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     

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     

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.     

Rotational brownian motion and fluorescence intensify fluctuations

A theory, which connects rotational brownian motion with intensity fluctuations of the light emitted from fluorescent molecules excited by linearly polarized light, is given. Analysis of rotational diffusion in this way does not depend on the close relationship between fluorescence lifetime and rotational relaxation times, which is necessary in present methods and thus makes an enlarged time range available for fluorescence spectroscopy.When short fluorescence lifetimes are used the rotational diffusion of the molecule in its ground state will be observed.     

The Effect of Lipid Composition on the Permeability of Fluorescent Markers from Photosensitized Membranes

There is evidence indicating that the cellular locus of PDT action by amphiphilic sensitizers are the cellular membranes. The photosensitization process causes oxidative damage to membrane components that can result in the cell's death. However, it was not yet established whether lipid oxidation can cause free passage of molecules through the membrane and, as a result, be the primary cause of the cell's death. In this work, we studied the effect of liposomes' lipid composition on the kinetics of the leakage of three fluorescent dyes, calcein, carboxyfluorescein and DTAF, which were trapped in the intraliposomal aqueous phase, after photosensitization with the photosensitizer deuteroporphyrin. We found that as the degree of fatty acid unsaturation increased, the photosensitized passage of these molecules through the lipid bilayer increased. We also found that the rate of leakage of these molecules was affected by their size and bulkiness as well as by their net electric charge. In liposomes that are composed of a lipid mixture similar to that of natural membranes, the observed passage of molecules through the membrane is slow. Thus, the photodynamic damage to lipids does not appear to be severe enough to be an immediate, primary cause of cell death in biological photosensitization.