A switch convergence for a small perturbation of a linear recurrence equation

In this article we study a small random perturbation of a linear recurrence equation. If all the roots of its corresponding characteristic equation have modulus strictly less than one, the random linear recurrence goes exponentially fast to its limiting distribution in the total variation distance as time increases. By assuming that all the roots of its corresponding characteristic equation have modulus strictly less than one and some suitable conditions, we prove that this convergence happens as a switch-type, i.e., there is a sharp transition in the convergence to its limiting distribution. This fact is known as a cut-off phenomenon in the context of stochastic processes.Comment: 19 pages. Brazilian Journal of Probability and Statistics 2020

Book review: Refugees, capitalism and the British state: implications for social workers, volunteers and activists

"Refugees, Capitalism and the British State: Implications for Social Workers, Volunteers and Activists." Tom Vickers. Ashgate. 2012. --- In this period of economic crisis, public sector cuts, and escalating class struggles, Marxist theory offers social workers and service users important tools to help understand the structures of oppression they face and to devise effective means of resistance. This book uses Marxism’s lost insights, reinterpreting them for the current context by focusing on one particular section of the international working class: refugees and asylum seekers in Britain. Shuo Liu finds that this book offers a unique understanding of the refugee’s position in Britain, and is a valuable contribution to the anti-racism effort

Book review: legions of peace: UN peacekeepers from the global south by Philip Cunliffe

The huge number of security forces stationed around the world as United Nations peace keepers is second only to the global military deployments of the USA. But most UN peacekeepers come from the emerging powers and developing states that comprise the global South. A major contribution of Legions of Peace is its critical review of UN peacekeeping, which rejects any blind, religious like faith in such a system. The analysis of contemporary peacekeeping operations is backed up by rich material, which brilliantly answers the research question with strong and concise arguments, writes Shuo Liu

Voting with public information

We study the effect of public information on collective decision-making in a committee with members of both common and conflicting interests. We show that the set of preferences that allow for the existence of an informative voting equilibrium can be heavily restricted by the presence of a public signal, regardless of the size of the committee and the choice of the voting threshold value. What's worse, the presence of the public information introduces an inefficient equilibrium which robustly exists across different voting rules. To mitigate the harmful effect of the public information, we propose to use a class of more flexible voting rules, whose threshold values depend on both the precision and the realization of the public signal, that may restore the informative voting equilibrium. In particular, in a standard setting with common interest agents, the contingent voting rule that we construct not only always restores the informative voting equilibrium but also achieves full informational efficiency

Multilevel Diversity Coding with Secure Regeneration: Separate Coding Achieves the MBR Point

The problem of multilevel diversity coding with secure regeneration (MDC-SR) is considered, which includes the problems of multilevel diversity coding with regeneration (MDC-R) and secure regenerating code (SRC) as special cases. Two outer bounds are established, showing that separate coding of different messages using the respective SRCs can achieve the minimum-bandwidth-regeneration (MBR) point of the achievable normalized storage-capacity repair-bandwidth tradeoff regions for the general MDC-SR problem. The core of the new converse results is an exchange lemma, which can be established using Han's subset inequality

Productions of heavy charged leptons via gluon fusion at LHC: A revisit

Heavy charged lepton productions via gluon fusion at the LHC are revisited. Full loop calculations are adopted with an updated parton distribution function and electroweak data. Including contribution from new generation quarks in the loop, pair production of the sequential heavy lepton via gluon fusion at the LHC dominates over that via the Drell-Yan mechanism in some heavy lepton mass range. Exotic lepton single production of vector-like lepton extended models is also calculated. In the later case, the gluon fusion mechanism via the Higgs exchange is emphasized. Our numerical results for both pair and single production of heavy leptons are smaller than previous studies especially for a large heavy lepton mass as a result of full loop calculation and due to the mixing angles.Comment: 18 pages, 7 figures; (v2) typos corrected, references adde