Scaling and tuning of EW and Higgs observables

We study deformations of the SM via higher dimensional operators. In particular, we explicitly calculate the one-loop anomalous dimension matrix for 13 bosonic dimension-6 operators relevant for electroweak and Higgs physics. These scaling equations allow us to derive RG-induced bounds, stronger than the direct constraints, on a universal shift of the Higgs couplings and some anomalous triple gauge couplings by assuming no tuning at the scale of new physics, i.e. by requiring that their individual contributions to the running of other severely constrained observables, like the electroweak oblique parameters or $\Gamma(h \rightarrow \gamma\gamma)$, do not exceed their experimental direct bounds. We also study operators involving the Higgs and gluon fields.Comment: v2: 41 pages, 12 tables, 4 figures. Plots of the RG-induced bounds from S and T added, presentation of our approach in sections 2 and 4 improved, a few typos fixed, references added, conclusions and analysis unchanged. Version to appear in JHE

Multiple defect interpretation based on Gaussian processes for MFL technology

Magnetic Flux Leakage (MFL) technology has been used in non-destructive testing for more than three decades. There have been several publications in detecting and sizing defects on metal pipes using machine learning techniques. Most of these literature focus on isolated defects, which is far from the real scenario. This study is towards the generalization of interpretation of the leakage flux in the presence of multiple defects based on simulation models, together with data-driven inference methodologies, such as Gaussian Process (GP) models. A MFL device has been simulated using both COMSOL Multiphysics and ANSYS software followed by prototyping the same device for experimental validations. Multiple defects with different geometrical configurations were introduced on a cast iron pipe sample and both radial and axial components of the leakage field have been measured. It was observed that both axial and radial components differ with different defect configurations. We propose to use GP to solve the inverse model problem by capturing such behaviors, i.e. to recover the profille of a cluster of defects from the measurements of a MFL device. The data was used to learn the non-parametric GP model with squared exponential covariance function and automatic relevance determination to solve this regression problem. Extensive quantitative and qualitative evaluations are presented using simulated and experimental data that validate the success of the proposed non-parametric methodology for interpreting the profiling of clusters of defects with MFL technology. © 2013 SPIE

Record statistics for biased random walks, with an application to financial data

We consider the occurrence of record-breaking events in random walks with asymmetric jump distributions. The statistics of records in symmetric random walks was previously analyzed by Majumdar and Ziff and is well understood. Unlike the case of symmetric jump distributions, in the asymmetric case the statistics of records depends on the choice of the jump distribution. We compute the record rate $P_n(c)$, defined as the probability for the $n$th value to be larger than all previous values, for a Gaussian jump distribution with standard deviation $\sigma$ that is shifted by a constant drift $c$. For small drift, in the sense of $c/\sigma \ll n^{-1/2}$, the correction to $P_n(c)$ grows proportional to arctan$(\sqrt{n})$ and saturates at the value $\frac{c}{\sqrt{2} \sigma}$. For large $n$ the record rate approaches a constant, which is approximately given by $1-(\sigma/\sqrt{2\pi}c)\textrm{exp}(-c^2/2\sigma^2)$ for $c/\sigma \gg 1$. These asymptotic results carry over to other continuous jump distributions with finite variance. As an application, we compare our analytical results to the record statistics of 366 daily stock prices from the Standard & Poors 500 index. The biased random walk accounts quantitatively for the increase in the number of upper records due to the overall trend in the stock prices, and after detrending the number of upper records is in good agreement with the symmetric random walk. However the number of lower records in the detrended data is significantly reduced by a mechanism that remains to be identified.Comment: 16 pages, 7 figure