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.

Drinfeld twists and symmetric Bethe vectors of supersymmetric fermion models

We construct the Drinfeld twists ( factorizing F-matrices) of the gl(m-n)-invariant fermion model. Completely symmetric representation of the pseudo-particle creation operators of the model are obtained in the basis provided by the F-matrix ( the F-basis). We resolve the hierarchy of the nested Bethe vectors in the F-basis for the gl(m-n) supersymmetric model.

Refining the perfusion-diffusion mismatch hypothesis

Background and Purpose-The Echoplanar Imaging Thrombolysis Evaluation Trial ( EPITHET) tests the hypothesis that perfusion-weighted imaging (PWI)-diffusion-weighted imaging (DWI) mismatch predicts the response to thrombolysis. There is no accepted standardized definition of PWI-DWI mismatch. We compared common mismatch definitions in the initial 40 EPITHET patients. Methods-Raw perfusion images were used to generate maps of time to peak (TTP), mean transit time (MTT), time to peak of the impulse response (Tmax) and first moment transit time (FMT). DWI, apparent diffusion coefficient ( ADC), and PWI volumes were measured with planimetric and thresholding techniques. Correlations between mismatch volume (PWIvol-DWIvol) and DWI expansion (T2(Day) (90-vol)-DWIAcute-vol) were also assessed. Results-Mean age was 68 +/- 11, time to MRI 4.5 +/- 0.7 hours, and median National Institutes of Health Stroke Scale (NIHSS) score 11 (range 4 to 23). Tmax and MTT hypoperfusion volumes were significantly lower than those calculated with TTP and FMT maps (P < 0.001). Mismatch >= 20% was observed in 89% (Tmax) to 92% (TTP/FMT/MTT) of patients. Application of a +4s ( relative to the contralateral hemisphere) PWI threshold reduced the frequency of positive mismatch volumes (TTP 73%/FMT 68%/Tmax 54%/MTT 43%). Mismatch was not significantly different when assessed with ADC maps. Mismatch volume, calculated with all parameters and thresholds, was not significantly correlated with DWI expansion. In contrast, reperfusion was correlated inversely with infarct growth (R= -0.51; P = 0.009). Conclusions-Deconvolution and application of PWI thresholds provide more conservative estimates of tissue at risk and decrease the frequency of mismatch accordingly. The precise definition may not be critical; however, because reperfusion alters tissue fate irrespective of mismatch.

The states, diffusion, and concentration distribution of water in radiation-formed PVA/PVP hydrogels

Hydrogels with various compositions of polyvinyl alcohol (PVA) and poly(1-vinyl-2-pyrrolidinone) (PVP) were prepared by irradiating mixtures of PVA and PVP in aqueous solutions with gamma-rays from Co-60 sources at room temperature. The states of water in the hydrogels were characterized using DSC and NMR T-2 relaxation measurements and the kinetics of water diffusion in the hydrogels were studied by sorption experiments and NMR imaging. The DSC endothermic peaks in the temperature range -10 to +10 degrees C implied that there are at least two kinds of freezable water present in the matrix. The difference between the total water content and the freezable water content was refer-red to as bound water, which is not freezable. The weight fraction of water at which only nonfreezable water is present in a hydrogel with F-VP = 0.19 has been estimated to be g(H2O)/g(Polymer) = 0.375. From water sorption experiments, it was demonstrated that the early stage of the diffusion of water into the hydrogels was Fickian. A curve-fit of the early-stage experimental data to the Fickian model allowed determination of the water diffusion coefficient, which was found to lie between 1.5 x 10(-11) m(2) s(-1) and 4.5 x 10(-11) m(2) s(-1), depending on the polymer composition, the cross-link density, and the temperature. It was also found that the energy barrier for diffusion of water molecules into PVA/PVP hydrogels was approximate to 24 kJ mol(-1). Additionally, the diffusion coefficients determined from NMR imaging of the volumetric swelling of the gels agreed well with the results obtained by the mass sorption method.

Double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones when they are heated uniformly from below. The fault zone is assumed to be more permeable than its surrounding rocks. In particular, we have derived exact analytical solutions to the total critical Rayleigh numbers of the double diffusion-driven convective flow. Using the corresponding total critical Rayleigh numbers, the double diffusion-driven convective instability of a fluid-saturated three-dimensional geological fault zone system has been investigated. The related theoretical analysis demonstrates that: (1) The relative higher concentration of the chemical species at the top of the three-dimensional geological fault zone system can destabilize the convective flow of the system, while the relative lower concentration of the chemical species at the top of the three-dimensional geological fault zone system can stabilize the convective flow of the system. (2) The double diffusion-driven convective flow modes of the three-dimensional geological fault zone system are very close each other and therefore, the system may have the similar chance to pick up different double diffusion-driven convective flow modes, especially in the case of the fault thickness to height ratio approaching 0. (3) The significant influence of the chemical species diffusion on the convective instability of the three-dimensional geological fault zone system implies that the seawater intrusion into the surface of the Earth is a potential mechanism to trigger the convective flow in the shallow three-dimensional geological fault zone system.

Acute Toxic Leukoencephalopathy: Potential for Reversibility Clinically and on MRI With Diffusion-Weighted and FLAIR Imaging

OBJECTIVE. Toxic leukoencephalopathy may present acutely or subacutely with symmetrically reduced diffusion in the periventricular and supraventricular white matter, hereafter referred to as periventricular white matter. This entity may reverse both on imaging and clinically. However, a gathering together of the heterogeneous causes of this disorder as seen on MRI with diffusion-weighted imaging (DWI) and an analysis of their likelihood to reverse has not yet been performed. Our goals were to gather causes of acute or subacute toxic leukoencephalopathy that can present with reduced diffusion of periventricular white matter in order to promote recognition of this entity, to evaluate whether DWI with apparent diffusion coefficient (ADC) values can predict the extent of chronic FLAIR abnormality ( imaging reversibility), and to evaluate whether DWI can predict the clinical outcome ( clinical reversibility). MATERIALS AND METHODS. Two neuroradiologists retrospectively reviewed the MRI examinations of 39 patients with acute symptoms and reduced diffusion of periventricular white matter. The reviewers then scored the extent of abnormality on DWI and FLAIR. ADC ratios of affected white matter versus the unaffected periventricular white matter were obtained. Each patient`s clinical records were reviewed to determine the cause and clinical outcome. Histology findings were available in three patients. Correlations were calculated between the initial MRI markers and both the clinical course and the follow-up extent on FLAIR using Spearman`s correlation coefficient. RESULTS. Of the initial 39 patients, seven were excluded because of a nontoxic cause (hypoxic-ischemic encephalopathy [HIE] or congenital genetic disorders) or because of technical errors. In the remaining 32 patients, no correlation was noted between any of the initial MRI markers (percentage of ADC reduction, DWI extent, or FLAIR extent) with the clinical outcome. Three patients had histologic correlation. However, moderate correlation was seen between the extent of abnormality on initial FLAIR and the extent on follow-up FLAIR (r = 0.441, p = 0.047). Of the 13 patients who underwent repeat MRI at 21 days or longer, the reduced diffusion resolved in all but one. Significant differences were noted between ADC values in affected white matter versus unaffected periventricular white matter on initial (p < 0.0001) but not on follow-up MRI (p = 0.13), and in affected white matter on initial versus follow-up (p = 0.0014) in those individuals who underwent repeat imaging on the same magnet (n = 9), confirming resolution of the DWI abnormalities. CONCLUSION. Acute toxic leukoencephalopathy with reduced diffusion may be clinically reversible and radiologically reversible on DWI, and may also be reversible, but to a lesser degree, on FLAIR MRI. None of the imaging markers measured in this study appears to correlate with clinical outcome, which underscores the necessity for prompt recognition of this entity. Alerting the clinician to this potentially reversible syndrome can facilitate treatment and removal of the offending agent in the early stages.

Numerical simulation of double-diffusion driven convective flow and rock alteration in three-dimensional fluid-saturated geological fault zones

Numerical methods are used to simulate the double-diffusion driven convective pore-fluid flow and rock alteration in three-dimensional fluid-saturated geological fault zones. The double diffusion is caused by a combination of both the positive upward temperature gradient and the positive downward salinity concentration gradient within a three-dimensional fluid-saturated geological fault zone, which is assumed to be more permeable than its surrounding rocks. In order to ensure the physical meaningfulness of the obtained numerical solutions, the numerical method used in this study is validated by a benchmark problem, for which the analytical solution to the critical Rayleigh number of the system is available. The theoretical value of the critical Rayleigh number of a three-dimensional fluid-saturated geological fault zone system can be used to judge whether or not the double-diffusion driven convective pore-fluid flow can take place within the system. After the possibility of triggering the double-diffusion driven convective pore-fluid flow is theoretically validated for the numerical model of a three-dimensional fluid-saturated geological fault zone system, the corresponding numerical solutions for the convective flow and temperature are directly coupled with a geochemical system. Through the numerical simulation of the coupled system between the convective fluid flow, heat transfer, mass transport and chemical reactions, we have investigated the effect of the double-diffusion driven convective pore-fluid flow on the rock alteration, which is the direct consequence of mineral redistribution due to its dissolution, transportation and precipitation, within the three-dimensional fluid-saturated geological fault zone system. (c) 2005 Elsevier B.V. All rights reserved.

Effects of immunosuppressants on hepatocyte cell mitosis during liver regeneration in growing animal models of partial hepatectomy

Objective. We sought to evaluate the effects of immunosuppressant drugs (corticosteroid, cyclosporine [CsA], and tacrolimus [Tac]) on liver regeneration in growing animals submitted to 70% hepatectomy. Materials and Methods. Newborn and weaning rats were submitted to 70% hepatectomy receiving separately methylprednisolone, CsA, or Tac. All animals were sacrificed 24 hours after the procedure. The remnant liver lobes were subjected to histomorphometric analyses with determination of hepatocyte mitotic index. Results., Administration of immunosuppressants did not change the mitotic index of the regenerating liver in newborn animals. In weaning rats, methylprednisolone reduced the mitotic index (P = .01) and Tac caused a greater increase in this rate (P = .001). CsA had no effect on mitotic index. The number of hepatocyte mitoses in newborn animal livers was greater than that in weaning animal livers (P = .001). Conclusion. In situations in which intense, fast processes of liver regeneration are crucial, the advantages of the use of Tac must be considered, such as in pediatric transplant patients.

Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Analysis of dynamic models for structural insight and model reduction .2. A multi-stage compressor shutdown case-study

In this second paper, the three structural measures which have been developed are used in the modelling of a three stage centrifugal synthesis gas compressor. The goal of this case study is to determine the essential mathematical structure which must be incorporated into the compressor model to accurately model the shutdown of this system. A simple, accurate and functional model of the system is created via three structural measures. It was found that the model can be correctly reduced into its basic modes and that the order of the differential system can be reduced from 51(st) to 20(th). Of the 31 differential equational 21 reduce to algebraic relations, 8 become constants and 2 can be deleted thereby increasing the algebraic set from 70 to 91 equations. An interpretation is also obtained as to which physical phenomena are dominating the dynamics of the compressor add whether the compressor will enter surge during the shutdown. Comparisons of the reduced model performance against the full model are given, showing the accuracy and applicability of the approach. Copyright (C) 1996 Elsevier Science Ltd

Discrete and continuous models for dry masonry columns

The dynamic response of dry masonry columns can be approximated with finite-difference equations. Continuum models follow by replacing the difference quotients of the discrete model by corresponding differential expressions. The mathematically simplest of these models is a one-dimensional Cosserat theory. Within the presented homogenization context, the Cosserat theory is obtained by making ad hoc assumptions regarding the relative importance of certain terms in the differential expansions. The quality of approximation of the various theories is tested by comparison of the dispersion relations for bending waves with the dispersion relation of the discrete theory. All theories coincide with differences of less than 1% for wave-length-block-height (L/h) ratios bigger than 2 pi. The theory based on systematic differential approximation remains accurate up to L/h = 3 and then diverges rapidly. The Cosserat model becomes increasingly inaccurate for L/h < 2 pi. However, in contrast to the systematic approximation, the wave speed remains finite. In conclusion, considering its relative simplicity, the Cosserat model appears to be the natural starting point for the development of continuum models for blocky structures.

Applying linear time-varying constraints to econometric models: With an application to demand systems

When linear equality constraints are invariant through time they can be incorporated into estimation by restricted least squares. If, however, the constraints are time-varying, this standard methodology cannot be applied. In this paper we show how to incorporate linear time-varying constraints into the estimation of econometric models. The method involves the augmentation of the observation equation of a state-space model prior to estimation by the Kalman filter. Numerical optimisation routines are used for the estimation. A simple example drawn from demand analysis is used to illustrate the method and its application.