Ego‐centered and local roles: A graph theoretic approach

Structural equivalence (Lorrain and White, 1971) and automorphic equivalence (Everett, 1985) are generalized to define neighborhood‐ and ego‐centered equivalences. It is shown that local versions of these equivalences can then be formulated quite naturally. In addition to these natural localizations, a generalized procedure capable of localizing any model of role equivalence is presented. From a theoretical point of view, local roles are recommended by the notion that network influences on ego diminish with distance. From a practical point of view, local roles help find structure in graphs where global equivalences find no two actors equivalent.     

A graph theoretic approach to the investigation of system‐environment relationships†

For any empirical structure consisting of a system S and its environment E, there is an associated digraph D whose points and arcs (directed lines) correspond to the elements and relationships of the structure. The arcs of D are thus of four types: (1) internal arcs, which join two points of S; (b) external arcs, which join two points of E; (c) out‐liaisons of S, which join a point of S to one of E; and (d) in‐liaisons of S, which join a point of E to one of S. The boundary of S is defined as the subgraph of D induced by the liaisons of S and corresponds to those elements and relationships of the structure directly involved in transactions between the system and its environment. The basic structural properties of boundaries are then identified, and it is shown how the points of S and E can be stratified according to their distances to (or from) the boundary of S. Next, several results are derived concerning system‐environment relationships in structures whose digraphs are symmetric, transitive, or signed. The concept of convexity is then introduced to deal with a certain kind of segregation of a system relative to its environment. And, finally, it is shown how the adjacency matrix of D can be employed to facilitate the analysis of such structures and the calculation of various indexes of system‐environment relationships.     

Co-op advertising models in manufacturer–retailer supply chains: A game theory approach

In the literature of cooperative (co-op) advertising, the focus of research is on a relationship in which a manufacturer is the leader and retailers are followers. This relationship implies the dominance of the manufacturer over retailers. Recent market structure reviews have shown a shift of retailing power from manufacturers to retailers. Retailers have equal or even greater power than a manufacturer when it comes to retailing. Based on this new market phenomenon, we intend to explore the role of vertical co-op advertising efficiency with respect to transactions between a manufacturer and a retailer through brand name investments, local advertising expenditures, and sharing rules of advertising expenses. Three co-op advertising models are discussed which are based on two noncooperative games and one cooperative game. In a leader–follower noncooperative game, the manufacturer is assumed to be a leader who first specifies the brand name investment and the co-op subsidization policy. The retailer, as a follower, then decides on the local advertising level. In a noncooperative simultaneous move game, the manufacturer and the retailer are assumed to act simultaneously and independently. In a cooperative game, the system profit is maximized for every Pareto efficient co-op advertising scheme, but not for any other schemes. All Pareto efficient co-op advertising schemes are associated with a single local advertising level and a single brand name investment level, but with variable sharing policies of advertising expenses. The best Pareto efficient advertising scheme is obtained taking members' risk attitudes into account. Utilizing the Nash bargaining model, we discuss two situations that (a) both members are risk averse, and (b) both members are risk neutral. Our results are consistent with the bargaining literature.     

A “Nonconvex+Nonconvex” approach for image restoration with impulse noise removal

In this paper, we propose a new method for image restoration problems, which are degraded by impulsive noise, with nonconvex data fitting term and nonconvex regularizer.The proposed method possesses the advantages of nonconvex data fitting and nonconvex regularizer simultaneously, namely, robustness for impulsive noise and efficiency for restoring neat edge images.Further, we propose an efficient algorithm to solve the “Nonconvex+Nonconvex” structure problem via using the alternating direction minimization, and prove that the algorithm is globally convergent when the regularization parameter is known. However, the regularization parameter is unavailable in general. Thereby, we combine the algorithm with the continuation technique and modified Morozov’s discrepancy principle to get an improved algorithm in which a suitable regularization parameter can be chosen automatically. The experiments reveal the superior performances of the proposed algorithm in comparison with some existing methods.     

New “large” groups of type I

All unitary representations of certain infinite-dimensional, completely disconnected groups of type I are described.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Vol. 16, pp. 31–52, 1980.     

The solution of the soccer “dream league” game

On January 5, 1996, Maariv, one of the two leading daily newspapers in Israel, announced “The Dream League” game. Every participant in this game was required to “purchase” from a pool of all the soccer players in the Israeli National League, a team which according to his judgment would be chosen as the best team at the end of the season. Purchasing the players was subject to a given budget and to several other constraints. After the soccer season was over, we were requested by Maariv to find the optimal “Dream Team”.The problem of finding the optimal team is shown to be a generalized version of the well-known knapsack problem. It is formulated as an integer program and solved to optimality by the software NAG. Evidently, the optimal Dream Team is much better (in terms of the total cumulative grade) than the actual winning team chosen by the readers of Maariv. A possible heuristic procedure for solving the game in larger settings is also discussed.     

On the nesting of Painlevé hierarchies: A Hamiltonian approach

We consider the phenomenon whereby two different Painlevé hierarchies, related to the same hierarchy of completely integrable equations, are such that solutions of one member of one of the Painlevé hierarchies are also solutions of a higher-order member of the other Painlevé hierarchy. An explanation is given in terms of the Hamiltonian structures of the related underlying completely integrable hierarchies, and is sufficiently generally formulated so as to be applicable equally to both continuous and discrete Painlevé hierarchies. Special integrals of a further Painlevé hierarchy related by Bäcklund transformation to the other Painlevé hierarchy mentioned above can also be constructed. Examples of the application of this approach to Painlevé hierarchies related to the Korteweg–de Vries, dispersive water wave, Toda and Volterra integrable hierarchies are considered. Our results provide further evidence of the importance of the underlying structures of related completely integrable hierarchies in understanding the properties of Painlevé hierarchies.     

Local stability “in the large” of the rigid layer of a sandwich plate in compression with bending

Experiments show that at certain geometrical and mechanical parameters of a sandwich plate subjected to compression with bending the loss of stability of its rigid layer occurs through a leap to a nonadjacent form of equilibrium. The current notion about the loss of stability of rigid layers of multilayer systems and calculation schemes correspond only to particular cases of the phenomenon and are true only in the framework of certain physical, mechanical, and geometrical characteristics of structures. The most general and closest to reality is the calculation method which takes into consideration the entire complex of deformations of all elements of a multilayer system. The study includes the experimental and theoretical analysis of the influence of bending rigidity, initial bend, and decisive deformational factors on the value of the critical force in the rigid layer of the plate having a light filler. The position of the local energetic extremum emerging in the process studied and the region where it is necessary to take into account the real character of the loss of stability in the large are determined.Moscow State University for Ecology and Environmental Studies, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 59–70, January–February, 1999.     

Control of systems with flexible multi-server pools: a shadow routing approach

A general model with multiple input flows (classes) and several flexible multi-server pools is considered. We propose a robust, generic scheme for routing new arrivals, which optimally balances server pools’ loads, without the knowledge of the flow input rates and without solving any optimization problem. The scheme is based on Shadow routing in a virtual queueing system. We study the behavior of our scheme in the Halfin–Whitt (or, QED) asymptotic regime, when server pool sizes and the input rates are scaled up simultaneously by a factor r growing to infinity, while keeping the system load within \(O(\sqrt{r}\,)\) of its capacity.The main results are as follows. (i) We show that, in general, a system in a stationary regime has at least \(O(\sqrt{r}\,)\) average queue lengths, even if the so called null-controllability (Atar et al., Ann. Appl. Probab. 16, 1764–1804, 2006) on a finite time interval is possible; strategies achieving this \(O(\sqrt{r}\,)\) growth rate we call order-optimal. (ii) We show that some natural algorithms, such as MaxWeight, that guarantee stability, are not order-optimal. (iii) Under the complete resource pooling condition, we prove the diffusion limit of the arrival processes into server pools, under the Shadow routing. (We conjecture that result (iii) leads to order-optimality of the Shadow routing algorithm; a formal proof of this fact is an important subject of future work.) Simulation results demonstrate good performance and robustness of our scheme.     

Comment on “A new approach of cooperative interval games: The interval core and Shapley value revisited”

The interval Shapley-like value for cooperative interval games was introduced by Han et al. (2012).A theorem of characterization of the interval Shapley-like value was provided in that paper. We show that there is an error in the proof of that theorem. We indicate how to avoid this error and complete the proof.     

A lattice gas automaton approach to “turbulent diffusion”

A periodic Kolmogorov type flow is implemented in a lattice gas automaton. For given aspect ratios of the automaton universe and within a range of Reynolds number values, the averaged flow evolves towards a stationary two-dimensional ABC type flow. We show the analogy between the streamlines of the flow in the automaton and the phase plane trajectories of a dynamical system. In practice flows are commonly studied by seeding the fluid with suspended particles which play the role of passive tracers. Since an actual flow is time-dependent and has fluctuations, the tracers exhibit interesting intrinsic dynamics. When tracers are implemented in the automaton and their trajectories are followed, we find that the tracers displacements obey a diffusion law, with “super-diffusion” in the direction orthogonal to the direction of the initial forcing.     

Performance evaluation of demodulation with diversity—a combinatorial approach II: bijective methods

This paper is devoted to the presentation of a combinatorial approach for analyzing the performance of a generic family of demodulation methods used in mobile telecommunications. We show that a fundamental formula in this context is in fact highly connected with a slight modification of a very classical bijection of Knuth between pairs of Young tableaux of conjugate shapes and $\{0,1\}$-matrices. These considerations allowed us to obtain the first explicit expressions for several important specializations of the performance evaluation formula that we studied.     

Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach

We describe a unified structure of solutions for all equations of the Ablowitz–Kaup–Newell–Segur hierarchy and their combinations. We give examples of solutions that satisfy different equations for different parameter values. In particular, we consider a rank-2 quasirational solution that can be used to investigate many integrable models in nonlinear optics. An advantage of our approach is the possibility to investigate changes in the behavior of a solution resulting from changing the model.     

Phase-field modeling of martensitic phase transformations in polycrystals coupled with crystal plasticity – A spectral-based approach

The purpose of this work is the phase-field modeling of fcc-to-bcc martensitic phase transformations in polycrystals and the coupling with crystal plasticity. Assuming microscopic periodic fields, Green-function- and fast Fourier transform (FFT)-methods are used to solve the quasi-static balance of linear momentum. The Allen-Cahn evolution equation is discretized based on a semi-implicit time integration scheme in Fourier space. Two-dimensional results are presented and the interplay between martensitic phase transformation and plastic slip is studied at different stages of the deformation. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A family of quadriphase sequences of period 4(2 n − 1) with low correlation and large linear span

In this paper, a new family of quadriphase sequences with period 4(2 ⁿ ? 1) is proposed for n = me, where m is an odd integer. The correlation values of the family, their distribution, and the linear spans of the proposed sequences are completely determined under two situations.     

Optimal investment–reinsurance with delay for mean–variance insurers: A maximum principle approach

This paper is concerned with an optimal investment and reinsurance problem with delay for an insurer under the mean–variance criterion. A three-stage procedure is employed to solve the insurer’s mean–variance problem. We first use the maximum principle approach to solve a benchmark problem. Then applying the Lagrangian duality method, we derive the optimal solutions for a variance-minimization problem. Based on these solutions, we finally obtain the efficient strategy and the efficient frontier of the insurer’s mean–variance problem. Some numerical examples are also provided to illustrate our results.     

A simple approach for determining the eigenvalues of the fourth-order Sturm–Liouville problem with variable coefficients

In this paper, a simple and efficient approach is presented to compute the eigenvalues of the fourth-order Sturm–Liouville equations with variable coefficients. By transforming the governing differential equation to a system of algebraic equation, we can get the corresponding polynomial characteristic equations for kinds of boundary conditions based on the polynomial expansion and integral technique. Moreover, the lower and higher-order eigenvalues can be determined simultaneously from the multi-roots. Several examples for estimating eigenvalues are given. The convergence and effectiveness of the method are confirmed by comparing numerical results with the exact and other existing numerical results.