Skewed parton distributions and the scale dependence of the transverse size parameter

We discuss the scale dependence of a skewed parton distribution of the pion obtained from a generalized light-cone wave function overlap formula. Using a simple ansatz for the transverse momentum dependence of the light-cone wave function and restricting ourselves to the case of a zero skewedness parameter, the skewed parton distribution can be expressed through an ordinary parton distribution multiplied by an exponential function. Matching the generalized and ordinary DGLAP evolution equations of the skewed and ordinary parton distributions, respectively, we derive a constraint for the scale dependence of the transverse size parameter, which describes the width of the pion wave function in transverse momentum space. This constraint has implications for the Fock state probability and valence distribution. We apply our results to the pion form factor.Comment: 10 pages, 4 figures; version to appear in Phys. Rev. D; Refs. added, new discussion of results for pion form factor in view of new dat

Conductance calculations for quantum wires and interfaces: mode matching and Green functions

Landauer's formula relates the conductance of a quantum wire or interface to transmission probabilities. Total transmission probabilities are frequently calculated using Green function techniques and an expression first derived by Caroli. Alternatively, partial transmission probabilities can be calculated from the scattering wave functions that are obtained by matching the wave functions in the scattering region to the Bloch modes of ideal bulk leads. An elegant technique for doing this, formulated originally by Ando, is here generalized to any Hamiltonian that can be represented in tight-binding form. A more compact expression for the transmission matrix elements is derived and it is shown how all the Green function results can be derived from the mode matching technique. We illustrate this for a simple model which can be studied analytically, and for an Fe|vacuum|Fe tunnel junction which we study using first-principles calculations.Comment: 14 pages, 5 figure

The Generalized Asymptotic Equipartition Property: Necessary and Sufficient Conditions

Suppose a string $X_1^n=(X_1,X_2,...,X_n)$ generated by a memoryless source $(X_n)_{n\geq 1}$ with distribution $P$ is to be compressed with distortion no greater than $D\geq 0$, using a memoryless random codebook with distribution $Q$. The compression performance is determined by the ``generalized asymptotic equipartition property'' (AEP), which states that the probability of finding a $D$-close match between $X_1^n$ and any given codeword $Y_1^n$, is approximately $2^{-n R(P,Q,D)}$, where the rate function $R(P,Q,D)$ can be expressed as an infimum of relative entropies. The main purpose here is to remove various restrictive assumptions on the validity of this result that have appeared in the recent literature. Necessary and sufficient conditions for the generalized AEP are provided in the general setting of abstract alphabets and unbounded distortion measures. All possible distortion levels $D\geq 0$ are considered; the source $(X_n)_{n\geq 1}$ can be stationary and ergodic; and the codebook distribution can have memory. Moreover, the behavior of the matching probability is precisely characterized, even when the generalized AEP is not valid. Natural characterizations of the rate function $R(P,Q,D)$ are established under equally general conditions.Comment: 19 page

The Establishment-Level Behavior of Vacancies and Hiring

This paper is the first to study vacancies, hires, and vacancy yields at the establishment level in the Job Openings and Labor Turnover Survey, a large sample of U.S. employers. To interpret the data, we develop a simple model that identifies the flow of new vacancies and the job-filling rate for vacant positions. The fill rate moves counter to aggregate employment but rises steeply with employer growth rates in the cross section. It falls with employer size, rises with worker turnover rates, and varies by a factor of four across major industry groups. We also develop evidence that the employer-level hiring technology exhibits mild increasing returns in vacancies, and that employers rely heavily on other instruments, in addition to vacancies, as they vary hires. Building from our evidence and a generalized matching function, we construct a new index of recruiting intensity (per vacancy). Recruiting intensity partly explains the recent breakdown in the standard matching function, delivers a better-fitting empirical Beveridge Curve, and accounts for a large share of fluctuations in aggregate hires. Our evidence and analysis provide useful inputs for assessing, developing and calibrating theoretical models of search, matching and hiring in the labor market.

The two-mass contribution to the three-loop pure singlet operator matrix element

We present the two-mass QCD contributions to the pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the structure function $F_2(x,Q^2)$ at $O(\alpha_s^3)$ as well as for the matching relations in the variable flavor number scheme and the heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals that include square root letters in the alphabet, depending also on the mass ratio through the main argument. Numerical results are presented.Comment: 28 papges Latex, 3 figure

Automatic adaptive multi-point moment matching for descriptor system model order reduction

We propose a novel automatic adaptive multi-point moment matching algorithm for model order reduction (MOR) of descriptor systems. The algorithm implements both adaptive frequency expansion point selection and automatic moment order control via a transfer function based error metric. Without a priori information of the system response, the proposed algorithm guarantees a much higher global accuracy compared with standard multi-point moment matching without adaptation. The moments are computed via a generalized Sylvester equation which is subsequently solved by a newly proposed generalized alternating direction implicit (GADI) method. Numerical examples then confirm the efficacy of the proposed schemes. © 2013 IEEE.published_or_final_versio

Kernel Exponential Family Estimation via Doubly Dual Embedding

We investigate penalized maximum log-likelihood estimation for exponential family distributions whose natural parameter resides in a reproducing kernel Hilbert space. Key to our approach is a novel technique, doubly dual embedding, that avoids computation of the partition function. This technique also allows the development of a flexible sampling strategy that amortizes the cost of Monte-Carlo sampling in the inference stage. The resulting estimator can be easily generalized to kernel conditional exponential families. We establish a connection between kernel exponential family estimation and MMD-GANs, revealing a new perspective for understanding GANs. Compared to the score matching based estimators, the proposed method improves both memory and time efficiency while enjoying stronger statistical properties, such as fully capturing smoothness in its statistical convergence rate while the score matching estimator appears to saturate. Finally, we show that the proposed estimator empirically outperforms state-of-the-artComment: 22 pages, 20 figures; AISTATS 201