We take a theoretical approach to the problem of identification, or “reverse engineering”, of gene regulatory networks. Through a mathematical model of a gene regulatory network, we examine fundamental questions on the limits and achievability of network identification. We apply simplifying assumptions to construct an acyclic binary model, and we assume that the identification strategy is restricted to perturbing the network by gene expression assignments, followed by expression profile measurements at steady-state. Further, we assume the presence of side information, which we call sensitivity, that is likely to be present in actual gene networks. We show that with sensitivity side information and realistic topology assumptions we can identify the topology of acyclic binary networks using O(n) assignments and measurements, n being the number of genes in the network. Our work establishes a theoretical framework for examining an important technological problem where a number of significant questions remain open.

This paper generalizes Blonder's graphical passwords to arbitrary images and solves a robustness problem that this generalization entails. The password consists of user-chosen click points in a displayed image. In order to store passwords in cryptographically hashed form, we need to prevent small uncertainties in the click points from having any effect on the password. We achieve this by introducing a robust discretization, based on multigrid discretization.

We analyze the wavelet shrinkage algorithm of Donoho and Johnstone (1994) in order to assess the quality of the reconstruction of a signal obtained from noisy samples. We give a deviation estimate for the maximum squared error (and, consequently, for the average squared error), under the assumption that the signal comes from a Holder class, and the noise samples are independent, of zero mean, and bounded. Our main technique is Talagrand's (1995) isoperimetric theorem. Our result shows a better behavior of the wavelet shrinkage.

The asymptotic performance of heuristic algorithms for the multiprocessor scheduling problem is considered. Let rLS denote the ratio of the makespan of any list schedule to the optimal makespan. Let m denote the number of processors and n the number of jobs. We show that the mean and variance of rLS have upper bounds which approach 1 and 0, respectively, at a rate of O(m log n/n), under the assumption that job processing times are independent, identically distributed according to any distribution F over (0, ∞) with ∫(0,∞) eαtdF(t) < ∞ for some α > 0. If the processing times are distributed over (0, 1], a slightly faster convergence rate of O(m/n) is obtained. Furthermore, we show that almost surely, rLS approaches 1 at a rate faster than O(m/n1−β) for any 0 < β < 1. Similar results are also obtained for the Multifit algorithm due to Coffman, Garey and Johnson. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.