The Value of Information Structures in Zero-sum Games with Lack of Information on One Side

Two players are engaged in a zero-sum game with lack of information on one side, in which player 1 (the informed player) receives some stochastic signal about the state of nature. I consider the value of the game as a function of player 1’s information structure, and study the properties of this function. It turns out that these properties reflect the fact that in zero sum situation the value of information for each player is positive.     

Statistical Physics of Fracture Surfaces Morphology

Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich phenomenology of anomalous scaling. We argue that traditional models of fracture fail to reproduce this rich phenomenology and new ideas and concepts are called for. We present some recent models that introduce the effects of deviations from homogeneous linear elasticity theory on the morphology of fracture surfaces, successfully reproducing the multiscaling phenomenology at least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel methods of analysis based on projecting the data on the irreducible representations of the SO(2) symmetry group. It appears that this approach organizes effectively the rich scaling properties. We end up proposing new experiments in which the rotational symmetry is not broken, such that the scaling properties should be particularly simple.     

Approximation Algorithms for MAX 4-SAT and Rounding Procedures for Semidefinite Programs

Karloff and Zwick obtained recently an optimal 7/8-approximation algorithm for MAX 3-SAT. In an attempt to see whether similar methods can be used to obtain a 7/8-approximation algorithm for MAX SAT, we consider the most natural generalization of MAX 3-SAT, namely MAX 4-SAT. We present a semidefinite programming relaxation of MAX 4-SAT and a new family of rounding procedures that try to cope well with clauses of various sizes. We study the potential, and the limitations, of the relaxation and of the proposed family of rounding procedures using a combination of theoretical and experimental means. We select two rounding procedures from the proposed family of rounding procedures. Using the first rounding procedure we seem to obtain an almost optimal 0.8721-approximation algorithm for MAX 4-SAT. Using the second rounding procedure we seem to obtain an optimal 7/8-approximation algorithm for satisfiable instances of MAX 4-SAT. On the other hand, we show that no rounding procedure from the family considered can be shown, using the current techniques, to yield an approximation algorithm for MAX 4-SAT whose performance guarantee for all instances of the problem is greater than 0.8724. We also show that the integrality ratio of the proposed relaxation, as a relaxation of MAX {1, 4}-SAT, is at most 0.8754.The 0.8721-approximation for MAX 4-SAT that we seem to obtain substantially improves the performance guarantees of all previous algorithms suggested for the problem. It is extremely close to being optimal as a (7/8 + ε)-approximation algorithm for MAX 4-SAT, for any fixed ε > 0, would imply that P = NP. Our investigation also indicates, however, that additional ideas are required in order to obtain optimal 7/8-approximation algorithms for MAX 4-SAT and MAX SAT.Although most of this paper deals specifically with the MAX 4-SAT problem, we believe that the new family of rounding procedures introduced and the methodology used in the design and in the analysis of the various rounding procedures considered have a much wider range of applicability.     

Routing complexity of faulty networks

One of the fundamental problems in distributed computing is how to efficiently perform routing in a faulty network in which each link fails with some probability. This article investigates how big the failure probability can be, before the capability to efficiently find a path in the network is lost. Our main results show tight upper and lower bounds for the failure probability, which permits routing both for the hypercube and for the d‐dimensional mesh. We use tools from percolation theory to show that in the d‐dimensional mesh, once a giant component appears—efficient routing is possible. A different behavior is observed when the hypercube is considered. In the hypercube there is a range of failure probabilities in which short paths exist with high probability, yet finding them must involve querying essentially the entire network. Thus the routing complexity of the hypercube shows an asymptotic phase transition. The critical probability with respect to routing complexity lies in a different location than that of the critical probability with respect to connectivity. Finally we show that an oracle access to links (as opposed to local routing) may reduce significantly the complexity of the routing problem. We demonstrate this fact by providing tight upper and lower bounds for the complexity of routing in the random graph G_n,p. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Quality control of wastewater treatment: A new approach

This paper presents a new approach to quality control of wastewater treatment. The first part formulates basic principles of statistical process control (SPC) and Taguchi Method. Then it is shown that the classical SPC technique used in industry, cannot be to applied to wastewater treatment plants without adaptation and that the Taguchi Method is inapplicable in this case. This is followed by an example from literature, which demonstrates the problems of applying the SPC method to wastewater treatment. The third part of the paper presents a case study where the performance of a greywater treatment plant is examined. The performance is analyzed by means of cross-correlation between input and output parameters. A new approach to SPC of wastewater treatment, either “Dynamic SPC” or “linear regression SPC”, is presented, and a permeability coefficient is developed (the ratio of the output and input energies). Both are proposed as monitoring tools for wastewater treatment systems.     

Oriented immobilization of periodateoxidized monoclonal antibodies on amino and hydrazide derivatives of eupergit C

Amino and hydrazyno derivatives of Eupergit C were prepared by reaction of the beads with hexamethylene diamine (HMD) and adipic acid dihydrazide (ADH), respectively. Monoclonal antibodies (mAbs) against carboxypeptidase A (CPA) and horse radish peroxidase (HRP) were prepared, and those that did not inhibit the respective enzymatic activities were selected. The carbohydrate moieties of these antibodies were oxidized by reaction with sodium periodate and then coupled onto the modified beads. The oxidation and coupling reactions were optimized to achieve highly active matrix-conjugated antibodies. Thus, antibody-matrix conjugates that possessed antigen-binding activities close to the theoretical value of 2 mol antigen bound/mol immobilized antibody were obtained.     

The γ-vector of a barycentric subdivision

We prove that the γ-vector of the barycentric subdivision of a simplicial sphere is the f-vector of a balanced simplicial complex. The combinatorial basis for this work is the study of certain refinements of Eulerian numbers used by Brenti and Welker to describe the h-vector of the barycentric subdivision of a boolean complex.     

On <Emphasis Type="Italic">γ</Emphasis>-Vectors Satisfying the Kruskal–Katona Inequalities

We present examples of flag homology spheres whose γ-vectors satisfy the Kruskal–Katona inequalities. This includes several families of well-studied simplicial complexes, including Coxeter complexes and the simplicial complexes dual to the associahedron and to the cyclohedron. In these cases, we construct explicit flag simplicial complexes whose f-vectors are the γ-vectors in question, and so a result of Frohmader shows that the γ-vectors satisfy not only the Kruskal–Katona inequalities but also the stronger Frankl–Füredi–Kalai inequalities. In another direction, we show that if a flag (d−1)-sphere has at most 2d+3 vertices its γ-vector satisfies the Frankl–Füredi–Kalai inequalities. We conjecture that if Δ is a flag homology sphere then γ(Δ) satisfies the Kruskal–Katona, and further, the Frankl–Füredi–Kalai inequalities. This conjecture is a significant refinement of Gal’s conjecture, which asserts that such γ-vectors are nonnegative.