Pseudo-Strong Regularity Around a Set

A generalization of strong regularity around a vertex subset C of a graph Γ, which makes sense even if Γis non-regular, is studied. Such a structure appears, together with a kind of distance-regularity around C , when an spectral bound concerning the so-called predistance polynomial of C is attained. As a main consequence of these results, it is shown that a regular (connected) graph Γwith d + 1 distinct eigenvalues is distance-regular, and its distance- d graph Γ d is strongly regular with parameters a = c , if and only if the number of vertices at distance d from each vertex satisfies an expression which depends only on the order of Γand the different eigenvalues of Γ.     

The G/M/1 queue revisited

The G/M/1 queue is one of the classical models of queueing theory. The goal of this paper is two-fold: (a) To introduce new derivations of some well-known results, and (b) to present some new results for the G/M/1 queue and its variants. In particular, we pay attention to the G/M/1 queue with a set-up time at the start of each busy period, and the G/M/1 queue with exceptional first service. Dedicated to Arie Hordijk on his 65th birthday, in friendship and admiration.     

Polyphenols and Visual Health: Potential Effects on Degenerative Retinal Diseases

Dietary polyphenols are a group of natural compounds that have been proposed to have beneficial effects on human health. They were first known for their antioxidant properties, but several studies over the years have shown that these compounds can exert protective effects against chronic diseases. Nonetheless, the mechanisms underlying these potential benefits are still uncertain and contradictory effects have been reported. In this review, we analyze the potential effects of polyphenol compounds on some visual diseases, with a special focus on retinal degenerative diseases. Current effective therapies for the treatment of such retinal diseases are lacking and new strategies need to be developed. For this reason, there is currently a renewed interest in finding novel ligands (or known ligands with previously unexpected features) that could bind to retinal photoreceptors and modulate their molecular properties. Some polyphenols, especially flavonoids (e.g., quercetin and tannic acid), could attenuate light-induced receptor damage and promote visual health benefits. Recent evidence suggests that certain flavonoids could help stabilize the correctly folded conformation of the visual photoreceptor protein rhodopsin and offset the deleterious effect of retinitis pigmentosa mutations. In this regard, certain polyphenols, like the flavonoids mentioned before, have been shown to improve the stability, expression, regeneration and folding of rhodopsin mutants in experimental in vitro studies. Moreover, these compounds appear to improve the integration of the receptor into the cell membrane while acting against oxidative stress at the same time. We anticipate that polyphenol compounds can be used to target visual photoreceptor proteins, such as rhodopsin, in a way that has only been recently proposed and that these can be used in novel approaches for the treatment of retinal degenerative diseases like retinitis pigmentosa; however, studies in this field are limited and further research is needed in order to properly characterize the effects of these compounds on retinal degenerative diseases through the proposed mechanisms.     

Strong Soret Effect in One Dimension

We consider a one-dimensional gas of two kinds of particles with different masses interacting through short range interactions. The system exhibits an extreme form of the Soret effect: when the ends of the system are in contact with thermal baths of different temperatures, there is complete separation of the species. We show how this separation can be well described in the Boltzmann approximation and discuss the origin of this odd behavior.