TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

Bayesian updating rules in continuous opinion dynamics models

Here, I investigate the use of Bayesian updating rules applied to modeling how social agents change their minds in the case of continuous opinion models. Given another agent statement about the continuous value of a variable, we will see that interesting dynamics emerge when an agent assigns a likelihood to that value that is a mixture of a Gaussian and a uniform distribution. This represents the idea that the other agent might have no idea about what is being talked about. The effect of updating only the first moments of the distribution will be studied, and we will see that this generates results similar to those of the bounded confidence models. On also updating the second moment, several different opinions always survive in the long run, as agents become more stubborn with time. However, depending on the probability of error and initial uncertainty, those opinions might be clustered around a central value.

An alternative to the Pythagorean rule? Reevaluating Problem 1 of cuneiform tablet BM 34 568

The first problem of the Seleucid mathematical cuneiform tablet BM 34 568 calculates the diagonal of a rectangle from its sides without resorting to the Pythagorean rule. For this reason, it has been a source of discussion among specialists ever since its first publication. but so far no consensus in relation to its mathematical meaning has been attained. This paper presents two new interpretations of the scribe`s procedure. based on the assumption that he was able to reduce the problem to a standard Mesopotamian question about reciprocal numbers. These new interpretations are then linked to interpretations of the Old Babylonian tablet Plimpton 322 and to the presence of Pythagorean triples in the contexts of Old Babylonian and Hellenistic mathematics. (C) 2007 Elsevier Inc. All rights reserved.

Profiles of xylose reductase, xylitol dehydrogenase and xylitol production under different oxygen transfer volumetric coefficient values

BACKGROUND: Xylitol is a sugar alcohol (polyalcohol) with many interesting properties for pharmaceutical and food products. It is currently produced by a chemical process, which has some disadvantages such as high energy requirement. Therefore microbiological production of xylitol has been studied as an alternative, but its viability is dependent on optimisation of the fermentation variables. Among these, aeration is fundamental, because xylitol is produced only under adequate oxygen availability. In most experiments with xylitol-producing yeasts, low oxygen transfer volumetric coefficient (K(L)a) values are used to maintain microaerobic conditions. However, in the present study the use of relatively high K(L)a values resulted in high xylitol production. The effect of aeration was also evaluated via the profiles of xylose reductase (XR) and xylitol clehydrogenase (XD) activities during the experiments. RESULTS: The highest XR specific activity (1.45 +/- 0.21 U mg(protein)(-1)) was achieved during the experiment with the lowest K(L)a value (12 h(-1)), while the highest XD specific activity (0.19 +/- 0.03 U mg(protein)(-1)) was observed with a K(L)a value of 25 h(-1). Xylitol production was enhanced when K(L)a was increased from 12 to 50 h(-1), which resulted in the best condition observed, corresponding to a xylitol volumetric productivity of 1.50 +/- 0.08 g(xylitol) L(-1) h(-1) and an efficiency of 71 +/- 6.0%. CONCLUSION: The results showed that the enzyme activities during xylitol bioproduction depend greatly on the initial KLa value (oxygen availability). This finding supplies important information for further studies in molecular biology and genetic engineering aimed at improving xylitol bioproduction. (C) 2008 Society of Chemical Industry

EFFECT OF CULTIVATION CONDITIONS ON GLUCOSE-6-PHOSPHATE DEHYDROGENASE PRODUCTION BY GENETICALLY MODIFIED Saccharomyces cerevisiae

The objective of this research was to improve Glucose-6-phosphate dehydrogenase (G6PD) production by Saccharomyces cerevisiae W303-181, which carry the plasmid YEpPGK-G6PD, by varying the following cultivation conditions: pH value (4.8, 5.7 and 6.6); inoculum concentration (0.1, 0.6 and 1.1 g/L) and initial glucose concentration (20.0, 30.0 and 40.0 g/L). The effect of those variables on G6PD production capability was studied by the application of response surface statistical analysis. The results showed that the highest G6PD production (1594.2 U/L), specific activity (1189.7 U/g(cell)) and productivity (45.6 U/L.h) occurred at pH 4.8, inoculum concentration of 0.1 g/L and initial glucose concentration of 20.0 g/L, under agitation of 150 rpm at 30 degrees C after 36 h. In this work, the strain expressed about 21 fold more activity than the wild S. cerevisiae strain, being an attractive and promising new source of this enzyme.

Effects of medium supplementation and pH control on lactic acid production from brewer`s spent grain

A cellulose pulp obtained by chemical pre-treatment of brewer`s spent grain was saccharified by a commercial cellulase preparation and the produced hydrolysate (50 g/l glucose) was fermented to lactic acid by Lactobacillus delbrueckii. The effects of pH control and nutrient supplementation of the hydrolysate on fermentation performance were investigated. Addition of 5g/l yeast extract enhanced the lactic acid volumetric productivity that attained 0.53 g/l h, value 18% higher than that obtained from non-supplemented hydrolysate. Addition of the MRS broth medium components (except the carbon source) was still better, providing a productivity of 0.79 g/l h. In all the cases, the lactic acid yield factor was of 0.7 g/g glucose consumed, but the fermentations stopped after 24 h due to the pH drop from 6.0 to 4.2, resulting in large amounts of residual glucose (38-41 g/l). Fermentation runs pH-controlled at 6.0 gave better results than those where the initial pH was not further controlled. The best result, 35.54 g/l lactic acid (0.99 g/g glucose consumed) was obtained during the pH-controlled fermentation of hydrolysate medium supplemented with MRS components. The volumetric productivity at the end of this fermentation was 0.59 g/l h, with a maximum of 0.82 g/l h during the first 12 h. (c) 2008 Elsevier B.V. All rights reserved.

Establishment of the optimum initial xylose concentration and nutritional supplementation of brewer`s spent grain hydrolysate for xylitol production by Candida guilliermondii

The effects of initial xylose concentration and nutritional supplementation of brewer`s spent grain hydrolysate on xylitol production by Candida guilliermondii were evaluated using experimental design methodology. The hydrolysate containing 55, 75 or 95 g/l xylose, supplemented or not with nutrients (calcium chloride, ammonium sulfate and rice bran extract), was used as fermentation medium. The increase in xylitol yield and productivity was related to the increase of initial xylose concentration, but up to a certain limit. above of which the yeast performance was not improved. The hydrolysate supplementation with nutrients did not interfere with xylose-to-xylitol conversion. By using the statistic tool the best conditions for maximum xylitol production were found. which consisted in using the non-supplemented hydrolysate containing 70 g/l initial xylose concentration. Under these conditions, a xylitol yield of 0.78 g/g and productivity of 0.58 g/(l h) were achieved. (C) 2008 Elsevier Ltd. All rights reserved.

Enzymatic Hydrolysis of Chemithermomechanically Pretreated Sugarcane Bagasse and Samples with Reduced Initial Lignin Content

Chemithermomechanical (CTM) processing was used to pretreat sugarcane bagasse with the aim of increasing cell wall accessibility to hydrolytic enzymes. Yields of the pretreated samples were in the range of 75-94%. Disk refining and alkaline-CTM and alkaline/sulfite-CTM pretreatments yielded pretreated materials with 21.7, 17.8, and 15.3% of lignin, respectively. Hemicellulose content was also decreased to some extent. Fibers of the pretreated materials presented some external fibrillation, fiber curling, increased swelling, and high water retention capacity. Cellulose conversion of the alkaline-CTM- and alkaline/sulfite-CTM-pretreated samples reached 50 and 85%, respectively, after 96 h of enzymatic hydrolysis. Two samples with low initial lignin content were also evaluated after the mildest alkaline-CTM pretreatment. One sample was a partially delignified mill-processed bagasse. The other was a sugarcane hybrid selected in a breeding program. Samples with lower initial lignin content were hydrolyzed considerably faster in the first 24 h of enzymatic digestion. For example, enzymatic hydrolysis of the sample with the lowest initial lignin content (14.2%) reached 64% cellulose conversion after only 24 h of hydrolysis when compared with the 30% observed for the mill-processed bagasse containing an initial lignin content of 24.4%. (C) 2011 American Institute of Chemical Engineers Biotechnol. Prog., 27: 395-401, 2011

The Influence of Initial Xylose Concentration, Agitation, and Aeration on Ethanol Production by Pichia stipitis from Rice Straw Hemicellulosic Hydrolysate

Rice straw hemicellulosic hydrolysate was used as fermentation medium for ethanol production by Pichia stipitis NRRL Y-7124. Shaking bath experiments were initially performed aiming to establish the best initial xylose concentration to be used in this bioconversion process. In the sequence, assays were carried out under different agitation (100 to 200 rpm) and aeration ((V) under bar (flask)/V(medium) ratio varying from 2.5 to 5.0) conditions, and the influence of these variables on the fermentative parameters values (ethanol yield factor, Y(P/S); cell yield factor, Y(X/S); and ethanol volumetric productivity, Q(P)) was investigated through a 2(2) full-factorial design. Initial xylose concentration of about 50 g/l was the most suitable for the development of this process, since the yeast was able to convert substrate in product with high efficiency. The factorial design assays showed a strong influence of both process variables in all the evaluated responses. The agitation and aeration increase caused a deviation in the yeast metabolism from ethanol to biomass production. The best results (Y(P/S) = 0.37 g/g and Q(P) = 0.39 g/l. h) were found when the lowest aeration (2.5 V(flask)/V(medium) ratio) and highest agitation (200 rpm) levels were employed. Under this condition, a process efficiency of 72.5% was achieved. These results demonstrated that the establishment of adequate conditions of aeration is of great relevance to improve the ethanol production from xylose by Pichia stipitis, using rice straw hemicellulosic hydrolysate as fermentation medium.

An algorithm for computerized automatic tuning of power system stabilizers

The main objective of this paper is to relieve the power system engineers from the burden of the complex and time-consuming process of power system stabilizer (PSS) tuning. To achieve this goal, the paper proposes an automatic process for computerized tuning of PSSs, which is based on an iterative process that uses a linear matrix inequality (LMI) solver to find the PSS parameters. It is shown in the paper that PSS tuning can be written as a search problem over a non-convex feasible set. The proposed algorithm solves this feasibility problem using an iterative LMI approach and a suitable initial condition, corresponding to a PSS designed for nominal operating conditions only (which is a quite simple task, since the required phase compensation is uniquely defined). Some knowledge about the PSS tuning is also incorporated in the algorithm through the specification of bounds defining the allowable PSS parameters. The application of the proposed algorithm to a benchmark test system and the nonlinear simulation of the resulting closed-loop models demonstrate the efficiency of this algorithm. (C) 2009 Elsevier Ltd. All rights reserved.

A boundary element formulation for analysis of elastoplastic plates with geometrical nonlinearity

In this paper a new boundary element method formulation for elastoplastic analysis of plates with geometrical nonlinearities is presented. The von Mises criterion with linear isotropic hardening is considered to evaluate the plastic zone. Large deflections are assumed but within the context of small strain. To derive the boundary integral equations the von Karman`s hypothesis is taken into account. An initial stress field is applied to correct the true stresses according to the adopted criterion. Isoparametric linear elements are used to approximate the boundary unknown values while triangular internal cells with linear shape function are adopted to evaluate the domain value influences. The nonlinear system of equations is solved by using an implicit scheme together with the consistent tangent operator derived along the paper. Numerical examples are presented to demonstrate the accuracy and the validity of the proposed formulation.

An extended BEM formulation for plates reinforced by rectangular beams

This article presents a BEM formulation developed particularly for analysis of plates reinforced by rectangular beams. This is an extended version of a Previous paper that only took into account bending effects. The problem is now re-formulated to consider bending and membrane force effects. The effects of the reinforcements are taken into account by using a simplified scheme that requires application of ail initial stress field to locally correct the bending and stretching stiffness of the reinforcement regions. The domain integrals due to the presence of the reinforcements are then transformed to the reinforcement/plate interface. To reduce the number of degrees of freedom related to the presence of the reinforcement, the proposed model was simplified to consider only bending and stretching rigidities in the direction of the beams. The complete model can be recovered by applying all six internal force correctors, corresponding to six degrees of freedom per node. Examples are presented to confirm the accuracy of the formulation and to illustrate the level of simplification introduced by this strong reduction in the number of degrees of freedom. (C) 2008 Elsevier Ltd. All rights reserved.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

The random barrier-crossing problem

This paper addresses the time-variant reliability analysis of structures with random resistance or random system parameters. It deals with the problem of a random load process crossing a random barrier level. The implications of approximating the arrival rate of the first overload by an ensemble-crossing rate are studied. The error involved in this so-called ""ensemble-crossing rate"" approximation is described in terms of load process and barrier distribution parameters, and in terms of the number of load cycles. Existing results are reviewed, and significant improvements involving load process bandwidth, mean-crossing frequency and time are presented. The paper shows that the ensemble-crossing rate approximation can be accurate enough for problems where load process variance is large in comparison to barrier variance, but especially when the number of load cycles is small. This includes important practical applications like random vibration due to impact loadings and earthquake loading. Two application examples are presented, one involving earthquake loading and one involving a frame structure subject to wind and snow loadings. (C) 2007 Elsevier Ltd. All rights reserved.