The last theorem of Lecture 9 assures us that in any Büchi game one of the two players has a positional winning strategy. Thus, for any alternating Büchi automaton (ABA ) A and word w, either the automaton or the pathfinder has a positional winning strategy in the game G(A,w). Thus, if A accepts w there is a positional run for A on w. Consider the ABA A1 from the previous lecture. Here is a pos...

We consider a gyroscopic system with two degrees of freedom under the action of small dissipative and non-conservative positional forces, which has its origin in the models of rotating bodies of revolution being in frictional contact. The spectrum of the unperturbed gyroscopic system forms a ”spectral mesh” in the plane ”frequency – gyroscopic parameter” with double semi-simple purely imaginary...

The concept of positional information is central to our understanding of how cells determine their location in a multicellular structure and thereby their developmental fates. Nevertheless, positional information has neither been defined mathematically nor quantified in a principled way. Here we provide an information-theoretic definition in the context of developmental gene expression patterns...

Three solutions to the problem of serial order can be identified: chaining, ordinal and positional theories. Error patterns in serial recall from short-term memory fail to support chaining theories, yet provide unequivocal evidence for positional theories. In a new model of short-term memory, the Start-End Model (SEM), the positions of items in a sequence are coded relative to the start and end...

This paper describes an implementation to compute positional ngram statistics (i.e. Frequency and Mutual Expectation) based on masks, suffix array-based data structures and multidimensional arrays. Positional ngrams are ordered sequences of words that represent continuous or discontinuous substrings of a corpus. In particular, the positional ngram model has shown successful results for the extr...

The Visual Language Compiler-Compiler (VLCC) is a grammar-based graphical system for the automatic generation of visual programming environments. In this paper the theoretical and algorithmic issues of VLCC are discussed in detail. The parsing methodology we present is based on the “positional grammar” model. Positional grammars naturally extend context-free grammars by considering new relation...

Osteochondrosis (OC) is a joint disorder that frequently causes leg weakness in growing pigs, resulting in welfare problems and economic losses. We aimed to detect molecular pathways relevant to the emergence of the disease and to identify candidate genes for the liability to the disorder. Therefore, we compared microarray-based expression patterns of articular cartilage with (n=11) and without...

INTRODUCTION Positional therapy is a simple means of therapy in sleep apnoea syndrome, but due to controversial or lacking evidence, it is not widely accepted as appropriate treatment. In this study, we analysed data to positional therapy with regard to successful reduction of AHI and predictors of success. METHODS All consecutive patients undergoing polysomnography between 2007 and 2011 were...

Positional specification by morphogen gradients is traditionally viewed as a two-step process. A gradient is formed and then interpreted, providing a spatial metric independent of the target tissue, similar to the concept of space in classical mechanics. However, the formation and interpretation of gradients are coupled, dynamic processes. We introduce a conceptual framework for positional spec...