Statistical physics approach to graphical games: local and global interactions

In a graphical game agents play with their neighbors on a graph to achieve an appropriate state of equilibrium. Here relevant problems are characterizing the equilibrium set and discovering efficient algorithms to find such an equilibrium (solution). We consider a representation of games that extends over graphical games to deal conveniently with both local a global interactions and use the cavity method of statistical physics to study the geometrical structure of the equilibria space. The method also provides a distributive and local algorithm to find an equilibrium. For simplicity we consider only pure Nash equilibria but the methods can as well be extended to deal with (approximated) mixed Nash equilirbia.     

Toward Analytic Solution of Nonlinear Differential Difference Equations via Extended Sensitivity Approach

In this paper an efficient computational method based on extending the sensitivity approach(SA) is proposed to find an analytic exact solution of nonlinear differential difference equations.In this manner we avoid solving the nonlinear problem directly.By extension of sensitivity approach for differential difference equations(DDEs),the nonlinear original problem is transformed into infinite linear differential difference equations,which should be solved in a recursive manner.Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained.Numerical examples are employed to show the effectiveness of the proposed approach.     

Character Connes amenability of dual Banach algebras

We study the notion of character Connes amenability of dual Banach algebras and show that if A is an Arens regular Banach algebra, then A^** is character Connes amenable if and only if A is character amenable, which will resolve positively Runde’s problem for this concept of amenability. We then characterize character Connes amenability of various dual Banach algebras related to locally compact groups. We also investigate character Connes amenability of Lau product and module extension of Banach algebras. These help us to give examples of dual Banach algebras which are not Connes amenable.     

DABCO‐Catalyzed Efficient Synthesis of Naphthopyran Derivatives via One‐Pot Three‐Component Condensation Reaction at Room Temperature

Diazabicyclo[2.2.2]octane (DABCO) has been used as a mild and efficient catalyst for synthesis of 2‐amino‐3‐cyano naphthopyran derivatives via a one‐pot three‐component reaction of aromatic aldehydes, naphthols, and malononitrile at room temperature. The short reaction times, easy workup, good to excellent yields, and mild reaction conditions make this domino Knoevenagel–Michael reaction both practical and attractive.     

A novel method for slant crack detection in rotors based on turning in two directions

This paper presents a novel way to detect fatigue slant cracks in rotors based on theoretical discussion. Hence, the dynamic behaviour of a Jeffcott rotor system with a mid-span slant crack under arbitrary crack orientations is studied. First, using concepts of fracture mechanics, the flexibility matrix and subsequently the system’s stiffness matrix are calculated. A symmetric relation for a global stiffness matrix is presented and proved. Next, the motion equations of the system that are obtained in four directions, two transverse, one torsional and one longitudinal, are solved using the Runge–Kutta numerical method. The characteristics of crack orientations for angles greater than 90° (transverse crack) are investigated in detail and their influence on the elements of the crack compliance matrix is presented. Also, slant crack characteristics with complementary angles are compared to each other. It is shown that the difference between cracked systems with complementary angles is only in 3rd row (3rd column) of the crack compliance matrix, and also it is shown that due to the presence of a slant crack, the system responses in forward and backward motion are different. Using the frequency responses of the shaft obtained, a technique to detect the existence of slant cracks on the shaft was proposed. This novel method is a simple way that can be used for slant crack detection in rotors.     

Synthesis of Pseudo‐Peptides Containing a Quinazolinone Skeleton via Ugi Four‐Component Reaction

A simple and efficient synthesis of quinazolinone pseudo‐peptide derivatives based on a new 3‐amino‐1,2,3,4‐tetrahydro‐4‐oxoquinazoline‐2‐carboxylic acid via Ugi four‐component reaction has been developed. This reaction was conducted under mild conditions with a broad scope of substrates.     

Facile,efficient and diastereoselective synthesis of α-hydrazine tetrazoles through a novel one-pot four-component reaction

A novel and efficient method for the diastereoselective synthesis of α-hydrazine tetrazoles via an isocyanide-based multicomponent reaction is reported in good yields. The α-hydrazine tetrazoles were obtained by a facile azide Ugi four-component reaction (U-4CR) using cyclic ketones, trimethylsilyl azide, hydrazides, and corresponding isocyanide without any catalyst and with high bond forming efficiency at room temperature.     

Stochastic matching problem

The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the deterministic case can be solved in polynomial time, stochastic variants are worst-case intractable. We propose an efficient method to solve stochastic matching problems which combines some features of the survey propagation equations and of the cavity method. We test it on random bipartite graphs, for which we analyze the phase diagram and compare the results with exact bounds. Our approach is shown numerically to be effective on the full range of parameters, and to outperform state-of-the-art methods. Finally we discuss how the method can be generalized to other problems of optimization under uncertainty.     

Module homomorphisms and multipliers on locally compact quantum groups

For a Banach algebra A with a bounded approximate identity, we investigate the A-module homomorphisms of certain introverted subspaces of A^∗, and show that all A-module homomorphisms of A^∗ are normal if and only if A is an ideal of A∗∗. We obtain some characterizations of compactness and discreteness for a locally compact quantum group G. Furthermore, in the co-amenable case we prove that the multiplier algebra of L¹(G) can be identified with M(G). As a consequence, we prove that G is compact if and only if LUC(G)=WAP(G) and M(G)≅Z(LUC^∗(G)); which partially answer a problem raised by Volker Runde.     

Investigation of a protein complex network

The budding yeast Saccharomyces cerevisiae is the first eukaryote whose genome has been completely sequenced. It is also the first eukaryotic cell whose proteome (the set of all proteins) and interactome (the network of all mutual interactions between proteins) has been analyzed. In this paper we study the structure of the yeast protein complex network in which weighted edges between complexes represent the number of shared proteins. It is found that the network of protein complexes is a small world network with scale free behavior for many of its distributions. However we find that there are no strong correlations between the weights and degrees of neighboring complexes. To reveal non-random features of the network we also compare it with a null model in which the complexes randomly select their proteins. Finally we propose a simple evolutionary model based on duplication and divergence of proteins.Received: 21 April 2004, Published online: 30 September 2004PACS: 89.75.-k Complex systems - 89.20.-a Interdisciplinary applications of physics - 89.90. + n Other topics in areas of applied and interdisciplinary physics