32 research outputs found
Scrambled and distributionally scrambled n-tuples
This article investigates the relation between the distributional chaos and
the existence of a scrambled triple. We show that for a continuous mapping
acting on a compact metric space , the possession of an infinite
extremal distributionally scrambled set is not sufficient for the existence of
a scrambled triple. We also construct an invariant Mycielski set with an
uncountable extremal distributionally scrambled set without any scrambled
triple
The Moment Problem for Finitely Additive Probabilities
We study the moment problem for finitely additive probabilities and show that the information provided by the moments is equivalent to the one given by the associated lower and upper distribution functions
Finitely additive extensions of distribution functions and moment sequences: The coherent lower prevision approach
We study the information that a distribution function provides about the finitely additive probability measure inducing it. We show that in general there is an infinite number of finitely additive probabilities associated with the same distribution function. Secondly, we investigate the relationship between a distribution function and its given sequence of moments. We provide formulae for the sets of distribution functions, and finitely additive probabilities, associated with some moment sequence, and determine under which conditions the moments determine the distribution function uniquely. We show that all these problems can be addressed efficiently using the theory of coherent lower previsions
Big Bang Nucleosynthesis with Independent Neutrino Distribution Functions
We have performed new Big Bang Nucleosynthesis calculations which employ
arbitrarily-specified, time-dependent neutrino and antineutrino distribution
functions for each of up to four neutrino flavors. We self-consistently couple
these distributions to the thermodynamics, the expansion rate and scale
factor-time/temperature relationship, as well as to all relevant weak,
electromagnetic, and strong nuclear reaction processes in the early universe.
With this approach, we can treat any scenario in which neutrino or antineutrino
spectral distortion might arise. These scenarios might include, for example,
decaying particles, active-sterile neutrino oscillations, and active-active
neutrino oscillations in the presence of significant lepton numbers. Our
calculations allow lepton numbers and sterile neutrinos to be constrained with
observationally-determined primordial helium and deuterium abundances. We have
modified a standard BBN code to perform these calculations and have made it
available to the community.Comment: 9 pages, 5 figure
Two results on entropy, chaos, and independence in symbolic dynamics
We survey the connections between entropy, chaos, and independence in
topological dynamics. We present extensions of two classical results placing
the following notions in the context of symbolic dynamics:
1. Equivalence of positive entropy and the existence of a large (in terms of
asymptotic and Shnirelman densities) set of combinatorial independence for
shift spaces.
2. Existence of a mixing shift space with a dense set of periodic points with
topological entropy zero and without ergodic measure with full support, nor any
distributionally chaotic pair.
Our proofs are new and yield conclusions stronger than what was known before.Comment: Comments are welcome! This preprint contains results from
arXiv:1401.5969v
A method of classification for multisource data in remote sensing based on interval-valued probabilities
An axiomatic approach to intervalued (IV) probabilities is presented, where the IV probability is defined by a pair of set-theoretic functions which satisfy some pre-specified axioms. On the basis of this approach representation of statistical evidence and combination of multiple bodies of evidence are emphasized. Although IV probabilities provide an innovative means for the representation and combination of evidential information, they make the decision process rather complicated. It entails more intelligent strategies for making decisions. The development of decision rules over IV probabilities is discussed from the viewpoint of statistical pattern recognition. The proposed method, so called evidential reasoning method, is applied to the ground-cover classification of a multisource data set consisting of Multispectral Scanner (MSS) data, Synthetic Aperture Radar (SAR) data, and digital terrain data such as elevation, slope, and aspect. By treating the data sources separately, the method is able to capture both parametric and nonparametric information and to combine them. Then the method is applied to two separate cases of classifying multiband data obtained by a single sensor. In each case a set of multiple sources is obtained by dividing the dimensionally huge data into smaller and more manageable pieces based on the global statistical correlation information. By a divide-and-combine process, the method is able to utilize more features than the conventional maximum likelihood method