Quadratic optimal functional quantization of stochastic processes and numerical applications

In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a Hilbert-valued random variable, using a nearest neighbour projection on a finite codebook. A special emphasis is made on the computational aspects and the numerical applications, in particular the pricing of some path-dependent European options.Comment: 41 page

Cross-sectional measures and modelled estimates of blood alcohol levels in UK nightlife and their relationships with drinking behaviours and observed signs of inebriation

<p>Abstract</p> <p>Background</p> <p>Management of nightlife in UK cities focuses on creating safe places for individuals to drink. Little is known about intoxication levels as measuring total alcohol consumption on nights out is complicated by early evening interviews missing subsequent consumption and later interviews risking individuals being too drunk to recall consumption or participate at all. Here we assess mixed survey and modelling techniques as a methodological approach to examining these issues.</p> <p>Methods</p> <p>Interviews with a cross sectional sample of nightlife patrons (n = 214) recruited at different locations in three cities established alcohol consumption patterns up to the point of interview, self-assessed drunkenness and intended drinking patterns throughout the remaining night out. Researchers observed individuals' behaviours to independently assess drunkenness. Breath alcohol tests and general linear modelling were used to model blood alcohol levels at participants' expected time of leaving nightlife settings.</p> <p>Results</p> <p>At interview 49.53% of individuals regarded themselves as drunk and 79.43% intended to consume more alcohol before returning home, with around one in ten individuals (15.38% males; 4.35% females) intending to consume >40 units (equal to 400 mls of pure alcohol). Self-assessed drunkenness, researcher observed measures of sobriety and blood alcohol levels all correlated well. Modelled estimates for blood alcohol at time of going home suggested that 71.68% of males would be over 0.15%BAC (gms alcohol/100 mls blood). Higher blood alcohol levels were related to drinking later into the night.</p> <p>Conclusions</p> <p>UK nightlife has used substantive health and judicial resources with the aim of creating safer and later drinking environments. Survey and modelling techniques together can help characterise the condition of drinkers when using and leaving these settings. Here such methods identified patrons as routinely getting drunk, with risks of drunkenness increasing over later nights. Without preventing drunkenness and sales to intoxicated individuals, extended drinking hours can simply act as havens for drunks. A public health approach to nightlife is needed to better understand and take into account the chronic effects of drunkenness, the damages arising after drunk individuals leave city centres and the costs of people avoiding drunken city centres at night.</p

Astrocytes: biology and pathology

Astrocytes are specialized glial cells that outnumber neurons by over fivefold. They contiguously tile the entire central nervous system (CNS) and exert many essential complex functions in the healthy CNS. Astrocytes respond to all forms of CNS insults through a process referred to as reactive astrogliosis, which has become a pathological hallmark of CNS structural lesions. Substantial progress has been made recently in determining functions and mechanisms of reactive astrogliosis and in identifying roles of astrocytes in CNS disorders and pathologies. A vast molecular arsenal at the disposal of reactive astrocytes is being defined. Transgenic mouse models are dissecting specific aspects of reactive astrocytosis and glial scar formation in vivo. Astrocyte involvement in specific clinicopathological entities is being defined. It is now clear that reactive astrogliosis is not a simple all-or-none phenomenon but is a finely gradated continuum of changes that occur in context-dependent manners regulated by specific signaling events. These changes range from reversible alterations in gene expression and cell hypertrophy with preservation of cellular domains and tissue structure, to long-lasting scar formation with rearrangement of tissue structure. Increasing evidence points towards the potential of reactive astrogliosis to play either primary or contributing roles in CNS disorders via loss of normal astrocyte functions or gain of abnormal effects. This article reviews (1) astrocyte functions in healthy CNS, (2) mechanisms and functions of reactive astrogliosis and glial scar formation, and (3) ways in which reactive astrocytes may cause or contribute to specific CNS disorders and lesions