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Full-Text Articles in Computer Engineering
I-Complexity And Discrete Derivative Of Logarithms: A Symmetry-Based Explanation, Vladik Kreinovich, Jaime Nava
I-Complexity And Discrete Derivative Of Logarithms: A Symmetry-Based Explanation, Vladik Kreinovich, Jaime Nava
Departmental Technical Reports (CS)
In many practical applications, it is useful to consider Kolmogorov complexity K(s) of a given string s, i.e., the shortest length of a program that generates this string. Since Kolmogorov complexity is, in general, not computable, it is necessary to use computable approximations K~(s) to K(s). Usually, to describe such an approximations, we take a compression algorithm and use the length of the compressed string as K~(s). This approximation, however, is not perfect: e.g., for most compression algorithms, adding a single bit to the string $s$ can drastically change the value K~(s) -- while …
Theoretical Explanation Of Bernstein Polynomials' Efficiency: They Are Optimal Combination Of Optimal Endpoint-Related Functions, Jaime Nava, Vladik Kreinovich
Theoretical Explanation Of Bernstein Polynomials' Efficiency: They Are Optimal Combination Of Optimal Endpoint-Related Functions, Jaime Nava, Vladik Kreinovich
Departmental Technical Reports (CS)
In many applications of interval computations, it turned out to be beneficial to represent polynomials on a given interval [x-, x+] as linear combinations of Bernstein polynomials (x- x - )k * (x+ - x)n-k. In this paper, we provide a theoretical explanation for this empirical success: namely, we show that under reasonable optimality criteria, Bernstein polynomials can be uniquely determined from the requirement that they are optimal combinations of optimal polynomials corresponding to the interval's endpoints.
Orthogonal Bases Are The Best: A Theorem Justifying Bruno Apolloni's Heuristic Neural Network Idea, Jaime Nava, Vladik Kreinovich
Orthogonal Bases Are The Best: A Theorem Justifying Bruno Apolloni's Heuristic Neural Network Idea, Jaime Nava, Vladik Kreinovich
Departmental Technical Reports (CS)