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Full-Text Articles in Computer Engineering
Towards Symmetry-Based Explanation Of (Approximate) Shapes Of Alpha-Helices And Beta-Sheets (And Beta-Barrels) In Protein Structure, Jaime Nava, Vladik Kreinovich
Towards Symmetry-Based Explanation Of (Approximate) Shapes Of Alpha-Helices And Beta-Sheets (And Beta-Barrels) In Protein Structure, Jaime Nava, Vladik Kreinovich
Departmental Technical Reports (CS)
Protein structure is invariably connected to protein function. There are two important secondary structure elements: alpha helices and beta-sheets (which sometimes come in a shape of beta-barrels). The actual shapes of these structures can be complicated, but in the first approximation, they are usually approximated by, correspondingly, cylindrical spirals and planes (and cylinders, for beta-barrels). In this paper, following the ideas pioneered by a renowned mathematician M. Gromov, we use natural symmetries to show that, under reasonable assumptions, these geometric shapes are indeed the best approximating families for secondary structures.
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)