Joel Spencer

Bio: Joel Spencer is an academic researcher from New York University. The author has contributed to research in topics: Random graph & Random walk. The author has an hindex of 54, co-authored 264 publications receiving 17799 citations. Previous affiliations of Joel Spencer include Stony Brook University & Massachusetts Institute of Technology.

The Probabilistic Method

Abstract: The use of randomness is now an accepted tool in Theoretical Computer Science but not everyone is aware of the underpinnings of this methodology in Combinatorics - particularly, in what is now called the probabilistic Method as developed primarily by Paul Erdoős over the past half century. Here I will explore a particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets. A central point will be the evolution of these problems from the purely existential proofs of Erdős to the algorithmic aspects of much interest to this audience.

The degree sequence of a scale-free random graph process

Abstract: Recently, Barabasi and Albert [2] suggested modeling complex real-world networks such as the worldwide web as follows: consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number of earlier vertices, selected with probabilities proportional to their degrees. In [2] and, with Jeong, in [3], Barabasi and Albert suggested that after many steps the proportion P(d) of vertices with degree d should obey a power law P(d)αd−γ. They obtained γ=2.9±0.1 by experiment and gave a simple heuristic argument suggesting that γ=3. Here we obtain P(d) asymptotically for all d≤n1/15, where n is the number of vertices, proving as a consequence that γ=3. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18, 279–290, 2001

Probabilistic Methods in Combinatorics

Abstract: In 1947 Paul Erdős [8] began what is now called the probabilistic method. He showed that if \(\left( {\begin{array}{*{20}{c}} n \\ k \\ \end{array} } \right){{2}^{{1 - \left( {\begin{array}{*{20}{c}} k \\ 2 \\ \end{array} } \right)}}} n.) In modern lanuage he considered the random graph G(n,.5) as described below. For each k-set S let BS denote the “bad” events that S is either a clique or an independent set. Then Pr[BS] = 21-(k/2) so that ΣPr[BS] < 1, hence ∧\( \wedge {\bar B_s}\) ≠ ∅ and a graph satisfying ∧\( \wedge {\bar B_s}\) must exist.

Explosive Percolation in Random Networks

Abstract: Networks in which the formation of connections is governed by a random process often undergo a percolation transition, wherein around a critical point, the addition of a small number of connections causes a sizable fraction of the network to suddenly become linked together. Typically such transitions are continuous, so that the percentage of the network linked together tends to zero right above the transition point. Whether percolation transitions could be discontinuous has been an open question. Here, we show that incorporating a limited amount of choice in the classic Erdos-Renyi network formation model causes its percolation transition to become discontinuous.

Ten lectures on the probabilistic method

Abstract: This is an examination of what is known about the probabilistic method. Based on the notes from the author's 1986 series of ten lectures, this edition features an additional lecture: The Janson Inequalities. These inequalities allow accurate approximation of extremely small probabilities.

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Abstract: 抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

The Structure and Function of Complex Networks

Abstract: Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

Random graphs

Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

The Probabilistic Method

Abstract: The use of randomness is now an accepted tool in Theoretical Computer Science but not everyone is aware of the underpinnings of this methodology in Combinatorics - particularly, in what is now called the probabilistic Method as developed primarily by Paul Erdoős over the past half century. Here I will explore a particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets. A central point will be the evolution of these problems from the purely existential proofs of Erdős to the algorithmic aspects of much interest to this audience.