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

Layzer-Irvine equation: new perspectives and the role of interacting dark energy

We derive the Layzer-Irvine equation in the presence of a homogeneous (or quasi-homogeneous) dark energy component with an arbitrary equation of state. We extend the Layzer-Irvine equation to homogeneous and isotropic universes with an arbitrary number of dimensions and obtain the corresponding virial relation for sufficiently relaxed objects. We find analogous equations describing the dynamics of cosmic string loops and other p-branes of arbitrary dimensionality, discussing the corresponding relativistic and non-relativistic limits. Finally, we generalize the Layzer-Irvine equation to account for a non-minimal interaction between dark matter and dark energy, discussing its practical use as a signature of such an interaction.Comment: 4 page

Realistic clocks, universal decoherence and the black hole information paradox

Ordinary quantum mechanics is formulated on the basis of the existence of an ideal classical clock external to the system under study. This is clearly an idealization. As emphasized originally by Salecker and Wigner and more recently by other authors, there exist limits in nature to how ``classical'' even the best possible clock can be. When one introduces realistic clocks, quantum mechanics ceases to be unitary and a fundamental mechanism of decoherence of quantum states arises. We estimate the rate of universal loss of unitarity using optimal realistic clocks. In particular we observe that the rate is rapid enough to eliminate the black hole information puzzle: all information is lost through the fundamental decoherence before the black hole can evaporate. This improves on a previous calculation we presented with a sub-optimal clock in which only part of the information was lost by the time of evaporation.Comment: 3 Pages, RevTex, no figure

Modelling the complex nature of the tumor microenvironment: 3D tumor spheroids as an evolving tool

Cancer remains a serious burden in society and while the pace in the development of novel and more effective therapeutics is increasing, testing platforms that faithfully mimic the tumor microenvironment are lacking. With a clear shift from animal models to more complex in vitro 3D systems, spheroids emerge as strong options in this regard. Years of development have allowed spheroid-based models to better reproduce the biomechanical cues that are observed in the tumor-associated extracellular matrix (ECM) and cellular interactions that occur in both a cellâ cell and cell-ECM manner. Here, we summarize some of the key cellular interactions that drive tumor development, progression and invasion, and how successfully are these interactions recapitulated in 3D spheroid models currently in use in the field. We finish by speculating on future advancements in the field and on how these can shape the relevance of spherical 3D models for tumor modelling.Authors would like to acknowledge the fnancial support from the European Research Council through the Starting Grant “CapBed” (ERC-2018-STG-805411) and FCT/MCTES (Fundação para a Ciência e a Tecnologia/ Ministério da Ciência, Tecnologia, e Ensino Superior) through the grant SFRH/BD/119756/2016 (D.B.R.). The authors would additionally like to thank the contributions to this work from the project “TERM RES Hub—Scientifc Infrastructure for Tissue Engineering and Regenerative Medicine”, reference PINFRA/22190/2016 (Norte-01-0145-FEDER-022190), funded by the Portuguese National Science Foundation (FCT) in cooperation with the Northern Portugal Regional Coordination and Development Commission (CCDR-N). Ultimately, we would like to equally acknowledge fnancial support fromhttps://doi.org/10.54499/ UIDB/50026/2020);https://doi.org/10.54499/UIDP/50026/2020) andhttps://doi. org/10.54499/LA/P/0050/2020)

The disease-linked Glu-26-Lys mutant version of Coronin 1A exhibits pleiotropic and pathwayspecific signaling defects

This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License.Coronin 1A (Coro1A) is involved in cytoskeletal and signaling events, including the regulation of Rac1 GTPase– and myosin II–dependent pathways. Mutations that generate truncated or unstable Coro1A proteins cause immunodeficiencies in both humans and rodents. However, in the case of the peripheral T-cell–deficient (Ptcd) mouse strain, the immunodeficiency is caused by a Glu-26-Lys mutation that targets a surface-exposed residue unlikely to affect the intramolecular architecture and stability of the protein. Here we report that this mutation induces pleiotropic effects in Coro1A protein, including the exacerbation of Coro1A-dependent actin-binding and -bundling activities; the formation of large meshworks of Coro1AE26K-decorated filaments endowed with unusual organizational, functional, and staining properties; and the elimination of Coro1A functions associated with both Rac1 and myosin II signaling. By contrast, it does not affect the ability of Coro1A to stimulate the nuclear factor of activated T-cells (NF-AT). Coro1AE26K is not a dominant-negative mutant, indicating that its pathological effects are derived from the inability to rescue the complete loss of the wild-type counterpart in cells. These results indicate that Coro1AE26K behaves as either a recessive gain-of-function or loss-of-function mutant protein, depending on signaling context and presence of the wild-type counterpart in cells.This work has been supported by grants to X.R.B. from the Castilla-León Autonomous Government (CSI101U13), the Spanish Ministry of Economy and Competitiveness (SAF2012-31371, RD12/0036/0002), the Solórzano Foundation, and the Ramón Areces Foundation. Spanish government–sponsored funding is partially supported by the European Regional Development Fund.Peer Reviewe

Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces

The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion systemwith cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with linear cross-diffusion in both u and v is presented. The finite element method is based on the approximation of the domain or surface by a triangulated domain or surface consisting of a union of triangles. For surfaces, the vertices of the triangulation lie on the continuous surface. A finite element space of functions is then defined by taking the continuous functions which are linear affine on each simplex of the triangulated domain or surface. To demonstrate the role of cross-diffusion to the theory of pattern formation, we compute patterns with model kinetic parameter values that belong only to the cross-diffusion parameter space; these do not belong to the standard parameter space for classical reaction-diffusion systems. Numerical results exhibited show the robustness, flexibility, versatility, and generality of our methodology; the methodology can deal with complicated evolution laws of the domain and surface, and these include uniform isotropic and anisotropic growth profiles as well as those profiles driven by chemical concentrations residing in the domain or on the surface

Shading Effect on Production and Protein Concentration of \u3cem\u3eDactylis Glomerata\u3c/em\u3e and \u3cem\u3eAgrostis Tenuis\u3c/em\u3e

Silvopastoral systems make compatible livestock and timber production and provide important advantages from economic and ecological points of view (Sibbald, 1996). Around one million ha of new afforested areas promoted by the EU Common Agricultural Policy have been established in the last decade, that can be used as potential silvopastoral system areas. Pasture production is usually reduced in dense stands as trees grow up due to the light interception by the tree crown, but the radiation reaching the soil will depend on the tree type and this will affect herbaceous species composition and development. The aim of this work was to evaluate the shading effect (0 and 50 % of light interception) on pasture production and composition of monocultures of cocksfoot (Dactylis glomerata L. var. Artabro) and bent grass (Agrostis tenuis Sibth. cv Highland) in simulated conditions

Thermomechanical analysis of cold formed steel sections

This work presents an experimental study about cold formed steel elements submitted to compression loads. The sections analyzed are C and Z sections made of steel sheet with 1.5 and 2 [mm] thick and three different cross section heights. The compression tests were made at ambient and elevated temperatures. In both cases a pined support was developed and used. The member resistance at ambient temperature was determined by applying an increasing compression load until the member collapse was achieved. The fire tests were performed in a fire resistance furnace, using the same type of end supports, and a mechanical load given by a specific degree of utilization that is maintained constant during the fire test. These tests allow the determination of the fire resistance time and member critical temperature. The experimental results are compared with the ones obtained with the Eurocode simplified models.info:eu-repo/semantics/publishedVersio

Thermomechanical analysis of cold formed steel sections

This work presents an experimental study about cold formed steel elements submitted to compression loads. The sections analyzed are C and Z sections made of steel sheet with 1.5 and 2 [mm] thick and three different cross section heights. The compression tests were made at ambient and elevated temperatures. In both cases a pined support was developed and used. The member resistance at ambient temperature was determined by applying an increasing compression load until the member collapse was achieved. The fire tests were performed in a fire resistance furnace, using the same type of end supports, and a mechanical load given by a specific degree of utilization that is maintained constant during the fire test. These tests allow the determination of the fire resistance time and member critical temperature. The experimental results are compared with the ones obtained with the Eurocode simplified models.info:eu-repo/semantics/publishedVersio

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