.html The articles [4], [6], [1], [2], [5], and [3] provide the notation and terminology for this paper. A natural number is an element of N. For simplicity, we use the following convention: x is a real number, k, l, m, n are natural numbers, h, i, j are natural numbers, and X is a subset of R

Abstract. Data analysis applications typically aggregate data across many dimensions looking for anomalies or unusual patterns. The SQL aggregate functions and the GROUP BY operator produce zero-dimensional or one-dimensional aggregates. Applications need the N-dimensional generalization

The processes by which communities come together, attract new members, and develop over time is a central research issue in the social sciences — political movements, professional organizations, and religious denominations all provide fundamental examples of such communities. In the digital domain

This paper develops the empirical and theoretical case that differences in economic institutions are the fundamental cause of differences in economic development. We first document the empirical importance of institutions by focusing on two “quasi-natural experiments” in history, the division

in the superconformal group (as opposed to just the super-Poincare group). The ’t Hooft limit of 3+1 N = 4 super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various AntideSitter spacetimes is dual to various conformal

is fundamentally higher dimensional with 4+n spacetime dimensions, then the effective four-dimensional (reduced) Planck scale, MPl = 2 ×10 18 GeV, is determined by the fundamental (4+n)-dimensional Planck scale, M, and the geometry of the extra dimensions.

: Reasoning about knowledge seems to play a fundamental role in distributed systems. Indeed, such reasoning is a central part of the informal intuitive arguments used in the design of distributed protocols. Communication in a distributed system can be viewed as the act of transforming the system

to the baseline n = 1 case, which by Shannon’s classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take

Let SN be the group of permutations of 1, 2,...,N. If π ∈ SN,wesaythat π(i1),...,π(ik) is an increasing subsequence in π if i1 <i2 <·· · <ikand π(i1) < π(i2) < ···<π(ik). Let lN (π) be the length of the longest increasing subsequence. For example, if N =5andπis the permutation 5 1

Abstract. For any n ∈ N we construct graph manifolds of genus 4n that have 3n-generated fundamental group. 1. introduction A Heegaard surface of an orientable closed 3-manifold M is an embedded orientable surface S such that M − S consists of 2 handlebodies V1 and V2. This decomposition of M