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The glassy phase of Gallager codes
UMR 8549, Unit′e Mixte de Recherche du Centre National de la Recherche Scientifi que et de l’ Ecole Normale Sup′erieure
2015/8/21
Gallager codes are the best error-correcting codes to-date. In this paper we study them by using the tools of statistical mechanics. The corresponding statistical mechanics model is a spin model on a ...
Scrambled geometric net integration over general product spaces
Discrepancy Multiresolution Rendering Scrambled net
2015/8/21
Quasi-Monte Carlo (QMC) sampling has been developed for integration over [0;1]s where it has superior accuracy to Monte Carlo (MC) for
integrands of bounded variation.
We discuss a method for curve estimation based on n noisy
data; one translates the empirical wavelet coecients towards the origin by
an amount p
2 log(n) =p
n. The method is nearly minimax for...
Coding for Network Coding
Sparse graph codes probabilistic channel models Shannon channel capacity network coding
2015/8/20
We consider communication over a noisy network under randomized linear network coding. Possible error mechanism include node- or link- failures, Byzantine behavior of nodes, or an over-estimate of the...
Classical statistical theory ignores model selection in assessing estimation accuracy. Here we consider
bootstrap methods for computing standard errors and con dence intervals that take model selecti...
讨论一类带有p-Laplacian算子非线性分数阶微分方程耦合系统边值问题解的存在性,给出解的存在性条件,利用不动点定理进行讨论.
Some of the Combinatorics Related To Michael’s Problem
Combinatorics Related Michael’s Problem
2015/8/17
We present some new methods for constructing a Michael space, a regular Lindel ofspace which has a non-Lindel of product with the space of irrationals. The central result is a combinatorial statement ...
Under Martin’s Axiom a c.c.c. nonseparable compact space is constructed which maps continuously into [0, 1] with linear fibers. Such a space can not, for instance, map onto [0, 1]ℵ1.
Random forcing and (S) and (L)
Random forcing (S) (L)
2015/8/17
In this article I will analyze the impact of forcing with a measure algebra on various topological statements. In particular our interest will focus on the study of hereditary separability and the her...
PROPER FORCING,CARDINAL ARITHMETIC,AND UNCOUNTABLE LINEAR ORDERS
PROPER FORCING CARDINAL ARITHMETIC UNCOUNTABLE LINEAR ORDERS
2015/8/17
In this paper I will communicate some new consequences of the Proper Forcing Axiom. First, the Bounded Proper Forcing Axiom implies that there is a well ordering of R which is Σ1-definable in (H(ω2), ...
LOCALLY COMPACT,LOCALLY COUNTABLE SPACES AND RANDOM REALS
LOCALLY COMPACT LOCALLY COUNTABLE SPACES RANDOM REALS
2015/8/17
In this note I will present a proof that, assuming PFA, if R is a measure algebra then after forcing with R every uncountable locally compact locally countable cometrizable space contains an uncountab...
A FIVE ELEMENT BASIS FOR THE UNCOUNTABLE LINEAR ORDERS
FIVE ELEMENT BASIS UNCOUNTABLE LINEAR ORDERS
2015/8/17
In this paper I will show that it is relatively consistent with the usual axioms of mathematics (ZFC) together with a strong form of the axiom of infinity (the existence of a supercompact cardinal) th...
ω1 and −ω1 May Be the Only Minimal Uncountable Linear Orders
ω1 and − ω1 May Only Minimal Uncountable Linear Orders
2015/8/17
In 1971 Laver proved the following result, confirming a long-standing conjecture of Fraïssé. Theorem 1.1 [10]. If Li (i < ω) is a sequence of σ-scattered linear orders, then there exist i < j suc...
Let us begin this paper by recalling the following classical metrization theorem of Birkhoff and Kakutani.
In this paper I will survey some recent developments in the combinatorics of Aronszajn trees. I will cover work on coherent and Lipschitz trees, the basis problem for uncountable linear orderings, sub...