Cellular automata and Lyapunov exponents

In this article we give a new definition of some analog of Lyapunov exponents for cellular automata . Then for a shift ergodic and cellular automaton invariant probability measure we establish an inequality between the entropy of the automaton, the entropy of the shift and the Lyapunov exponent

The organisational and human resource challenges facing primary care trusts : protocol of a multiple case study

BACKGROUND: The study is designed to assess the organisational and human resource challenges faced by Primary Care Trusts (PCTs). Its objectives are to: specify the organisational and human resources challenges faced by PCTs in fulfilling the roles envisaged in government and local policy; examine how PCTs are addressing these challenges, in particular, to describe the organisational forms they have adopted, and the OD/HR strategies and initiatives they have planned or in place; assess how effective these structures, strategies and initiatives have been in enabling the PCTs to meet the organisational and human resources challenges they face; identify the factors, both internal to the PCT and in the wider health community, which have contributed to the success or failure of different structures, strategies and initiatives. METHODS: The study will be undertaken in three stages. In Stage 1 the key literature on public sector and NHS organisational development and human resources management will be reviewed, and discussions will be held with key researchers and policy makers working in this area. Stage 2 will focus on detailed case studies in six PCTs designed to examine the organisational and human resources challenges they face. Data will be collected using semi-structured interviews, group discussion, site visits, observation of key meetings and examination of local documentation. The findings from the case study PCTs will be cross checked with a Reference Group of up to 20 other PCG/Ts, and key officers working in organisational development or primary care at local, regional and national level. In Stage 3 analysis of findings from the preparatory work, the case studies and the feedback from the Reference Group will be used to identify practical lessons for PCTs, key messages for policy makers, and contributions to further theoretical development

Eluding SUSY at every genus on stable closed string vacua

In closed string vacua, ergodicity of unipotent flows provide a key for relating vacuum stability to the UV behavior of spectra and interactions. Infrared finiteness at all genera in perturbation theory can be rephrased in terms of cancelations involving only tree-level closed strings scattering amplitudes. This provides quantitative results on the allowed deviations from supersymmetry on perturbative stable vacua. From a mathematical perspective, diagrammatic relations involving closed string amplitudes suggest a relevance of unipotent flows dynamics for the Schottky problem and for the construction of the superstring measure.Comment: v2, 17 pages, 8 figures, typos corrected, new figure added with 3 modular images of long horocycles,(obtained with Mathematica

Insecurity for compact surfaces of positive genus

A pair of points in a riemannian manifold $M$ is secure if the geodesics between the points can be blocked by a finite number of point obstacles; otherwise the pair of points is insecure. A manifold is secure if all pairs of points in $M$ are secure. A manifold is insecure if there exists an insecure point pair, and totally insecure if all point pairs are insecure. Compact, flat manifolds are secure. A standing conjecture says that these are the only secure, compact riemannian manifolds. We prove this for surfaces of genus greater than zero. We also prove that a closed surface of genus greater than one with any riemannian metric and a closed surface of genus one with generic metric are totally insecure.Comment: 37 pages, 11 figure

Conservation Laws in Cellular Automata

If X is a discrete abelian group and B a finite set, then a cellular automaton (CA) is a continuous map F:B^X-->B^X that commutes with all X-shifts. If g is a real-valued function on B, then, for any b in B^X, we define G(b) to be the sum over all x in X of g(b_x) (if finite). We say g is `conserved' by F if G is constant under the action of F. We characterize such `conservation laws' in several ways, deriving both theoretical consequences and practical tests, and provide a method for constructing all one-dimensional CA exhibiting a given conservation law.Comment: 19 pages, LaTeX 2E with one (1) Encapsulated PostScript figure. To appear in Nonlinearity. (v2) minor changes/corrections; new references added to bibliograph

Synaptotagmin 13 is neuroprotective across motor neuron diseases

In amyotrophic lateral sclerosis (ALS) and spinal muscular atrophy (SMA), spinal and lower brainstem motor neurons degenerate, but some motor neuron subtypes are spared, including oculomotor neurons (OMNs). The mechanisms responsible for this selective degeneration are largely unknown, but the molecular signatures of resistant and vulnerable motor neurons are distinct and offer clues to neuronal resilience and susceptibility. Here, we demonstrate that healthy OMNs preferentially express Synaptotagmin 13 (SYT13) compared to spinal motor neurons. In end-stage ALS patients, SYT13 is enriched in both OMNs and the remaining relatively resilient spinal motor neurons compared to controls. Overexpression of SYT13 in ALS and SMA patient motor neurons in vitro improves their survival and increases axon lengths. Gene therapy with Syt13 prolongs the lifespan of ALS mice by 14% and SMA mice by 50% by preserving motor neurons and delaying muscle denervation. SYT13 decreases endoplasmic reticulum stress and apoptosis of motor neurons, both in vitro and in vivo. Thus, SYT13 is a resilience factor that can protect motor neurons and a candidate therapeutic target across motor neuron diseases

The Role of Culture in Sports Sponsorship: an Update

Nowadays Sponsorship is an important part of sports events. Sports sponsorship offers more benefits, more variety and also it’s a more powerful form of marketing. In general, sponsorship holds a unique position in the marketing mix because it is effective in building brand awareness, provides different marketing platforms and valuable networking and hospitality opportunities. Sponsorship marketing efforts can be influenced by culture. Especially when global sponsorship in sports which refers to sports events in different countries with different cultures, is under consideration. In such situations, sponsorship aspects can be affected by cultural obligations which are discussed in this article

Heavy-Ion-Induced Electronic Desorption of Gas from Metals

During heavy-ion operation in several particle accelerators worldwide, dynamic pressure rises of orders of magnitude were triggered by lost beam ions that bombarded the vacuum chamber walls. This ion-induced molecular desorption, observed at CERN, GSI, and BNL, can seriously limit the ion beam lifetime and intensity of the accelerator. From dedicated test stand experiments we have discovered that heavy-ion-induced gas desorption scales with the electronic energy loss (dEe/dx) of the ions slowing down in matter; but it varies only little with the ion impact angle, unlike electronic sputtering