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Polynomial-time Isomorphism Test for Groups with Abelian Sylow Towers
polynomial-time algorithm, group isomorphism, solvable group
2012/12/3
We consider the problem of testing isomorphism of groups of order n given by Cayley tables. The trivial nlog n bound on the time complexity for the general case has not been improved over the past fou...
On the Distribution of Critical Points of a Polynomial
Critical Points Polynomial Probability
2012/7/11
This paper proves that if points $Z_1,Z_2,...$ are chosen independently and identically using some measure $\mu$ from the unit circle in the complex plane, with $p_n(z) = (z-Z_1)(z-Z_2)...(z-Z_n)$, th...
A nilpotent IP polynomial multiple recurrence theorem
ergodic Ramsey theory IP-sets nilpotent Hales-Jewett theorem nilpotent Szemeredi theorem
2012/6/14
We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibm...
On the algebraic K-theory of truncated polynomial algebras in several variables
algebraic K-theory truncated polynomial algebras several variables Algebraic Topology
2012/6/14
We consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables, K(k[x_1, ..., x_n]/(x_1^a_1, ..., x_n^a_n)). This naturally leads to a new generalization of the bi...
A quasi-tree expansion of the Krushkal polynomial
quasi-tree expansion Krushkal polynomial Combinatorics
2012/5/24
We introduce a generalization of the Krushkal polynomial to nonorientable surfaces, and prove that this polynomial has a natural quasi-tree expansion. This generalized Krushkal polynomial contains the...
Symmetries of Julia sets of polynomial skew products on C^2
Complex dynamics skew product Green function
2012/4/18
We consider the symmetries of Julia sets of polynomial skew products on C^2, which are birationally conjugate to rotational products. Our main results give the classification of the polynomial skew pr...
A Structure Theorem for Poorly Anticoncentrated Gaussian Chaoses and Applications to the Study of Polynomial Threshold Functions
Structure Theorem Anticoncentrated Gaussian Chaoses Study of Polynomial Threshold Functions
2012/4/18
We prove a structural result for degree-$d$ polynomials. In particular, we show that any degree-$d$ polynomial, $p$ can be approximated by another polynomial, $p_0$, which can be decomposed as some fu...
Computation of the Smith Form for Multivariate Polynomial Matrices Using Maple
Smith Form Unimodular Equivalence Quillen-Suslin Theorem Maple
2013/1/30
In this paper we show how the transformations associated with the reduction to the Smith form of some classes of multivariate polynomial matrices are computed. Using a Maple implementation of a constr...
Postcritical sets and saddle basic sets for Axiom A polynomial skew products on C^2
Postcritical sets saddle basic sets Axiom A polynomial skew products C^2
2012/2/29
Investigating the link between postcritical behaviors and the relations of saddle basic sets for Axiom A polynomial skew products on C^2, we characterize various properties concerning the three kinds ...
Simple G-graded algebras and their polynomial identities
graded algebra polynomial identity
2011/9/19
Abstract: Let G be any group and F an algebraically closed field of characteristic zero. We show that any two G-graded finite dimensional G-simple algebras over F are G-graded isomorphic if and only i...
Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups
Residually nilpotent group entropy of automorphisms of groups pseudo-Anosov dilatation
2011/9/15
Abstract: We study the word length entropy of automorphisms of residually nilpotent groups, and how the entropy of such group automorphisms relates to the entropy of induced automorphisms on various n...
Local Polynomial Regression Based on Functional Data
Local polynomial smoothing derivative estimation functional data sampling density optimal bandwidth asymptotic normality
2011/9/15
Abstract: Suppose that $n$ statistical units are observed, each following the model $Y(x_j)=m(x_j)+ \epsilon(x_j),\, j=1,...,N,$ where $m$ is a regression function, $0 \leq x_1 <...
The twisted Alexander polynomial for finite abelian covers over three manifolds with boundary
Reidemeister torsion:Twisted Alexander polynomial:branched cover:links:Homology orientation
2011/9/13
Abstract: We consider a sign--determined Reidemeister torsion with multivariables for three manifolds with boundary. This invariant is often called the twisted Alexander polynomial when we consider li...
Approximate Interval Method for Epistemic Uncertainty Propagation using Polynomial Chaos and Evidence Theory
Approximate Interval Method Epistemic Uncertainty Propagation Evidence Theory
2011/9/29
Abstract: The paper builds upon a recent approach to find the approximate bounds of a real function using Polynomial Chaos expansions. Given a function of random variables with compact support probabi...
Controller Synthesis for Robust Invariance of Polynomial Dynamical Systems using Linear Programming
Controller Synthesis Robust Invariance Polynomial Dynamical Systems Linear Programming
2011/8/30
Abstract: In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances and with input constraints. More precisely, we aim at synth...