Spectra of modular and small-world matrices

We compute spectra of symmetric random matrices describing graphs with general modular structure and arbitrary inter- and intra-module degree distributions, subject only to the constraint of finite mean connectivities. We also evaluate spectra of a certain class of small-world matrices generated from random graphs by introducing shortcuts via additional random connectivity components. Both adjacency matrices and the associated graph Laplacians are investigated. For the Laplacians, we find Lifshitz-type singular behaviour of the spectral density in a localized region of small |?| values. In the case of modular networks, we can identify contributions of local densities of state from individual modules. For small-world networks, we find that the introduction of short cuts can lead to the creation of satellite bands outside the central band of extended states, exhibiting only localized states in the band gaps. Results for the ensemble in the thermodynamic limit are in excellent agreement with those obtained via a cavity approach for large finite single instances, and with direct diagonalization results.

The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

Cidadania e educação física : matrizes históricas e políticas, contradições e perspectivas = Citizenship and physical education : historical and political matrices, perspectives and contradictions

Universidade Estadual de Campinas . Faculdade de Educação Física

Porcine skin as a source of biodegradable matrices: alkaline treatment and glutaraldehyde crosslinking

In this work, the modifications promoted by alkaline hydrolysis and glutaraldehyde (GA) crosslinking on type I collagen found in porcine skin have been studied. Collagen matrices were obtained from the alkaline hydrolysis of porcine skin, with subsequent GA crosslinking in different concentrations and reaction times. The elastin content determination showed that independent of the treatment, elastin was present in the matrices. Results obtained from in vitro trypsin degradation indicated that with the increase of GA concentration and reaction time, the degradation rate decreased. From thermogravimetry and differential scanning calorimetry analysis it can be observed that the collagen in the matrices becomes more resistant to thermal degradation as a consequence of the increasing crosslink degree. Scanning electron microscopy analysis indicated that after the GA crosslinking, collagen fibers become more organized and well-defined. Therefore, the preparations of porcine skin matrices with different degradation rates, which can be used in soft tissue reconstruction, are viable.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

Disordered ensembles of random matrices

It is shown that the families of generalized matrix ensembles recently considered which give rise to an orthogonal invariant stable Levy ensemble can be generated by the simple procedure of dividing Gaussian matrices by a random variable. The nonergodicity of this kind of disordered ensembles is investigated. It is shown that the same procedure applied to random graphs gives rise to a family that interpolates between the Erdos-Renyi and the scale free models.

Spin Hall effect due to intersubband-induced spin-orbit interaction in symmetric quantum wells

We investigate the intrinsic spin Hall effect in two-dimensional electron gases in quantum wells with two subbands, where a new intersubband-induced spin-orbit coupling is operative. The bulk spin Hall conductivity sigma(z)(xy) is calculated in the ballistic limit within the standard Kubo formalism in the presence of a magnetic field B and is found to remain finite in the B=0 limit, as long as only the lowest subband is occupied. Our calculated sigma(z)(xy) exhibits a nonmonotonic behavior and can change its sign as the Fermi energy (the carrier areal density n(2D)) is varied between the subband edges. We determine the magnitude of sigma(z)(xy) for realistic InSb quantum wells by performing a self-consistent calculation of the intersubband-induced spin-orbit coupling.

POLAR ACTIONS ON CERTAIN PRINCIPAL BUNDLES OVER SYMMETRIC SPACES OF COMPACT TYPE

We study polar actions with horizontal sections on the total space of certain principal bundles G/K -> G/H with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In particular, we exhibit examples of hyperpolar actions with cohomogeneity greater than one on locally irreducible homogeneous spaces with nonnegative curvature which are not homeomorphic to symmetric spaces.

Protein-polysaccharide viscoelastic matrices: synergic effects of amylose on lysozyme physical gelation in aqueous dimethylsulfoxide

A synergic effect of amylose on rheological characteristics of lysozyme physical gels evolved out of dimethylsulfoxide-water was verified and analyzed. The dynamics of the gels were experimentally approached by oscillatory rheology. The synergic effect was characterized by a decrease in the threshold DMSO volume fraction required for lysozyme gelation, and by a significant strengthening of the gel structure at over-critical solvent and protein concentrations. Drastic changes in the relaxation and creep curve patterns for systems in the presence of amylose were verified. Complex viscosity dependence on temperature was found to conform to an Arrhenius-like equation, allowing the determination of an activation energy term (Ea, apparent) for discrimination of gel rigidity. A dilatant effect was found to be induced by temperature on the flow behavior of lysozyme dispersions in DMSO-H(2)O in sub-critical conditions for gelation, which was greatly intensified by the presence of amylose in the samples. That transition was interpreted as reflecting a change from a predominant colloidal flow regime, where globular components are the prevailing structural elements, to a mainly fibrillar, polymeric flow behavior.

Morphological and mechanical properties of hybrid matrices of polysiloxane-polyvinyl alcohol prepared by sol-gel technique and their potential for immobilizing enzyme

Hybrid matrices of polysiloxane-polyvinyl alcohol (POS-PVA) were prepared by sol-gel technique using different concentrations of the organic component (polyvinyl alcohol, PVA) in the synthesis medium. The goal was to prepare carriers for immobilizing enzyme by taking into consideration properties as hardness, mean pore diameter, specific surface area and pore size distribution. The matrices were activated with sodium metaperiodate to render functional groups for binding the lipase from Candida rugosa, used here as a study model. Results showed that low proportion of PVA gave POS-PVA with low surface area and pore volume, although with higher hardness. The chemical activation decreased the pore volume and increased the pore size with a decrease on the surface area of about 60-75%. The matrices for enzyme immobilization were chosen considering the best combination of high surface area and hardness. Thus, the POS-PVA prepared with 5.56 x 10(-5) M of PVA with a surface area of 123 m(2)/g and hardness of 71 HV (50 gf 30 s) was shown to be suitable to immobilize the lipase, with an immobilization yield of about 40%. (c) 2008 Elsevier B.V. All rights reserved.

Evaluation of the catalytic properties of Burkholderia cepacia lipase immobilized on non-commercial matrices to be used in biodiesel synthesis from different feedstocks

The objective of this work was to produce an immobilized form of lipase from Burkholderia cepacia (lipase PS) with advantageous catalytic properties and stability to be used in the ethanolysis of different feedstocks, mainly babassu oil and tallow beef. For this purpose lipase PS was immobilized on two different non-commercial matrices, such as inorganic matrix (niobium oxide, Nb(2)O(5)) and a hybrid matrix (polysiloxane-polyvinyl alcohol, SiO(2)-PVA) by covalent binding. The properties of free and immobilized enzymes were searched and compared. The best performance regarding all the analyzed parameters (biochemical properties, kinetic constants and thermal stability) were obtained when the lipase was immobilized on SiO(2)-PVA. The superiority of this immobilized system was also confirmed in the transe-sterification of both feedstocks, attained higher yields and productivities. (C) 2010 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.

Bio-Dis and the Paddle Dissolution Apparatuses Applied to the Release Characterization of Ketoprofen from Hypromellose Matrices

The purposes of this work were: (1) to comparatively evaluate the effects of hypromellose viscosity grade and content on ketoprofen release from matrix tablets, using Bio-Dis and the paddle apparatuses, (2) to investigate the influence of the pH of the dissolution medium on drug release. Furthermore, since direct compression had not shown to be appropriate to obtain the matrices under study, it was also an objective (3) to evaluate the impact of granulation on drug release process. Six formulations of ketoprofen matrix tablets were obtained by compression, with or without previous granulation, varying the content and viscosity grade of hypromellose. Dissolution tests were carried out at a fixed pH, in each experiment, with the paddle method (pH 4.5, 6.0, 6.8, or 7.2), while a pH gradient was used in Bio-Dis (pH 1.2 to 7.2). The higher the hypromellose viscosity grade and content were, the lower the amount of ketoprofen released was in both apparatuses, the content effect being more expressive. Drug dissolution enhanced with the increase of the pH of the medium due to its pH-dependent solubility. Granulation caused an increase in drug dissolution and modified the mechanism of the release process.

Twisted quantum affine superalgebra Uq[gl(m|n)(2)] and new Uq[osp(m|n)] invariant R-matrices

The minimal irreducible representations of U-q[gl(m|n)], i.e. those irreducible representations that are also irreducible under U-q[osp(m|n)] are investigated and shown to be affinizable to give irreducible representations of the twisted quantum affine superalgebra U-q[gl(m|n)((2))]. The U-q[osp(m|n)] invariant R-matrices corresponding to the tensor product of any two minimal representations are constructed, thus extending our twisted tensor product graph method to the supersymmetric case. These give new solutions to the spectral-dependent graded Yang-Baxter equation arising from U-q[gl(m|n)((2))], which exhibit novel features not previously seen in the untwisted or non-super cases.

Expokit: A software package for computing matrix exponentials

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.