Matrix-F5 algorithms and tropical Gr\"obner bases computation

Let $K$ be a field equipped with a valuation. Tropical varieties over $K$ can be defined with a theory of Gr\"obner bases taking into account the valuation of $K$. Because of the use of the valuation, this theory is promising for stable computations over polynomial rings over a $p$-adic fields.We design a strategy to compute such tropical Gr\"obner bases by adapting the Matrix-F5 algorithm. Two variants of the Matrix-F5 algorithm, depending on how the Macaulay matrices are built, are available to tropical computation with respective modifications. The former is more numerically stable while the latter is faster.Our study is performed both over any exact field with valuation and some inexact fields like $\mathbb{Q}\_p$ or $\mathbb{F}\_q \llbracket t \rrbracket.$ In the latter case, we track the loss in precision, and show that the numerical stability can compare very favorably to the case of classical Gr\"obner bases when the valuation is non-trivial. Numerical examples are provided

SUSY Production From TeV Scale Blackhole at LHC

If the fundamental Planck scale is near a TeV, then we should expect to see TeV scale black holes at the LHC. Similarly, if the scale of supersymmetry breaking is sufficiently low, then we might expect to see light supersymmetric particles in the next generation of colliders. If the mass of the supersymmetric particle is of order a TeV and is comparable to the temperature of a typical TeV scale black hole, then such sparticles will be copiously produced via Hawking radiation: The black hole will act as a resonance for sparticles, among other things. In this paper we compared various signatures for SUSY production at LHC, and we contrasted the situation where the sparticles are produced directly via parton fusion processes with the situation where they are produced indirectly through black hole resonances. We found that black hole resonances provide a larger source for heavy mass SUSY (squark and gluino) production than the direct pQCD-SUSY production via parton fusion processes depending on the values of the Planck mass and blackhole mass. Hence black hole production at LHC may indirectly act as a dominant channel for SUSY production. We also found that the differential cross section d\sigma/dp_t for SUSY production increases as a function of the p_t (up to p_t equal to about 1 TeV or more) of the SUSY particles (squarks and gluinos), which is in sharp contrast with the pQCD predictions where the differential cross section d\sigma/dp_t decreases as p_t increases for high p_t about 1 TeV or higher. This is a feature for any particle emission from TeV scale blackhole as long as the temperature of the blackhole is very high (~ TeV). Hence measurement of increase of d\sigma/dp_t with p_t for p_t up to about 1 TeV or higher for final state particles might be a useful signature for blackhole production at LHC.Comment: Final Version, To Appear in Phys. Rev.

Mitofusins Mfn1 and Mfn2 coordinately regulate mitochondrial fusion and are essential for embryonic development

Mitochondrial morphology is determined by a dynamic equilibrium between organelle fusion and fission, but the significance of these processes in vertebrates is unknown. The mitofusins, Mfn1 and Mfn2, have been shown to affect mitochondrial morphology when overexpressed. We find that mice deficient in either Mfn1 or Mfn2 die in midgestation. However, whereas Mfn2 mutant embryos have a specific and severe disruption of the placental trophoblast giant cell layer, Mfn1-deficient giant cells are normal. Embryonic fibroblasts lacking Mfn1 or Mfn2 display distinct types of fragmented mitochondria, a phenotype we determine to be due to a severe reduction in mitochondrial fusion. Moreover, we find that Mfn1 and Mfn2 form homotypic and heterotypic complexes and show, by rescue of mutant cells, that the homotypic complexes are functional for fusion. We conclude that Mfn1 and Mfn2 have both redundant and distinct functions and act in three separate molecular complexes to promote mitochondrial fusion. Strikingly, a subset of mitochondria in mutant cells lose membrane potential. Therefore, mitochondrial fusion is essential for embryonic development, and by enabling cooperation between mitochondria, has protective effects on the mitochondrial population

Topical delivery of a Rho-kinase inhibitor to the cornea via mucoadhesive film

The application of inhibitors of the Rho kinase pathway (ROCK inhibitors) to the surface of the eye in the form of eyedrops has beneficial effects which aid the recovery of diseased or injured endothelial cells that line the inner surface of the cornea. The aim of this study was to test the plausibility of delivering a selective ROCK inhibitor, Y-27,632, to the cornea using a thin polymeric film. Mucoadhesive polymeric thin films were prepared incorporating Y-27,632 and diffusional release into PBS was determined. Topical ocular delivery from the applied film was investigated using freshly excised porcine eyes and eyedrops of equivalent concentration acted as comparators; after 24 h the formulations were removed and the corneas extracted. Drug-loaded thin polymeric films, with high clarity and pliability were produced. ROCK inhibitor Y-27,632 was weakly retained within the film, with release attaining equilibrium after 1 h. This in turn facilitated its rapid ocular delivery, and an approximately three-fold greater penetration of Y-27,632 into cryoprobe-treated corneas was observed from the thin film (p < 0.01) compared to eyedrop. These findings support the further development of ROCK inhibitor delivery to the cornea via release from thin mucoadhesive films to treat vision loss cause by corneal endothelial dysfunction

Course of FEV1 after Onset of Bronchiolitis Obliterans Syndrome in Lung Transplant Recipients

Rationale: Bronchiolitis obliterans syndrome (BOS), defined by loss of lung function, develops in the majority of lung transplant recipients. However, there is a paucity of information on the subsequent course of lung function in these patients. Objectives: To characterize the course of FEV1 over time after development of BOS and to determine the predictors that influence the rate of functional decline of FEV1. Methods: FEV1% predicted (FEV1%pred) trajectories were studied in 111 lung transplant recipients with BOS by multivariate, linear, mixed-effects statistical models. Measurements and Main Results: FEV1%pred varied over time after BOS onset, with the steepest decline typically seen in the first 6 months (12% decline; p < 0.0001). Bilateral lung transplant recipients had significantly higher FEV1%pred at BOS diagnosis (71 vs. 47%; p < 0.0001) and at 24 months after BOS onset (58 vs. 41%; p = 0.0001). Female gender and pretransplant diagnosis of idiopathic pulmonary fibrosis were associated with a steeper decline in FEV1%pred in the first 6 months after BOS diagnosis (p = 0.02 and 0.04, respectively). A fall in FEV1 greater than 20% in the 6 months preceding BOS (termed “rapid onset”) was associated with shorter time to BOS onset (p = 0.01), lower FEV1%pred at BOS onset (p < 0.0001), steeper decline in the first 6 months (p = 0.03), and lower FEV1%pred at 2 years after onset (p = 0.0002). Conclusions: Rapid onset of BOS, female gender, pretransplant diagnosis of idiopathic pulmonary fibrosis, and single-lung transplantation are associated with worse pulmonary function after BOS onset.Supported in part by National Institutes of Health grants K23 HL077719 (V.N.L.) and K24 HL04212 (F.J.M.), and by a grant from the American Society of Transplantation/ Chest Foundation (V.N.L.).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91969/1/2007 AJRCCM Course of FEV1 after Onset of Bronchiolitis Obliterans Syndrome in Lung Transplant Recipients.pd