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In many applications, we have numerous molecules that are obtained from a " template " molecule like benzene C6H6 or cubane C8H8 by replacing some of its hydrogen atoms with other atoms or atom groups (called ligands). Depending on how many original atoms are replaced and which ones are replaced, we obtain a large number of different chemical substances. It(More)
One of the main problems with neural networks is that they are often very slow in learning the desired dependence. To speed up neural networks, Bruno Apolloni proposed to othogonalize neurons during training, i.e., to select neurons whose output functions are orthogonal to each other. In this paper, we use symmetries to provide a theoretical explanation for(More)
—It is well known that an arbitrary continuous function on a bounded set – e.g., on an interval [a, b] – can be, with any given accuracy, approximated by a polynomial or by a piece-wise polynomial function (spline). Usually, polynomials are described as linear combinations of monomials. It turns out that in many computational problems, it is more efficient(More)
In describing expert knowledge, it is often important to properly take into account hedges like " very " , " somewhat " , etc. In particular, fuzzy logic provides a consistent way of describing hedges. For some of the hedges, a repetition changes the meaning: e.g., " very very small " is smaller than " very small ". However, other hedges – like " somewhat "(More)
Protein structure is invariably connected to protein function. There are two im-1 portant secondary structure elements: alpha helices and beta-sheets (which sometimes come 2 in a shape of beta-barrels). The actual shapes of these structures can be complicated, but in 3 the first approximation, they are usually approximated by, correspondingly, cylindrical(More)
• The best way to describe the complexity of a given string s is to find its Kolmogorov complexity K(s). • K(s) is the shortest length of a program that computes s. • For example, a sequence is random if and only if its Kolmogorov complexity is close to its length. • We can check how close are two DNA sequences s and s by comparing K(ss) with K(s) + K(s): –(More)