the pseudometric $d(A,B)$ = $\mu^{\ast}(A \triangle B)$ is $\sigma$-algebra isomorphic and isometric to the Caratheodory Extension ... More

Approximation scheme based on effective interactions for stochastic gene regulationSep 16 2010Since gene regulatory systems contain sometimes only a small number of molecules, these systems are not described well by macroscopic rate equations; a master equation approach is needed for such cases. We develop an approximation scheme for dealing with ... More

The stochastic pump current and the non-adiabatic geometrical phaseDec 04 2007Feb 29 2008We calculate a pump current in a classical two-state stochastic chemical kinetics by means of the non-adiabatic geometrical phase interpretation. The two-state system is attached to two particle reservoirs, and under a periodic perturbation of the kinetic ... More

A field theoretic approach to master equations and a variational method beyond the Poisson ansatzAug 28 2007Sep 20 2007We develop a variational scheme in a field theoretic approach to a stochastic process. While various stochastic processes can be expressed using master equations, in general it is difficult to solve the master equations exactly, and it is also hard to ... More

Finite element approximations of symmetric tensors on simplicial grids in Rn: the high order caseSep 27 2014Apr 14 2015The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress space is the ... More

Intrinsic and extrinsic origins of the polar Kerr effect in a chiral p-wave superconductorJul 29 2008Apr 30 2010Recently, the measurement of the polar Kerr effect (PKE) in the quasi two-dimensional superconductor Sr2RuO4, which is motivated to observe the chirality of px + i py-wave pairing, has been reported. We clarify that the PKE has intrinsic and extrinsic ... More

Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed $S^3$ with $SU(2)\times U(1)$ IsometrySep 12 2013Jul 30 2014Localization of supersymmetric $\mathcal{N}=2$ Chern-Simons-Matter theory on a squashed $S^3$ with $SU(2)\times U(1)$ isometry has been studied by different groups of authors. In this paper, we localize the theory on a squashed $S^3$ with $SU(2)\times ... More

Monodromies of Algebraic Connections on the Trivial BundleJun 25 2000In this note, we study monodromies of algebraic connections on the trivial vector bundle. We prove that on a smooth complex affine curve, any monodromy arises as the underlying local system of an algebraic connection on the trivial bundle. We give a generalization ... More

Association schemes and HypergroupsJul 18 2016We study a certain class of hypergroups (realizable hypergroups) which can be canonically obtained from association schemes. This paper consists of three parts. In the first part, we study algebraic aspects of realizable hypergroups. In the second part, ... More

Specific viscosity of neutron-rich nuclear matter from a relaxation time approachOct 02 2011Dec 05 2011The specific viscosity of neutron-rich nuclear matter is studied from the relaxation time approach using an isospin- and momentum-dependent interaction and the nucleon-nucleon cross sections taken as those from the experimental data modified by the in-medium ... More

A Special Theorem Related to the Fagnano's ProblemJun 21 2016A special theorem related to the Fagnano's problem is proved and an example of the theorem is shown in a golden rectangle.

Probing light-quark Yukawa couplings via hadronic event shapes at lepton collidersAug 05 2016We propose a novel idea for probing the Higgs boson couplings through the measurement of hadronic event shape distributions in the decay of the Higgs boson at lepton colliders. The method provides a unique test of the Higgs boson couplings and of QCD ... More

Quantum Electrodynamics in a Uniform Magnetic FieldDec 28 2005A systematic formalism for quantum electrodynamics in a classical uniform magnetic field is discussed. The first order radiative correction to the ground state energy of an electron is calculated. This then leads to the anomalous magnetic moment of an ... More

Model for Motions of Impurities in Bose-Einstein CondensatesJul 28 2004Jan 21 2005A model for classical impurities moving in Bose-Einstein Condensate (BEC) is proposed in the framework of quantum field theory and is solved within the Bogoliubov approximation at zero temperature. Several formulae are obtained for physical quantities ... More

$\bar{D}Σ^*_c$ and $\bar{D}^*Σ_c$ interactions and LHCb pentaquarksNov 22 2016Recently, LHCb collaboration reported the observation of two hidden-charmed resonances $P_c(4380)$ and $P_c(4450)$ consistent with hidden-charmed pentaquarks. We perform a dynamical investigation about the $\bar{D}\Sigma_c^*(2520)$ and $\bar{D}^*\Sigma_c(2455)$ ... More

Symplectic structure perturbations and continuity of symplectic invariantsOct 03 2016This paper studies how some symplectic invariants which are born from Hamiltonian Floer theory (e.g. spectral invariant, boundary depth, (partial) symplectic quasi-state) change with respect to symplectic structure perturbations, i.e., new symplectic ... More

A Conic Section Problem Involving the Maximum Generalized Golden Right TriangleJun 29 2016An interesting conic section problem involving the maximum generalized golden right triangle $T_2$ is solved, and two simple constructions of $T_2$ are shown.

The fractional Brownian motion and the halo mass functionOct 16 2006The fractional Brownian motion with index $\alpha$ is introduced to construct the fractional excursion set model. A new mass function with single parameter $\alpha$ is derived within the formalism, of which the Press-Schechter mass function (PS) is a ... More

A Lower Bound of The First Eigenvalue of a Closed Manifold with Positive Ricci CurvatureJun 22 2004Dec 08 2004We give an estimate on the lower bound of the first non-zero eigenvalue of the Laplacian for a closed Riemannian manifold with positive Ricci curvature in terms of the in-diameter and the lower bound of the Ricci curvature.

Lower Bounds of the First Closed and Neumann Eigenvalues of Compact Manifolds with Positive Ricci CurvatureJun 15 2004Jan 12 2005We give new estimates on the lower bounds for the first closed or Neumann eigenvalue for a compact manifold with positive Ricci curvature in terms of the diameter and the lower bound of Ricci curvature. The results improve the previous estimates.

A Function obstruction to the Existence of Complex StructuresJan 05 2019We construct a function for almost-complex Riemannian manifolds. Non-vanishing of the function for the almost-complex structure implies the almost-complex structure is not integrable. Therefore the constructed function is an obstruction for the existence ... More

The profinite completions of knot groups determine the Alexander polynomialsFeb 13 2017Mar 23 2018We study several properties of the completed group ring $\widehat{\mathbb{Z}}[[t^{\widehat{\mathbb{Z}}}]]$ and the completed Alexander modules of knots. Then we prove that if the profinite completions of the groups of two knots $J$ and $K$ are isomorphic, ... More

Some Asymptotic Behavior of the first Eigenvalue along the Ricci FlowOct 23 2007We study some asymptotic behavior of the first nonzero eigenvalue of the Lalacian along the normalized Ricci flow and give a direct short proof for an asymptotic upper limit estimate.

Properties of disks and spiral arms along the Hubble sequenceMar 14 2002This paper presents some new statistical correlations between the properties of disks and spiral arms with some physical properties of galaxies. Our results show that the thickness of spiral disks tend to diminish along the Hubble sequence in the sense ... More

New $ubvri$ photometry of 234 M33 star clustersJan 07 2013This is the second paper of our series. In this paper, we present $UBVRI$ photometry for 234 star clusters in the field of M33. For most of these star clusters, there is photometry in only two bands in previous studies. The photometry of these star clusters ... More

An updated catalog of M33 clusters and candidates: $UBVRI$ photometry, and some statistical resultsMay 22 2012We present $UBVRI$ photometry for 392 star clusters and candidates in the field of M33, which are selected from the most recent star cluster catalog. In this catalog, the authors listed star clusters' parameters such as cluster positions, magnitudes and ... More

Valuations of SemiringsMar 04 2015Mar 28 2017We develop notions of valuations on a semiring, with a view toward extending the classical theory of abstract nonsingular curves and discrete valuation rings to this general algebraic setting; the novelty of our approach lies in the implementation of ... More

The number of simple modules for the Hecke algebras of type G(r,p,n) (with an appendix by Xiaoyi Cui)Jan 24 2006Nov 19 2007We derive a parameterization of simple modules for the cyclotomic Hecke algebras of type $G(r,p,n)$ over field of any (coprime to $p$) characteristic. We give explicit formulas for the number of simple modules over these cyclotomic Hecke algebras.

Fuzzy signed measureMay 30 2008we will define a fuzzy signed measure on $\sigma$-algebras, as well as positive and negative sets. Herein, we will show that the Fuzzy Hahn Decomposition Theorem, which is a generalization of the classical Hahn Decomposition Theorem, decompose any space ... More

Variational principle of counting statistics in master equationsJun 29 2009We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the similar path integral ... More

Free energy of disordered urn models in the canonical ensembleMay 15 2007Aug 02 2007We calculate the free energy of the disordered urn model using the law of large numbers. It is revealed that the saddle point equation obtained by the usage of the law of large numbers is the same as that obtained by the replica method. Hence, we conclude ... More

Duality-based calculations for transition probabilities in birth-death processesSep 24 2015Transition probabilities in birth-death processes are fomulated via the corresponding dual birth-death processes. In order to obtain the corresponding dual processes, the Doi-Peliti formalism is employed. Conventional numerical evaluation enables us to ... More

Lie algebraic discussions for time-inhomogeneous linear birth-death processes with immigrationApr 21 2014Analytical solutions for time-inhomogeneous linear birth-death processes with immigration are derived. While time-inhomogeneous linear birth-death processes without immigration have been studied by using a generating function approach, the processes with ... More

Karlin-McGregor-like formula in a simple time-inhomogeneous birth-death processApr 10 2014A novel approach is employed and developed to derive transition probabilities for a simple time-inhomogeneous birth-death process. Algebraic probability theory and Lie algebraic treatments make it easy to treat the time-inhomogeneous cases. As a result, ... More

Nonlinear Kalman filter based on duality relations between continuous and discrete-state stochastic processesFeb 10 2014Sep 24 2015A new application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, we here employ numerical solutions of the dual processes and investigate ... More

Noncyclic geometric phase in counting statistics and its role as an excess contributionMar 04 2013Jun 06 2013We propose an application of fiber bundles to counting statistics. The framework of the fiber bundles gives a splitting of a cumulant generating function for current in a stochastic process, i.e., contributions from the dynamical phase and the geometric ... More

Logic With Verbs and its Mathematical StructureJan 20 2010Aug 04 2010The aim of this paper is to introduce the idea of Logic with Verbs and to show its mathematical structure.

Specht filtrations and tensor spaces for the Brauer algebraApr 26 2006Dec 22 2006Let $m, n\in{\mathbb N}$. In this paper we study the right permutation action of the symmetric group ${\mathfrak S}_{2n}$ on the set of all the Brauer $n$-diagrams. A new basis for the free ${\mathbb Z}$-module ${\mathfrak B}_n$ spanned by these Brauer ... More

Picard groups of the moduli spaces of vector bundles over algebraic surfacesApr 16 1995We determined the Picard group of the moduli of rank two stable sheaves on an arbitrary algebraic surface up to finite index

Artin-Schelter Regular Algebras, Subalgebras, and PushoutsDec 16 2007Sep 02 2010Take $A$ to be a regular quadratic algebra of global dimension three. We observe that there are examples of $A$ containing a dimension three regular cubic algebra $C$. If $B$ is another dimension three regular quadratic algebra, also containing $C$ as ... More

CIJET: a program for computation of jet cross sections induced by quark contact interactions at hadron collidersJan 30 2013We describe CIJET1.0, a Fortran program that aiming for the calculation of single-inclusive jet or dijet production cross sections induced by quark contact interactions from new physics at hadron colliders, up to next-to-leading order in QCD. It covers ... More

Period determinant of an irregular connection over an elliptic curveFeb 12 2003In this article, we calculate the period determinant of an irrgular singular connection d+dy on the legendre curve U: y^2 =x(x-1)(x- lambda). We calculate its de Rham cohomology and the cycles in the homology of the dual connection and describe the period ... More

Valley Spin Sum Rule for Dirac Fermions: Topological ArgumentOct 01 2010Feb 25 2011We consider a two-dimensional bipartite lattice system. In such a system, the Bloch band spectrum can have some valley points, around which Dirac fermions appear as the low-energy excitations. Each valley point has a valley spin +1 or -1. In such a system, ... More

Impurity Induced Polar Kerr Effect in A Chiral p-wave SuperconductorJun 03 2008Jul 24 2008We discuss the polar Kerr effect (PKE) in a chiral p-wave (p_x+i p_y-wave) superconductor. It is found that the off-diagonal component of a current-current correlation function is induced by impurity scattering in the chiral p-wave condensate, and a nonzero ... More

Cech Cohomology of Semiring SchemesMar 04 2015Jun 18 2015A semiring scheme generalizes a scheme in such a way that the underlying algebra is that of semirings. We generalize \v{C}ech cohomology theory and invertible sheaves to semiring schemes. In particular, when $X=\mathbb{P}^n_M$, a projective space over ... More

A parabolic flow toward solutions of the optimal transportation problem on domains with boundaryJul 26 2010Dec 14 2010We consider a parabolic version of the mass transport problem, and show that it converges to a solution of the original mass transport problem under suitable conditions on the cost function, and initial and target domains.

An iterative scheme for solving the optimal transportation problemAug 25 2012Oct 09 2012We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of iterations necessary ... More

Radiation from accelerated impurities in Bose-Einstein condensateAug 25 2010We investigate radiation spectra arising from accelerated point-like impurities in the homogeneous Bose-Einstein condensate. A general formula for the radiation spectrum is obtained in the integral form as a function of given impurity trajectory. The ... More

Entanglement detection from channel parameter estimation problemJun 25 2015We derive a general criterion to detect entangled states in multi-partite systems based on the symmetric logarithmic derivative quantum Fisher information. This criterion is a direct consequence of the fact that separable states do not improve the accuracy ... More

Qubit subalgebra and tensor product in Weyl algebra of angular momentum systemDec 03 2014We analyze Weyl algebra of quantum angular momentum system and construct qubit subalgebra out of it. We show that the commutant of this qubit subalgebra is isomorphic to the original algebra and prove the tensor product structure between qubit subalgebra ... More

Creation of excitations from a uniform impurity motion in the condensateMay 29 2013We investigate a phenomenon of creation of excitations in the homogenous Bose-Einstein condensate due to an impurity moving with a constant velocity. A simple model is considered to take into account dynamical effects due to motions of the impurity. Based ... More

On the refined Gan-Gross-Prasad conjecture for cusp forms of GSp(4)Dec 31 2015Jun 13 2016We prove a conjectural formula relating the Bessel period of certain automorphic forms on $\mathrm{GSp}_4$ to a central $L$-value. This formula is proposed by Liu \cite{liu} as the refined Gan-Gross-Prasad conjecture for the groups $(\SO(5), \SO(2))$. ... More

Max-Margin Nonparametric Latent Feature Models for Link PredictionJun 18 2012We present a max-margin nonparametric latent feature model, which unites the ideas of max-margin learning and Bayesian nonparametrics to discover discriminative latent features for link prediction and automatically infer the unknown latent social dimension. ... More

A Lower Bound of the First Eigenvalue of a Closed Manifold with Negative Lower Bound of the Ricci CurvatureJun 28 2004Dec 08 2004Along the line of the Yang Conjecture, we give a new estimate on the lower bound of the first non-zero eigenvalue of a closed Riemannian manifold with negative lower bound of Ricci curvature in terms of the in-diameter and the lower bound of Ricci curvature. ... More

Coherent cohomology of Shimura varieties and automorphic formsOct 29 2018We show that the cohomology of canonical extensions of automorphic vector bundles over toroidal compactifications of Shimura varieties can be computed by relative Lie algebra cohomology of automorphic forms. Our result is inspired by and parallel to Borel ... More

On the dimension datum of a subgroup. IIMar 16 2018This paper studies three aspects around dimension datum: (1), a generalization of the dimension datum, which we call the tau-dimension datum; (2), dimension data of disconnected subgroups; (3), compactness of isospectral sets of normal homogeneous spaces. ... More

A Class of Monotonic Quantities along the Ricci FlowOct 23 2007Oct 24 2007We construct a class of monotonic quantities along the normalized Ricci flow on closed n-dimensional manifolds.

Nonlinear Large Deviations: Beyond the HypercubeMar 27 2017Jul 11 2018We present a framework to calculate large deviations for nonlinear functions of independent random variables supported on compact sets in Banach spaces, by extending the result in Chatterjee and Dembo [6]. Previous research on nonlinear large deviations ... More

Chaotic itinerancy and power-law residence time distribution in stochastic dynamical systemOct 15 2004Feb 23 2005To study a chaotic itinerant motion among varieties of ordered states, we propose a stochastic model based on the mechanism of chaotic itinerancy. The model consists of a random walk on a half-line, and a Markov chain with a transition probability matrix. ... More

A Degeneration formula of GW-invariantsOct 10 2001This is the second part of the paper "A degeneration of stable morphisms and relative stable morphisms", (math.AG/0009097). In this paper, we constructed the relative Gromov-Witten invariants of a pair of a smooth variety and a smooth divisor. We then ... More

Subsonic Flows for the Full Euler Equations in Half PlaneOct 19 2007We study the subsonic flows governed by full Euler equations in the half plane bounded below by a piecewise smooth curve asymptotically approaching x1-axis. Nonconstant conditions in the far field are prescribed to ensure the real Euler flows. The Euler ... More

BMW algebra, quantized coordinate algebra and type C Schur--Weyl dualityAug 22 2007Nov 17 2009We prove an integral version of the Schur--Weyl duality between the specialized Birman--Murakami--Wenzl algebra $B_n(-q^{2m+1},q)$ and the quantum algebra associated to the symplectic Lie algebra sp_{2m}. In particular, we deduce that this Schur--Weyl ... More

Generalized Kashaev invariants for knots in three manifoldsDec 02 2013Dec 15 2013Kashaev's invariants for a knot in a three sphere are generalized to invariants of a knot in a three manifold. A relation between the newly constructed invariants and the hyperbolic volume of the knot complement is observed for some knots in lens spaces. ... More

Mullineux involution and twisted affine Lie algebrasDec 05 2005Apr 02 2006We use Naito-Sagaki's work [S. Naito & D. Sagaki, J. Algebra 245 (2001) 395--412, J. Algebra 251 (2002) 461--474] on Lakshmibai-Seshadri paths fixed by diagram automorphisms to study the partitions fixed by Mullineux involution. We characterize the set ... More

Branching rules for Hecke Algebras of Type $D_{n}$Dec 09 2005In this paper we study the branching problems for Hecke algebra $\H(D_n)$ of type $D_n$. We explicitly describe the decompositions of the socle of the restriction of each irreducible $\H(D_n)$-representation to $\H(D_{n-1})$ into irreducible modules by ... More

A general method to construct cube-like categories and applications to homotopy theoryFeb 26 2015In this paper, we introduce a method to construct new categories which look like "cubes", and discuss model structures on the presheaf categories over them. First, we introduce a notion of thin-powered structure on small categories, which provides a generalized ... More

Extended duality relations between birth-death processes and partial differential equationsApr 15 2013Sep 03 2013Duality relations between continuous-state and discrete-state stochastic processes with continuous-time have already been studied and used in various research fields. We propose extended duality relations, which enable us to derive discrete-state stochastic ... More

On dualities for SSEP and ASEP with open boundary conditionsJun 17 2016Duality relations for simple exclusion processes with general open boundaries are discussed. It is shown that a combination of spin operators and bosonic operators enables us to have an unified discussion for the duality relations with the open boundaries. ... More

Nonparametric model reconstruction for stochastic differential equation from discretely observed time-series dataJul 04 2011Dec 12 2011A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion coefficients in advance. ... More

Superspace Formulation of N=4 Super Yang-Mills Theory with a Central ChargeDec 19 2005A superspace formulation using superconnections and supercurvatures is specifically constructed for N=4 extended super Yang-Mills theory with a central charge in four dimensions, first proposed by Sohnius, Stelle and West long ago. We find that the constraints, ... More