Nadcházející semináře

  • Ing. Roman Špánek, PhD. (Technical University Liberec): Bioinformatics and computational biology

    8.4.2019 14:00 @ Hora Informaticae

    Bioinformatics is an interdisciplinary field involving several research disciplines including molecular biology and genetics, computer science, mathematics, and statistics. In this talk we will shortly discuss tasks common for bioinformatics, particularly (i) collection of biological data, (ii) building a computational model; (iii) solving the computational model and finally (iv) test and evaluate results and the model itself. The talk will also discuss several topics related to computer science and statistics like identification of homologs, multiple sequence alignment, searching sequence patterns, incomplete/missing/ erroneous data handling and evolutionary analyses. In case of a gene/taxon/pathway for the data usually represented as matrices there is a need for statistical analysis, classification, and clustering approaches. Moreover, biological networks such as gene regulatory networks, metabolic pathways, and protein-protein interaction networks are usually modeled as graphs and therefore graph theoretic approaches are used to solve associated problems such as construction and analysis of large-scale networks.

  • Zuzana Hanikova (ICS CAS): Computing the validity degree in Lukasiewicz logic

    10.4.2019 16:00 @ Applied Mathematical Logic

    This talk will consider provability/validity degrees in propositional Lukasiewicz logic in the context of other optimization problems. In order to de_ne provability degrees of propositional formulas, rational constants are employed, so one in fact works in a conservative extension called Rational Pavelka logic (RPL). On the other hand, no constants are necessary to introduce the validity degree; for a formula F, its validity degree under a theory T is the in_mum of values of F under assignments that make T true in the standard MV-algebra on [0,1]. Pavelka completeness states that in RPL the provability degree coincides with the validity degree. For T and F to be even considered as a computational problem, T needs to be finite, whereupon the provability/validity degree becomes rational; one can moreover show that the size of the denominator of this rational is polynomial in the sizes of T and F. I will discuss how the optimization problem relates to finite consequence in RPL taken as a decision problem (shown to be coNP-complete by Hájek), which can be viewed as an upper bound. Further, I will try to provide a lower bound using the taxonomy of optimization problems provided by [M. Krentel, The complexity of optimization problems].

  • Tommaso Moraschini (ICS CAS): The poset of all logics

    24.4.2019 16:00 @ Applied Mathematical Logic

    A notion of interpretability between arbitrary propositional logics is introduced, and shown to be a preorder on the class of all logics. Accordingly, we refer to its associated poset as to the „poset of all logics". In this talk we shall explore the structure of this poset. In particular, we observe that that it has infima of arbitrarily large sets, but even finite suprema may fail to exist. This should not come as a surprise, since the universe of the poset of all logics is indeed a proper class. The formalism of interpretability is subsequently exploited to introduce the notion of a Leibniz class of logics, and we refer to the complete lattice of Leibniz class as to the Leibniz hierarchy. This order-theoretic perspective allows us to address in mathematical terms the following foundational question: do the classes traditionally associated to the Leibniz hierarchy (e.g. that of protoalgebraic logics) capture „fundamental" concepts?