A new Jacobian matrix for optimal learning of single-layer neural networks

This paper investigates the learning of a wide class of single-hidden-layer feedforward neural networks (SLFNs) with two sets of adjustable parameters, i.e., the nonlinear parameters in the hidden nodes and the linear output weights. The main objective is to both speed up the convergence of second-order learning algorithms such as Levenberg-Marquardt (LM), as well as to improve the network performance. This is achieved here by reducing the dimension of the solution space and by introducing a new Jacobian matrix. Unlike conventional supervised learning methods which optimize these two sets of parameters simultaneously, the linear output weights are first converted into dependent parameters, thereby removing the need for their explicit computation. Consequently, the neural network (NN) learning is performed over a solution space of reduced dimension. A new Jacobian matrix is then proposed for use with the popular second-order learning methods in order to achieve a more accurate approximation of the cost function. The efficacy of the proposed method is shown through an analysis of the computational complexity and by presenting simulation results from four different examples.

2-D R-matrix propagation: A large scale electron scattering simulation dominated by the multiplication of dynamically changing matrices

We examine the computational aspects of propagating a global R-matrix, R, across sub-regions in a 2-D plane. This problem originates in the large scale simulation of electron collisions with atoms and ions at intermediate energies. The propagation is dominated by matrix multiplications which are complicated because of the dynamic nature of R, which changes the designations of its rows and columns and grows in size as the propagation proceeds. The use of PBLAS to solve this problem on distributed memory HPC machines is the main focus of the paper.

Ionic liquid-reconstituted cellulose composites as solid support matrices for biocatalyst immobilization

Preparation of cellulose-polyamine composite films and beads, which provide high loading of primary amines on the surface allowing direct one-step bioconjugation of active species, is reported using an ionic liquid (IL) dissolution and regeneration process. Films and bead architectures were prepared and used as immobilization supports for laccase as a model system demonstrating the applicability of this approach. Performance of these materials, compared to commercially available products, has been assessed using millimeter-sized beads of the composites and the lipase-catalyzed transesterification of ethyl butyrate.

Comparison of porcine urine and bile as matrices to screen for the residues of two sulfonamides using a semi-automated enzyme immunoassay.

Porcine urine enzyme immunoassays for sulfamethazine and sulfadiazine have previously been employed as screening tests to predict the concentrations of the drugs in the corresponding tissues (kidneys), If a urine was found positive (> 800 ng ml(-1)) the corresponding kidney was then analysed by an enzyme immunoassay and, if found positive, a confirmatory analysis by HPLC was performed. Urine was chosen as the screening matrix since sulfonamides are mainly eliminated through this body fluid, However, after obtaining a number of false positive predictions, an investigation was carried out to assess the possibility of using an alternative body fluid which would act as a superior indicator of the presence of sulfonamides in porcine kidney, An initial study indicated that serum, plasma and bile could all be used as screening matrices. From these, bile was chosen as the preferred sample matrix and an extensive study followed to compare the efficiencies of sulfonamide positive bile and urine at predicting sulphonamide positive kidneys, Bile was found to be 17 times more efficient than urine at predicting a sulfamethazine positive kidney and 11 times more efficient at predicting a sulfadiazine positive kidney, With this enhanced performance of the initial screening test, the need for the costly and time consuming kidney enzyme immunoassay, prior to HPLC analysis, was eliminated

Pharmacokinetics of UC781-loaded intravaginal ring segments in rabbits: a comparison of polymer matrices

UC781 is a potent and poorly water-soluble nonnucleoside reverse transcriptase inhibitor being investi- gated as a potential microbicide for preventing sexual transmission of HIV-1. This study was designed to evaluate the in vivo release and pharmacokinetics of UC781 delivered from matrix-type intravaginal ring segments in rabbits. Three polymer matrices (polyurethane, ethylene vinyl acetate copolymer, and silicone elastomer) and two drug loadings (5 and 15 mg/segment) were evaluated in at least one of two independent studies for up to 28 days in vivo. Inter-study comparison of in vivo release, vaginal tissue, and plasma concentrations for similar formulations demonstrated good reproducibility of the animal model. Mean estimates for a 28-day in vivo release ranged from 0.35 to 3.17 mg UC781 per segment. Mean proximal vaginal tissue levels (adjacent to the IVR segment) were 8– 410 ng/g and did not change significantly with time for most formulations. Distal vaginal tissue levels of UC781 were 6- to 49-fold lower than proximal tissue levels. Mean UC781 plasma levels were low for all formulations, at 0.09–0.58 ng/mL. All formulations resulted in similar UC781 concentrations in vaginal tissue and plasma, except the low loading polyurethane group which provided significantly lower levels. Loading dependent release and pharmacokinetics were only clearly observed for the polyurethane matrix. Based on these results, intravaginal ring segments loaded with UC781 led to vaginal tissue concen- trations ranging from below to approximately two orders of magnitude higher than UC781’s EC50 under in vitro conditions (2.8 ng/mL), with little influence by polymer matrix or UC781 loading. Moreover, these findings support the use of rabbit vaginal pharmacokinetic studies in preclinical testing of microbicide intravaginal rings.

Distribution of the Demmel Condition Number of Wishart Matrices

This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.

Determination of thyreostat residues from bovine matrices using high-performance liquid chromatography

High-performance liquid chromatography (HPLC) methodologies were evaluated for the detection and quantification of thyreostatic drug residues in cattle serum and thyroid tissue. The paper details a protocol, using a simple ethyl acetate extraction for the determination of thiouracil, tapazole, methyl thiouracil, propyl thiouracil and phenyl thiouracil in thyroid tissue. Using two sequential HPLC injections, and quantitative analysis, in two steps, all five thyreostats were detectable at concentrations greater than 2.45-4.52 ng/g. Modifications to a published method for detection of thyreostatic residues in serum involving the addition of mercaptoethanol and a freezing step are described. The modifications improved sensitivity and allowed detection of the five thyreostats at levels greater than 16.98-35.25 ng/ml. Young bulls were treated with thyreostats to demonstrate the validity of the methodologies described. Administered thyreostats were not absorbed equally by the test animals and the compounds were not all detected in the serum samples removed at 7 days following drug withdrawal. These experiments indicate the necessity to be able to detect thyreostat residues in a variety of matrices. (C) 1998 Elsevier Science B.V. All rights reserved.

On the Condition Number Distribution of Complex Wishart Matrices

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading. © 2010 IEEE.

Efficient Marginal Likelihood Computation for Gaussian Process Regression

In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional hyperparameters which need to be tuned in order to achieve optimum predictive performance; this operation can be efficiently performed in an Empirical Bayes fashion by maximizing the posterior marginal likelihood of the observed data. Since the score function of this optimization problem is in general characterized by the presence of local optima, it is necessary to resort to global optimization strategies, which require a large number of function evaluations. Given that the evaluation is usually computationally intensive and badly scaled with respect to the dataset size, the maximum number of observations that can be treated simultaneously is quite limited. In this paper, we consider the case of hyperparameter tuning in Gaussian process regression. A straightforward implementation of the posterior log-likelihood for this model requires O(N^3) operations for every iteration of the optimization procedure, where N is the number of examples in the input dataset. We derive a novel set of identities that allow, after an initial overhead of O(N^3), the evaluation of the score function, as well as the Jacobian and Hessian matrices, in O(N) operations. We prove how the proposed identities, that follow from the eigendecomposition of the kernel matrix, yield a reduction of several orders of magnitude in the computation time for the hyperparameter optimization problem. Notably, the proposed solution provides computational advantages even with respect to state of the art approximations that rely on sparse kernel matrices.

In Vitro Release from Reverse Poloxamine/alpha-Cyclodextrin Matrices: Modelling and Comparison of Dissolution Profiles

Gels obtained by complexation of octablock star polyethylene oxide/polypropylene oxide copolymers (Tetronic 90R4) with -cyclodextrin (-CD) were evaluated as matrices for drug release. Both molecules are biocompatible so they can be potentially applied to drug delivery systems. Two different types of matrices of Tetronic 90R4 and -CD were evaluated: gels and tablets. These gels are capable to gelifying in situ and show sustained erosion kinetics in aqueous media. Tablets were prepared by freeze-drying and comprising the gels. Using these two different matrices, the release of two model molecules, L-tryptophan (Trp), and a protein, bovine serum albumin (BSA), was evaluated. The release profiles of these molecules from gels and tablets prove that they are suitable for sustained delivery. Mathematical models were applied to the release curves from tablets to elucidate the drug delivery mechanism. Good correlations were found for the fittings of the release curves to different equations. The results point that the release of Trp from different tablets is always governed by Fickian diffusion, whereas the release of BSA is governed by a combination of diffusion and tablet erosion.