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Journals and Conferences
In this paper we prove the semi-circular law for the eigenvalues of regular random graph Gn,d in the case d→∞, complementing a previous result of McKay for fixed d. We also obtain a upper bound on the infinity norm of eigenvectors of Erdős-Rényi random graph G(n, p), answering a question raised by Dekel-Lee-Linial.
The Email Mining Toolkit (EMT) is a data mining system that computes behavior profiles or models of user email accounts. These models may be used for a variety of forensic analyses and detection tasks. In this paper we focus on the application of these models to detect the early onset of a viral propagation without "contentbased" (or signature-based)… (More)
This paper is concerned with the inhomogeneous nonlinear Shrödinger equation (INLS-equation) iut +∆u+ V ( x)|u|u = 0, x ∈ R . In the critical and supercritical cases p ≥ 4/N, with N ≥ 2, it is shown here that standing-wave solutions of (INLS-equation) on H1(RN ) perturbation are nonlinearly unstable or unstable by blow-up under certain conditions on the… (More)
All Rights Reserved iii Acknowledgements I am grateful to my advisor Peter Schröder for his guiding me into this field and for his never-failing support. I started working with Peter in April 2005 when I was a fourth-year PhD student still seeking an advisor. Peter accepted me as his student when my life hit bottom. Looking backward, I have benefited so… (More)
Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on properties of eigenvectors when the matrix (or graph) is random.
This article concerns the study of stochastic Gilpin-Ayala mutualism models with white noise and Poisson jumps. Firstly, an explicit solution for one-dimensional Gilpin-Ayala mutualism model with jumps is obtained and the asymptotic pathwise behavior is analyzed. Then, sufficient conditions for the existence of global positive solutions, stochastically… (More)
Counting is one of the most basic procedures in mathematics and statistics. In statistics literature it is usually done via the proportion estimation method. In this article we manifest a radically different counting procedure first proposed in the late 1990’s based on the techniques of quantum computation. It combines two major tools in quantum… (More)
In applications that require cost efficiency, sample sizes are typically small so that the problem of empty strata may often occur in judgment poststratification (JPS), an important variant of balanced ranked set sampling. In this article, we consider estimation of population cumulative distribution functions (CDF) from JPS samples with empty strata. In the… (More)
In this paper, a two-stage stochastic unit commitment (UC) model considering flexible scheduling of demand response (DR) is proposed. In the proposed UC model, the DR resources can be scheduled: (1) in the first stage, as resources on a day-ahead basis to integrate the predicted wind fluctuation with lower uncertainty; (2) in the second stage, as resources… (More)