Benford's Law, Values of L-functions and the 3x+1 Problem

We show the leading digits of a variety of systems satisfying certain conditions follow Benford's Law. For each system proving this involves two main ingredients. One is a structure theorem of the limiting distribution, specific to the system. The other is a general technique of applying Poisson Summation to the limiting distribution. We show the distribution of values of L-functions near the central line and (in some sense) the iterates of the 3x+1 Problem are Benford.Comment: 25 pages, 1 figure; replacement of earlier draft (corrected some typos, added more exposition, added results for characteristic polynomials of unitary matrices

Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues

We present two graph quantities Psi(G,S) and Psi_2(G) which give constant factor estimates to the Dirichlet and Neumann eigenvalues, lambda(G,S) and lambda_2(G), respectively. Our techniques make use of a discrete Hardy-type inequality due to Muckenhoupt

Downsizing and Structural Holes: Their Impact on Layoff Survivors’ Perceptions of Organizational Chaos and Openness to Change

Organizational downsizing places many strains on surviving employees. Despite the implicit relationship between changes to communication networks and employee responses, few studies examine downsizing-induced network changes or the impact of these changes on employees. This longitudinal investigation examined fluctuations in structural holes within a hospitality company\u27s corporate headquarters resulting from the loss and gain of communication contacts. Building on Burt\u27s treatise on structural holes, we tested a measurement of structural holes and its relationship to layoff survivors\u27 perceptions of organizational chaos and their willingness to participate in planned, post downsizing changes. Although the downsizing had a modest impact on surviving employees\u27 structural hole experiences overall, the structural hole index was a significant predictor in longitudinal and within time period comparisons of employees’ perceptions of chaos and openness to change

A collective, probabilistic approach to schema mapping using diverse noisy evidence

We propose a probabilistic approach to the problem of schema mapping. Our approach is declarative, scalable, and extensible. It builds upon recent results in both schema mapping and probabilistic reasoning and contributes novel techniques in both fields. We introduce the problem of schema mapping selection, that is, choosing the best mapping from a space of potential mappings, given both metadata constraints and a data example. As selection has to reason holistically about the inputs and the dependencies between the chosen mappings, we define a new schema mapping optimization problem which captures interactions between mappings as well as inconsistencies and incompleteness in the input. We then introduce Collective Mapping Discovery (CMD), our solution to this problem using state-of-the-art probabilistic reasoning techniques. Our evaluation on a wide range of integration scenarios, including several real-world domains, demonstrates that CMD effectively combines data and metadata information to infer highly accurate mappings even with significant levels of noise

A Near-Total Decline in Caribou on Prince of Wales, Somerset, and Russell Islands, Canadian Arctic

The number of caribou (Rangifer tarandus) on Prince of Wales, Somerset, and Russell islands in the south-central Canadian Arctic declined by 98% in 15 years, from an estimated 6048 (16% calves) in 1980 to an estimated 100 (0% calves) in 1995. Those estimates were obtained by systematic aerial surveys that used the same design and methods and comparable survey coverage. We do not have the data needed to determine the rate of decrease between 1980 and 1995 or its possible causes. There is no evidence for large-scale winter mortality in any one year or few consecutive years. A probable explanation for the decline is consequential reductions in long-term survival rates, both of breeding females and of calves in their first year of life, associated with continued caribou harvesting and markedly increased wolf (Canis lupus) predation on the dwindling number of caribou through the 1980s and early 1990s. The delay in detecting the decline and the lack of understanding of its causes will handicap the development of an ecologically sound recovery plan. As previous caribou declines have been followed by recovery, some comfort may be drawn from the likelihood of unaided recovery. However, the number of caribou has declined to the point where recovery will be tenuous and lengthy, at best. Unaided recovery could easily fail to occur, so we should not be complacent, especially as extirpation of these few remaining caribou would remove a distinct genetic group and reduce the biodiversity of caribou on Canada’s Arctic Islands.Le nombre de caribous (Rangifer tarandus) se trouvant sur les îles Prince of Wales, Somerset et Russell, dans le centresud de l’Arctique canadien, a chuté de 98 % en 15 ans, passant d’un nombre estimé à 6 048 (dont 16 % étaient des veaux) en 1980 à un nombre estimé à 100 (dont aucun veau) en 1995. Ces estimations ont été obtenues au moyen de relevés aériens systématiques recourant aux mêmes définitions, aux mêmes méthodes et à des aires de relevés comparables. On ne possède pas les données nécessaires pour déterminer le taux de diminution entre 1980 et 1995 ou les causes possibles de cette diminution. Par ailleurs, rien n’indique qu’un taux de mortalité hivernal élevé a été enregistré pendant une année quelconque ou pendant quelques années de suite. Il se peut que le déclin du nombre de caribous enregistré dans les années 1980 et au début des années 1990 soit attribuable aux réductions correspondantes des taux de survie à long terme chez les femelles de reproduction et les veaux pendant leur première année de vie, le tout jumelé au prélèvement continuel des caribous ainsi qu’à la prédation grandement accrue des caribous par les loups (Canis lupus). Le retard à détecter ce déclin et le manque de compréhension de ses causes pourront nuire à l’élaboration d’un plan de récupération solide du point de vue écologique. Puisque les déclins précédents de caribous ont été suivis de récupération, on peut se consoler en se disant qu’il est possible que la récupération se fasse spontanément. Cependant, le nombre de caribous a chuté au point où la récupération sera longue et difficile, même dans le meilleur des cas. Il se peut qu’il n’y ait pas de récupération spontanée et par conséquent, on ne devrait pas se contenter de cette situation, surtout puisque l’extirpation des quelques caribous qui restent pourrait éliminer un groupe génétique distinct et réduire la biodiversité du caribou dans l’archipel Arctique canadien

Methods of Measuring Vapor Pressures of Lubricants With Their Additives Using TGA and/or Microbalances

The life of a space system may be critically dependent on the lubrication of some of its moving parts. The vapor pressure, the quantity of the available lubricant, the temperature and the exhaust venting conductance passage are important considerations in the selection and application of a lubricant. In addition, the oil additives employed to provide certain properties of low friction, surface tension, antioxidant and load bearing characteristics, are also very important and need to be known with regard to their amounts and vapor pressures. This paper reports on the measurements and analyses carried out to obtain those parameters for two often employed lubricants, the Apiezon(TM)-C and the Krytox(TM) AB. The measurements were made employing an electronic microbalance and a thermogravimetric analyzer (TGA) modified to operate in a vacuum. The results have been compared to other data on these oils when available. The identification of the mass fractions of the additives in the oil and their vapor pressures as a function of the temperature were carried out. These may be used to estimate the lubricant life given its quantity and the system vent exhaust conductance. It was found that the Apiezon(TM)-C has three main components with different rates of evaporation while the Krytox(TM) did not indicate any measurable additive

Immigration Enforcement and Fairness to Would-Be Immigrants

This chapter argues that governments have a duty to take reasonably effective and humane steps to minimize the occurrence of unauthorized migration and stay. While the effects of unauthorized migration on a country’s citizens and institutions have been vigorously debated, the literature has largely ignored duties of fairness to would-be immigrants. It is argued here that failing to take reasonable steps to prevent unauthorized migration and stay is deeply unfair to would-be immigrants who are not in a position to bypass visa regulations. Importantly, the argument here is orthogonal to the debate as to how much and what kinds of immigration ought to be allowed