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Statistical Learnability of Generalized Additive Models based on Total Variation RegularizationFeb 08 2018A generalized additive model (GAM, Hastie and Tibshirani (1987)) is a nonparametric model by the sum of univariate functions with respect to each explanatory variable, i.e., $f({\mathbf x}) = \sum f_j(x_j)$, where $x_j\in\mathbb{R}$ is $j$-th component ... More

Statistical Learnability of Generalized Additive Models based on Total Variation RegularizationFeb 08 2018Feb 16 2018A generalized additive model (GAM, Hastie and Tibshirani (1987)) is a nonparametric model by the sum of univariate functions with respect to each explanatory variable, i.e., $f({\mathbf x}) = \sum f_j(x_j)$, where $x_j\in\mathbb{R}$ is $j$-th component ... More

Grafting for Combinatorial Boolean Model using Frequent Itemset MiningNov 07 2017Nov 13 2017This paper introduces the combinatorial Boolean model (CBM), which is defined as the class of linear combinations of conjunctions of Boolean attributes. This paper addresses the issue of learning CBM from labeled data. CBM is of high knowledge interpretability ... More

Distributed Stochastic Optimization of the Regularized RiskJun 17 2014Jun 09 2015Many machine learning algorithms minimize a regularized risk, and stochastic optimization is widely used for this task. When working with massive data, it is desirable to perform stochastic optimization in parallel. Unfortunately, many existing stochastic ... More

DS-MLR: Exploiting Double Separability for Scaling up Distributed Multinomial Logistic RegressionApr 16 2016Aug 03 2018Scaling multinomial logistic regression to datasets with very large number of data points and classes is challenging. This is primarily because one needs to compute the log-partition function on every data point. This makes distributing the computation ... More

WordRank: Learning Word Embeddings via Robust RankingJun 09 2015Sep 27 2016Embedding words in a vector space has gained a lot of attention in recent years. While state-of-the-art methods provide efficient computation of word similarities via a low-dimensional matrix embedding, their motivation is often left unclear. In this ... More

Totally Corrective Boosting with Cardinality PenalizationApr 07 2015We propose a totally corrective boosting algorithm with explicit cardinality regularization. The resulting combinatorial optimization problems are not known to be efficiently solvable with existing classical methods, but emerging quantum optimization ... More

DS-MLR: Exploiting Double Separability for Scaling up Distributed Multinomial Logistic RegressionApr 16 2016Multinomial logistic regression is a popular tool in the arsenal of machine learning algorithms, yet scaling it to datasets with very large number of data points and classes has not been trivial. This is primarily because one needs to compute the log-partition ... More

Correction to four-loop RG functions in the two-dimensional lattice O(n) $σ$-modelOct 12 1998Mar 12 2001We report the result of our evaluation of the Feynman diagrams appearing in the determination of the four-loop renormalization group functions in the two-dimensional lattice O($n$) $\sigma$-model by Caracciolo and Pelissetto. In the list of the integrals ... More

A determination of the mass gap in the O(n) sigma modelNov 06 1996Mar 12 2001We calculate the finite volume mass gap $M(L)$ at 3-loop level in the non-linear O($n$) $\sigma$-model in two dimensions in small volumes. By applying the Monte Carlo measurements of the running coupling $\bar g^2(L)=2nM(L)L/(n-1)$ by L\"uscher, Weisz ... More

Cumulant Generating Function of Codeword Lengths in Variable-Length Lossy Compression Allowing Positive Excess Distortion ProbabilityJan 05 2018Jan 11 2018This paper considers the problem of variable-length lossy source coding. The performance criteria are the excess distortion probability and the cumulant generating function of codeword lengths. We derive a non-asymptotic fundamental limit of the cumulant ... More

Fundamental structural characteristics of planar granular assemblies: scaling away friction and initial stateJul 12 2012Macroscopic properties of granular packs are mainly determined by the micro-structure. We study the dependence of the micro-structure on inter-granular friction and initial conditions using numerical experiments. The experiments consist of isotropic compaction ... More

Non-Asymptotic Fundamental Limits of Guessing Subject to DistortionAug 19 2018Jan 09 2019This paper investigates the problem of guessing subject to distortion, which was introduced by Arikan and Merhav. While the primary concern of the previous study was asymptotic analysis, our primary concern is non-asymptotic analysis. We prove non-asymptotic ... More

Application of a coordinate space method for the evaluation of lattice Feynman diagrams in two dimensionsJun 17 1997Mar 21 1998We apply a new coordinate space method for the evaluation of lattice Feynman diagrams suggested by L\"uscher and Weisz to field theories in two dimensions. Our work is to be presented for the theories with massless propagators. The main idea is to deal ... More

On universal structural characteristics of granular packsMay 27 2013Nov 01 2013Dependence of structural self-organization of granular materials on preparation and grain parameters is key to predictive modelling. We study 60 different mechanically equilibrated polydisperse disc packs, generated numerically by two protocols. We show ... More

Covariance Evolution for Spatially "Mt. Fuji" Coupled LDPC CodesApr 10 2019A spatially "Mt. Fuji" coupled low-density parity check ensemble is a modified version of the original spatially coupled low-density parity check ensemble. It is known that it has almost the same decoding error probability as and require less number of ... More

Covariance Evolution for Spatially "Mt. Fuji" Coupled LDPC CodesApr 10 2019Apr 16 2019A spatially `Mt. Fuji' coupled low-density parity check ensemble is a modified version of the original spatially coupled low-density parity check ensemble. It is known that it has almost the same decoding error probability as and requires less number ... More

Closed-string Tachyon Condensation and the On-shell Effective Action of Open-string TachyonsMay 07 2001Dec 12 2001We study how the effect of closed-string tachyon condensation can enter into the on-shell effective action of open-string tachyons in the bosonic case. We also consider open-string one-loop quantum corrections to the on-shell action. We use a sigma-model ... More

The ~U(12)-Classification Scheme, Static U(4)-Spin Symmetry for Light-Quarks and "Exotic" HadronsNov 02 2005Nov 03 2005Several years ago we have proposed a manifestly covariant $\tilde{U}(12)_{SF}$-classification scheme of hadrons, which maintains the successful $SU(6)_{SF}\otimes O(3)_{L}$ framework in Non-Relativistic Quark Model and is also reconcilable with the mechanism ... More

Controversies on and a Reasoning for Existence of the light sigma-particleMay 06 1999The light sigma-particle is, regardless of the strong criticism, reviving recently due to the works done from various sides. I review essential points of the controversies (especially related to our works) and of their answer: Conventionally a large concentration ... More

Physical Origin of Chiral States and Near-Threshold Resonances Observed at BESDec 27 2006The purpose of my talk is to explain physical backgrounds of the chiral states, which are predicted to exist generally in the low mass regions of hadrons, containing light quarks, and to stimulate the experimental and phenomenological search for their ... More

On existence of the σ(600) - Its physical implications and related problemsDec 02 1997We make a re-analysis of I=0 \pi\pi scattering phase shift \delta_0^0 through a new method of S-matrix parametrization (IA; interfering amplitude method), and show a result suggesting strongly for the existence of \sigma-particle -- long-sought Chiral ... More

Crossing changes, Delta moves, and sharp moves on welded knotsOct 09 2015Oct 13 2015We prove that the crossing changes, Delta moves, and sharp moves are unknotting operations on welded knots.

Vacua, walls and junctions in $G_{N_F,N_C}$Apr 16 2018We discuss vacua, walls and three-pronged wall junctions in the Grassmann manifold $G_{N_F,N_C}=\frac{SU(N_F)}{SU(N_C)\times SU(N_F-N_C)\times U(1)}$.

Generalized complex marginal deformation of pp-waves and giant gravitonsMay 14 2015We present the Penrose limits of a complex marginal deformation of $AdS_5\times S^5$, which incorporates the $SL(2,\mathbb{R})$ symmetry of type IIB theory, along the $(J,0,0)$ geodesic and along the $(J,J,J)$ geodesic. We discuss giant gravitons on the ... More

Ramification theory and perfectoid spacesApr 22 2013May 22 2013Let K and F be complete discrete valuation fields of residue characteristic p>0. Let m be a positive integer no more than their absolute ramification indices. Let s and t be their uniformizers. Let L/K and E/F be finite extensions such that the modulo ... More

Smearing Effect in Plane-Wave Matrix ModelDec 22 2008Dec 27 2008Motivated by the usual D2-D0 system, we consider a configuration composed of flat membrane and fuzzy sphere membrane in plane-wave matrix model, and investigate the interaction between them. The configuration is shown to lead to a non-trivial interaction ... More

Construction of Liouville Brownian motion via Dirichlet form theoryJan 23 2019The Liouville Brownian motion which was introduced in \cite{GRV} is a natural diffusion process associated with a random metric in two dimensional Liouville quantum gravity. In this paper we construct the Liouville Brownian motion via Dirichlet form theory. ... More

On the classification of 4-dimensional $(m,ρ)$-quasi-Einstein manifolds with harmonic Weyl curvatureJun 05 2016In this paper we study 4-dimensional $(m,\rho)$-quasi-Einstein manifolds with harmonic Weyl curvature when $m\notin\{0,\pm1,-2,\pm\infty\}$ and $\rho\notin\{\frac{1}{4},\frac{1}{6}\}$. We prove that a non-trivial $(m,\rho)$-quasi-Einstein metric $g$ (not ... More

Comparison of Sobol' sequences in financial applicationsSep 10 2018Feb 05 2019Sobol' sequences are widely used for quasi-Monte Carlo methods that arise in financial applications. Sobol' sequences have parameter values called direction numbers, which are freely chosen by the user, so there are several implementations of Sobol' sequence ... More

Discriminative Learning of the Prototype Set for Nearest Neighbor ClassificationSep 27 2015Aug 21 2016The nearest neighbor rule is one of the most widely used models for classification, and selecting a compact set of prototype instances is a primary challenges for its applications. Many existing approaches for prototype selection exploit instance-based ... More

Negative Differential Resistivity from HolographyJun 21 2010Sep 16 2011Negative differential resistivity (NDR) in a (3+1)-dimensional quantum system of strongly correlated charge carriers is theoretically reproduced by using the AdS/CFT correspondence. Our system is microscopically defined, and the analysis does not rely ... More

Comments on Chemical Potentials in AdS/CFTNov 10 2007Dec 30 2008We propose a method for identifying holographic chemical potentials of conserved charges. The guiding principle is the consistency of the identification with the thermodynamic relations and the Legendre transformation. We consider the baryon-charge chemical ... More

On a properness of the Hilbert eigenvariety at integral weights: the case of quadratic residue fieldsJan 05 2016Let p be a rational prime. Let F be a totally real number field such that F is unramified over p and the residue degree of any prime ideal of F dividing p is 1 or 2. In this paper, we show that the eigenvariety for Res_{F/Q}(GL_2), constructed by Andreatta-Iovita-Pilloni, ... More

Dimension variation of Gouvêa-Mazur type for Drinfeld cuspforms of level $Γ_1(t)$Jun 22 2018Let $p$ be a rational prime and $q>1$ a $p$-power. Let $S_k(\Gamma_1(t))$ be the space of Drinfeld cuspforms of level $\Gamma_1(t)$ and weight $k$ for $\mathbb{F}_q[t]$. For any non-negative rational number $\alpha$, we denote by $d(k,\alpha)$ the dimension ... More

The cohomological Brauer group of a torsion $\mathbb{G}_{m}$-gerbeMay 02 2018Let $S$ be a scheme and let $\pi : \mathcal{G} \to S$ be a $\mathbb{G}_{m,S}$-gerbe corresponding to a torsion class $[\mathcal{G}]$ in the cohomological Brauer group $\mathrm{Br}'(S)$ of $S$. We show that the cohomological Brauer group $\mathrm{Br}'(\mathcal{G})$ ... More

Intracluster Supernova as a Possible Extra Energy Source of ClustersNov 09 2000The observed luminosity -- temperature relation of clusters is considerably steeper than that expected from a simple scaling relation. Although extra energy input is a likely solution, its source has not been identified. We propose intracluster supernova ... More

A characterization of Burniat surfaces with $K^{2}=4$ and of non nodal typeJul 22 2014Jul 13 2015Let $S$ be a minimal surface of general type with $p_{g}(S)=0$ and $K^{2}_{S}=4$. Assume the bicanonical map $\varphi$ of $S$ is a morphism of degree $4$ such that the image of $\varphi$ is smooth. Then we prove that the surface $S$ is a Burniat surface ... More

WRS: Waiting Room Sampling for Accurate Triangle Counting in Real Graph StreamsSep 10 2017Sep 19 2017If we cannot store all edges in a graph stream, which edges should we store to estimate the triangle count accurately? Counting triangles (i.e., cycles of length three) is a fundamental graph problem with many applications in social network analysis, ... More

A New Bijection Between Forests and Parking FunctionsOct 02 2008Oct 03 2008In 1980, G. Kreweras gave a recursive bijection between forests and parking functions. In this paper we construct a nonrecursive bijection from forests onto parking functions, which answers a question raised by R. Stanley. As a by-product, we obtain a ... More

Base-point-free pencils on triple covers of smooth curvesJun 11 2008Let $X$ be a smooth algebraic curve. Suppose that there exists a triple covering $f : X \to Y$ where $Y$ is a smooth algebraic curve. In this paper, we investigate the existence of morphisms from $X$ to the projective line $\mathbf{P}^1$ which do not ... More

Canonical subgroups via Breuil-Kisin modulesDec 06 2010Nov 26 2012Let p>2 be a rational prime and K/Q_p be an extension of complete discrete valuation fields. Let G be a truncated Barsotti-Tate group of level n, height h and dimension d over O_K with 0<d<h. In this paper, we show that an upper ramification subgroup ... More

Nonequilibrium Phase Transitions and a Nonequilibrium Critical Point from Anti-de Sitter Space and Conformal Field Theory CorrespondenceApr 09 2012Oct 04 2012We find novel phase transitions and critical phenomena that occur only outside the linear-response regime of current-driven nonequilibrium states. We consider the strongly-interacting (3+1)-dimensional N=4 large-Nc SU(Nc) supersymmetric Yang-Mills theory ... More

Strict decomposition of diffusions associated to degenerate (sub)-elliptic formsJun 19 2016For degenerate symmetric (sub)-elliptic forms, we construct weak solutions to the corresponding stochastic differential equations starting from all points in Euclidean space. By virtue of transition density estimate, stochastic calculus, and strict Fukushima ... More

Localization of Dirac Operators on 4n+2 Dimensional Open Spin^c ManifoldsJun 03 2013Jan 21 2014An integer valued topological index of a Dirac operator is introduced for a pair of a 4n+2 dimensional open Spin^c manifold and a section of the determinant line bundle satisfying some property. We show a relation between the index and an index of a Dirac ... More

Extension and its characteristics of ECRH plasma in the LHDOct 24 2004One of the main objectives of the LHD is to extend the plasma confinement database for helical systems and to demonstrate such extended plasma confinement properties to be sustained in steady state. Among the various plasma parameter regimes, the study ... More

Light neutralino dark matter in light Higgs scenario related with the CoGeNT and DAMA/LIBRA resultsNov 29 2010Recently, the CoGeNT collaboration reported the WIMP candidate signal events exceeding the known backgrounds where the light WIMP with large cross section is supported. Motivated by this issue, we analyze a light neutralino dark matter scenario with a ... More

Toeplitz operators on concave corners and topologically protected corner statesFeb 05 2019We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for these operators to be Fredholm. We further construct a Fredholm concave corner Toeplitz operator of index ... More

A refined bijection between alternating permutations and 0-1-2 increasing treesMar 24 2010We construct a refined bijection $\phi$ between alternating permutations and 0-1-2 increasing trees with degree at most 2. It satisfies that the first element of alternating permutation $\pi$ is equal to the first vertex in $\phi(\pi)$ in the postorder. ... More

A search for extensible low-WAFOM point setsSep 30 2013Jun 20 2016Matsumoto, Saito, and Matoba recently proposed the Walsh figure of merit (WAFOM), which is a computable criterion for quasi-Monte Carlo point sets using digital nets. Several algorithms have been proposed for finding low-WAFOM point sets. In the existing ... More

Strict decomposition of diffusions associated to degenerate (sub)-elliptic formsJun 19 2016Jun 14 2018For given strongly local Dirichlet forms with possibly degenerate symmetric (sub)-elliptic matrix, we show the existence of weak solutions to the stochastic differential equations (associated with the Dirichlet forms) starting from all points in $\R^d$. ... More

Vortex solutions of parity and time reversal invariant Maxwell-Dirac-Chern-Simons gauge theoryFeb 17 1997Nov 18 1997We construct parity and time reversal invariant Maxwell-Chern-Simons gauge theory coupled to fermions with adding the parity partner to the matter and the gauge fields, which can give nontopological vortex solutions depending on the sign of the Chern-Simons ... More

Three-dimensional Ricci-degenerate Riemannian manifolds satisfying geometric equationsJan 01 2018Mar 09 2018In this paper, we study a three-dimensional Ricci-degenerate Riemannian manifold $(M^3,g)$ that admits a smooth nonzero solution $f$ to the equation \begin{align} \label{a1a} \nabla df=\psi Rc+\phi g, \end{align} where $\psi,\phi$ are given smooth functions ... More

Algebraic degrees of stretch factors in mapping class groupsJan 08 2014Sep 23 2015We explicitly construct pseudo-Anosov maps on the closed surface of genus $g$ with orientable foliations whose stretch factor $\lambda$ is a Salem number with algebraic degree $2g$. Using this result, we show that there is a pseudo-Anosov map whose stretch ... More

Infinitesimal deformations of complements of plumbings of rational curvesOct 10 2010We construct infinitesimal deformations on an open domain of a smooth projective surface given by a complement of plumbings of disjoint linear chains of smooth rational curves. We show that the infinitesimal deformations are not small deformations, that ... More

Extended Okounkov bodies and multi-point Seshadri constantsOct 12 2017Jun 25 2018Based on the work of Okounkov, Kaveh-Khovanskii and Lazarsfeld-Mustata independently associated a convex body, called the Okounkov body, to a big divisor on a normal projective variety with respect to an admissible flag. Although the Okounkov bodies carry ... More

On lower ramification subgroups and canonical subgroupsAug 27 2012Nov 09 2012Let p be a rational prime, k be a perfect field of characteristic p and K be a finite totally ramified extension of the fraction field of the Witt ring of k. Let G be a finite flat commutative group scheme over O_K killed by some p-power. In this paper, ... More

Canonical subgroups via Breuil-Kisin modules for p=2Sep 20 2011Jul 26 2012Let p be a rational prime and K/Q_p be an extension of complete discrete valuation fields. Let G be a truncated Barsotti-Tate group of level n, height h and dimension d over O_K with 0<d<h. In this paper, we prove the existence of higher canonical subgroups ... More

Simultaneous auctions for complementary goodsDec 10 2013This paper studies an environment of simultaneous, separate, first-price auctions for complementary goods. Agents observe private values of each good before making bids, and the complementarity between goods is explicitly incorporated in their utility. ... More

Dirichlet Boundary Conditions in Generalized Liouville Theory toward a QCD StringApr 25 2000Sep 25 2000We consider bosonic noncritical strings as QCD strings and we present a basic strategy to construct them in the context of Liouville theory. We show that Dirichlet boundary conditions play important roles in generalized Liouville theory. Specifically, ... More

Recoiling D-branesJun 22 2004Dec 20 2004We propose a new method to describe a recoiling D-brane that is elastically scattered by closed strings in the non-relativistic region. We utilize the low-energy effective field theory on the worldvolume of the D-brane, and the velocity of the D-brane ... More

Three-dimensional Ricci-degenerate Riemannian manifolds satisfying geometric equationsJan 01 2018In this paper, we study a three dimensional Ricci-degenerate Riemannian manifold $(M^3,g)$ which admits a smooth nonzero solution $f$ to the following equation: \begin{align} \label{a1a} \nabla df=\psi(f)Rc+\phi(f)g, \end{align} where $Rc$ is the Ricci ... More

Weak-supervision for Deep Representation Learning under Class ImbalanceOct 30 2018Class imbalance is a pervasive issue among classification models including deep learning, whose capacity to extract task-specific features is affected in imbalanced settings. However, the challenges of handling imbalance among a large number of classes, ... More

The Brauer group of $\mathscr{M}_{1,1}$ over algebraically closed fields of characteristic $2$May 03 2017Feb 26 2018We prove that the Brauer group of the moduli stack of elliptic curves $\mathscr{M}_{1,1,k}$ over an algebraically closed field $k$ of characteristic $2$ is isomorphic to $\mathbb{Z}/(2)$. We also compute the Brauer group of $\mathscr{M}_{1,1,k}$ where ... More

On Non-linear Action for Gauged M2-braneDec 04 2009Mar 17 2010We propose a non-linear extension of U(1) \times U(1) (abelian) ABJM model including T_{M2} (higher derivative) corrections. The action proposed here is expected to describe a single M2-brane proving C^4/Z_k target space. The model includes couplings ... More

$T^3$ deformations and $β$-deformed geometriesNov 05 2013Mar 19 2014We discuss $\beta$-deformed geometries on two types of $T^3$'s where the direction along the third coordinate is not orthogonal to the direction along the second coordinate or the direction along the first coordinate. We show that the intersection angle ... More

Conversion of Mersenne Twister to double-precision floating-point numbersAug 20 2017Sep 02 2018The 32-bit Mersenne Twister generator MT19937 is a widely used random number generator. To generate numbers with more than 32 bits in bit length, and particularly when converting into 53-bit double-precision floating-point numbers in $[0,1)$ in the IEEE ... More

The minimal degree of plane models of double covers of smooth curvesSep 10 2008Oct 12 2009If $X$ is a smooth curve such that the minimal degree of its plane models is not too small compared with its genus, then $X$ has been known to be a double cover of another smooth curve $Y$ under some mild condition on the genera. However there are no ... More

Glueball Mass Spectrum in KK Monopole BackgroundSep 04 1999We consider typeIIA supergravity solution of D2-branes and D3-branes localized within D6-branes in the near-core region of D6-branes. With these solutions we can calculate the spectrum of the glueball mass in QCD3 and QCD4. The equation of motion describing ... More

Toeplitz operators on concave corners and topologically protected corner statesFeb 05 2019May 05 2019We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for these operators to be Fredholm. We further construct a Fredholm concave corner Toeplitz operator of index ... More

Topological invariants and corner states for Hamiltonians on a three-dimensional latticeNov 29 2016Mar 19 2018Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two topological invariants ... More

Liouville distorted Brownian motionJan 23 2019The Liouville Brownian motion was introduced in \cite{GRV} as a time changed process $B_{A_t^{-1}}$ of a planar Brownian motion $(B_t)_{t \ge 0}$, where $(A_t)_{t \ge 0}$ is the positive continuous additive functional of $(B_t)_{t \ge 0}$ in the strict ... More

The Complexity of Approximating a Bethe EquilibriumSep 08 2011Mar 21 2013This paper resolves a common complexity issue in the Bethe approximation of statistical physics and the Belief Propagation (BP) algorithm of artificial intelligence. The Bethe approximation and the BP algorithm are heuristic methods for estimating the ... More

Higher syzygies on abelian surfacesAug 22 2016Sep 05 2017Based on the theory of an infinitesimal Newton-Okounkov body, we extend the results of Lazarsfeld-Pareschi-Popa on abelian surfaces. Moreover, we show that the higher syzygies of $(X,L)$ are completely determined by its Seshadri constant when $L^{2}$ ... More

Topologically non-trivial configurations in 3-dimensional Yang-Mills theoryOct 31 2000Recently Anishetty, Majumdar and Sharatchandra have proposed a way of characterizing topologically non-trivial configurations for 2+1-dimensional Yang-Mills theory in a local and manifestly gauge invariant manner. Here we develop criteria to locate such ... More

Numerical evidence for monopoles in 3-dimensional Yang-Mills theorySep 28 2000Jan 05 2001Recently Anishetty, Majumdar and Sharatchandra have proposed a way of characterizing topologically non-trivial configurations for 2+1 dimensional Yang-Mills theory in a local and manifestly gauge invariant manner. In this paper paper we develop criteria ... More

On a ramification bound of torsion semi-stable representations over a local fieldJan 14 2008Jun 20 2009For a rational prime p, let k be a perfect field of characteristic p, K be a finite totally ramified extension of Frac(W(k)) of degree e and r be a non-negative integer satisfying r<p-1. In this article, we prove the upper numbering ramification group ... More

Topological invariants and corner states for Hamiltonians on a three dimensional latticeNov 29 2016Periodic Hamiltonians on a three dimensional lattice which have a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for quarter-plane Toeplitz algebras, two topological invariants ... More

Higher syzygies on abelian surfaces and on their double coversAug 22 2016Let $(X,L)$ be a polarized abelian surface and $f:Y \rightarrow X$ a double cover of $X$ branched over a smooth divisor $B=D^{\otimes 2}$. Based on the theory of infinitesimal Newton-Okounkov body, we show the $N_{p}$ property of $f^{*}L$ by using the ... More

Decay Rates of Fixed Planes and Closed-string Tachyons on Unstable OrbifoldsMay 07 2003Apr 12 2004We consider closed-string tachyon condensation in the twisted sectors on the C/Z_{2n+1} \times R^{7,1} orbifold. We calculate the localized energy density in the fixed plane on the orbifold at the one-loop level, and we obtain the decay rate per unit ... More

Duality of Drinfeld modules and $\wp$-adic properties of Drinfeld modular formsJun 23 2017Sep 08 2017Let $p$ be a rational prime and $q$ a power of $p$. Let $\wp$ be a monic irreducible polynomial of degree $d$ in $\mathbf{F}_q[t]$. In this paper, we define an analogue of the Hodge-Tate map which is suitable for the study of Drinfeld modules over $\mathbf{F}_q[t]$ ... More

Ultradiscrete limit of Bessel function type solutions of the Painlevé III equationSep 05 2014An ultradiscrete analog of the Bessel function is constructed by taking the ultradiscrete limit for a $q$-difference analog of the Bessel function. Then, a direct relationship between a class of special solutions for the ultradiscrete Painlev\'{e} III ... More

A New Method to Estimate Cosmological Parameters Using Baryon Fraction of Clusters of GalaxiesNov 05 1996We propose a new method to estimate cosmological parameters using the baryon fraction of clusters of galaxies for a range of redshifts. The basic assumption is that the baryon fraction of clusters is constant, which is a reasonable assumption when it ... More

Junctions of mass-deformed nonlinear sigma models on the Grassmann manifoldApr 29 2019We study vacua and walls of the mass-deformed nonlinear sigma model on the Grassmann manifold $G_{N_F,N_C}=\frac{SU(N_F)}{SU(N_C)\times SU(N_F-N_C)\times U(1)}$ and discuss three-pronged junctions for $N_C=1,2,3$ in four dimensions.

On the $\mathbb{F}_2$-linear relations of Mersenne Twister pseudorandom number generatorsJan 23 2013Nov 06 2013Sequence generators obtained by linear recursions over the two-element field $\mathbb{F}_2$, i.e., $\mathbb{F}_2$-linear generators, are widely used as pseudorandom number generators. For example, the Mersenne Twister MT19937 is one of the most successful ... More

Ramification correspondence of finite flat group schemes over equal and mixed characteristic local fieldsJul 19 2010May 17 2012Let p>2 be a rational prime, k be a perfect field of characteristic p and K be a finite totally ramified extension of the fractional field of the Witt ring of k. Let G and H be finite flat commutative group schemes killed by p over O_K and k[[u]], respectively. ... More

Fixed-point property for affine actions on a Hilbert spaceMay 07 2017Gromov showed that for fixed, arbitrarily large C, any uniformly C-Lipschitz affine action of a random group in his graph model on a Hilbert space has a fixed point. We announce a theorem stating that more general affine actions of the same random group ... More

Spectral radius of a star with one long armSep 26 2017A tree is said to be starlike if exactly one vertex has degree greater than two. In this paper, we will study the spectral properties of $S(n,k \cdot 1)$, that is, the starlike tree with $k$ branches of length 1 and one branch of length $n$. The largest ... More

Bulk-edge correspondence and the cobordism invariance of the indexNov 24 2016Apr 06 2018We show that the bulk-edge correspondence for two-dimensional type A and type AII topological insulators follows directly from the cobordism invariance of the index.

Quasi-Monte Carlo point sets with small $t$-values and WAFOMJun 08 2014Jan 01 2015The $t$-value of a $(t, m, s)$-net is an important criterion of point sets for quasi-Monte Carlo integration, and many point sets are constructed in terms of the $t$-values, as this leads to small integration error bounds. Recently, Matsumoto, Saito, ... More

Almost complex manifolds are (almost) complexMar 24 2019We analyze the differential relation corresponding to integrability of almost complex structures, reformulated as a directed immersion relation by Demailly and Gaussier. We prove that the relation has formal solutions up to complex dimension 77, and that, ... More

Slices of Okounkov bodies of big divisors on Mori dream spacesApr 26 2016May 03 2016The purpose of this paper is to study the slices of the Okounkov bodies of Mori dream spaces. First, we analyze all the slices of the Okounkov bodies of big divisors on Mori dream spaces associated to some admissible flags. As a byproduct, we obtain their ... More

A bound for the Milnor sum of projective plane curves in terms of GITFeb 25 2015Sep 28 2015Let $C$ be a projective plane curve of degree $d$ whose singularities are all isolated. Suppose $C$ is not concurrent lines. P{\l}oski proved that the Milnor number of an isolated singlar point of $C$ is less than or equal to $(d-1)^{2}-\lfloor \frac{d}{2} ... More

Geometric structures modeled on smooth projective horospherical varieties of Picard number oneOct 05 2016Geometric structures modeled on rational homogeneous manifolds are studied to characterize rational homogeneous manifolds and to prove their deformation rigidity. To generalize these characterizations and deformation rigidity results to quasihomogeneous ... More

Contact geometric descriptions of vector fields on dually flat spaces and their applications in electric circuit models and nonequilibrium statistical mechanicsDec 03 2015Contact geometry has been applied to various mathematical sciences, and it has been proposed that a contact manifold and a strictly convex function induce a dually flat space that is used in information geometry. Here, such a dually flat space is related ... More

Can Dark Matter Annihilation Dominate the Extragalactic Gamma-Ray Background?Mar 01 2005Annihilating dark matter (DM) has been discussed as a possible source of gamma-rays from the galactic center (GC) and contributing to the extragalactic gamma-ray background (EGB). Assuming universality of the density profile of DM halos, we show that ... More

Decaying neutrinos and implications from the supernova relic neutrino observationJul 13 2003Aug 07 2003We propose that supernova relic neutrino (SRN) observation can be used to set constraints on the neutrino decay models. Because of the long distance scale from cosmological supernovae to the Earth, SRN have possibility to provide much stronger limit than ... More

Asymmetric neutrino emission due to neutrino-nucleon scatterings in supernova magnetic fieldsJul 01 2003We derive the cross section of neutrino-nucleon scatterings in supernova magnetic fields, including weak-magnetism and recoil corrections. Since the weak interaction violates the parity, the scattering cross section asymmetrically depends on the directions ... More

Cosmic Star Formation History and the Future Observation of Supernova Relic NeutrinosJan 25 2004Mar 17 2004We investigate the flux and event rate of supernova relic neutrinos (SRNs) and discuss their implications for the cosmic star formation rate. As reference models, we adopt the supernova rate model based on recent observations and the supernova neutrino ... More

Non-geometric Five-branes in Heterotic SupergravityAug 04 2016Aug 10 2016We study T-duality chains of five-branes in heterotic supergravity where the first order $\alpha'$-corrections are present. By performing the $\alpha'$-corrected T-duality transformations of the heterotic NS5-brane solutions, we obtain the KK5-brane and ... More