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Optimality Conditions and Finite Convergence of Lasserre's HierarchyJun 01 2012Apr 15 2013Lasserre's hierarchy is a sequence of semidefinite relaxations for solving polynomial optimization problems globally. This paper studies the relationship between optimality conditions in nonlinear programming theory and finite convergence of Lasserre's ... More

Symmetric Tensor Nuclear NormsMay 28 2016This paper studies nuclear norms of symmetric tensors. As recently shown by Friedland and Lim, the nuclear norm of a symmetric tensor can be achieved at a symmetric decomposition. We discuss how to compute symmetric tensor nuclear norms, depending on ... More

Nearly Low Rank Tensors and Their ApproximationsDec 23 2014The low rank tensor approximation problem (LRTAP) is to find a tensor whose rank is small and that is close to a given one. This paper studies the LRTAP when the tensor to be approximated is close to a low rank one. Both symmetric and nonsymmetric tensors ... More

Discriminants and Nonnegative PolynomialsFeb 10 2010Apr 23 2010For a semialgebraic set K in R^n, let P_d(K) be the cone of polynomials in R^n of degrees at most d that are nonnegative on K. This paper studies the geometry of its boundary. When K=R^n and d is even, we show that its boundary lies on the irreducible ... More

Polynomial Matrix Inequality and Semidefinite RepresentationAug 03 2009Mar 28 2011Consider a convex set S defined by a matrix inequality of polynomials or rational functions over a domain. The set S is called semidefinite programming (SDP) representable or just semidefinite representable if it equals the projection of a higher dimensional ... More

Generating Polynomials and Symmetric Tensor DecompositionsAug 25 2014Oct 02 2015This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial. The homogenization ... More

An Exact Jacobian SDP Relaxation for Polynomial OptimizationJun 11 2010Given polynomials f(x), g_i(x), h_j(x), we study how to minimize f on the semialgebraic set S = { x \in R^n: h_1(x)=...=h_{m_1}(x) =0, g_1(x) >= 0, ..., g_{m_2}(x) >= 0}. Let f_{min} be the minimum of f on S. Suppose S is nonsingular and f_{min} is achievable ... More

First Order Conditions for Semidefinite Representations of Convex Sets Defined by Rational or Singular PolynomialsJun 28 2008A set is called semidefinite representable or semidefinite programming (SDP) representable if it can be represented as the projection of a higher dimensional set which is represented by some Linear Matrix Inequality (LMI). This paper discuss the semidefinite ... More

The Hierarchy of Local Minimums in Polynomial OptimizationNov 17 2013Nov 25 2014This paper studies the hierarchy of local minimums of a polynomial in the space. For this purpose, we first compute H-minimums, for which the first and second order optimality conditions are satisfied. To compute each H-minimum, we construct a sequence ... More

Certifying Convergence of Lasserre's Hierarchy via Flat TruncationJun 13 2011Aug 06 2012This paper studies how to certify the convergence of Lasserre's hierarchy of semidefinite programming relaxations for solving multivariate polynomial optimization. We propose flat truncation as a general certificate for this purpose. Assume the set of ... More

The A-truncated K-moment problemOct 25 2012Aug 28 2014Let A be a finite subset of N^n, and K be a compact semialgebraic set in R^n. An A-tms is a vector y indexed by elements in A. The A-truncated K-moment problem (A-TKMP) studies whether a given A-tms y admits a K-measure or not. This paper proposes a numerical ... More

Linear Optimization with Cones of Moments and Nonnegative PolynomialsMay 13 2013Jul 17 2014Let A be a finite subset of N^n and R[x]_A be the space of real polynomials whose monomial powers are from A. Let K be a compact basic semialgebraic set of R^n such that R[x]_A contains a polynomial that is positive on K. Denote by P_A(K) the cone of ... More

Polynomial Optimization with Real VarietiesNov 08 2012Jun 04 2013We consider the optimization problem of minimizing a polynomial f(x) subject to polynomial constraints h(x)=0, g(x)>=0. Lasserre's hierarchy is a sequence of sum of squares relaxations for finding the global minimum. Let K be the feasible set. We prove ... More

Convex Hulls of Quadratically Parameterized Sets With Quadratic ConstraintsOct 11 2011Let V be a semialgebraic set parameterized by quadratic polynomials over a quadratic set T. This paper studies semidefinite representation of its convex hull by projections of spectrahedra (defined by linear matrix inequalities). When T is defined by ... More

Local Versus Global Conditions in Polynomial OptimizationMay 01 2015This paper reviews local and global optimality conditions in polynomial optimization. We summarize the relationship between them.

Sum of Squares Method for Sensor Network LocalizationMay 24 2006Sep 18 2007This paper has been withdrawn by the author due to its publication

Algebraic Degree of Polynomial OptimizationFeb 09 2008Consider the polynomial optimization problem whose objective and constraints are all described by multivariate polynomials. Under some genericity assumptions, %% on these polynomials, we prove that the optimality conditions always hold on optimizers, ... More

Real Eigenvalues of nonsymmetric tensorsMar 24 2015This paper discusses the computation of real Z-eigenvalues and H-eigenvalues of nonsymmetric tensors. A general nonsymmetric tensor has finitely many Z-eigenvalues, while there may be infinitely many ones for special tensors. In the contrast, every nonsymmetric ... More

On the complexity of Putinar's PositivstellensatzDec 14 2008We prove an upper bound on the degree complexity of Putinar's Positivstellensatz. This bound is much worse than the one obtained previously for Schm\"udgen's Positivstellensatz but it depends on the same parameters. As a consequence, we get information ... More

Regularization Methods for SDP Relaxations in Large Scale Polynomial OptimizationSep 19 2009Dec 05 2011We study how to solve semidefinite programming relaxations for large scale polynomial optimization. When interior-point methods are used, typically only small or moderately large problems could be solved. This paper studies regularization methods for ... More

On the complexity of Putinar's PositivstellensatzOct 14 2005Sep 18 2007This paper has been withdrawn by the author due to its publication

A Matrix Positivstellensatz with lifting polynomialsJan 15 2018Given the projections of two semialgebraic sets defined by polynomial matrix inequalities, it is in general difficult to determine whether one is contained in the other. To address this issue we propose a new matrix Positivstellensatz that uses lifting ... More

Matrix Cubes Parametrized by EigenvaluesApr 28 2008An elimination problem in semidefinite programming is solved by means of tensor algebra. It concerns families of matrix cube problems whose constraints are the minimum and maximum eigenvalue function on an affine space of symmetric matrices. An LMI representation ... More

Semidefinite Relaxations for Best Rank-1 Tensor ApproximationsAug 29 2013May 28 2014This paper studies the problem of finding best rank-1 approximations for both symmetric and nonsymmetric tensors. For symmetric tensors, this is equivalent to optimizing homogeneous polynomials over unit spheres; for nonsymmetric tensors, this is equivalent ... More

Positive Maps and Separable MatricesApr 24 2015Mar 26 2016A linear map between real symmetric matrix spaces is positive if all positive semidefinite matrices are mapped to positive semidefinite ones. A real symmetric matrix is separable if it can be written as a summation of Kronecker products of positive semidefinite ... More

Sparse SOS Relaxations for Minimizing Functions that are Summations of Small PolynomialsJun 20 2006Oct 05 2007This paper discusses how to find the global minimum of functions that are summations of small polynomials (``small'' means involving a small number of variables). Some sparse sum of squares (SOS) techniques are proposed. We compare their computational ... More

Positivity of Riesz Functionals and Solutions of Quadratic and Quartic Moment ProblemsAug 22 2009Sep 16 2009We employ positivity of Riesz functionals to establish representing measures (or approximate representing measures) for truncated multivariate moment sequences. For a truncated moment sequence $y$, we show that $y$ lies in the closure of truncated moment ... More

Structured Semidefinite Representation of Some Convex SetsFeb 13 2008Linear matrix Inequalities (LMIs) have had a major impact on control but formulating a problem as an LMI is an art. Recently there is the beginnings of a theory of which problems are in fact expressible as LMIs. For optimization purposes it can also be ... More

Sufficient and Necessary Conditions for Semidefinite Representability of Convex Hulls and SetsSep 25 2007Dec 07 2008A set $S\subseteq \re^n$ is called to be {\it Semidefinite (SDP)} representable if $S$ equals the projection of a set in higher dimensional space which is describable by some Linear Matrix Inequality (LMI). The contributions of this paper are: (i) For ... More

Semidefinite Representation of Convex SetsMay 28 2007Jul 21 2008Let $S =\{x\in \re^n: g_1(x)\geq 0, ..., g_m(x)\geq 0\}$ be a semialgebraic set defined by multivariate polynomials $g_i(x)$. Assume $S$ is convex, compact and has nonempty interior. Let $S_i =\{x\in \re^n: g_i(x)\geq 0\}$, and $\bdS$ (resp. $\bdS_i$) ... More

Shape Optimization of Transfer FunctionsNov 09 2004Sep 18 2007This paper has been withdrawn due to its publication

Minimum Ellipsoid Bounds for Solutions of Polynomial Systems via Sum of SquaresNov 05 2004Sep 18 2007This paper has been withdrawn by the authors due to its publication

A Semidefinite Approach for Truncated K-Moment ProblemsMay 02 2011Sep 06 2012A truncated moment sequence (tms) of degree d is a vector indexed by monomials whose degree is at most d. Let K be a semialgebraic set.The truncated K-moment problem (TKMP) is: when does a tms y admit a positive Borel measure supported? This paper proposes ... More

An elementary and constructive solution to Hilbert's 17th Problem for matricesOct 12 2006Oct 27 2006We give a short and elementary proof of a theorem of Procesi, Schacher and (independently) Gondard, Ribenboim that generalizes a famous result of Artin. Let $A$ be an $n \times n$ symmetric matrix with entries in the polynomial ring $\mathbb R[x_1,...,x_m]$. ... More

The Saddle Point Problem of PolynomialsSep 04 2018This paper studies the saddle point problem of polynomials. We give an algorithm for computing saddle points. It is based on solving Lasserre's hierarchy of semidefinite relaxations. Under some genericity assumptions on defining polynomials, we show that: ... More

Semidefinite Representation of the $k$-EllipseJan 31 2007The $k$-ellipse is the plane algebraic curve consisting of all points whose sum of distances from $k$ given points is a fixed number. The polynomial equation defining the $k$-ellipse has degree $2^k$ if $k$ is odd and degree $2^k{-}\binom{k}{k/2}$ if ... More

Bilevel Polynomial Programs and Semidefinite Relaxation MethodsAug 27 2015Nov 03 2016A bilevel program is an optimization problem whose constraints involve another optimization problem. This paper studies bilevel polynomial programs (BPPs), i.e., all the functions are polynomials. We reformulate BPPs equivalently as semi-infinite polynomial ... More

Minimizing Polynomials Over Semialgebraic SetsFeb 17 2005This paper concerns a method for finding the minimum of a polynomial on a semialgebraic set, i.e., a set in $\re^m$ defined by finitely many polynomial equations and inequalities, using the Karush-Kuhn-Tucker (KKT) system and sum of squares (SOS) relaxations. ... More

Global Minimization of Rational Functions and the Nearest GCDsJan 05 2006Sep 18 2007This paper has been withdrawn by the authors due to its publication

The Algebraic Degree of Semidefinite ProgrammingNov 19 2006Sep 08 2008Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically, this degree counts ... More

Tensor Eigenvalue Complementarity ProblemsJan 20 2016This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial optimization. When one ... More

Bilevel Polynomial Programs and Semidefinite Relaxation MethodsAug 27 2015May 24 2016A bilevel program is an optimization problem whose constraints involve another optimization problem. This paper studies bilevel polynomial programs (BPPs), i.e., all the functions are polynomials. We reformulate BPPs equivalently as semi-infinite polynomial ... More

Minimizing Polynomials via Sum of Squares over the Gradient IdealNov 15 2004Sep 18 2007This paper has been withdrawn by the authors due to its publication

Nonlinear compressed sensing based on composite mappings and its pointwise linearizationJun 07 2015Classical compressed sensing (CS) allows us to recover structured signals from far few linear measurements than traditionally prescribed, thereby efficiently decreasing sampling rates. However, if there exist nonlinearities in the measurements, is it ... More

Electronic Instability and Anharmonicity in SnSeApr 24 2016May 04 2016The binary compound SnSe exhibits record high thermoelectric performance, largely because of its very low thermal conductivity. The origin of the strong phonon anharmonicity leading to the low thermal conductivity of SnSe is investigated through first-principles ... More

Semidefnite Relaxation Bounds for Indefinite Homogeneous Quadratic OptimizationJan 02 2007In this paper we study the relationship between the optimal value of a homogeneous quadratic optimization problem and that of its Semidefinite Programming (SDP) relaxation. We consider two quadratic optimization models: (1) $\min \{x^* C x \mid x^* A_k ... More

First-principles theory and calculation of flexoelectricityJun 29 2013Oct 31 2013We develop a general and unified first-principles theory of piezoelectric and flexoelectric tensor, formulated in such a way that the tensor elements can be computed directly in the context of density-functional calculations, including electronic and ... More

Mapping the energy surface of PbTiO3 in multidimensional electric-displacement spaceJun 28 2011Sep 15 2011In recent years, methods have been developed that allow first-principles electronic-structure calculations to be carried out under conditions of fixed electric field. For some purposes, however, it is more convenient to work at fixed electric displacement ... More

All Real Eigenvalues of Symmetric TensorsMar 14 2014Dec 13 2014This paper studies how to compute all real eigenvalues of a symmetric tensor. As is well known, the largest or smallest eigenvalue can be found by solving a polynomial optimization problem, while the other middle eigenvalues can not. We propose a new ... More

The noncommutative Waring problemMar 14 2019This paper poses and treats a noncommutative version of the classical Waring problem for polynomials. That is, for a homogeneous \nc \ polynomial $p$, we find a condition equivalent to $p$ being expressible as sums of powers of homogeneous \nc \ polynomials. ... More

Free Semidefinite Representation of Matrix Power FunctionsMay 18 2013Oct 09 2014Consider the matrix power function X^p defined over the cone of positive definite matrices S^{n}_{++}. It is known that X^p is convex over S^{n}_{++} if p is in [-1,0] or [1,2] and X^p is concave over S^{n}_{++} if p is in [0,1]. We show that the hypograph ... More

Adaptive Channel Allocation Spectrum Etiquette for Cognitive Radio NetworksFeb 07 2006In this work, we propose a game theoretic framework to analyze the behavior of cognitive radios for distributed adaptive channel allocation. We define two different objective functions for the spectrum sharing games, which capture the utility of selfish ... More

Logic Blog 2014Apr 30 2015The 2014 Logic Blog starts with open questions from the May IMS program in Singapore. It contains results on randomness, including answers to some open questions in higher randomness. There are structural results on equivalence relations, and metric spaces. ... More

Variational bounds on the ground-state energy of three electrons and one hole in two-dimensionDec 31 2000Jan 09 2001We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon ^2 \hbar ^2 ... More

An Alternative Explanation on the Two Relaxation Rates in Cuprate SuperconductorsNov 22 2000Dec 05 2000Transport properties of high transition temperature (high-Tc) superconductors have been shown to have two distinct relaxation rates. We argue that this apparent inconsistence can be resolved with an effective carrier density n linear in temperature T. ... More

Intrinsic construction of invariant functions on simple Lie algebrasMar 05 2013Apr 06 2014An algorithm for constructing primitive adjoint-invariant functions on a complex simple Lie algebra is presented. The construction is intrinsic in the sense that it does not resort to any representation. A primitive invariant function on the whole Lie ... More

On the Minimum Area of Null Homotopies of Curves Traced TwiceNov 29 2014Dec 31 2014We provide an efficient algorithm to compute the minimum area of a homotopy between two closed plane curves, given that they divide the plane into finite number of regions. For any positive real number $\varepsilon>0$, we construct a closed plane curve ... More

A Functor Converting Equivariant Homology to HomotopyMar 18 2006Aug 01 2007In this paper, we prove an equivariant version of the classical Dold-Thom theorem. Associated to a finite group, a CW-complex on which this group acts and a covariant coefficient system in the sense of Bredon, we functorially construct a topological abelian ... More

An Application of Maximum Principle to space-like Hypersurfaces with Constant Mean Curvature in Anti-de Sitter SpaceAug 16 2011In this paper, we study complete hypersurfaces with constant mean curvature in anti-de Sitter space $H^{n+1}_1(-1)$. we prove that if a complete space-like hypersurface with constant mean curvature $x:\mathbf M\rightarrow H^{n+1}_1(-1) $ has two distinct ... More

On Sha's secondary Chern-Euler classJan 17 2009Feb 08 2010For a manifold with boundary, the restriction of Chern's transgression form of the Euler curvature form over the boundary is closed. Its cohomology class is called the secondary Chern-Euler class and used by Sha to formulate a relative Poincar\'e-Hopf ... More

Coding Methods in Computability Theory and Complexity TheoryAug 29 2013A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees, it has been ... More

Regularity of A Complex Monge-Ampère Equation on Hermitian ManifoldsNov 18 2013We obtain higher order estimates for a parabolic flow on a compact Hermitian manifold. As an application, we prove that a bounded $\hat{\omega}$-plurisubharmonic solution of an elliptic complex Monge-Amp\`{e}re equation is smooth under an assumption on ... More

Toda field theories and integral curves of standard differential systemsOct 16 2015Aug 08 2016This paper establishes three relations between the Toda field theory associated to a simple Lie algebra and the integral curves of the standard differential system on the corresponding complete flag variety. The motivation comes from the viewpoint on ... More

Solving Toda field theories and related algebraic and differential propertiesMar 05 2013Toda field theories are important integrable systems. They can be regarded as constrained WZNW models, and this viewpoint helps to give their explicit general solutions, especially when a Drinfeld-Sokolov gauge is used. The main objective of this paper ... More

Topologically slice $(1,1)$-knots which are not smoothly sliceJan 23 2019We prove that there are infinitely many $(1,1)$-knots which are topologically slice, but not smoothly slice, which was a conjecture proposed by B\'ela Andr\'as R\'acz.

Zeta functions of trinomial curves and maximal curvesAug 10 2014We determine the zeta functions of trinomial curves in terms of Gauss sums and Jacobi sums, and we obtain an explicit formula of the genus of a trinomial curve over a finite field, then we study the conditions for a trinomial curve to be a maximal curve ... More

Regular Submanifolds in the Conformal Space ${\mathbb Q}^n_p$Aug 15 2011There is a Lorenzian group acting on the conformal space ${\mathbb Q}^n_p$. We study the regular submanifolds in the conformal space ${\mathbb Q}^n_p$ and construct general submanifold theory in the conformal space ${\mathbb Q}^n_p$. Finally we give the ... More

On transgression in associated bundlesJun 22 2009Feb 03 2011We formulate and prove a formula for transgressing characteristic forms in general associated bundles following a method of Chern. As applications, we derive D. Johnson's explicit formula for such general transgression and Chern's first transgression ... More

A stochastic approach to a new type of parabolic variational inequalitiesMar 21 2012Mar 23 2012We study the following quasilinear partial differential equation with two subdifferential operators: $${\frac{\partial u}{\partial s}(s,x)} + (\mathcal{L}u)(s,x,u(s,x),(\nabla u(s,x))^\ast\sigma(s,x,u(s,x))) + f(s,x,u(s,x),(\nabla u(s,x))^\ast\sigma(s,x,u(s,x))) ... More

On isomorphism numbers of "$F$-crystals"Mar 09 2014In this note, we show that for an ``$F$-crystal" (the equal characteristic analogue of $F$-crystals), its {\it isomorphism number} and its {\it level torsion} coincide. This confirms a conjure of Vasiu \cite{Va} in the equal characteristic case.

The convolution algebra structure on $K^G(\mathcal{B} \times \mathcal{B})$Nov 08 2011We show that the convolution algebra $K^G(\mathcal{B} \times \mathcal{B})$ is isomorphic to the Based ring of the lowest two-sided cell of the extended affine Weyl group associated to $G$, where $G$ is a connected reductive algebraic group over the field ... More

Logic Blog 2012Feb 15 2013The 2012 logic blog has focussed on the following: Randomness and computable analysis/ergodic theory; Systematizing algorithmic randomness notions; Traceability; Higher randomness; Calibrating the complexity of equivalence relations from computability ... More

Logic Blog 2011Mar 23 2014This year's logic blog has focussed on: 1. Demuth randomness 2. traceability 3. The connection of computable analysis and randomness 4. $K$-triviality in metric spaces.

Logic Blog 2013Mar 23 2014Jun 19 2014The 2013 logic blog has focussed on the following: 1. Higher randomness. Among others, the Borel complexity of $\Pi^1_1$ randomness and higher weak 2 randomness is determined. 2. Reverse mathematics and its relationship to randomness. For instance, what ... More

Calibrating the complexity of Delta 2 sets via their changesFeb 03 2013The computational complexity of a Delta 2 set will be calibrated by the amount of changes needed for any of its computable approximations. Firstly, we study Martin-Loef random sets, where we quantify the changes of initial segments. Secondly, we look ... More

The complexity of isomorphism between countably based profinite groupsApr 03 2016A topological group G is profinite if it is compact and totally disconnected. Equivalently, G is the inverse limit of a surjective system of finite groups carrying the discrete topology. We discuss how to represent a countably based profinite group as ... More

Rescaling Limits in Non-Archimedean DynamicsDec 03 2016Suppose $\{f_t\}$ is an analytic one-parameter family of rational maps defined over a non-Archimedean field $K$. We prove a finiteness theorem for the set of rescalings for $\{f_t\}$. This complements results of J. Kiwi.

Secondary Chern-Euler forms and the Law of Vector FieldsSep 25 2009Aug 14 2010The Law of Vector Fields is a term coined by Gottlieb for a relative Poincar\'e-Hopf theorem. It was first proved by Morse and expresses the Euler characteristic of a manifold with boundary in terms of the indices of a generic vector field and the inner ... More

Secondary Chern-Euler class for general submanifoldJun 22 2009Jul 13 2009We define and study the secondary Chern-Euler class for a general submanifold of a Riemannian manifold. Using this class, we define and study index for a vector field with non-isolated singularities on a submanifold. As an application, our studies give ... More

Meromorphic cubic differentials and convex projective structuresMar 09 2015Extending the Labourie-Loftin correspondence, we establish, on any punctured oriented surface of finite type, a one-to-one correspondence between convex projective structures with specific types of ends and punctured Riemann surface structures endowed ... More

The quasi-Poisson Goldman formulaJan 22 2013Feb 10 2013We prove a quasi-Poisson bracket formula for the space of representations of the fundamental groupoid of a surface with boundary, which generalizes Goldman's Poisson bracket formula. We also deduce a similar formula for quasi-Poisson cross-sections.

On characteristic integrals of Toda field theoriesMar 05 2013Apr 06 2014Characteristic integrals of Toda field theories associated to simple Lie algebras are presented in the most explicit forms, both in terms of the formulas and in terms of the proofs.

Karoubi's Construction for Motivic Cohomology OperationsMar 19 2006We use an analogue of Karoubi's construction in the motivic situation to give some cohomology operations in motivic cohomology. We prove many properties of these operations, and we show that they coincide, up to some nonzero constants, with the reduced ... More

Calculus of Cost FunctionsMar 05 2017Cost functions provide a framework for constructions of sets Turing below the halting problem that are close to computable. We carry out a systematic study of cost functions. We relate their algebraic properties to their expressive strength. We show that ... More

On the Hilbert geometry of simplicial Tits setsNov 05 2011Jul 11 2014The moduli space of convex projective structures on a simplicial hyperbolic Coxeter orbifold is either a point or the real line. Answering a question of M. Crampon, we prove that in the latter case, when one goes to infinity in the moduli space, the entropy ... More

Logic Blog 2015fFeb 14 2016The 2015 Logic Blog contains a large variety of results connected to logic, some of them unlikely to be submitted to a journal. For the first time there is a group theory part. There are results in higher randomness, and in computable ergodic theory.

Subtle Features in Transport Properties: Evidence for a Possible Coexistence of Holes and Electrons in Cuprate SuperconductorsMar 06 2000Mar 08 2000Transport properties of high transition temperature (high Tc) cuprate superconductors are investigated within a two-band model. The doping dependent Hall coefficients of La_{2-x}Sr_xCuO_4 (LSCO) and Nd_{2-x}Ce_xCuO_4 (NCCO) are explained by assuming the ... More

X-rays from Proton Bremsstrahlung: Evidence from Fusion Reactors and Its Implication in AstrophysicsOct 20 2009In a fusion reactor, a proton and a neutron generated in previous reactions may again fuse with each other. Or they can in turn fuse with or be captured by an un-reacted deuteron. The average center-of-mass (COM) energy for such reaction is around 10 ... More

Lowness, randomness, and computable analysisJul 24 2016Analytic concepts contribute to our understanding of randomness of reals via algorithmic tests. They also influence the interplay between randomness and lowness notions. We provide a survey, written on the occasion of Rod Downey's 60th birthday.

Entropy degeneration of convex projective surfacesMar 15 2015Nov 17 2015We show that the volume entropy of the Hilbert metric on a closed convex projective surface tends to zero as the corresponding Pick differential tends to infinity. The proof is based on the theorem, due to Benoist and Hulin, that the Hilbert metric and ... More

The Space-like Surfaces with Vanishing Conformal Form in the Conformal SpaceAug 15 2011The conformal geometry of surfaces in the conformal space $\mathbf Q^n_1$ is studied. We classify the space-like surfaces in $\mathbf Q^n_1$ with vanishing conformal form up to conformal equivalence.

Non-monotonic thickness dependence of Curie temperature and ferroelectricity in Two-dimensional SnTe filmMay 18 2018Recently, the observation of atomic thin film SnTe with a Curie temperature (Tc) higher than that of the bulk (Chang et. al., Science 353, 274 (2016)) has boosted the research on two-dimensional (2D) ferroic materials tremendously. However, the origin ... More

Analytical method to determine flexoelectric coupling coefficient at nanoscaleApr 30 2016Flexoelectricity is defined as the coupling between strain gradient and polarization, which is expected to be remarkable at nanoscale. However, measuring the flexoelectricity at nanoscale is challenging. In the present work, an analytical method for measuring ... More

Spin-phonon coupling effects in transition-metal perovskites:a DFT+$U$ and hybrid-functional studyDec 21 2011Feb 03 2012Spin-phonon coupling effects, as reflected in phonon frequency shifts between ferromagnetic (FM) and G-type antiferromagnetic (AFM) configurations in cubic CaMnO$_3$, SrMnO$_3$, BaMnO$_3$, LaCrO$_3$, LaFeO$_3$ and La$_2$(CrFe)O$_6$, are investigated using ... More

Anti-lock Brake System for Integrated Electric Parking Brake Actuator Based on Sliding-mode ControlOct 26 2018Nov 08 2018Integrated electric parking brake (iEPB) is popularizing on passenger cars due to its easier operation and automatic functions. As a parking brake, EPB have to act as the secondary brake system in case of hydraulic brake failure. To guarantee the stability ... More

Non-Greedy L21-Norm Maximization for Principal Component AnalysisMar 28 2016Principal Component Analysis (PCA) is one of the most important unsupervised methods to handle high-dimensional data. However, due to the high computational complexity of its eigen decomposition solution, it hard to apply PCA to the large-scale data with ... More

Latent Regression Bayesian Network for Data RepresentationJun 15 2015Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the intractable inference. ... More

Linear restrictions on cone polynomialsOct 15 2015For a set $S$ of $d$ points in the $n$-dimensional projective space over a field of characteristic zero, we prove that the polynomials of degree $d$ whose zero sets are cones over $S$ do not span the vector space of polynomials of degree $d$ vanishing ... More

b -> s gamma in the left-right supersymmetric modelFeb 15 2002The rare decay $b \to s \gamma$ is studied in the left-right supersymmetric model. We give explicit expressions for all the amplitudes associated with the supersymmetric contributions coming from gluinos, charginos and neutralinos in the model to one-loop ... More

Closure of resource-bounded randomness notions under polynomial time permutationsSep 26 2017An infinite bit sequence is called recursively random if no computable strategy betting along the sequence has unbounded capital. It is well-known that the property of recursive randomness is closed under computable permutations. We investigate analogous ... More