Sensitivity of constrained Markov decision processes

We consider the optimization of finite-state, finite-action Markov decision processes under constraints. Costs and constraints are of the discounted or average type, and possibly finite-horizon. We investigate the sensitivity of the optimal cost and optimal policy to changes in various parameters. We relate several optimization problems to a generic linear program, through which we investigate sensitivity issues. We establish conditions for the continuity of the optimal value in the discount factor. In particular, the optimal value and optimal policy for the expected average cost are obtained as limits of the dicounted case, as the discount factor goes to one. This generalizes a well-known result for the unconstrained case. We also establish the continuity in the discount factor for certain non-stationary policies. We then discuss the sensitivity of optimal policies and optimal values to small changes in the transition matrix and in the instantaneous cost functions. The importance of the last two results is related to the performance of adaptive policies for constrained MDP under various cost criteria [3,5]. Finally, we establish the convergence of the optimal value for the discounted constrained finite horizon problem to the optimal value of the corresponding infinite horizon problem.     

On complete Tchebycheff-systems

It is shown under what condition a Tchebycheff-space on a real set containing at most one end point, has a Tchebycheff subspace of codimension 1. It is also shown when a complete Tchebycheff-system on a real set M, is also a complete Tchebycheff-system on .     

Evidence for a cubic-to-icosahedral transition of quasi-free Pd-H-clusters controlled by the hydrogen content

An in situ synchrotron radiation study of quasi-free five nanometer-sized palladium clusters during hydrogen absorption is combined with molecular dynamics simulations to investigate the structural development. In the diffraction patterns, strong intensity changes are found that provide evidence for a structural phase transformation that is significantly different from the α--Pd-H bulk phase transition. The structural transition is reversible and driven by the hydrogen concentration. The intensity changes are consistent with a cubic-to-icosahedral structural phase transition obtained in molecular dynamical simulations using embedded-atom-method potentials. Received 15 October 2001 and Received in final form 7 February 2002     

Note on ethene and other low-molecular weight hydrocarbons in environmental tobacco smoke

Levels of ethene and propene, together with those of some other light hydrocarbons (propane, butane, isobutane and ethyne), have been measured under realistic conditions in environmental tobacco smoke (ETS) as a step towards the elucidation of the sources of 2-hydroxyethyl and 2-hydroxypropyl adducts of hemoglobin observed in non-smokers. These adducts may reflect in vivo doses of carcinogenic epoxides that are metabolites of the respective alkenes. The data show that 2.0 mg ethene, 1.4 mg propene, and 0.7 mg propane together with smaller amounts of butane, isobutane and ethyne are released per cigarette smoked (0.66 g tobacco) of a common Swedish brand. The alkenes in ETS should be considered as contributing factors to a risk of systemic cancer from passive smoking. With regard to alkene intake, even a relatively mild exposure to ETS (2 cigarettes per h for 5 h per day in a 33 m3 room with one air change per hour is estimated to correspond to the active smoking of about one cigarette per day.     

Inactivation of erythrocytic, lymphocytic and myelocytic leukemic cells by photoexcitation of endogenous porphyrins

The photodynamic sensitization of leukemic cells (erythrocytic, myelocytic and lymphocytic) via light activation of endogenous porphyrins is described. Human myelocytic-erythrocytic K562 cells and murine Friend erythroleukemia (FELC) and T-cell lymphoma Eb-Esb cells were stimulated to synthesize and accumulate porphyrins. K562 cells accumulated high amounts of protoporphyrin by stimulation with 5-aminolevulinic acid (ALA) plus sodium butyrate or hemin. For Friend and Eb-Ebs cells ALA was an adequate stimulator. The high-metastatic Esb lymphoma cells accumulated comparatively more porphyrin than the low-metastatic Eb cell line. Maximal porphyrin accumulation produced mortality rates of more than 99% after 10 min of photoactivation of the three leukemic lines. Thymidine incorporation was inhibited by the photodynamic effect depending on porphyrin concentration. These results confirm the photodynamic ability of endogenous porphyrins to inactivate cancer cells of different origins.     

Calcium carbonate modifications in the mineralized shell of the freshwater snail Biomphalaria glabrata

The mineralized shell (consisting of calcium carbonate) of the tropical freshwater snail Biomphalaria glabrata was investigated with high resolution synchrotron X-ray powder diffractometry and X-ray absorption spectroscopy (EXAFS). Parts from different locations of the snail shell were taken from animals of different age grown under various keeping conditions. Additionally, eggs with ages of 60, 72, 120, and 140 hours were examined. Traces of aragonite were found as first crystalline phase in 120 h old eggs, however, Ca K-edge EXAFS indicated the presence of aragonitic structures already in the X-ray amorphous sample of 72 h age. The main component of the shell of adult animals was aragonite in all cases, but in some cases minor amounts of vaterite (below 1.5%) are formed. The content of vaterite is generally low in the oldest part of the shell (the center) and increases towards the mineralizing zone (the shell margin). In juvenile snails, almost no vaterite was detectable in any part of the shell.     

Spectroscopic probing of the acid-base properties and photosensitization of a fluorinated phthalocyanine in organic solutions and liposomes

A perfluorinated derivative of phthalocyanine was synthesized as the free base, hexadeca-(2,2,2-trifluoroethoxy) phthalocyanine (H2F48Pc), and as a zinc complex, hexadeca-(2,2,2-trifluoroethoxy)-phthalocyaninatozinc (ZnF48Pc), and their spectroscopic and photochemical properties were studied. The absorption bands are shifted bathochromically relative to simple phthalocyanines, exhibiting the longest wavelength band near 735 nm (H2F48Pc) and 705 (ZnF48Pc). The solvatochromism of both compounds was modeled by Reichardt's ET(30) parameter and Kamlet, Abboud and Taft multiparameter approach. The former, simpler, model was found to be adequate. We found that H2F48Pc undergoes unique basic and acidic titrations in organic solvents. These titration processes are accompanied by spectral changes that are explained on the basis of the chromophore's symmetry. Singular value decomposition was employed to resolve the spectra into the contributions of the species at various stages of protonation and to obtain the equilibrium constants. Nuclear magnetic resonance spectra (1H, 19F and 13C) for the free base were obtained in a tetrahydrofurand8 solution. The carbon spectrum, taken as a function of temperature, provided evidence for the presence of a tautomerization process, which switches the two internal hydrogens between the four central nitrogen atoms. As far as we know, this is the first report of the measurement of the free energy of activation for such process (delta G = 10.6-11.4 kcal mol-1 between 217 and 330 K) for a phthalocyanine, in solution. Like most other phthalocyanines these two compounds also act as photosensitizers and as generators of singlet molecular oxygen. The absolute quantum yields (phi delta) for ZnF48Pc was 0.58 +/- 0.01 in benzene and 0.35 +/- 0.01 in lipid vesicles. H2F48Pc had lower yields, 0.16 and 0.005, respectively. Either protonation or deprotonation of the pyrrole nitrogens in H2F48Pc lowered the phi delta.     

A comparison between different semiclassical approximations for optical response functions in nonpolar liquid solutions

The temporal behavior of optical response functions (ORFs) reflects the quantum dynamics of an electronic superposition state, and as such lacks a well-defined classical limit. In this paper, we consider the importance of accounting for the quantum nature of the dynamics when calculating ORFs of different types. To this end, we calculated the ORFs associated with the linear absorption spectrum and the nonlinear two-pulse photon-echo experiment, via the following approaches: (1) the semiclassical forward-backward approach; (2) an approach based on linearizing the path-integral forward-backward action in terms of the difference between the forward and backward paths; (3) an approach based on ground state nuclear dynamics. The calculations were performed on a model that consists of a two-state chromophore solvated in a nonpolar liquid. The different methods were found to yield very similar results for the absorption spectrum and "diagonal" two-pulse photon echo (i.e., the homodyne-detected signal at time t=t(0) after the second pulse, where t(0) is the time interval between the two pulses). The different approximations yielded somewhat different results in the case of the time-integrated photon-echo signal. The reasons for the similarity between the predictions of different approximations are also discussed.     

Vibrational energy relaxation rates via the linearized semiclassical approximation: applications to neat diatomic liquids and atomic-diatomic liquid mixtures

We report the results obtained from the application of our previously proposed linearized semiclassical method for computing vibrational energy relaxation (VER) rates (J. Phys. Chem. A 2003, 107, 9059, 9070) to neat liquid oxygen, neat liquid nitrogen, and liquid mixtures of oxygen and argon. Our calculations are based on a semiclassical approximation for the quantum-mechanical force-force correlation function, which puts it in terms of the Wigner transforms of the force and the product of the Boltzmann operator and the force. The calculation of the multidimensional Wigner integrals is made feasible by the introduction of a local harmonic approximation. A systematic analysis has been performed of the temperature and mole-fraction dependences of the VER rate constant, as well as the relative contributions of centrifugal and potential forces, and of different types of quantum effects. The results were found to be in very good quantitative agreement with experiment, and they suggest that this semiclassical approximation can capture the quantum enhancement, by many orders of magnitude, of the experimentally observed VER rate constants over the corresponding classical predictions.     

SPECTROSCOPIC PROPERTIES OF THE POTENTIOMETRIC PROBE MEROCYANINE-540 IN SOLUTIONS AND IN LIPOSOMES

Absorption, fluorescence and resonance Raman spectra of the membrane dye merocyanine-540 (MC540) were measured. The aggregation of the dye, its binding to lipid membranes and its response to crossmembrane electric potential differences were studied. The dye was found to aggregate even at micromolar concentrations in water, but not in organic solvents. The dimerization constant was evaluated by spectroscopic techniques. The binding constant to liposomes was estimated by a spectroscopic titration method. Resonance Raman spectra of MC540 were measured for the first time. Distinct changes were observed in the vibrational spectrum upon the generation of a valinomycin-induced K⁺ diffusion potential (Nernst potential) on liposomes. The ratio of Raman band intensities, which was found to be related to the membrane potential, can be used to evaluate the absolute value of the electric potential.