Annals of Mathematics and Artificial Intelligence 

About: Annals of Mathematics and Artificial Intelligence is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Computer science & Logic programming. It has an ISSN identifier of 1012-2443. Over the lifetime, 1486 publications have been published receiving 36436 citations. The journal is also known as: Annals of mathematical science. Series B, Annals of mathematics and artificial intelligence.

Coverage for robotics – A survey of recent results

Abstract: This paper surveys recent results in coverage path planning, a new path planning approach that determines a path for a robot to pass over all points in its free space. Unlike conventional point-to-point path planning, coverage path planning enables applications such as robotic de-mining, snow removal, lawn mowing, car-body painting, machine milling, etc. This paper will focus on coverage path planning algorithms for mobile robots constrained to operate in the plane. These algorithms can be classified as either heuristic or complete. It is our conjecture that most complete algorithms use an exact cellular decomposition, either explicitly or implicitly, to achieve coverage. Therefore, this paper organizes the coverage algorithms into four categories: heuristic, approximate, partial-approximate and exact cellular decompositions. The final section describes some provably complete multi-robot coverage algorithms.

Logic programs with stable model semantics as a constraint programming paradigm

Abstract: Logic programming with the stable model semantics is put forward as a novel constraint programming paradigm. This paradigm is interesting because it bring advantages of logic programming based knowledge representation techniques to constraint programming and because implementation methods for the stable model semantics for ground (variabledfree) programs have advanced significantly in recent years. For a program with variables these methods need a grounding procedure for generating a variabledfree program. As a practical approach to handling the grounding problem a subclass of logic programs, domain restricted programs, is proposed. This subclass enables efficient grounding procedures and serves as a basis for integrating builtdin predicates and functions often needed in applications. It is shown that the novel paradigm embeds classical logical satisfiability and standard (finite domain) constraint satisfaction problems but seems to provide a more expressive framework from a knowledge representation point of view. The first steps towards a programming methodology for the new paradigm are taken by presenting solutions to standard constraint satisfaction problems, combinatorial graph problems and planning problems. An efficient implementation of the paradigm based on domain restricted programs has been developed. This is an extension of a previous implementation of the stable model semantics, the Smodels system, and is publicly available. It contains, e.g., builtdin integer arithmetic integrated to stable model computation. The implementation is described briefly and some test results illustrating the current level of performance are reported.

Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines

Abstract: A vine is a new graphical model for dependent random variables Vines generalize the Markov trees often used in modeling multivariate distributions They differ from Markov trees and Bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence A general formula for the density of a vine dependent distribution is derived This generalizes the well-known density formula for belief nets based on the decomposition of belief nets into cliques Furthermore, the formula allows a simple proof of the Information Decomposition Theorem for a regular vine The problem of (conditional) sampling is discussed, and Gibbs sampling is proposed to carry out sampling from conditional vine dependent distributions The so-called ‘canonical vines’ built on highest degree trees offer the most efficient structure for Gibbs sampling

Theoretical Comparison between the Gini Index and Information Gain Criteria

Abstract: Knowledge Discovery in Databases (KDD) is an active and important research area with the promise for a high payoff in many business and scientific applications. One of the main tasks in KDD is classification. A particular efficient method for classification is decision tree induction. The selection of the attribute used at each node of the tree to split the data (split criterion) is crucial in order to correctly classify objects. Different split criteria were proposed in the literature (Information Gain, Gini Index, etc.). It is not obvious which of them will produce the best decision tree for a given data set. A large amount of empirical tests were conducted in order to answer this question. No conclusive results were found. In this paper we introduce a formal methodology, which allows us to compare multiple split criteria. This permits us to present fundamental insights into the decision process. Furthermore, we are able to present a formal description of how to select between split criteria for a given data set. As an illustration we apply the methodology to two widely used split criteria: Gini Index and Information Gain.

NIST Digital Library of Mathematical Functions

Abstract: The National Institute of Standards and Technology is preparing a Digital Library of Mathematical Functions (DLMF) to provide useful data about special functions for a wide audience. The initial products will be a published handbook and companion Web site, both scheduled for completion in 2003. More than 50 mathematicians, physicists and computer scientists from around the world are participating in the work. The data to be covered include mathematical formulas, graphs, references, methods of computation, and links to software. Special features of the Web site include 3D interactive graphics and an equation search capability. The information technology tools that are being used are, of necessity, ones that are widely available now, even though better tools are in active development. For example, LaTeX files are being used as the common source for both the handbook and the Web site. This is the technology of choice for presentation of mathematics in print but it is not well suited to equation search, for example, or for input to computer algebra systems. These and other problems, and some partially successful work-arounds, are discussed in this paper and in the companion paper by Miller and Youssef.