Browsing Publications  Mathematics, Statistics, and Computer Science by Issue Date
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Classification of δInvariant Amalgamation Classes
(Journal of Symbolic Logic, 199912)Hrushovski's generalization of the Fraisse construction has provided a rich source of examples in model theory, model theoretic algebra and random graph theory. The construction assigns to a dimension function s and a class ... 
OPTIMAL DESIGNS FOR 2(k) FACTORIAL EXPERIMENTS WITH BINARY RESPONSE.
(Academia Sinica, Institute of Statistical Science, 200101)We consider the problem of obtaining Doptimal designs for factorial experiments with a binary response and k qualitative factors each at two levels. We obtain a characterization of locally Doptimal designs. We then develop ... 
Notes on Quasiminimality and Excellence
(Association for Symbolic Logic, 200409)This paper ties together much of the model theory of the last 50 years. Shelaha's attempts to generalize the Morley theorem beyond Þrst order logic led to the notion of excellence, which is a key to the structure theory ... 
Subsets of Superstable Structures are Weakly Benign
(Association for Symbolic Logic, 200503)Baizhanov and Baldwin [1] introduce the notions of benign and weakly benign sets to investigate the preservation of stability by naming arbitrary subsets of a stable structure. They connect the notion with work of Baldwin, ... 
The Metamathematics of Random Graphs
(Elsevier Masson, 2006)We explain and summarize the use of logic to provide a uniform perspective for studying limit laws on finite probability spaces. This work connects developments in stability theory, finite model theory, abstract model ... 
Categoricity, Amalgamation, and Tameness
(Springer Verlag, 2007)Theorem: For each 2 ≤ k < ω there is an Lω1,ω sentence ϕk such that (1) ϕk is categorical in μ if μ≤ℵk−2; (2) ϕk is not ℵk−2Galois stable (3) ϕk is not categorical in any μ with μ>ℵk−2; (4) ϕk has the disjoint ... 
On the minimum number of colors for knots.
(Elsevier, 200801)In this article we take up the calculation of the minimum number of colors needed to produce a nontrivial coloring of a knot. This is a knot invariant and we use the torus knots of type (2, n) as our case study. We ... 
Examples of NonLocality
(Association for Symbolic Logic, 200809)We use kappafree but not Whitehead Abelian groups to construct Abstract Elementary Classes (AEC) which satisfy the amalgamation property but fail various conditions on the locality of Galoistypes. We introduce the notion ... 
The Amalgamation Spectrum
(Association for Symbolic Logic, 200909)We study when classes can have the disjoint amalgamation property for a proper initial segment of cardinals. Theorem A For every natural number k, there is a class Kk defined by a sentence in Lω₁,ω that has no models ... 
Traveling waves in deep water with gravity and surface tension
(Society for Industrial and Applied Mathematics, 2010)This paper is concerned with the simulation of periodic traveling deepwater freesurface water waves under the influence of gravity and surface tension in two and three dimensions. A variety of techniques is utilized, ... 
Sparse supervised dimension reduction in high dimensional classification
(Institute of Mathematical Statistics, 2010)Supervised dimension reduction has proven effective in analyzing data with complex structure. The primary goal is to seek the reduced subspace of minimal dimension which is sufficient for summarizing the data structure of ... 
Dynamics of threedimensional gravitycapillary solitary waves in deep water
(Society for Industrial and Applied Mathematics, 2010)A model equation for gravitycapillary waves in deep water is proposed. This model is a quadratic approximation of the deep water potential flow equations and has wavepackettype solitary wave solutions. The model equation ... 
Nuclearmagneticresonance quantum calculations of the Jones polynomial
(American Physical Society, 201003)The repertoire of problems theoretically solvable by a quantum computer recently expanded to include the approximate evaluation of knot invariants, specifically the Jones polynomial. The experimental implementation of this ... 
Local holomorphic De Rham cohomology
(International Press, 201003)Local holomorphic De Rham cohomology introduced in this paper and punctured local holomorphic De Rham cohomology introduced by HuangLukYau are two important local invariants for varieties with isolated singularities. We ... 
A Rapid Method for Characterization of Protein Relatedness Using Feature Vectors
(Public Library of Science, 20100305)We propose a feature vector approach to characterize the variation in large data sets of biological sequences. Each candidate sequence produces a single feature vector constructed with the number and location of amino acids ... 
Multivariable Hodge Theoretical Invariants of Germs of Plane Curves
(World Scientific Publishing, 20100419)We describe methods for calculation of polytopes of quasiadjunction for plane curve singularities which are invariants giving a Hodge theoretical refinements of the zero sets of multivariable Alexander polynomials. In ... 
Linear Series on Ribbons
(American Mathematical Society, 20100518)A ribbon is a double structure on P1. The geometry of a ribbon is closely related to that of a smooth curve. In this paper we consider linear series on ribbons. Our main result is an explicit determinantal description for ... 
Numerical Estimation of the Relative Entropy of Entanglement
(American Physical Society, 20101129)We propose a practical algorithm for the calculation of the relative entropy of entanglement (REE), defined as the minimum relative entropy between a state and the set of states with positive partial transpose. Our algorithm ... 
Complete reducibility theorems for modules over pointed Hopf algebras
(Elsevier, 20101201)We investigate the representation theory of a large class of pointed Hopf algebras, extending results of Lusztig and others. We classify all simple modules in a suitable category and determine the weight multiplicities; ... 
Counting substructures I: Color critical graphs
(Elsevier, 20101201)Let F be a graph which contains an edge whose deletion reduces its chromatic number. We prove tight bounds on the number of copies of F in a graph with a prescribed number of vertices and edges. Our results extend those ...