Teichmüller theory and collapse of flat manifolds

We provide an algebraic description of the Teichmüller space and moduli space of flat metrics on a closed manifold or orbifold and study its boundary, which consists of (isometry classes of) flat orbifolds to which the original object may collapse. It is also shown that every closed flat orbifold can be obtained by collapsing closed flat manifolds, and the collapsed limits of closed flat 3-manifolds are classified

Neural network determination of the non-singlet quark distribution

We summarize the main features of our approach to parton fitting, and we show a preliminary result for the non-singlet structure function. When comparing our result to other PDF sets, we find a better description of large x data and larger error bands in the extrapolation regions.Comment: 4 pages, 1 eps figure. Presented at the XIV International Workshop on Deep Inelastic Scattering (DIS2006), Tsukuba, Japan, 20-24 April 200

Monte Carlo analysis of CLAS data

We present a fit of the virtual-photon scattering asymmetry of polarized Deep Inelastic Scattering which combines a Monte Carlo technique with the use of a redundant parametrization based on Neural Networks. We apply the result to the analysis of CLAS data on a polarized proton target.Comment: To appear in the proceedings of 16th International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2008), 7-11 April 2008, University College London, U

A determination of alpha_s from scaling violations with truncated moments

We describe a determination of the strong coupling alpha_s(M_Z) from scaling violations of the nonsinglet DIS structure function, which is based on two novel techniques aimed at controlling and minimizing the theoretical error: a neural network parametrization of BCDMS and NMC data, and QCD evolution by means of truncated Mellin moments.Comment: 5 pages, no figures. Talk given by L. Magnea at QCD02, Montpellier, July 200

Progress on neural parton distributions

We give a status report on the determination of a set of parton distributions based on neural networks. In particular, we summarize the determination of the nonsinglet quark distribution up to NNLO, we compare it with results obtained using other approaches, and we discuss its use for a determination of $\alpha_s$.Comment: 4 pages, 2 figs, uses dis2007.cls, to appear in the DIS 2007 workshop proceeding

Recent progress on NNPDF for LHC

We present recent results of the NNPDF collaboration on a full DIS analysis of Parton Distribution Functions (PDFs). Our method is based on the idea of combining a Monte Carlo sampling of the probability measure in the space of PDFs with the use of neural networks as unbiased universal interpolating functions. The general structure of the project and the features of the fit are described and compared to those of the traditional approaches.Comment: 4 pages, 6 figures, contribution for the proceedings of the conference "Rencontres de Moriond, QCD and High Energy Interactions

Predicting resistive wall mode stability in NSTX through balanced random forests and counterfactual explanations

Recent progress in the disruption event characterization and forecasting framework has shown that machine learning guided by physics theory can be easily implemented as a supporting tool for fast computations of ideal stability properties of spherical tokamak plasmas. In order to extend that idea, a customized random forest (RF) classifier that takes into account imbalances in the training data is hereby employed to predict resistive wall mode (RWM) stability for a set of high beta discharges from the NSTX spherical tokamak. More specifically, with this approach each tree in the forest is trained on samples that are balanced via a user-defined over/under-sampler. The proposed approach outperforms classical cost-sensitive methods for the problem at hand, in particular when used in conjunction with a random under-sampler, while also resulting in a threefold reduction in the training time. In order to further understand the model’s decisions, a diverse set of counterfactual explanations based on determinantal point processes (DPP) is generated and evaluated. Via the use of DPP, the underlying RF model infers that the presence of hypothetical magnetohydrodynamic activity would have prevented the RWM from concurrently going unstable, which is a counterfactual that is indeed expected by prior physics knowledge. Given that this result emerges from the data-driven RF classifier and the use of counterfactuals without hand-crafted embedding of prior physics intuition, it motivates the usage of counterfactuals to simulate real-time control by generating the β N levels that would have kept the RWM stable for a set of unstable discharges

The first eigenvalue of a homogeneous CROSS

We provide explicit formulae for the first eigenvalue of the Laplace-Beltrami operator on a compact rank one symmetric space (CROSS) endowed with any homogeneous metric. As consequences, we prove that homogeneous metrics on CROSSes are isospectral if and only if they are isometric, and also discuss their stability (or lack thereof) as solutions to the Yamabe problem.Comment: LaTeX2e, 40 page

Multiple ectopic leiomyomas of the abdominal rectus muscles after gasless laparoscopic uterine myomectomy

To describe and analyze the first case of multiple ectopic leiomyomas of the abdominal rectus muscles in a patient who had undergone gasless laparoscopic uterine myomectomy (GLM) 10 years before