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Text-based LSTM networks for Automatic Music CompositionApr 18 2016In this paper, we introduce new methods and discuss results of text-based LSTM (Long Short-Term Memory) networks for automatic music composition. The proposed network is designed to learn relationships within text documents that represent chord progressions ... More

Similarity measures for vocal-based drum sample retrieval using deep convolutional auto-encodersFeb 14 2018The expressive nature of the voice provides a powerful medium for communicating sonic ideas, motivating recent research on methods for query by vocalisation. Meanwhile, deep learning methods have demonstrated state-of-the-art results for matching vocal ... More

Convolutional Recurrent Neural Networks for Music ClassificationSep 14 2016We introduce a convolutional recurrent neural network (CRNN) for music tagging. CRNNs take advantage of convolutional neural networks (CNNs) for local feature extraction and recurrent neural networks for temporal summarisation of the extracted features. ... More

Towards Music Captioning: Generating Music Playlist DescriptionsAug 17 2016Descriptions are often provided along with recommendations to help users' discovery. Recommending automatically generated music playlists (e.g. personalised playlists) introduces the problem of generating descriptions. In this paper, we propose a method ... More

Understanding Music PlaylistsNov 22 2015As music streaming services dominate the music industry, the playlist is becoming an increasingly crucial element of music consumption. Con- sequently, the music recommendation problem is often casted as a playlist generation prob- lem. Better understanding ... More

Explaining Deep Convolutional Neural Networks on Music ClassificationJul 08 2016Deep convolutional neural networks (CNNs) have been actively adopted in the field of music information retrieval, e.g. genre classification, mood detection, and chord recognition. However, the process of learning and prediction is little understood, particularly ... More

Towards Playlist Generation Algorithms Using RNNs Trained on Within-Track TransitionsJun 07 2016We introduce a novel playlist generation algorithm that focuses on the quality of transitions using a recurrent neural network (RNN). The proposed model assumes that optimal transitions between tracks can be modelled and predicted by internal transitions ... More

Automatic tagging using deep convolutional neural networksJun 01 2016We present a content-based automatic music tagging algorithm using fully convolutional neural networks (FCNs). We evaluate different architectures consisting of 2D convolutional layers and subsampling layers only. In the experiments, we measure the AUC-ROC ... More

Convolutional Recurrent Neural Networks for Music ClassificationSep 14 2016Nov 03 2016We introduce a convolutional recurrent neural network (CRNN) for music tagging. CRNNs take advantage of convolutional neural networks (CNNs) for local feature extraction and recurrent neural networks for temporal summarisation of the extracted features. ... More

Adiabatic Quantum Algorithms for the NP-Complete Maximum-Weight Independent Set, Exact Cover and 3SAT ProblemsApr 13 2010The problem Hamiltonian of the adiabatic quantum algorithm for the maximum-weight independent set problem (MIS) that is based on the reduction to the Ising problem (as described in [Choi08]) has flexible parameters. We show that by choosing the parameters ... More

Distribution of integral Fourier Coefficients of a Modular Form of Half Integral Weight Modulo PrimesMar 31 2007Recently, Bruinier and Ono classified cusp forms $f(z) := \sum_{n=0}^{\infty} a_f(n)q ^n \in S_{\lambda+1/2}(\Gamma_0(N),\chi)\cap \mathbb{Z}[[q]]$ that does not satisfy a certain distribution property for modulo odd primes $p$. In this paper, using Rankin-Cohen ... More

Multiplicity of the Protostar Serpens SMM 1 Revealed by Millimeter ImagingOct 13 2009The Serpens SMM 1 region was observed in the 6.9 mm continuum with an angular resolution of about 0.6 arcsec. Two sources were found to have steep positive spectra suggesting emission from dust. The stronger one, SMM 1a, is the driving source of the bipolar ... More

Distributed Source Coding with One Distortion Criterion and Correlated MessagesAug 15 2009In this paper, distributed (or multiterminal) source coding with one distortion criterion and correlated messages is considered. This problem can be also called ``Berger-Yeung problem with correlated messages''. It corresponds to the source coding part ... More

Construction of a Kinematic Variable Sensitive to the Mass of the Standard Model Higgs Boson in H->WW*->l l nu nu-bar using Symbolic RegressionJun 25 2010We derive a kinematic variable that is sensitive to the mass of the Standard Model Higgs boson (M_H) in the H->WW*->l l nu nu-bar channel using symbolic regression method. Explicit mass reconstruction is not possible in this channel due to the presence ... More

Axino as a sterile neutrinoApr 14 2001We present a supersymmetric axion model in which the fermionic superpartner of axion, i.e. the axino, corresponds to a sterile neutrino which would accommodate the LSND data with atmospheric and solar neutrino oscillations.

Light Quark Masses and Quarkonium DecaysJun 24 1992After discussing the intrinsic ambiguity in determining the light quark mass ratio $m_u/m_d$, we reexamine the recent proposal that this ambiguity can be resolved by applying the QCD multipole expansion for the heavy quarkonium decays. It is observed ... More

Thermal Production of Axino Dark MatterFeb 21 2012We discuss certain features of the low energy effective interactions of axion supermultiplet, which are relevant for axino cosmology, and examine the implication to thermal production of axino in the early Universe.

Persistence of Hölder continuity for non-local integro-differential equationsDec 28 2011In this paper, we consider non-local integro-differential equations under certain natural assumptions on the kernel, and obtain persistence of H\"{o}lder continuity for their solutions. In other words, we prove that a solution stays in $C^\beta$ for all ... More

Maximal multiplier on Stratified groupsJun 13 2012Mar 17 2013In this paper, we prove Lp boundedness of maximal multipliers on stratified groups and maximal multipliers on product spaces of those groups.

Oscillating convolution operators on the Heisenberg groupApr 25 2012Jun 13 2012In this paper, we consider oscillating convolution operotors on the Heisenberg group $H^n_a$ with respect to the norm $\rho(x,t) = \rho_1(b x, b t)$ with $\rho_1(x,t)= (|x|^4 + t^2)^{1/4}$. We obtain $L^2$ boundedness properties using the oscillatory ... More

Near-Online Multi-target Tracking with Aggregated Local Flow DescriptorApr 09 2015In this paper, we focus on the two key aspects of multiple target tracking problem: 1) designing an accurate affinity measure to associate detections and 2) implementing an efficient and accurate (near) online multiple target tracking algorithm. As the ... More

Directly finite algebras of pseudofunctions on locally compact groupsMay 19 2012Nov 12 2014An algebra $A$ is said to be directly finite if each left invertible element in the (conditional) unitization of $A$ is right invertible. We show that the reduced group ${\rm C}^\ast$-algebra of a unimodular group is directly finite, extending known results ... More

A note on some group $C^*$-algebras which are quasi-directly finiteMar 08 2010Jun 06 2010An algebra is said to be quasi-directly finite when any left-invertible element in its unitization is automatically right-invertible. It is an old observation of Kaplansky that the von Neumann algebra of a discrete group has this property; in this note, ... More

Group representations with empty residual spectrumJun 16 2009Jan 19 2010Let $X$ be a Banach space on which a discrete group $\Gamma$ acts by isometries. For certain natural choices of $X$, every element of the group algebra, when regarded as an operator on $X$, has empty residual spectrum. We show, for instance, that this ... More

Injective convolution operators on ${\ell}^{\infty}(Γ)$ are surjectiveJun 15 2006Aug 01 2007Let $\Gamma$ be a discrete group and let $f \in \ell^1(\Gamma)$. We observe that if the natural convolution operator $\rho_f:\ell^{\infty}(\Gamma)\to \ell^{\inf ty}(\Gamma)$ is injective, then f is invertible in $\ell^1(\Gamma)$. Our proof simplifies ... More

A Semidefinite Program for Structured BlockmodelsNov 16 2016Semidefinite programs have recently been developed for the problem of community detection, which may be viewed as a special case of the stochastic blockmodel. Here, we develop a semidefinite program that can be tailored to other instances of the blockmodel, ... More

Genus zero BPS invariants for local P^1Jun 23 2011Oct 09 2012We study the equivariant version of the genus zero BPS invariants of the total space of a rank 2 bundle on P^1 whose determinant is O(-2). We define the equivariant genus zero BPS invariants by the residue integrals on the moduli space of stable sheaves ... More

The definability criterions for convex projective polyhedral reflection groupsJun 11 2012Oct 14 2013Following Vinberg, we find the criterions for a subgroup generated by reflections $\Gamma \subset \SL^{\pm}(n+1,\mathbb{R})$ and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed Noetherian ring in ... More

Stability of thermodynamic and dynamical order in a system of globally coupled rotorsJun 01 2005A system of globally coupled rotors is studied in a unified framework of microcanonical and canonical ensembles. We consider the Fokker-Planck equation governing the time evolution of the system, and examine various stationary as well as non-stationary ... More

Different Adiabatic Quantum Optimization Algorithms for the NP-Complete Exact Cover and 3SAT ProblemsOct 06 2010May 31 2011One of the most important questions in studying quantum computation is: whether a quantum computer can solve NP-complete problems more efficiently than a classical computer? In 2000, Farhi, et al. (Science, 292(5516):472--476, 2001) proposed the adiabatic ... More

Spectroscopy results from BelleJan 29 2011We report recent results on the charmonium and charmoniumlike states based on a large data sample recorded at the $\Upsilon(4S)$ and $\Upsilon(5S)$ resonances with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider.

The PL-methods for hyperbolic 3-manifolds to prove tamenessFeb 23 2006Using PL-methods, we prove the Marden's conjecture that a hyperbolic 3-manifold $M$ with finitely generated fundamental group and with no parabolics are topologically tame. Our approach is to form an exhaustion $M_i$ of $M$ and modify the boundary to ... More

Classification of Bott manifolds up to dimension eightDec 11 2011We show that three- and four-stage Bott manifolds are classified up to diffeomorphism by their integral cohomology rings. In addition, any cohomology ring isomorphism between two three-stage Bott manifolds can be realized by a diffeomorphism between the ... More

Closed flat affine 3-manifolds are primeJul 16 2014Nov 01 2014An (flat) affine $3$-manifold is a $3$-manifold with an atlas of charts to an affine space ${\mathbf R}^3$ with transition maps in the affine transformation group $Aff({\mathbf R}^3)$. Equivalently an affine $3$-manifold is a $3$-manifold with a flat ... More

A classification of radial or totally geodesic ends of real projective orbifolds I: a survey of resultsJan 02 2015Jan 26 2016Real projective structures on $n$-orbifolds are useful in understanding the space of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$ or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolic manifolds deform to ... More

Convex and concave decompositions of affine $3$-manifoldsNov 05 2014Sep 27 2016An (flat) affine $3$-manifold is a $3$-manifold with an atlas of charts to an affine space ${\mathbf R}^3$ with transition maps in the affine transformation group $Aff({\mathbf R}^3)$. We will show that a closed affine $3$-manifold is either an affine ... More

A gap theorem for the ZL-amenability constant of a finite groupOct 20 2014May 19 2015It was shown in [A. Azimifard, E. Samei, N. Spronk, JFA 2009; arxiv 0805.3685] that the ZL-amenability constant of a finite group is always at least 1, with equality if and only if the group is abelian. It was also shown in the same paper that for any ... More

Triviality of the generalized Lau product associated to a Banach algebra homomorphismNov 24 2015Jan 08 2016Several papers have, as their raison d'etre, the exploration of the \emph{generalized Lau product} associated to a homomorphism $T:B\to A$ of Banach algebras. In this short note, we demonstrate that the generalized Lau product is isomorphic as a Banach ... More

Maximal multipliers on compact manifolds without boundaryJul 01 2012Mar 20 2014Hormander-Mihklin type multiplier theorem on compacts manifolds withour boundary has been obtained by using the wave kernels. We consider maximal multiplies on this setting. To obtain the result, we carefully deal with the remainder terms and find an ... More

Relativistic spin operator and Lorentz transformation of spin state of a massive Dirac particleSep 20 2012Jul 08 2013We have shown the covariant relativistic spin operator is equivalent to the spin operator commuting with the free Dirac Hamiltonian. This implies that the covariant relativistic spin operator is a good quantum observable. The covariant relativistic spin ... More

Physical approach to price momentum and its application to momentum strategyAug 14 2012Aug 20 2014We introduce various quantitative and mathematical definitions for price momentum of financial instruments. The price momentum is quantified with velocity and mass concepts originated from the momentum in physics. By using the physical momentum of price ... More

The warped product approach to magnetically charged GMGHS spacetimeJul 24 2014In the framework of Lorentzian multiply warped products we study the magnetically charged Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) interior spacetime in the string frame. We also investigate geodesic motion in various hypersurfaces, and compare ... More

Quantum Key Distribution Using Quantum Faraday RotatorsDec 26 2006Aug 26 2007We propose a new quantum key distribution (QKD) protocol based on the fully quantum mechanical states of the Faraday rotators. The protocol is unconditionally secure against collective attacks for multi-photon source up to two photons on a noisy environment. ... More

Topological quantization and degeneracy in Josephson-junction arraysMar 20 2001We consider the conductivity quantization in two-dimensional arrays of mesoscopic Josephson junctions, and examine the associated degeneracy in various regimes of the system. The filling factor of the system may be controlled by the gate voltage as well ... More

Co-clustering of Nonsmooth GraphonsJul 22 2015Performance bounds are given for exploratory co-clustering/ blockmodeling of bipartite graph data, where we assume the rows and columns of the data matrix are samples from an arbitrary population. This is equivalent to assuming that the data is generated ... More

The two components of the SO(3)-character space of the fundamental group of a closed surface of genus 2Feb 16 2010Sep 02 2010We use geometric techniques to explicitly find the topological structure of the space of SO(3)-representations of the fundamental group of a closed surface of genus 2 quotient by the conjugation action by SO(3). There are two components of the space. ... More

Geometric structures on orbifolds and holonomy representationsJul 24 2001Jul 29 2003An orbifold is a topological space modeled on quotient spaces of a finite group actions. We can define the universal cover of an orbifold and the fundamental group as the deck transformation group. Let $G$ be a Lie group acting on a space $X$. We show ... More

The convex real projective orbifolds with radial or totally geodesic ends: a survey of some partial resultsJan 26 2016Aug 18 2016A real projective orbifold is an $n$-dimensional orbifold modeled on ${\mathbf R}P^n$ with the group $PGL(n+1, {\mathbf R})$-action. We concentrate on an orbifold that contains a compact codimension $0$ submanifold whose complement is a union of neighborhoods ... More

The classification of ends of properly convex real projective orbifolds II: Properly convex radial ends and totally geodesic endsJan 02 2015Jul 02 2015Real projective structures on $n$-orbifolds are useful in understanding the space of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$ or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolic manifolds deform to ... More

SUSY Breaking at the Tip of Throat and Mirage MediationMay 23 2007May 27 2007We discuss some features of supersymmetry breaking induced by a brane-localized source which is stabilized at the IR end of warped throat, and also the resulting mirage mediation pattern of soft terms of the visible fields which are localized in the bulk ... More

Axions and the Strong CP Problem in M-theoryJun 25 1997We examine the possibility that the strong CP problem is solved by string-theoretic axions in strong-coupling limit of the E_8 x E_8 heterotic string theory (M-theory). We first discuss some generic features of gauge kinetic functions in compactified ... More

Cosmology of Radiatively Generated Axion ScaleJan 05 1997We discuss some cosmological aspects of supersymmetric axion models in which the axion scale is radiatively generated in terms of the weak scale and the Planck scale. They include thermal inflation, axions produced by the decay of oscillating Peccei-Quinn ... More

Anisotropy universe in doubly warped product schemeAug 10 2014Jan 11 2016We study the GMGHS spacetimes to analyze the evolution of the anisotropy universe, which can be treated as a doubly warped products manifold possessing warping functions (or scale factor) having the Kantowski-Sachs solution which represents homogeneous ... More

Spontaneous symmetry breaking of arbitrageJul 26 2011Apr 18 2012We introduce the concept of spontaneous symmetry breaking to arbitrage modeling. In the model, the arbitrage strategy is considered as being in the symmetry breaking phase and the phase transition between arbitrage mode and no-arbitrage mode is triggered ... More

Approximately multiplicative maps from weighted semilattice algebrasMar 30 2012May 06 2013We investigate which weighted convolution algebras $\ell^1_\omega(S)$, where $S$ is a semilattice, are AMNM in the sense of Johnson (JLMS, 1986). We give an explicit example where this is not the case. We show that the unweighted examples are all AMNM, ... More

A twisted inclusion between tensor products of operator spaces, with an application to 2-cocyclesJun 20 2016Given operator spaces $V$ and $W$, let $\widetilde{W}$ denote the opposite operator space structure on the same underlying Banach space. Although the identity map $W\to \widetilde{W}$ is in general not completely bounded, we show that the identity map ... More

Realization of compact spaces as cb-Helson setsApr 14 2015Jul 29 2015We show that, given a compact Hausdorff space $\Omega$, there is a compact group ${\mathbb G}$ and a homeomorphic embedding of $\Omega$ into ${\mathbb G}$, such that the restriction map ${\rm A}({\mathbb G})\to C(\Omega)$ is a complete quotient map of ... More

Hochschild homology and cohomology of {\ell}^1({\mathbb Z}_+^k)Sep 20 2007Sep 02 2008Building on the recent determination of the simplicial cohomology groups of the convolution algebra ${\ell}^1({\mathbb Z}_+^k)$ [Gourdeau, Lykova, White, 2005] we investigate what can be said for cohomology of this algebra with more general symmetric ... More

Simplicial homology of strong semilattices of Banach algebrasSep 15 2006Feb 25 2008Certain semigroups are known to admit a `strong semilattice decomposition' into simpler pieces. We introduce a class of Banach algebras that generalise the $\ell^1$-convolution algebras of such semigroups, and obtain a disintegration theorem for their ... More

Different moment-angle manifolds arising from two polytopes having the same bigraded Betti numbersSep 04 2012Two simple polytopes of dimension 3 having the identical bigraded Betti numbers but non-isomorphic Tor-algebras are presented. These polytopes provide two homotopically different moment-angle manifolds having the same bigraded Betti numbers. These two ... More

Minor-Embedding in Adiabatic Quantum Computation: I. The Parameter Setting ProblemApr 30 2008We show that the NP-hard quadratic unconstrained binary optimization (QUBO) problem on a graph $G$ can be solved using an adiabatic quantum computer that implements an Ising spin-1/2 Hamiltonian, by reduction through minor-embedding of $G$ in the quantum ... More

Faster Algorithms for Constructing a Concept (Galois) LatticeFeb 19 2006Jun 01 2006In this paper, we present a fast algorithm for constructing a concept (Galois) lattice of a binary relation, including computing all concepts and their lattice order. We also present two efficient variants of the algorithm, one for computing all concepts ... More

Dynamical gauge coupling unification from moduli stabilizationJun 12 2006In D-brane models, different part of the 4-dimensional gauge group might originate from D-branes wrapping different cycles in the internal space, and then the standard model gauge couplings at the compactification scale are determined by different cycle-volume ... More

Flavor Structure of Scherk-Schwarz Supersymmetry Breaking for Quasi-Localized Matter FieldDec 27 2003We discuss the flavor structure of soft supersymmetry breaking parameters in 5-dimensional orbifold field theories in which N=1 supersymmetry is broken by the Scherk-Schwarz boundary condition and hierarchical 4-dimensional Yukawa couplings are obtained ... More

Small Flavor Conserving CP Violation in Superstring ModelsFeb 21 1994It is well known that supersymmetric models allow new sources for CP violation that arise from soft supersymmetry breaking terms. If unsuppressed, these new CP-violating phases would give too large a neutron electric dipole moment. We discuss a mechanism ... More

Small SUSY phases in string-inspired supergravityNov 24 1993In supersymmetric models, there are new CP violating phases which, if unsuppressed, would give a too large neutron electric dipole moment. We examine the possibility of small SUSY phases in string-inspired supergravity models in which supersymmetry is ... More

Generalized Faraday law derived from classical forces in a rotating frameApr 02 2009Aug 19 2009We show the additional spin dependent classical force due to the rotation of an electron spin's rest frame is essential to derive a spin-Faraday law by using an analogy with the usual Faraday law. The contribution of the additional spin dependent force ... More

A classification of radial and totally geodesic ends of properly convex real projective orbifolds III: the convex but nonproperly convex and non-complete-affine radial endsJul 03 2015Real projective structures on $n$-orbifolds are useful in understanding the space of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$ or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolic manifolds deform to ... More

Dimensionally Constrained Symbolic RegressionJun 20 2011We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP. However, in ... More

The maximal tubes under the deformations of a class of 3-dimensional hyperbolic cone-manifoldsMay 14 2004Recently, Hodgson and Kerckhoff found a small bound on Dehn surgered 3-manifolds from hyperbolic knots not admitting hyperbolic structures using deformations of hyperbolic cone-manifolds. They asked whether the area normalized meridian length squared ... More

The Lane-Emden system near the critical hyperbola on nonconvex domainsMay 26 2015Jan 05 2016In this paper we study the asymptotic behavior of minimal energy solutions to the Lane-Emden system $-\Delta u = v^p$ and $-\Delta v = u^q$ on bounded domains as the index $(p,q)$ approaches to the critical hyperbola from below. Precisely, we remove the ... More

Singly generated operator algebras satisfying weakened versions of amenabilityFeb 06 2012Aug 03 2012We construct a singly generated subalgebra of ${\mathcal K}({\mathcal H})$ which is non-amenable, yet is boundedly approximately contractible. The example embeds into a homogeneous von Neumann algebra. We also observe that there are singly generated, ... More

The module category weight of compact exceptional Lie groupsJul 14 2013We compute the lower bound estimate for the module category weight of compact exceptional Lie groups by analyzing several Eilenberg--Moore type spectral sequences.

Severi Degrees in Cogenus 4Jan 15 1996Jan 15 1996In this paper, we give closed-form formulae for Severi degrees in cogenus 3 and 4 using Ran's method. These formulae coincide with those of I. Vainsencher and for cogenus 3 case, that of J. Harris and R. Pandharipande. Another result of this paper is ... More

On commutative, operator amenable subalgebras of finite von Neumann algebrasDec 20 2010Sep 12 2011An open question, raised independently by several authors, asks if a closed amenable subalgebra of ${\mathcal B}({\mathcal H})$ must be similar to an amenable C*-algebra; the question remains open even for singly-generated algebras. In this article we ... More

Multiply Warped Products with Non-Smooth MetricsApr 25 2002In this article we study manifolds with $C^{0}$-metrics and properties of Lorentzian multiply warped products. We represent the interior Schwarzschild space-time as a multiply warped product space-time with warping functions and we also investigate the ... More

Twisted traces of singular moduli of weakly holomorphic modular functionsMay 06 2011Zagier proved that the generating series for the traces of singular moduli is a \textit{weakly holomorphic} modular form of weight 3/2 on $\Gamma_0(4)$. Bruinier and Funke extended the results of Zagier to modular curves of arbitrary genus. Zagier also ... More

Splitting maps and norm bounds for the cyclic cohomology of biflat Banach algebrasOct 27 2009Apr 25 2010We revisit the old result that biflat Banach algebras have the same cyclic cohomology as $\mathbb C$, and obtain a quantitative variant (which is needed in forthcoming joint work of the author). Our approach does not rely on the Connes-Tsygan exact sequence, ... More

Uniform bounds for point cohomology of $\ell^1({\mathbb Z}_+)$ and related algebrasAug 16 2008May 14 2009It is well-known that the point cohomology of the convolution algebra $\ell^1({\mathbb Z}_+)$ vanishes in degrees 2 and above. We sharpen this result by obtaining splitting maps whose norms are bounded independently of the choice of point module. Our ... More

Simplicial cohomology of augmentation ideals in ${\ell}^1(G)$Nov 23 2007Aug 14 2008Let $G$ be a discrete group. We give a decomposition theorem for the Hochschild cohomology of $\ell^1(G)$ with coefficients in certain $G$-modules. Using this we show that if $G$ is commutative-transitive, the canonical inclusion of bounded cohomology ... More

Torus actions on cohomology complex generalized Bott manifoldsJan 29 2011Aug 31 2012A torus manifold is a closed smooth manifold of dimension $2n$ having an effective smooth $T^n = (S^1)^n$-action with non-empty fixed points. Petrie \cite{petrie:1973} has shown that any homotopy equivalence between a complex projective space $\CP^n$ ... More

Toroidal graphs containing neither $K_5^{-}$ nor 6-cycles are 4-choosableJul 11 2013The choosability $\chi_\ell(G)$ of a graph $G$ is the minimum $k$ such that having $k$ colors available at each vertex guarantees a proper coloring. Given a toroidal graph $G$, it is known that $\chi_\ell(G)\leq 7$, and $\chi_\ell(G)=7$ if and only if ... More

Avoid First Order Quantum Phase Transition by Changing Problem HamiltoniansOct 06 2010Aug 03 2011In Amin and Choi \cite{AC09}, we show that an adiabatic quantum algorithm for the NP-hard maximum independent set (MIS) problem on a set of special family of graphs in which there are exponentially many local maxima would have the exponentially small ... More

Minor-embedding in adiabatic quantum computation: II. Minor-universal graph designJan 18 2010Jan 19 2010In [Choi08], we introduced the notion of minor-embedding in adiabatic quantum optimization. A minor-embedding of a graph G in a quantum hardware graph U is a subgraph of U such that G can be obtained from it by contracting edges. In this paper, we describe ... More

A sharp bound on the convergence rate of an aggregation-based algebraic multi-grid method applied to a 1D model problemOct 28 2012Mar 19 2013We consider the linear system Ax=b arising from one-dimensional Poisson's equation with Dirichlet boundary conditions, where A is the square matrix with the stencil form [-1 2 -1]. Here we show that a pairwise aggregation-based algebraic 2-grid method ... More

Newton-Wigner position operator and its corresponding spin operator in relativistic quantum mechanicsDec 01 2014A relativistic spin operator is to be the difference between the total and orbital angular momentum. As the unique position operator for a localized state, the remarkable Newton-Wigner position operator, which has all desirable commutation relations as ... More

Moduli stabilization and the pattern of sparticle spectraSep 19 2008We discuss the pattern of low energy sparticle spectra which appears in some class of moduli stabilization scenario. In case that light moduli are stabilized by non-perturbative effects encoded in the superpotential and a phenomenologically viable de ... More

Moduli stabilization and the pattern of soft SUSY breaking termsNov 14 2005In string compactification preserving N=1 SUSY, moduli fields are plausible candidates for the messenger of SUSY breaking at low energy scales. In a scenario that moduli-mediated SUSY breaking is significant, the pattern of soft SUSY breaking terms depends ... More

A QCD Axion from Higher Dimensional Gauge FieldAug 04 2003We point out that a QCD axion solving the strong CP problem can arise naturally from parity-odd gauge field C_M in 5-dimensional (5D) orbifold field theory. The required axion coupling to the QCD anomaly comes from the 5D Chern-Simons coupling, and all ... More

Combinatorial embedded contact homology for toric contact manifoldsAug 29 2016Computing embedded contact homology (ECH) and related invariants of certain toric 3-manifolds (in the sense of Lerman) has led to interesting new results in the study of symplectic embeddings. Here, we give a combinatorial formulation of ECH chain complexes ... More

Quintessence, Flat Potential and String/M Theory AxionDec 02 1999A slow-rolling scalar field (Quintessence) has been proposed as the origin of accelerating universe at present. We discuss some features of quintessence, particularly those related with the {\it flatness} of its potential. We distinguish two types of ... More

String or M theory axion as a quintessenceFeb 10 1999May 29 2000A slow-rolling scalar field ($Q\equiv$ Quintessence) with potential energy $V_Q\sim (3\times 10^{-3} {\rm eV})^4$ has been proposed as the origin of accelerating universe at present. We investigate the effective potential of $Q$ in the framework of supergravity ... More

Goldstone Supermultiplet as the Messenger of Supersymmetry BreakingOct 01 1995We consider supersymmetric models in which a (pseudo) Goldstone supermultiplet plays the role of the messenger of supersymmetry breaking. Such models lead to a highly predictive form of flavor and CP conserving soft terms, particularly the soft scalar ... More

The convex real projective orbifolds with radial or totally geodesic ends: The closedness and openness of deformationsNov 04 2010May 28 2014A real projective orbifold is an $n$-dimensional orbifold modeled on $\mathbb{RP}^n$ with the group $PGL(n+1, \mathbb{R})$. We concentrate on an orbifold that contains a compact codimension $0$ submanifold whose complement is a union of neighborhoods ... More

Drilling cores of hyperbolic 3-manifolds to prove tamenessOct 18 2004We supply a proof of the fact that a hyperbolic 3-manifold $M$ with finitely generated fundamental group and with no parabolics is topologically tame. This proves the Marden's conjecture. Our approach is to form an exhaustion $M_i$ of $M$ and modify the ... More

Canonical decomposition of manifolds with flat real projective structure into (n-1)-convex manifolds and concave affine manifoldsApr 23 1998We try to understand the geometric properties of $n$-manifolds ($n\geq 2$) with geometric structures modeled on $(\bR P^n, \PGL(n+1, \bR))$, i.e., $n$-manifolds with projectively flat torsion free affine connections. We define the notion of $i$-convexity ... More

The decomposition and classification of radiant affine 3-manifoldsDec 19 1997Jul 17 2000An affine manifold is a manifold with torsion-free flat affine connection. A geometric topologist's definition of an affine manifold is a manifold with an atlas of charts to the affine space with affine transition functions; a radiant affine manifold ... More

The universal cover of an affine three-manifold with holonomy of shrinkable dimension $\leq 2$Jun 23 1997Dec 21 1999An affine manifold is a manifold with an affine structure, i.e. a torsion-free flat affine connection. We show that the universal cover of a closed affine 3-manifold $M$ with holonomy group of shrinkable dimension (or discompacit\'e in French) less than ... More

Hadron and Quarkmonium ExoticaMar 07 2014A number of charmonium-(bottmonium-)like states have been observed in $B$-factory experiments. Recently the BESIII experiment has joined this search with a unique data sample collected at the different center of mass energies ranging from 3.9 GeV to 4.42 ... More