Search results for "Probability"
showing 10 items of 3417 documents
A space on which diameter-type packing measure is not Borel regular
1999
We construct a separable metric space on which 1-dimensional diameter-type packing measure is not Borel regular.
The simplex dispersion ordering and its application to the evaluation of human corneal endothelia
2009
A multivariate dispersion ordering based on random simplices is proposed in this paper. Given a R^d-valued random vector, we consider two random simplices determined by the convex hulls of two independent random samples of sizes d+1 of the vector. By means of the stochastic comparison of the Hausdorff distances between such simplices, a multivariate dispersion ordering is introduced. Main properties of the new ordering are studied. Relationships with other dispersion orderings are considered, placing emphasis on the univariate version. Some statistical tests for the new order are proposed. An application of such ordering to the clinical evaluation of human corneal endothelia is provided. Di…
Testing for selectivity in the dependence of random variables on external factors
2008
Random variables AA and BB, whose joint distribution depends on factors (x,y)(x,y), are selectively influenced by xx and yy, respectively, if AA and BB can be represented as functions of, respectively, (x,SA,C)(x,SA,C) and (y,SB,C)(y,SB,C), where SA,SB,CSA,SB,C are stochastically independent and do not depend on (x,y)(x,y). Selective influence implies selective dependence of marginal distributions on the respective factors: thus no parameter of AA may depend on yy. But parameters characterizing stochastic interdependence of AA and BB, such as their mixed moments, are generally functions of both xx and yy. We derive two simple necessary conditions for selective dependence of (A,B)(A,B) on (x…
Estimating norms inC*-algebras of discrete groups
1976
LetG be a discrete group, letK be a finite subset ofG and let χ K be the characteristic function ofK. Then χ K acts by convolution as a bounded operator onL2(G). We will prove that the norm |||χ K ||| of this operator always satisfies the following estimate: $$|||\chi _{\rm K} |||^2 \leqq k + 2\sqrt {w\left( {k - 1} \right)\left( {k - w} \right)} + \left( {k - 2} \right)\left( {k - w} \right)$$ . Here .
The McKay conjecture and Galois automorphisms
2004
The main problem of representation theory of finite groups is to find proofs of several conjectures stating that certain global invariants of a finite group G can be computed locally. The simplest of these conjectures is the ?McKay conjecture? which asserts that the number of irreducible complex characters of G of degree not divisible by p is the same if computed in a p-Sylow normalizer of G. In this paper, we propose a much stronger version of this conjecture which deals with Galois automorphisms. In fact, the same idea can be applied to the celebrated Alperin and Dade conjectures.
Extensions of cocycles for hyperfinite actions and applications
1997
Given a countable, hyperfinite, ergodic and measure-preserving equivalence relationR on a standard probability space (X, ℬ, μ) and an elementW of the normalizerN (R) ofR, we investigate the problem of extendingR-cocycles to\(\bar R\), where\(\bar R\) is the relation generated byR andW. As an application, we obtain that for a Bernoulli automorphism the smallest family of natural factors in sense of [6] consists of all factors. Given an automorphism which is embeddable in a measurable flow and a compact, metric group, we show that for a typical cocycle we cannot lift the whole flow to the centralizer of the corresponding group extension.
Optimization problem in inductive inference
1995
Algorithms recognizing to which of n classes some total function belongs are constructed (n > 2). In this construction strategies determining to which of two classes the function belongs are used as subroutines. Upper and lower bounds for number of necessary strategies are obtained in several models: FIN- and EX-identification and EX-identification with limited number of mindchanges. It is proved that in EX-identification it is necessary to use n(n−1)/2 strategies. In FIN-identification [3n/2 − 2] strategies are necessary and sufficient, in EX-identification with one mindchange- n log2n+o(n log2n) strategies.
Rigidity transition in two-dimensional random fiber networks
2000
Rigidity percolation is analyzed in two-dimensional random fibrous networks. The model consists of central forces between the adjacent crossing points of the fibers. Two strategies are used to incorporate rigidity: adding extra constraints between second-nearest crossing points with a probability p(sn), and "welding" individual crossing points by adding there four additional constraints with a probability p(weld), and thus fixing the angles between the fibers. These additional constraints will make the model rigid at a critical probability p(sn)=p(sn)(c) and p(weld)=p(weld)(c), respectively. Accurate estimates are given for the transition thresholds and for some of the associated critical e…
Local dimensions of sliced measures and stability of packing dimensions of sections of sets
2004
Abstract Let m and n be integers with 0 R n to certain properties of plane sections of μ. This leads us to prove, among other things, that the lower local dimension of (n−m)-plane sections of μ is typically constant provided that the Hausdorff dimension of μ is greater than m. The analogous result holds for the upper local dimension if μ has finite t-energy for some t>m. We also give a sufficient condition for stability of packing dimensions of section of sets.
Lower and Upper Probability Bounds for Some Conjunctions of Two Conditional Events
2018
In this paper we consider, in the framework of coherence, four different definitions of conjunction among conditional events. In each of these definitions the conjunction is still a conditional event. We first recall the different definitions of conjunction; then, given a coherent probability assessment (x, y) on a family of two conditional events \(\{A|H,B|K\}\), for each conjunction \((A|H) \wedge (B|K)\) we determine the (best) lower and upper bounds for the extension \(z=P[(A|H) \wedge (B|K)]\). We show that, in general, these lower and upper bounds differ from the classical Frechet-Hoeffding bounds. Moreover, we recall a notion of conjunction studied in recent papers, such that the res…