Coherence in Modal Logic

A variety is said to be coherent if the finitely generated subalgebras of its finitely presented members are also finitely presented. In a recent paper by the authors it was shown that coherence forms a key ingredient of the uniform deductive interpolation property for equational consequence in a variety, and a general criterion was given for the failure of coherence (and hence uniform deductive interpolation) in varieties of algebras with a term-definable semilattice reduct. In this paper, a more general criterion is obtained and used to prove the failure of coherence and uniform deductive interpolation for a broad family of modal logics, including K, KT, K4, and S4

Algebraic foundations for qualitative calculi and networks

A qualitative representation $\phi$ is like an ordinary representation of a relation algebra, but instead of requiring $(a; b)^\phi = a^\phi | b^\phi$, as we do for ordinary representations, we only require that $c^\phi\supseteq a^\phi | b^\phi \iff c\geq a ; b$, for each $c$ in the algebra. A constraint network is qualitatively satisfiable if its nodes can be mapped to elements of a qualitative representation, preserving the constraints. If a constraint network is satisfiable then it is clearly qualitatively satisfiable, but the converse can fail. However, for a wide range of relation algebras including the point algebra, the Allen Interval Algebra, RCC8 and many others, a network is satisfiable if and only if it is qualitatively satisfiable. Unlike ordinary composition, the weak composition arising from qualitative representations need not be associative, so we can generalise by considering network satisfaction problems over non-associative algebras. We prove that computationally, qualitative representations have many advantages over ordinary representations: whereas many finite relation algebras have only infinite representations, every finite qualitatively representable algebra has a finite qualitative representation; the representability problem for (the atom structures of) finite non-associative algebras is NP-complete; the network satisfaction problem over a finite qualitatively representable algebra is always in NP; the validity of equations over qualitative representations is co-NP-complete. On the other hand we prove that there is no finite axiomatisation of the class of qualitatively representable algebras.Comment: 22 page

Indexing arbitrary-length kk-mers in sequencing reads

We propose a lightweight data structure for indexing and querying collections of NGS reads data in main memory. The data structure supports the interface proposed in the pioneering work by Philippe et al. for counting and locating $k$-mers in sequencing reads. Our solution, PgSA (pseudogenome suffix array), based on finding overlapping reads, is competitive to the existing algorithms in the space use, query times, or both. The main applications of our index include variant calling, error correction and analysis of reads from RNA-seq experiments

Politologia w ofercie dydaktycznej polskich uczelni. Informacja i analiza

The paper focuses on political science as a field of study offered by Polish schools of higher education (public, non-public and sponsored by the Roman Catholic Church). When presenting the qualitative and quantitative aspects of education in political science, the author relies on materials from the Ministry of Science and Higher Education, Poland’s Central Board of Tertiary Education, National Accreditation Committee, University Accreditation Committee, Central Committee for Degrees and Titles and available publications. The paper also brings an overview of legał acts which regulate degree programmes in political science, as well as results of analysis of political science programmes available from various schools of higher education.Artykuł poświęcony jest politologii jako kierunkowi kształcenia w ofercie polskich uczelni publicznych, kościelnych i niepublicznych. Przedstawiając ilościowe i jakościowe aspekty kształcenia w zakresie politologii, autor opiera się na materiałach Ministerstwa Nauki i Szkolnictwa Wyższego, Rady Głównej Szkolnictwa Wyższego, Państwowej Komisji Akredytacyjnej, Uniwersyteckiej Komisji Akredytacyjnej, Centralnej Komisji do spraw Stopni i Tytułów oraz dostępnych publikacjach. Opracowanie zawiera również przegląd aktów prawnych, które regulują prowadzenie studiów politologicznych, a także wyniki analizy oferty dydaktycznej poszczególnych typów uczelni w zakresie politologii

Z Szekspirem w tle. "Opowieść zimowa" Erica Rohmera

The paper aims at analyzing the relationship between Eric Rohmer’s A Tale of Winter (Conte d’hiver, 1992) and Shakespeare’s late comedy. Although both works are entitled similarly, at first glance they have hardly anything in common, aside from one scene in which the two main characters watch Shakespeare’s play staged in a theatre. The author argues, however, that many references to original comedy, both on the level of plot and structure, can be found in Rohmer’s movie, which can therefore be perceived as a loose adaptation of Shakespeare’s work. The paper aims at analyzing the relationship between Eric Rohmer’s A Tale of Winter (Conte d’hiver, 1992) and Shakespeare’s late comedy. Although both works are entitled similarly, at first glance they have hardly anything in common, aside from one scene in which the two main characters watch Shakespeare’s play staged in a theatre. The author argues, however, that many references to original comedy, both on the level of plot and structure, can be found in Rohmer’s movie, which can therefore be perceived as a loose adaptation of Shakespeare’s work.