An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

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.

EXISTENCE RESULTS FOR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

In this paper we discuss the existence of mild, strict and classical solutions for a class of abstract integro-differential equations in Banach spaces. Some applications to ordinary and partial integro-differential equations are considered.

GLOBAL SOLUTIONS FOR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.

Weighted S-Asymptotically omega-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted S-asymptotically omega-periodic mild solutions for a class of abstract fractional differential equations of the form u' = partial derivative (alpha vertical bar 1)Au + f(t, u), 1 < alpha < 2, where A is a linear sectorial operator of negative type.

EXISTENCE RESULTS FOR ABSTRACT NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract partial neutral functional differential equations.

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.

Lsa21, a novel leptospiral protein binding adhesive matrix molecules and present during human infection

Background: It has been well documented over past decades that interaction of pathogens with the extracellular matrix (ECM) plays a primary role in host cell attachment and invasion. Adherence to host tissues is mediated by surface-exposed proteins expressed by the microorganisms during infection. The mechanisms by which pathogenic leptospires invade and colonize the host remain poorly understood since few virulence factors contributing to the pathogenesis of the disease have been identified. Whole-genome sequencing analysis of L. interrogans allowed identification of a repertoire of putative leptospiral surface proteins. Results: Here, we report the identification and characterization of a new leptospiral protein that exhibits extracellular matrix-binding properties, called as Lsa21 (leptospiral surface adhesin, 21 kDa). Compatible with its role in adhesion, the protein was shown to be surface-exposed by indirect immunofluorescence. Attachment of Lsa21 to laminin, collagen IV, and plasma fibronectin was specific and dose dependent. Laminin oxidation by sodium metaperiodate reduced the protein-laminin interaction in a concentration-dependent manner, indicating that laminin sugar moieties are crucial for this interaction. The gene coding for Lsa21 is present in pathogenic strains belonging to the L. interrogans species but was not found in the saprophytic L. biflexa serovar Patoc strain Patoc 1. Loss of gene expression occurs upon culture attenuation of pathogenic strains. Environmental factors such as osmolarity and temperature affect Lsa21 expression at the transcriptional level. Moreover, anti-Lsa21 serum labeled liver and kidney tissues of human fatal cases of leptospirosis. Conclusion: Our data suggest a role of Lsa21 in the pathogenesis of leptospirosis.

Interethnic Differences in the Distribution of Matrix Metalloproteinases Genetic Polymorphisms Are Consistent with Interethnic Differences in Disease Prevalence

Interethnic differences exist in disease prevalence, especially with regard to cancer and cardiovascular diseases, which involve altered expression or activity of matrix metalloproteinases (MMPs). The hypothesis being tested in this study is that interethnic differences exist between blacks and whites with regard to the distribution of genetic variants of MMP polymorphisms and haplotypes. We examined the distribution of polymorphisms of MMP-2 and MMP-9 genes in 177 black and 140 white subjects. We studied the following polymorphisms: the C(-1306)T in the promoter of the MMP-2 gene, the C(-1562)T and a microsatellite -90(CA)(14-24) in the promoter, and the Q279R in exon 6 of the MMP-9 gene. We have also compared our results with those from Hapmap or Seattle SNPs Projects and estimated the haplotype frequency in these two ethnic groups. The ""C'' allele for the C(-1306)T polymorphism was more common in blacks (91.5%) than in whites (80.4%; p<0.0001). The ""T'' allele for the C(-1562)T polymorphism was more common in blacks (15.0%) than in whites (8.9%; p=0.0279), as well as the alleles with >21 repeats for the -90(CA)(14-24) were more common in blacks than in whites (61.9% in blacks and 49.3% in whites; p=0.0017). We found no interethnic differences for the Q279R polymorphism. Moreover, two haplotypes that combine ""detrimental'' alleles were found at higher frequencies in blacks than in whites (31% vs. 16.4%, respectively; p<0.05). The interethnic differences being reported here replicate those previously found with smaller number of subjects in the Hapmap or Seattle SNPs data and may help explain the higher prevalence of cancer and cardiovascular diseases in blacks compared with whites. Our findings suggest a proportional significance of these polymorphisms in each ethnic group.

Characterization of Novel OmpA-Like Protein of Leptospira interrogans That Binds Extracellular Matrix Molecules and Plasminogen

Leptospira interrogans is the etiological agent of leptospirosis, a zoonotic disease of human and veterinary concern. The identification of novel proteins that mediate host-pathogen interactions is important for understanding the bacterial pathogenesis as well as to identify protective antigens that would help fight the disease. We describe in this work the cloning, expression, purification and characterization of three predicted leptospiral membrane proteins, LIC10258, LIC12880 (Lp30) and LIC12238. We have employed Escherichia coli BL21 (SI) strain as a host expression system. Recently, we have identified LIC12238 as a plasminogen (PLG)-binding receptor. We show now that Lp30 and rLIC10258 are also PLG-receptors of Leptospira, both exhibiting dose-dependent and saturating binding (K(D), 68.8 +/- 25.2 nM and 167.39 +/- 60.1 nM, for rLIC10258 and rLIC12880, respectively). In addition, LIC10258, which is a novel OmpA-like protein, binds laminin and plasma fibronectin ECM molecules and hence, it was named Lsa66 (Leptospiral surface adhesin of 66 kDa). Binding of Lsa66 to ECM components was determined to be specific, dose-dependent and saturable, with a KD of 55.4 +/- 15.9 nM to laminin and of 290.8 +/- 11.8 nM to plasma fibronectin. Binding of the recombinant proteins to PLG or ECM components was assessed by using antibodies against each of the recombinant proteins obtained in mice and confirmed by monoclonal anti-polyhistidine antibodies. Lsa66 caused partial inhibition on leptospiral adherence to immobilized ECM and PLG. Moreover, this adhesin and rLIC12238 are recognized by antibodies in serum samples of confirmed leptospirosis cases. Thus, Lsa66 is a novel OmpA-like protein with dual activity that may promote the attachment of Leptospira to host tissues and may contribute to the leptospiral invasion. To our knowledge, this is the first leptospiral protein with ECM and PLG binding properties reported to date.

Collagen Hydrolysate Intake Increases Skin Collagen Expression and Suppresses Matrix Metalloproteinase 2 Activity

The effect of daily ingestion of collagen hydrolysate (CH) on skin extracellular matrix proteins was investigated. Four-week-old male Wistar rats were fed a modified AIN-93 diet containing 12% casein as the reference group or CH as the treatment group. A control group was established in which animals were fed a non-protein-modified AIN-93 diet. The diets were administered continuously for 4 weeks when six fresh skin samples from each group were assembled and subjected to extraction of protein. Type I and IV collagens were studied by immunoblot, and activities of matrix metalloproteinase (MMP) 2 and 9 were assessed by zymography. The relative amount of type I and IV collagens was significantly (P<.05) increased after CH intake compared with the reference diet group (casein). Moreover, CH uptake significantly decreased both proenzyme and active forms of MMP2 compared with casein and control groups (P<.05). In contrast, CH ingestion did not influence on MMP9 activity. These results suggest that CH may reduce aging-related changes of the extracellular matrix by stimulating anabolic processes in skin tissue.

SOLITON SOLUTIONS TO SYSTEMS OF COUPLED SCHRODINGER EQUATIONS OF HAMILTONIAN TYPE

We study the existence of positive solutions of Hamiltonian-type systems of second-order elliptic PDE in the whole space. The systems depend on a small parameter and involve a potential having a global well structure. We use dual variational methods, a mountain-pass type approach and Fourier analysis to prove positive solutions exist for sufficiently small values of the parameter.

LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

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.