6,577 research outputs found
A survey of max-type recursive distributional equations
In certain problems in a variety of applied probability settings (from
probabilistic analysis of algorithms to statistical physics), the central
requirement is to solve a recursive distributional equation of the form X =^d
g((\xi_i,X_i),i\geq 1). Here (\xi_i) and g(\cdot) are given and the X_i are
independent copies of the unknown distribution X. We survey this area,
emphasizing examples where the function g(\cdot) is essentially a ``maximum''
or ``minimum'' function. We draw attention to the theoretical question of
endogeny: in the associated recursive tree process X_i, are the X_i measurable
functions of the innovations process (\xi_i)?Comment: Published at http://dx.doi.org/10.1214/105051605000000142 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Optimization as a design strategy. Considerations based on building simulation-assisted experiments about problem decomposition
In this article the most fundamental decomposition-based optimization method
- block coordinate search, based on the sequential decomposition of problems in
subproblems - and building performance simulation programs are used to reason
about a building design process at micro-urban scale and strategies are defined
to make the search more efficient. Cyclic overlapping block coordinate search
is here considered in its double nature of optimization method and surrogate
model (and metaphore) of a sequential design process. Heuristic indicators apt
to support the design of search structures suited to that method are developed
from building-simulation-assisted computational experiments, aimed to choose
the form and position of a small building in a plot. Those indicators link the
sharing of structure between subspaces ("commonality") to recursive
recombination, measured as freshness of the search wake and novelty of the
search moves. The aim of these indicators is to measure the relative
effectiveness of decomposition-based design moves and create efficient block
searches. Implications of a possible use of these indicators in genetic
algorithms are also highlighted.Comment: 48 pages. 12 figures, 3 table
The challenge of complexity for cognitive systems
Complex cognition addresses research on (a) high-level cognitive processes â mainly problem solving, reasoning, and decision making â and their interaction with more basic processes such as perception, learning, motivation and emotion and (b) cognitive processes which take place in a complex, typically dynamic, environment. Our focus is on AI systems and cognitive models dealing with complexity and on psychological findings which can inspire or challenge cognitive systems research. In this overview we first motivate why we have to go beyond models for rather simple cognitive processes and reductionist experiments. Afterwards, we give a characterization of complexity from our perspective. We introduce the triad of cognitive science methods â analytical, empirical, and engineering methods â which in our opinion have all to be utilized to tackle complex cognition. Afterwards we highlight three aspects of complex cognition â complex problem solving, dynamic decision making, and learning of concepts, skills and strategies. We conclude with some reflections about and challenges for future research
Behavioural Economics: Classical and Modern
In this paper, the origins and development of behavioural economics, beginning with the pioneering works of Herbert Simon (1953) and Ward Edwards (1954), is traced, described and (critically) discussed, in some detail. Two kinds of behavioural economics â classical and modern â are attributed, respectively, to the two pioneers. The mathematical foundations of classical behavioural economics is identified, largely, to be in the theory of computation and computational complexity; the corresponding mathematical basis for modern behavioural economics is, on the other hand, claimed to be a notion of subjective probability (at least at its origins in the works of Ward Edwards). The economic theories of behavior, challenging various aspects of 'orthodox' theory, were decisively influenced by these two mathematical underpinnings of the two theoriesClassical Behavioural Economics, Modern Behavioural Economics, Subjective Probability, Model of Computation, Computational Complexity. Subjective Expected Utility
Tracking moving optima using Kalman-based predictions
The dynamic optimization problem concerns finding an optimum in a changing environment. In the field of evolutionary algorithms, this implies dealing with a timechanging fitness landscape. In this paper we compare different techniques for integrating motion information into an evolutionary algorithm, in the case it has to follow a time-changing optimum, under the assumption that the changes follow a nonrandom law. Such a law can be estimated in order to improve the optimum tracking capabilities of the algorithm. In particular, we will focus on first order dynamical laws to track moving objects. A vision-based tracking robotic application is used as testbed for experimental comparison
Analyzing the effect of local rounding error propagation on the maximal attainable accuracy of the pipelined Conjugate Gradient method
Pipelined Krylov subspace methods typically offer improved strong scaling on
parallel HPC hardware compared to standard Krylov subspace methods for large
and sparse linear systems. In pipelined methods the traditional synchronization
bottleneck is mitigated by overlapping time-consuming global communications
with useful computations. However, to achieve this communication hiding
strategy, pipelined methods introduce additional recurrence relations for a
number of auxiliary variables that are required to update the approximate
solution. This paper aims at studying the influence of local rounding errors
that are introduced by the additional recurrences in the pipelined Conjugate
Gradient method. Specifically, we analyze the impact of local round-off effects
on the attainable accuracy of the pipelined CG algorithm and compare to the
traditional CG method. Furthermore, we estimate the gap between the true
residual and the recursively computed residual used in the algorithm. Based on
this estimate we suggest an automated residual replacement strategy to reduce
the loss of attainable accuracy on the final iterative solution. The resulting
pipelined CG method with residual replacement improves the maximal attainable
accuracy of pipelined CG, while maintaining the efficient parallel performance
of the pipelined method. This conclusion is substantiated by numerical results
for a variety of benchmark problems.Comment: 26 pages, 6 figures, 2 tables, 4 algorithm
Algorithmic and Statistical Perspectives on Large-Scale Data Analysis
In recent years, ideas from statistics and scientific computing have begun to
interact in increasingly sophisticated and fruitful ways with ideas from
computer science and the theory of algorithms to aid in the development of
improved worst-case algorithms that are useful for large-scale scientific and
Internet data analysis problems. In this chapter, I will describe two recent
examples---one having to do with selecting good columns or features from a (DNA
Single Nucleotide Polymorphism) data matrix, and the other having to do with
selecting good clusters or communities from a data graph (representing a social
or information network)---that drew on ideas from both areas and that may serve
as a model for exploiting complementary algorithmic and statistical
perspectives in order to solve applied large-scale data analysis problems.Comment: 33 pages. To appear in Uwe Naumann and Olaf Schenk, editors,
"Combinatorial Scientific Computing," Chapman and Hall/CRC Press, 201
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