Two-dimensional models of type theory

We describe a non-extensional variant of Martin-L\"of type theory which we call two-dimensional type theory, and equip it with a sound and complete semantics valued in 2-categories.Comment: 46 pages; v2: final journal versio

Logics for complexity classes

A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered structures, and another form to define them on unordered non-Aristotelian structures. Using the canonical forms, logics are developed for complete problems in various complexity classes. Evidence is shown that there cannot be any complete problem on Aristotelian structures for several complexity classes. Our approach is extended beyond complete problems. Using a similar form, a logic is developed to capture the complexity class $NP\cap coNP$ which very likely contains no complete problem.Comment: This article has been accepted for publication in Logic Journal of IGPL Published by Oxford University Press; 23 pages, 2 figure

Towards journalometrical analysis of a scientific periodical: a case study

In this paper we use several approaches to analyse a scientific journal as a complex system and to make a possibly more complete description of its current state and evolution. Methods of complex networks theory, statistics, and queueing theory are used in this study. As a subject of the analysis we have chosen the journal ``Condensed Matter Physics'' (http://www.icmp.lviv.ua/journal/). In particular, based on the statistical data regarding the papers published in this journal since its foundation in 1993 up to now we have composed the co-authorship network and extracted its main quantitative characteristics. Further, we analyse the priorities of scientific trends reflected in the journal and its impact on the publications in other editions (the citation ratings). Moreover, to characterize an efficiency of the paper processing, we study the time dynamics of editorial processing in terms of queueing theory and human activity analysis

Counting invertible Schr\"odinger Operators over Finite Fields for Trees, Cycles and Complete Graphs

We count invertible Schr\"odinger operators (perturbations by diagonal matrices of the adjacency matrix) over finite fieldsfor trees, cycles and complete graphs.This is achieved for trees through the definition and use of local invariants (algebraic constructions of perhapsindependent interest).Cycles and complete graphs are treated by ad hoc methods.Comment: Final version to appear in Electronic Journal of Combinatoric