Exact and approximate results for deposition and annihilation processes on graphs

We consider random sequential adsorption processes where the initially empty sites of a graph are irreversibly occupied, in random order, either by monomers which block neighboring sites, or by dimers. We also consider a process where initially occupied sites annihilate their neighbors at random times. We verify that these processes are well defined on infinite graphs, and derive forward equations governing joint vacancy/occupation probabilities. Using these, we derive exact formulae for occupation probabilities and pair correlations in Bethe lattices. For the blocking and annihilation processes we also prove positive correlations between sites an even distance apart, and for blocking we derive rigorous lower bounds for the site occupation probability in lattices, including a lower bound of 1/3 for Z^2. We also give normal approximation results for the number of occupied sites in a large finite graph.Comment: Published at http://dx.doi.org/10.1214/105051604000000765 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimising Matrix Product State Simulations of Shor's Algorithm

We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on $r$, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.Comment: 8 pages, 2 figures, 2 tables. v2 using PDFLaTeX compiler. v3 to include extra references. v4 for publication in Quantu

Franch-Canadian Communities in the American Upper Midwest during the Nineteenth Century

La distribution des établissements canadiens-français dans l'Ouest américain au XIXe siècle n'avait aucune relation avec la distribution des postes de traite de fourrures du siècle précédent. Les Canadiens français du XIXe siècle furent attirés par les opportunités d'emploi le long des frontières agricole, minière et forestière. Détroit, Chicago et Minneapolis-St-Paul ont vu naître des paroisses canadiennes-françaises qui entretenaient des liens avec les communautés rurales. Le maintien de la langue française, l'héritage culturel et l'affiliation à l'église catholique variaient à travers la région. L'américanisation des Canadiens français fut directement reliée à leur réussite économique. Une identité canadienne-française a été maintenue dans les régions rurales les plus pauvres et marginales du nord des états du Michigan, du Winsconsin et du Minnesota.The pattern of nineteenth-century French-Canadian settlements in the American Midwest bore no relation to the pattern of fur-trading posts of the eighteenth century. French-Canadians of the nine-teenth century were attracted by employment opportunities along the farming, lumbering, and mining frontiers. Detroit, Chicago, and Minneapolis-St. Paul developed French-Canadian parishes which maintained links with rural communities. Survival of the French language, cultural heritage, and affiliation with the Catholic Church varied throughout the region. Americanization of French-Canadians went hand in hand with their commercial success. A French-Canadian identity survived in the poorest, marginal, rural areas of northern Michigan, Wisconsin, and Minnesota

You Must Defeat [The Tutorial] To Stand a Chance : Learning To Play Competitive Fighting Video Games

Modern competitive video games are complex systems that require players to learn techniques and develop strategies in response to computer- or human-controlled opponents. Building on the work of both game studies scholars and game designers, this thesis analyzes various learning spaces within and surrounding competitive video games, including in-game tutorials, arcades, and online communities. It focuses on “fighting games,” those competitive video games in which, typically, two players control characters to face off in single combat. Through analysis of the interfaces used, the audio-visual artifacts present within the tutorial sections of fighting games, and the paratextual materials produced by members of the fighting game community to instruct others on how to play, this thesis highlights the learning principles active within this genre of video games

A True Sense of Security: How Kirschner v. J.P. Morgan Chase Illustrates the Failings of the Reves Family-Resemblance Test and the Need to Recognize Some Syndicated Loans as Securities for the Sake of the Financial System

Following the 2008 financial crisis, Congress implemented a number of reforms aimed at ensuring that such a man-made disaster—fueled by greed and willful ignorance—is not permitted to happen again. On the surface, these reforms appear to be a success; however, under the surface, there is currently a capital market that is effectively ignored, not only by the reforms passed in the wake of the financial crisis, but by virtually all securities regulation. This capital market, which revolves around so-called syndicated loans, is estimated to be larger than the subprime-mortgage collateralized debt obligations market was at its apex, and yet it is unregulated, in large part due to the application of the Reves family resemblance test—the test courts use to determine if something is a security, and thus subject to securities laws. This test is outdated and fails to account for the modern-day syndicated loan market, which has undergone considerable changes in the last decade. In order to ensure that courts are properly classifying securities as securities, this note proposes an updated test for subjecting investment vehicles to securities laws and regulations, which properly takes into account the modern-day realities of the syndicated loan market. This solution will promote increased accountability and diligence in the syndicated loan market, which is necessary to ensure that Congress’s goal of preventing another financial crisis is realized

Bayesian regression discontinuity designs: Incorporating clinical knowledge in the causal analysis of primary care data

The regression discontinuity (RD) design is a quasi-experimental design that estimates the causal effects of a treatment by exploiting naturally occurring treatment rules. It can be applied in any context where a particular treatment or intervention is administered according to a pre-specified rule linked to a continuous variable. Such thresholds are common in primary care drug prescription where the RD design can be used to estimate the causal effect of medication in the general population. Such results can then be contrasted to those obtained from randomised controlled trials (RCTs) and inform prescription policy and guidelines based on a more realistic and less expensive context. In this paper we focus on statins, a class of cholesterol-lowering drugs, however, the methodology can be applied to many other drugs provided these are prescribed in accordance to pre-determined guidelines. NHS guidelines state that statins should be prescribed to patients with 10 year cardiovascular disease risk scores in excess of 20%. If we consider patients whose scores are close to this threshold we find that there is an element of random variation in both the risk score itself and its measurement. We can thus consider the threshold a randomising device assigning the prescription to units just above the threshold and withholds it from those just below. Thus we are effectively replicating the conditions of an RCT in the area around the threshold, removing or at least mitigating confounding. We frame the RD design in the language of conditional independence which clarifies the assumptions necessary to apply it to data, and which makes the links with instrumental variables clear. We also have context specific knowledge about the expected sizes of the effects of statin prescription and are thus able to incorporate this into Bayesian models by formulating informative priors on our causal parameters.Comment: 21 pages, 5 figures, 2 table