A characterization of stochastically stable networks

Jackson and Watts (J Econ Theory 71: 44–74, 2002) have examined the dynamic formation and stochastic evolution of networks. We provide a refinement of pairwise stability, p-pairwise stability, which allows us to characterize the stochastically stable networks without requiring the “tree construction” and the computation of resistance that may be quite complex. When a -pairwise stable network exists, it is unique and it coincides with the unique stochastically stable network. To solve the inexistence problem of p-pairwise stable networks, we define its set-valued extension with the notion of p-pairwise stable set. The -pairwise stable set exists and is unique. Any stochastically stable networks is included in the -pairwise stable set. Thus, any network outside the -pairwise stable set must be considered as a non-robust network. We also show that the -pairwise stable set can contain no pairwise stable network and we provide examples where a set of networks is more “stable” than a pairwise stable network.     

Estimating Job Flow-Times in a Job Shop for Contractually Negotiated Due-Dates

One of the most important aspects of job shop planning is the contract negotiation process. In this process the job shop vendor must negotiate a job due-date acceptable to both job shop and the customer. Failure to obtain reasonably accurate predictions of the job completion time can result in penalties and/or lost future sales for the job shop. As such, estimation of job flow-times is critical to successful job shop operation. This paper presents a network modelling approach to the difficult and complex task of estimating job flow-times not previously presented in the literature. The approach is demonstrated via a case example where the system model is developed as a Q-GERT network and simulation results are obtained.     

Nonlinear stable adaptive control based upon Elman networks

Elman networks‘ dynamical modeling capability is discussed in this paper firstly. According to Elman networks‘ unique structure ,a weight training algorithm is designed and a nonlinear adaptive controller is constructed. Without the PE presumption, neural networks controller‘s closed-loop properties are studied and the whole Elman networks‘ passivity is demonstrated.     

二元稳定网络的算法及模型

通过建立JW(Jackson-Wolinsky)规则之下二元稳定网络的等价条件, 给出其完整算法. 引入边支付后, 证明了增连接情形具有边支付的二元稳定网络集合是二元稳定网络集合与具有边支付的二元稳定网络集合的交集. 考察两个特定的网络模型, 系统分析了它们的二元稳定性.     

A note on stable flow-equivalent aggregation in closed networks

We introduce the Conditional Mean Value Analysis (CMVA) algorithm, an exact solution method for product-form load-dependent closed queueing networks that provides a numerically stable solution of models where the load-dependent Mean Value Analysis (MVA) is numerically unstable. Similarly to the MVA algorithm for constant-rate queues, CMVA performs operations in terms of mean quantities only, i.e., queue-lengths, throughput, response times. Numerical stability derives from a new version of the MVA arrival theorem for load-dependent models which is expressed in terms of mean queue-lengths instead of marginal probabilities. The formula is obtained by the analysis of the conditional state spaces which describe network equilibrium as seen by jobs during their residence times at queues. We also provide a generalization of CMVA to multiclass models that preserves the numerical stability property.     

On the existence and uniqueness of pairwise stable networks

In this paper we show how externalities between links affect the existence and uniqueness of pairwise stable (PS) networks. For this we introduce the properties ordinal convexity (concavity) and ordinal strategic complements (substitutes) of utility functions on networks. It is shown that there exists at least one PS network if the profile of utility functions is ordinal convex and satisfies the ordinal strategic complements property. On the other hand, ordinal concavity and ordinal strategic substitutes are sufficient for some uniqueness properties of PS networks. Additionally, we elaborate on the relation of the link externality properties to definitions in the literature.     

Theory of viscoelastic behavior of regular polymeric networks with stable points linking four chains

A regular stable network formed by flexible macromolecules connected into four functional points is considered. Each point of the network is acted on by the elastic forces from neighbors, by the force of viscous resistances, proportional to the relative velocity of the point, and by the effective force of Brownian movement. The kinetic equation is written for the network points in the case of deformation, and the moments of the second-order distribution function are calculated. The relaxation times of the system are found, and the behavior of the network in the presence of homogeneous sinusoidal deformation due to extension and shear is discussed. The complex modulus of elasticity of the network is calculated as a function of the network parameters and frequency.Branch of the Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow Region. Translated from Mekhanika Polimerov, No. 2, pp. 209–216, March–April, 1970.     

The variation of a stable path is stable

Summary Let X(t) be a separable symmetric stable process of index . Let P be a finite partition of [0,1], and a collection of partitions. The variation of a path X(t) is defined in three ways in terms of the sum collection . Under certain conditions on and on the parameters and , the distribution of the variation is shown to be a stable law. Under other conditions the distribution of the variational sum converges to a stable distribution.The author wishes to thank Prof. J. Chover for several helpful suggestions.     

Convex sets of schur stable and stable matrices

We derive characterizations for the Schur stability and the stability of all convex combinations of kk≥2, given real square matrices. Moreover, we characterize these properties for the set r(A, B) (c(A,B), resp.) of square matrices whose rows (columns, resp.) are independent convex combinations of the rows (columns, resp.) of two real matrices A and B. Our results can be viewed as contributions to the problem of robustness of matrix properties. This paper continues our paper [4].     

Embedding unconditional stable banach spaces into symmetric stable banach spaces

In this paper we prove the following result which solves a question raised by A. Pelczynski: “Every stable Banach space with an unconditional basis is isomorphic to a complemented subspace of some stable Banach space with a symmetric basis.” Moreover, we show that all the interpolation spacesl ^p ,l ^q _θ,X,1 1≦p, q<∞ andX stable, are stable.     

Real stable ranks

Several new notions of stable ranks for commutative Banach algebras are introduced. Due to the fact that they depend on certain orthogonal groups, they are called real stable ranks and are finer than their complex counterparts.     

Log-fractional stable processes

The first problem attacked in this paper is answering the question whether all 1/-self-similar -stable processes with stationary increments are -stable motions. The answer is yes for = 2, no for 1<2 and unknown for 0<<1. We single out the log-fractional stable processes for 1<2, different from -stable motions for ≠2. They can be regarded as the limit of fractional stable processes as the exponent in the kernel tends to 0. The paper ends with a limit theorem for partial sum processes of moving averages of iid random variables in the domain of attraction of a strictly stable law, with log-fractional stable processes as limits in law. The conditions involve de Haan's class Π of slowly varying functions.     

A stable solution

It is proven that an autonomous system verifying some conditions has exactly one stable stationary trajectory. The proof of the result is based upon continuation methods.     

Farsightedly stable tariffs

This article analyzes the tariff negotiation game between two countries when the countries are sufficiently farsighted. It extends the research of Nakanishi (2000) and Oladi (2005) for the tariff retaliation game in which countries take into account subsequent retaliations that may occur after their own retaliation. We show that when countries are sufficiently farsighted, all farsighted stable sets of the tariff game of Nakanishi (2000) are singletons, which are Pareto efficient and strictly individually rational tariff combinations. These results hold regardless of whether coalitional deviations are allowed or not.     

Tempering stable processes

A tempered stable Lévy process combines both the α$\alpha$-stable and Gaussian trends. In a short time frame it is close to an α$\alpha$-stable process while in a long time frame it approximates a Brownian motion. In this paper we consider a general and robust class of multivariate tempered stable distributions and establish their identifiable parametrization. We prove short and long time behavior of tempered stable Lévy processes and investigate their absolute continuity with respect to the underlying α$\alpha$-stable processes. We find probabilistic representations of tempered stable processes which specifically show how such processes are obtained by cutting (tempering) jumps of stable processes. These representations exhibit α$\alpha$-stable and Gaussian tendencies in tempered stable processes and thus give probabilistic intuition for their study. Such representations can also be used for simulation. We also develop the corresponding representations for Ornstein–Uhlenbeck-type processes.     

Star stable domains

We introduce and study the notion of ?-stability with respect to a semistar operation ? defined on a domain R; in particular we consider the case where ? is the w-operation. This notion allows us to generalize and improve several properties of stable domains and totally divisorial domains.     

Progressive stable interpolation

In this paper, we study several interpolating and smoothing methods for data which are known “progressively”. The algorithms proposed are governed by recurrence relations and our principal goal is to study their stability. A recurrence relation will be said stable if the spectral radius of the associated matrix is less than one. The iteration matrices depend on shape parameters which come either from the connection at the knots, or from the nature of the interpolant between two knots. We obtain various stability domains. Moving the parameters inside these domains leads to interesting shape effects. This revised version was published online in June 2006 with corrections to the Cover Date.