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5.6.2017 14:00 @ Hora Informaticae
Abstract: The term "black-box optimization" refers to optimization of functions without knowing their mathematical expression (neither an explicit one, as a composition of known functions, nor an implicit one, as a solution of explicitly stated equations). Values of black-ox functions can be obtained only empirically, through measurements or simulations. Most successful in black-box optimization are evolutionary algorithms, due to weak assumptions about the optimized function (which is in the evolutionary context usually called fitness). However, working only with function values of the fitness, an evolutionary algorithm needs a large number of its evaluations, which causes problems in situations when the empirical evaluation of the black-box fitness is time-consuming and/or costly. As a remedy, data mining has been used for approximately 15 years, applied to data from the previous generations of the evolutionary algorithm. It yields a regression model approximating of the black-box fitness, a.k.a. its surrogate model, which is used instead of the original fitness in a substantiv part of its evaluations. The talk will attempt to illustrate both the theoretical research in surrogate modelling for evolutionary optimizition, by Lukáš Bajer, Zbyněk Pitra, Jakub Repický and myself, and its applicability to real-world problems. In the theoretical context, it will present surrogate modelling primarily in connection with the state-of-the-art evolutionary algorithm for black-box optimization, the covariance matrix adaptation evolution strategy. It will concentrate on the most sophisticated among the encountered surrogated models, Gaussian processes, though it will briefly sketch also random forests and models based on various kinds of articial neural networks. As a real-world application, the talk will show how evolutionary optimization and its extension with surrogate models are used to optimize catalysts for given chemical reactions.
7.6.2017 10:00 @ Applied Mathematical Logic
Since its introduction by Pogorzelski in 1971, the notion of a structurally complete logic (i.e. a logic which cannot be properly extended without properly extending its set of theorems) has become a standard part of the study non-classical logics, in particular modal and superintuitionistic ones. In this talk we shall study its natural dual defined in terms of antitheorems rather than theorems. Our goal will be to provide for a given logic several equivalent descriptions of its antistructural completion, i.e. its largest extension with the same set of antitheorems. In particular, we establish a connection between the logic given by the so-called antiadmissible rules of L and the extension of L obtained by restricting to its simple models. Trying to find natural conditions under which this connection can be simplified then naturally leads to the study of variants of so-called inconsistency lemmas, initiated recently by Raftery.
14.6.2017 10:00 @ Applied Mathematical Logic
A natural generalization of the classical Kripke semantics for modal logic is to evaluate formulas in an arbitrary complete lattice. We investigate completeness of some such logics, based on so-called expressible matrices. For every element x of such a matrix, there is a set of unary operators, E(x), such that x is the unique element that precisely the operators in E(x) send to a designated value. We describe general properties of any proof system complete for the non-modal fragment sufficient for the system to be complete for the whole lattice based-modal logic.