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Cleaning tasks knowledge transfer between heterogeneous robots: a deep learning approachMar 13 2019Nowadays, autonomous service robots are becoming an important topic in robotic research. Differently from typical industrial scenarios, with highly controlled environments, service robots must show an additional robustness to task perturbations and changes ... More

Genetic-Gated Networks for Deep ReinforcementNov 26 2018We introduce the Genetic-Gated Networks (G2Ns), simple neural networks that combine a gate vector composed of binary genetic genes in the hidden layer(s) of networks. Our method can take both advantages of gradient-free optimization and gradient-based ... More

Ultrafast zero balance of the oscillator-strength sum rule in grapheneSep 10 2013Oscillator-strength sum rule in light-induced transitions is one general form of quantum-mechanical identities. Although this sum rule is well established in equilibrium photo-physics, an experimental corroboration for the validation of the sum rule in ... More

SpherePHD: Applying CNNs on a Spherical PolyHeDron Representation of 360 degree ImagesNov 20 2018Omni-directional cameras have many advantages over conventional cameras in that they have a much wider field-of-view (FOV). Several approaches have been recently proposed to apply convolutional neural networks (CNNs) to omni-directional images to solve ... More

Charge-spin correlation in van der Waals antiferromagenet NiPS3Jun 20 2017Jun 26 2017Strong charge-spin coupling is found in a layered transition-metal trichalcogenide NiPS3, a van derWaals antiferromagnet, from our study of the electronic structure using several experimental and theoretical tools: spectroscopic ellipsometry, x-ray absorption ... More

Residual Features and Unified Prediction Network for Single Stage DetectionJul 17 2017Jan 05 2018Recently, a lot of single stage detectors using multi-scale features have been actively proposed. They are much faster than two stage detectors that use region proposal networks (RPN) without much degradation in the detection performances. However, the ... More

BOOK: Storing Algorithm-Invariant Episodes for Deep Reinforcement LearningSep 05 2017Feb 12 2018We introduce a novel method to train agents of reinforcement learning (RL) by sharing knowledge in a way similar to the concept of using a book. The recorded information in the form of a book is the main means by which humans learn knowledge. Nevertheless, ... More

Greedy Sparse Signal Recovery with Tree PruningSep 19 2014Recently, greedy algorithm has received much attention as a cost-effective means to reconstruct the sparse signals from compressed measurements. Much of previous work has focused on the investigation of a single candidate to identify the support (index ... 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.

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Automatic Knowledge Base Evolution by Learning InstancesApr 04 2016Knowledge base is the way to store structured and unstructured data throughout the web. Since the size of the web is increasing rapidly, there are huge needs to structure the knowledge in a fully automated way. However fully-automated knowledge-base evolution ... More

Private Web Search with an Expected Constant RoundApr 11 2016Web searching is becoming an essential activity because it is often the most effective and convenient way of finding information. However, a Web search can be a threat to the privacy of the searcher because the queries may reveal sensitive information ... More

Euler characteristic of analogues of a Deligne-Lusztig variety for $GL_n$Jun 12 2016In this paper we give a combinatorial formula to calculate the Euler characteristic of an analogue of a Deligne-Lusztig variety if we replace Frobenius morphism with conjugation by an element for $GL_n$. The main theorem states that it only depends on ... More

The Conley-Zehnder indices of the Euler problem of two fixed centersJan 08 2016Jun 14 2016We give the thorough analysis for the rotation functions of the critical orbits. From this one can understand bifurcations of periodic orbits. Moreover, we give explicit formulas of the Conley-Zehnder indices of the interior and exterior collision orbits ... More

Convolutional Neural Networks for Sentence ClassificationAug 25 2014Sep 03 2014We report on a series of experiments with convolutional neural networks (CNN) trained on top of pre-trained word vectors for sentence-level classification tasks. We show that a simple CNN with little hyperparameter tuning and static vectors achieves excellent ... More

OPE Constraints and the Leading Order Hadronic Contribution to (g-2)_muNov 13 2006OPE constraints are studied as a means of distinguishing between the versions of the I=1 vector spectral function extracted from (i) inclusive I=1 hadronic electroproduction cross-sections and (ii) inclusive I=1 hadronic tau decay data, with the goal ... More

Heavy Quark Analogues of the Theta and Their ExcitationsAug 11 2004Predictions for the low-lying excitation spectrum of positive parity pentaquark systems containing one c or b antiquark and four light u,d quarks are obtained in the quark model picture for models with spin-dependent interactions given either by effective ... More

Problems With Extracting $m_s$ from Flavor Breaking in Hadronic $τ$ DecaysApr 15 1998A numerical error is pointed out in the existing expression for the order $\alpha_s^2$ longitudinal component of the squared-mass (D=2) contribution to the hadronic $\tau$ decay rate. The corrected version is found to be such that, to order $\alpha_s^2$, ... More

Status of the Lattice and Tau Decay Determinations of alpha_sNov 28 2010The two highest precision determinations of alpha_s(M_Z^2), that based on the analysis of short-distance-sensitive lattice observables, and that based on an analysis of hadronic tau decay data, have, until very recently, given results which are not in ... More

On the Leading ORder Hadronic Contribution to (g-2)_muDec 26 2005Sum rule constraints dominated by the independent high-scale input, alpha_s(M_Z), are shown to be satisfied by I=1 spectral data from hadronic tau decays, but violated by the pre-2005 electroproduction (EM) cross-section data. Determinations of the Standard ... More

Arithmetic Chern-Simons Theory IOct 20 2015May 12 2016In this paper, we apply ideas of Dijkgraaf and Witten on 2+1 dimensional topological quantum field theory to arithmetic curves, that is, the spectra of rings of integers in algebraic number fields. In the first three sections, we define classical Chern-Simons ... More

A note on Szpiro's inequality for curves of higher genusOct 23 2002This is a short addendum to a note of Beauville on the subject of the title. We prove an inequality that takes into account the constant part of the Jacobian.

The average number of divisors of the Euler functionMay 16 2016The upper bound and the lower bound of average numbers of divisors of Euler Phi function and Carmichael Lambda function are obtained by Luca and Pomerance (see ~\cite{LP}). We improve the lower bound and provide a heuristic argument which suggests that ... More

Massey products for elliptic curves of rank 1Jan 29 2009For an elliptic curve over Q of analytic rank 1, we use the level-two Selmer variety and secondary cohomology products to find explicit analytic defining equations for global integral points inside the set of p-adic points.

ABC inequalities for some moduli spaces of log-general typeSep 26 1998We prove a new bound for the Arakelov-Faltings height of an abelian variety over a function field of characteristic zero and relate it to inequalities of ABC-type as conjectured by Buium and Vojta.

Status of the KIMS-NaI experimentOct 30 2015KIMS-NaI is a direct detection experiment searching for Weakly Interacting Massive Particles (WIMP) via their scattering off of nuclei in a NaI(Tl) crystal. The KIMS-NaI collaboration has carried out tests of six crystals in the Yangyang underground laboratory ... More

Intersecting Noncommutative D-branes and Baryons in Magnetic FieldsFeb 10 2000Feb 16 2000We study supersymmetric intersecting configurations of D-branes with B-field backgrounds. Noncommutative D-brane or M-brane pairs can intersect supersymmetrically over (p-1)-brane, as well as over (p-2)-brane like ordinary branes. d=10 and d=11 supergravity ... More

Time-periodic solutions of massive scalar fields in AdS background: perturbative constructionsNov 06 2014Nov 25 2014We consider scalar fields which are coupled to Einstein gravity with a negative cosmological constant, and construct periodic solutions perturbatively. In particular, we study tachyonic scalar fields whose mass is at or above the Breitenlohner-Freedman ... More

Relating decision and search algorithms for rational points on curves of higher genusJan 20 2002For affine plane curves defined over the rationals of genus at least two, we show that a decision algorithm for the existence of solutions also yields a search algorithm for all solutions.

An analytic study of the ionization from an ultrathin quantum well in a weak electrostatic fieldJun 12 2007We consider the time evolution of a particle bound by an attractive one-dimensional delta-function potential (at x = 0) when a uniform electrostatic field (F) is applied. We explore explicit expressions for the time-dependent wavefunction \psi_F(x,t) ... More

Heat transport through a quantum Brownian harmonic chain beyond the weak-coupling regime: An exact treatmentApr 04 2013Apr 02 2014We consider a linear chain of quantum harmonic oscillators, in which the number of the individual oscillators is given by an arbitrary number N, and each oscillator is coupled at an arbitrary strength kappa to its nearest neighbors ("intra-coupling"), ... More

The Nature of the Dark MatterOct 18 1995We review some recent determinations of the amount of dark matter on galactic and larger scales, with special attention to the dark matter in the Milky Way. We then briefly review the motivation for and basic physics of several dark matter candidates, ... More

The relative Breuil-Kisin classification of $p$-divisible groups and finite flat group schemesDec 30 2011Oct 29 2013Assume that $p>2$, and let $\mathscr{O}_K$ be a $p$-adic discrete valuation ring with residue field admitting a finite $p$-basis, and let $R$ be a formally smooth formally finite-type $\mathscr{O}_K$-algebra. (Indeed, we allow slightly more general rings ... More

Leptogenesis and Bi-Unitary Parametrization of Neutrino Yukawa MatrixMar 10 2003Apr 03 2003We analyze the neutrino Yukawa matrix by considering three constraints: the out-of-equilibrium condition of lepton number violating process responsible for leptogenesis, the upper bound of branching ratio of lepton flavor violating decay, and the prediction ... More

The unipotent Albanese map and Selmer varieties for curvesOct 20 2005Sep 28 2006We discuss $p$-adic unipotent Albanese maps for curves of positive genus, extending the theory of $p$-adic multiple polylogarithms. This construction is then used to relate linear Diophantine conjectures of `Birch and Swinnerton-Dyer type' to non-linear ... More

ALICE results on system-size dependence of charged-particle multiplicity density in p-Pb, Pb-Pb and Xe-Xe collisionsJul 24 2018Sep 18 2018Particle production at LHC energies involves the interplay of hard (perturbative) and soft (non-perturbative) QCD processes. Global observables, such as the charged-particle multiplicity, are related to the initial geometry and the energy density produced ... More

Limit sets for convex cocompact groups in higher rank symmetric spacesApr 30 2018We show that every limit point of a Zariski dense discrete subgroup $\Gamma$ of the isometry group of a symmetric space of noncompact type is conical if and only if $\Gamma$ is convex cocompact.

Identities involving Frobenius-Euler polynomials arising from non-linear differential equationsJan 24 2012In this paper we consider non-linear differential equations which are closely related to the generating functions of Frobenius-Euler polynomials. From our non-linear differential equations, we derive some new identities between the sums of products of ... More

Transverse single spin asymmetry for very forward $π^{0}$ production in polarized proton-proton collisions at $\sqrt{s}$ = 510 GeVFeb 21 2019Transverse single spin asymmetry, $A_{N}$, of very forward $\pi^{0}$ production from polarized $p + p$ collisions provides new information toward an understanding of its production mechanism. $A_{N}$ of forward $\pi^{0}$ in the pseudorapidity region of ... More

A note on p-adic q-integrals associated with q-Euler numbersJun 29 2007In this we give a detailed proof of fermionic p-adic q-measures on Z_p and we will treat some interesting formulae related q-extension of Euler numbers and polynomials.

A note on the q-Genocchi numbers and polynomialsMar 16 2007In ths paper we discuss the new concept of the q-extension of Genocchi numbers and give the some relations between q-Genocchi polynomials and q-Euler numbers.

Filtration of the classical knot concordance group and Casson-Gordon invariantsJul 24 2002It is known that if any prime power branched cyclic cover of a knot in the 3-sphere is a homology sphere, then the knot has vanishing Casson-Gordon invariants. We construct infinitely many examples of (topologically) non-slice knots in the 3-sphere whose ... More

Note on on Dedekind type DC sumsDec 13 2008In this paper we consider Dedekind type DC sums and prove receprocity laws related to DC sums.

Fundamental groups and Diophantine geometryApr 07 2008We give a brief exposition on the uses of non-commutative fundamental groups for the study of Diophantine problems via a non-abelian Albanese map.

q-Bernstein polynomials, q-Stirling numbers and q-Bernoulli polynomialsAug 26 2010In this paper, we give new identities involving Phillips q-Bernstein polynomials and we derive some interesting properties of q-Berstein polynomials associated with q-Stirling numbers and q-Bernoulli polynomials.

On the (h,q)-zeta functions associated with (h,q)-Bernoulli numbers and polynomialsAug 11 2010In this paper we study (h,q)-zeta functions associated with (h,q)-Bernoulli numbers and polynomials.

On the q-extension of higher-order Euler polynomialsDec 24 2009Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.

Note on q-Dedekind type sums related to q-Euler polynomialsJul 29 2009it is the purpose of this paper to construct a p-adic continuous function for an odd prime to contain a p-adic q-analogue of higher order Dedekind type sums related to q-Euler polynomials and numbers.

New approach to q-Genocch, Euler numbers and polynomials and their interpolation functionsJan 04 2009We give a new construction of q-Genocchi numbers, Euler numbers of higher order, which are different than the q-Genocchi numbers of Cangul-Ozden-Simsek. By using our q-Genoucchi, Euler nimbers of higher order, we can investigate the interesting relationship ... More

Euler Numbers and polynomials associated with zeta functionsJan 02 2008In this paper we give some interesting identities between Euler numbers and zeta functions. Finally we will give the new values of Euler zeta function at positive even integers.

Degenerate Cauchy numbers and polynomials of the second kindAug 24 2017Recently, degenerate Cauchy numbers and polynomials are introduced in [10]. In this paper, we study the degenerate Cauchy numbers and polynomials which are different from the previous degenerate Cauchy numbers and polynomials. In addition, we give some ... More

A note on degenerate stirling polynomials of the second kindApr 07 2017In this paper, we consider the degenerate Stirling polynomials of the second kind which are derived from the generating function. In addition, we give some new identities for these polynomials.

On degenerate Carlitz q-Bernoulli polynomialsJul 17 2015In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.

A note on q-Bernoulli numbers and polynomialsFeb 16 2005By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.

On the explicit formula of Euler numbers and polynomials of higher orderFeb 16 2005We study the explicit formula of Euler numbers and polynomials of higher order

Tangency and a ruled surface associated with a Hitchin systemAug 26 2011Oct 11 2011We will generalize the Treibich-Verdier theory about elliptic solitons to a Hitchin system by constructing a particular ruled surface and we will propose a generalization of a tangency condition associated with elliptic solitons to a Hitchin system. In ... More

Shellable complexes and topology of diagonal arrangementsOct 30 2006Apr 12 2008We prove that if a simplicial complex is shellable, then the intersection lattice for the corresponding diagonal arrangement is homotopy equivalent to a wedge of spheres. Furthermore, we describe precisely the spheres in the wedge, based on the data of ... More

Complex spectral analysis and test function spacesOct 25 2012Mar 12 2014We consider complex eigenstates of unstable Hamiltonian and its physically meaningful regions. Starting from a simple model of a discrete state interacting with a continuum via a general potential, we show that its Lippmann-Schwinger solution set can ... More

A proof of the Riemann hypothesis using the remainder term of the Dirichlet eta functionJul 30 2015May 24 2016The Dirichlet eta function can be divided into $n$-th partial sum $\eta_{n}(s)$ and remainder term $R_{n}(s)$. We focus on the remainder term which can be approximated by the expression for $n$. And then, to increase reliability, we make sure that the ... More

Uniqueness of real Lagrangians up to cobordismFeb 04 2019Feb 13 2019We prove that a real Lagrangian submanifold in a closed symplectic manifold is unique up to cobordism. We then discuss the classification of real Lagrangians in $\mathbb{C} P^2$ and $S^2\times S^2$. In particular, we show that a real Lagrangian in $\mathbb{C} ... More

Nonexistence of perfect $2$-error-correcting Lee codes in certain dimensionsJan 29 2017May 31 2017The Golomb--Welch conjecture states that there are no perfect $e$-error-correcting codes in $\mathbb{Z}^n$ for $n \ge 3$ and $e \ge 2$. In this note, we prove the nonexistence of perfect $2$-error-correcting codes for a certain class of $n$, which is ... More

Existence of a Radner equilibrium in a model with transaction costsFeb 06 2017Feb 23 2018We prove the existence of a Radner equilibrium in a model with proportional transaction costs on an infinite time horizon and analyze the effect of transaction costs on the endogenously determined interest rate. Two agents receive exogenous, unspanned ... More

Parabolic equations with measurable coefficients in $L_p$-spaces with mixed normsMay 25 2007The unique solvability of parabolic equations in Sobolev spaces with mixed norms is presented. The second order coefficients (except $a^{11}$) are assumed to be only measurable in time and one spatial variable, and VMO in the other spatial variables. ... More

Stability of Utility Maximization in Nonequivalent MarketsOct 03 2014Jun 24 2015Stability of the utility maximization problem with random endowment and indifference prices is studied for a sequence of financial markets in an incomplete Brownian setting. Our novelty lies in the nonequivalence of markets, in which the volatility of ... More

On central leaves of Hodge-type Shimura varieties with parahoric level structureMar 13 2017May 10 2018Kisin and Pappas constructed integral models of Hodge-type Shimura varieties with parahoric level structure at $p>2$, such that the formal neighbourhood of a mod~$p$ point can be interpreted as a deformation space of $p$-divisible group with some Tate ... More

On the large-scale structure of the tall peaks for stochastic heat equations with fractional LaplacianOct 10 2015We consider stochastic heat equations with fractional Laplacian on $\mathbb{R}^d$. Here, the driving noise is generalized Gaussian which is white in time but spatially homogenous and the spatial covariance is given by the Riesz kernels. We study the large-scale ... More

Rigidity of noncompact complete Bach-flat manifoldsJan 15 2010Let $(M,g)$ be a noncompact complete Bach-flat manifold with positive Yamabe constant. We prove that $(M,g)$ is flat if $(M, g)$ has zero scalar curvature and sufficiently small $L_{2}$ bound of curvature tensor. When $(M, g)$ has nonconstant scalar curvature, ... More

Existence of a Unique Local Solution to the Many-body Maxwell-Schrödinger Initial Value ProblemFeb 15 2014We study the many-body problem of charged particles interacting with their self-generated electromagnetic field. We model the dynamics of the particles by the many-body Maxwell-Schr\"odinger system, where the particles are treated quantum mechanically ... More

Amenable signatures, algebraic solutions, and filtrations of the knot concordance groupJun 22 2016Aug 24 2017It is known that each of the successive quotient groups of the grope and solvable filtrations of the knot concordance group has an infinite rank subgroup. The generating knots of these subgroups are constructed using iterated doubling operators. In this ... More

A classification of transitive links and periodic linksApr 07 2015We generalized the periodic links to \emph{transitive} links in a $3$-manifold $M$. We find a complete classification theorem of transitive links in a $3$-dimensional sphere $\mathbb{R}^3$. We study these links from several different aspects including ... More