Zero-sum constrained stochastic games with independent state processes

We consider a zero-sum stochastic game with side constraints for both players with a special structure. There are two independent controlled Markov chains, one for each player. The transition probabilities of the chain associated with a player as well as the related side constraints depend only on the actions of the corresponding player; the side constraints also depend on the player’s controlled chain. The global cost that player 1 wishes to minimize and that player 2 wishes to maximize, depend however on the actions and Markov chains of both players. We obtain a linear programming formulations that allows to compute the value and saddle point policies for this problem. We illustrate the theoretical results through a zero-sum stochastic game in wireless networks in which each player has power constraints     

On the stability of retrial queues

We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ > λ is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers. This revised version was published online in June 2006 with corrections to the Cover Date.     

Third order nonoscillatory central scheme for hyperbolic conservation laws

Summary. A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: 1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given cell averages; and 2. A central differencing based on staggered evolution of the reconstructed cell averages. This results in a third-order central scheme, an extension along the lines of the second-order central scheme of Nessyahu and Tadmor \cite{NT}. The scalar scheme is non-oscillatory (and hence – convergent), in the sense that it does not increase the number of initial extrema (– as does the exact entropy solution operator). Extension to systems is carried out by componentwise application of the scalar framework. In particular, we have the advantage that, unlike upwind schemes, no (approximate) Riemann solvers, field-by-field characteristic decompositions, etc., are required. Numerical experiments confirm the high-resolution content of the proposed scheme. Thus, a considerable amount of simplicity and robustness is gained while retaining the expected third-order resolution. Received April 10, 1996 / Revised version received January 20, 1997     

Asymptotic properties of constrained Markov Decision Processes

We present in this paper several asymptotic properties of constrained Markov Decision Processes (MDPs) with a countable state space. We treat both the discounted and the expected average cost, with unbounded cost. We are interested in (1) the convergence of finite horizon MDPs to the infinite horizon MDP, (2) convergence of MDPs with a truncated state space to the problem with infinite state space, (3) convergence of MDPs as the discount factor goes to a limit. In all these cases we establish the convergence of optimal values and policies. Moreover, based on the optimal policy for the limiting problem, we construct policies which are almost optimal for the other (approximating) problems. Based on the convergence of MDPs with a truncated state space to the problem with infinite state space, we show that an optimal stationary policy exists such that the number of randomisations it uses is less or equal to the number of constraints plus one. We finally apply the results to a dynamic scheduling problem.This work was partially supported by the Chateaubriand fellowship from the French embassy in Israel and by the European Grant BRA-QMIPS of CEC DG XIII     

FLUORESCENCE SPECTRAL CHANGES OF HEMATOPORPHYRIN DERIVATIVE UPON BINDING TO LIPID VESICLES, Staphylococcus aureus AND Escherichia coli CELLS

Abstract— The binding of hematoporphyrin derivated (Hpd) to lipid vesicles and bacterial membranes was determined by fluorescence spectroscopy. The fluorescence measurements of Hpd in aqueous solutions showed two bands at 613 and 677 nm. In lipid environments of lecithin vesicles the fluorescence spectrum was shifted to 631 and 692 nm, respectively. Hpd was rapidly bound to the cell membrane of Staphylococcus aureus while much less binding occurred in the presence of Escherichia coli. At the same time, spheroplasts of both bacteria were shown to bind Hpd to a similar extent. These results are well correlated with the photoinactivation of the gram positive bacteria with Hpd while the gram negative cells were shown to be resistant. The pH dependence of both Hpd binding to S. aureus as well as the photodynamic inhibitory effect of the same bacteria are similar. It is concluded that the segregation of Hpd to the cell membrane is a prerequisite for its photodynamic effect.     

Ferromagnetism in a dinuclear nickel(II) complex containing triethylenetetramine and tricyanomethanide

Triethylenetetramine (L(4)) was used as a tetradentate blocking ligand that, after complexation with Ni(II), leaves two sites ready for ligation with tricyanomethanide. The formed binuclear complex [L(4)Ni(NCC(CN)CN)(2)NiL(4)](ClO(4))(2) exhibits a ferromagnetic coupling with J/hc = +0.15 cm(-1) and g(Ni) = 2.126; below 16 K, a ferromagnetic ordering is evidenced by ac magnetic susceptibility (both in-phase and out-of-phase), magnetization, field-cooled magnetization, and zero-field-cooled magnetization measurements.     

Novel methyl helianthrones as photosensitizers: synthesis and biological evaluation

A combination of light, oxygen and a photosensitizer is used to induce death of cancer cells by photodynamic therapy. In this study, we have synthesized several new methyl helianthrone derivatives and compared their phototoxicity with that of hypericin. In contrast to hypericin, methyl helianthrones are soluble in aqueous solutions and have a broad range of light absorbance, which allows the use of polychromatic light. Structural modifications of methyl helianthrone demonstrated that substitution of hydrogen atoms of methyl helianthrone at Positions 2 and 5 with Br atoms or methylation of its phenolic hydroxyls, significantly increases the corresponding singlet oxygen quantum yield and their phototoxicity toward alphaT3-1, M2R and LNCaP cells. The phototoxicity of some of these compounds was similar to that of hypericin. Methyl helianthrones, like hypericin, accumulated mainly in the perinuclear region as evident by confocal microscopy. Irradiation of cells pretreated with methyl helianthrone derivatives generates intracellular reactive oxygen species and lipid free radicals, as shown by a fluorescentic probe and electron paramagnetic resonance methods, respectively. The phototoxicity of these methyl helianthrones as well as their ability to oxidize membrane lipids were significantly decreased on addition of specific Type-II inhibitors, suggesting the involvement of singlet oxygen as the main oxidant.     

THE EFFECT OF LIPOSOMES'' MEMBRANE COMPOSITION ON THE BINDING OF THE PHOTOSENSITIZERS HPD AND PHOTOFRIN II

Abstract— Photofrin II (PF-II) is the commercial name of the active photosensitizer which is used in photodynamic therapy of cancer. The effect of the composition of lipid membranes on the binding of PF-II was studied and compared to hematoporphyrin derivative (Hpd), which is a complex mixture of porphyrins and from which PF-II is separated. We find that increasing the content of cholesterol in the bilayer decreases the partitioning of PF-II into the bilayer, similar to what we have found earlier with Hpd. However, inserting DMPC or DPPC into the membrane, which was shown to decrease the binding of Hpd, causes the opposite trend with PF-H. A membrane fluidizer such as benzyl alcohol also has different effects on the membrane binding of Hpd and PF-II. The rate of binding of PF-II to a lipid membrane is about 10 times lower than that of Hpd. These results as well as I^- quenching of the fluorescence of the two porphyrins indicate that PF-II is immersed less homogeneously and deeper in the bilayer than Hpd. The unique additive-dependent binding of PF-II to lipid membranes calls for care in using Hpd as a model photosensitizer.     

Tetragonal low-temperature structure of LiAl

The cubic face-centered structure of LiAl (, at ) transforms into a tetragonal body-centered structure (I4₁/amd, , at ). This first-order phase transition at about during heating is probably the reason for the so-called “ anomalies” in some physical properties like specific heat, electrical resistivity and nuclear-spin lattice relaxation. This transition seems to be correlated with the composition Li:Al of the alloy and the amount of Li vacancies.