Extreme shock models: An alternative perspective

Extreme shock models have been introduced in Gut and Hüsler (1999) to study systems that at random times are subject to a shock of random magnitude. These systems break down when the shock overcomes a given resistance level.In this paper we propose an alternative approach to extreme shock models using reinforced urn processes. As a consequence of this we are able to look at the same problem under a Bayesian nonparametric perspective, providing the predictive distribution of systems’ defaults.     

On the Representation Theory of Lie Triple Systems

In this paper, we take a new look at the representation theory of Lie triple systems. We consider both ordinary Lie triple systems and restricted Lie triple systems in the sense of [14]. In a final section, we begin a study of the cohomology of Lie triple systems.

     

On the class of infinite horizon optimal control problems affine,which are structurally stable

We prove in this article that there is in the set of all problems we consider a subset, which is residual. Every problem in this subset is shown to be structurally stable and defines a dynamical system, which looks like the graph of the figure given in Section  1 , contrary to what happens for ordinary dynamical systems, that is, the ones associated with ODEs. There, the initial value problem (in the smooth case) is uniquely solvable; the structurally stable systems look like the figure given in Section  1 , but sources are equilibria. Copyright © 2015 John Wiley & Sons, Ltd.     

Linear-quadratic control and quadratic differential forms for multidimensional behaviors

This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear quadratic control problem where the performance functional is the integral of a quadratic differential form. We look for characterizations of the set of stationary trajectories and of the set of local minimal trajectories with respect to compact support variations, turning out that they are equal if the system is dissipative. Finally we provide conditions for regular implementability of this set of trajectories and give an explicit representation of an optimal controller.     

A retrial queue with redundancy and unreliable server

Retrial queues are useful in the stochastic modelling of computer and telecommunication systems amongst others. In this paper we study a version of the retrial queue with variable service. Such a point of view gives another look at the unreliable retrial queueing problem which includes the redundancy model.By using the theory of piecewise Markovian processes, we obtain the analogue of the Pollaczek-Khintchine formula for such retrial queues, which is useful for operations researchers to obtain performance measures of interest.     

Bayesian policy support for adaptive strategies using computer models for complex physical systems

In this paper, we discuss combining expert knowledge and computer simulators in order to provide decision support for policy makers managing complex physical systems. We allow future states of the complex system to be viewed after initial policy is made, and for those states to influence revision of policy. The potential for future observations and intervention impacts heavily on optimal policy for today and this is handled within our approach. We show how deriving policy dependent system uncertainty using computer models leads to an intractable backwards induction problem for the resulting decision tree. We introduce an algorithm for emulating an upper bound on our expected loss surface for all possible policies and discuss how this might be used in policy support. To illustrate our methodology, we look at choosing an optimal CO₂ abatement strategy, combining an intermediate complexity climate model and an economic utility model with climate data.     

Fermat versus Wilson congruences,arithmetic derivatives and zeta values

We look at two analogs each for the well-known congruences of Fermat and Wilson in the case of polynomials over finite fields. When we look at them modulo higher powers of primes, we find interesting relations linking them together, as well as linking them with derivatives and zeta values. The link with the zeta value carries over to the number field case, with the zeta value at 1 being replaced by Euler's constant.     

Some aspects of intuitionistic fuzzy sets

We first discuss the significant role that duality plays in many aggregation operations involving intuitionistic fuzzy subsets. We then consider the extension to intuitionistic fuzzy subsets of a number of ideas from standard fuzzy subsets. In particular we look at the measure of specificity. We also look at the problem of alternative selection when decision criteria satisfaction is expressed using intuitionistic fuzzy subsets. We introduce a decision paradigm called the method of least commitment. We briefly look at the problem of defuzzification of intuitionistic fuzzy subsets.     

Uncertain and negative evidence in continuous time Bayesian networks

The continuous time Bayesian network (CTBN) enables reasoning about complex systems by representing the system as a factored, finite-state, continuous-time Markov process. Inference over the model incorporates evidence, given as state observations through time. The time dimension introduces several new types of evidence that are not found with static models. In this work, we present a comprehensive look at the types of evidence in CTBNs. Moreover, we define and extend inference to reason under uncertainty in the presence of uncertain evidence, as well as negative evidence, concepts extended to static models but not yet introduced into the CTBN model.     

Topologically transitive skew-products of backward shift operators and hypercyclicity

In this article we look at skew-products of multiples of the backward shift and examine conditions under which the skew-product is topologically transitive or hypercyclic in the second coordinate. We also give an application of the theory to iterated function systems of multiples of backward shift operators.

     

Observability of Nonlinear Systems

We consider the observability of systems of the form = Ax +Nx, y = Fx, where A is a linear operator and N and F are nonlinear.We show that if the system is linearized about an equilibriumpoint x_e and the linearized system is continuously initiallyobservable, then the nonlinear system is continuously initiallyobservable in some neighbourhood of x_e. We then look at conditionsunder which solutions of the nonlinear system can be extendedfor all time and consider the problem of stabilizing the systemby feedback controls such that the solutions are eventuallyin the observability neighbourhood of x_e. Finally, we applythese ideas to two systems: a wave equation and a diffusionequation with nonlinear perturbations and nonlinear observations.     

An isoperimetric inequality related to a Bernoulli problem

Given a bounded domain Ω we look at the minimal parameter Λ(Ω) for which a Bernoulli free boundary value problem for the p-Laplacian has a solution minimising an energy functional. We show that amongst all domains of equal volume Λ(Ω) is minimal for the ball. Moreover, we show that the inequality is sharp with essentially only the ball minimising Λ(Ω). This resolves a problem related to a question asked in Flucher et al. (Reine Angew Math 486:165–204, 1997).     

Hierarchic Control for the Wave Equation

This paper deals with the hierarchical control of the wave equation. We use Stackelberg–Nash strategies. As usual, we consider one leader and two followers. To each leader we associate a Nash equilibrium corresponding to a bi-objective optimal control problem; then, we look for a leader that solves an exact controllability problem. We consider linear and semilinear equations.     

时延混成系统的切换控制器合成

如何设计安全、可靠的信息物理融合系统是计算机科学和控制理论面临的一个重大挑战.时延现象在信息物理融合系统中普遍存在,时延对系统的稳定性、安全性和控制性能具有实质性影响.但是在已有时延系统验证和控制器合成的工作中往往忽略时延因素,这会导致在不考虑时延情况下能保证稳定和安全的系统在实际运行时因为时延原因而不再稳定和安全.因为时延使得系统的行为演化不仅与当前状态有关,还依赖于系统的历史状态,所以时延混成系统的验证和控制合成更加困难.本文研究信息物理融合系统在考虑时延情形下切换控制器合成问题,提出基于不变式生成技术的控制器合成方法.首先,利用谱分析和线性化技术将时延系统的微分不变式生成问题归结为有界时间的可达集计算问题;然后,提出基于抽象精化的算法计算时延系统有界时间可达集的上近似;最后,实现本文算法并使用实例验证该方法的有效性.     

Analysis of third-order methods for secular equations

Third-order numerical methods are analyzed for secular equations. These equations arise in several matrix problems and numerical linear algebra applications. A closer look at an existing method shows that it can be considered as a classical method for an equivalent problem. This not only leads to other third-order methods, it also provides the means for a unifying convergence analysis of these methods and for their comparisons. Finally, we consider approximated versions of the aforementioned methods.

     

Recursive state estimation for hybrid systems

The paper deals with recursive state estimation for hybrid systems. An unobservable state of such systems is changed both in a continuous and a discrete way. Fast and efficient online estimation of hybrid system state is desired in many application areas. The presented paper proposes to look at this problem via Bayesian filtering in the factorized (decomposed) form. General recursive solution is proposed as the probability density function, updated entry-wise. The paper summarizes general factorized filter specialized for (i) normal state-space models; (ii) multinomial state-space models with discrete observations; and (iii) hybrid systems. Illustrative experiments and comparison with one of the counterparts are provided.     

Ibragimov-type invariants for a system of two linear parabolic equations

We obtain new semi-invariants for a system of two linear parabolic type partial differential equations (PDEs) in two independent variables under equivalence transformations of the dependent variables only. This is achieved for a class of systems of two linear parabolic type PDEs that correspond to a scalar complex linear (1 + 1) parabolic equation. The complex transformations of the dependent variables which map the complex scalar linear parabolic PDE to itself provide us with real transformations that map the corresponding system of linear parabolic type PDEs to itself with different coefficients in general. The semi-invariants deduced for this class of systems of two linear parabolic type equations correspond to the complex Ibragimov invariants of the complex scalar linear parabolic equation. We also look at particular cases of the system of parabolic type equations when they are uncoupled or coupled in a special manner. Moreover, we address the inverse problem of when systems of linear parabolic type equations arise from analytic continuation of a scalar linear parabolic PDE. Examples are given to illustrate the method implemented.     

Tiling Polygons with Lattice Triangles

Given a simple polygon with rational coordinates having one vertex at the origin and an adjacent vertex on the x-axis, we look at the problem of the location of the vertices for a tiling of the polygon using lattice triangles (i.e., triangles which are congruent to a triangle with the coordinates of the vertices being integer). We show that the coordinates of the vertices in any tiling are rationals with the possible denominators odd numbers dependent on the cotangents of the angles in the triangles.     

On Linear Fractional Programming Problem and its Computation Using a Neural Network Model

In this paper we consider linear fractional programming problem and look at its linear complementarity formulation. In the literature, uniqueness of solution of a linear fractional programming problem is characterized through strong quasiconvexity. We present another characterization of uniqueness through complementarity approach and show that the solution set of a fractional programming problem is convex. Finally we formulate the complementarity condition as a set of dynamical equations and prove certain results involving the neural network model. A computational experience is also reported.      

Register Allocation in Structured Programs

In this article we look at the register allocation problem. In the literature this problem is frequently reduced to the general graph coloring problem and the solutions to the problem are obtained from graph coloring heuristics. Hence, no algorithm with a good performance guarantee is known. Here we show that when attention is restricted tostructured programswhich we define to be programs whose control-flow graphs are series-parallel, there is an efficient algorithm that produces a solution which is within a factor of 2 of the optimal solution. We note that even with the previous restriction the resulting coloring problem is NP-complete.We also consider how to delete a minimum number of edges from arbitrary control-flow graphs to make them series-parallel and to apply our algorithm. We show that this problem is Max SNP hard. However, we define the notion of anapproximate articulation pointand we give efficient algorithms to find approximate articulation points. We present a heuristic for the edge deletion problem based on this notion which seems to work well when the given graph is close to series-parallel.