On Chern-Simons theory with an inhomogeneous gauge group and BF theory knot invariants

We study the Chern-Simons topological quantum field theory with an inhomogeneous gauge group, a non-semi-simple group obtained from a semi-simple one by taking its semi-direct product with its Lie algebra. We find that the standard knot observables (i.e. traces of holonomies along knots) essentially vanish, but yet, the non-semi-simplicity of our gauge group allows us to consider a class of un-orthodox observables which breaks gauge invariance at one point and which lead to a non-trivial theory on long knots in $\mathbb{R}^3$. We have two main morals : 1. In the non-semi-simple case, there is more to observe in Chern-Simons theory! There might be other interesting non semi-simple gauge groups to study in this context beyond our example. 2. In our case of an inhomogeneous gauge group, we find that Chern-Simons theory with the un-orthodox observable is actually the same as 3D BF theory with the Cattaneo-Cotta-Ramusino-Martellini knot observable. This leads to a simplification of their results and enables us to generalize and solve a problem they posed regarding the relation between BF theory and the Alexander-Conway polynomial. Our result is that the most general knot invariant coming from pure BF topological quantum field theory is in the algebra generated by the coefficients of the Alexander-Conway polynomial.Comment: To appear in Journal of Mathematical Physics vol.46 issue 12. Available on http://link.aip.org/link/jmapaq/v46/i1

The universal Khovanov link homology theory

We determine the algebraic structure underlying the geometric complex associated to a link in Bar-Natan's geometric formalism of Khovanov's link homology theory (n=2). We find an isomorphism of complexes which reduces the complex to one in a simpler category. This reduction enables us to specify exactly the amount of information held within the geometric complex and thus state precisely its universality properties for link homology theories. We also determine its strength as a link invariant relative to the different topological quantum field theories (TQFTs) used to create link homology. We identify the most general (universal) TQFT that can be used to create link homology and find that it is "smaller" than the TQFT previously reported by Khovanov as the universal link homology theory. We give a new method of extracting all other link homology theories (including Khovanov's universal TQFT) directly from the universal geometric complex, along with new homology theories that hold a controlled amount of information. We achieve these goals by making a classification of surfaces (with boundaries) modulo the 4TU/S/T relations, a process involving the introduction of genus generating operators. These operators enable us to explore the relation between the geometric complex and its algebraic structure.Comment: This is the version published by Algebraic & Geometric Topology on 1 November 200

Numerical Calculation of Three-Dimensional Turbulent Flow in Compound Rectangular Open Channels

The hydrodynamic response of the turbulent flow in a compound rectangular open channel to the flood plain depth, roughness, and symmetry and to the channel Reynolds number was demonstrated. The flow in the four basic asymmetric channels measured by Tominaga and Nezu (1991) was numerically simulated, as well as other channel configurations including symmetric channels. Turbulence was modeled by the energy dissipation model, combined with the algebraic stress model suggested by Naot and Rodi (1982). The three-dimensional flow with secondary currents in compound open channels was solved numerically using the parabolic pressure correction algorithm of Patankar and Spalding (1972). The examples suggest data bases for the estimation of friction factors, and for the mass exchange rate between the flood plain interior and its threshold. A possible explanation for the multi-cellular structure in wide open channels is also given

Universal Model of Finite-Reynolds Number Turbulent Flow in Channels and Pipes

In this Letter we suggest a simple and physically transparent analytical model of the pressure driven turbulent wall-bounded flows at high but finite Reynolds numbers Re. The model gives accurate qualitative description of the profiles of the mean-velocity and Reynolds-stresses (second order correlations of velocity fluctuations) throughout the entire channel or pipe in the wide range of Re, using only three Re-independent parameters. The model sheds light on the long-standing controversy between supporters of the century-old log-law theory of von-K\`arm\`an and Prandtl and proposers of a newer theory promoting power laws to describe the intermediate region of the mean velocity profile.Comment: 4 pages, 6 figs, re-submitted PRL according to referees comment

Ghrelin is an Osteoblast Mitogen and Increases Osteoclastic Bone Resorption In Vitro

Ghrelin is released in response to fasting, such that circulating levels are highest immediately prior to meals. Bone turnover is acutely responsive to the fed state, with increased bone resorption during fasting and suppression during feeding. The current study investigated the hypothesis that ghrelin regulates the activity of bone cells. Ghrelin increased the bone-resorbing activity of rat osteoclasts, but did not alter osteoclast differentiation in a murine bone marrow assay nor bone resorption in ex vivo calvarial cultures. Ghrelin showed mitogenic activity in osteoblasts, with a strong effect in human cells and a weaker effect in rat osteoblasts. The expression of the human ghrelin receptor, GHSR, varied among individuals and was detectable in 25–30% of bone marrow and osteoblast samples. However, the rodent Ghsr expression was undetectable in bone cells and cell lines from rat and mouse. These data suggest that elevated levels of ghrelin may contribute to the higher levels of bone turnover that occurs in the fasted state

Changes in body composition and metabolic profile during interleukin 6 inhibition in rheumatoid arthritis

Background Rheumatoid arthritis (RA) is a chronic inflammatory disease characterized by increased mortality associated with cardiometabolic disorders including dyslipidaemia, insulin resistance, and cachectic obesity. Tumour necrosis factor inhibitors and interleukin 6 receptor blocker licensed for the treatment of RA decrease inflammation and could thus improve cardiovascular risk, but their effects on body composition and metabolic profile need to be clarified. We investigated the effects of tocilizumab (TCZ), a humanized anti‐interleukin 6 receptor antibody, on body composition and metabolic profile in patients treated for RA. Methods Twenty‐one active RA patients treated with TCZ were included in a 1 year open follow‐up study. Waist circumference, body mass index, blood pressure, lipid profile, fasting glucose, insulin, serum levels of adipokines and pancreatic/gastrointestinal hormones, and body composition (dual‐energy X‐ray absorptiometry) were measured at baseline and 6 and 12 months of treatment. At baseline, RA patients were compared with 21 non‐RA controls matched for age, sex, body mass index, and metabolic syndrome. Results Compared with controls, body composition was altered in RA with a decrease in total and appendicular lean mass, whereas fat composition was not modified. Among RA patients, 28.6% had a skeletal muscle mass index below the cut‐off point for sarcopaenia (4.8% of controls). After 1 year of treatment with TCZ, there was a significant weight gain without changes for fat mass. In contrast, an increase in lean mass was observed with a significant gain in appendicular lean mass and skeletal muscle mass index between 6 and 12 months. Distribution of the fat was modified with a decrease in trunk/peripheral fat ratio and an increase in subcutaneous adipose tissue. No changes for waist circumference, blood pressure, fasting glucose, and atherogenic index were observed. Conclusions Despite weight gain during treatment with TCZ, no increase in fat but a modification in fat distribution was observed. In contrast, muscle gain suggests that blocking IL‐6 might be efficient in treating sarcopaenia associated with RA

Juvenile Paget’s disease with compound heterozygous mutations in TNFRSF11B presenting with recurrent clavicular fractures and a mild skeletal phenotype

Juvenile Paget’s disease (JPD) is a rare recessively-inherited bone dysplasia. The great majority of cases described to date have had homozygous mutations in TNFRSF11B, the gene encoding osteoprotegerin. We describe a boy who presented with recurrent clavicular fractures following minor trauma (8 fractures from age 2 to 11). He was of normal height and despite mild lateral bowing of the thighs and anterior bowing of the shins he remained physically active. Abnormal modelling was noted in ribs and humeri on clavicular radiographs, and a skeletal survey at the age of 7 showed generalised diaphyseal expansion of the long bones with thickening of the periosteal and endosteal surfaces of the cortices. On biochemical evaluation, serum alkaline phosphatase was noted to be persistently elevated. The diagnosis of JPD was confirmed by the finding of compound heterozygous mutations in TNFRSF11B: a maternally-inherited A > G missense mutation at position 1 of the first amino acid codon (previously reported) and a paternally-inherited splice acceptor site mutation in intron 3 at a highly conserved position (not previously reported). Bioinformatics analysis suggested both mutations were disease-causing. Compound heterozygote mutations in TNFRSF11B causing JPD have been previously reported only once – in a boy who also had a relatively mild skeletal phenotype. The milder features may lead to delay in diagnosis and diagnostic confusion with other entities, but the extraskeletal features of JPD may nonetheless develop

Determining leaf area index and leafy tree roughness using terrestrial laser scanning

Vegetation roughness, and more specifically forest roughness, is a necessary component in better defining flood dynamics both in the sense of changes in river catchment characteristics and the dynamics of forest changes and management. Extracting roughness parameters from riparian forests can be a complicated process involving different components for different required scales and flow depths. For flow depths that enter a forest canopy, roughness at both the woody branch and foliage level is necessary. This study attempts to extract roughness for this leafy component using a relatively new remote sensing technique in the form of terrestrial laser scanning. Terrestrial laser scanning is used in this study due to its ability to obtain millions of points within relatively small forest stands. This form of lidar can be used to determine the gaps present in foliaged canopies in order to determine the leaf area index. The leaf area index can then be directly input into resistance equations to determine the flow resistance at different flow depths. Leaf area indices created using ground scanning are compared in this study to indices calculated using simple regression equations. The dominant riparian forests investigated in this study are planted and natural poplar forests over a lowland section of the Garonne River in Southern France. Final foliage roughness values were added to woody branch roughness from a previous study, resulting in total planted riparian forest roughness values of around Manning's n = 0.170–0.195 and around n = 0.245–330 for in-canopy flow of 6 and 8 m, respectively, and around n = 0.590 and around n = 0.750 for a natural forest stand at the same flow depths