The EU regulation on cross-border trade of electricity: A two-stage equilibrium model

The regulation on cross-border exchanges of electricity in the European Union is meant to enhance the trade of electricity between Member States, by facilitating access to the network and improving the management of congestion at the interconnections. This paper presents a computational model that embeds these two features. The problem is cast in the form of a two-stage equilibrium between regional Regulators. In the first stage, they decide on the allocation of their regional network costs between generators and customers. Either they maximise their regional welfare non-cooperatively (Nash equilibrium), or they centralise the decision as a super-regulator (leading to a cooperative equilibrium). In the second-stage equilibrium, the consequences of first-stage’s decisions are assessed by modelling the energy market as the result of imperfect competition equilibrium on competitive market, coupled with regulated pricing on the domestic less competitive markets. The “rules” that come out of the first-stage game largely influence the final equilibrium. We illustrate this on an extensive numerical example, showing that the model behaves properly and identifying policy issues worth of further investigations.     

Dynamic graphs and continuous Boolean networks,I: A hybrid model for gene regulation

In this paper we propose a new theoretical framework for describing continuous Boolean networks, which is based on dynamic graphs. It is shown that mathematical representations of this type allow for a broad range of interactions between the discrete and continuous variables in the system. Since the form of these interactions determines the dynamic properties of the network, the number of possible configurations can be significantly expanded in this way. In the context of gene regulation, this added flexibility can be used to formulate models that better reflect the physical nature of the underlying biochemical processes.     

具有反馈控制的非自治Logistic模型的正周期解

A nonautonomous delayed logistic model with linear feedback regulation is pro- posed in this paper.Sufficient conditions are derived for the existence,uniqueness and global asymptotic stability of positive periodic solution of the model.     

Mathematical analysis of the Tyson model of the regulation of the cell division cycle

In this paper, we study the mathematical properties of a family of models of Eukaryotic cell cycle, which extend the qualitative model proposed by Tyson [Proc. Natl. Acad. Sci. 88 (1991) 7328–7332]. By means of some recent results in the theory of Lienard's systems, conditions for the uniqueness of the limit cycle and on the global asymptotic stability of the unique equilibrium (idest of the arrest of the cell division) are given.     

A generalized linear production model: A unifying model

We introduce a generalized linear production model whose attractive feature being that the resources held by any subset of producersS is not restricted to be the vector sum of the resources held by the members ofS. We provide sufficient conditions for the non-emptiness of the core of the associated generalized linear production game, and show that if the core of the game is not empty then a solution in it can be produced from a dual optimal solution to the associated linear programming problem. Our generalized linear production model is a proper generalization of the linear production model introduced by Owen, and it can be used to analyze cooperative games which cannot be studied in the ordinary linear production model framework. We use the generalized model to show that the cooperative game induced by a network optimization problem in which players are the nodes of the network has a non-empty core. We further employ our model to prove the non-emptiness of the core of two other classes of cooperative games, which were not previously studied in the literature, and we also use our generalized model to provide an alternative proof for the non-emptiness of the core of the class of minimum cost spanning tree games. Thus, it appears that the generalized linear production model is a unifying model which can be used to explain the non-emptiness of the core of cooperative games generated by various, seemingly different, optimization models.This research was partially done while the author was visiting the Graduate School of Business Administration at Tel-Aviv University. The research was partially supported by Natural Sciences and Engineering Research Council Canada Grant A4181 and by SSHRC leave fellowship 451-83-0030.Dedicated to George B. Dantzig.     

A note on yardstick regulation of fishery monopolies

This note considers a two-period model of a fishery exploited by two firms selling their harvests in separate local markets. Assuming the harvesting cost is a private information to the firms, there is an agency that can regulate the market. I propose a contract in the realm of yardstick competition framework that allows the regulator to solve the information asymmetry problem and achieve cooperation.     

A model of evolution

The theory of evolution is too general to be able to make predictions. However, like every other hypergeneral scientific theory, it can be enriched with specific assumptions and data, and thus become a specific model for a particular evolutionary line. This paper exhibits such a model. It accounts for the evolution of a biopopulation in terms of genetic and environmental variables. The results is a system of linear finite difference equations that enable one to pin down the necessary and sufficient conditions for evolution proper to occur, as well as to predict the average numbers of the final varieties originating from the parent population. It is estimated that the main value of the paper is methodological rather than substantive, in that it suggests a way of building models of biological lineages.     

A model of self-supervision

Systems which supervise their behavior by themselves play an increasingly important role, for example in the field of data processing. Self-checking is normally carried out by means of on-line and/or periodical testing. These self-tests, however, are not absolutely reliable as system defects will influence the self-test mechanism. Based on a model of self-supervising systems with periodical self-tests and renewals the diagnosability, the mean up time, and the optimal test interval with respect to cost are determined.

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Zusammenfassung Systeme, die ihre Funktionsweise selbsttätig überwachen können, spielen eine immer größere Rolle vor allem auch auf dem Gebiet der Datenverarbeitung. Selbstüberwachung basiert in der Regel auf funktionsbegleitenden und/oder periodisch durchgeführten Selbsttests. Diesen Selbsttests kann jedoch nicht voll vertraut werden, da Systemdefekte auch den Selbsttestmechanismus beeinflussen können. Anhand eines Modells eines sich selbstüberwachenden Systems mit periodischen Selbsttests und Erneuerungsmöglichkeit wird die Diagnostizierbarkeit, die mittlere Intaktzeit und das kostenoptimale Testintervall bestimmt.

     

A nucleation-and-growth model

Summary. We consider the following simple nucleation-and-growth model. On the lattice ℤ ^d , starting with all sites unoccupied, a site becomes occupied at rate e ^−ℬΓ if it has no occupied neighbors, at rate ɛ= e ^−βγ if it has 1 occupied neighbor, and at rate 1 if it has 2 or more occupied neighbors. Occupied sites remain occupied forever. The parameters Γ≧γ are fixed, and we are interested in the behavior of the system as β→∞. We show that the relaxation time of this system scales as e ^βκc , where κ _c = max {γ,( Γ + γ)/(d+1)}. Received: 20 February 1996 / In revised form: 15 June 1996     

Positive periodic solution of a more realistic three-species Lotka-Volterra model with delay and density regulation

In the paper, a more realistic three-species ratio-dependent Lotka-Volterra model with delay and diffusive and density regulation is investigated. By mean of the powerful and effective coincidence degree theory, we establish sufficient conditions for the existence of at least one positive periodic solution of the model. What’s more, the conditions are easily verifiable.     

A model of the neocortex

We try to explain the function of the cerebral cortex by representing it as a large array of small computers, each of which applies a certain algorithm for learning to predict the inputs from the senses or other parts of the brain. This view ignores the role of the brain as a classifying device, but it puts forward its role as a learner of the laws of evolution of sequences of patterns. Memory is not seen here as a list of facts but as an operator predicting certain parameters of the future states of reality from its present and past states. The problem of connecting the classifying or listing capacity of the brain with the structures described here is still open.     

A model of general systems

In this paper a mathematical model of general systems with not only one, but also more than one relation between the objects of the systems, was introduced. Among others, the concepts of partial systems, similarity of systems, embeddability of systems and free sum of systems were introduced. The following theorem was proved: there is no system whose object set consists of all systems.     

A model of concept formation

At first we model the way an intelligence “I” constructs statements from phrases, and then how “I” interlocks these statements to form a string of statements to attain a concept. These strings of statements are called progressions. That is, starting with an initial stimulating relation between two phrases, we study how “I” forms the first statement of the progression and continues from this first statement to form the remaining statements in these progressions to construct a concept. We assume that “I” retains the progressions that it has constructed. Then we show how these retained progressions provide “I” with a platform to incrementally constructs more and more sophisticated conceptual structures. The reason for the construction of these conceptual structures is to achieve additional concepts. Choice plays a very important role in the progression and concept formation. We show that as “I” forms new concepts, it enriches its conceptual structure and makes further concepts attainable. This incremental attainment of concepts is a way in which we humans learn, and this paper studies the attainability of concepts from previously attained concepts. We also study the ability of “I” to apply its progressions and also the ability of “I” to electively manipulate its conceptual structure to achieve new concepts. Application and elective manipulation requires of “I” ingenuity and insight. We also show that as “I” attains new concepts, the conceptual structures change and circumstances arise where unanticipated conceptual discoveries are attainable. As the conceptual structure of “I” is developed, the logical and structural relationships between concepts embedded in this structure also develop. These relationships help “I” understand concepts in the context of other concepts and help “I₁” communicate to another “I₂” information and concept structures. The conceptual structures formed by “I” give rise to a directed web of statement paths which is called a convolution web. The convolution web provides “I” with the paths along which it can reason and obtain new concepts and alternative ways to attain a given concept.This paper is an extension of the ideas introduced in [1]. It is written to be self-contained and the required background is supplied as needed.     

A finite model of mobility

The Markov chains with stationary transition probabilities have not proved satisfactory as a model of human mobility. A modification of this simple model is the ‘duration specific’ chain incorporating the axiom of cumulative inertia: the longer a person has been in a state the less likely he is to leave it. Such a process is a Markov chain with a denumerably infinite number of states, specifying both location and duration of time in the location. Here we suggest that a finite upper bound be placed on duration, thus making the process into a finite state Markov chain. Analytic representations of the equilibrium distribution of the process are obtained under two conditions: (a) the maximum duration is an absorbing state, for all locations; and (b) the maximum duration is non‐absorbing. In the former case the chain is absorbing, in the latter it is regular.     

A discussion of Hong-Stein model

In this paper,we discuss a kind of behavioral asset pricing model,called Hong-Stein model.Although this model succeeded in explaining the momentum and reversal effects,we find it usually reaches two extremes:the absolute value of autocorrelation of return sequence is so large that the direction of returns could be easily forecasted,or the value is so small that the elements in return sequence are almost independent of each other.The empirical results show that these two extremes are not supported by the real market data.     

A model of relativistic dynamics

A model of relativistic dynamics is proposed for classical (nonquantum) multiparticle systems within the Lagrangian formalism on the space of world lines.