Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

Synthesis of lupeol derivatives and their antileishmanial and antitrypanosomal activities

The natural product lupeol 1 was isolated from aerial parts of Vernonia scorpioides with satisfactory yield, which made it viable to be used as starting material in semisynthetic approach. Ten lupeol derivatives 2–11 were prepared by classical procedures. Including, five new esters derivatives 7–11, which were obtained by structural modifications in the isopropylidene fragment. All semisynthetic compounds and lupeol 1–11 were confirmed by ¹H NMR, ¹³C NMR and HRMS. Their antiprotozoal activity was evaluated in vitro against L. amazonensis and T. cruzi. Derivative 6 showed the best antitrypanosomal activity (IC₅₀ = 12.48 μg/mL) and the lowest cytotoxic derivative (CC₅₀ = 161.50 μg/mL). The mechanism of action of the most active derivatives (4, 6 and 11) is not dependent from the enzyme trypanothione reductase.     

Three terminals optoelectronics devices integrated into a silicon on silicon waveguide

In this paper we describe two different kind of optoelectronic devices both based on a three terminals active device and exploit the plasma dispersion effect to achieve the desired working. The first device exploits this effect in order to obtain an optical modulation. The second device is an optoelectronic router based on the mode-mixing principle together with the injection-induced optical phase shift. Both devices are integrated into a Silicon on Silicon optical channel waveguide which can be realized using a standard bipolar process. The possibility of using standard, well-known technology presents several advantages with respect to III–V Optoelectronics. The active three terminal device used is a Bipolar Mode Field Effect Transistor (BMFET). Numerical simulation results are presented on both devices.     

Fluorine containing phosphazene polymers

In this paper we highlighted the synthesis, characterization, and practical exploitation of different types of polyphosphazenes substituted with fluorinated groups. There are several ways in which fluorine atoms can be inserted into polyphosphazenes, all of which leading to different polymers showing a wide range of characteristics. In general it is true that the insertion of fluorine atoms into phosphazene macromolecules leads to an enhancement of the thermal stability, flame resistance, low-temperature elastomericity, and chemical inertness of the phosphazenes obtained. The contribution of Italian research groups to the preparation and exploitation of organic commercial macromolecules grafted onto fluorinated polyphosphazenes is also reviewed.     

A landscape of time asymmetry

This is a conceptual overview on a polemical subject: the problem of time asymmetry. It is proved that time asymmetry can be considered as a global generalized symmetry breaking, produced by a choice of a physically admissible state space, in a global Gel'fand triplet. The well-known physics of irreversible process can be studied using this mathematical structure and all the arrows of time can be explained and coordinated. But the deeper problems of time definition and time arrow in quantum gravity remain outside of this landscape.     

The semigroup generated by certain operators on the congruence lattice of a clifford semigroup

Communicated by N. R. Reilly