Stochastic evolution of four species in cyclic competition

We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios, from single species domination to coexistence between non-interacting species. Using exact results and numerical simulations we discuss the temporal evolution of the system for different values of $N$, for different values of the reaction rates, as well as for different initial conditions. As expected, the stochastic evolution is found to closely follow the mean-field result for large $N$, with notable deviations appearing in proximity of extinction events. Different ways of characterizing and predicting extinction events are discussed.Comment: 19 pages, 6 figures, submitted to J. Stat. Mec

Some triviality results for quasi-Einstein manifolds and Einstein warped products

In this paper we prove a number of triviality results for Einstein warped products and quasi-Einstein manifolds using different techniques and under assumptions of various nature. In particular we obtain and exploit gradient estimates for solutions of weighted Poisson-type equations and adaptations to the weighted setting of some Liouville-type theorems.Comment: 15 pages, fixed minor mistakes in Section

Compression load failure of aluminum plates due to fire

An experimental study was performed to quantify the response and failure of 5083-H116 and 6082-T6 aluminum plates under compression load while being subjected to a constant heat flux representing a fire exposure. Using an intermediate scale loading frame with integrated heating, the study evaluated the effects of geometry, aluminum type, fire exposure, load, and fire protection. Intermediate scale aluminum panels which were more than 0.7 m high and 0.2 m wide were used to gain insights into the structural behavior of large structural sections exposed to fire. Failure temperatures were measured to range from 100 to 480 C and were dependent on applied stress and aluminum type. This indicates that the use of a single temperature criterion in fire resistance without load as typically done is not sufficient for evaluating structural response during fire. An empirical failure model was developed to account for fire exposure conditions, aluminum type, and geometr

A Map of Update Constraints in Inductive Inference

We investigate how different learning restrictions reduce learning power and how the different restrictions relate to one another. We give a complete map for nine different restrictions both for the cases of complete information learning and set-driven learning. This completes the picture for these well-studied \emph{delayable} learning restrictions. A further insight is gained by different characterizations of \emph{conservative} learning in terms of variants of \emph{cautious} learning. Our analyses greatly benefit from general theorems we give, for example showing that learners with exclusively delayable restrictions can always be assumed total.Comment: fixed a mistake in Theorem 21, result is the sam

Comparative analysis of rigidity across protein families

We present a comparative study in which 'pebble game' rigidity analysis is applied to multiple protein crystal structures, for each of six different protein families. We find that the main-chain rigidity of a protein structure at a given hydrogen bond energy cutoff is quite sensitive to small structural variations, and conclude that the hydrogen bond constraints in rigidity analysis should be chosen so as to form and test specific hypotheses about the rigidity of a particular protein. Our comparative approach highlights two different characteristic patterns ('sudden' or 'gradual') for protein rigidity loss as constraints are removed, in line with recent results on the rigidity transitions of glassy networks

Stroke Quality Measures in Mexican Americans and Non-Hispanic Whites

Mexican Americans (MAs) have been shown to have worse outcomes after stroke than non-Hispanic Whites (NHWs), but it is unknown if ethnic differences in stroke quality of care may contribute to these worse outcomes. We investigated ethnic differences in the quality of inpatient stroke care between MAs and NHWs within the population-based prospective Brain Attack Surveillance in Corpus Christi (BASIC) Project (February 2009- June 2012). Quality measures for inpatient stroke care, based on the 2008 Joint Commission Primary Stroke Center definitions were assessed from the medical record by a trained abstractor. Two summary measure of overall quality were also created (binary measure of defect-free care and the proportion of measures achieved for which the patient was eligible). 757 individuals were included (480 MAs and 277 NHWs). MAs were younger, more likely to have hypertension and diabetes, and less likely to have atrial fibrillation than NHWs. MAs were less likely than NHWs to receive tPA (RR: 0.72, 95% confidence interval (CI) 0.52, 0.98), and MAs with atrial fibrillation were less likely to receive anticoagulant medications at discharge than NHWs (RR 0.73, 95% CI 0.58, 0.94). There were no ethnic differences in the other individual quality measures, or in the two summary measures assessing overall quality. In conclusion, there were no ethnic differences in the overall quality of stroke care between MAs and NHWs, though ethnic differences were seen in the proportion of patients who received tPA and anticoagulant at discharge for atrial fibrillation

Cauchy's formulas for random walks in bounded domains

Cauchy's formula was originally established for random straight paths crossing a body $B \subset \mathbb{R}^{n}$ and basically relates the average chord length through $B$ to the ratio between the volume and the surface of the body itself. The original statement was later extended in the context of transport theory so as to cover the stochastic paths of Pearson random walks with exponentially distributed flight lengths traversing a bounded domain. Some heuristic arguments suggest that Cauchy's formula may also hold true for Pearson random walks with arbitrarily distributed flight lengths. For such a broad class of stochastic processes, we rigorously derive a generalized Cauchy's formula for the average length travelled by the walkers in the body, and show that this quantity depends indeed only on the ratio between the volume and the surface, provided that some constraints are imposed on the entrance step of the walker in $B$. Similar results are obtained also for the average number of collisions performed by the walker in $B$, and an extension to absorbing media is discussed.Comment: 12 pages, 6 figure

General flux to a trap in one and three dimensions

The problem of the flux to a spherical trap in one and three dimensions, for diffusing particles undergoing discrete-time jumps with a given radial probability distribution, is solved in general, verifying the Smoluchowski-like solution in which the effective trap radius is reduced by an amount proportional to the jump length. This reduction in the effective trap radius corresponds to the Milne extrapolation length.Comment: Accepted for publication, in pres