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Belief functions induced by multimodal probability density functions, an application to the search and rescue problem

P.-E. Doré, A. Martin, I. Abi-Zeid, A.-L. Jousselme, P. Maupin (2010)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension n. We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two...

Belief functions induced by multimodal probability density functions, an application to the search and rescue problem

P.-E. Doré, A. Martin, I. Abi-Zeid, A.-L. Jousselme, P. Maupin (2011)

RAIRO - Operations Research

In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension n. We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two...

Bias-variance decomposition in Genetic Programming

Taras Kowaliw, René Doursat (2016)

Open Mathematics

We study properties of Linear Genetic Programming (LGP) through several regression and classification benchmarks. In each problem, we decompose the results into bias and variance components, and explore the effect of varying certain key parameters on the overall error and its decomposed contributions. These parameters are the maximum program size, the initial population, and the function set used. We confirm and quantify several insights into the practical usage of GP, most notably that (a) the...

Bi-directional nearness in a network by AHP (Analytic Hierarchy Process) and ANP (Analytic Network Process)

Kazutomo Nishizawa (2010)

RAIRO - Operations Research

In this paper we study bi-directional nearness in a network based on AHP (Analytic Hierarchy Process) and ANP (Analytic Network Process). Usually we use forward (one-dimensional) direction nearness based on Euclidean distance. Even if the nearest point to i is point j, the nearest point to j is not necessarily point i. Sowe propose the concept of bi-directional nearness defined by AHP'ssynthesizing of weights “for” direction and “from” direction. This concept of distance is a relative distance...

Bidirectional string assembling systems

Martin Kutrib, Matthias Wendlandt (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We introduce and investigate several variants of a bidirectional string assembling system, which is a computational model that generates strings from copies of assembly units. The underlying mechanism is based on two-sided piecewise assembly of a double-stranded sequence of symbols, where the upper and lower strand have to match. The generative capacities and the relative power of the variants are our main interest. In particular, we prove that bidirectional string assembling system generate languages...

Bi-infinitary codes

Do Long Van, D. G. Thomas, K. G. Subramanian, Rani Siromoney (1990)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Binary equality words with two b ’s

Štěpán Holub, Jiří Sýkora (2018)

Commentationes Mathematicae Universitatis Carolinae

Deciding whether a given word is an equality word of two nonperiodic morphisms is also known as the dual Post correspondence problem. Although the problem is decidable, there is no practical decision algorithm. Already in the binary case, the classification is a large project dating back to 1980s. In this paper we give a full classification of binary equality words in which one of the letters has two occurrences.

Binary operations on automatic functions

Juhani Karhumäki, Jarkko Kari, Joachim Kupke (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Real functions on the domain [ 0 , 1 ) n – often used to describe digital images – allow for different well-known types of binary operations. In this note, we recapitulate how weighted finite automata can be used in order to represent those functions and how certain binary operations are reflected in the theory of these automata. Different types of products of automata are employed, including the seldomly-used full cartesian product. We show, however, the infeasibility of functional composition; simple examples...

Binary operations on automatic functions

Juhani Karhumäki, Jarkko Kari, Joachim Kupke (2007)

RAIRO - Theoretical Informatics and Applications

Real functions on the domain [0,1)n – often used to describe digital images – allow for different well-known types of binary operations. In this note, we recapitulate how weighted finite automata can be used in order to represent those functions and how certain binary operations are reflected in the theory of these automata. Different types of products of automata are employed, including the seldomly-used full Cartesian product. We show, however, the infeasibility of functional composition; simple...

Binary patterns in binary cube-free words: Avoidability and growth

Robert Mercaş, Pascal Ochem, Alexey V. Samsonov, Arseny M. Shur (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The avoidability of binary patterns by binary cube-free words is investigated and the exact bound between unavoidable and avoidable patterns is found. All avoidable patterns are shown to be D0L-avoidable. For avoidable patterns, the growth rates of the avoiding languages are studied. All such languages, except for the overlap-free language, are proved to have exponential growth. The exact growth rates of languages avoiding minimal avoidable patterns are approximated through computer-assisted upper...

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