The Diffusion Kernel Filter

A particle filter method is presented for the discrete-time filtering problem with nonlinear ItA ` stochastic ordinary differential equations (SODE) with additive noise supposed to be analytically integrable as a function of the underlying vector-Wiener process and time. The Diffusion Kernel Filter is arrived at by a parametrization of small noise-driven state fluctuations within branches of prediction and a local use of this parametrization in the Bootstrap Filter. The method applies for small noise and short prediction steps. With explicit numerical integrators, the operations count in the Diffusion Kernel Filter is shown to be smaller than in the Bootstrap Filter whenever the initial state for the prediction step has sufficiently few moments. The established parametrization is a dual-formula for the analysis of sensitivity to gaussian-initial perturbations and the analysis of sensitivity to noise-perturbations, in deterministic models, showing in particular how the stability of a deterministic dynamics is modeled by noise on short times and how the diffusion matrix of an SODE should be modeled (i.e. defined) for a gaussian-initial deterministic problem to be cast into an SODE problem. From it, a novel definition of prediction may be proposed that coincides with the deterministic path within the branch of prediction whose information entropy at the end of the prediction step is closest to the average information entropy over all branches. Tests are made with the Lorenz-63 equations, showing good results both for the filter and the definition of prediction.

The matrix-tolerance hypothesis: an empirical test with frogs in the Atlantic Forest

The matrix-tolerance hypothesis suggests that the most abundant species in the inter-habitat matrix would be less vulnerable to their habitat fragmentation. This model was tested with leaf-litter frogs in the Atlantic Forest where the fragmentation process is older and more severe than in the Amazon, where the model was first developed. Frog abundance data from the agricultural matrix, forest fragments and continuous forest localities were used. We found an expected negative correlation between the abundance of frogs in the matrix and their vulnerability to fragmentation, however, results varied with fragment size and species traits. Smaller fragments exhibited stronger matrix-vulnerability correlation than intermediate fragments, while no significant relation was observed for large fragments. Moreover, some species that avoid the matrix were not sensitive to a decrease in the patch size, and the opposite was also true, indicating significant differences with that expected from the model. Most of the species that use the matrix were forest species with aquatic larvae development, but those species do not necessarily respond to fragmentation or fragment size, and thus affect more intensively the strengthen of the expected relationship. Therefore, the main relationship expected by the matrix-tolerance hypothesis was observed in the Atlantic Forest; however we noted that the prediction of this hypothesis can be substantially affected by the size of the fragments, and by species traits. We propose that matrix-tolerance model should be broadened to become a more effective model, including other patch characteristics, particularly fragment size, and individual species traits (e. g., reproductive mode and habitat preference).

Importance of estimating matrix quality for modeling species distribution in complex tropical landscapes: a test with Atlantic forest small mammals

Information to guide decision making is especially urgent in human dominated landscapes in the tropics, where urban and agricultural frontiers are still expanding in an unplanned manner. Nevertheless, most studies that have investigated the influence of landscape structure on species distribution have not considered the heterogeneity of altered habitats of the matrix, which is usually high in human dominated landscapes. Using the distribution of small mammals in forest remnants and in the four main altered habitats in an Atlantic forest landscape, we investigated 1) how explanatory power of models describing species distribution in forest remnants varies between landscape structure variables that do or do not incorporate matrix quality and 2) the importance of spatial scale for analyzing the influence of landscape structure. We used standardized sampling in remnants and altered habitats to generate two indices of habitat quality, corresponding to the abundance and to the occurrence of small mammals. For each remnant, we calculated habitat quantity and connectivity in different spatial scales, considering or not the quality of surrounding habitats. The incorporation of matrix quality increased model explanatory power across all spatial scales for half the species that occurred in the matrix, but only when taking into account the distance between habitat patches (connectivity). These connectivity models were also less affected by spatial scale than habitat quantity models. The few consistent responses to the variation in spatial scales indicate that despite their small size, small mammals perceive landscape features at large spatial scales. Matrix quality index corresponding to species occurrence presented a better or similar performance compared to that of species abundance. Results indicate the importance of the matrix for the dynamics of fragmented landscapes and suggest that relatively simple indices can improve our understanding of species distribution, and could be applied in modeling, monitoring and managing complex tropical landscapes.

Human Stem Cell Cultures from Cleft Lip/Palate Patients Show Enrichment of Transcripts Involved in Extracellular Matrix Modeling By Comparison to Controls

Nonsyndromic cleft lip and palate (NSCL/P) is a complex disease resulting from failure of fusion of facial primordia, a complex developmental process that includes the epithelial-mesenchymal transition (EMT). Detection of differential gene transcription between NSCL/P patients and control individuals offers an interesting alternative for investigating pathways involved in disease manifestation. Here we compared the transcriptome of 6 dental pulp stem cell (DPSC) cultures from NSCL/P patients and 6 controls. Eighty-seven differentially expressed genes (DEGs) were identified. The most significant putative gene network comprised 13 out of 87 DEGs of which 8 encode extracellular proteins: ACAN, COL4A1, COL4A2, GDF15, IGF2, MMP1, MMP3 and PDGFa. Through clustering analyses we also observed that MMP3, ACAN, COL4A1 and COL4A2 exhibit co-regulated expression. Interestingly, it is known that MMP3 cleavages a wide range of extracellular proteins, including the collagens IV, V, IX, X, proteoglycans, fibronectin and laminin. It is also capable of activating other MMPs. Moreover, MMP3 had previously been associated with NSCL/P. The same general pattern was observed in a further sample, confirming involvement of synchronized gene expression patterns which differed between NSCL/P patients and controls. These results show the robustness of our methodology for the detection of differentially expressed genes using the RankProd method. In conclusion, DPSCs from NSCL/P patients exhibit gene expression signatures involving genes associated with mechanisms of extracellular matrix modeling and palate EMT processes which differ from those observed in controls. This comparative approach should lead to a more rapid identification of gene networks predisposing to this complex malformation syndrome than conventional gene mapping technologies.

Matrix metalloproteinases, TIMPs and growth factors regulating ameloblastoma behaviour

Aims: Ameloblastoma is an odontogenic neoplasm with local invasiveness and recurrence. We have previously suggested that growth factors and matrix metalloproteinases (MMPs) influence ameloblastoma invasiveness(1). The aim was to study expression of MMPs, tissue inhibitor of metalloproteinases (TIMPs) and growth factors in ameloblastoma. Methods and results: Thirteen cases of solid/multicystic ameloblastoma were examined. As a control, calcifying cystic odontogenic tumour (CCOT), a non-invasive odontogenic neoplasm with ameloblastomatous epithelium was also studied. Immunohistochemistry detected MMPs, TIMPs and growth factors in ameloblastoma and CCOT. The labelling index (LI) of MMP-9 and TIMP-2 was significantly higher in ameloblastoma compared with CCOT. The LI of epidermal growth factor (EGF), transforming growth factor (TGF)-alpha and epidermal growth factor receptor (EGFR) was also increased in ameloblastoma. This neoplasm showed greater expression of MMPs, TIMPs and growth factors compared with CCOT. We then analysed these molecules in ameloblastoma cells and stroma. Ameloblastoma cells exhibited increased LI of MMP-1, -2 and EGFR. We found a positive correlation between EGF and TIMP-1, and between TGF-alpha and TIMP-2. It is known that signals generated by growth factors are transduced by the ERK pathway. Ameloblastoma stroma exhibited the phosphorylated (activated) form of ERK. Conclusions: These results suggest an interplay involving growth factors MMPs and TIMPs that may contribute to ameloblastoma behaviour. Signals generated by this molecular network would be transduced by ERK 1/2 pathway.

Delayed local inflammatory response induced by Thalassophryne nattereri venom is related to extracellular matrix degradation

Symptoms evoked by Thalassophryne nattereri fish envenomation include local oedema, severe pain and intense necrosis with strikingly inefficient healing, continuing for several weeks or months. Investigations carried out in our laboratory showed that, in the venom-induced acute inflammation, thrombosis in venules and constrictions in arterioles were highly visible, in contrast to a notable lack of inflammatory cell. Nevertheless, the reason that the venom toxins favour delayed local inflammatory response is poorly defined. In this study, we analysed the movement of leucocytes after T. nattereri venom injection in the intraplantar region of Swiss mice, the production of pro-inflammatory mediators and the venom potential to elicit matrix metalloproteinase production and extracellular matrix degradation. Total absence of mononuclear and neutrophil influx was observed until 14 days, but the venom stimulates pro-inflammatory mediator secretion. Matrix metalloproteinases (MMP)-2 and MMP-9 were detected in greater quantities, accompanied by tissue degradation of collagenous fibre. An influx of mononuclear cells was noted very late and at this time the levels of IL-6, IL-1 beta and MMP-2 remained high. Additionally, the action of venom on the cytoskeletal organization was assessed in vitro. Swift F-actin disruption and subsequent loss of focal adhesion was noted. Collectively these findings show that the altered specific interaction cell-matrix during the inflammatory process creates an inadequate environment for infiltration of inflammatory cells.

Matrix metalloproteinases cleave the beta(2)-adrenergic receptor in spontaneously hypertensive rats

Rodrigues SF, Tran ED, Fortes ZB, Schmid-Schonbein GW. Matrix metalloproteinases cleave the beta(2)-adrenergic receptor in spontaneously hypertensive rats. Am J Physiol Heart Circ Physiol 299: H25-H35, 2010. First published April 9, 2010; doi:10.1152/ajpheart.00620.2009.-We recently observed the enhanced serine and matrix metalloproteinase (MMP) activity in the spontaneously hypertensive rat (SHR) compared with its normotensive Wistar-Kyoto (WKY) rat and the cleavage of membrane receptors in the SHR by MMPs. We demonstrate in vivo that MMP-7 and MMP-9 injection leads to a vasoconstrictor response in microvessels of rats that is blocked by a specific MMP inhibitor (GM-6001, 1 mu M). Multiple pathways may be responsible. Since the beta(2)-adrenergic receptor (beta(2)-AR) is susceptible to the action of endogenous MMPs, we hypothesize that MMPs in the plasma of SHRs are able to cleave the extracellular domain of the beta(2)-AR. SHR arterioles respond in an attenuated fashion to beta(2)-AR agonists and antagonists. Aorta and heart muscle of control Wistar rats were exposed for 24 h (37 C) to fresh plasma of male Wistar and WKY rats and SHRs with and without doxycycline (30 mu M) and EDTA (10 mM) to reduce MMP activity. The density of extracellular and intracellular domains of beta(2)-AR was determined by immunohistochemistry. The density of the extracellular domain of beta(2)-AR is reduced in aortic endothelial cells and cardiac microvessels of SHRs compared with that of WKY or Wistar rats. Treatment of the aorta and the heart of control Wistar rats with plasma from SHRs, but not from WKY rats, reduced the number of extracellular domains, but not intracellular domains, of beta(2)-AR in aortic endothelial cells and cardiac microvessels. MMP inhibitors (EDTA and doxycycline) prevented the cleavage of the extracellular domain. Thus MMPs may contribute to the reduced density of the extracellular domain of beta(2)-AR in blood vessels and to the increased arteriolar tone of SHRs compared with normotensive rats.

Maternal diabetes affects specific extracellular matrix components during placentation

During embryo implantation, invasive trophoblast cells mediate embryo invasion into the decidualized stroma, forming a rich network of lacunae that connect the embryonic tissues to the maternal blood vessels. Placentation is probably guided by the composition and organization of the endometrial extracellular matrix. Certain pathological conditions that occur during pregnancy, including diabetes, have been linked to abnormal placental morphology and consequent fetal morbidity. We used immunoperoxidase techniques to identify members of the collagen, proteoglycan and glycoprotein families in the various compartments of the rat placenta and to determine whether experimentally induced diabetes affects placental morphology and alters the distribution of these molecules during pregnancy. Single injections of alloxan (40 mg kg(-1) i.v.) were used to induce diabetes on day 2 of pregnancy in Wistar rats. Placentas were collected on days 14, 17, and 20. Type I and III collagen, as well as the proteoglycans decorin and biglycan, were found to be distributed throughout the placentas of control and diabetic rats. In both groups, laminin expression decreased at the end of pregnancy. In contrast, fibronectin was detected in the labyrinth region of diabetic rats at all gestational stages studied, whereas it was detected only at term pregnancy in the placentas of control rats. These results show for the first time that some extracellular matrix molecules are modulated during placental development. However, as diabetic rats presented increased fibronectin deposition exclusively in the labyrinth region, we speculate that diabetes alters the microenvironment at the maternal-fetal interface, leading to developmental abnormalities in the offspring.

Matrix metalloproteinases with gelatinolytic activity induced by Paracoccidioides brasiliensis infection

P>Matrix metalloproteinases (MMPs) modulate extracellular matrix turnover, inflammation and immunity. We studied MMP-9 and MMP-2 in experimental paracoccidioidomycosis. At 15 and 120 days after infection (DAI) with virulent Paracoccidioides brasiliensis, MMP-9 was positive by immunohistochemistry in multinucleated giant cells, in mononuclear cells with macrophage and lymphocyte morphologies and also in fungal cells in the lesions of susceptible and resistant mice. Using gelatin zymography, pro- and active MMP-9 and active MMP-2 were detected in all infected mice, but not in controls. Gelatinolytic activity was not observed in P. brasiliensis extracts. Semiquantitative analysis of gelatinolytic activities revealed weak or absent MMP-2 and strong MMP-9 activity in both mouse strains at 15 DAI, declining at 120 DAI. Avirulent P. brasiliensis-infected mice had residual lesions with MMP-9-positive pseudoxantomatous macrophages, but no gelatinase activity at 120 DAI. Our findings demonstrate the induction of MMPs, particularly MMP-9, in experimental paracoccidioidomycosis, suggesting a possible influence in the pattern of granulomas and in fungal dissemination.

INDEFINITE QUASILINEAR ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS WITH EXPONENTIAL CRITICAL GROWTH

This paper is concerned with the existence of solutions for the quasilinear problem {-div(vertical bar del u vertical bar(N-2) del u) + vertical bar u vertical bar(N-2) u = a(x)g(u) in Omega u = 0 on partial derivative Omega, where Omega subset of R(N) (N >= 2) is an exterior domain; that is, Omega = R(N)\omega, where omega subset of R(N) is a bounded domain, the nonlinearity g(u) has an exponential critical growth at infinity and a(x) is a continuous function and changes sign in Omega. A variational method is applied to establish the existence of a nontrivial solution for the above problem.

MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS

This paper proves the multiplicity of positive solutions for the following class of quasilinear problems: {-epsilon(p)Delta(p)u+(lambda A(x) + 1)vertical bar u vertical bar(p-2)u = f(u), R(N) u(x)>0 in R(N), where Delta(p) is the p-Laplacian operator, N > p >= 2, lambda and epsilon are positive parameters, A is a nonnegative continuous function and f is a continuous function with subcritical growth. Here, we use variational methods to get multiplicity of positive solutions involving the Lusternick-Schnirelman category of intA(-1)(0) for all sufficiently large lambda and small epsilon.

Soliton solutions for quasilinear Schrodinger equations with critical growth

In this paper we establish the existence of standing wave solutions for quasilinear Schrodinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one. whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9]. (C) 2009 Elsevier Inc. All rights reserved.

SINGULARITY THEORY AND FORCED SYMMETRY BREAKING IN EQUATIONS

A theory of bifurcation equivalence for forced symmetry breaking bifurcation problems is developed. We classify (O(2), 1) problems of corank 2 of low codimension and discuss examples of bifurcation problems leading to such symmetry breaking.

DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES

Let a > 0, Omega subset of R(N) be a bounded smooth domain and - A denotes the Laplace operator with Dirichlet boundary condition in L(2)(Omega). We study the damped wave problem {u(tt) + au(t) + Au - f(u), t > 0, u(0) = u(0) is an element of H(0)(1)(Omega), u(t)(0) = v(0) is an element of L(2)(Omega), where f : R -> R is a continuously differentiable function satisfying the growth condition vertical bar f(s) - f (t)vertical bar <= C vertical bar s - t vertical bar(1 + vertical bar s vertical bar(rho-1) + vertical bar t vertical bar(rho-1)), 1 < rho < (N - 2)/(N + 2), (N >= 3), and the dissipativeness condition limsup(vertical bar s vertical bar ->infinity) s/f(s) < lambda(1) with lambda(1) being the first eigenvalue of A. We construct the global weak solutions of this problem as the limits as eta -> 0(+) of the solutions of wave equations involving the strong damping term 2 eta A(1/2)u with eta > 0. We define a subclass LS subset of C ([0, infinity), L(2)(Omega) x H(-1)(Omega)) boolean AND L(infinity)([0, infinity), H(0)(1)(Omega) x L(2)(Omega)) of the `limit` solutions such that through each initial condition from H(0)(1)(Omega) x L(2)(Omega) passes at least one solution of the class LS. We show that the class LS has bounded dissipativeness property in H(0)(1)(Omega) x L(2)(Omega) and we construct a closed bounded invariant subset A of H(0)(1)(Omega) x L(2)(Omega), which is weakly compact in H(0)(1)(Omega) x L(2)(Omega) and compact in H({I})(s)(Omega) x H(s-1)(Omega), s is an element of [0, 1). Furthermore A attracts bounded subsets of H(0)(1)(Omega) x L(2)(Omega) in H({I})(s)(Omega) x H(s-1)(Omega), for each s is an element of [0, 1). For N = 3, 4, 5 we also prove a local uniqueness result for the case of smooth initial data.

Averaging for retarded functional differential equations

We consider retarded functional differential equations in the setting of Kurzweil-Henstock integrable functions and we state an averaging result for these equations. Our result generalizes previous ones. (C) 2011 Elsevier Inc. All rights reserved.