On the local uniqueness of steady states for the Vlasov-Poisson system

Motivated by recent results of Lemou-M\'ehats-R\"aphael and Lemou concerning the quatitative stability of some suitable steady states for the Vlasov-Poisson system, we investigate the local uniqueness of steady states near these one. This research is inspired by analogous results of Couffrut and \v{S}ver\'ak in the context of the 2D Euler equations

Arbitrary Justice?: A Comparative Analysis of Canadian Death Sentence Passed and Commuted during the First World War

The topic of military executions has dominated the study of discipline and punishment during the First World War. Considering the relatively small number of men who were executed, 361 in British and Dominion forces combined, it is startling how much attention the subject has garnered. The morality of the practice has been widely discussed and debated and it has spawned recent pardons campaigns in the United Kingdom, New Zealand and Canada. Yet, virtually ignored in these debates have been the stories of the 3,080 men of the British and Dominion forces who were also sentenced to death, but saw their sentences commuted. What was the fate of these men and what accounts for their salvation when the luck of others had run out? The main focus of this article is a comparison between those death sentences confirmed and those commuted. The topic has been solely researched within a Canadian context in which 222 death sentences were passed during the course of the war, and 25 Canadians actually faced with a firing squad. Similar to British statistics as a whole, 89 per cent of all Canadian death sentences were commuted in the First World War. For the purpose of this article, the court-martial and personnel records of 50 Canadian soldiers have been studied. An attempt has been made to find patterns and consistencies to explain why some death sentences were confirmed and others were not. Preliminary findings suggest that the timing of a particular offense, the disciplinary state of an accused soldier’s battalion and the opinions of divisional commanders were the most important influences acting upon the final decision of a military court martial. However, where an individual soldier’s personal disciplinary record was taken into account, the decisions of the courts-martial appear, more often than not, to have been quite random and arbitrary

The end time of SIS epidemics driven by random walks on edge-transitive graphs

Network epidemics is a ubiquitous model that can represent different phenomena and finds applications in various domains. Among its various characteristics, a fundamental question concerns the time when an epidemic stops propagating. We investigate this characteristic on a SIS epidemic induced by agents that move according to independent continuous time random walks on a finite graph: Agents can either be infected (I) or susceptible (S), and infection occurs when two agents with different epidemic states meet in a node. After a random recovery time, an infected agent returns to state S and can be infected again. The End of Epidemic (EoE) denotes the first time where all agents are in state S, since after this moment no further infections can occur and the epidemic stops. For the case of two agents on edge-transitive graphs, we characterize EoE as a function of the network structure by relating the Laplace transform of EoE to the Laplace transform of the meeting time of two random walks. Interestingly, this analysis shows a separation between the effect of network structure and epidemic dynamics. We then study the asymptotic behavior of EoE (asymptotically in the size of the graph) under different parameter scalings, identifying regimes where EoE converges in distribution to a proper random variable or to infinity. We also highlight the impact of different graph structures on EoE, characterizing it under complete graphs, complete bipartite graphs, and rings

First-order transition in Potts models with "invisible' states: Rigorous proofs

In some recent papers by Tamura, Tanaka and Kawashima [arXiv:1102.5475, arXiv:1012.4254], a class of Potts models with "invisible" states was introduced, for which the authors argued by numerical arguments and by a mean-field analysis that a first-order transition occurs. Here we show that the existence of this first-order transition can be proven rigorously, by relatively minor adaptations of existing proofs for ordinary Potts models. In our argument we present a random-cluster representation for the model, which might be of independent interest

Diagnostic, Prognostic and Therapeutic Value of Gene Signatures

Gene expression studies have revealed diagnostic profiles and upregulation of specific pathways in many solid tumors. Some gene-expression signatures are already used as predictors of relapse in early breast cancer patients. The explosion of new information in gene expression profiling could potentially lead to the development of tailored treatments in many solid tumors. In addition, many studies are ongoing to validate these signatures also in predicting response to hormonal, chemotherapeutic, and targeted agents in breast cancer as well as in other tumors. This book has been carried out with the aim of providing readers a useful and comprehensive resource about the range of applications of microarray technology on oncological diseases. The book is principally addressed to resident and fellow physicians, medical oncologists, molecular biologists, biotechnologists, and those who study oncological diseases. The chapters have been written by leading international researchers on these topics who have prepared their manuscripts according to current literature and field experience with microarray technology