1,720,961 research outputs found
Random Function Iterations for Stochastic Fixed Point Problems
No full textWe study the convergence of random function iterations for finding an invariant measure of the
corresponding Markov operator. We call the problem of finding such an invariant measure the
stochastic fixed point problem. This generalizes earlier work of the authors [Random function it-
erations for consistent stochastic feasibility, Numer. Funct. Analysis Opt. 40/4 (2019) 386–420]
studying the stochastic feasibility problem, namely, to find points that are, with probability 1,
fixed points of the random functions. When no such points exist, the stochastic feasibility problem
is called inconsistent, but still under certain assumptions, the more general stochastic fixed point
problem has a solution and the random function iteration converges to an invariant measure for
the corresponding Markov operator. We show how common structures in deterministic fixed point
theory can be exploited to establish existence of invariant measures and convergence in distribution
of the Markov chain. This framework specializes to many applications of current interest includ-
ing, for instance, stochastic algorithms for large-scale distributed computation, and deterministic
iterative procedures with computational error. The theory developed in this study provides a solid
basis for describing the convergence of simple computational methods without the assumption of
infinite precision arithmetic or vanishing computational errors
Random Function Iterations for Stochastic Fixed Point Problems
No full textWe study the convergence of random function iterations for finding an invariant measure of the
corresponding Markov operator. We call the problem of finding such an invariant measure the
stochastic fixed point problem. This generalizes earlier work of the authors [Random function it-
erations for consistent stochastic feasibility, Numer. Funct. Analysis Opt. 40/4 (2019) 386–420]
studying the stochastic feasibility problem, namely, to find points that are, with probability 1,
fixed points of the random functions. When no such points exist, the stochastic feasibility problem
is called inconsistent, but still under certain assumptions, the more general stochastic fixed point
problem has a solution and the random function iteration converges to an invariant measure for
the corresponding Markov operator. We show how common structures in deterministic fixed point
theory can be exploited to establish existence of invariant measures and convergence in distribution
of the Markov chain. This framework specializes to many applications of current interest includ-
ing, for instance, stochastic algorithms for large-scale distributed computation, and deterministic
iterative procedures with computational error. The theory developed in this study provides a solid
basis for describing the convergence of simple computational methods without the assumption of
infinite precision arithmetic or vanishing computational errors
Expansive Markov Operators
No full textWe provide conditions that guarantee local rates of convergence in distribution of iterated random functions that are not nonexpansive mappings in locally compact Hadamard spaces. Our results are applied to stochastic instances of common algorithms in optimization, stochastic tomography for X-FEL imaging and a stochastic algorithm for the computation of Fréchet means in model spaces for phylogenetic trees
Nonexpansive Markov Operators and Random Function Iterations for Stochastic Fixed Point Problems
No full text
Nonexpansive Markov Operators and Random Function Iterations for Stochastic Fixed Point Problems
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Random Function Iterations for Stochastic Feasibility Problems
Full text linkThe aim of this thesis is to develop a theory that describes errors in fixed point iterations
stochastically, treating the iterations as a Markov chain and analyzing them for
convergence in distribution. These particular Markov chains are also called iterated random
functions. The convergence theory for iterated random averaged operators turns out
to be simple in : If an invariant measure for the Markov operator exists, the chain
converges to an invariant measure, which may depend on the initial distribution. The
stochastic fixed point problem is hence to find invariant measures of the Markov operator.
We formulate different error models and study whether the corresponding Markov
operator possesses an invariant measure; in some cases also rates of convergence w.r.t.
metrics on the space of probability measures can be computed (geometric rates).
There occur two major types of convergence. Weak convergence of the distributions of
the iterates (or their average) and almost sure convergence. The stochastic fixed point
problem can be seen as either consistent or inconsistent stochastic feasibility problem,
where almost sure convergence is observed in the former and weak convergence
in the latter. The type of convergence turns out to determine the consistency of the
problem. We give conditions for which we can expect convergence in the above terms for
general assumptions on the underlying metric space, and nonexpansive, paracontractive
or averaged mappings.
Since the focus of this thesis is probabilistic, when applied to algorithms for optimization,
convergence is in distribution and the fixed points are measures. This perspective is
particularly useful when the underlying problem models systems with measurement errors,
or even when the problem is deterministic, but the algorithm for its numerical solution is
implemented on conventional computers with finite-precision arithmetic
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