Separated longitudinal and transverse structure functions for the reaction 1 H͑e, e 0 p 1 ͒n were measured in the momentum transfer region Q 2 0.6 1.6 ͑GeV͞c͒ 2 at a value of the invariant mass W 1.95 GeV. New values for the pion charge form factor were extracted from the longitudinal cross section by using a recently developed Regge model. The results indicate that the pion form factor in this region is larger than previously assumed and is consistent with a monopole parametrization fitted to very low Q 2 elastic data. DOI: 10.1103/PhysRevLett.86.1713 The pion occupies an important place in the study of the quark-gluon structure of hadrons. This is exemplified by the many calculations that treat the pion as one of their prime examples [1][2][3][4][5][6][7][8]. One of the reasons is that the valence structure of the pion, being ͗qq͘, is relatively simple. Hence it is expected that the value of the four-momentum transfer squared Q 2 , down to which a perturbative QCD (pQCD) approach to the pion structure can be applied, is lower than, e.g., for the nucleon. Furthermore, the asymptotic normalization of the pion wave function, in contrast to that of the nucleon, is known from the pion decay.The charge form factor of the pion, F p ͑Q 2 ͒, is an essential element of the structure of the pion. Its behavior at very low values of Q 2 , which is determined by the charge radius of the pion, has been determined up to Q 2 0.28 ͑GeV͞c͒ 2 from scattering high-energy pions from atomic electrons [9]. For the determination of the pion form factor at higher values of Q 2 one has to use high-energy electroproduction of pions on a nucleon, i.e., employ the 1 H͑e, e 0 p 1 ͒n reaction. For selected kinematical conditions this process can be described as quasielastic scattering of the electron from a virtual pion in the proton. In the t-pole approximation the longitudinal cross section s L is proportional to the square of the pion form factor. In this way the pion form factor has been studied for Q 2 values from 0.4 to 9.8 ͑GeV͞c͒ 2 at CEA͞Cornell [10] and for Q 2 0.7 ͑GeV͞c͒ 2 at DESY [11]. In the DESY experiment a longitudinal͞transverse (L͞T ) separation was performed by taking data at two values of the electron energy. In the experiments done at CEA͞Cornell this was done in a few cases only, and even 0031-9007͞01͞86(9)͞1713(4)$15.00

The charged pion form factor, F π (Q 2 ), is an important quantity that can be used to advance our knowledge of hadronic structure. However, the extraction of F π from data requires a model of the 1 H(e, e π + )n reaction and thus is inherently model dependent. Therefore, a detailed description of the extraction of the charged pion form factor from electroproduction data obtained recently at Jefferson Lab is presented, with particular focus given to the dominant uncertainties in this procedure. Results for F π are presented for Q 2 = 0.60-2.45 GeV 2 . Above Q 2 = 1.5 GeV 2 , the F π values are systematically below the monopole parametrization that describes the low Q 2 data used to determine the pion charge radius. The pion form factor can be calculated in a wide variety of theoretical approaches, and the experimental results are compared to a number of calculations. This comparison is helpful in understanding the role of soft versus hard contributions to hadronic structure in the intermediate Q

We construct genomic predictors for heritable but extremely complex human quantitative traits (height, heel bone density, and educational attainment) using modern methods in high dimensional statistics (i.e., machine learning). The constructed predictors explain, respectively, $40, 20, and 9% of total variance for the three traits, in data not used for training. For example, predicted heights correlate $0.65 with actual height; actual heights of most individuals in validation samples are within a few centimeters of the prediction. The proportion of variance explained for height is comparable to the estimated common SNP heritability from genome-wide complex trait analysis (GCTA), and seems to be close to its asymptotic value (i.e., as sample size goes to infinity), suggesting that we have captured most of the heritability for SNPs. Thus, our results close the gap between prediction R-squared and common SNP heritability. The $20k activated SNPs in our height predictor reveal the genetic architecture of human height, at least for common variants. Our primary dataset is the UK Biobank cohort, comprised of almost 500k individual genotypes with multiple phenotypes. We also use other datasets and SNPs found in earlier genome-wide association studies (GWAS) for out-of-sample validation of our results.

Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We use Noether's second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether's second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether's second theorem and known results in the recent literature. Our approach suggests a novel point of view with important physical consequences.