Estimating the Distribution of Random Parameters in a Diffusion Equation Forward Model for a Transdermal Alcohol Biosensor

We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the blood alcohol concentration and the output being the transdermal alcohol concentration. Our approach is based on the idea of reformulating the underlying dynamical system in such a way that the random parameters are now treated as additional space variables. When the distribution to be estimated is assumed to be defined in terms of a joint density, estimating the distribution is equivalent to estimating the diffusivity in a multi-dimensional diffusion equation and thus well-established finite dimensional approximation schemes, functional analytic based convergence arguments, optimization techniques, and computational methods may all be employed. We use our technique to estimate a bivariate normal distribution based on data for multiple drinking episodes from a single subject.Comment: 10 page

Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed

Sleep deprivation causes memory deficits by negatively impacting neuronal connectivity in hippocampal area CA1

Brief periods of sleep loss have long-lasting consequences such as impaired memory consolidation. Structural changes in synaptic connectivity have been proposed as a substrate of memory storage. Here, we examine the impact of brief periods of sleep deprivation on dendritic structure. In mice, we find that five hours of sleep deprivation decreases dendritic spine numbers selectively in hippocampal area CA1 and increased activity of the filamentous actin severing protein cofilin. Recovery sleep normalizes these structural alterations. Suppression of cofilin function prevents spine loss, deficits in hippocampal synaptic plasticity, and impairments in long-term memory caused by sleep deprivation. The elevated cofilin activity is caused by cAMP-degrading phosphodiesterase-4A5 (PDE4A5), which hampers cAMP-PKA-LIMK signaling. Attenuating PDE4A5 function prevents changes in cAMP-PKA-LIMK-cofilin signaling and cognitive deficits associated with sleep deprivation. Our work demonstrates the necessity of an intact cAMP-PDE4-PKA-LIMK-cofilin activation-signaling pathway for sleep deprivation-induced memory disruption and reduction in hippocampal spine density

Computation of nonparametric, mixed effects, maximum likelihood, biosensor data based-estimators for the distributions of random parameters in an abstract parabolic model for the transdermal transport of alcohol

The existence and consistency of a maximum likelihood estimator for the joint probability distribution of random parameters in discrete-time abstract parabolic systems was established by taking a nonparametric approach in the context of a mixed effects statistical model using a Prohorov metric framework on a set of feasible measures. A theoretical convergence result for a finite dimensional approximation scheme for computing the maximum likelihood estimator was also established and the efficacy of the approach was demonstrated by applying the scheme to the transdermal transport of alcohol modeled by a random parabolic partial differential equation (PDE). Numerical studies included show that the maximum likelihood estimator is statistically consistent, demonstrated by the convergence of the estimated distribution to the "true" distribution in an example involving simulated data. The algorithm developed was then applied to two datasets collected using two different transdermal alcohol biosensors. Using the leave-one-out cross-validation (LOOCV) method, we found an estimate for the distribution of the random parameters based on a training set. The input from a test drinking episode was then used to quantify the uncertainty propagated from the random parameters to the output of the model in the form of a 95 error band surrounding the estimated output signal

Sharp transition towards shared vocabularies in multi-agent systems

What processes can explain how very large populations are able to converge on the use of a particular word or grammatical construction without global coordination? Answering this question helps to understand why new language constructs usually propagate along an S-shaped curve with a rather sudden transition towards global agreement. It also helps to analyze and design new technologies that support or orchestrate self-organizing communication systems, such as recent social tagging systems for the web. The article introduces and studies a microscopic model of communicating autonomous agents performing language games without any central control. We show that the system undergoes a disorder/order transition, going trough a sharp symmetry breaking process to reach a shared set of conventions. Before the transition, the system builds up non-trivial scale-invariant correlations, for instance in the distribution of competing synonyms, which display a Zipf-like law. These correlations make the system ready for the transition towards shared conventions, which, observed on the time-scale of collective behaviors, becomes sharper and sharper with system size. This surprising result not only explains why human language can scale up to very large populations but also suggests ways to optimize artificial semiotic dynamics.Comment: 12 pages, 4 figure

Changes in lipid profile in response to three different protocols of whole-body cryostimulation treatments

Systemic cryostimulation is useful treatment, both in sport and medicine, during which human body is exposed to very low, cryogenic temperature (below -100 \ub0C). Although there exists some evidence of its beneficial effect in biological regeneration, so far it has not been unequivocally determined if the positive effect of repeated stimulations depends on their number in a series. The aim of this research was to estimate the influence of 5, 10 and 20 sessions of 3. min-long exposures to cryogenic temperature (-130 \ub0C) on the lipid profile in physically active men. Sixty-nine healthy volunteers participated in the study. The blood samples were taken in the morning, after overnight fasting, before the first cryostimulation session, and the following morning after the last one (5th,10th, 20th). In serum specimens the concentration of total cholesterol (TCh), HDL cholesterol and triglicerydes were determined using enzymatic methods. LDL cholesterol level was calculated using Friedewald formula. The changes in lipid profile (LDL decrease with simultaneously HDL increase) occurred after at least 10 sessions of cryostimulation

Bipolaron Binding in Quantum Wires

A theory of bipolaron states in quantum wires with a parabolic potential well is developed applying the Feynman variational principle. The basic parameters of the bipolaron ground state (the binding energy, the number of phonons in the bipolaron cloud, the effective mass, and the bipolaron radius) are studied as a function of sizes of the potential well. Two cases are considered in detail: a cylindrical quantum wire and a planar quantum wire. Analytical expressions for the bipolaron parameters are obtained at large and small sizes of the quantum well. It is shown that at $R\gg 1$ [where $R$ means the radius (halfwidth) of a cylindrical (planar) quantum wire, expressed in Feynman units], the influence of confinement on the bipolaron binding energy is described by the function $\sim 1/R^{2}$ for both cases, while at small sizes this influence is different in each case. In quantum wires, the bipolaron binding energy $W(R)$ increases logarithmically with decreasing radius. The shapes and the sizes of a nanostructure, which are favorable for observation of stable bipolaron states, are determined.Comment: 17 pages, 6 figures, E-mail addresses: [email protected]; [email protected]