Exponential dichotomies of evolution operators in Banach spaces

This paper considers three dichotomy concepts (exponential dichotomy, uniform exponential dichotomy and strong exponential dichotomy) in the general context of non-invertible evolution operators in Banach spaces. Connections between these concepts are illustrated. Using the notion of Green function, we give necessary conditions and sufficient ones for strong exponential dichotomy. Some illustrative examples are presented to prove that the converse of some implication type theorems are not valid

Generalized nonuniform dichotomies and local stable manifolds

We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform dichotomy for the evolution operator that contains the nonuniform exponential and polynomial dichotomies as a very particular case. The family of dichotomies considered allow situations for which the classical Lyapunov exponents are zero. Additionally, we give new examples of application of our stable manifold theorem and study the behavior of the dynamics under perturbations.Comment: 18 pages. New version with minor corrections and an additional theorem and an additional exampl

Unravelling the path to create a cell sheet-based model of skin scar-like tissue

Regardless of the advances in understanding the mechanisms and the pathophysiology behind skin deformities, scaring continues to be an unsolved clinical problem. The underlying wound healing process involves a series of key cells which play different key roles. Fibroblasts are known to suffer the influence of local biochemical (e.g TGF-B1) and biomechanical signaling upon a wound scenario leading to a phenotypical change into myofibroblasts. The latter enhance immature extracellular matrix (ECM) synthesis and generate tensional forces that leads to ECM reorganization. Certain skin pathologies (e.g hypertrophic scars) rise from a dysfunction of this underlying regulatory mechanism which in turn drives myofibroblast persistence in the wound. When trying to study the mechanisms behind scarring human ex vivo samples are many times scarce and most of the current in vitro systems rely on standard 2D cultures of keloid/hypertrophic scar fibroblasts. Taking all of this into consideration we propose the use of cell sheet technology to create an in vitro 3D scar model. Herein we report the effect of TGF-B1 in human dermal fibroblast cell sheets as the first step to attain cell sheets with a myofibroblast-like phenotype in which cells are embedded in a scar-like ECM. To further strengthen our concept we performed the stacking of pre-formed cell sheets generating a cohesive 3D scar-like tissue. Human dermal fibroblast (hDFbs) cell sheets were produced as previously described1, and stimulated with TGF-B1 (10ng/ml) over 7, 14 and 21 days. Following phenotype and ECM characterization, cell sheets were stacked in order to obtain a 3D structure composed of 2 or 3 cell-sheets. The analysis of key genes (q-PCR) and proteins (Western blot and immunocytochemistry) showed that hDFbs cell sheets, when stimulated with TGF-B1 present an increased expression of a-SMA, fibronectin (FN) ED- A and FN ED-B, characteristic of a myofibroblast-like phenotype. When looking into the expression of scar ECM-associated proteins, hDFbs cell sheets obtained in the presence of TGF-B1 produced higher amounts of fibronectin and collagen I. Stable 3D constructs with a noticeable level of integration after a total of 21 days of culture, were further created upon stacking of the cell sheets obtained after 7days of culture in the presence of TGF-B1. In conclusion, this work suggested that it is possible to promote the secretion of scar-like ECM in hDFbs cell sheets due to phenotypic changes into myofibroblast-like cells when stimulated with TGF-B1. Cohesive 3D scar-like tissue structures were obtained which opens the possibility to develop a highly accurate in vitro 3D scar model to study underlying cellular mechanisms involved in the wound healing deregulation. Grant IF/00945/2014 funded by FCT/MCTES, Project “NORTE-08-5369-FSE-000044”, funded by Programa Operacional Norte 2020 Fundo Social Europeu, and GENE2SKIN Twinning Project, Horizon 2020, funded by the European Commissioninfo:eu-repo/semantics/publishedVersio

In vitro 3D cell sheet-based model for unraveling scar pathophysiology

Fibroblasts are key players in the scarring process. In hypertrophic scars, fibroblasts suffer phenotypical changes into myofibroblasts persisting in the wound under the influence of local biochemical (TGFb1) and biomechanical signaling leading to enhanced immature extracellular matrix (ECM) synthesis. Benchtop models of hypertrophic scars rely on scarce human ex vivo samples or standard 2D cultures of hypertrophic scar fibroblasts. We therefore propose the use of human dermal fibroblast cell sheets (hDFbsCS) as the first step to attain cell sheets with a myofibroblast-like phenotype to generate cohesive in vitro 3D scar-like tissues. hDFbsCS were produced as previously described (Cerqueira, 2014), and stimulated with TGFb1 up to 21 days. Following phenotype and ECM characterization, 3 hDFbsCS were stacked to obtain a 3D structure. Gene and protein analysis showed that upon TGFb1 stimulation, hDFbsCS present a higher expression of aSMA, fibronectin EDA and EDB, characteristic of amyofibroblast-like phenotype. Regarding the expression of scar ECM-associated proteins, TGFb1 stimulated hDFbsCS produced increased fibronectin and collagen I. Upon stacking of hDFbsCS obtained after 7 days of culture in the presence of TGFb1, stable and integrated 3D constructs were obtained. This work suggests that it is possible to create cohesive 3D scar-like tissue structures from hDFbsCS opening the possibility to develop in vitro 3D scar models to study wound healing deregulation pathophysiology. Acknowledgments: Grant IF.00945.2014 and SFRH.BD. 119756.2016 (FCT MCTES), NORTE.08.5369.FSE.000044 (funded by Programa Operacional Norte 2020 Fundo Social Europeu), GENE2SKIN Twinning Project, Horizon 2020 (European Commission).Grant IF.00945.2014 and SFRH.BD.119756.2016 (FCT_MCTES), NORTE.08.5369.FSE.000044 (funded by Programa_Operacional_Norte_2020 Fundo Social Europeu), GENE2SKIN Twinning Project, Horizon_2020 (European Commission).info:eu-repo/semantics/publishedVersio

Correlação funcional e ecográfica no tratamento cirúrgico da coifa dos rotadores com seguimento superior a 5 anos

bjectivo: a reparação cirúrgica da coifa dos rotadores visa eliminar a dor e restaurar a função, com sucesso entre 5-90%. A dimensão da ruptura condiciona o resultado. Este estudo visa a eficácia do tratamento cirúrgico com o mínimo de 5 anos de seguimento e correlaciona resultado funcional com achados ecográficos. Material e Métodos: entre 2002 e 2007 o mesmo cirurgião realizou 166 suturas da coifa dos rotadores em 156 doentes. As ecografias pré e pós-operatórias foram sempre realizadas pelo mesmo radiologista. Retrospectivamente avaliou-se tipo de ruptura, cirurgia, sutura e material, complicações, dor (VAS), retorno laboral/atividades e inquirido o grau de satisfação. Completaram follow-up (FU) com avaliação funcional (Constant-Murley Score e UCLA Shoulder Score) e ecográfica 77 doentes, correspondendo a 87 rupturas. Resultados: A idade média foi 55,6 anos (22-77) com FU de 7,4 anos (5-11). Verificaram-se 145 (87,3%) rupturas completas sendo 14 (9,7%) maciças e 61 (42,1%) grandes. Realizaram-se 122 (73,5%) suturas artroscópicas, sendo 44 (26,5%) por mini-open. A avaliação funcional foi 72 (31-100) Constant Score e 29 (19-35) UCLA Score. O VAS foi 2,89 (0-8) com 29 (43,3%) doentes assintomáticos. Ocorreram 4 complicações (2,4%). Ecograficamente, verificou-se 29/87 (33,3%) re-rupturas, 32,3% artroscópicas e 40,1% abertas, lembrando que a sutura aberta foi usada em rupturas maiores. Retomaram atividades 95,5% dos doentes. Registou-se 100% de satisfação relativamente ao pré-operatório. Conclusão: este estudo reforça o impacto do tratamento cirúrgico na dor e verifica eficácia consistente se houver seleção criteriosa. A re-ruptura avaliada ecograficamente nem sempre se correlaciona com função, intervindo outros factores

Dominated Splitting and Pesin's Entropy Formula

Let $M$ be a compact manifold and $f:\,M\to M$ be a $C^1$ diffeomorphism on $M$. If $\mu$ is an $f$-invariant probability measure which is absolutely continuous relative to Lebesgue measure and for $\mu$ $a.\,\,e.\,\,x\in M,$ there is a dominated splitting $T_{orb(x)}M=E\oplus F$ on its orbit $orb(x)$, then we give an estimation through Lyapunov characteristic exponents from below in Pesin's entropy formula, i.e., the metric entropy $h_\mu(f)$ satisfies $$h_{\mu}(f)\geq\int \chi(x)d\mu,$$ where $\chi(x)=\sum_{i=1}^{dim\,F(x)}\lambda_i(x)$ and $\lambda_1(x)\geq\lambda_2(x)\geq...\geq\lambda_{dim\,M}(x)$ are the Lyapunov exponents at $x$ with respect to $\mu.$ Consequently, by using a dichotomy for generic volume-preserving diffeomorphism we show that Pesin's entropy formula holds for generic volume-preserving diffeomorphisms, which generalizes a result of Tahzibi in dimension 2

Thermodynamic formalism for contracting Lorenz flows

We study the expansion properties of the contracting Lorenz flow introduced by Rovella via thermodynamic formalism. Specifically, we prove the existence of an equilibrium state for the natural potential $\hat\phi_t(x,y, z):=-t\log J_{(x, y, z)}^{cu}$ for the contracting Lorenz flow and for $t$ in an interval containing $[0,1]$. We also analyse the Lyapunov spectrum of the flow in terms of the pressure

Entropy of semiclassical measures for nonpositively curved surfaces

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of nonpositive sectional curvature. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound. We follow the same main strategy as in the Anosov case (arXiv:0809.0230). We focus on the main differences and refer the reader to (arXiv:0809.0230) for the details of analogous lemmas.Comment: 20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work (arXiv:0809.0230, version 2

Lyapunov spectrum of asymptotically sub-additive potentials

For general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov exponents, measure-theoretic entropies and topological pressures in this general situation. Most of our results are obtained without the assumption of the existence of unique equilibrium measures or the differentiability of pressure functions. Some examples are constructed to illustrate the irregularity and the complexity of multifractal behaviors in the sub-additive case and in the case that the entropy map that is not upper-semi continuous.Comment: 44 page

Multifractal properties of return time statistics

Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets of dimensions is established. Theoretical analysis and numerical examples of dynamical systems in the class of Iterated Functions are presented.Comment: 4 pages, 3 figure