Perturbation treatment of symmetry breaking within random matrix theory

We discuss the applicability, within the random matrix theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both two-fold and three-fold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an appropriate number of eigenfrequencies is considered to be missing in the sample. Our findings are relevant for symmetry violation studies in general. (C) 2008 Elsevier B.V. All rights reserved.

Multifractality in the random parameter model for multivariate time series

The Random Parameter model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we explore the scaling properties of the model, as observed in the multifractal structure of the simulated time series. We use the Wavelet Transform Modulus Maxima technique to obtain the multifractal spectrum dependence with the parameters of the model. The model shows a scaling structure compatible with the stylized facts for a reasonable choice of the parameter values. (C) 2009 Elsevier B.V. All rights reserved.

Missing levels in acoustic resonators

It is shown that the deviations of the experimental statistics of six chaotic acoustic resonators from Wigner-Dyson random matrix theory predictions are explained by a recent model of random missing levels. In these resonatorsa made of aluminum plates a the larger deviations occur in the spectral rigidity (SRs) while the nearest-neighbor distributions (NNDs) are still close to the Wigner surmise. Good fits to the experimental NNDs and SRs are obtained by adjusting only one parameter, which is the fraction of remaining levels of the complete spectra. For two Sinai stadiums, one Sinai stadium without planar symmetry, two triangles, and a sixth of the three-leaf clover shapes, was found that 7%, 4%, 7%, and 2%, respectively, of eigenfrequencies were not detected.

Deformed Gaussian-orthogonal-ensemble description of small-world networks

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

Deformations of the Tracy-Widom distribution

In random matrix theory, the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists of removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristic of extreme values of an uncorrelated sequence, is obtained.

INFERENCE FOR EIGENVALUES AND EIGENVECTORS OF GAUSSIAN SYMMETRIC MATRICES

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3 x 3 and 2 x 2 symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered in this paper, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure.

Decomposition of spectral density in individual eigenvalue contributions

The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of all eigenvalues, for medium matrix sizes, are described with a good precision by nearly normal distributions.

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.

Dynamic Imaging in Electrical Impedance Tomography of the Human Chest With Online Transition Matrix Identification

One of the electrical impedance tomography objectives is to estimate the electrical resistivity distribution in a domain based only on electrical potential measurements at its boundary generated by an imposed electrical current distribution into the boundary. One of the methods used in dynamic estimation is the Kalman filter. In biomedical applications, the random walk model is frequently used as evolution model and, under this conditions, poor tracking ability of the extended Kalman filter (EKF) is achieved. An analytically developed evolution model is not feasible at this moment. The paper investigates the identification of the evolution model in parallel to the EKF and updating the evolution model with certain periodicity. The evolution model transition matrix is identified using the history of the estimated resistivity distribution obtained by a sensitivity matrix based algorithm and a Newton-Raphson algorithm. To numerically identify the linear evolution model, the Ibrahim time-domain method is used. The investigation is performed by numerical simulations of a domain with time-varying resistivity and by experimental data collected from the boundary of a human chest during normal breathing. The obtained dynamic resistivity values lie within the expected values for the tissues of a human chest. The EKF results suggest that the tracking ability is significantly improved with this approach.

Evaluation of in vitro human gingival fibroblast seeding on acellular dermal matrix

The acellular dermal matrix (ADM) was introduced in periodontology as a substitute for the autogenous grafts, which became restricted because of the limited source of donor's tissue. The aim of this study was to investigate, in vitro, the distribution, proliferation and viability of human gingival fibroblasts seeded onto ADM. ADM was seeded with human gingival fibroblasts for up to 21 days. The following parameters were evaluated: cell distribution, proliferation and viability. Results revealed that, at day 7, fibroblasts were adherent and spread on ADM surface, and were unevenly distributed, forming a discontinuous single cell layer; at day 14, a confluent fibroblastic monolayer lining ADM surface was noticed. At day 21, the cell monolayer exhibited a reduction in cell density. At 7 days, about to 90% of adherent cells on ADM surface were cycling while at 14 and 21 days this proportion was significantly reduced. A high proportion of viable cell was detected on AMD surface both on 14 and 21 days. The results suggest that fibroblast seeding onto ADM for 14 days can allow good conditions for cell adhesion and spreading on the matrix; however, migration inside the matrix was limited.

Metronidazole release using natural rubber latex as matrix

Natural Rubber Latex (NRL) can be used successfully in controlled release drug delivery due to their excellent matrix forming properties. Recently, NRL has shown to stimulate angiogenesis, cellular adhesion and the formation of extracellular matrix, promoting the replacement and regeneration of tissue. A dermatological delivery system comprising a topically acceptable, inert support impregnated with a metronidazole (MET) solution was developed. MET 2-(2- methyl- 5-nitro- 1H- imidazol- 1-yl) ethanol, has been widely used for the treatment of protozoa and anaerobic bacterial infections. MET is a nitroimidazole anti-infective medication used mainly in the treatment of infections caused by susceptible organisms, particularly anaerobic bacteria and protozoa. In a previous study, we have tested NRL as an occlusive membrane for GBR with promising results. One possible way to decrease the inflammatory process, it was incorporated the MET in NRL. MET was incorporated into the NRL, by mixing it in solution for in vitro protein delivery experiments. The solutions of latex and MET were polymerized at different temperatures, from -100 to 40 °C, in order to control the membrane morphology. SEM microscopy analysis showed that the number, size and distribution of pores in NRL membranes varied depending on polymerization temperature, as well as its overall morphology. Results demonstrated that the best drug-delivery system was the membrane polymerized at -100 °C, which does release 77,1% of its MET content for up 310 hours.

Synthesis and structural characterization of block and random low molecular weight copolymers composed of L-lactic acid and isosorbide succinate moieties

Isosorbide succinate moieties were incorporated into poly(L-lactide) (PLLA) backbone in order to obtain a new class of biodegradable polymer with enhanced properties. This paper describes the synthesis and characterization of four types of low molecular weight copolymers. Copolymer I was obtained from monomer mixtures of L-lactide, isosorbide, and succinic anhydride; II from oligo(L-lactide) (PLLA), isosorbide, and succinic anhydride; III from oligo(isosorbide succinate) (PIS) and L-lactide; and IV from transesterification reactions between PLLA and PIS. MALDI-TOFMS and 13C-NMR analyses gave evidence that co-oligomerization was successfully attained in all cases. The data suggested that the product I is a random co-oligomer and the products II-IV are block co-oligomers.

Modulation of extracellular matrix by nutritional hepatotrophic factors in thioacetamide-induced liver cirrhosis in the rat

Nutritional substances associated to some hormones enhance liver regeneration when injected intraperitoneally, being denominated hepatotrophic factors (HF). Here we verified if a solution of HF (glucose, vitamins, salts, amino acids, glucagon, insulin, and triiodothyronine) can revert liver cirrhosis and how some extracellular matrices are affected. Cirrhosis was induced for 14 weeks in 45 female Wistar rats (200 mg) by intraperitoneal injections of thioacetamide (200 mg/kg). Twenty-five rats received intraperitoneal HF twice a day for 10 days (40 mL·kg-1·day-1) and 20 rats received physiological saline. Fifteen rats were used as control. The HF applied to cirrhotic rats significantly: a) reduced the relative mRNA expression of the genes: Col-α1 (-53%), TIMP-1 (-31.7%), TGF-β1 (-57.7%), and MMP-2 (-41.6%), whereas Plau mRNA remained unchanged; b) reduced GGT (-43.1%), ALT (-17.6%), and AST (-12.2%) serum levels; c) increased liver weight (11.3%), and reduced liver collagen (-37.1%), regenerative nodules size (-22.1%), and fibrous septum thickness. Progranulin protein (immunohistochemistry) and mRNA (in situ hybridization) were found in fibrous septa and areas of bile duct proliferation in cirrhotic livers. Concluding, HF improved the histology and serum biochemistry of liver cirrhosis, with an important reduction of interstitial collagen and increased extracelullar matrix degradation by reducing profibrotic gene expression.

Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

Expression of matrix metalloproteinase 2 (MMP-2) and tissue inhibitor of metalloproteinase 2 (TIMP-2) in medullary thyroid carcinoma: Prognostic implications

Background: Metalloproteinase 2 (MMP-2) and tissue inhibitor of metalloproteinase 2 (TIMP-2) participate in the degeneration of the extracellular matrix and are associated with carcinogenesis. MMP-2 is one of the main metalloproteinases active in neoplasia and is a marker of the malignant phenotype. Since the biological behavior of medullary thyroid carcinoma (MTC) varies widely, the present study was undertaken to determine if there is a correlation between the clinical evolution of MTC and the immunohistochemically detected expression of these enzymes in thyroid surgical specimens containing MTC. If so, their expression would be a novel indicator of the prognosis of MTC. Methods: Thirty-seven patients with MTC who had undergone thyroid surgery were followed for an average of 73 months. Immunohistochemical staining for metalloproteinase-related enzymes was performed in surgical paraffin blocks. The clinical status of the patients after surgery and at the end of the study period was characterized to determine correlations between these and the immunohistochemical markers. A value of p < 0.05 was considered statistically significant. Results: At the end of the study period, 15 patients (40.5%) were alive and without evidence of MTC, 17 (45.9%) had persistent MTC, and 5 (13.5%) had a relapse of their neoplasia. Four patients (10.8%) died during the course of the study. There was a significant correlation (p = 0.0005) between the immunohistochemical staining for MMP-2 and the clinical condition of the patients at the end of the study period, and a correlation between the state of apparent cure compared to persistence of MTC after thyroid surgery (p = 0.0207). No significant correlations were observed between either TIMP-2 expression or immune marking of metastatic lymph nodes and the clinical variables studied. Conclusion: Immunohistochemical expression of MMP-2 in thyroid surgical specimens from patients with MTC is a novel indicator of the prognosis of this cancer.