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On the structure of braid groups on complexesAug 15 2015We consider the braid groups $\mathbf{B}_n(X)$ on finite simplicial complexes $X$, which are generalizations of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between geometric decompositions ... More

Uplink Time Scheduling with Power Level Modulation in Wireless Powered Communication NetworksOct 05 2018In this paper, we propose downlink signal design and optimal uplink scheduling for the wireless powered communication networks (WPCNs). Prior works give attention to resource allocation in a static channel because users are equipped with only energy receiver ... More

A Generalization Method of Partitioned Activation Function for Complex NumberFeb 08 2018A method to convert real number partitioned activation function into complex number one is provided. The method has 4em variations; 1 has potential to get holomorphic activation, 2 has potential to conserve complex angle, and the last 1 guarantees interaction ... More

Interference Alignment Schemes Using Latin Square for Kx3 MIMO X ChannelOct 12 2018In this paper, we study an interference alignment (IA) scheme with finite time extension and beamformer selection method with low computational complexity for X channel. An IA scheme with a chain structure by the Latin square is proposed for Kx3 multiple-input ... More

Design of Irregular SC-LDPC Codes With Non-Uniform Degree Distributions by Linear ProgramingFeb 21 2018Mar 27 2018In this paper, we propose a new design method of irregular spatially-coupled low-density parity-check (SC-LDPC) codes with non-uniform degree distributions by linear programming (LP). In general, irregular SC-LDPC codes with non-uniform degree distributions ... More

Distance-based Control of K4 Formation with Almost Global ConvergenceJun 06 2016In this paper, we propose a distance-based formation control strategy that can enable four mobile agents, which are modelled by a group of single-integrators, to achieve the desired formation shape specified by using six consistent inter-agent distances ... More

Far-Ultraviolet Observations of the Spica Nebula and the Interaction ZoneJul 10 2013Jul 19 2013We report the analysis results of far ultraviolet (FUV) observations, made for a broad region around $\alpha$ Vir (Spica) including the interaction zone of Loop I and the Local Bubble. The whole region was optically thin and a general correlation was ... More

The Cost of Bounded CurvatureJun 30 2011Nov 02 2012We study the motion-planning problem for a car-like robot whose turning radius is bounded from below by one and which is allowed to move in the forward direction only (Dubins car). For two robot configurations $\sigma, \sigma'$, let $\ell(\sigma, \sigma')$ ... More

SPEAR Far Ultraviolet Spectral Images of the Cygnus LoopJan 26 2006We present far-ultraviolet (FUV) spectral images, measured at C IV 1550, He II 1640, Si IV+O IV] 1400, and O III] 1664, of the entire Cygnus Loop, observed with the Spectroscopy of Plasma Evolution from Astrophysical Radiation (SPEAR) instrument, also ... More

SRM : A Style-based Recalibration Module for Convolutional Neural NetworksMar 26 2019Following the advance of style transfer with Convolutional Neural Networks (CNNs), the role of styles in CNNs has drawn growing attention from a broader perspective. In this paper, we aim to fully leverage the potential of styles to improve the performance ... More

Keep and Learn: Continual Learning by Constraining the Latent Space for Knowledge Preservation in Neural NetworksMay 28 2018Data is one of the most important factors in machine learning. However, even if we have high-quality data, there is a situation in which access to the data is restricted. For example, access to the medical data from outside is strictly limited due to ... More

Fast Non-Monotone Submodular Maximisation Subject to a Matroid ConstraintMar 17 2017Mar 21 2017In this work we present the first practical $\left(\frac{1}{e}-\epsilon\right)$-approximation algorithm to maximise a general non-negative submodular function subject to a matroid constraint. Our algorithm is based on combining the decreasing-threshold ... More

Anonymous Hedonic Game for Task Allocation in a Large-Scale Multiple Agent SystemNov 18 2017Jul 25 2018This paper proposes a novel game-theoretical autonomous decision-making framework to address a task allocation problem for a swarm of multiple agents. We consider cooperation of self-interested agents, and show that our proposed decentralized algorithm ... More

Bio-Inspired Local Information-Based Control for Probabilistic Swarm Distribution GuidanceNov 18 2017This paper addresses a task allocation problem for a large-scale robotic swarm, namely swarm distribution guidance problem. Unlike most of the existing frameworks handling this problem, the proposed framework suggests utilising local information available ... More

Sample Greedy Gossip Distributed Kalman FilterMar 27 2019This paper investigates the problem of distributed state estimation over a sensor network and proposes a new sample greedy gossip distributed Kalman filter. The proposed algorithm leverages the information weighted fusion concept and a new sample greedy ... More

Fast submodular maximization subject to k-extendible system constraintsNov 19 2018As the scales of data sets expand rapidly in some application scenarios, increasing efforts have been made to develop fast submodular maximization algorithms. This paper presents a currently the most efficient algorithm for maximizing general non-negative ... More

KMTNet Nearby Galaxy Survey I. : Optimal strategy for low surface brightness imaging with KMTNetOct 04 2018In hierarchical galaxy formation models, galaxies evolve through mergers and accretions. Tidally-disrupted debris from these processes can remain as diffuse, faint structures, which can provide useful insight into the assembly history of galaxies. To ... More

Power Generation and Distribution via Distributed Coordination ControlJul 18 2014This paper presents power coordination, power generation, and power flow control schemes for supply-demand balance in distributed grid networks. Consensus schemes using only local information are employed to generate power coordination, power generation ... More

Characteristics of graph braid groupsJan 13 2011We give formulae for the first homology of the $n$-braid group and the pure 2-braid group over a finite graph in terms of graph theoretic invariants. As immediate consequences, a graph is planar if and only if the first homology of the $n$-braid group ... More

Numbers of points of surfaces in the projective $3$-space over finite fieldsSep 20 2014In the previous paper, we established an elementary bound for numbers of points of surfaces in the projective $3$-space over ${\Bbb F}_q$. In this paper, we give the complete list of surfaces that attain the elementary bound. Precisely those surfaces ... More

Sample Greedy Based Task Allocation for Multiple Robot SystemsJan 10 2019This paper addresses the task allocation problem for multi-robot systems. The main issue with the task allocation problem is inherent complexity that makes finding an optimal solution within a reasonable time almost impossible. To hand the issue, this ... More

The second largest number of points of plane curves over finite fieldsSep 08 2015A basis of the ideal of the complement of a linear subspace in a projective space over a finite field is given. As an application, the second largest number of points of plane curves of degree $d$ over the finite field of $q$ elements is also given for ... More

Projective deformations of weakly orderable hyperbolic Coxeter orbifoldsJul 15 2012Nov 01 2014A Coxeter $n$-orbifold is an $n$-dimensional orbifold based on a polytope with silvered boundary facets. Each pair of adjacent facets meet on a ridge of some order $m$, whose neighborhood is locally modeled on ${\mathbb R}^n$ modulo the dihedral group ... More

Anti-de Sitter strictly GHC-regular groups which are not latticesAug 07 2017Feb 28 2018For $d=4, 5, 6, 7, 8$, we exhibit examples of $\mathrm{AdS}^{d,1}$ strictly GHC-regular groups which are not quasi-isometric to the hyperbolic space $\mathbb{H}^d$, nor to any symmetric space. This provides a negative answer to Question 5.2 in [9A12] ... More

On the Number of Edges of Fan-Crossing Free GraphsNov 08 2013A graph drawn in the plane with n vertices is k-fan-crossing free for k > 1 if there are no k+1 edges $g,e_1,...e_k$, such that $e_1,e_2,...e_k$ have a common endpoint and $g$ crosses all $e_i$. We prove a tight bound of 4n-8 on the maximum number of ... More

Joint Source, Channel and Space-time Coding of Progressive Sources in MIMO SystemsOct 14 2016Sep 14 2017The optimization of joint source and channel coding for a sequence of numerous progressive packets is a challenging problem. Further, the problem becomes more complicated if the space-time coding is also involved with the optimization in a multiple-input ... More

Spin 3/2 Baryons and Form Factors in AdS/QCDApr 23 2009We study the 5D Rarita-Schwinger fields to describe spin 3/2 baryons in AdS/QCD. We calculate the spectrum of spin 3/2 baryons (Delta resonances) and their form factors, together with meson-baryon couplings from AdS/QCD. The transition form-factors between ... More

Graph braid groups and right-angled Artin groupsMay 01 2008Jun 13 2010We give a necessary and sufficient condition for a graph to have a right-angled Artin group as its braid group for braid index $\ge 5$. In order to have the necessity part, graphs are organized into small classes so that one of homological or cohomological ... More

Ultraviolet Radiative Transfer Modeling of Nearby Galaxies with Extraplanar DustsNov 12 2015In order to examine their relation to the host galaxy, the extraplanar dust of six nearby galaxies are modeled, employing a three dimensional Monte Carlo radiative transfer code. The targets are from the highly-inclined galaxies that show dust-scattered ... More

Hitchin components for orbifoldsNov 13 2018Nov 14 2018We extend the notion of Hitchin component from surface groups to orbifold groups and prove that this gives new examples of Higher Teichm\"{u}ller spaces. We show that the Hitchin component of an orbifold group is homeomorphic to an open ball, and we compute ... More

Convex projective generalized Dehn fillingNov 08 2016Mar 30 2018For $d=4, 5, 6$, we exhibit the first examples of complete finite volume hyperbolic $d$-manifolds $M$ with cusps such that infinitely many $d$-orbifolds $M_{m}$ obtained from $M$ by generalized Dehn filling admit properly convex real projective structures. ... More

Graph 4-braid groups and Massey productsJul 14 2014We first show that the braid group over a graph topologically containing no $\Theta$-shape subgraph has a presentation related only by commutators. Then using discrete Morse theory and triple Massey products, we prove that a graph topologically contains ... More

Jets from HollowsOct 15 2012This fluid dynamics video presents the gravity-driven jets induced by the relaxation of large prolate bubbles or large holes at a free liquid surface. It shows that the jet developing inside a bubble can be strong enough to give rise to liquid projections ... More

Quark mass effects in high energy neutrino nucleon scatteringJan 23 2010May 27 2010We evaluate the neutrino nucleon charged current cross section at next-to-leading order in quantum chromodynamic corrections in the variable flavor number scheme and the fixed flavor number scheme, taking into account quark masses. The number scheme dependence ... More

The Spectroscopy of Plasma Evolution from Astrophysical Radiation MissionJan 26 2006The Spectroscopy of Plasma Evolution from Astrophysical Radiation (or the Far-ultraviolet Imaging Spectrograph) instruments, flown aboard the STSAT-1 satellite mission, have provided the first large-area spectral mapping of the cosmic far ultraviolet ... More

Dynamic MDS Matrices for Substantial Cryptographic StrengthAug 31 2011Ciphers get their strength from the mathematical functions of confusion and diffusion, also known as substitution and permutation. These were the basics of classical cryptography and they are still the basic part of modern ciphers. In block ciphers diffusion ... More

Orchestrating Product Provenance Story: When IOTA ECOSYSTEM Meets The Electronics Supply Chain SpaceFeb 12 2019"Trustworthy data" is the fuel for ensuring the transparent traceability, precise decision-making, and cogent coordination in the supply chain (SC) space. However, the disparate data silos act as a trade barrier in orchestrating the provenance of product ... More

Text-Adaptive Generative Adversarial Networks: Manipulating Images with Natural LanguageOct 29 2018Nov 28 2018This paper addresses the problem of manipulating images using natural language description. Our task aims to semantically modify visual attributes of an object in an image according to the text describing the new visual appearance. Although existing methods ... More

Infinitesimal Weak Rigidity, Formation Control of Three Agents, and Extension to 3-dimensional SpaceMar 26 2018In this paper, we introduce new concepts of weak rigidity matrix and infinitesimal weak rigidity for planar frameworks. The weak rigidity matrix is used to directly check if a framework is infinitesimally weakly rigid while previous work can check a weak ... More

High-Dimensional Poisson DAG Model Learning Using $\ell_1$-Regularized RegressionOct 05 2018Dec 25 2018In this paper, we develop a new approach to learning high-dimensional Poisson directed acyclic graphical (DAG) models from only observational data without strong assumptions such as faithfulness and strong sparsity. A key component of our method is to ... More

Structural versus electronic distortions of symmetry-broken IrTe$_2$Oct 21 2014We investigate atomic and electronic structures of the intriguing low temperature phase of IrTe2 using high-resolution scanning tunneling microscopy and spectroscopy. We confirm various stripe superstructures such as $\times$3, $\times$5, and $\times$8. ... More

The BINP HLS to measurement vertical changes on PAL-XFEL building and groundJun 16 2016PAL-XFEL, a 4th generation light source, is currently being installed and will be completed by December of 2015 so that users can be supported beginning in 2016. PAL-XFEL equipment should continuously maintain the bunch-to-bunch beam parameter (60Hz, ... More

On shellability for a poset of even subgraphs of a graphMay 18 2017Feb 08 2018Given a simple graph $G$, a poset of its even subgraphs was firstly considered by S. Choi and H. Park to study the topology of a real toric manifold associated with $G$. S. Choi and the authors extended this to a graph allowing multiple edges, motivated ... More

Evolution of Kinetic and Magnetic Energy in Intra Cluster MediaApr 12 2015Jul 13 2015Intra Cluster Media (ICMs) located at galaxy clusters is in the state of hot, tenuous, magnetized, and highly ionized X-ray emitting plasmas. This overall collisionless, viscous, and conductive magnetohydrodynamic (MHD) turbulence in ICM is simulated ... More

Graph invariants and Betti numbers of real toric manifoldsDec 31 2017May 01 2018For a graph $G$, a graph cubeahedron $\square_G$ and a graph associahedron $\triangle_G$ are simple convex polytopes which admit (real) toric manifolds. In this paper, we introduce a graph invariant, called the $b$-number, and we show that the $b$-numbers ... More

Generalized Cross-correlation Properties of Chu SequencesAug 05 2008In this paper, we analyze the cross-correlation properties for Chu sequences, which provide information on the distribution of the maximum magnitudes of the cross-correlation function. Furthermore, we can obtain the number of available sequences for a ... More

Identifying ECUs Using Inimitable Characteristics of Signals in Controller Area NetworksJul 02 2016In the last several decades, the automotive industry has come to incorporate the latest Information and Communications (ICT) technology, increasingly replacing mechanical components of vehicles with electronic components. These electronic control units ... More

Linear Detrending Subsequence Matching in Time-Series DatabasesJun 28 2010Each time-series has its own linear trend, the directionality of a timeseries, and removing the linear trend is crucial to get the more intuitive matching results. Supporting the linear detrending in subsequence matching is a challenging problem due to ... More

Pappus Theorem, Schwartz Representations and Anosov RepresentationsOct 13 2016Feb 02 2018In the paper "Pappus's theorem and the modular group", R. Schwartz constructed a 2-dimensional family of faithful representations $\rho_\Theta$ of the modular group $\mathrm{PSL}(2,\mathbb{Z})$ into the group $\mathscr{G}$ of projective symmetries of ... More

Construction of High-Rate Regular Quasi-Cyclic LDPC Codes Based on Cyclic Difference FamiliesNov 16 2012For a high-rate case, it is difficult to randomly construct good low-density parity-check (LDPC) codes of short and moderate lengths because their Tanner graphs are prone to making short cycles. Also, the existing high-rate quasi-cyclic (QC) LDPC codes ... More

Leakage Mitigation and Internal Delay Compensation in FMCW Radar for Small Drone DetectionJul 17 2018One of the notorious problems of frequency modulated continuous-wave (FMCW) radar is leakage between the transmitter and the receiver. The phase noise of the leakage is expressed as a skirt around the leakage signal on power spectrum. It causes the deterioration ... More

Sparsity-Preserving Difference of Positive Semidefinite Matrix Representation of Indefinite MatricesSep 21 2016We consider the problem of writing an arbitrary symmetric matrix as the difference of two positive semidefinite matrices. We start with simple ideas such as eigenvalue decomposition. Then, we develop a simple adaptation of the Cholesky that returns a ... More

Fatou's theorem for subordinate Brownian motions with Gaussian components on $C^{1,1}$ open setsDec 24 2015Sep 15 2016We prove Fatou's theorem for nonnegative harmonic functions with respect to subordinate Brownian motions with Gaussian components on bounded $C^{1,1}$ open sets $D$. We prove that nonnegative harmonic functions with respect to such processes on $D$ converge ... More

D^0-$\bar D^0$ Mixing and CP Violation from FOCUS ExperimentNov 16 2000Nov 27 2000Measurement results on $D^0$-$\bar D^0$ mixing and CP violation are presented. FOCUS, a fixed target experiment at Fermilab, collected a high statistics photo-produced charm sample collected during the 96-97 run. We reconstructed more than 1 million charmed ... More

Sensitivity Analysis of Long-Term Cash FlowsNov 12 2015In this article, a sensitivity analysis of long-term cash flows with respect to perturbations in the underlying process is presented. For this purpose, we employ the martingale extraction through which a pricing operator is transformed into what is easier ... More

Ross Recovery with Recurrent and Transient ProcessesOct 08 2014Oct 17 2015Recently, Ross showed that it is possible to recover an objective measure from a risk-neutral measure. His model assumes that there is a finite-state Markov process X that drives the economy in discrete time. Many authors extended his model to a continuous-time ... More

Dynamics of Entanglement in Three Coupled Harmonic Oscillator System with Arbitrary Time-Dependent Frequency and Coupling ConstantsNov 15 2018The dynamics of mixedness and entanglement is examined by solving the time-dependent Schr\"{o}dinger equation for three coupled harmonic oscillator system with arbitrary time-dependent frequency and coupling constants parameters. We assume that part of ... More

Entanglement Degradation in the presence of $(4+n)$-dimensional Schwarzschild Black HoleAug 31 2012Mar 05 2013In this short paper we compute the various bipartite quantum correlations in the presence of the $(4+n)$-dimensional Schwarzschild black hole. In particular, we focus on the $n$-dependence of various bosonic bipartite entanglements. For the case between ... More

Four-Qubit Monogamy and Four-Way EntanglementJan 24 2018We examine the various properties of the three four-qubit monogamy relations, all of which introduce the power factors in the three-way entanglement to reduce the tripartite contributions. On the analytic ground as much as possible we try to find the ... More

Tripartite Entanglement Dynamics in the presence of Non-Markovian EnvironmentJan 03 2016May 13 2016We study on the tripartite entanglement dynamics when each party is initially entangled with other parties, but they locally interact with their own non-Markovian environment. First, we consider three GHZ-type initial states, all of which have GHZ symmetry ... More

Frame Potentials and Orthogonal VectorsFeb 25 2019An extension is given of a recent result of Glazyrin, showing that an orthonormal basis $\{e_{i}\}_{i=1}^{d}$ joined with the vectors $\{e_{j}\}_{j=1}^{m}$, where $1\leq m < d$ minimizes the $p$-frame potential for $p\in[1,2\log{\frac{2m+1}{2m}}/\log{\frac{m+1}{m}}]$ ... More

On hypersurfaces containing projective varietiesApr 29 2011Classical Castelnuovo's Lemma shows that the number of linearly independent quadratic equations of a nondegenerate irreducible projective variety of codimension $c$ is at most ${{c+1} \choose {2}}$ and the equality is attained if and only if the variety ... More

Regulators on additive higher Chow groupsMay 27 2006May 28 2008As an attempt to understand motives over $k[x]/(x^m)$, we define the cubical additive higher Chow groups with modulus for all dimensions extending the works of S. Bloch, H. Esnault and K. R\"ulling on 0-dimensional cycles. We give an explicit construction ... More

Geometric models of twisted differential K-theory IFeb 06 2016Aug 03 2017This is the first in a series of papers constructing geometric models of twisted differential K-theory. In this paper we construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion class. By differential ... More

Complete Linear Series on a Hyperelliptic CurveAug 01 2008In this paper we study complete linear series on a hyperelliptic curve $C$ of arithmetic genus $g$. Let $A$ be the unique line bundle on $C$ such that $|A|$ is a $g^1_2$, and let $\mathcal{L}$ be a line bundle on $C$ of degree $d$. Then $\mathcal{L}$ ... More

Holographic renormalization group flow from UV to IRDec 26 2018We construct a three-dimensional geometry interpolating two different AdS spaces. From the dual quantum field theory viewpoint, it corresponds to a nontrivial renormalization group flow from a UV to another IR conformal field theory. On this geometry, ... More

Holographic renormalization in dense mediumMay 07 2014Aug 21 2014We investigate the holographic renormalization of a charged black brane with or without a dilaton field, whose dual field theory describes a dense medium at finite temperature. In a dense medium, two different thermodynamic descriptions are possible due ... More

On black hole thermodynamics with a momentum relaxationJun 23 2016We investigate black hole thermodynamics involving a scalar hair which is dual to a momentum relaxation of the dual field theory. This black hole geometry is able to be classified by two parameters. One is a momentum relaxation and the other is a mass ... More

Almost universality of a sum of normsFeb 11 2013Nov 26 2015In this paper the author considers a particular type of polynomials with integer coefficients, consisting of a perfect power and two norm forms of abelian number fields with coprime discriminants. It is shown that such a polynomial represents every natural ... More

Inequality on $t_ν(K)$ defined by Livingston and Naik and its applicationsMar 15 2016Let $D_+(K,t)$ denote the positive $t$-twisted double of $K$. For a fixed integer-valued additive concordance invariant $\nu$ that bounds the smooth four genus of a knot and determines the smooth four genus of positive torus knots, Livingston and Naik ... More

Quasi-multiplicativity of typical cocyclesMar 10 2019Mar 27 2019We show that typical (in the sense of Bonatti-Viana) H\"{o}lder and fiber-bunched $GL_d(\mathbb{R})$-valued cocycles over a subshift of finite type are uniformly quasi-multiplicative with respect to all singular value potentials. We prove the continuity ... More

On the Inverse Transfer of (Non-)Helical Magnetic Energy in a Decaying Magnetohydrodynamic TurbulenceSep 18 2017In our conventional understanding, large-scale magnetic fields are thought to originate from an inverse cascade in the presence of magnetic helicity, differential rotation, or a magneto-rotational instability. However, as recent simulations have given ... More

Principle of Helical \& Nonhelical Dynamo and $α$ effect in Field Structure modelAug 02 2018Aug 17 2018We explain the (non)helical dynamo process using a field-structure model based on magnetic induction equation in an intuitive way. We show how nonhelical kinetic energy converts into magnetic energy and cascades toward smaller eddies in a mechanically ... More

Reidemeister torsion, Complex volume, and Zograf infinite product for hyperbolic 3-manifolds with cuspsDec 22 2017In this paper, we prove an equality which involves Reidemeister torsion, complex volume, and Zograf infinite product for hyperbolic 3-manifolds with cusps.

Clipping Noise Cancellation for OFDM and OFDMA Systems Using Compressed SensingOct 19 2011Dec 08 2011In this paper, we propose clipping noise cancellation scheme using compressed sensing (CS) for orthogonal frequency division multiplexing (OFDM) systems. In the proposed scheme, only the data tones with high reliability are exploited in reconstructing ... More

Anomalous polarization dependence of Raman scattering and crystallographic orientation of black phosphorusOct 12 2015Nov 09 2015We investigated polarization dependence of the Raman modes in black phosphorus (BP) using five different excitation wavelengths. The crystallographic orientation was determined by comparing polarized optical microscopy with high-resolution transmission ... More

Simulation of Cosmic Microwave Background Polarization Fields for AMiBA ExperimentMar 20 2002Jul 04 2002We have made a topological study of cosmic microwave background (CMB) polarization maps by simulating the AMiBA experiment results. A $\Lambda$CDM CMB sky is adopted to make mock interferometric observations designed for the AMiBA experiment. CMB polarization ... More

Distributed stabilization control of rigid formations with prescribed orientationJun 10 2016Most rigid formation controllers reported in the literature aim to only stabilize a rigid formation shape, while the formation orientation is not controlled. This paper studies the problem of controlling rigid formations with prescribed orientations in ... More

A construction of slice knots via annulus modificationsDec 01 2015We define an operation on homology ${B}^4$ which we call an $n$-twist annulus modification. We give a new construction of smoothly slice knots and exotically slice knots via $n$-twist annulus modifications. As an application, we present a new example ... More

A Quantile Implementation of the EM Algorithm and Its Applications to Parameter Estimation with Interval DataMar 20 2012The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the expectation in each ... More

The weighted composition operators on the large weighted Bergman spacesAug 20 2017May 10 2018In this paper, we characterize bounded, compact or Schatten class weighted composition operators acting on Bergman spaces with the exponential type weights. Moreover, we give the proof of the necessary part for the boundedness of composition operators ... More

Amicable pairs and aliquot cycles on averageMar 23 2014Silverman and Stange defined the notion of an aliquot cycle of length $L$ for a fixed elliptic curve $E/\mathbb{Q}$, and conjectured an order of magnitude for the function that counts such aliquot cycles. We show that the conjectured upper bound holds ... More

Greenberger-Horne-Zeilinger Symmetry in Four Qubit SystemNov 30 2016Like a three-qubit Greenberger-Horne-Zeilinger(GHZ) symmetry we explore a corresponding symmetry in the four-qubit system, which we call GHZ$_4$ symmetry. While whole GHZ-symmetric states can be represented by two real parameters, the whole set of the ... More

Space-state complexity of Korean chess and Chinese chessJul 23 2015This article describes how to calculate exact space-state complexities of Korean chess and Chinese chess. The state-space complexity (a.k.a. search-space complexity) of a game is defined as the number of legal game positions reachable from the initial ... More

A smooth variant of Hopkins-Singer differential K-theoryJul 29 2016Oct 15 2017We introduce a smooth variant of the Hopkins-Singer model of differential K-theory. We prove that our model is naturally isomorphic to the Hopkins-Singer model and also to the Tradler-Wilson-Zeinalian model of differential K-theory.

Quantum Circuits for Scale TransformationsMar 18 2019In this note we develop quantum circuits for exactly simulating the thermal properties of the quantum XY/Ising chain. These circuits are applicable to the simplest integrable lattice models for which the exact momentum-space scattering-matrix can be constructed ... More

Intermediate Jacobians and the slice filtrationAug 03 2017Let $X$ be an $n$-dimensional connected scheme smooth and projective over ${\bf C}$. We decompose the motive $\underline{\rm Hom}({\bf L}^{n-2},M(X))$ using intermediate Jacobians. We also construct a morphism $M_{2n-2}(X)\rightarrow M(X)$ induced by ... More

A Generalization of Multiple Choice Balls-into-Bins: Tight BoundsJan 16 2012Jul 11 2016This paper investigates a general version of the multiple choice model called the $(k,d)$-choice process in which $n$ balls are assigned to $n$ bins. In the process, $k<d$ balls are placed into $k$ least loaded out of $d$ bins chosen independently and ... More

Exotic smooth structures on 3{CP}^2#8{-CP}^2Jul 05 2005Aug 29 2005Motivated by Stipsicz and Szab\'{o}'s exotic 4-manifolds with b_2^+=3 and b_2^-=8, we construct a family of simply connected smooth 4-manifolds with b_2^+=3 and b_2^-=8. As a corollary, we conclude that the topological 4-manifold 3{CP}^2#8{-CP}^2 admits ... More

Note on the closed-form MLEs of k-component load-sharing systemsMar 16 2012Recently Kim and Kvam (2004) and Singh, Sharma, Kumar (2008) proposed different load-sharing models and developed parametric inference for the these models. However, their parametric estimates are calculated using iterative numerical methods. In this ... More

Regular filtered (phi,N)-modules of dimension 3Nov 14 2012Dec 01 2012We classify 3-dimensional semi-stable representations of the Galois group of Q_p with coefficients and regular Hodge--Tate weights, by determining the isomorphism classes of admissible filtered (phi,N)-modules of Hodge type (0,r,s) with 0 < r < s.

Design of Multiple-Edge Protographs for QC LDPC Codes Avoiding Short Inevitable CyclesOct 15 2012There have been lots of efforts on the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with large girth. However, most of them are focused on protographs with single edges and little research has been done for the construction ... More

Relative Entropy of Entanglement for Two-Qubit State with $z$-directional Bloch VectorsMay 26 2010So far there is no closed formula for relative entropy of entanglement of arbitrary two-qubit states. In this paper we present a method, which guarantees the derivation of the relative entropy of entanglement for most states that have $z$-directional ... More

Entanglement Classification of Restricted Greenberger-Horne-Zeilinger Symmetric States in Four-Qubit SystemMay 09 2013May 21 2014Similar to the three-qubit Greenberger-Horne-Zeilinger (GHZ) symmetry we explore the four-qubit GHZ symmetry group and its subgroup called restricted GHZ symmetry group. While the set of symmetric states under the whole group transformation is represented ... More

Quantum Aspects of Massive GravitySep 22 2010We consider the effect of quantum interactions on Pauli-Fierz massive gravity. With generic graviton cubic interactions, we observe that the 1-loop counterterms do not conform to the tree level structure of Pauli-Fierz action, resulting in the reappearance ... More

Simply connected symplectic 4-manifolds with $b_2^+ =1$ and $c_1^2 =2$Nov 22 2003Mar 26 2004In this article we construct a new family of simply connected symplectic 4-manifolds with $b_2^+ =1$ and $c_1^2 =2$ which are not diffeomorphic to rational surfaces by using rational blow-down technique. As a corollary, we conclude that a rational surface ... More

Logarithmic Corrections to the Entanglement EntropyMay 15 2015Dec 31 2015In a $d$-dimensional conformal field theory, it has been known that a relevant deformation operator with the conformal dimension, $\Delta=\frac{d+2}{2}$, generates a logarithmic correction to the entanglement entropy. In the large 't Hooft coupling limit, ... More

Holographic aspects of a relativistic non-conformal theorySep 05 2012May 16 2013We study a general D-dimensional Schwarzschild-type black brane solution of the Einstein-dilaton theory and derive, by using the holographic renormalization, its thermodynamics consistent with the geometric results. Using the membrane paradigm, we calculate ... More

Meson's Correlation Functions in a Nuclear MediumMar 13 2016Jun 27 2016We investigate meson's spectrum, decay constant and form factor in a nuclear medium through holographic two- and three-point correlation functions. To describe a nuclear medium composed of protons and neutrons, we consider a hard wall model on the thermal ... More

A Quantile Variant of the EM Algorithm and Its Applications to Parameter Estimation with Interval DataMar 20 2012May 11 2018The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the expectation in each ... More