Quantitative isoperimetric inequalities for log-convex probability measures on the line

The purpose of this paper is to analyze the isoperimetric inequality for symmetric log-convex probability measures on the line. Using geometric arguments we first re-prove that extremal sets in the isoperimetric inequality are intervals or complement of intervals (a result due to Bobkov and Houdr\'e). Then we give a quantitative form of the isoperimetric inequality, leading to a somehow anomalous behavior. Indeed, it could be that a set is very close to be optimal, in the sense that the isoperimetric inequality is almost an equality, but at the same time is very far (in the sense of the symmetric difference between sets) to any extremal sets! From the results on sets we derive quantitative functional inequalities of weak Cheeger type

On isoperimetric inequalities with respect to infinite measures

We study isoperimetric problems with respect to infinite measures on $R ^n$. In the case of the measure $\mu$ defined by $d\mu = e^{c|x|^2} dx$, $c\geq 0$, we prove that, among all sets with given $\mu-$measure, the ball centered at the origin has the smallest (weighted) $\mu-$perimeter. Our results are then applied to obtain Polya-Szego-type inequalities, Sobolev embeddings theorems and a comparison result for elliptic boundary value problems.Comment: 25 page

Canalization and Creative Evolution: Images of Life in Bergson and Whitehead

Whitehead famously wrote that the status of life in nature constituted the modernproblem both of philosophy and science. But Bergson could just as easily have penned thosewords. Indeed, his Creative Evolution stands as one of the most serious engagements with theproblem of life in recent philosophical history. Life, for Bergson, was to be thought of as a kindof impetus, a drive or force. But he insisted that this was only an image borrowed frompsychology, the best one available, but an image no less. This is because images are essential tothe organization of scientific discourse and practice. We think through them, use them not onlyas explanatory aids, but as callipers first: without them, we are unable to grasp and articulate ourobjects of study, even before the endeavour to communicate what it is that we have managed tograsp. Perhaps most famous of the various images that animate Creative Evolution is that of thecanal, or canalization. It is striking that this image managed to find its way, through Whitehead’sProcess and Reality, into modern embryology, where it continues to serve as an image for theway epigenetic landscapes operate in order to bring about, or canalize, a small number of endresults form a large number of developmental potentialities.This paper briefly traces the history of that image from out of Bergson’s philosophy oflife, through Whitehead’s creative metaphysical appropriation of it, and into the embryology ofC.H. Waddington. In order to make sense of that history, I do three things: first, I situate theimage of the canal in Bergson’s Creative Evolution, elucidating its context and aims; second, Idemonstrate its utility for Whitehead’s metaphysics, the new purposes for which it was deployed;and third, I argue that it was this latter reconfiguration of the concept that prepared it for itsenlistment as a key moment in embryological explanation.I claim that the canal occupies a privileged position in Bergson’s philosophy of life, for itis an image of life that is turned against itself as an image, meant to demonstrate the limits ofimagistic thought. I conclude the paper with a series of comments on this suggestion: that it wasthe image of the canal that found its way into modern embryology tells us something importantabout the relation between science and philosophy, or between image and imagination, matterand life. On these points, Bergson and Whitehead converge on a novel philosophy of nature thatis capable both of responding to scientific discoveries as well as of accommodating them withinan enlarged process-oriented metaphysics

Update on the Laboratory Diagnosis of Invasive Fungal Infections

Recent advances in the management of patients with haematological malignancies and transplant recipients have paralleled an increase in the incidence of fungal diseases due to pathogenic genera such as Candida and Aspergillus and the emergence of less common genera including Fusarium and Zygomycetes. Despite availability of new antifungal agents these opportunistic infections have high mortality. Rapid and reliable species identification is essential for antifungal treatment, but detection of the increasing diversity of fungal pathogens by conventional phenotypic methods remains difficult and time-consuming, and the results may sometimes be inconclusive, especially for unusual species. New diagnostic techniques (e.g., 1,3-beta-d-glucan detection) could improve this scenario, although further studies are necessary to confirm their usefulness in clinical practice