Monitoring cooperative equilibria in a stochastic differential game

This paper deals with a class of equilibria which are based on the use of memory strategies in the context of continuous-time stochastic differential games. In order to get interpretable results, we will focus the study on a stochastic differential game model of the exploitation of one species of fish by two competing fisheries. We explore the possibility of defining a so-called cooperative equilibrium, which will implement a fishing agreement. In order to obtain that equilibrium, one defines a monitoring variable and an associated retaliation scheme. Depending on the value of the monitoring variable, which provides some evidence of a deviation from the agreement, the probability increases that the mode of a game will change from a cooperative to a punitive one. Both the monitoring variable and the parameters of this jump process are design elements of the cooperative equilibrium. A cooperative equilibrium designed in this way is a solution concept for a switching diffusion game. We solve that game using the sufficient conditions for a feedback equilibrium which are given by a set of coupled HJB equations. A numerical analysis, approximating the solution of the HJB equations through an associated Markov game, enables us to show that there exist cooperative equilibria which dominate the classical feedback Nash equilibrium of the original diffusion game model.This research was supported by FNRS-Switzerland, NSERC-Canada, FCAR-Quebec.     

Accelerations for global optimization covering methods using second derivatives

Two improvements for the algorithm of Breiman and Cutler are presented. Better envelopes can be built up using positive quadratic forms. Better utilization of first and second derivative information is attained by combining both global aspects of curvature and local aspects near the global optimum. The basis of the results is the geometric viewpoint developed by the first author and can be applied to a number of covering type methods. Improvements in convergence rates are demonstrated empirically on standard test functions.Partially supported by an University of Canterbury Erskine grant.     

Integral global optimization method for solution of nonlinear complementarity problems

The mapping in a nonlinear complementarity problem may be discontinuous. The integral global optimization algorithm is proposed to solve a nonlinear complementarity problem with a robust piecewise continuous mapping. Numerical examples are given to illustrate the effectiveness of the algorithm.     

A Goal Programming model of the reference point method

Real-life decision problems are usually so complex they cannot be modeled with a single objective function, thus creating a need for clear and efficient techniques of handling multiple criteria to support the decision process. The most commonly used technique is Goal Programming. It is clear and appealing, but in the case of multiobjective optimization problems strongly criticized due to its noncompliance with the efficiency (Pareto-optimality) principle. On the other hand, the reference point method, although using similar control parameters as Goal Programming, always generates efficient solutions. In this paper, we show how the reference point method can be modeled within the Goal Programming methodology. It allows us to simplify implementations of the reference point method as well as shows how Goal Programming with relaxation of some traditional assumptions can be extended to a multiobjective optimization technique meeting the efficiency principle.     

A nonsmooth Newton method for variational inequalities,I: Theory

This paper presents a modified damped Newton algorithm for solving variational inequality problems based on formulating this problem as a system of equations using the Minty map. The proposed modified damped-Newton method insures convergence and locally quadratic convergence under the assumption of regularity. Under the assumption ofweak regularity and some mild conditions, the modified algorithm is shown to always create a descent direction and converge to the solution. Hence, this new algorithm is often suitable for many applications where regularity does not hold. Part II of this paper presents the results of extensive computational testing of this new method.Corresponding author.     

Quantum Fourier Transform-Based Arithmetic Logic Unit on a Quantum Processor

This study proposes and construct a primitive quantum arithmetic logic unit (qALU) based on the quantum Fourier transform (QFT). The qALU is capable of performing arithmetic ADD (addition) and logic NAND gate operations. It designs a scalable quantum circuit and presents the circuits for driving ADD and NAND operations on two-input and four-input quantum channels, respectively. By comparing the required number of quantum gates for serial and parallel architectures in executing arithmetic addition, it evaluates the performance. It also execute the proposed quantum Fourier transform-based qALU design on real quantum processor hardware provided by IBM. The results demonstrate that the proposed circuit can perform arithmetic and logic operations with a high success rate. Furthermore, it discusses in detail the potential implementations of the qALU circuit in the field of computer science, highlighting the possibility of constructing a soft-core processor on a quantum processing unit.     

Resonant-interaction-induced Rydberg antiblockade and its applications

Different from the conventional Rydberg antiblockade (RAB) regime that either requires weak Rydberg-Rydberg interaction (RRI), or compensates the RRI-induced energy shift by introducing off-resonant interactions, we show that RAB regime can be achieved by resonantly driving the transitions between ground state and Rydberg state under strong RRI. The Rabi frequencies are of small amplitude and time-dependent harmonic oscillation, which plays a critical role for the presented RAB. The proposed unconventional RAB regime is used to construct high-fidelity controlled-Z (CZ) gate and controlled-not (CNOT) gate in one step. Each atom requires single external driving. And the atomic addressability is not required for the presented unconventional RAB, which would simplify experimental complexity and reduce resource consumption.     

Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics

The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.     

On the greedy solution in integer linear programming

A version of the greedy method not using any knapsack relaxation of the integer programming problem is considered in this paper. It is based on a natural partial ordering of the vectors. Our aim is to determine a large class of problems where the greedy solution is always optimal. The results generalize some theorems of an early paper of Magazine, Nemhauser and Trotter and at the same time show a connection between two different notions of combinatorics: the greedy method and the Hilbert basis.

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Zusammenfassung In dieser Arbeit wird eine Version des Greedy-Algorithmus zur Lösung ganzzahliger linearer Optimierungsprobleme benutzt, die kein Rucksackproblem als Relaxation verwendet. Das Verfahren basiert auf der natürlichen partiellen Ordnung von Vektoren. Ziel der Arbeit ist es, eine möglichst große Problemklasse zu beschreiben, für die die Greedy-Lösung optimal ist. Die Ergebnisse verallgemeinern Sätze einer früheren Arbeit von Magazine, Nemhauser und Trotter und zeigen gleichzeitig einen Bezug zwischen zwei verschiedenen Gebieten der Kombinatorik auf: des Greedy-Verfahrens und von Hubert-Basen.

     

Chaotic dynamics in biological information processing: A heuristic outline

Summary A given but otherwise random environmental time series impinging on the input of a certain biological processor passes through with overwhelming probability practically undetected. A very small percentage of environmental stimuli, though, is ?captured? by the processor's nonlinear dissipative operator asinitial conditions, that is, assolutions of the processor's dissipative dynamics. The processor, then, is in such cases instrumental in compressing or abstracting those stimuli, thereby making the external world to collapse from a previous regime of a ?pure state? of suspended animation onto a set of stable eigenfunctions or ?categories?—chaotic strange attractors. The characteristics of this cognitive set depend on the operator involved and the hierarchical level where the abstraction takes place. In this paper we model the physics of such a cognitive process and the role that the thalamo-cortical pacemaker of the (human) brain plays in both stimulating the individual attractors and permutating them on a time division multiplexing basis. A synthesis of the Markovian processes taking place within each individual attractor-memory and the Markovian or semi-Markovian process involving the intermittent jumping among the different attractor-memories are discussed.

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Riassunto Una data ma casuale serie temporale ambientale che influisce sull'immissione di un determinato processore biologico passa con schiacciante probabilità praticamente inosservata. Una piccolissima percentuale di stimoli ambientali, tuttavia, è catturata dall'operatore dissipativo non lineare del processore comecondizioni iniziali, cioè comesoluzioni della dinamica dissipativa del processore. Il processore è quindi, in tali casi, strumentale nel comprimere o estrarre quegli stimoli, facendo perciò collassare il mondo esterno da un precedente regime di ?stato puro? ad animazione sospesa ad un gruppo di autofunzioni stabili o ?categorie?—attrattori caotici strani. Le caratteristiche di questo gruppo cognitivo dipendono dall'operatore coinvolto e dal livello gerarchico in cui l'estrazione ha luogo. In questo lavoro si modella la fisica di tale processo cognitivo e il ruolo che lo stimolatore talamo-corticale del cervello (umano) ha sia nello stimolare gli attrattori individuali che nel permutarli su una base che manda segnali multiplex a divisione temporale. Si discute una sintesi dei processi markoviani che hanno luogo all'interno di ogni attrattore-memoria individuale e il processo markoviano o semimarkoviano che interessa il salto intermittente tra i diversi attrattori-memoria.

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Резюме Временная последовательность на входе некоторого биологического процессора может иметь практически недетектируемую вероятность. Очень небольшой процент стимулов окружающей среды ?захватывается? нелинейным диссипативным оператором процессора как начальные условия, т.е. представляется как решение диссипативпой динамики процессора. Затем процессор обрабатывает внешние стимулы, вынуждая внешний мир коллапсировать из предыдущего режима ?чистого состояния? приостановленного оживления в систему собственных функций или ?категорий?. Характеристики зтой познавательной системы зависят от используемого оператора и иерархического уровня, на котором происходит абстрагирование. В зтой статье мы моделируем физику такого познавательного процесса. Обсуждается синтез марковских процессов, происходящий внутри отдельного злемента ?атрактор-память?, и марковский или полумарковский процесс, включающий пережежающиеся прыжки между различными злементами ?атракторпамять?.