Asymptotics of Two-boundary First-exit-time Densities for Gauss-Markov Processes

Methodology and Computing in Applied Probability - The problem of escape times from a region confined by two time-dependent boundaries is considered for a class of Gauss-Markov processes....     

The Norton–Simon hypothesis and the onset of non-genetic resistance to chemotherapy induced by stochastic fluctuations

By studying a simple but realistic biophysical model of tumor growth in the presence of a constant continuous chemotherapy, we show that if an extended Norton–Simon hypothesis holds, the system may have multiple equilibria. Thus, the stochastic bounded fluctuations that affect both the tumor carrying capacity and/or the drug pharmacodynamics (and/or the drug pharmacokinetics) may cause the transition from a small equilibrium to a far larger one, not compatible with the life of the host. In particular, we mainly investigated the effects of fluctuations that involve parameters nonlinearly affecting the deterministic model. We propose to frame the above phenomena as a new and non-genetic kind of resistance to chemotherapy.     

Synthesis of pyrano[3,4-c]pyrazole and pyrazolo[3,4-d][1,2]diazepine derivatives

By the action of thionyl chloride on 3(5)-R-4-phenacylpyrazole-5(3)-carboxylic acid ( 3c,d ), 3-R-5-phenylpyrano[3,4-c]pyrazole-7-(1H)ones ( 4c,d ) were obtained. When 4c,d were treated with hydrazine hydrate followed by refluxing in ethanol containing acetic acid, 4,7-dihydro-3-R-5-phenylpyrazolo[3,4-d][1,2]-diazepin-8-(1H)ones ( 6c,d ) were formed. Compounds 6c,d , in turn, were refluxed in ethanol saturated with hydrochloric acid to yield 6-amino-1,6-dihydro-3-R-5-phenyl-7H-pyrazolo[3,4-c]pyridin-7-ones ( 7c,d ). Compounds 7c,d could be obtained directly from 5c,d. The starting materials 3c,d were prepared by hydrolysis of the oxime of 3(5)-R-4-phenacyl-5(3)carboalcoxypyrazoles ( 1a,b ). Structural assignments rested on correct elemental analysis, molecular weights determined by mass spectrometry, and spectroscopic evidence.     

Energy loss of deuterons in 3He gas: a threshold effect

The energy loss of deuterons in ³He gas was measured at E _d = 15 to 100 keV using the ³He pressure dependence of the ³He(d,p)⁴He cross-section at a given incident energy. At the highest energies, the observed energy loss is in good agreement with a standard compilation. However, with decreasing energy the experimental values drop steadily below the theoretical values and near E _d = 18 keV they drop sharply (within 1 keV) reaching the domain of nuclear stopping power. This threshold behavior is due to the minimum 1s → 2s electron excitation of the He target atoms, i.e. it is a quantum effect. Some consequences are discussed.     

Gravity driven instabilities in miscible non-Newtonian fluid displacements in porous media

Gravity driven instabilities in model porous packings of 1 mm diameter spheres are studied by comparing the broadening of the displacement front between fluids of slightly different densities in stable and unstable configurations. Water, water–glycerol and water–polymer solutions are used to vary independently viscosity and molecular diffusion and study the influence of shear-thinning properties. Both injected and displaced solutions are identical but for a different concentration of NaNO₃ salt used as an ionic tracer and to introduce the density contrast. Dispersivity in stable configuration increases with polymer concentration – as already reported for double porosity packings of porous grains. Gravity-induced instabilities are shown to develop below a same threshold Péclet number Pe for water and water–glycerol solutions of different viscosities and result in considerable increases of the dispersivity. Measured threshold Pe values decrease markedly on the contrary with polymer concentration. The quantitative analysis demonstrates that the development of the instabilities is controlled by viscosity through a characteristic gravity number G (ratio between hydrostatic and viscous pressure gradients). A single threshold value of G accounts for results obtained on Newtonian and non-Newtonian solutions.     

Dynamic behaviour of a discrete-time SIR model with information dependent vaccine uptake

This paper proposes and analyzes a discrete-time deterministic SIR model with information dependent immunization behaviour, where vaccination coverage at birth during any period of time is a general phenomenological function of the risk of infection that is perceived at the beginning of the period. Results on existence of equilibria, their local stability, and system persistence are proved. Then, by considering the noteworthy subcase of a piecewise linear ‘prevalence-dependent’ coverage function, the local stability of the endemic state is proved and conditions for its global asymptotic stability are given. Some insight on both Neimarck-Sacher and period-doubling bifurcations are provided. Overall we show that prevalence-dependent coverage is an essentially stabilising force. However period-doubling bifurcations are possible though under stressed parameter constellations.     

Determination of preferential interaction parameters by multicomponent diffusion. applications to poly(ethylene glycol)-salt-water ternary mixtures

Poly(ethylene glycol) (PEG) is a hydrophilic nonionic polymer used in many biochemical and pharmaceutical applications. We report the four diffusion coefficients for the PEG-KCl-water ternary system at 25 degrees C using precision Rayleigh interferometry. Here, the molecular weight of PEG is 20 kg mol(-1), which is comparable to that of proteins. The four diffusion coefficients are examined and used to determine thermodynamic preferential interaction coefficients. We find that the PEG preferential hydration in the presence of KCl is 1 order of magnitude larger than that previously obtained under the same conditions for lysozyme, a protein of similar molecular weight. In correspondence, the coupled diffusion in the PEG case was greater than that observed in the lysozyme case. We attribute this difference to the greater exposure of polymer coils to the surrounding fluid compared to that of globular compact proteins. Moreover, we observe that the PEG preferential hydration significantly decreases as salt concentration increases and attribute this behavior to the polymer collapse. Finally, we have also employed the equilibrium isopiestic method to validate the accuracy of the preferential interaction coefficients extracted from the diffusion coefficients. This experimental comparison represents an important contribution to the relation between diffusion and equilibrium thermodynamics.