Static flow on complete noncompact manifolds I: short-time existence and asymptotic expansions at conformal infinity

In this paper, we study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant. For a static vacuum $(M^n,g,V),$ we also compute the asymptotic expansions of $g$ and $V$ at conformal infinity.Comment: 25 page

MACI - a new era?

Full thickness articular cartilage defects have limited regenerative potential and are a significant source of pain and loss of knee function. Numerous treatment options exist, each with their own advantages and drawbacks. The goal of this review is to provide an overview of the problem of cartilage injury, a brief description of current treatment options and outcomes, and a discussion of the current principles and technique of Matrix-induced Autologous Chondrocyte Implantation (MACI). While early results of MACI have been promising, there is currently insufficient comparative and long-term outcome data to demonstrate superiority of this technique over other methods for cartilage repair

Gene Expression Profiling of Soft and Firm Atlantic Salmon Fillet

Texture of salmon fillets is an important quality trait for consumer acceptance as well as for the suitability for processing. In the present work we measured fillet firmness in a population of farmed Atlantic salmon with known pedigree and investigated the relationship between this trait and gene expression. Transcriptomic analyses performed with a 21 K oligonucleotide microarray revealed strong correlations between firmness and a large number of genes. Highly similar expression profiles were observed in several functional groups. Positive regression was found between firmness and genes encoding proteasome components (41 genes) and mitochondrial proteins (129 genes), proteins involved in stress responses (12 genes), and lipid metabolism (30 genes). Coefficients of determination (R2) were in the range of 0.64–0.74. A weaker though highly significant negative regression was seen in sugar metabolism (26 genes, R2 = 0.66) and myofiber proteins (42 genes, R2 = 0.54). Among individual genes that showed a strong association with firmness, there were extracellular matrix proteins (negative correlation), immune genes, and intracellular proteases (positive correlation). Several genes can be regarded as candidate markers of flesh quality (coiled-coil transcriptional coactivator b, AMP deaminase 3, and oligopeptide transporter 15) though their functional roles are unclear. To conclude, fillet firmness of Atlantic salmon depends largely on metabolic properties of the skeletal muscle; where aerobic metabolism using lipids as fuel, and the rapid removal of damaged proteins, appear to play a major role

Seaweed polysaccharide-based hydrogels used for the regeneration of articular cartilage

This manuscript provides an overview of the in vitro and in vivo studies reported in the literature focusing on seaweed polysaccharides based hydrogels that have been proposed for applications in regenerative medicine, particularly, in the field of cartilage tissue engineering. For a better understanding of the main requisites for these specific applications, the main aspects of the native cartilage structure, as well as recognized diseases that affect this tissue are briefly described. Current available treatments are also presented to emphasize the need for alternative techniques. The following part of this review is centered on the description of the general characteristics of algae polysaccharides, as well as relevant properties required for designing hydrogels for cartilage tissue engineering purposes. An in-depth overview of the most well known seaweed polysaccharide, namely agarose, alginate, carrageenan and ulvan biopolymeric gels, that have been proposed for engineering cartilage is also provided. Finally, this review describes and summarizes the translational aspect for the clinical application of alternative systems emphasizing the importance of cryopreservation and the commercial products currently available for cartilage treatment.Authors report no declarations of interest. Authors thank the Portuguese Foundation for Science and Technology (FCT) for the PhD fellowship of Elena G. Popa (SFRH/BD/64070/2009) and research project (MIT/ECE/0047/2009). The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement no REGPOT-CT2012-316331-POLARIS

Ricci solitons, Ricci flow, and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua

The elliptic Einstein-DeTurck equation may be used to numerically find Einstein metrics on Riemannian manifolds. Static Lorentzian Einstein metrics are considered by analytically continuing to Euclidean time. Ricci-DeTurck flow is a constructive algorithm to solve this equation, and is simple to implement when the solution is a stable fixed point, the only complication being that Ricci solitons may exist which are not Einstein. Here we extend previous work to consider the Einstein-DeTurck equation for Riemannian manifolds with boundaries, and those that continue to static Lorentzian spacetimes which are asymptotically flat, Kaluza-Klein, locally AdS or have extremal horizons. Using a maximum principle we prove that Ricci solitons do not exist in these cases and so any solution is Einstein. We also argue that Ricci-DeTurck flow preserves these classes of manifolds. As an example we simulate Ricci-DeTurck flow for a manifold with asymptotics relevant for AdS_5/CFT_4. Our maximum principle dictates there are no soliton solutions, and we give strong numerical evidence that there exists a stable fixed point of the flow which continues to a smooth static Lorentzian Einstein metric. Our asymptotics are such that this describes the classical gravity dual relevant for the CFT on a Schwarzschild background in either the Unruh or Boulware vacua. It determines the leading O(N^2) part of the CFT stress tensor, which interestingly is regular on both the future and past Schwarzschild horizons.Comment: 48 pages, 7 figures; Version 2 - section 2.2.1 on manifolds with boundaries substantially modified, corrected and extended. Discussion in section 3.1 amended. References added and minor change