From a kinetic equation to a diffusion under an anomalous scaling

A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), i(t), Y(t)), where (K(t), i(t)) is an autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance, and Y(t) is an additive functional of K(t). We prove that under an anomalous rescaling Y converges in distribution to a two-dimensional Brownian motion. As a consequence, the appropriately rescaled solution of the Boltzmann equation converges to a diffusion equation

Autonomous clustering using rough set theory

This paper proposes a clustering technique that minimises the need for subjective human intervention and is based on elements of rough set theory. The proposed algorithm is unified in its approach to clustering and makes use of both local and global data properties to obtain clustering solutions. It handles single-type and mixed attribute data sets with ease and results from three data sets of single and mixed attribute types are used to illustrate the technique and establish its efficiency

Evaluating social science and humanities knowledge production: An exploratory analysis of dynamics in science systems

Knowledge is gaining increasing importance in modern-day society as a factor of production and, ultimately, growth. This article explores the dynamics in university knowledge production and its effect on the state of university-industry-policy exchange in the Netherlands. Science systems are said to be in transformation. The university has evolved from performing conventional research and educational functions to serving as an innovation-promoting knowledge hub; dynamics that have received mixed reactions. The social sciences and humanities (SSH) take a special position, insofar as their focus seems primarily to be placed on conventional research and educational functions, and not directly on (commercial) valorization. Societal changes are, however, pressing for a reconsideration of the role of SSH. In our article, we distinguish between three important new movements that seem to be affecting SSH. It is believed that these movements, which are already having an impact today, will considerably influence SSH in the future. These developments are further differentiation, synthesis between the various subdisciplines of SSH and the natural sciences, and shifts in paradigms. The aims of this article are twofold: (1) to assess what is believed to be the most likely development of SSH by means of discovering relevant subsets of factors influencing university knowledge production; and (2) to discover whether the knowledge production factors show characteristics of a general development similar to the "Mode 2" concept. A systematic qualitative database was created by means of 22 semi-structured personal interviews with key representatives from business, university and the policy sector. Our explanatory framework employs an artificial intelligence method, i.e. rough set analysis. On the basis of these results, we find that a small minority of the respondents prefers a closer relationship of SSH to society, government and industry, and other institutional centers of authority, whilst interdisciplinarity in particular is regarded as having an overall positive influence on the future of SSH in the Netherlands. Consequently, the idea of a clear distinction between Mode 1 and Mode 2 knowledge production, i.e. traditional knowledge and knowledge carried out in the context of application, is not supported by our data. © 2009 Interdisciplinary Centre for Comparative Research in the Social Sciences and ICCR Foundation

Thermal conductivity in harmonic lattices with random collisions

We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of nonlinearities of anharmonic chains and the resulting dynamics have similar macroscopic behaviour. In particular there is a superdiffusion of energy for unpinned acoustic chains. The corresponding evolution of the temperature profile is governed by a fractional heat equation. In non-acoustic chains we have normal diffusivity, even if momentum is conserved.Comment: Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.

SICTIN: Rapid footprinting of massively parallel sequencing data

BACKGROUND: Massively parallel sequencing allows for genome-wide hypothesis-free investigation of for instance transcription factor binding sites or histone modifications. Although nucleotide resolution detailed information can easily be generated, biological insight often requires a more general view of patterns (footprints) over distinct genomic features such as transcription start sites, exons or repetitive regions. The construction of these footprints is however a time consuming task. METHODS: The presented software generates a binary representation of the signals enabling fast and scalable lookup. This representation allows for footprint generation in mere minutes on a desktop computer. Several different input formats are accepted, e.g. the SAM format, bed-files and the UCSC wiggle track. CONCLUSIONS: Hypothesis-free investigation of genome wide interactions allows for biological data mining at a scale never before seen. Until recently, the main focus of analysis of sequencing data has been targeted on signal patterns around transcriptional start sites which are in manageable numbers. Today, focus is shifting to a wider perspective and numerous genomic features are being studied. To this end, we provide a system allowing for fast querying in the order of hundreds of thousands of features

Rough Sets Determined by Quasiorders

In this paper, the ordered set of rough sets determined by a quasiorder relation $R$ is investigated. We prove that this ordered set is a complete, completely distributive lattice. We show that on this lattice can be defined three different kinds of complementation operations, and we describe its completely join-irreducible elements. We also characterize the case in which this lattice is a Stone lattice. Our results generalize some results of J. Pomykala and J. A. Pomykala (1988) and M. Gehrke and E. Walker (1992) in case $R$ is an equivalence.Comment: 18 pages, major revisio