New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.

Characterization of pore size distributions of mesoporous materials from adsorption isotherms

In this article, a new hybrid model for estimating the pore size distribution of micro- and mesoporous materials is developed, and tested with the adsorption data of nitrogen, oxygen, and argon on ordered mesoporous materials reported in the literature. For the micropore region, the model uses the Dubinin-Rudushkevich (DR) isotherm with the Chen-Yang modification. A recent isotherm model of the authors for nonporous materials, which uses a continuum-mechanical model for the multilayer region and the Unilan model for the submonolayer region, has been extended for adsorption in mesopores. The experimental data is inverted using regularization to obtain the pore size distribution. The present model was found to be successful in predicting the pore size distribution of pure as well as binary physical mixtures of MCM-41 synthesized with different templates, with results in agreement with those from the XRD method and nonlocal density functional theory. It was found that various other recent methods, as well as the classical Broekhoff and de Beer method, underpredict the pore diameter of MCM-41. The present model has been successfully applied to MCM-48, SBA's, CMK, KIT, HMS, FSM, MTS, mesoporous fly ash, and a large number of other regular mesoporous materials.

Residence time distributions of gas flowing through rotating drum bioreactors

Residence time distribution studies of gas through a rotating drum bioreactor for solid-state fermentation were performed using carbon monoxide as a tracer gas. The exit concentration as a function of time differed considerably from profiles expected for plug flow, plug flow with axial dispersion, and continuous stirred tank reactor (CSTR) models. The data were then fitted by least-squares analysis to mathematical models describing a central plug flow region surrounded by either one dead region (a three-parameter model) or two dead regions (a five-parameter model). Model parameters were the dispersion coefficient in the central plug flow region, the volumes of the dead regions, and the exchange rates between the different regions. The superficial velocity of the gas through the reactor has a large effect on parameter values. Increased superficial velocity tends to decrease dead region volumes, interregion transfer rates, and axial dispersion. The significant deviation from CSTR, plug flow, and plug flow with axial dispersion of the residence time distribution of gas within small-scale reactors can lead to underestimation of the calculation of mass and heat transfer coefficients and hence has implications for reactor design and scaleup. (C) 2001 John Wiley & Sons, Inc.

Use of bulk density profiles from X-radiography to examine structural crust models

Exponential and sigmoidal functions have been suggested to describe the bulk density profiles of crusts. The present work aims to evaluate these conceptual models using high resolution X-radiography. Repacked seedbeds from two soil materials, air-dried or prewetted by capillary rise, were subjected to simulated rain, which resulted in three types of structural crusts, namely, slaking, infilling, and coalescing. Bulk density distributions with depth were generated using high-resolution (70 mum), calibrated X-ray images of slices from the resin-impregnated crusted seedbeds. The bulk density decreased progressively with depth, which supports the suggestion that a crust should be considered as a nonuniform layer. For the slaking and the coalescing crusts, the exponential function underestimated the strong change in bulk density across the morphologically defined transition between the crust and the underlying material; the sigmoidal function provided a better description. Neither of these crust models effectively described the shape of the bulk density profiles through the whole seedbed. Below the infilling and slaking crusts, bulk density increased linearly with depth as a result of slumping. In the coalescing crusted seedbed, the whole seedbed uniformly collapsed and most of the bulk density change within the crust could be ascribed to slumping (0.33 g cm(-3)) rather than to crusting (0.12 g cm(-3)). Finally, (i) X-radiography appears as a unique tool to generate high resolution bulk density profiles and (ii) in structural crusts, bulk density profiles could be modeled using the existing exponential and sigmoidal crusting models, provided a slumping model would be coupled.

Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach

We prove that, once an algorithm of perfect simulation for a stationary and ergodic random field F taking values in S(Zd), S a bounded subset of R(n), is provided, the speed of convergence in the mean ergodic theorem occurs exponentially fast for F. Applications from (non-equilibrium) statistical mechanics and interacting particle systems are presented.

Expectation Propagation with Factorizing Distributions: A Gaussian Approximation and Performance Results for Simple Models

We discuss the expectation propagation (EP) algorithm for approximate Bayesian inference using a factorizing posterior approximation. For neural network models, we use a central limit theorem argument to make EP tractable when the number of parameters is large. For two types of models, we show that EP can achieve optimal generalization performance when data are drawn from a simple distribution.

Limiting conditional distributions for birth-death processes

In a recent paper [16], one of us identified all of the quasi-stationary distributions for a non-explosive, evanescent birth-death process for which absorption is certain, and established conditions for the existence of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of directions. We shall consider separately two cases depending on whether or not the process is evanescent. In the former case we shall relax the condition that absorption is certain. Furthermore, we shall allow for the possibility that the minimal process might be explosive, so that the transition rates alone will not necessarily determine the birth-death process uniquely. Although we shall be concerned mainly with the minimal process, our most general results hold for any birth-death process whose transition probabilities satisfy both the backward and the forward Kolmogorov differential equations.

Cumulative sedimentation analysis of Escherichia coli debris size

A new method to measure Escherichia coil cell debris size after homogenization is presented. It is based on cumulative sedimentation analysis under centrifugal force, coupled with Sodium Dodecyl Sulfate-Polyacrylamide Gel Electrophoresis (SDS-PAGE) analysis of sedimented proteins. The effects that fermentation and homogenization conditions have on the resulting debris distributions were investigated using this method. Median debris size decreased significantly from approximately 0.5 mu m to 0.3 mu m as the number of homogenization passes increased from 2 to 10. Under identical homogenization conditions, uninduced host cells in stationary phase had a larger debris size than exponential cells after 5 homogenizer passes. This difference was not evident after 2 or in passes, possibly because of confounding intact cells and the existence of a minimum debris size for the conditions investigated. Recombinant cells containing protein inclusion bodies had the smallest debris size following homogenization. The method was also used to measure the size distribution of inclusion bodies. This result compared extremely well with an independent determination using centrifugal disc photosedimentation (CDS), thus validating the method. This is the first method that provides accurate size distributions of E. coli debris without the need for sample pretreatment, theoretical approximations (e.g. extinction coefficients), or the separation of debris and inclusion bodies prior to analysis. (C) 1997 John Wiley & Sons, Inc.

Microscopic origin of non-Gaussian distributions of financial returns

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters. (c) 2007 Elsevier B.V. All rights reserved.

Spontaneous Interblink Time Distributions in Patients with Graves` Orbitopathy and Normal Subjects

PURPOSE. To determine the shape of spontaneous interblink time interval distributions obtained in a long observation period in normal subjects and patients with Graves` orbitopathy. METHODS. The magnetic search coil technique was used to register the spontaneous blinking activity during 1 hour of video observation of two groups of 10 subjects each (normal controls aged 27-61 years, mean +/- SD = 46.0 +/- 13.6; patients with Graves` orbitopathy aged 33-61 years, mean +/- SD +/- 46.7 +/- 8.9). The spontaneous blink rate of each subject was calculated for the entire period of observation and for 56 five-minute bins. Histograms of the interblink time interval were plotted for each measurement of blink rate. RESULTS. Neither the overall mean blink rate (controls, 19.8 +/- 4.9; Graves`, 17.6 +/- 5.4) nor the interblink time (controls, 5.2 +/- 3.1, Graves`, 7.9 +/- 3.5) differed between the two groups. There was a large variation of both measurements when the 5-minute bins were considered. The interblink time distribution of all subjects was highly positively skewed when the 1-hour period was measured. A significant number of the 5-minute bin distributions deviated from the overall pattern and became symmetric. CONCLUSIONS. The normal blinking process is characterized by highly positively skewed interblink time distributions. This result means that most blinks have a short time interval, and occasionally a small number of blinks have long time intervals. The different patterns of distribution described in the early literature probably represent artifacts because of the small samples analyzed. (Invest Ophthalmol Vis Sci. 2011;52:3419-3424) DOI:10.1167/iovs.10-7060

Drosophila melanogaster lipins are tissue-regulated and developmentally regulated and present specific subcellular distributions

Lipins constitute a novel family of Mg2+-dependent phosphatidate phosphatases that catalyze the dephosphorylation of phosphatidic acid to yield diacylglycerol, an important intermediate in lipid metabolism and cell signaling. Whereas a single lipin is detected in less complex organisms, in mammals there are distinct lipin isoforms and paralogs that are differentially expressed among tissues. Compatible with organism tissue complexity, we show that the single Drosophila Lpin1 ortholog (CG8709, here named DmLpin) expresses at least three isoforms (DmLpinA, DmLpinK and DmLpinJ) in a temporal and spatially regulated manner. The highest levels of lipin in the fat body, where DmLpinA and DmLpinK are expressed, correlate with the highest levels of triacylglycerol (TAG) measured in this tissue. DmLpinK is the most abundant isoform in the central nervous system, where TAG levels are significantly lower than in the fat body. In the testis, where TAG levels are even lower, DmLpinJ is the predominant isoform. Together, these data suggest that DmLpinA might be the isoform that is mainly involved in TAG production, and that DmLpinK and DmLpinJ could perform other cellular functions. In addition, we demonstrate by immunofluorescence that lipins are most strongly labeled in the perinuclear region of the fat body and ventral ganglion cells. In visceral muscles of the larval midgut and adult testis, lipins present a sarcomeric distribution. In the ovary chamber, the lipin signal is concentrated in the internal rim of the ring canal. These specific subcellular localizations of the Drosophila lipins provide the basis for future investigations on putative novel cellular functions of this protein family.