Evaluating the robustness of temporal networks considering spatiality of connections

Network robustness has been a hot research area of studies on complex networks. Finding out the explanations behind the phenomena that networked systems can still function efficiently after some structural damages or the malfunction of certain nodes is meaningful to both the design of solid systems and the defend against failures. It is still indistinct what kind of resilience networked systems which change their topological structures incessantly over time might have. Nevertheless, earlier studies have frequently overlooked to consider the temporal characteristics which in many real scenarios are of great concern, or have considered only the temporality without spatiality which is not reasonable in the real world case. In this paper, we first take the spatiality of connections and communications between nodes, except for the temporal ordering of connection events which has solely been noticed by previous studies, into consideration for measuring and assessing the robustness of the temporal network. We propose a novel temporal efficiency metric, and correspondingly, develop a new temporal robustness evaluation method for temporal network models. The proposed metric and method show their validity through numerical simulations of three temporal network models and we give our evaluations and discussions.     

Completeness of a functional system for surjective functions

Combining modalities has proven to have interesting applications and many approaches that combine time with other types of modalities have been developed. One of these approaches uses accessibility functions between flows of time to study the basic properties of the functions, such as being total or partial, injective, surjective, etc. The completeness of certain systems expressing many of these properties, with the exception of surjectivity, has been proven. In this paper we propose a language with nominals to denote the initial and final sets of each function in a model in order to obtain a complete system for reasoning about surjective partial functions.     

On the limitations of classical benchmark functions for evaluating robustness of evolutionary algorithms

Although evolutionary algorithms (EAs) have some operators which let them explore the whole search domain, still they get trapped in local minima when multimodality of the objective function is increased. To improve the performance of EAs, many optimization techniques or operators have been introduced in recent years. However, it seems that these modified versions exploit some special properties of the classical multimodal benchmark functions, some of which have been noted in previous research and solutions to eliminate them have been proposed.In this article, we show that quite symmetric behavior of the available multimodal test functions is another example of these special properties which can be exploited by some EAs such as covariance matrix adaptation evolution strategy (CMA-ES). This method, based on its invariance properties and good optimization results for available unimodal and multimodal benchmark functions, is considered as a robust and efficient method. However, as far as black box optimization problems are considered, no special trend in the behavior of the objective function can be assumed; consequently this symmetry limits the generalization of optimization results from available multimodal benchmark functions to real world problems. To improve the performance of CMA-ES, the Elite search sub-algorithm is introduced and implemented in the basic algorithm. Importance and effect of this modification is illustrated experimentally by dissolving some test problems in the end.     

Computationally tractable pairwise complexity profile

Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the information to describe a system as a function of the scale at which it is observed. We present a new formulation of the complexity profile, which expands its possible application to high‐dimensional real‐world and mathematically defined systems. The new method is constructed from the pairwise dependencies between components of the system. The pairwise approach may serve as both a formulation in its own right and a computationally feasible approximation to the original complexity profile. We compare it to the original complexity profile by giving cases where they are equivalent, proving properties common to both methods, and demonstrating where they differ. Both formulations satisfy linear superposition for unrelated systems and conservation of total degrees of freedom (sum rule). The new pairwise formulation is also a monotonically nonincreasing function of scale. Furthermore, we show that the new formulation defines a class of related complexity profile functions for a given system, demonstrating the generality of the formalism. © 2013 Wiley Periodicals, Inc. Complexity 18:20–27, 2013     

Orthorecursive Fourier-Stieltjes expansions

Orthorecursive Fourier-Stieltjes expansions are defined, and two examples of expansions are considered. The first example deals with orthogonal systems of functions (which include the Haar system as a particular case), and properties of Fourier-Stieltjes expansions in these systems are proved. It is pointed out that in the case of the Haar system, the integrated Fourier-Stieltjes expansion of a continuous function coincides, up to a constant, with the Faber-Schauder series expansion. The second example deals with nonorthogonal systems of functions that are structurally related to the earlier considered orthogonal systems. Properties of orthorecursive Fourier-Stieltjes expansions in these systems are established.     

An existence theorem for the Scheinkman-Weiss economic model

The Scheinkman-Weiss model and later works by Conze-Lasry-Scheinkman provide insights on cycles and correlations of economies with incomplete markets, namely with borrowing constraints. This work gives a mathematical solution in the case of high relative risk aversion, which has not yet been solved. The existence of an equilibrium results from the solution of a system of nonlinear functional differential equations. High risk aversion leads to new mathematical difficulties, not present in previous papers on this subject.This work is an extension of previous works done under the direction of Professor Jean-Michel Lasry, University of Paris 9, Dauphine. The author is sincerely grateful to Professor Lasry who suggested the idea of this article and whose remarks were always of help.     

A technique to construct symmetric variable-stepsize linear multistep methods for second-order systems

Some previous works show that symmetric fixed- and variable-stepsize linear multistep methods for second-order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems. In this paper, we give a technique to construct variable-stepsize symmetric methods from their fixed-stepsize counterparts, in such a way that the former have the same order as the latter. The order and symmetry of the integrators obtained is proved independently of the order of the underlying fixed-stepsize integrators. As this technique looks for efficiency, we concentrate on explicit linear multistep methods, which just make one function evaluation per step, and we offer some numerical comparisons with other one-step adaptive methods which also show a good long-term behaviour.

     

非线性控制系统的梯度扩张的能达性

研究了仿射非线性控制系统的梯度扩张系统.利用非线性控制系统的微分几何理论,通过计算梯度扩张系统的输出函数沿着输入向量场和系统向量场的李导数,讨论仿射非线性控制系统的梯度扩张系统的能达性分布,研究了非线性控制系统和它的梯度扩张系统的能达性之间的关系,证明了如果梯度扩张系统是能达的,则原非线性控制系统也是能达的.     

Sequent Calculi with Analytic Cut for Logics of Time and Knowledge with Perfect Recall

In this paper, we consider two logics of time and knowledge. These logics involve the discrete time linear temporal logic operators ``next' and ``until'. In addition, they contain an indexed set of unary epistemic modalities ``agent $i$ knows'. In these logics, the temporal and epistemic dimensions may interact. The particular interactions we consider capture perfect recall. We consider perfect recall in synchronously distributed systems and in systems without any assumptions. For these logics, we present sequent calculi with an analytic cut rule. Thus, we get proof systems where proof-search becomes decidable. The soundness and completeness of these calculi are proved.     

Geometric Criterium in the Center Problem

In this paper, we use a geometric criterium based on the classical method of the construction of Lyapunov functions to determine if a differential system has a focus or a center at a singular point. This criterium is proved to be useful for several examples studied in previous works with other more specific methods.     

Argumentation update in YALLA (Yet Another Logic Language for Argumentation)

This article proposes a complete framework for handling the dynamics of an abstract argumentation system. This frame can encompass several belief bases under the form of several argumentation systems, more precisely it is possible to express and study how an agent who has her own argumentation system can interact on a target argumentation system (that may represent a state of knowledge at a given stage of a debate). The two argumentation systems are defined inside a reference argumentation system called the universe which constitutes a kind of “common language”. This paper establishes three main results. First, we show that change in argumentation in such a framework can be seen as a particular case of belief update. Second, we have introduced a new logical language called YALLA in which the structure of an argumentation system can be encoded, enabling to express all the basic notions of argumentation theory (defense, conflict-freeness, extensions) by formulae of YALLA. Third, due to previous works about dynamics in argumentation we have been in position to provide a set of new properties that are specific for argumentation update.     

Cyclic multiple-robot scheduling with time-window constraints using a critical path approach

An automated production system is considered in which several robots are used for transporting parts between workstations following a given route in a carousel mode. The problem is to maximize the throughput rate. Extending previous works treating scheduling problems for a single robot, we consider a more realistic case in which workstations are served by multiple robots. A graph model of the production process is developed, making it possible to apply PERT–CPM solution techniques. The problem is proved to be solvable in polynomial time.     

Knowledge Representation, Reasoning and Integration Using Temporal Logic with Clocks

Representation, reasoning about and integrating knowledge based on multiple time granularities in knowledge-based systems is important, especially when talking about events that take place in the real world. Formal approaches based on temporal logics have been successfully applied in many application domains of knowledge-based systems where the evolution of a system and its environment through time is central. This paper presents a methodology based on temporal logic to deal with knowledge based on multiple time granularities in knowledge-based systems. The temporal logic we consider is especially suitable for modelling events with different rates and/or scales of progress. The methodology includes an approach to the representation of timing systems, a method used for representing facts and rules in a knowledge-based system that involve multiple time granularities using temporal logic, and several deductive reasoning techniques. The work presented in this article has been supported in part by The Australian Research Council and Macquarie University. Note that this paper is an extended and revised version of Orgun, Liu and Nayak [37].     

Optimality conditions and adjoint state for a perturbed boundary optimal control system

In this paper, we are concerned with finding optimal controls for a class of linear boundary optimal control systems associated to a Laplace operator on a regular bounded domain in the n-dimensional Euclidean space. For these systems, in previous works (see [1,2]), we proved existence of the (perturbed) states and optimal controls, and studied their behaviour. The purpose of this paper is to establish the system of optimality conditions, investigate the adjoint states, and prove their strong convergence in some Sobolev spaces.     

Monotonicity properties and functional inequalities for the Volterra and incomplete Volterra functions

In this paper we prove some monotonicity, log–convexity and log–concavity properties for the Volterra and incomplete Volterra functions. Moreover, as consequences of these results, we present some functional inequalities (like Turán type inequalities) as well as we determined sharp upper and lower bounds for the normalized incomplete Volterra functions in terms of weighted power means.     

Embedding Theorems for General Multianisotropic Spaces

An integral representation and embedding theorems for functions in multianisotropic Sobolev spaces are proved. Unlike in previous works, the general case where the characteristic Newton polyhedron in ?ⁿ has an arbitrary number of vertices is considered.     

Dualizable Shearlet Frames and Sparse Approximation

Shearlet systems have been introduced as directional representation systems, which provide optimally sparse approximations of a certain model class of functions governed by anisotropic features while allowing faithful numerical realizations by a unified treatment of the continuum and digital realm. They are redundant systems, and their frame properties have been extensively studied. In contrast to certain band-limited shearlets, compactly supported shearlets provide high spatial localization but do not constitute Parseval frames. Thus reconstruction of a signal from shearlet coefficients requires knowledge of a dual frame. However, no closed and easily computable form of any dual frame is known. In this paper, we introduce the class of dualizable shearlet systems, which consist of compactly supported elements and can be proved to form frames for \(L^2({\mathbb {R}}^2)\). For each such dualizable shearlet system, we then provide an explicit construction of an associated dual frame, which can be stated in closed form and is efficiently computed. We also show that dualizable shearlet frames still provide near optimal sparse approximations of anisotropic features.     

Past–future separation and normal forms in temporal predicate logic specifications

Temporal specifications are often used when phenomena are modelled where dynamics play a main role. If simulation is one of the aims of modelling, usually a restricted, executable modelling language format is used, based on some form of past to future implications. In this paper a detailed transformation procedure is described that takes any temporal predicate logic specification and generates a specification in a past-implies-future normal format. The procedure works for temporal specifications in which the atoms either express time ordering relations or are state-related, i.e., include only one time variable.     

A Semi-Analytical Method of Solving the Fokker-Planck-Equation for High-Dimensional Nonlinear Mechanical Systems

Stochastic processes are a common way of describing systems that are subjected to random influences. Technical systems may be excited by road roughness or wind gusts, for example, as well as fluctuating system parameters, which can all be described by stochastic differential equations. In previous works by the author and others (see [1], for example) it has been demonstrated how a Galerkin-method can be used to obtain global numerical solutions of the Fokker-Planck-Equation (FPE) for nonlinear random systems. Computational efforts are reduced by orthogonal polynomial expansion of approximate solutions so that probability density functions (pdfs) for comparably high-dimensional problems have been computed successfully. Stationary mechanical systems with dimensions up to d = 10 have been investigated, including polynomial as well as non-smooth nonlinearities. This article presents results for different energy-harvester-systems under stochastic excitation, a field of research that has become the subject of increasing attention in the last years. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)