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Polyakov loop fluctuations in the presence of external fieldsJan 24 2018We study the implications of the spontaneous and explicit Z(3) center symmetry breaking for the Polyakov loop susceptibilities. To this end, ratios of the susceptibilities of the real and imaginary parts, as well as of the modulus of the Polyakov loop ... More

Matching the Hagedorn mass spectrum with Lattice QCD resultsJul 23 2015Nov 06 2015Based on recent Lattice QCD (LQCD) results obtained at finite temperature, we discuss modeling of the hadronic phase of QCD in the framework of Hadron Resonance Gas (HRG) with discrete and continuous mass spectra. We focus on fluctuations of conserved ... More

Interplay between antiferromagnetic order and spin polarization in ferromagnetic metal/electron-doped cuprate superconductor junctionsAug 24 2009Recently we proposed a theory of point-contact spectroscopy and argued that the splitting of zero-bias conductance peak (ZBCP) in electron-doped cuprate superconductor point-contact spectroscopy is due to the coexistence of antiferromagnetic (AF) and ... More

Thermal contribution of unstable statesFeb 08 2019Within the framework of the Lee model, we analyze in detail the difference between the energy derivative of the phase shift and the standard spectral function of the unstable state. The fact that the model is exactly solvable allows us to demonstrate ... More

Confinement Models at Finite Temperature and DensityAug 27 2009Feb 12 2010In-medium chiral symmetry breaking in confining potential models of QCD is examined. Past attempts to analyse these models have been hampered by infrared divergences that appear at non-zero temperature. We argue that previous attempts to circumvent this ... More

Polyakov loop fluctuations and deconfinement in the limit of heavy quarksJun 16 2014We explore the influence of heavy quarks on the deconfinement phase transition in an effective model for gluons interacting with dynamical quarks in color SU(3). With decreasing quark mass, the strength of the explicit breaking of the Z(3) symmetry grows ... More

Emergence of topological phases from the extension of two-dimensional lattice with nonsymmorphic symmetriesApr 15 2018Young and Kane have given a great insight for 2D Dirac semimetals with nontrivial topology in the presence of nonsymmorphic crystalline symmetry. Based on one of 2D nonsymmorphic square lattice structures they proposed, we further construct a set of 3D ... More

Overlap between Lattice QCD and HRG with in-medium effects and parity doublingNov 29 2017We investigate the fluctuations and correlations involving baryon number in hot hadronic matter with modified masses of negative-parity baryons, in the context of the hadron resonance gas. Temperature-dependent masses are adopted from the recent lattice ... More

S-matrix analysis of the baryon electric charge correlationOct 07 2017We compute the correlation of the net baryon number with the electric charge ($\chi_{BQ}$) for an interacting hadron gas using the S-matrix formulation of statistical mechanics. The observable $\chi_{BQ}$ is particularly sensitive to the details of the ... More

Thermodynamics of strange baryon system from coupled-channel analysis and missing statesJun 06 2018Dec 14 2018We study the thermodynamics of the strange baryon system using an S-matrix formulation of statistical mechanics. For this purpose, we employ an existing coupled-channel study involving $\bar{K} N$, $\pi \Lambda$, and $\pi \Sigma$ interactions in the $S=-1$ ... More

Validity of Landauer principle and quantum memory effects via collision modelsNov 28 2018We study the validity of Landauer principle in the non-Markovian regime by means of collision models where the intracollisions inside the reservoir cause memory effects generating system-environment correlations. We adopt the system-environment correlations ... More

Effects of $ρ$-meson width on pion distributions in heavy-ion collisionsAug 24 2016The influence of the finite width of $\rho$ meson on the pion momentum distribution is studied quantitatively in the framework of the S-matrix approach combined with a blast-wave model to describe particle emissions from an expanding fireball. We find ... More

Repulsive interactions and their effects on the thermodynamics of hadron gasFeb 28 2017We compare two approaches in modeling repulsive interactions among hadrons: the excluded volume approximation and the S-matrix formalism. These are applied to study the thermodynamics of the $\pi N \Delta$ system. It is shown that the introduction of ... More

Fourier coefficients of the net-baryon number density and chiral criticalityMay 11 2018Jun 28 2018We investigate the Fourier coefficients $b_k(T)$ of the net--baryon number density in strongly interacting matter at nonzero temperature and density. The asymptotic behavior of the coefficients at large $k$ is determined by the singularities of the partition ... More

The thermal proton yield anomaly in Pb-Pb collisions at the LHC and its resolutionAug 09 2018Jan 27 2019We propose a resolution of the discrepancy between the proton yield predicted by the statistical hadronization approach and data on hadron production in ultra-relativistic nuclear collisions at the LHC. Applying the S-matrix formulation of statistical ... More

Strangeness fluctuations from $K-π$ interactionsJul 15 2015Nov 06 2015Motivated by recent lattice QCD studies, we explore the effects of interactions on strangeness fluctuations in strongly interacting matter at finite temperature. We focus on S-wave $K\pi$ scattering and discuss the role of the $K_0^*(800)$ and $K^*(1430)$ ... More

Fourier coefficients of the net-baryon number density and chiral criticalityMay 11 2018Aug 03 2019We investigate the Fourier coefficients $b_k(T)$ of the net--baryon number density in strongly interacting matter at nonzero temperature and density. The asymptotic behavior of the coefficients at large $k$ is determined by the singularities of the partition ... More

Polyakov loop fluctuations in SU(3) lattice gauge theory and an effective gluon potentialJul 23 2013We calculate the Polyakov loop susceptibilities in the SU(3) lattice gauge theory using the Symanzik improved gauge action on different-sized lattices. The longitudinal and transverse fluctu- ations of the Polyakov loop, as well as, that of its absolute ... More

Probing Deconfinement with Polyakov Loop SusceptibilitiesJun 21 2013The susceptibilities of the real and imaginary parts, as well as of the modulus of the Polyakov loop, are computed in SU(3) lattice gauge theory. We show that the ratios of these susceptibilities are excellent probes of the deconfinement transition, independent ... More

Effects of $ρ$-meson width on pion distributions in heavy-ion collisionsAug 24 2016Apr 01 2017The influence of the finite width of $\rho$ meson on the pion momentum distribution is studied quantitatively in the framework of the S-matrix approach combined with a blast-wave model to describe particle emissions from an expanding fireball. We find ... More

On finding all positive integers $a,b$ such that $b\pm a$ and $ab$ are palindromicDec 20 2018Jan 13 2019It is proven that the only integer solutions $(a,b)$ such that $a+b$ and $ab$ are palindromic are $(2,5\cdot 10^k-3)$, $(3,24)$ and $(9,9)$, and in a similar fashion, $b-a$ and $ab$ are only palindromic at $(a,b)=(3,147\cdot 10^{4(k+1)}+5247\sum_{i=0}^k10^{4i})$, ... More

The partition bundle of type A_{N-1} (2, 0) theoryDec 20 2010Dec 27 2010Six-dimensional (2, 0) theory can be defined on a large class of six-manifolds endowed with some additional topological and geometric data (i.e. an orientation, a spin structure, a conformal structure, and an R-symmetry bundle with connection). We discuss ... More

Automorphic properties of (2, 0) theory on T6Nov 30 2009We consider ADE-type (2, 0) theory on a family of flat six-tori endowed with flat Sp(4) connections coupled to the R-symmetry. Our main objects of interest are the components of the `partition vector' of the theory. These constitute an element of a certain ... More

Zero-mode dynamics in supersymmetric Yang-Mills-Chern-Simons theoryDec 20 2012We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus in the limit when the torus becomes small. The zero-modes of the fields then decouple from the non-zero modes and give rise to a spectrum of states ... More

Surface observables and the Weyl anomalyAug 27 1999I review the computation of the conformal anomaly of a Wilson surface observable in free two-form gauge theory in six dimensions.

Boundary conditions for GL-twisted N=4 SYMJun 20 2011Jul 04 2011We consider topologically twisted N=4 supersymmetric Yang-Mills theory on a four-manifold of the form V = W \times R_+ or V = W \times I, where W is a Riemannian three-manifold. Different kinds of boundary conditions apply at infinity or at finite distance. ... More

The low-energy spectrum of (2,0) theory on T^5 x RSep 24 2008We consider the ADE-series of (2, 0) supersymmetric quantum theories on T^5 \times R, where the first factor is a flat spatial five-torus, and the second factor denotes time. The quantum states of such a theory \Phi are characterized by a discrete quantum ... More

Wilson-'t Hooft operators and the theta angleMar 24 2006We consider $(3+1)$-dimensional $SU(N)/\mathbb Z_N$ Yang-Mills theory on a space-time with a compact spatial direction, and prove the following result: Under a continuous increase of the theta angle $\theta\to\theta+2\pi$, a 't Hooft operator $T(\gamma)$ ... More

Ground states of supersymmetric Yang-Mills-Chern-Simons theorySep 09 2012We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus. The Witten index may be computed in the weak coupling limit, where the ground state wave-functions localize on the moduli space of flat gauge ... More

World-sheet aspects of mirror symmetryOct 20 1994(Talk given at the Oskar Klein centenary symposium 19-21 September 1994 in Stockholm, Sweden, to appear in the proceedings.) The first half of this talk is a non-technical discussion of some general aspects of string theory, in particular the problem ... More

Self-dual strings in six dimensions: Anomalies, the ADE-classification, and the world-sheet WZW-modelMay 07 2004Nov 10 2004We consider the (2, 0) supersymmetric theory of tensor multiplets and self-dual strings in six space-time dimensions. Space-time diffeomorphisms that leave the string world-sheet invariant appear as gauge transformations on the normal bundle of the world-sheet. ... More

Commutation relations for surface operators in six-dimensional (2, 0) theoryDec 08 2000The A_{N - 1} (2, 0) superconformal theory has an observable associated with every two-cycle in six dimensions. We make a natural guess for the commutation relations of these operators, which reduces to the commutation relations of Wilson and 't Hooft ... More

BPS-spectra in four dimensions from M-theoryNov 11 1997I review my work together with Piljin Yi on the spectrum of BPS-saturated states in N = 2 supersymmetric Yang-Mills theories. In an M-theory description, such states are realized as certain two-brane configurations. We first show how the central charge ... More

Predicting Earth's Carrying Capability of Human Population as the Predator and the Natural Resources as the Prey in the Modified Lokta-Volterra Equations with Time-dependent ParametersApr 10 2019We modified the Lotka-Volterra Equations with the assumption that two of the original four constant parameters in the traditional equations are time dependent. In the first place, we assumed that the human population (borrowed from the T-Function) plays ... More

On the Solutions of the Three Dimensional Navier-Stokes ProblemMar 07 2008May 13 2008The aim of this paper is to solve the three dimensional Navier-Stokes problem with conservative source term. We use convolution methods to construct "well behaved" smooth solutions of the initial boundary value problem for the system of Navier-Stokes ... More

Fourier-Mukai transforms of slope stable torsion-free sheaves on Weierstrass elliptic surfacesOct 12 2017On a Weierstra{\ss} elliptic surface $X$, we define a `limit' of Bridgeland stability conditions, denoted $Z^l$-stability, by varying the polarisation in the definition of Bridgeland stability along a curve in the ample cone of $X$. We show that a slope ... More

Torsion pairs and filtrations in abelian categories with tilting objectsFeb 13 2013Given a noetherian abelian category $\mathcal Z$ of homological dimension two with a tilting object $T$, the abelian category $\mathcal Z$ and the abelian category of modules over $\text{End} (T)^{\textit{op}}$ are related by a sequence of two tilts; ... More

Polynomial Bridgeland Stable Objects and Reflexive SheavesDec 19 2011Aug 01 2012On a smooth projective threefold, we show that there are only two isomorphism types for the moduli of stable objects with respect to Bayer's standard polynomial Bridgeland stability - the moduli of Gieseker-stable sheaves and the moduli of PT-stable objects ... More

Restoration of tetragonal $C_4$ symmetry coexistent with filamentary superconductivity in the pressure induced intermediate phase in the iron-based superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$Jul 07 2015Jul 09 2015The hole doped Fe-based superconductors Ba$_{1-x}$A$_x$Fe$_2$As$_2$ (where A=Na or K) show a particular rich phase diagram. It was observed that an intermediate re-entrant tetragonal phase forms within the orthorhombic antiferromagnetically-ordered stripe-type ... More

Volume entropy for surface groups via Bowen-Series like mapsAug 25 2009We define a Bowen-Series like map for every geometric presentation of a co-compact surface group and we prove that the volume entropy of the presentation is the topological entropy of this particular (circle) map. Finally we find the minimal volume entropy ... More

T-structures on elliptic fibrationsSep 10 2015We consider t-structures that naturally arise on elliptic fibrations. By filtering the category of coherent sheaves on an elliptic fibration using the torsion pairs corresponding to these t-structures, we prove results describing equivalences of t-structures ... More

Moduli of PT-semistable objects IINov 29 2010May 04 2011We generalise the techniques of semistable reduction for flat families of sheaves to the setting of the derived category $D^b(X)$ of coherent sheaves on a smooth projective three-fold $X$. Then we construct the moduli of PT-semistable objects in $D^b(X)$ ... More

Fourier-Mukai transforms of slope stable torsion-free sheaves and stable 1-dimensional sheaves on Weierstrass elliptic threefoldsOct 10 2017We focus on a class of Weierstrass elliptic threefolds that allows the base of the fibration to be a Fano surface or a numerically $K$-trivial surface. In the first half of this article, we define the notion of limit tilt stability, which is closely related ... More

Fourier-Mukai transforms of slope stable torsion-free sheaves on a product elliptic threefoldOct 09 2017On the product elliptic threefold $X = C \times S$ where $C$ is an elliptic curve and $S$ is a K3 surface of Picard rank 1, we define a notion of limit tilt stability, which satisfies the Harder-Narasimhan property. We show that under the Fourier-Mukai ... More

Stability and Fourier-Mukai transforms on elliptic fibrationsJun 19 2012Jan 17 2014We systematically develop Bridgeland's and Bridgeland-Maciocia's techniques for studying elliptic fibrations, and identify criteria that ensure 2-term complexes are mapped to torsion-free sheaves under a Fourier-Mukai transform. As an application, we ... More

On some moduli of complexes on K3 surfacesMar 07 2012We consider moduli stacks of Bridgeland semistable objects that previously had only set-theoretic identifications with Uhlenbeck compactification spaces. On a K3 surface $X$, we give examples where such a moduli stack is isomorphic to a moduli stack of ... More

A short representation of the six-dimensional (2, 0) algebraApr 20 2001We construct a BPS-saturated representation of the six-dimensional (2, 0) algebra with a certain non-zero value of the `central' charge. This representation is naturally carried by strings with internal degrees of freedom rather than by point particles. ... More

The light spectrum near the Argyres-Douglas pointJun 07 1999We consider N = 2 super Yang-Mills theory with SU(2) gauge group and a single quark hypermultiplet in the fundamental representation. For a specific value of the quark bare mass and at a certain point in the moduli space of vacua, the central charges ... More

The Holographic Weyl anomalyJun 11 1998Jun 17 1998We calculate the Weyl anomaly for conformal field theories that can be described via the adS/CFT correspondence. This entails regularizing the gravitational part of the corresponding supergravity action in a manner consistent with general covariance. ... More

Low-energy spectrum of N = 4 super-Yang-Mills on T^3: flat connections, bound states at threshold, and S-dualityMar 19 2007Jun 10 2007We study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial three-torus. The low energy spectrum consists of a number of continua of states of arbitrarily low energies. Although the theory has no mass-gap, it appears that the dimensions ... More

Comment on "Theory of high-force DNA stretching and overstretching"Sep 09 2004Recently Storm and Nelson [1] (Phys.Rev. E67, 51906 (2003)) introduced the discrete persistent chain model which contains both features of the freely jointed chain (FJC) and the wormlike chain (WLC) models. Equation (20) of their paper is correct only ... More

Nonnegative Trigonometric Polynomials and Sturms TheoremJul 02 2015Jul 03 2015In an earlier article [3], we presented an algorithm that can be used to rigorously check whether a specific cosine or sine polynomial is nonnegative in a given interval or not. The algorithm proves to be an indispensable tool in establishing some recent ... More

Theta functions and quiver GrassmanniansJun 28 2019In this article, we use the relationship between cluster scattering diagrams and stability scattering diagrams to relate quiver representations with these diagrams. With a notion of positive crossing of a path $\gamma$, we show that if $\gamma$ has positive ... More

Leptogenesis and CPT ViolationDec 05 2010Jul 13 2011We construct a model in which neutrinos and anti-neutrinos acquire the same mass but slightly different energy dispersion relations.Despite CPT violation, spin-statistics is preserved. We find that leptogenesis can be easily explained within this model, ... More

On Three Alternative Characterizations of Combined TracesNov 03 2010Oct 17 2011The combined trace (i.e., comtrace) notion was introduced by Janicki and Koutny in 1995 as a generalization of the Mazurkiewicz trace notion. Comtraces are congruence classes of step sequences, where the congruence relation is defined from two relations ... More

On the Early In Situ Formation of Pluto's Small SatellitesMar 06 2018The formation of Pluto's small satellites - Styx, Nix, Keberos and Hydra - remains a mystery. Their orbits are nearly circular and are near mean-motion resonances and nearly coplanar with Charon's orbit. One scenario suggests that they all formed close ... More

Zero-energy states of N = 4 SYM on T^3: S-duality and the mapping class groupFeb 05 2008We continue our studies of the low-energy spectrum of N=4 super-Yang-Mills theory on a spatial three-torus. In two previous papers, we computed the spectrum of normalizable zero-energy states for all choices of gauge group and all values of the electric ... More

Weyl anomaly for Wilson surfacesMay 22 1999We consider a free two-form in six dimensions and calculate the conformal anomaly associated with a Wilson surface observable.

Photon-number tomography and fidelityDec 23 2012The scheme of photon-number tomography is discussed in the framework of star-product quantization. The connection of dual quantization scheme and observables is reviewed. The quantizer and dequantizer operators and kernels of star product of tomograms ... More

The wobbling-to-swimming transition of rotated helicesFeb 14 2014A growing body of work aims at designing and testing micron-scale synthetic swimmers. One method, inspired by the locomotion of flagellated bacteria, consists of applying a rotating magnetic field to a rigid, helically-shaped, propeller attached to a ... More

Diversity and Origin of 2:1 Orbital Resonances in Extrasolar Planetary SystemsJan 21 2004May 07 2004(Abridged) A diversity of 2:1 resonance configurations can be expected in extrasolar planetary systems, and their geometry can provide information about the origin of the resonances. Assembly during planet formation by the differential migration of planets ... More

Modelling Concurrent Behaviors in the Process Specification LanguageJul 16 2009In this paper, we propose a first-order ontology for generalized stratified order structure. We then classify the models of the theory using model-theoretic techniques. An ontology mapping from this ontology to the core theory of Process Specification ... More

A Characterization of Combined Traces Using Labeled Stratified Order StructuresApr 01 2010Apr 09 2010This paper defines a class of labeled stratified order structures that characterizes exactly the notion of combined traces (i.e., comtraces) proposed by Janicki and Koutny in 1995. Our main technical contributions are the representation theorems showing ... More

Statechart Verification with iStateSep 08 2009This paper is the longer version of the extended abstract with the same name published in FM 06. We describe in detail the algorithm to generate verification conditions from statechart structures implemented in the iState tool. This approach also suggests ... More

Geometric and algebraic parameterizations for Dirac cohomology of simple modules in $\mathcal{O}^\mathfrak{p}$ and their applicationsJul 22 2019In this paper, we show that the Dirac cohomology $H_{D}(L(\lambda))$ of a simple highest weight module $L(\lambda)$ in $\mathcal{O}^\mathfrak{p}$ can be parameterized by a specific set of weights: a subset $\mathcal{W}_I(\lambda)$ of the orbit of the ... More

ML(n)BiCGStabt: A ML(n)BiCGStab variant with A-transposeNov 04 2013The 1980 IDR method plays an important role in the history of Krylov subspace methods. It started the research of transpose-free Krylov subspace methods. In this paper, we make a first attempt to bring back A-transpose to the research area by presenting ... More

Ring to Mountain Transition in Deposition Pattern of DryingFeb 16 2016When a droplet containing a non-volatile component is dried on a substrate, it leaves a ringlike deposit on the substrate. We propose a theory which predicts the deposit distribution based on a model of fluid flow and contact line motion of the droplet. ... More

Counting Curves with Modular FormsFeb 27 1996Apr 30 1996We consider the type IIA string compactified on the Calabi-Yau space given by a degree 12 hypersurface in the weighted projective space ${\bf P}^4_{(1, 1, 2,2, 6)}$. We express the prepotential of the low-energy effective supergravity theory in terms ... More

A New Family of Nonnegative Sine PolynomialsJul 28 2016We present a new family of sine polynomials that are nonnegative for all $x$ in $[0,\pi]$. We also characterize all nonnegative sine polynomials of degree 3 and all nonnegative cosine polynomials of degree 2.

ML(n)BiCGStab: Reformulation, Analysis and ImplementationNov 24 2010With the aid of index functions, we re-derive the ML(n)BiCGStab algorithm in a paper by Yeung and Chan in 1999 in a more systematic way. It turns out that there are n ways to define the ML(n)BiCGStab residual vector. Each definition will lead to a different ... More

The flat Grothendieck-Riemann-Roch theorem without adiabatic techniquesMar 15 2012May 31 2016In this paper we give a simplified proof of the flat Grothendieck-Riemann-Roch theorem. The proof makes use of the local family index theorem and basic computations of the Chern-Simons form. In particular, it does not involve any adiabatic limit computation ... More

Blockchain moderated by empty blocks to reduce the energetic impact of crypto-moneysJan 24 2018Aug 18 2019While cryptocurrencies and blockchain applications continue to gain popularity, their energy cost is evidently becoming unsustainable. In most instances, the main cost comes from the required amount of energy for the Proof-of-Work, and this cost is inherent ... More

Quantum Tomography Approach in Signal AnalysisJun 02 1999Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to the fractional ... More

Poincare duality in Morava K-theory for classifying spaces of orbifoldsMay 13 2013Greenlees and Sadofsky showed that the classifying spaces of finite groups are self-dual with respect to Morava K-theory K(n). Their duality map was constructed using a transfer map. We generalize their duality map and prove a K(n)-version of Poincare ... More

On differential characteristic classesNov 15 2013Oct 16 2014In this paper we give explicit formulas of differential characteristic classes of principal $G$-bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes, differential Pontryagin ... More

An introduction to ML(n)BiCGStabJun 18 2011ML(n)BiCGStab is a Krylov subspace method for the solution of large, sparse and non-symmetric linear systems. In theory, it is a method that lies between the well-known BiCGStab and GMRES/FOM. In fact, when n = 1, ML(1)BiCGStab is BiCGStab and when n ... More

Bound states in N = 4 SYM on T^3: Spin(2n) and the exceptional groupsJun 19 2007The low energy spectrum of (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial three-torus contains a certain number of bound states, characterized by their discrete abelian magnetic and electric 't Hooft fluxes. At weak coupling, the ... More

Holography and the Weyl anomalyDec 03 1998We review our calculation of the Weyl anomaly for d-dimensional conformal field theories that have a description in terms of a (d + 1)-dimensional gravity theory.

On the Treewidth of Dynamic GraphsDec 13 2011May 25 2012Dynamic graph theory is a novel, growing area that deals with graphs that change over time and is of great utility in modelling modern wireless, mobile and dynamic environments. As a graph evolves, possibly arbitrarily, it is challenging to identify the ... More

BI model - An Extension of Starobinsky model induced by SUGRAApr 08 2019Apr 12 2019We analyze BI model in a complete form and compare the predictions with that of Starobinsky model. Under the parameter constraints in Planck 2018, we find that the dynamics of the whole inflation process described by BI and Starobinsky models are nearly ... More

Refined hexagons for differential cohomologyOct 02 2013Dec 07 2014Cheeger-Simons differential characters and differential $K$-theory are refinements of ordinary cohomology theory and topological $K$-theory respectively, and they are examples of differential cohomology. Each of these differential cohomology theories ... More

A New Family of Nonnegative Sine PolynomialsJul 28 2016Aug 03 2017We present a new family of sine polynomials that are nonnegative for all $x$ in $[0,\pi]$. We also characterize all nonnegative sine polynomials of degree 3 and all nonnegative cosine polynomials of degree 2. In the latest version, typos in (1.4) and ... More

Slow-roll Analysis of Double Field Axion InflationFeb 08 2018Apr 11 2019We adopt the double field natural inflation model motivated by the non-perturbative effects of supergravity and superstring theory to do the slow roll analysis. We show that when the parameters are suitably chosen, there exist ranges of initial values ... More

Simplicial Monoid Actions and The Associated Universal Simplicial Monoid ConstructionMar 15 2013The reduced universal monoid on the action category associated to a pointed simplicial M-set has appeared in the guise of various simplicial monoid and group constructions. These include the classical constructions of Milnor and James, as well as their ... More

Four-dimensional BPS-spectra via M-theoryJul 30 1997Aug 13 1997We consider the realization of four-dimensional theories with N = 2 supersymmetry as M-theory configurations including a five-brane. Our emphasis is on the spectrum of massive states, that are realized as two-branes ending on the five-brane. We start ... More

Non-Asymptotic Convergence Analysis of Inexact Gradient Methods for Machine Learning Without Strong ConvexityAug 31 2013Many recent applications in machine learning and data fitting call for the algorithmic solution of structured smooth convex optimization problems. Although the gradient descent method is a natural choice for this task, it requires exact gradient computations ... More

Nonnegative Trigonometric Polynomials, Sturms Theorem, and Symbolic ComputationFeb 27 2014Apr 26 2016In this paper, we explain a procedure based on a classical result of Sturm that can be used to determine rigorously whether a given trigonometric polynomial is nonnegative in a certain interval or not. Many examples are given. This technique has been ... More

Sparse Bayesian Learning Using Approximate Message Passing with Unitary TransformationAug 17 2019Sparse Bayesian learning (SBL) can be implemented with low complexity based on the approximate message passing (AMP) algorithm. However, it is vulnerable to `difficult' measurement matrices as AMP can easily diverge. Damped AMP has been used to alleviate ... More

On the uniqueness of Ricci flowJun 21 2017Oct 20 2018In this note, we study the problem of uniqueness of Ricci flow on complete noncompact manifolds. We consider the class of solutions with curvature bounded above by C/t when t > 0. In paricular, we proved uniqueness if in addition the initial curvature ... More

Combining Partial Order Alignment and Progressive Near-Optimal AlignmentDec 15 2009Apr 10 2010In this paper, I proposed to utilize partial-order alignment technique as a heuristic method to cope with the state-space explosion problem in progressive near-optimal alignment. The key idea of my approach is a formal treatment of progressive partial ... More

Weak Convergence (IA). Sequences of Random VectorsOct 18 2016(English) This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in $\mathbb{R}^k$. In some places, a more general formulation in metric spaces is provided. It lays out the necessary foundation that ... More

Some examples of tilt-stable objects on threefoldsSep 12 2012We investigate properties and describe examples of tilt-stable objects on a smooth complex projective threefold. We give a structure theorem on slope semistable sheaves of vanishing discriminant, and describe certain Chern classes for which every slope ... More

A multipartite version of the Hajnal-Szemerédi theorem for graphs and hypergraphsAug 21 2011Dec 30 2012A perfect $K_t$-matching in a graph $G$ is a spanning subgraph consisting of vertex disjoint copies of $K_t$. A classic theorem of Hajnal and Szemer\'edi states that if $G$ is a graph of order $n$ with minimum degree $\delta(G) \ge (t-1)n/t$ and $t| n$, ... More

Misere Hackenbush FlowersDec 24 2012Jan 07 2013We show that any disjunctive sum of Hackenbush Flowers $G$ has as evil twin $G^* \in {G, G+*}$ such that the outcomes of $G$ under normal and mis\`ere play are the same as the outcomes of $G^*$ under mis\`ere and normal play respectively. We also show ... More

Order Parameters for Non-Abelian Gauge TheoriesNov 18 1994Owing to subtle issues concerning quantum fluctuations and gauge fixing, a formulation of a general procedure to specify the realization of non-Abelian gauge symmetry has evaded all earlier attempts. In this Letter, we discuss these subtleties and present ... More

Classical Communication Cost in Distributed Quantum Information Processing - A generalization of Quantum Communication ComplexityDec 02 1999Apr 14 2000We study the amount of classical communication needed for distributed quantum information processing. In particular, we introduce the concept of "remote preparation" of a quantum state. Given an ensemble of states, Alice's task is to help Bob in a distant ... More

Elusive Order Parameters for Non-Abelian Gauge TheoriesFeb 14 1995Sep 28 1995In this Letter, we construct a set of order parameters for non-Abelian gauge theories which probe directly the unbroken group and are free of the deficiencies caused by quantum fluctuations and gauge fixing which have plagued all previous attempts. These ... More

Scattering from Electroweak StringsApr 15 1994Apr 26 1994The scattering of a charged fermion from an electroweak string is studied. Owing to an amplification of the wave function at the core radius, the cross sections for helicity flip processes can be largely enhanced. For $0 <\sin^2 \theta_w < 1/2 $ (where ... More

Mathematical Foundations of Probability TheoryAug 06 2018In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited theory. The book ... More

Invariance principles for random sums of random variablesOct 09 2016This note investigates invariance principles for sums of N(nt) iid radom variables, where n is an integer, t is a positive real number and N(u) is a stochastic process with nonnegative integer values. We show that the sequence of sums of these random ... More