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

A local glucose-and oxygen concentration-based insulin secretion model for pancreatic islets

<p>Abstract</p> <p>Background</p> <p>Because insulin is the main regulator of glucose homeostasis, quantitative models describing the dynamics of glucose-induced insulin secretion are of obvious interest. Here, a computational model is introduced that focuses not on organism-level concentrations, but on the quantitative modeling of local, cellular-level glucose-insulin dynamics by incorporating the detailed spatial distribution of the concentrations of interest within isolated avascular pancreatic islets.</p> <p>Methods</p> <p>All nutrient consumption and hormone release rates were assumed to follow Hill-type sigmoid dependences on local concentrations. Insulin secretion rates depend on both the glucose concentration and its time-gradient, resulting in second-and first-phase responses, respectively. Since hypoxia may also be an important limiting factor in avascular islets, oxygen and cell viability considerations were also built in by incorporating and extending our previous islet cell oxygen consumption model. A finite element method (FEM) framework is used to combine reactive rates with mass transport by convection and diffusion as well as fluid-mechanics.</p> <p>Results</p> <p>The model was calibrated using experimental results from dynamic glucose-stimulated insulin release (GSIR) perifusion studies with isolated islets. Further optimization is still needed, but calculated insulin responses to stepwise increments in the incoming glucose concentration are in good agreement with existing experimental insulin release data characterizing glucose and oxygen dependence. The model makes possible the detailed description of the intraislet spatial distributions of insulin, glucose, and oxygen levels. In agreement with recent observations, modeling also suggests that smaller islets perform better when transplanted and/or encapsulated.</p> <p>Conclusions</p> <p>An insulin secretion model was implemented by coupling local consumption and release rates to calculations of the spatial distributions of all species of interest. The resulting glucose-insulin control system fits in the general framework of a sigmoid proportional-integral-derivative controller, a generalized PID controller, more suitable for biological systems, which are always nonlinear due to the maximum response being limited. Because of the general framework of the implementation, simulations can be carried out for arbitrary geometries including cultured, perifused, transplanted, and encapsulated islets.</p

A Conserved Behavioral State Barrier Impedes Transitions between Anesthetic-Induced Unconsciousness and Wakefulness: Evidence for Neural Inertia

One major unanswered question in neuroscience is how the brain transitions between conscious and unconscious states. General anesthetics offer a controllable means to study these transitions. Induction of anesthesia is commonly attributed to drug-induced global modulation of neuronal function, while emergence from anesthesia has been thought to occur passively, paralleling elimination of the anesthetic from its sites in the central nervous system (CNS). If this were true, then CNS anesthetic concentrations on induction and emergence would be indistinguishable. By generating anesthetic dose-response data in both insects and mammals, we demonstrate that the forward and reverse paths through which anesthetic-induced unconsciousness arises and dissipates are not identical. Instead they exhibit hysteresis that is not fully explained by pharmacokinetics as previously thought. Single gene mutations that affect sleep-wake states are shown to collapse or widen anesthetic hysteresis without obvious confounding effects on volatile anesthetic uptake, distribution, or metabolism. We propose a fundamental and biologically conserved concept of neural inertia, a tendency of the CNS to resist behavioral state transitions between conscious and unconscious states. We demonstrate that such a barrier separates wakeful and anesthetized states for multiple anesthetics in both flies and mice, and argue that it contributes to the hysteresis observed when the brain transitions between conscious and unconscious states

Metatranscriptomics and Pyrosequencing Facilitate Discovery of Potential Viral Natural Enemies of the Invasive Caribbean Crazy Ant, Nylanderia pubens

BACKGROUND: Nylanderia pubens (Forel) is an invasive ant species that in recent years has developed into a serious nuisance problem in the Caribbean and United States. A rapidly expanding range, explosive localized population growth, and control difficulties have elevated this ant to pest status. Professional entomologists and the pest control industry in the United States are urgently trying to understand its biology and develop effective control methods. Currently, no known biological-based control agents are available for use in controlling N. pubens. METHODOLOGY AND PRINCIPAL FINDINGS: Metagenomics and pyrosequencing techniques were employed to examine the transcriptome of field-collected N. pubens colonies in an effort to identify virus infections with potential to serve as control agents against this pest ant. Pyrosequencing (454-platform) of a non-normalized N. pubens expression library generated 1,306,177 raw sequence reads comprising 450 Mbp. Assembly resulted in generation of 59,017 non-redundant sequences, including 27,348 contigs and 31,669 singlets. BLAST analysis of these non-redundant sequences identified 51 of potential viral origin. Additional analyses winnowed this list of potential viruses to three that appear to replicate in N. pubens. CONCLUSIONS: Pyrosequencing the transcriptome of field-collected samples of N. pubens has identified at least three sequences that are likely of viral origin and, in which, N. pubens serves as host. In addition, the N. pubens transcriptome provides a genetic resource for the scientific community which is especially important at this early stage of developing a knowledgebase for this new pest