891 research outputs found
A domain-theoretic investigation of posets of sub-sigma-algebras (extended abstract)
Given a measurable space (X, M) there is a (Galois) connection between
sub-sigma-algebras of M and equivalence relations on X. On the other hand
equivalence relations on X are closely related to congruences on stochastic
relations. In recent work, Doberkat has examined lattice properties of posets
of congruences on a stochastic relation and motivated a domain-theoretic
investigation of these ordered sets. Here we show that the posets of
sub-sigma-algebras of a measurable space do not enjoy desired domain-theoretic
properties and that our counterexamples can be applied to the set of smooth
equivalence relations on an analytic space, thus giving a rather unsatisfactory
answer to Doberkat's question
Random walks on semaphore codes and delay de Bruijn semigroups
We develop a new approach to random walks on de Bruijn graphs over the
alphabet through right congruences on , defined using the natural
right action of . A major role is played by special right congruences,
which correspond to semaphore codes and allow an easier computation of the
hitting time. We show how right congruences can be approximated by special
right congruences.Comment: 34 pages; 10 figures; as requested by the journal, the previous
version of this paper was divided into two; this version contains Sections
1-8 of version 1; Sections 9-12 will appear as a separate paper with extra
material adde
Sequences of commutator operations
Given the congruence lattice L of a finite algebra A with a Mal'cev term, we
look for those sequences of operations on L that are sequences of higher
commutator operations of expansions of A.
The properties of higher commutators proved so far delimit the number of such
sequences: the number is always at most countably infinite; if it is infinite,
then L is the union of two proper subintervals with nonempty intersection.Comment: 9 pages, submitted for publicatio
Uniform Labeled Transition Systems for Nondeterministic, Probabilistic, and Stochastic Process Calculi
Labeled transition systems are typically used to represent the behavior of
nondeterministic processes, with labeled transitions defining a one-step state
to-state reachability relation. This model has been recently made more general
by modifying the transition relation in such a way that it associates with any
source state and transition label a reachability distribution, i.e., a function
mapping each possible target state to a value of some domain that expresses the
degree of one-step reachability of that target state. In this extended
abstract, we show how the resulting model, called ULTraS from Uniform Labeled
Transition System, can be naturally used to give semantics to a fully
nondeterministic, a fully probabilistic, and a fully stochastic variant of a
CSP-like process language.Comment: In Proceedings PACO 2011, arXiv:1108.145
Lattices of varieties of plactic-like monoids
We study the equational theories and bases of meets and joins of several
varieties of plactic-like monoids. Using those results, we construct
sublattices of the lattice of varieties of monoids, generated by said
varieties. We calculate the axiomatic ranks of their elements, obtain
plactic-like congruences whose corresponding factor monoids generate varieties
in the lattice, and determine which varieties are joins of the variety of
commutative monoids and a finitely generated variety. We also show that the
hyposylvester and metasylvester monoids generate the same variety as the
sylvester monoid.Comment: 36 pages, 3 figures, 1 tabl
Aspects of Algebraic Quantum Theory: a Tribute to Hans Primas
This paper outlines the common ground between the motivations lying behind
Hans Primas' algebraic approach to quantum phenomena and those lying behind
David Bohm's approach which led to his notion of implicate/explicate order.
This connection has been made possible by the recent application of orthogonal
Clifford algebraic techniques to the de Broglie-Bohm approach for relativistic
systems with spin.Comment: 18 pages. No figure
Information geometric methods for complexity
Research on the use of information geometry (IG) in modern physics has
witnessed significant advances recently. In this review article, we report on
the utilization of IG methods to define measures of complexity in both
classical and, whenever available, quantum physical settings. A paradigmatic
example of a dramatic change in complexity is given by phase transitions (PTs).
Hence we review both global and local aspects of PTs described in terms of the
scalar curvature of the parameter manifold and the components of the metric
tensor, respectively. We also report on the behavior of geodesic paths on the
parameter manifold used to gain insight into the dynamics of PTs. Going
further, we survey measures of complexity arising in the geometric framework.
In particular, we quantify complexity of networks in terms of the Riemannian
volume of the parameter space of a statistical manifold associated with a given
network. We are also concerned with complexity measures that account for the
interactions of a given number of parts of a system that cannot be described in
terms of a smaller number of parts of the system. Finally, we investigate
complexity measures of entropic motion on curved statistical manifolds that
arise from a probabilistic description of physical systems in the presence of
limited information. The Kullback-Leibler divergence, the distance to an
exponential family and volumes of curved parameter manifolds, are examples of
essential IG notions exploited in our discussion of complexity. We conclude by
discussing strengths, limits, and possible future applications of IG methods to
the physics of complexity.Comment: review article, 60 pages, no figure
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