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.

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.

Compound Charcot-Marie-Tooth disease may determine unusual and milder phenotypes

Compound forms of Charcot-Marie-Tooth (CMT) disease have been recently associated with unusually severe neuropathies, an observation that prompted the proposition that the additive effects of two mutations should be searched in patients whose clinical severity falls outside the common CMT phenotypes. In this report, we present a father and a daughter with a very mild and unusual disease that segregates with two mutations in PMP22 gene, the 17p11.2-p12 duplication and a Ser72Leu point mutation. We propose that the deleterious effects of each mutation are partially compensated by the functional effect of the other.

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

Compound 48/80 induces endothelium-dependent and histamine release-independent relaxation in rabbit aorta

Compound 48/80 (C48/80) is a synthetic condensation product of N-methyl-p-methoxyphenethyl am me with formaldehyde and is an experimental drug used since the 1950s to induce anaphylactic shock through histamine release. This study was carried out to further elucidate the mechanism by which this drug induces nitric oxide (NO) release. Our specific goals were: (a) to verify if C48/80`s relaxation occurs through the stimulation of histamine receptors; (b) to evaluate the endothelium-dependent relaxation induced by C48/80; (c) to identify NO as the endothelium-relaxing factor released by C48/80; (d) to identify the NO synthase (NOS) responsible for NO release; and (e) to verify if the relaxation induced by C48/80 is calcium and cyclic guanidine monophosphate (cGMP) dependent. Rabbit aorta segments, with and without endothelium, were suspended in organ chambers (25 ml) filled with Krebs solution maintained at 37 degrees C, bubbled with 95% O-2/5% CO2 (pH 7.4). Phenylephrine was used to contract the segments. Other protocol drugs included H-1- and H-2-receptor antagonists, cyclooxygenase, NOS, guanylyl cyclase and phospholipase C (PLC) inhibitors. Endothelium-dependent relaxation induced by C48/80 was also studied in calcium-free Krebs solution associated with a calcium chelator. In summary, our investigation demonstrated that the C48/80 vasodilating action: (a) does not depend on H-1 and H-2 histamine receptors; (b) is NO endothelium-dependent; (c) is dependent on the endothelial constitutive NOS (NOS-3) isoform activation; (d) is cGMP-dependent; and that NOS-3 activation by C48/80: (a) is independent of PLC up to 25 mu g/ml and (b) is partially dependent of this lipase in higher doses. (C) 2007 Elsevier Inc. All rights reserved.

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.

Pharmacokinetics of ingested fluoride: Lack of effect of chemical compound

Fluoride in drinking water may be present from natural sources or added as sodium fluoride (NaF), sodium silicofluoride (Na2SiF6) or fluorosilicic acid (H2SiF6). Results from an early study with rats suggested that, when ingested as Na2SiF6, the absorption and excretion of fluoride were greater than when ingested as NaF. Objective: The present single-blind, crossover study with 10 adults was done to determine three key pharmacokinetic parameters: the maximum plasma fluoride concentrations (C-max), the elapsed time to reach the maximum concentrations (T-max) and the 6-h areas under the time-plasma concentration curves (AUCs) after ingestion of 500 ml, of water containing 0.67 or 5.45 mg F/L present naturally or added as NaF or H2SiF6. Design: Blood was collected prior to and at nine time points during 6 h after ingestion of the test solutions. Plasma was analysed by electrode after HMDS-facilitated diffusion and the data were analysed for statistically significant differences using repeated measures ANOVA. Results: The C-max, T-max and AUC values after ingestion of the solutions containing natural fluoride, NaF or H2SiF6 did not differ significantly at either dose level. Further, the Tmax values associated with the 0.67 and SAS mg/L solutions did not differ significantly indicating that the absorption, distribution and elimination rates were not affected by the dose size. Conclusions: Considered together with published reports, the present findings support the conclusion that the major features of fluoride metabolism are not affected differently by the chemical compounds commonly used to fluoridate water nor are they affected by whether the fluoride is present naturally or added artificially. (C) 2008 Elsevier Ltd. All rights reserved.

Models involving two inverse Weibull distributions

In this paper, we look at three models (mixture, competing risk and multiplicative) involving two inverse Weibull distributions. We study the shapes of the density and failure-rate functions and discuss graphical methods to determine if a given data set can be modelled by one of these models. (C) 2001 Elsevier Science Ltd. All rights reserved.

Fitting mixtures of Kent distributions to aid in joint set identification

When examining a rock mass, joint sets and their orientations can play a significant role with regard to how the rock mass will behave. To identify joint sets present in the rock mass, the orientation of individual fracture planer can be measured on exposed rock faces and the resulting data can be examined for heterogeneity. In this article, the expectation-maximization algorithm is used to lit mixtures of Kent component distributions to the fracture data to aid in the identification of joint sets. An additional uniform component is also included in the model to accommodate the noise present in the data.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.