Off-forward parton distributions and impact parameter dependence of parton structure

The connection between parton distributions as a function of the impact parameter and off-forward parton distributions is discussed in the limit of vanishing skewedness parameter $\zeta$, i.e. when the off-forwardness is purely transverse. For the $2^{nd}$ moment it is also illustrated how to relate $\zeta\neq 0$ data to $\zeta=0$ data, which is important for experimental measurements of these observables.Comment: invited talk presented at `Light-Cone Meeting on Non-Perturbative QCD and Hadron Phenomenology', Heidelberg, June 2000, 10 pages, elsart.st

Generalized Parton Distributions and the Spin Structure of the Nucleon

Generalized parton distributions are a new type of hadronic observables which has recently stimulated great interest among theorists and experimentalists alike. Introduced to delineate the spin structure of the nucleon, the orbital angular momentum of quarks in particular, the new distributions contain vast information about the internal structure of the nucleon, with the usual electromagnetic form factors and Feynman parton distributions as their special limits. While new perturbative QCD processes, such as deeply virtual Compton scattering and exclusive meson production, have been found to measure the distributions directly in experiments, lattice QCD offers a great promise to provide the first-principle calculations of these interesting observables.Comment: 9 pages, plenary talk given at Lattice 2002, Cambridge, MA, US

Form factor decomposition of generalized parton distributions at leading twist

We extend the counting of generalized form factors presented in PRD63(2000) by Ji and Lebed to the axial vector and the tensor operator at twist-2 level. Following this, a parameterization of all higher moments in x of the tensor (helicity flip) operator is given in terms of generalized form factors.Comment: 9 page

Prime Graphs and Exponential Composition of Species

In this paper, we enumerate prime graphs with respect to the Cartesian multiplication of graphs. We use the unique factorization of a connected graph into the product of prime graphs given by Sabidussi to find explicit formulas for labeled and unlabeled prime graphs. In the case of species, we construct the exponential composition of species based on the arithmetic product of species of Maia and M\'endez and the quotient species, and express the species of connected graphs as the exponential composition of the species of prime graphs.Comment: 30 pages, 7 figures, 1 tabl

A Provable Smoothing Approach for High Dimensional Generalized Regression with Applications in Genomics

In many applications, linear models fit the data poorly. This article studies an appealing alternative, the generalized regression model. This model only assumes that there exists an unknown monotonically increasing link function connecting the response $Y$ to a single index $X^T\beta^*$ of explanatory variables $X\in\mathbb{R}^d$. The generalized regression model is flexible and covers many widely used statistical models. It fits the data generating mechanisms well in many real problems, which makes it useful in a variety of applications where regression models are regularly employed. In low dimensions, rank-based M-estimators are recommended to deal with the generalized regression model, giving root-$n$ consistent estimators of $\beta^*$. Applications of these estimators to high dimensional data, however, are questionable. This article studies, both theoretically and practically, a simple yet powerful smoothing approach to handle the high dimensional generalized regression model. Theoretically, a family of smoothing functions is provided, and the amount of smoothing necessary for efficient inference is carefully calculated. Practically, our study is motivated by an important and challenging scientific problem: decoding gene regulation by predicting transcription factors that bind to cis-regulatory elements. Applying our proposed method to this problem shows substantial improvement over the state-of-the-art alternative in real data.Comment: 53 page

On scale dependence of QCD string operators

We have obtained a general solution of evolution equations for QCD twist-2 string operators in form of expansion over complete set of orthogonal eigenfunctions of evolution kernels in coordinate-space representation. In the leading logarithmic approximation the eigenfunctions can be determined using constraints imposed by conformal symmetry. Explicit formulae for the LO scale-dependence of quark and gluon twist-2 string operators are given