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Knowledge Representation and Reasoning for the Design of Resilient Sensor Networks
Published in Fei Hu, Qi Hao, Intelligent Sensor Networks, 2012
David Kelle, Touria El-Mezyani, Sanjeev Srivastava, David Cartes
An algebra is a collection of mathematical objects along with specific rules for their interactions. Algebras can provide languages in which problems of different types can be discussed. A path algebra in graph theory is a set of paths equipped with two binary operations that satisfy certain requirements. Path algebras are used to solve problems like finding optimal paths between two vertices [12], finding all paths emanating from a source or converging to a target [17], determining shortest and longest paths, etc. In [5], the authors applied simplicial complexes to the problem of solving IQ test analogy questions by selecting deformations that had fewer steps and preserved the most properties, but did not develop a rigorous algebra of these deformations or use them for reasoning. We define this algebra by extending path algebras from graph theory to ASC so that it can be used to solve problems with analogies in a simplicial KR.
Tidy data
Published in Benjamin S. Baumer, Daniel T. Kaplan, Nicholas J. Horton, Modern Data Science with R, 2021
Benjamin S. Baumer, Daniel T. Kaplan, Nicholas J. Horton
In algebra, a variable is an unknown quantity. In data, a variable is known—it has been measured. Rather, the word variable refers to a specific quantity or quality that can vary from case to case. There are two major types of variables: Categorical variables: record type or category and often take the form of a word.Quantitative variables: record a numerical attribute. A quantitative variable is just what it sounds like: a number.
Algebra and graphs
Published in Allan Bonnick, Automotive Science and Mathematics, 2008
An expression such as 5x−5y has two terms and 5 is common to both of them. 5 is therefore a common factor. A factor is defined as a common part of two or more terms that make up an algebraic expression. The expression 5x−5y can be written as 5(x−y), and the factors of the expression are 5 and (x−y).
A new fitness function in genetic programming for classification of imbalanced data
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2022
Genetic programming (GP) is an evolutionary computational method proposed by Koza (Koza, 1992). GP, motivated by Darwin’s natural evolution principles, focuses on the survival of the fittest. In GP, there is a set of Individuals, called the population. These individuals are called Programs. These programs represent solutions for considered problems. A Program represents a mathematical polynomial. A polynomial is an algebraic expression that consists of variables, coefficients, and constants. Variable represents the input feature variable of the data set. In the GP framework, dimensionality reduction is implicit in the form of feature selection. GP Programs are generated stochastically, and if a Program contains the best features, there is a higher chance that those programs or programs similar to that will go to the next or final generation. These Programs are expressed as a tree (Figure 1). An arithmetic function called the fitness function, is used for evaluation of programs. The whole population processes to multiple generations till the required good solution is not found or a predefined criterion is not met. Three nature-inspired genetic operators: crossover, mutation, and reproduction are used for processing the population. By applying genetic operators, the GP framework ensures that the best individual’s fitness is converged to one, over a generation by generation. The functioning of the GP can be given as follows:
Algebra for Enterprise Ontology: towards analysis and synthesis of enterprise models
Published in Enterprise Information Systems, 2018
Algebra, one of the major parts of mathematics, is the study of mathematical symbols and the manipulation of those symbols. This is analogous to model manipulation. Among its wide variations, universal algebra is the mathematical study of algebraic structures themselves (class), in contrast to examples (instances) of algebraic structures. This research employs an algebraic formalization and theorization due to the following benefits attributable to the general characteristics of algebra: Ability to extract objects that have a similar structure in a certain sense of mathematics and develop arguments on those objects in a lump.Ability to conclude statements that are applicable to all objects without depending on each specific object by describing similarities among different objects as axioms and deriving theorems only from the axioms.