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AMENABILITY AND RAMSEY THEORY
RAMSEY THEORY
2015/8/17
The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey theoretic reformulation of amenability constitutes a...
Linear matrix inequalities in system and control theory
Linear matrix inequality system the control theory and linear matrix inequality affine combination symmetric positive semidefinite matrix
2015/8/12
A wide variety of problems in system and control theory can be formulated (or reformulated) as convex optimization problems involving linear matrix inequalities, that is, constraints requiring an affi...
History of linear matrix inequalities in control theory
Linear matrix inequality control control theory tool control applications
2015/8/12
The purpose of this paper is to give a historical view of Linear Matrix Inequalities in control and system theory. Not surprisingly, it appears that LMIs have been involved in some of the major events...
Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
Electronic structure Kohn–Sham density functional theory Discontinuous Galerkin Adaptive local basis set Enrichment functions Eigenvalue problem
2015/7/14
Kohn–Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn–Sham Hamiltonian generally result...
Optimized local basis set for Kohn–Sham density functional theory
Electronic structure Kohn–Sham density functional theory Optimized local basis set Discontinuous Galerkin Trace minimization Molecular dynamics Pulay force GMRES Preconditioning
2015/7/14
We develop a technique for generating a set of optimized local basis functions to solve models in the Kohn–Sham density functional theory for both insulating and metallic systems. The optimized local ...
Element orbitals for Kohn-Sham density functional theory
Element orbitals Kohn-Sham density functional theory
2015/7/14
We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as plane wa...
A SHORT PROOF OF THE CONJECTURE WITHOUT GROMOV-WITTEN THEORY: HURWITZ THEORY AND THE MODULI OF CURVES
HURWITZ THEORY THE MODULI OF CURVES
2015/7/14
I. P. GOULDEN, D. M. JACKSON AND R. VAKILConjecture. The
approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the \polynomiality" of Hurwitz numbers, from which we pick...
A SHORT PROOF OF THE CONJECTURE WITHOUT GROMOV-WITTEN THEORY: HURWITZ THEORY AND THE MODULI OF CURVES
HURWITZ THEORY THE MODULI OF CURVES
2015/7/14
I. P. GOULDEN, D. M. JACKSON AND R. VAKILConjecture. The
approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the \polynomiality" of Hurwitz numbers, from which we pick...
From shuffling cards to walking around the building:An Inetroduction to modern markov chain theory
Shuffle CARDS walk around buildings markov chain theory
2015/7/14
From shuffling cards to walking around the building:An Inetroduction to modern markov chain theory。
Consistency of Bayes Estimates for Nonparametric Regression: Normal Theory
Consistency Bayes estimates model selection binary regression
2015/7/14
Performance characteristics of Bayes estimates are studied. More exactly, for each subject in a data
set, let 5 be a vector of binary covariates and let Y be a normal response variable, with
E{YIE...
A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method:Theory and Insights
Differential Equation Modeling Nesterov’s Accelerated Gradient Method
2015/7/8
We derive a second-order ordinary differential equation (ODE), which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can...
This paper records the path of a letter that Marty Isaacs wrote to a stranger. The tools in the letter are used to illustrate a di erent way of studying random walk on the Heisenberg group. The author...
Hopf algebras and Markov chains: Two examples and a theory
By-products hopf algebra markov chain complex lie algebra combination
2015/7/7
The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied meth...
CARRIES, GROUP THEORY, AND ADDITIVE COMBINATORICS
Data occurred along the equalization algorithm minimize proportion
2015/7/7
When numbers are added in the usual way carries occur along the route. These carries cause a mess and it is natural to seek ways to minimize them. This paper proves that balanced arithmetic minimizes ...
Derived Representation Theory and the Algebraic K-theory of Fields
Algebraic K-theory of Fields Derived Representation Theory
2015/7/7
Quillen’s higher algebraic K-theory for fields F has been the object of intense
study since their introduction in 1972 [26]. The main direction of research has
been the construction of “descen...