A Product Integration type Method for solving Nonlinear Integral Equations in L

This paper deals with nonlinear Fredholm integral equations of the second kind. We study the case of a weakly singular kernel and we set the problem in the space L 1 ([a, b], C). As numerical method, we extend the product integration scheme from C 0 ([a, b], C) to L 1 ([a, b], C)

Note on the Norm Involved in the Definition of the ε-spectrum

AbstractThere exist many definitions of the ε-spectrum. Unlike the spectrum, the ε-spectrum definitions depend on the choice of the norm. We propose to study the conditions on the norm that make all these definitions equivalent. The spectral radius of a related matrix is a useful tool in the eigenvalues perturbation analysis. The study of its connection with the ε-spectrum provides a new definition of the ε-spectrum. In most articles dealing with this subject, the chosen norm is the spectral one. In this paper, we intend to justify this choice

How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation

This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials ("spike trains") produced by neuronal networks ? and; (ii) what are the effects of synaptic plasticity on these statistics ? We introduce a framework in which spike trains are associated to a coding of membrane potential trajectories, and actually, constitute a symbolic coding in important explicit examples (the so-called gIF models). On this basis, we use the thermodynamic formalism from ergodic theory to show how Gibbs distributions are natural probability measures to describe the statistics of spike trains, given the empirical averages of prescribed quantities. As a second result, we show that Gibbs distributions naturally arise when considering "slow" synaptic plasticity rules where the characteristic time for synapse adaptation is quite longer than the characteristic time for neurons dynamics.Comment: 39 pages, 3 figure

A discrete time neural network model with spiking neurons II. Dynamics with noise

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky integrate and fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.Comment: 43 pages - revised version - to appear il Journal of Mathematical Biolog

Mutations in the Polycomb Group Gene polyhomeotic Lead to Epithelial Instability in both the Ovary and Wing Imaginal Disc in Drosophila

Most human cancers originate from epithelial tissues and cell polarity and adhesion defects can lead to metastasis. The Polycomb-Group of chromatin factors were first characterized in Drosophila as repressors of homeotic genes during development, while studies in mammals indicate a conserved role in body plan organization, as well as an implication in other processes such as stem cell maintenance, cell proliferation, and tumorigenesis. We have analyzed the function of the Drosophila Polycomb-Group gene polyhomeotic in epithelial cells of two different organs, the ovary and the wing imaginal disc.Clonal analysis of loss and gain of function of polyhomeotic resulted in segregation between mutant and wild-type cells in both the follicular and wing imaginal disc epithelia, without excessive cell proliferation. Both basal and apical expulsion of mutant cells was observed, the former characterized by specific reorganization of cell adhesion and polarity proteins, the latter by complete cytoplasmic diffusion of these proteins. Among several candidate target genes tested, only the homeotic gene Abdominal-B was a target of PH in both ovarian and wing disc cells. Although overexpression of Abdominal-B was sufficient to cause cell segregation in the wing disc, epistatic analysis indicated that the presence of Abdominal-B is not necessary for expulsion of polyhomeotic mutant epithelial cells suggesting that additional polyhomeotic targets are implicated in this phenomenon.Our results indicate that polyhomeotic mutations have a direct effect on epithelial integrity that can be uncoupled from overproliferation. We show that cells in an epithelium expressing different levels of polyhomeotic sort out indicating differential adhesive properties between the cell populations. Interestingly, we found distinct modalities between apical and basal expulsion of ph mutant cells and further studies of this phenomenon should allow parallels to be made with the modified adhesive and polarity properties of different types of epithelial tumors

Rab11 Is Required for Epithelial Cell Viability, Terminal Differentiation, and Suppression of Tumor-Like Growth in the Drosophila Egg Chamber

The Drosophila egg chamber provides an excellent system in which to study the specification and differentiation of epithelial cell fates because all of the steps, starting with the division of the corresponding stem cells, called follicle stem cells, have been well described and occur many times over in a single ovary.Here we investigate the role of the small Rab11 GTPase in follicle stem cells (FSCs) and in their differentiating daughters, which include main body epithelial cells, stalk cells and polar cells. We show that rab11-null FSCs maintain their ability to self renew, even though previous studies have shown that FSC self renewal is dependent on maintenance of E-cadherin-based intercellular junctions, which in many cell types, including Drosophila germline stem cells, requires Rab11. We also show that rab11-null FSCs give rise to normal numbers of cells that enter polar, stalk, and epithelial cell differentiation pathways, but that none of the cells complete their differentiation programs and that the epithelial cells undergo premature programmed cell death. Finally we show, through the induction of rab11-null clones at later points in the differentiation program, that Rab11 suppresses tumor-like growth of epithelial cells. Thus, rab11-null epithelial cells arrest differentiation early, assume an aberrant cell morphology, delaminate from the epithelium, and invade the neighboring germline cyst. These phenotypes are associated with defects in E-cadherin localization and a general loss of cell polarity.While previous studies have revealed tumor suppressor or tumor suppressor-like activity for regulators of endocytosis, our study is the first to identify such activity for regulators of endocytic recycling. Our studies also support the recently emerging view that distinct mechanisms regulate junction stability and plasticity in different tissues

Stroma Regulates Increased Epithelial Lateral Cell Adhesion in 3D Culture: A Role for Actin/Cadherin Dynamics

Cell shape and tissue architecture are controlled by changes to junctional proteins and the cytoskeleton. How tissues control the dynamics of adhesion and cytoskeletal tension is unclear. We have studied epithelial tissue architecture using 3D culture models and found that adult primary prostate epithelial cells grow into hollow acinus-like spheroids. Importantly, when co-cultured with stroma the epithelia show increased lateral cell adhesions. To investigate this mechanism further we aimed to: identify a cell line model to allow repeatable and robust experiments; determine whether or not epithelial adhesion molecules were affected by stromal culture; and determine which stromal signalling molecules may influence cell adhesion in 3D epithelial cell cultures.The prostate cell line, BPH-1, showed increased lateral cell adhesion in response to stroma, when grown as 3D spheroids. Electron microscopy showed that 9.4% of lateral membranes were within 20 nm of each other and that this increased to 54% in the presence of stroma, after 7 days in culture. Stromal signalling did not influence E-cadherin or desmosome RNA or protein expression, but increased E-cadherin/actin co-localisation on the basolateral membranes, and decreased paracellular permeability. Microarray analysis identified several growth factors and pathways that were differentially expressed in stroma in response to 3D epithelial culture. The upregulated growth factors TGFβ2, CXCL12 and FGF10 were selected for further analysis because of previous associations with morphology. Small molecule inhibition of TGFβ2 signalling but not of CXCL12 and FGF10 signalling led to a decrease in actin and E-cadherin co-localisation and increased paracellular permeability.In 3D culture models, paracrine stromal signals increase epithelial cell adhesion via adhesion/cytoskeleton interactions and TGFβ2-dependent mechanisms may play a key role. These findings indicate a role for stroma in maintaining adult epithelial tissue morphology and integrity

As Memórias de Lacroix: a instrução pública na França revolucionária, em geral, e o ensino de Matemática, em particular

O artigo - um exame hermenêutico do livro Essais sur l'enseignement en général, et sur celui des mathématiques en particulier, de 1805, de Sylvestre-François Lacroix, enfatizando sua segunda parte, na qual o autor discute seu Curso de Matemática Elementar, uma série de manuais escolares elaborados para a Escola Central das Quatro Nações - tem sua fundamentação ligada à Hermenêutica de Profundidade de Thompson conjugada a procedimentos de investigação textual sugeridos por Genette quanto aos paratextos editoriais. Defende que o livro de Lacroix é uma obra auto-referencial, de cunho claramente autobiográfico, que responde mais aos ideais iluministas da França do Setecentos que às perspectivas do século XIX, quando a obra circulou, tendo sido reeditada por quatro vezes, sob Napoleão, na primeira metade do Oitocentos. Raramente focalizado em trabalhos de pesquisa, o livro - cujas edições estão disponíveis eletronicamente - tem uma única tradução, ainda inédita, para o português