School districts that implement stable matchings face various decisions that affect students’ assignments to schools. We study properties of the rank distribution of students with random preferences when schools use different tie-breaking rules to rank equivalent students. Under a single tie-breaking rule, where all schools use the same ranking, a constant fraction of students are assigned to o...

We consider recovery of low-rank matrices from noisy data by hard thresholding of singular values, in which empirical singular values below a threshold λ are set to 0. We study the asymptotic MSE (AMSE) in a framework where the matrix size is large compared to the rank of the matrix to be recovered, and the signal-to-noise ratio of the low-rank piece stays constant. The AMSE-optimal choice of h...

The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf's Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto's or Benford's, but contrary to po...

We discuss the problem of ranking instances. In our framework, each instance is associated with a rank or a rating, which is an integer in 1 to k. Our goal is to find a rank-prediction rule that assigns each instance a rank that is as close as possible to the instance's true rank. We discuss a group of closely related online algorithms, analyze their performance in the mistake-bound model, and ...

We discuss the problem of ranking instances. In our framework each instance is associated with a rank or a rating, which is an integer from 1 to k. Our goal is to find a rank-prediction rule that assigns each instance a rank which is as close as possible to the instance 's true rank. We describe a simple and efficient online algorithm, analyze its performance in the mistake bound model, and pro...

Previous analysis of the rules regarding how much more a female should invest in a litter of size C rather than producing a litter with one more offspring revealed an invariance relationship between litter size and the range of resources per offspring in any litter size. The rule is that the range of resources per offspring should be inversely proportional to litter size. Here we present a modi...

Many psychology studies are statistically underpowered. In part, this may be because many researchers rely on intuition, rules of thumb, and prior practice (along with practical considerations) to determine the number of subjects to test. In Study 1, we surveyed 291 published research psychologists and found large discrepancies between their reports of their preferred amount of power and the ac...

Background and Objectives: Active presence of hospitals on the Internet is becoming a hallmark of hospitals’ commitment to quality healthcare services delivery. For insightful planning towards a strong Internet-based information delivery and communication, there is a need for continuous monitoring of hospital website’s status. Built on this need, this paper provides, for the first time, a ranki...

This paper describes continuing progress on the development of a repository of transformation rules relevant to indefinite integration. The methodology, however, is not restricted to integration. Several optimization goals are being pursued, including achieving the best form for the output, reducing the size of the repository while retaining its scope, and minimizing the number of steps require...