On the optimality of regularity in mixing Markovian decision rules for MDP control

In this paper we study Markov Decision Process (MDP) problems with the restriction that at decision epochs only a finite number of given Markovian decision rules may be applied. The elements of the finite set of allowed decision rules should be mixed to improve the performance. The set of allowed Markovian decision rules could for example consist of some easy-implementable decision rules, but also many open-loop control problems can be modelled as an MDP for which the applicable decision rules are restricted. For various subclasses of Markovian policies methods to maximize the performance are obtained, analyzed and illustrated with examples. Advantages and disadvantages of optimizing over particular subclasses of applicable policies are discussed and optimal performances are compared. One of the main results gives sufficient conditions for the existence of an optimal Markovian policy belonging to the subclass of applicable policies having a so-called regular structure

On the optimal policy for deterministic and exponential polling systems

In this paper, we consider deterministic (both fluid and discrete) polling systems with N queues with infinite buffers and we show how to compute the best polling sequence (minimizing the average total workload). With two queues, the best polling sequence is always periodic when the system is stable and forms a regular sequence. The fraction of time spent by the server in the first queue is highly non continuous in the parameters of the system (arrival rate and service rate) and shows a fractal behavior. Convexity properties are shown in Appendix as well as a generalization of the computations to the stochastic exponential case

Optimal balanced control for call centers

In this paper we study a challenging call center operation problem. The goal of our analysis is to identify an optimal policy for allocating tasks to agents. As a first step, we discuss promising randomized policies and use stochastic approximation for finding the optimal randomized policy when implemented via a Bernoulli scheme. As we will show in this paper, the performance of the call center can be improved if the randomized policy is implemented by a deterministic sequence satisfying some regularity conditions. Such sequences are called balanced and we will show that implementing randomized policies by balanced sequences provide an additional step in optimization and control. This motivates our new approach where we avoid the intermediate step of first finding an optimal randomized control and directly find the optimal balanced sequence for control of the call center via stochastic approximation

Performance variability in perioperative sentinel events: report on a nationwide data set

Action Contro

Electronic structure, charge transfer, and intrinsic luminescence of gadolinium oxide nanoparticles: Experiment and theory

The cubic (c) and monoclinic (m) polymorphs of Gd2O3 were studied using the combined analysis of several materials science techniques - X-ray diffraction (XRD), scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), and photoluminescence (PL) spectroscopy. Density functional theory (DFT) based calculations for the samples under study were performed as well. The cubic phase of gadolinium oxide (c-Gd2O3) synthesized using a precipitation method exhibits spheroidal-like nanoclusters with well-defined edges assembled from primary nanoparticles with an average size of 50 nm, whereas the monoclinic phase of gadolinium oxide (m-Gd2O3) deposited using explosive pyrolysis has a denser structure compared with natural gadolinia. This phase also has a structure composed of three-dimensional complex agglomerates without clear-edged boundaries that are ~21 nm in size plus a cubic phase admixture of only 2 at. % composed of primary edge-boundary nanoparticles ~15 nm in size. These atomic features appear in the electronic structure as different defects ([Gd...O-OH] and [Gd...O-O]) and have dissimilar contributions to the charge-transfer processes among the appropriate electronic states with ambiguous contributions in the Gd 5p - O 2s core-like levels in the valence band structures. The origin of [Gd...O-OH] defects found by XPS was well-supported by PL analysis. The electronic and atomic structures of the synthesized gadolinias calculated using DFT were compared and discussed on the basis of the well-known joint OKT-van der Laan model, and good agreement was established.Comment: 27 pages, 10 figures, accepted in Appl. Surf. Sc

Axiomatizations of two types of Shapley values for games on union closed systems

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the Shapley value. In the literature various models of games with restricted cooperation can be found. So, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper, we consider such sets of feasible coalitions that are closed under union, i.e. for any two feasible coalitions also their union is feasible. We consider and axiomatize two solutions or rules for these games that generalize the Shapley value: one is obtained as the conjunctive permission value using a corresponding superior graph, the other is defined as the Shapley value of a modified game similar as the Myerson value for games with limited communication. © 2010 The Author(s)

The transition from the adiabatic to the sudden limit in core level photoemission: A model study of a localized system

We consider core electron photoemission in a localized system, where there is a charge transfer excitation. The system is modelled by three electron levels, one core level and two outer levels. The model has a Coulomb interaction between these levels and the continuum states into which the core electron is emitted. The model is simple enough to allow an exact numerical solution, and with a separable potential an analytic solution. We calculate the ratio r(omega) between the weights of the satellite and the main peak as a function of the photon energy omega. The transition from the adiabatic to the sudden limit takes place for quite small photoelectron kinetic energies. For such small energies, the variation of the dipole matrix element is substantial and described by the energy scale Ed. Without the coupling to the photoelectron, the corresponding ratio r0(omega) is determined by Ed and the satellite excitation energy dE. When the interaction potential with the continuum states is introduced, a new energy scale Es=1/(2Rs^2) enters, where Rs is a length scale of the interaction potential. At threshold there is typically a (weak) constructive interference between intrinsic and extrinsic contributions, and the ratio r(omega)/r0(omega) is larger than its limiting value for large omega. The interference becomes small or weakly destructive for photoelectron energies of the order Es. For larger energies r(omega)/r0(omega) therefore typically has a weak undershoot. If this undershoot is neglected, r(omega)/r0(omega) reaches its limiting value on the energy scale Es.Comment: 18 pages, latex2e, 13 eps figure

Component efficient solutions in line-graph games with applications

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. We investigate a class of cooperative games that generalizes some economic applications with a similar structure. These are the so-called line-graph games being cooperative TU-games in which the players are linearly ordered. Examples of situations that can be modeled like this are sequencing situations and water distribution problems. We define four properties with respect to deleting edges that each selects a unique component efficient solution on the class of line-graph games. We interpret these solutions and properties in terms of dividend distributions, and apply them to economic situations. © 2006 Springer-Verlag

Theoretical overview on high-energy emission in microquasars

Microquasar (MQ) jets are sites of particle acceleration and synchrotron emission. Such synchrotron radiation has been detected coming from jet regions of different spatial scales, which for the instruments at work nowadays appear as compact radio cores, slightly resolved radio jets, or (very) extended structures. Because of the presence of relativistic particles and dense photon, magnetic and matter fields, these outflows are also the best candidates to generate the very high-energy (VHE) gamma-rays detected coming from two of these objects, LS 5039 and LS I +61 303, and may be contributing significantly to the X-rays emitted from the MQ core. In addition, beside electromagnetic radiation, jets at different scales are producing some amount of leptonic and hadronic cosmic rays (CR), and evidences of neutrino production in these objects may be eventually found. In this work, we review on the different physical processes that may be at work in or related to MQ jets. The jet regions capable to produce significant amounts of emission at different wavelengths have been reduced to the jet base, the jet at scales of the order of the size of the system orbital semi-major axis, the jet middle scales (the resolved radio jets), and the jet termination point. The surroundings of the jet could be sites of multiwavelegnth emission as well, deserving also an insight. We focus on those scenarios, either hadronic or leptonic, in which it seems more plausible to generate both photons from radio to VHE and high-energy neutrinos. We briefly comment as well on the relevance of MQ as possible contributors to the galactic CR in the GeV-PeV range.Comment: Astrophysics & Space Science, in press (invited talk in the conference: The multimessenger approach to the high-energy gamma-ray sources", Barcelona/Catalonia, in July 4-7); 10 pages, 6 figures, 2 tables (one reference corrected