Asymptotics of repeated interaction quantum systems

A quantum system S interacts in a successive way with elements E of a chain of identical independent quantum subsystems. Each interaction lasts for a duration τ and is governed by a fixed coupling between S and E. We show that the system, initially in any state close to a reference state, approaches a repeated interaction asymptotic state in the limit of large times. This state is τ-periodic in time and does not depend on the initial state. If the reference state is chosen so that S and E are individually in equilibrium at positive temperatures, then the repeated interaction asymptotic state satisfies an average second law of thermodynamics.     

通讯网络的极小费用树

本文针对ＭＣＭ９１问题Ｂ所给的９个通讯站，建立路径最短的数学模型，然后根据虚设站与路径的相互关系，以合并或分解虚设站为线索逐渐修改模型，最后确定的模型费用为１３４．８４，比美国马里兰州里斯勃莱州立大学数学科学系（ＭＣＭ的Ｄｉｒｅｃｔｏｒ）Ｂ．Ａ．Ｆｕｓａｒｏ提供的原文的费用少１．０５．本文新颖之处是改进图论中求最小生成树的方法，创造性地给出一个解决实际问题的新思路．     

Global boundary controllability of the Saint-Venant system for sloped canals with friction

We consider a sloped canal with friction that is governed by the Saint-Venant system with source term. We show that starting sufficiently close to a stationary constant subcritical initial state, we can control the system in finite time to a state in a C¹$C^1$ neighbourhood of any other stationary constant subcritical state by boundary control at the ends of the canal in such a way that during the process the system state remains continuously differentiable.     

Sur le caractère entropique des schémas de relaxation appliqués à une équation d'état non classique

In this Note, we show that the relaxation scheme theory applied to a non-classical equation of state allows to build in a very easy way a family of entropic schemes. It is very easy to build this kind of scheme because there exists a kinetic model whose fluid limit gives this non-classical equation of state.     

An adaptive parameter approach for an approximate solution of optimal control problems

In this paper, we consider a class of nonlinear optimal control problems (Bolza-problems) with constraints of the control vector, initial and boundary conditions of the state vectors. The time interval is fixed. Our approach to parametrize both the state functions and the control functions is described by general piecewise polynomials with unknown coefficients (parameters), where a fixed partition of the time interval is used. Here each of these functions in a suitable way individually will be approximated by such polynomials. The optimal control problem thus is reduced to a mathematical programming problem for these parameters. The existence of an optimal solution is assumed. Convergence properties of this method are not considered in this paper.     

Systems on universe spaces

The paper studies the class of analytic input/state/output systems for which the vector fields and the observation functions are only partially defined. The state space of the system is a universe space — a newly defined concept. As an example, quotient systems and observability are studied in detail. Observability is defined in a new way, consistent with the universe approach.     

基于两层对策系统的编队协同对地攻防对抗决策分析研究

基于学者Cruz建立的军事对抗的动态、离散的状态空间模型,在两层Stackelber-Nash决策方法的基础上,针对编队协同对地攻击的攻防对抗系统的强对抗性、多目标性和多层次性,建立了两层对策系统——Nash-Stackelberg-Nash决策模型,着重解决军事对抗中的多层次对抗决策问题.将该决策方法应用于Cruz建立的基本战场想定,并将单决策层的Nash对抗决策与两层对策系统的Nash-Stackelberg-Nash决策方法进行了对比,仿真结果表明该决策方法相对单层Nash对抗决策有明显改进,并为作战对抗提供了有力的战场分析依据.     

Mini-Maximizers for Reaction-Diffusion Systems with Skew-Gradient Structure

A reaction-diffusion system with skew-gradient structure is a sort of activator-inhibitor system that consists of two gradient systems coupled in a skew-symmetric way. Any steady state of such a system corresponds to a critical point of some functional. The aim of this paper is to study the relation between a stability property as a steady state of the reaction-diffusion system and a mini-maximizing property as a critical point of the functional. It is shown that a steady state of the skew-gradient system is stable regardless of time constants if and only if it is a mini-maximizer of the functional. It is also shown that the mini-maximizing property is closely related with the diffusion-induced instability. Moreover, by using the property that any mini-maximizer on a convex domain is spatially homogeneous, quite a general instability criterion is obtained for some activator-inhibitor systems. These results are applied to the diffusive FitzHugh-Nagumo system and the Gierer-Meinhardt system.     

Optimal information structure in a simple economic system

In a highly simplified version of a common economic model, the planner can choose among alternative time-varying designs for the information structure in order to steer the system to a target state in an optimal way. The resulting problem is imbedded into a more general one with bilinear dynamics, that is, linear in the control and the state variables but not in both. The existence of a feasible decentralized information structure is studies and designs are found which make the system optimal, given a performance function assigning losses to deviations froma target state. The conditions under which a decentralized structure is optimal are also studied and a numerical case is considered.     

On the state of a bounded multiparticle cluster

The state equation and the energy of a space-bounded multiparticle cluster with a power-like interaction of the particles in the degenerate state have been obtained in the quasi-classical representation. The interaction of the particles with the cluster surface is accounted for in a simple way.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 2, pp. 270–278, November, 1996.     

The impact of process deterioration on production and maintenance policies

This paper examines a single-stage production system that deteriorates with production actions, and improves with maintenance. The condition of the process can be in any of several discrete states, and transitions from state to state follow a semi-Markov process. The firm can produce multiple products, which differ by profit earned, expected processing time, and impact on equipment deterioration. The firm can also perform different maintenance actions, which differ by cost incurred, expected down time, and impact on the process condition. The firm needs to determine the optimal production and maintenance choices in each state in a way that maximizes the long-run expected average reward per unit time.     

Minimal system inverses for linear multivariable systems

The problem of minimal inverses for linear time invariant multivariable systems is formulated and constructively solved in a state space setting. Unknown initial states as well as zero initial states are considered. The spectrum of the minimal inverse is shown to be unique and constructable from the original system without first calculating the whole inverse. This leads to a simple way of introducing the equivalence of “zeros” in state space terminology.     

Some Conditions for Maximal Monotonicity of Bifunctions

We present necessary and sufficient conditions for a monotone bifunction to be maximally monotone, based on a recent characterization of maximally monotone operators. These conditions state the existence of solutions to equilibrium problems obtained by perturbing the defining bifunction in a suitable way.     

Stochastic optimal control and algorithm of the trajectory of horizontal wells

This paper presents a nonlinear, multi-phase and stochastic dynamical system according to engineering background. We show that the stochastic dynamical system exists a unique solution for every initial state. A stochastic optimal control model is constructed and the sufficient and necessary conditions for optimality are proved via dynamic programming principle. This model can be converted into a parametric nonlinear stochastic programming by integrating the state equation. It is discussed here that the local optimal solution depends in a continuous way on the parameters. A revised Hooke–Jeeves algorithm based on this property has been developed. Computer simulation is used for this paper, and the numerical results illustrate the validity and efficiency of the algorithm.     

Limited risk control of the ornstein-uhleeck process

We consider the problem of steering a system described by a simple one dimensional: linear stochastic differential equation in such a way as to maximize the upper allowable limit that is exceeded by the final state with a prescribed probability. The optimal controls are computed by applying the maximum principle to an equivalent deterministic problem.. This model can be used among other things to find optimal strategies for specific advertising. activities of a firm.     

Distribution of Statistics of Hidden State Sequences Through the Sum-Product Algorithm

We compute exact distributions of statistics of hidden state sequences in general settings. Distributions are computed for undirected and directed graphical models that are represented using conditional random fields and factor graphs. The methods discussed are relevant for graphs with a sparseness of edges that allows exact computation of the normalization constant. The distributions are obtained in an efficient manner by integrating sequential updates of the statistic’s value with the sum-product algorithm. Applications of this work include discrete hidden state sequences perturbed by noise and/or missing values, and state sequences that serve to classify observations. In the case of classification, the methods give a way to quantify the uncertainty in statistics associated with the classifications. The algorithm is applied to model-based false discovery distributions for protein-protein interactions and distributions related to CpG island lengths in DNA sequences.     

Multiphase free discontinuity problems: Monotonicity formula and regularity results

The purpose of this paper is to analyze regularity properties of local solutions to free discontinuity problems characterized by the presence of multiple phases. The key feature of the problem is related to the way in which two neighboring phases interact: the contact is penalized at jump points, while no cost is assigned to no-jump interfaces which may occur at the zero level of the corresponding state functions. Our main results state that the phases are open and the jump set (globally considered for all the phases) is essentially closed and Ahlfors regular. The proof relies on a multiphase monotonicity formula and on a sharp collective Sobolev extension result for functions with disjoint supports on a sphere, which may be of independent interest.     

On the Accuracy of the MAP Inference in HMMs

In a hidden Markov model, the underlying Markov chain is usually unobserved. Often, the state path with maximum posterior probability (Viterbi path) is used as its estimate. Although having the biggest posterior probability, the Viterbi path can behave very atypically by passing states of low marginal posterior probability. To avoid such situations, the Viterbi path can be modified to bypass such states. In this article, an iterative procedure for improving the Viterbi path in such a way is proposed and studied. The iterative approach is compared with a simple batch approach where a number of states with low probability are all replaced at the same time. It can be seen that the iterative way of adjusting the Viterbi state path is more efficient and it has several advantages over the batch approach. The same iterative algorithm for improving the Viterbi path can be used when it is possible to reveal some hidden states and estimating the unobserved state sequence can be considered as an active learning task. The batch approach as well as the iterative approach are based on classification probabilities of the Viterbi path. Classification probabilities play an important role in determining a suitable value for the threshold parameter used in both algorithms. Therefore, properties of classification probabilities under different conditions on the model parameters are studied.     

Adaptive finite element methods for mixed control-state constrained optimal control problems for elliptic boundary value problems

Mixed control-state constraints are used as a relaxation of originally state constrained optimal control problems for partial differential equations to avoid the intrinsic difficulties arising from measure-valued multipliers in the case of pure state constraints. In particular, numerical solution techniques known from the pure control constrained case such as active set strategies and interior-point methods can be used in an appropriately modified way. However, the residual-type a posteriori error estimators developed for the pure control constrained case can not be applied directly. It is the essence of this paper to show that instead one has to resort to that type of estimators known from the pure state constrained case. Up to data oscillations and consistency error terms, they provide efficient and reliable estimates for the discretization errors in the state, a regularized adjoint state, and the control. A documentation of numerical results is given to illustrate the performance of the estimators.