6,818 research outputs found
Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs
This paper deals with linear-quadratic optimal control problems constrained by a parametric or stochastic elliptic or parabolic PDE. We address the (difficult) case that the state equation depends on a countable number of parameters i.e., on with , and that the PDE operator may depend non-affinely on the parameters. We consider tracking-type functionals and distributed as well as boundary controls. Building on recent results in [CDS1, CDS2], we show that the state and the control are analytic as functions depending on these parameters . We
establish sparsity of generalized polynomial chaos (gpc) expansions of both, state and control, in terms of the stochastic coordinate sequence of the random inputs, and prove convergence rates of best -term truncations of these expansions. Such truncations are the key for subsequent computations since they do {\em not} assume that the stochastic input data has a finite expansion. In the follow-up paper [KS2], we explain two methods how such best -term truncations can practically be computed, by greedy-type algorithms
as in [SG, Gi1], or by multilevel Monte-Carlo methods as in
[KSS]. The sparsity result allows in conjunction with adaptive wavelet Galerkin schemes for sparse, adaptive tensor discretizations of control problems constrained by linear elliptic and parabolic PDEs developed in [DK, GK, K], see [KS2]
A Family of Binary Sequences with Optimal Correlation Property and Large Linear Span
A family of binary sequences is presented and proved to have optimal
correlation property and large linear span. It includes the small set of Kasami
sequences, No sequence set and TN sequence set as special cases. An explicit
lower bound expression on the linear span of sequences in the family is given.
With suitable choices of parameters, it is proved that the family has
exponentially larger linear spans than both No sequences and TN sequences. A
class of ideal autocorrelation sequences is also constructed and proved to have
large linear span.Comment: 21 page
Discrepancy convergence for the drunkard's walk on the sphere
We analyze the drunkard's walk on the unit sphere with step size theta and
show that the walk converges in order constant/sin^2(theta) steps in the
discrepancy metric. This is an application of techniques we develop for
bounding the discrepancy of random walks on Gelfand pairs generated by
bi-invariant measures. In such cases, Fourier analysis on the acting group
admits tractable computations involving spherical functions. We advocate the
use of discrepancy as a metric on probabilities for state spaces with isometric
group actions.Comment: 20 pages; to appear in Electron. J. Probab.; related work at
http://www.math.hmc.edu/~su/papers.htm
Remarks on a cyclotomic sequence
We analyse a binary cyclotomic sequence constructed via generalized cyclotomic classes by Bai et al. (IEEE Trans Inforem Theory 51: 1849-1853, 2005). First we determine the linear complexity of a natural generalization of this binary sequence to arbitrary prime fields. Secondly we consider k-error linear complexity and autocorrelation of these sequences and point out certain drawbacks of this construction. The results show that the parameters for the sequence construction must be carefully chosen in view of the respective application
The Lattice Dynamics of Completely Entangled States and its Application to Communication Schemes
(Presented at conference on Fundamental Problems in Physics - UMBC - June
1994) It is shown that among the orthogonal sets of EPR (completely entangled)
states there is a unique basis (up to equivalence) that is a also a perfectly
resolved set of coherent states with respect to a pair of complementary
observables. This basis defines a lattice phase space in which quadratic
Hamiltonians constructed from the observables induce site-to-site hopping at
discrete time intervals. When recently suggested communication
schemes\cite{BENa} are adapted to the lattice they are greatly enhanced,
because the finite Heisenberg group structure allows dynamic generation of
signal sequences using the quadratic Hamiltonians. We anticipate the
possibility of interferometry by determining the relative phases between
successive signals produced by the simplest Hamiltonians of this type, and we
show that they exhibit a remarkable pattern determined by the number-theoretic
Legendre symbol.Comment: 10 pages, Latex, 27.5
Modelling the formation of phonotactic restrictions across the mental lexicon
Experimental data shows that adult learners of an artificial language with a phonotactic restriction learned this restriction better when being trained on word types (e.g. when they were presented with 80 different words twice each) than when being trained on word tokens (e.g. when presented with 40 different words four times each) (Hamann & Ernestus submitted). These findings support Pierrehumbertâs (2003) observation that phonotactic co-occurrence restrictions are formed across lexical entries, since only lexical levels of representation can be sensitive to type frequencies
- âŠ