Irregular time dependent obstacles

We study the obstacle problem for the Evolutionary p-Laplace Equation when the obstacle is discontinuous and does not have regularity in the time variable. Two quite different procedures yield the same solution.     

Setting staffing requirements for time dependent queueing networks: The case of accident and emergency departments

An incentive scheme aimed at reducing patients’ waiting times in accident and emergency departments was introduced by the UK government in 2000. It requires 98% of patients to be discharged, transferred, or admitted to inpatient care within 4 hours of arrival. Setting the minimal hour by hour medical staffing levels for achieving the government target, in the presence of complexities like time-varying demand, multiple types of patients, and resource sharing, is the subject of this paper. Building on extensive body of research on time dependent queues, we propose an iterative scheme which uses infinite server networks, the square root staffing law, and simulation to come up with a good solution. The implementation of this algorithm in a typical A&E department suggests that significant improvement on the target can be gained, even without increase in total staff hours.     

Parabolic equations in time dependent Reifenberg domains

In this paper we define time dependent parabolic Reifenberg domains and study Lp estimates for weak solutions of uniformly parabolic equations in divergence form on these domains. The basic assumption is that the principal coefficients are of parabolic BMO space with small parabolic BMO seminorms. It is shown that Lp estimates hold for time dependent parabolic δ-Reifenberg domains.     

positivity in time dependent linear transport theory

We present methods using positive semigroups and perturbation theory in the application to the linear Boltzmann equation. Besides being a review, this paper also presents generalizations of known results and develops known methods in a more abstract setting.In Section 1 we present spectral properties of the semigroup operatorsW _a(t) of the absorption semigroup and its generatorT _a. In Section 2 we treat the full semigroup (W(t);t0) as a perturbation of the absorption semigroup. We discuss part of the problems (perturbation arguments and existence of eigenvalues) which have to be solved in order to obtain statements about the large time behaviour ofW(·). In Section 3 we discuss irreducibility ofW(·).In four appendices we present abstract methods used in Sections 1, 2 and 3.     

A time minimising transportation problem with quality dependent time

The usual assumption made in time minimising transportation problem is that the time for transporting a positive amount in a route is independent of the actual amount transported in that route. In this paper we make a more general and natural assumption that the time depends on the actual amount transported. We assume that the time function for each route is an increasing piecewise constant function. Four algorithms - (1) a threshold algorithm, (2) an upper bounding technique, (3) a primal dual approach, and (4) a branch and bound algorithm - are presented to solve the given problem. A method is also given to compute the minimum bottle-neck shipment corresponding to the optimal time. A numerical example is solved illustrating the algorithms presented in this paper.     

The Dynamics of Closeness and Betweenness

Although both betweenness and closeness centrality are claimed to be important for the effectiveness of someone's network position, it has not been comprehensively studied which networks emerge if actors strive to optimize their centrality in the network in terms of betweenness and closeness. We study each of these centrality measures separately, but we also analyze what happens if actors value betweenness and closeness simultaneously. Network dynamics differ considerably in a scenario with either betweenness or closeness incentives compared with a scenario in which closeness and betweenness incentives are combined. There are not only more stable networks if actors’ betweenness and closeness are combined, but also these stable networks are less stylized.     

Exponential stability for time dependent potentials

For a classical Hamiltonian system on a torus defined by a time dependent, bounded and analytic potential we establish global and quantitative bounds for the solutions over an exponentially long interval of time by using techniques which go back to Nekhoroshev.     

Queues with waiting time dependent service

Motivated by service levels in terms of the waiting-time distribution seen, for instance, in call centers, we consider two models for systems with a service discipline that depends on the waiting time. The first model deals with a single server that continuously adapts its service rate based on the waiting time of the first customer in line. In the second model, one queue is served by a primary server which is supplemented by a secondary server when the waiting of the first customer in line exceeds a threshold. Using level crossings for the waiting-time process of the first customer in line, we derive steady-state waiting-time distributions for both models. The results are illustrated with numerical examples.     

Asymptotic behaviour in time of KdV type equations with time dependent coefficients

We study the asymptotic behaviour in time of the solutions of a class of evolution equations whose simplest representative would be the Korteweg de Vries equation with variable coefficients. Specific rates of decay are given in either the “conservative” or the dissipative case.     

Calendarization of time planning in MPM networks

A calendar contains working days and non-working days. How to make time planning for a project, when some activities cannot be interrupted by non-working days or in some time distances between start times of activities also non-working days count, is a problem often facing us when undertaking a project realization. In this paper an exact method to solve this problem is presented and the optimality of this method is proved.     

Queueing networks with dependent nodes and concurrent movements

Classical queueing network processes are useful for modeling the movement of discrete units in a network in which the nodes operate independently, the routing of units is independent of the congestion, only one unit moves at a time and its equilibrium distribution is a well-understood product form. Actual networks, however, typically have dependent nodes and concurrent movement of units. Imagine the dependencies associated with the network movements of telephone calls, manufacturing material, computer data packets, messages in a parallel-processing simulation, etc. A second generation of queueing network processes is beginning to evolve for modeling such “intelligent” networks with dependent nodes and concurrent movements. This paper describes the following fundamental processes that have been developed in this regard:

? A basic queueing network process for dependent nodes and single-unit movements. Examples include the classical Jackson, BCMP, Kelly and Kelly-Whittle networks and networks with interacting subpopulations.

? Reversible queueing network processes for dependent nodes and concurrent movements. An example is a multivariate, compound birth-death process.

? Miscellaneous partially balanced queueing networks. Examples include extensions of the basic network processes and weakly coupled and quasi-reversible networks.

     

Semilinear wave equation with time dependent potential

We consider the following semilinear wave equation: (1) for (t,x) ∈ ?_t × ?. We prove that if the potential V(t,x) is a measurable function that satisfies the following decay assumption: ∣V(t,x)∣?C(1+t)(1+∣x∣) for a.e. (t,x) ∈ ?_t × ? where C, σ₀>0 are real constants, then for any real number λ that satisfies there exists a real number ρ(f,g,λ)>0 such that the equation has a global solution provided that 0<ρ?ρ(f,g,λ). Copyright © 2004 John Wiley & Sons, Ltd.     

Erratum: Betweenness Centralization for Bipartite Graphs

We address two related issues. First, we analyze the effects of risk preferences on cooperation in social dilemmas. Second, we compare social dilemmas in which outcomes represent gains with dilemmas where outcomes represent losses. We show that predictions on gain‐loss asymmetries with respect to conditions for cooperation crucially depend on assumptions concerning risk preferences. Under the assumption of risk aversion for gains as well as losses together with an assumption of decreasing absolute risk aversion, conditions for cooperation are less restrictive if outcomes represent losses than if outcomes represent gains. Conversely ‐ and counterintuitively ‐ under the assumption of S‐shaped utility, conditions for cooperation are more restrictive if outcomes represent losses than if outcomes represent gains. We provide an experimental test of such predictions. Only a minority of subjects behaves consistent with the assumption of S‐shaped utility. Furthermore, we find no empirical evidence for a general difference between cooperation in social dilemmas in which outcomes represent gains and dilemmas where outcomes represent losses. We do find evidence that risk preferences affect cooperation rates.     

Updating credal networks is approximable in polynomial time

Credal networks relax the precise probability requirement of Bayesian networks, enabling a richer representation of uncertainty in the form of closed convex sets of probability measures. The increase in expressiveness comes at the expense of higher computational costs. In this paper, we present a new variable elimination algorithm for exactly computing posterior inferences in extensively specified credal networks, which is empirically shown to outperform a state-of-the-art algorithm. The algorithm is then turned into a provably good approximation scheme, that is, a procedure that for any input is guaranteed to return a solution not worse than the optimum by a given factor. Remarkably, we show that when the networks have bounded treewidth and bounded number of states per variable the approximation algorithm runs in time polynomial in the input size and in the inverse of the error factor, thus being the first known fully polynomial-time approximation scheme for inference in credal networks.     

Dynamical networks: Continuous time and general discrete time models

Dynamical networks are characterized by 1) their topology (structure of the graph of interactions among the elements of a network); 2) the interactions between the elements of the network; 3) the intrinsic (local) dynamics of the elements of the network. A general approach to studying the commulative effect of all these three factors on the evolution of networks of a very general type has been developed in [1]. Besides, in this paper there were obtained sufficient conditions for a global stability (generalized strong synchronization) of networks with an arbitrary topology and the dynamics which is a composition (action of one after another) of a local dynamics of the elements of a network and of the interactions between these elements. Here we extend the results of [1] on global stability (generalized strong synchronization) to the case of a general dynamics in discrete time dynamical networks and to general dynamical networks with continuous time.