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In many practical applications, it is useful to represent a signal or an image by its average values on several fuzzy sets. The corresponding F-transform technique has many useful applications in signal and image processing. In principle, we can use different membership functions. Somewhat surprisingly, in many applications, the best results occur when we(More)
In natural language, “or” sometimes means “inclusive or” and sometimes means “exclusive or”. To adequately describe commonsense and expert knowledge, it is therefore important to have not only t-conorms describing fuzzy “inclusive or” operations, but also fuzzy “exclusive or” operations f⊕(a, b). Since the degrees of certainty are only approximately(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)
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) · (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(More)
(J. Pretz). A.U. Abeysekara , R. Alfaro , C. Alvarez , J.D. Álvarez , R. Arceo , J.C. Arteaga-Velázquez , H.A. Ayala Solares , A.S. Barber , B.M. Baughman , N. Bautista-Elivar , E. Belmont , S.Y. BenZvi , D. Berley , M. Bonilla Rosales , J. Braun , R.A. Caballero-Lopez , A. Carramiñana , M. Castillo , U. Cotti , J. Cotzomi , E. de la Fuente, C. De León , T.(More)
To describe physics properly, we need to take into account quantum effects. Thus, for every nonquantum physical theory, we must come up with an appropriate quantum theory. A traditional approach is to replace all the scalars in the classical description of this theory by the corresponding operators. The problem with the above approach is that due to(More)
In fuzzy control, two approaches are mainly used: Mamdani's approach, in which we represent the knowledge base as a disjunction of statements A<inf>i</inf>(x) &amp; B<inf>i</inf>(u) corresponding to individual rules, and logical approach, in which the knowledge base is represented as a conjunction of the rules themselves A<inf>i</inf>(x) &#x2192;(More)
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)
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(More)
In many practical situations, molecules can be obtained from a “template” molecule like benzene by replacing some of its hydrogen atoms with ligands (other atoms or atom groups). There can be many possible replacements of this type. To avoid time-consuming testing of all possible replacements, it is desirable to test some of the replacements and then(More)