Stochastic switching in infinite dimensions with applications to random parabolic PDEs

We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.Comment: 30 pages. Published version containing some minor corrections and improvement

MARKET SEGMENTATION: IDENTIFYING THE HIGH-GROWTH EXPORT MARKETS FOR U.S. AGRICULTURE

A cluster analysis based on a five-year growth rate of agricultural imports from the United States was conducted on 86 countries and revealed two significant market segments for U.S. agriculture: the high-growth markets and the low-growth markets. Multiple discriminant analysis was then used to test the significance of the countries' trade-related and macroeconomic variables to their market growth classification. The discriminant function was used to predict the high-growth markets for U.S. agriculture in 1994. High-growth markets for U.S. agriculture exhibit faster GDP and agricultural import growth rates, are relatively agriculturally self-sufficient, and are near the United States. On the other hand, low-growth markets exhibit slower GDP and agricultural import growth rates, and are geographically distant from the United States.International Relations/Trade,

A Stochastic Compartmental Model for Fast Axonal Transport

In this paper we develop a probabilistic micro-scale compartmental model and use it to study macro-scale properties of axonal transport, the process by which intracellular cargo is moved in the axons of neurons. By directly modeling the smallest scale interactions, we can use recent microscopic experimental observations to infer all the parameters of the model. Then, using techniques from probability theory, we compute asymptotic limits of the stochastic behavior of individual motor-cargo complexes, while also characterizing both equilibrium and non-equilibrium ensemble behavior. We use these results in order to investigate three important biological questions: (1) How homogeneous are axons at stochastic equilibrium? (2) How quickly can axons return to stochastic equilibrium after large local perturbations? (3) How is our understanding of delivery time to a depleted target region changed by taking the whole cell point-of-view

FIN 48: The Impact On Staffing, Internal Control Processes And Expertise Of Privately-Held Companies

While FASB Interpretation 48 (FIN 48), Accounting for Uncertainty in Income Taxes-An Interpretation of Statement of Financial Accounting Standards (SFAS) 109, Accounting for Income Taxes applies to both privately-held and publicly traded companies, privately-held companies have characteristics that can impact implementation.  This paper reports the findings of a survey of the top 100 privately-held companies to determine how these organizations are addressing the staffing of tax department personnel, process controls and knowledge acquisition during the implementation of FIN 48

Reconciling diverse lacustrine and terrestrial system response to penultimate deglacial warming in southern Europe

Unlike the most recent deglaciation, the regional expression of climate changes during the penultimate deglaciation remains understudied, even though it led into a period of excess warmth with estimates of global average temperature 1–2 °C, and sea level ∼6 m, above pre-industrial values. We present the first complete high-resolution southern European diatom record capturing the penultimate glacial-interglacial transition, from Lake Ioannina (northwest Greece). It forms part of a suite of proxies selected to assess the character and phase relationships of terrestrial and aquatic ecosystem response to rapid climate warming, and to resolve apparent conflicts in proxy evidence for regional paleohydrology. The diatom data suggest a complex penultimate deglaciation driven primarily by multiple oscillations in lake level, and provide firm evidence for the regional influence of abrupt changes in North Atlantic conditions. There is diachroneity in lake and terrestrial ecosystem response to warming at the onset of the last interglacial, with an abrupt increase in lake level occurring ∼2.7 k.y. prior to sustained forest expansion with peak precipitation. We identify the potentially important role of direct input of snow melt and glacial meltwater transfer to the subterranean karst system in response to warming, which would cause rising regional groundwater levels. This explanation, and the greater sensitivity of diatoms to subtle changes in temperature, reconciles the divergent lacustrine and terrestrial proxy evidence and highlights the sensitivity of lakes situated in mountainous karstic environments to past climate warming

On the master equation approach to kinetic theory: linear and nonlinear Fokker--Planck equations

We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one non-linear) and the Kolmogorov (a.k.a. master) equations of certain N-body diffusion processes, in the context of Kac's "propagation of chaos" limit. The linear Fokker-Planck equations are well-known, but here they are derived as a limit N->infty of a simple linear diffusion equation on (3N-C)-dimensional N-velocity spheres of radius sqrt(N) (with C=1 or 4 depending on whether the system conserves energy only or energy and momentum). In this case, a spectral gap separating the zero eigenvalue from the positive spectrum of the Laplacian remains as N->infty,so that the exponential approach to equilibrium of the master evolution is passed on to the limiting Fokker-Planck evolution in R^3. The non-linear Fokker-Planck equation is known as Landau's equation in the plasma physics literature. Its N-particle master equation, originally introduced (in the 1950s) by Balescu and Prigogine (BP), is studied here on the (3N-4)-dimensional N-velocity sphere. It is shown that the BP master equation represents a superposition of diffusion processes on certain two-dimensional sub-manifolds of R^{3N} determined by the conservation laws for two-particle collisions. The initial value problem for the BP master equation is proved to be well-posed and its solutions are shown to decay exponentially fast to equilibrium. However, the first non-zero eigenvalue of the BP operator is shown to vanish in the limit N->infty. This indicates that the exponentially fast approach to equilibrium may not be passed from the finite-N master equation on to Landau's nonlinear kinetic equation.Comment: 20 pages; based on talk at the 18th ICTT Conference. Some typos and a few minor technical fixes. Modified title slightl

The use of acute oxygen supplementation upon muscle tissue saturation during repeat sprint cycling

This study examined performance and physiological responses (power output, tissue saturation index) to repeat sprint cycling with oxygen supplementation (O2Supp [fraction of inspired oxygen 1.00]). Fourteen amateur male cyclists took part. Two visits to the laboratory entailed; 15min relative intensity warm-up, 10min of passive recovery, followed by 10x15s repeated sprints, during which air inspired had FiO2 1.00 oxygen or normal air. Outcome measures include, mean power (W) and change in Tissue Saturation Index (ΔTSI%). Repeated measures ANOVA were used to examine difference between conditions in mean power output. Paired samples t-tests were used to examine differences between conditions in ΔTSI (%) and rate of muscle reoxygenation and deoxygenation (%·s-1). Mean power output was 4% higher in the oxygen condition compared to normoxia (p < .01). There was a significant positive correlation between power output and reoxygenation rate during O2Supp (r = 0.65, p = .04). No correlation was seen between power output and reoxygenation rate during normoxia (r = -0.30, p = .40). A significantly increased deoxy rate was seen in the O2Supp condition compared to normoxia (p = .05). Oxygen supplementation appears to elicit the greatest performance improvements in mean power, potentially facilitated by an increasing muscle reoxygenation rate. This evidences the utility of oxygen as an ergogenic aid to in cycling performance

Wave operator bounds for 1-dimensional Schr\"odinger operators with singular potentials and applications

Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.Comment: 16 pages, 0 figure