Model Systems for Evidencing the Mediator Role of Riboflavin in the UVA Cross-Linking Treatment of Keratoconus

Riboflavin under UVA radiation generates reactive oxygen species (ROS) that can induce various changes in biological systems. Under controlled conditions, these processes can be used in some treatments for ocular or dermal diseases. For instance, corneal cross-linking (CXL) treatment of keratoconus involves UVA irradiation combined with riboflavin aiming to induce the formation of new collagen fibrils in cornea. To reduce the damaging effect of ROS formed in the presence of riboflavin and UVA, the CXL treatment is performed with the addition of polysaccharides (dextran). Hyaluronic acid is a polysaccharide that can be found in the aqueous layer of the tear film. In many cases, keratoconus patients also present dry eye syndrome that can be reduced by the application of topical solutions containing hyaluronic acid. This study presents physico-chemical evidence on the effect of riboflavin on collagen fibril formation revealed by the following methods: differential scanning microcalorimetry, rheology, and STEM images. The collagen used was extracted from calf skin that contains type I collagen similar to that found in the eye. Spin trapping experiments on collagen/hyaluronic acid/riboflavin solutions evidenced the formation of ROS species by electron paramagnetic resonance measurements.     

Singular cosphere bundle reduction

This paper studies singular contact reduction for cosphere bundles at the zero value of the momentum map. A stratification of the singular quotient, finer than the contact one and better adapted to the bundle structure of the problem, is obtained. The strata of this new stratification are a collection of cosphere bundles and coisotropic or Legendrian submanifolds of their corresponding contact components.

     

Multirate multicast service provisioning II: a tâtonnement process for rate allocation

In multirate multicast different users in the same multicast group can receive services at different rates depending on their own requirements and the congestion level of the network. In this two-part paper we present a general framework for addressing the optimal rate control problem in multirate multicast where the objective is the maximization of a social welfare function expressed by the sum of the users’ utility functions. In Part II we present a market based mechanism and an adjustment process that have the following features. They satisfy the informational constraints imposed by the nature of multirate multicast; and when they are combined with the results of Part I they result in an optimal solution of the corresponding centralized multirate multicast problem.     

Homogeneous-inhomogeneous transitions in a Landau level with spin splitting

The homogeneous-inhomogeneous transitions of a two-dimensional electron gas in a strong perpendicular magnetic field are studied in the particular case when half of the states in a spin splitted Landau level are occupied. To this end the dielectric susceptibility in the homogeneous states as well as the free energy in the modulated states are calculated. Unless theg factor dos not exceed a certain value the charge-density waves are stable in an interval of finite temperatures.     

Weak convergence to the fractional Brownian sheet in Besov spaces

In this paper we study the problem of the approximation in law of the fractional Brownian sheet in the topology of the anisotropic Besov spaces. We prove the convergence in law of two families of processes to the fractional Brownian sheet: the first family is constructed from a Poisson procces in the plane and the second family is defined by the partial sums of two sequences of real independent fractional brownian motions.     

A strong approximation for double subfractional integrals

A Riemann–Stieltjes integral strong approximation to double Stratonovich integrals with respect to odd and even fractional Brownian motions is considered. We prove the convergence in quadratic mean, uniformly on compact time intervals, of the ordinary double integral process obtained by linear interpolation of the odd and even fractional Brownian motions, to the double Stratonovich integral. The deterministic integrands are continuous or are given by bimeasures.     

On a Theorem of Deutsch and Singer

We introduce the notion of a starshaped set-valued function, and relate it to convex set-valued functions. We prove a theorem which, in the convex case, implies that single-valuedness is exceptional if the function is not everywhere single-valued. A second result shows a remarkable costantness of images for starshaped set-valued functions. Both theorems were inspired from a result of Deutsch and Singer, which they strengthen.     

ϵ-Optimal and Optimal Controls for the Stochastic Linear-Quadratic Problem

We study the stochastic regulator problem in Hilbert spaces for systems governed by linear stochastic differential equations with retarded controls and with state and control dependent noise. We use integral Riccati equations and no reference to a Riccati differential equation or to the Ito formula is made.