Evolution in complex systems

What features characterize complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analyzed to confirm this effect. The strain arises from local frustration. As the strain is released through “quakes,” some system variable undergoes record statistics with accompanying log‐Poisson statistics for the quake event times. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology and show how quantitative indications of aging can be found. © 2004 Wiley Periodicals, Inc. Complexity 10: 49–56, 2004     

Coin-tossing measures and their Fourier transforms

A coin-tossing measure μ on [0,1] is a probability measure satisfying

     

Norm-attaining functionals onC(Q, X)

Functionals (vector measures) defined on the spaceC(Q, X) of continuous abstract functions (whereQ is a compact Hausdorff space andX is a Banach space) and attaining their norm on the unit sphere are considered. A characterization of such functionals is given in terms of the Radon-Nikodym derivative of the vector measure with respect to the variation of the measure and in terms of analogs of the derivative. Applications to the characterization of finite-codimensional subspaces with the best approximation property are given. Similar results are obtained for the spaceB(Q, Σ, X) of uniform limits of simple functions. Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 45–56, January, 1997. Translated by V. E. Nazaikinskii     

Measure-valued almost periodic functions

We consider Stepanov almost periodic functions μ ∈ ranging in the metric space of Borel probability measures on a complete separable metric space is equipped with the Prokhorov metric). The main result is as follows: a function , belongs to if and only if for each bounded continuous function , the function is Stepanov almost periodic (of order 1) and

Cone-valued Lyapunov functions and stability for impulsive functional differential equations

The stability criteria in terms of two measures for impulsive functional differential equations are established via cone-valued Lyapunov functions and Razumikhin technique. The stability can be deduced from the (Q₀,Q)-stability of comparison impulsive differential equations. An example is given to illustrate the advantages of the results obtained.     

Carleson Measures for the Bloch Space

In this paper we study the positive Borel measures μ on the unit disc in for which the Bloch space is continuously included in , 0 < p < ∞. We call such measures p-Bloch-Carleson measures. We give two conditions on a measure μ in terms of certain logarithmic integrals one of which is a necessary condition and the other a sufficient condition for μ being a p-Bloch-Carleson measure. We also give a complete characterization of the p-Bloch-Carleson measures within certain special classes of measures. It is also shown that, for p > 1, the p-Bloch-Carleson measures are exactly those for which the Toeplitz operator , defined by , maps continuously into the Bergman space A ¹, . Furthermore, we prove that if p > 1, α >-1 and ω is a weight which satisfies the Bekollé-Bonami -condition, then the measure defined by is a p-Bloch-Carleson-measure. We also consider the Banach space of those functions f which are analytic in and satisfy , as . The Bloch space is contained in . We describe the p-Carleson measures for and study weighted composition operators and a class of integration operators acting in this space. We determine which of these operators map continuously to the weighted Bergman space and show that they are automatically compact. This research is partially supported by several grants from “the Ministerio de Educación y Ciencia, Spain” (MTM2005-07347, MTM2007-60854, MTM2006-26627-E, MTM2007-30904-E and Ingenio Mathematica (i-MATH) No. CSD2006-00032); from “La Junta de Andalucía” (FQM210 and P06-FQM01504); from “the Academy of Finland” (210245) and from the European Networking Programme “HCAA” of the European Science Foundation.     

Characterizations of classes of risk measures by dispersive orders

In this paper, a class C₁ of risk measures, which generalizes the class of risk measures for the right-tail deviation suggested by Wang [Wang, S., 1998. An actuarial index of the right-tail risk. North Amer. Actuarial J. 2, 88–101], is characterized in terms of dispersive order. If dispersive order does not hold, unanimous comparisons are still possible by restricting our attention to a subclass C₂C₁ and then the criterion is the excess-wealth order. Sufficient conditions for stochastic equivalence of excess-wealth ordered random variables are derived in terms of some particular measures of C₂.     

Carleson measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on complex balls

For 0?σ<1/2 we characterize Carleson measures μ for the analytic Besov-Sobolev spaces on the unit ball Bn in Cn by the discrete tree condition

     

Some criteria for the existence of invariant measures and asymptotic stability for random dynamical systems on polish spaces

Tomasz Szarek presented interesting criteria for the existence of invariant measures and asymptotic stability of Markov operators on Polish spaces. Hans Crauel in his book presented the theory of random probabilistic measures on Polish spaces showing that notions of compactness and tightness for such measures are in one-to-one correspondence with such notions for non-random measures on Polish spaces, in addition to the criteria under which the space of random measures is itself a Polish space. This result allowed the transfer of results of Szarek to the case of random dynamical systems in the sense of Arnold. These criteria are interesting because they allow to use the existence of simple deterministic Lyapunov type function together with additional conditions to show the existence of invariant measures and asymptotic stability of random dynamical systems on general Polish spaces.     

网络舆情的研究与发展—以涉警网络舆情为例

网络舆情传播速度快、波及范围广,同时具有很强的突发性、不确定性、难以控制等特点,对相关部门进行涉警网络舆情干预和引导带来巨大挑战。目前有关网络舆情引导、管控机制、应对策略研究等成果丰富、但是对网络舆情危机的演变和干预多停留在定性分析之上、定量分析研究相对欠缺。现有网络舆情研究多针对舆情发展某一阶段进行研究,未结合网络舆情发展的多阶段属性展开全生命周期研究,为数不多的网络舆情多阶段干预决策机制研究也比较粗略,缺乏一套科学、规范的干预决策机制作为支撑。因此,结合网络舆情的多阶段属性、应用定量分析方法,是未来网络舆情干预决策机制研究的方向之一。本文通过对网络舆情发展过程的描述,给出一定量的状态表述和行动刻画,构建一个分类多阶段决策模型框架。