132 research outputs found
Random subshifts of finite type
Let be an irreducible shift of finite type (SFT) of positive entropy, and
let be its set of words of length . Define a random subset
of by independently choosing each word from with some
probability . Let be the (random) SFT built from the set
. For each and tending to infinity, we compute
the limit of the likelihood that is empty, as well as the limiting
distribution of entropy for . For near 1 and tending
to infinity, we show that the likelihood that contains a unique
irreducible component of positive entropy converges exponentially to 1. These
results are obtained by studying certain sequences of random directed graphs.
This version of "random SFT" differs significantly from a previous notion by
the same name, which has appeared in the context of random dynamical systems
and bundled dynamical systems.Comment: Published in at http://dx.doi.org/10.1214/10-AOP636 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Orders of accumulation of entropy
For a continuous map of a compact metrizable space with finite
topological entropy, the order of accumulation of entropy of is a countable
ordinal that arises in the context of entropy structure and symbolic
extensions. We show that every countable ordinal is realized as the order of
accumulation of some dynamical system. Our proof relies on functional analysis
of metrizable Choquet simplices and a realization theorem of Downarowicz and
Serafin. Further, if is a metrizable Choquet simplex, we bound the ordinals
that appear as the order of accumulation of entropy of a dynamical system whose
simplex of invariant measures is affinely homeomorphic to . These bounds are
given in terms of the Cantor-Bendixson rank of \overline{\ex(M)}, the closure
of the extreme points of , and the relative Cantor-Bendixson rank of
\overline{\ex(M)} with respect to \ex(M). We also address the optimality of
these bounds.Comment: 48 page
Human Trafficking: a Growing, Global Concern
This thesis is intended to describe and explain the lasting impacts trafficking have on individuals and societies. A general description of the forms, as well as the effects of trafficking will be reviewed. Perhaps more importantly, proposed responses will be discussed in depth. But the primary goal is to spread awareness and educate the reader about the crime of trafficking in human beings. Awareness by the public is the first step in eradicating trafficking in human beings. It is the author\u27s hope to elevate this awareness through her research and writing
Consistency of maximum likelihood estimation for some dynamical systems
We consider the asymptotic consistency of maximum likelihood parameter
estimation for dynamical systems observed with noise. Under suitable conditions
on the dynamical systems and the observations, we show that maximum likelihood
parameter estimation is consistent. Our proof involves ideas from both
information theory and dynamical systems. Furthermore, we show how some
well-studied properties of dynamical systems imply the general statistical
properties related to maximum likelihood estimation. Finally, we exhibit
classical families of dynamical systems for which maximum likelihood estimation
is consistent. Examples include shifts of finite type with Gibbs measures and
Axiom A attractors with SRB measures.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1259 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Design of Crystalline Solids
We are investigating methods to prepare porous crystalline solids based on metal-organic frameworks (MOFs) composed of organic molecules and metal ions. MOFs are new functional materials that are now being used in a range of applications that include storage of gases (e.g., hydrogen), delivery of drugs, catalysis of organic reactions, and molecular separations. Toward this goal, we are investigating using solid-state synthesis to synthesize MOFs by grinding organic ligands and transition metal salts together in the absence of solvents. Here we report the attempts at room temperature and hydrothermal synthesis along with the successful solid-state synthesis and characterization of a MOF composed of urocanic acid (3-(3H-imidazol-4-yl)prop-2-enoic acid) and copper (II) nitrate
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