Entropy and the variational principle for actions of sofic groups

Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective we develop a more general approach to sofic entropy which produces both measure and topological dynamical invariants, and we establish the variational principle in this context. In the case of residually finite groups we use the variational principle to compute the topological entropy of principal algebraic actions whose defining group ring element is invertible in the full group C*-algebra.Comment: 44 pages; minor changes; to appear in Invent. Mat

Structured computer-based training in the interpretation of neuroradiological images

Computer-based systems may be able to address a recognised need throughout the medical profession for a more structured approach to training. We describe a combined training system for neuroradiology, the MR Tutor that differs from previous approaches to computer-assisted training in radiology in that it provides case-based tuition whereby the system and user communicate in terms of a well-founded Image Description Language. The system implements a novel method of visualisation and interaction with a library of fully described cases utilising statistical models of similarity, typicality and disease categorisation of cases. We describe the rationale, knowledge representation and design of the system, and provide a formative evaluation of its usability and effectiveness

The UK risk assessment scheme for all non-native species

1. A pest risk assessment scheme, adapted from the EPPO (European and Mediterranean Plant Protection Organisation) scheme, was developed to assess the risks posed to UK species, habitats and ecosystems by non-native taxa. 2. The scheme provides a structured framework for evaluating the potential for non-native organisms, whether intentional or unintentional introductions, to enter, establish, spread and cause significant impacts in all or part of the UK. Specialist modules permit the relative importance of entry pathways, the vulnerability of receptors and the consequences of policies to be assessed and appropriate risk management options to be selected. Spreadsheets for summarising the level of risk and uncertainty, invasive attributes and economic impact were created. In addition, new methods for quantifying economic impact and summarising risk and uncertainty were explored. 3. Although designed for the UK, the scheme can readily be applied elsewhere

Property (T)(T) for noncommutative universal lattices

We establish a new spectral criterion for Kazhdan's property $(T)$ which is applicable to a large class of discrete groups defined by generators and relations. As the main application, we prove property $(T)$ for the groups $EL_n(R)$, where $n\geq 3$ and $R$ is an arbitrary finitely generated associative ring. We also strengthen some of the results on property $(T)$ for Kac-Moody groups from a paper of Dymara and Januszkiewicz (Invent. Math 150 (2002)).Comment: 47 pages; final versio

Generation of Porous Particle Structures using the Void Expansion Method

The newly developed "void expansion method" allows for an efficient generation of porous packings of spherical particles over a wide range of volume fractions using the discrete element method. Particles are randomly placed under addition of much smaller "void-particles". Then, the void-particle radius is increased repeatedly, thereby rearranging the structural particles until formation of a dense particle packing. The structural particles' mean coordination number was used to characterize the evolving microstructures. At some void radius, a transition from an initially low to a higher mean coordination number is found, which was used to characterize the influence of the various simulation parameters. For structural and void-particle stiffnesses of the same order of magnitude, the transition is found at constant total volume fraction slightly below the random close packing limit. For decreasing void-particle stiffness the transition is shifted towards a smaller void-particle radius and becomes smoother.Comment: 9 pages, 8 figure

Water sensitive urban design in the city of the future

With timeframes for addressing the issues of the City of the Future (CotF) rapidly approaching (e.g. 2020, 2025, 2050), this paper integrates international research knowledge and expertise from four continents. It critically evaluates the role of water sensitive urban design (WSUD) in the CotF in terms of overlapping theory and practice. The aspirations of water sensitive cities are reviewed and multiple drivers for applying WSUD are described from developing and developed country perspectives In addition, the potential for WSUD to support cities in ‘leap-frogging’ towards their visions are explored. The role of WSUD within the wider context of achieving sustainable living objectives (e.g. greater resilience, low carbon living, sustainable transportation, local food supply and social stability) is debated and the concept of the ‘multi-objective city’ introduced. Conclusions are drawn regarding opportunities for the WSUD process to provide a framework within which professionals from many disciplines can support landscape architects and urban planners in achieving multiobjective liveable cities are identified

A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself

We give an example of an exact, stably finite, simple. separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank zero and stable rank one, has a unique tracial state, and the order on projections over D is determined by traces. It also absorbs the Jiang-Su algebra Z, and in fact absorbs the 3^{\infty} UHF algebra. We can also explicitly compute the K-theory of D, namely K_0 (D) = Z[1/3] with the standard order, and K_1 (D) = 0, as well as the Cuntz semigroup of D.Comment: 16 pages; AMSLaTeX. The material on other possible K-groups for such an algebra has been moved to a separate paper (1309.4142 [math.OA]

One-Loop QCD Corrections to the Thermal Wilson Line Model

We calculate the time independent four-point function in high temperature (T) QCD and obtain the leading momentum dependent terms. Furthermore, we relate these derivative interactions to derivative terms in a recently proposed finite T effective action based on the SU(3) Wilson Line and its trace, the Polyakov Loop. By this procedure we thus obtain a perturbative matching at finite T between QCD and the effective model. In particular, we calculate the leading perturbative QCD-correction to the kinetic term for the Polyakov Loop.Comment: Minor changes, one reference adde