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

Three-Loop Results in QCD with Wilson Fermions

We calculate the third coefficient of the lattice beta function in QCD with Wilson fermions, extending the pure gauge results of Luescher and Weisz; we show how this coefficient modifies the scaling function on the lattice. We also calculate the three-loop average plaquette in the presence of Wilson fermions. This allows us to compute the lattice scaling function both in the standard and energy schemes.Comment: 3 pages, LaTeX (fleqn.sty, espcrc2.sty), contribution to Lattice'97. Table caption corrected. The longer write-ups are in hep-lat/9801007 (beta function) and hep-lat/9801003 (plaquette

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

The supersymmetric Ward identities on the lattice

Supersymmetric (SUSY) Ward identities are considered for the N=1 SU(2) SUSY Yang Mills theory discretized on the lattice with Wilson fermions (gluinos). They are used in order to compute non-perturbatively a subtracted gluino mass and the mixing coefficient of the SUSY current. The computations were performed at gauge coupling $\beta$=2.3 and hopping parameter $\kappa$=0.1925, 0.194, 0.1955 using the two-step multi-bosonic dynamical-fermion algorithm. Our results are consistent with a scenario where the Ward identities are satisfied up to O(a) effects. The vanishing of the gluino mass occurs at a value of the hopping parameter which is not fully consistent with the estimate based on the chiral phase transition. This suggests that, although SUSY restoration appears to occur close to the continuum limit of the lattice theory, the results are still affected by significant systematic effects.Comment: 34 pages, 7 figures. Typo corrected, last sentence reformulated, reference added. To appear in Eur. Phys. J.

The three-loop beta function of SU(N) lattice gauge theories with Wilson fermions

We calculate the third coefficient of the lattice beta function associated with the Wilson formulation for both gauge fields and fermions. This allows us to evaluate the three-loop correction (linear in $g_0^2$) to the relation between the lattice Lambda-parameter and the bare coupling $g_0$, which is important in order to verify asymptotic scaling predictions. Our calculation also leads to the two-loop relation between the coupling renormalized in the MSbar scheme and $g_0$. The original version of this paper contained a numerical error in one of the diagrams, which has now been corrected. The calculations, as well as the layout of the paper have remained identical, but there are some important changes in the numerical results.Comment: One 14-page LaTeX file, one PostScript file containing 2 figures. Corrected a numerical error in one of the diagrams. The calculations, as well as the layout of the paper have remained unaffected, but there are some important changes in the numerical result

Detecting significant features in modeling microRNA-target interactions

MicroRNAs (miRNAs) are small non-coding RNA molecules mediating the translational repression and degradation of target mRNAs in the cell. Mature miRNAs are used as a template by the RNA-induced silencing complex (RISC) to recognize the complementary mRNAs to be regulated. Up to 60% of human genes are putative targets of one or more miRNAs. Several prediction tools are available to suggest putative miRNA targets, however, only a small part of the interaction pairs has been validated by experimental approaches. The analysis of the expression profile of the RNA fraction immunoprecipitated (IP) with the RISC proteins is an established method to detect which genes are actually regulated by the RISC machinery. In fact, genes that result over-expressed in the IP sample with respect to the whole cell lysate RNA, are considered as involved in the RISC complex, then miRNA targets. Here, we aim to find the features useful to predict which genes are overexpressed in IP, i.e. miRNA targets, without actually performing the IP experiments. To this purpose, we compiled and analyzed a novel high throughput data set suitable to unravel the features involved in the miRNA regulatory activities. We analyzed IP samples obtained by the immunoprecipitation of two RISC proteins, AGO2 and GW182. The two proteins shows different behaviors, in terms of enriched genes and features characterizing the immunoprecipitated RNA fractio. Further analysis is needed to unravel the reason of such different behavior

Pro-invasive stimuli and the interacting protein Hsp70 favour the route of alpha-enolase to the cell surface

Cell surface expression of alpha-enolase, a glycolytic enzyme displaying moonlighting activities, has been shown to contribute to the motility and invasiveness of cancer cells through the protein non-enzymatic function of binding plasminogen and enhancing plasmin formation. Although a few recent records indicate the involvement of protein partners in the localization of alpha-enolase to the plasma membrane, the cellular mechanisms underlying surface exposure remain largely elusive. Searching for novel interactors and signalling pathways, we used low-metastatic breast cancer cells, a doxorubicin-resistant counterpart and a non-tumourigenic mammary epithelial cell line. Here, we demonstrate by a combination of experimental approaches that epidermal growth factor (EGF) exposure, like lipopolysaccharide (LPS) exposure, promotes the surface expression of alpha-enolase. We also establish Heat shock protein 70 (Hsp70), a multifunctional chaperone distributed in intracellular, plasma membrane and extracellular compartments, as a novel alpha-enolase interactor and demonstrate a functional involvement of Hsp70 in the surface localization of alpha-enolase. Our results contribute to shedding light on the control of surface expression of alpha-enolase in non-tumourigenic and cancer cells and suggest novel targets to counteract the metastatic potential of tumours

An excess power statistic for detection of burst sources of gravitational radiation

We examine the properties of an excess power method to detect gravitational waves in interferometric detector data. This method is designed to detect short-duration (< 0.5 s) burst signals of unknown waveform, such as those from supernovae or black hole mergers. If only the bursts' duration and frequency band are known, the method is an optimal detection strategy in both Bayesian and frequentist senses. It consists of summing the data power over the known time interval and frequency band of the burst. If the detector noise is stationary and Gaussian, this sum is distributed as a chi-squared (non-central chi-squared) deviate in the absence (presence) of a signal. One can use these distributions to compute frequentist detection thresholds for the measured power. We derive the method from Bayesian analyses and show how to compute Bayesian thresholds. More generically, when only upper and/or lower bounds on the bursts duration and frequency band are known, one must search for excess power in all concordant durations and bands. Two search schemes are presented and their computational efficiencies are compared. We find that given reasonable constraints on the effective duration and bandwidth of signals, the excess power search can be performed on a single workstation. Furthermore, the method can be almost as efficient as matched filtering when a large template bank is required. Finally, we derive generalizations of the method to a network of several interferometers under the assumption of Gaussian noise.Comment: 22 pages, 6 figure