Model of the early development of thalamo-cortical connections and area patterning via signaling molecules

The mammalian cortex is divided into architectonic and functionally distinct areas. There is growing experimental evidence that their emergence and development is controlled by both epigenetic and genetic factors. The latter were recently implicated as dominating the early cortical area specification. In this paper, we present a theoretical model that explicitly considers the genetic factors and that is able to explain several sets of experiments on cortical area regulation involving transcription factors Emx2 and Pax6, and fibroblast growth factor FGF8. The model consists of the dynamics of thalamo- cortical connections modulated by signaling molecules that are regulated genetically, and by axonal competition for neocortical space. The model can make predictions and provides a basic mathematical framework for the early development of the thalamo-cortical connections and area patterning that can be further refined as more experimental facts become known.Comment: brain, model, neural development, cortical area patterning, signaling molecule

The Weyl-Heisenberg Group on the Noncommutative Two-Torus: A Zoo of Representations

In order to assess possible observable effects of noncommutativity in deformations of quantum mechanics, all irreducible representations of the noncommutative Heisenberg algebra and Weyl-Heisenberg group on the two-torus are constructed. This analysis extends the well known situation for the noncommutative torus based on the algebra of the noncommuting position operators only. When considering the dynamics of a free particle for any of the identified representations, no observable effect of noncommutativity is implied.Comment: 24 pages, no figure

A further improvement of the quantitative Subspace Theorem

In 2002, Evertse and Schlickewei obtained a quantitative version of the so-called Absolute Parametric Subspace Theorem. This result deals with a parametrized class of twisted heights. One of the consequences of this result is a quantitative version of the Absolute Subspace Theorem, giving an explicit upper bound for the number of subspaces containing the solutions of the Diophantine inequality under consideration. In the present paper, we further improve Evertse's and Schlickewei's quantitative version of the Absolute Parametric Subspace Theorem, and deduce an improved quantitative version of the Absolute Subspace Theorem. We combine ideas from the proof of Evertse and Schlickewei (which is basically a substantial refinement of Schmidt's proof of his Subspace Theorem from 1972, with ideas from Faltings' and Wuestholz' proof of the Subspace Theorem.Comment: 93 page

Classes of Skorokhod Embeddings for the Simple Symmetric Random Walk

The Skorokhod Embedding problem is well understood when the underlying process is a Brownian motion. We examine the problem when the underlying is the simple symmetric random walk and when no external randomisation is allowed. We prove that any measure on Z can be embedded by means of a minimal stopping time. However, in sharp contrast to the Brownian setting, we show that the set of measures which can be embedded in a uniformly integrable way is strictly smaller then the set of centered probability measures: specifically it is a fractal set which we characterise as an iterated function system. Finally, we define the natural extension of several known constructions from the Brownian setting and show that these constructions require us to further restrict the sets of target laws

Representing fuzzy decision tables in a fuzzy relational database environment.

In this paper the representation of decision tables in a relational database environment is discussed. First, crisp decision tables are defined. Afterwards a technique to represent decision tables in a relational system is presented. Next, fuzzy extensions are made to crisp decision tables in order to deal with imprecision and uncertainty. As a result, with crisp decision tables as special cases fuzzy decision tables are defined which include fuzziness in the conditions as well as in the actions. Analogous to the crisp case, it is demonstrated how fuzzy decision tables can be stored in a fuzzy relational database environment. Furthermore, consultation of these tables is discussed using fuzzy queries.Decision making;

Operator product expansion and analyticity

We discuss the current use of the operator product expansion in QCD calculations. Treating the OPE as an expansion in inverse powers of an energy-squared variable (with possible exponential terms added), approximating the vacuum expectation value of the operator product by several terms and assuming a bound on the remainder along the euclidean region, we observe how the bound varies with increasing deflection from the euclidean ray down to the cut (Minkowski region). We argue that the assumption that the remainder is constant for all angles in the cut complex plane is not justified. Making specific assumptions on the properties of the expanded function, we obtain bounds on the remainder in explicit form and show that they are very sensitive both to the deflection angle and to the class of functions chosen. The results obtained are discussed in connetcion with calculations of the coupling constant \alpha_{s} from the \tau decay.Comment: Preprint PRA-HEP 99/04, 20 page

A review of governmental management accounting : research around the turn of the century

This paper shows that governmental management accounting research around the turn of the century, as published in FAM, MAR and EAR, is different from general management accounting research in some respects. Although there are variations related to topics, theories and research methods, a mainstream in governmental management accounting research seems to exist. Research is predominantly directed to the way in which technical management accounting innovations are used, including organizational and contextual factors that might influence the use of these new techniques. Qualitatively oriented case and field studies are the dominant research methods, and the research is inspired by various theoretical viewpoints, e.g. economics, organization theory and neo-institutional theory. NPM, regarded as a lower level economic theory, turns out to be highly influential. The paper gives recommendations for governmental management accounting research in the future: more attention has to be paid to quantitative research, impact studies on NPM must be promoted, and jointly conducted research projects by management accounting and public administration researchers are welcomed.