Approximately counting semismooth integers

An integer $n$ is $(y,z)$-semismooth if $n=pm$ where $m$ is an integer with all prime divisors $\le y$ and $p$ is 1 or a prime $\le z$. arge quantities of semismooth integers are utilized in modern integer factoring algorithms, such as the number field sieve, that incorporate the so-called large prime variant. Thus, it is useful for factoring practitioners to be able to estimate the value of $\Psi(x,y,z)$, the number of $(y,z)$-semismooth integers up to $x$, so that they can better set algorithm parameters and minimize running times, which could be weeks or months on a cluster supercomputer. In this paper, we explore several algorithms to approximate $\Psi(x,y,z)$ using a generalization of Buchstab's identity with numeric integration.Comment: To appear in ISSAC 2013, Boston M

A Randomized Sublinear Time Parallel GCD Algorithm for the EREW PRAM

We present a randomized parallel algorithm that computes the greatest common divisor of two integers of n bits in length with probability 1-o(1) that takes O(n loglog n / log n) expected time using n^{6+\epsilon} processors on the EREW PRAM parallel model of computation. We believe this to be the first randomized sublinear time algorithm on the EREW PRAM for this problem

Two Compact Incremental Prime Sieves

A prime sieve is an algorithm that finds the primes up to a bound $n$. We say that a prime sieve is incremental, if it can quickly determine if $n+1$ is prime after having found all primes up to $n$. We say a sieve is compact if it uses roughly $\sqrt{n}$ space or less. In this paper we present two new results: (1) We describe the rolling sieve, a practical, incremental prime sieve that takes $O(n\log\log n)$ time and $O(\sqrt{n}\log n)$ bits of space, and (2) We show how to modify the sieve of Atkin and Bernstein (2004) to obtain a sieve that is simultaneously sublinear, compact, and incremental. The second result solves an open problem given by Paul Pritchard in 1994

Space and social capital : The degree of locality in entrepreneurs' contacts and its consequences for firm success

Social capital is valuable for entrepreneurs starting a business. Although many small businesses are located at the entrepreneurs’ dwelling, little is known about entrepreneurs’ local ties and their relevance for firm success. Distinguishing between local and non-local social capital, this contribution looks at the following: (1) The availability of local social capital (2) The relation between social capital and local social capital, and characteristics of firms and entrepreneurs (3) The relation between social capital and local social capital and firm performance. Analysing data from the Survey of the Social Networks of Entrepreneurs, which contains information on entrepreneurs and their networks in 141 Dutch neighbourhoods, this study finds a positive relation between social capital and firm performance.

VerdictDB: Universalizing Approximate Query Processing

Despite 25 years of research in academia, approximate query processing (AQP) has had little industrial adoption. One of the major causes of this slow adoption is the reluctance of traditional vendors to make radical changes to their legacy codebases, and the preoccupation of newer vendors (e.g., SQL-on-Hadoop products) with implementing standard features. Additionally, the few AQP engines that are available are each tied to a specific platform and require users to completely abandon their existing databases---an unrealistic expectation given the infancy of the AQP technology. Therefore, we argue that a universal solution is needed: a database-agnostic approximation engine that will widen the reach of this emerging technology across various platforms. Our proposal, called VerdictDB, uses a middleware architecture that requires no changes to the backend database, and thus, can work with all off-the-shelf engines. Operating at the driver-level, VerdictDB intercepts analytical queries issued to the database and rewrites them into another query that, if executed by any standard relational engine, will yield sufficient information for computing an approximate answer. VerdictDB uses the returned result set to compute an approximate answer and error estimates, which are then passed on to the user or application. However, lack of access to the query execution layer introduces significant challenges in terms of generality, correctness, and efficiency. This paper shows how VerdictDB overcomes these challenges and delivers up to 171$\times$ speedup (18.45$\times$ on average) for a variety of existing engines, such as Impala, Spark SQL, and Amazon Redshift, while incurring less than 2.6% relative error. VerdictDB is open-sourced under Apache License.Comment: Extended technical report of the paper that appeared in Proceedings of the 2018 International Conference on Management of Data, pp. 1461-1476. ACM, 201

PEER HARASSMENT UNDER TITLE IX OF THE EDUCATION AMENDMENTS OF 1972: WHERE\u27S THE INTENT

This Note argues that in peer harassment cases, school districts should face liability under a “known or should have known” standard where the school’s intent to discriminate may be determined by the circumstances of the case. Part I provides a brief historical overview of Title IX and the traditional forms of hostile environment harassment that it has been used to combat, demonstrating that courts use the statute to punish harassment where the school has reason to know of the harassment and fails to take appropriate action. Part II explores a subset of hostile environment cases where U.S. circuit courts are divided – peer sexual harassment cases, and analyzes the rationale supporting each position. Part III provides guidelines for when courts should extend Title IX protection to peer sexual harassment claims and articulates standards for school liability