Alternative criterion for two-dimensional wrapping percolation

Based on the differences between a spanning cluster and a wrapping cluster, an alternative criterion for testing wrapping percolation is provided for two-dimensional lattices. By following the Newman-Ziff method, the finite size scaling of estimates for percolation thresholds are given. The results are consistent with those from Machta's method.Comment: 4 pages, 2 figure

Evaluation of a composite mobile holographic nondestructive test system

A simplified theoretical model for the interpretation of the double-exposure holographic interference fringe loci due to the general three-dimensional displacements was derived for the specific composite mobile holographic nondestructive test system. The model, representing a good approximation to a more tedious theoretical result, predicts that a combination of in-plane and out-of-plane displacements of the surface will produce concentric circular-shaped fringe patterns with locations of their center affected by the displacements. Appropriate experiments were designed and carried out for the test of the validity of the theory. These experiments include the taking of double-exposure holograms of in-plane translations and combined in-plane and out-of-plane translations. The simplified model agreed quite well with the experimental results. Experimentally observed effects due to the curvature of the test plate and the variations of the angles of incidence of the laser light suggest that in order for the simplified model to be able to predict the test results more accurately, incidence and reflection of the laser light should be chosen as nearly perpendicular to the surface of the tested object as possible

On the size of binary decision diagrams representing Boolean functions

AbstractWe consider the size of the representation of Boolean functions by several classes of binary decision diagrams (BDDs) (also called branching programs), namely the classes of arbitrary BDDs of real time BDD (RBDD) (i.e. BDDs where each computation path is limited to the number of variables), of free BDDs (FBDDs) (also called read-once-only branching programs), of ordered BDDs (OBDDS) i.e. FBDDs where variables are tested in the same order along all paths), and binary decision trees (BDTs).Using well-known techniques, we first establish asymptotically sharp bounds as a function of n on the minimum size of arbitrary BDDs representing almost all Boolean functions of n variables and provide asymptotic lower and upper bounds, differing only by a factor of two, on the minimum size OBDDs representing almost all Boolean functions of n variables.We then, using a method to obtain exponential lower bounds on complexity of computation of Boolean functions by RBDD, FBDD and OBDD that originated in (Breitbart, 1968), present the highest such bounds to date and also present improved bounds on the relative economy of description of particular Boolean functions by the above classes of BDDs. For each nontrivial pair of BDD classes considered, we exhibit infinite families of Boolean functions representable much more concisely by BDDs in one class than by BDDs in the other

Redox regulation of the mitogen-activated protein kinase pathway during lymphocyte activation

AbstractWe have previously demonstrated an obligatory requirement for intracellular reactive oxygen species generation during T lymphocyte activation, and have proposed that intracellular reactive oxygen species may act as signalling agents in the regulation of certain cellular processes, for example, during cell cycle entry. To test this hypothesis, we have been interested to determine which, if any, cell cycle entry events are affected by oxidative signalling. In earlier studies, we have identified the transcription factors NF-κB and AP-1 as molecular targets for oxidative signalling processes during cell cycle entry, and have shown that oxidative signalling is involved in the regulation of early changes in gene expression during the G0 to G1 phase transition. To extend these initial observations, we have examined the effect of antioxidant treatment on the activity of the mitogen-activated protein kinases erk1 and erk2, as members of a signal transduction pathway known to directly regulate transcription factor function. Using as a probe cysteamine, an aminothiol compound with both antioxidant and antiproliferative activity, we have identified erk2, a key element of the MAP kinase pathway, as being responsive to oxidative signalling during lymphocyte activation. These observations provide further evidence to suggest a role for intracellular oxidant generation as a regulatory mechanism during cell cycle entry, and establish a link between oxidative signalling and other aspects of the intracellular signalling network that is activated in response to mitogenic stimulation

Childhood development stages and learning on global issues

This helpdesk report provides a summary of available literature and evidence relating to childhood development stages; specifically, when is the best time to influence children’s thinking on global issues. This question is related to a second query covered in a separate helpdesk report that examines the development education landscape in the UK: specifically, what else apart from British Council’s Connecting Classrooms Programme is going on to build partnerships between schools in the UK and schools overseas? How many children/schools are part of something like this? These helpdesk reports are designed to help inform a business case and guide the Department for International Development’s thinking for a new approach to delivering development education in the UK when the current phases of Connecting Classrooms and the Global Learning Programme ends. K4D helpdesk reports provide summaries of current research, evidence and lessons learned. This report was commissioned by DFID

Phase transition in a log-normal Markov functional model

We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically large volatilities, respectively. These volatility regimes are separated by a phase transition at some critical value of the volatility. We investigate the conditions under which this phase transition occurs, and show that it is related to the position of the zeros of an appropriately defined generating function in the complex plane, in analogy with the Lee-Yang theory of the phase transitions in condensed matter physics.Comment: 9 pages, 5 figures. v2: Added asymptotic expressions for the convexity-adjusted Libors in the small and large volatility limits. v3: Added one reference. Final version to appear in Journal of Mathematical Physic

Hopping Conduction and Bacteria: Transport in Disordered Reaction-Diffusion Systems

We report some basic results regarding transport in disordered reaction-diffusion systems with birth (A->2A), death (A->0), and binary competition (2A->A) processes. We consider a model in which the growth process is only allowed to take place in certain areas--"oases"--while the rest of space--the "desert"--is hostile to growth. In the limit of low oasis density, transport is mediated through rare "hopping" events, necessitating the inclusion of discreteness effects in the model. By first considering transport between two oases, we are able to derive an approximate expression for the average time taken for a population to traverse a disordered medium.Comment: 4 pages, 2 figure