Quantitative isoperimetric inequalities for log-convex probability measures on the line

The purpose of this paper is to analyze the isoperimetric inequality for symmetric log-convex probability measures on the line. Using geometric arguments we first re-prove that extremal sets in the isoperimetric inequality are intervals or complement of intervals (a result due to Bobkov and Houdr\'e). Then we give a quantitative form of the isoperimetric inequality, leading to a somehow anomalous behavior. Indeed, it could be that a set is very close to be optimal, in the sense that the isoperimetric inequality is almost an equality, but at the same time is very far (in the sense of the symmetric difference between sets) to any extremal sets! From the results on sets we derive quantitative functional inequalities of weak Cheeger type

Non perturbative study of QCD on a 2+2 anisotropic lattice

We present preliminary results for a non perturbative determination of the parameters in the action required to restore Lorentz invariance in long distance correlators, using the static interquark potential. Comparison with analytical results is made and further applications are discussed.Comment: 3 pages, Lattice2003 (improvement

Evaluation of the Water Film Weber Number in Glaze Icing Scaling

Icing scaling tests were performed in the NASA Glenn Icing Research Tunnel to evaluate a new scaling method, developed and proposed by Feo for glaze icing, in which the scale liquid water content and velocity were found by matching reference and scale values of the nondimensional water-film thickness expression and the film Weber number. For comparison purpose, tests were also conducted using the constant We(sub L) method for velocity scaling. The reference tests used a full-span, fiberglass, 91.4-cm-chord NACA 0012 model with velocities of 76 and 100 knot and MVD sizes of 150 and 195 microns. Scale-to-reference model size ratio was 1:2.6. All tests were made at 0deg AOA. Results will be presented for stagnation point freezing fractions of 0.3 and 0.5

Post-translational deregulation of YAP1 is genetically controlled in rat liver cancer and determines the fate and stem-like behavior of the human disease

Previous studies showed that YAP1 is over-expressed in hepatocellular carcinoma (HCC). Here we observed higher expression of Yap1/Ctgf axis in dysplastic nodules and HCC chemically-induced in F344 rats, genetically susceptible to hepatocarcinogenesis, than in lesions induced in resistant BN rats. In BN rats, highest increase in Yap1-tyr357, p73 phosphorylation and Caspase 3 cleavage occurred. In human HCCs with poorer prognosis ( 3 years survival; HCCB). In the latter, higher levels of phosphorylated YAP1-ser127, YAP1-tyr357 and p73, YAP1 ubiquitination, and Caspase 3 cleavage occurred. Expression of stemness markers NANOG, OCT-3/4, and CD133 were highest in HCCP and correlated with YAP1 and YAP1-TEAD levels. In HepG2, Huh7, and Hep3B cells, forced YAP1 over-expression led to stem cell markers expression and increased cell viability, whereas inhibition of YAP1 expression by specific siRNA, or transfection of mutant YAP1 which does not bind to TEAD, induced opposite alterations. These changes were associated, in Huh7 cells transfected with YAP1 or YAP1 siRNA, with stimulation or inhibition of cell migration and invasivity, respectively. Furthermore, transcriptome analysis showed that YAP1 transfection in Huh7 cells induces over-expression of genes involved in tumor stemness. In conclusion, Yap1 post-translational modifications favoring its ubiquitination and apoptosis characterize HCC with better prognosis, whereas conditions favoring the formation of YAP1-TEAD complexes are associated with aggressiveness and acquisition of stemness features by HCC cells

Phase diagram of the lattice Wess-Zumino model from rigorous lower bounds on the energy

We study the lattice N=1 Wess-Zumino model in two dimensions and we construct a sequence $\rho^{(L)}$ of exact lower bounds on its ground state energy density $\rho$, converging to $\rho$ in the limit $L\to\infty$. The bounds $\rho^{(L)}$ can be computed numerically on a finite lattice with $L$ sites and can be exploited to discuss dynamical symmetry breaking. The transition point is determined and compared with recent results based on large-scale Green Function Monte Carlo simulations with good agreement.Comment: 32 pages, 12 figure

Pleiotropic effects of methionine adenosyltransferases deregulation as determinants of liver cancer progression and prognosis

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The Three-Loop Lattice Free Energy

We calculate the free energy of SU(N) gauge theories on the lattice, to three loops. Our result, combined with Monte Carlo data for the average plaquette, gives a more precise estimate of the gluonic condensate.Comment: 5 pages + 2 figures (PostScript); report no. IFUP-TH 17/9

A Model for QCD at High Density and Large Quark Mass

We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion and choosing Polyakov type of loops as the main dynamical variables representing the fermionic matter. To get a first idea of the phase structure, the model is analyzed in strong coupling expansion and using a mean field approximation. In numerical simulations, the model still shows the so-called sign problem, a difficulty peculiar to non-zero chemical potential, but it permits the development of algorithms which ensure a good overlap of the Monte Carlo ensemble with the true one. We review the main features of the model and present calculations concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the diquark susceptibility, which may be used to characterize the various phases expected at high baryonic density. We obtain in this way information about the phase structure of the model and the corresponding phase transitions and cross over regions, which can be considered as hints for the behaviour of non-zero density QCD.Comment: 21 pages, 29 figure

The Supersymmetric Ward-Takahashi Identity in 1-Loop Lattice Perturbation Theory. I. General Procedure

The one-loop corrections to the lattice supersymmetric Ward-Takahashi identity (WTi) are investigated in the off-shell regime. In the Wilson formulation of the N=1 supersymmetric Yang-Mills (SYM) theory, supersymmetry (SUSY) is broken by the lattice, by the Wilson term and is softly broken by the presence of the gluino mass. However, the renormalization of the supercurrent can be realized in a scheme that restores the continuum supersymmetric WTi (once the on-shell condition is imposed). The general procedure used to calculate the renormalization constants and mixing coefficients for the local supercurrent is presented. The supercurrent not only mixes with the gauge invariant operator $T_\mu$. An extra mixing with other operators coming from the WTi appears. This extra mixing survives in the continuum limit in the off-shell regime and cancels out when the on-shell condition is imposed and the renormalized gluino mass is set to zero. Comparison with numerical results are also presented.Comment: 16 pages, 2 figures. Typos error correcte