Two Dimensional Optimal Mechanism Design for a Sequencing Problem

We consider optimal mechanism design for a sequencing problem with $n$ jobs which require a compensation payment for waiting. The jobs' processing requirements as well as unit costs for waiting are private data. Given public priors for this private data, we seek to find an optimal mechanism, that is, a scheduling rule and incentive compatible payments that minimize the total expected payments to the jobs. Here, incentive compatible refers to a Bayes-Nash equilibrium. While the problem can be efficiently solved when jobs have single dimensional private data along the lines of a seminal paper by Myerson, we here address the problem with two dimensional private data. We show that the problem can be solved in polynomial time by linear programming techniques. Our implementation is randomized and truthful in expectation. The main steps are a compactification of an exponential size linear program, and a combinatorial algorithm to compute from feasible interim schedules a convex combination of at most n deterministic schedules. In addition, in computational experiments with random instances, we generate some more theoretical insights

Games and Mechanism Design in Machine Scheduling – An Introduction

In this paper, we survey different models, techniques, and some recent results to tackle machine scheduling problems within a distributed setting. In traditional optimization, a central authority is asked to solve a (computationally hard) optimization problem. In contrast, in distributed settings there are several agents, possibly equipped with private information that is not publicly known, and these agents need to interact in order to derive a solution to the problem. Usually the agents have their individual preferences, which induces them to behave strategically in order to manipulate the resulting solution. Nevertheless, one is often interested in the global performance of such systems. The analysis of such distributed settings requires techniques from classical Optimization, Game Theory, and Economic Theory. The paper therefore briefly introduces the most important of the underlying concepts, and gives a selection of typical research questions and recent results, focussing on applications to machine scheduling problems. This includes the study of the so-called price of anarchy for settings where the agents do not possess private information, as well as the design and analysis of (truthful) mechanisms in settings where the agents do possess private information.computer science applications;

Compressed Genotyping

Significant volumes of knowledge have been accumulated in recent years linking subtle genetic variations to a wide variety of medical disorders from Cystic Fibrosis to mental retardation. Nevertheless, there are still great challenges in applying this knowledge routinely in the clinic, largely due to the relatively tedious and expensive process of DNA sequencing. Since the genetic polymorphisms that underlie these disorders are relatively rare in the human population, the presence or absence of a disease-linked polymorphism can be thought of as a sparse signal. Using methods and ideas from compressed sensing and group testing, we have developed a cost-effective genotyping protocol. In particular, we have adapted our scheme to a recently developed class of high throughput DNA sequencing technologies, and assembled a mathematical framework that has some important distinctions from 'traditional' compressed sensing ideas in order to address different biological and technical constraints.Comment: Submitted to IEEE Transaction on Information Theory - Special Issue on Molecular Biology and Neuroscienc

Simple Sequencing Problems with Interdependent Costs

In this paper we analyze sequencing situations under incomplete information where agents have interdependent costs. We first argue why Vickrey-Clarke-Groves (or VCG) mechanism fails to implement a simple sequencing problem in dominant strategies. Given this impossibility, we try to implement simple sequencing problems in ex-post equilibrium. We show that a simple sequencing problem is implementable if and only if the mechanism is a `generalized VCG mechanism'. We then show that for implementable n agent simple sequencing problems, with polynomial cost function of order (n-2) or less, one can achieve first best implementability. Moreover, for the class of simple sequencing problems with ``sufficiently well behaved'' cost function, this is the only class of first best implementable simple sequencing problems.Simple Sequencing Problems, Ex-post Equilibrium, First Best Implementability

Two-dimensional gel electrophoresis in proteomics: A tutorial

Two-dimensional electrophoresis of proteins has preceded, and accompanied, the birth of proteomics. Although it is no longer the only experimental scheme used in modern proteomics, it still has distinct features and advantages. The purpose of this tutorial paper is to guide the reader through the history of the field, then through the main steps of the process, from sample preparation to in-gel detection of proteins, commenting the constraints and caveats of the technique. Then the limitations and positive features of two-dimensional electrophoresis are discussed (e.g. its unique ability to separate complete proteins and its easy interfacing with immunoblotting techniques), so that the optimal type of applications of this technique in current and future proteomics can be perceived. This is illustrated by a detailed example taken from the literature and commented in detail. This Tutorial is part of the International Proteomics Tutorial Programme (IPTP 2)