On the mistake in the implementation of the minimal model of the dual parameterization and resulting inability to describe the high-energy DVCS data

We correct the mistaken claim made in \cite{Guzey:2005ec,Guzey:2006xi} that the minimal model of the dual parameterization of nucleon generalized parton distributions (GPDs) gives a good, essentially model-independent description of high-energy data on deeply virtual Compton scattering (DVCS). In the implementation of the dual parameterization in \cite{Guzey:2005ec,Guzey:2006xi}, the numerical prefactor of two in front of the DVCS amplitude was missing. We show that the corrected minimal model of the dual parameterization significantly overestimates the HERA data (H1 and ZEUS) on the DVCS cross section.Comment: 8 pages, 1 figur

The dual parameterization of the proton generalized parton distribution functions H and E and description of the DVCS cross sections and asymmetries

We develop the minimal model of a new leading order parameterization of GPDs introduced by Shuvaev and Polyakov. The model for GPDs H and E is formulated in terms of the forward quark distributions, the Gegenbauer moments of the D-term and the forward limit of the GPD E. The model is designed primarely for small and medium-size values of x_B, x_B \leq 0.2. We examined two different models of the t-dependence of the GPDs: The factorized exponential model and the non-factorized Regge-motivated model. Using our model, we successfully described the DVCS cross section measured by H1 and ZEUS, the moments of the beam-spin A_{LU}^{\sin \phi}, beam-charge A_{C}^{\cos \phi} and transversely-polarized target A_{UT}^{\sin \phi \cos \phi} DVCS asymmetries measured by HERMES and A_{LU}^{\sin \phi} measured by CLAS. The data on A_{C}^{\cos \phi} prefers the Regge-motivated model of the t-dependence of the GPDs. The data on A_{UT}^{\sin \phi \cos \phi} indicates that the u and d quarks carry only a small fraction of the proton total angular momentum.Comment: 33 pages, 11 figure

Lorentz invariance relations and Wandzura-Wilczek approximation

A complete list of the so-called Lorentz invariance relations between parton distribution functions is given and some of their consequences are discussed, such as the Burkhardt-Cottingham sum rule. The violation of these relations is considered in a model independent way. It is shown that several Lorentz invariance relations are not violated in a generalized Wandzura-Wilczek approximation, indicating that numerically their violation may be small.Comment: 10 pages; Proceedings of the workshop "Recent Advances in Perturbative QCD and Hadronic Physics", July 20-24, 2009, at ECT*, Trento (Italy), in honor of Anatoli V. Efremov on the occasion of his 75th birthday; to appear in Mod. Phys. Lett.

Are there approximate relations among transverse momentum dependent distribution functions?

Certain exact relations among transverse momentum dependent parton distribution functions due to QCD equations of motion turn into approximate ones upon the neglect of pure twist-3 terms. On the basis of available data from HERMES we test the practical usefulness of one such ``Wandzura-Wilczek-type approximation'', namely of that connecting h_{1L}^{\perp(1)a}(x) to h_L^a(x), and discuss how it can be further tested by future CLAS and COMPASS data.Comment: 9 pages, 3 figure

Complexity Analysis of Accelerated MCMC Methods for Bayesian Inversion

We study Bayesian inversion for a model elliptic PDE with unknown diffusion coefficient. We provide complexity analyses of several Markov Chain-Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the Bayesian posterior distribution, given data $\delta$. Particular attention is given to bounds on the overall work required to achieve a prescribed error level $\varepsilon$. Specifically, we first bound the computational complexity of "plain" MCMC, based on combining MCMC sampling with linear complexity multilevel solvers for elliptic PDE. Our (new) work versus accuracy bounds show that the complexity of this approach can be quite prohibitive. Two strategies for reducing the computational complexity are then proposed and analyzed: first, a sparse, parametric and deterministic generalized polynomial chaos (gpc) "surrogate" representation of the forward response map of the PDE over the entire parameter space, and, second, a novel Multi-Level Markov Chain Monte Carlo (MLMCMC) strategy which utilizes sampling from a multilevel discretization of the posterior and of the forward PDE. For both of these strategies we derive asymptotic bounds on work versus accuracy, and hence asymptotic bounds on the computational complexity of the algorithms. In particular we provide sufficient conditions on the regularity of the unknown coefficients of the PDE, and on the approximation methods used, in order for the accelerations of MCMC resulting from these strategies to lead to complexity reductions over "plain" MCMC algorithms for Bayesian inversion of PDEs.

International Consensus Based Review and Recommendations for Minimum Reporting Standards in Research on Transcutaneous Vagus Nerve Stimulation (Version 2020).

Given its non-invasive nature, there is increasing interest in the use of transcutaneous vagus nerve stimulation (tVNS) across basic, translational and clinical research. Contemporaneously, tVNS can be achieved by stimulating either the auricular branch or the cervical bundle of the vagus nerve, referred to as transcutaneous auricular vagus nerve stimulation(VNS) and transcutaneous cervical VNS, respectively. In order to advance the field in a systematic manner, studies using these technologies need to adequately report sufficient methodological detail to enable comparison of results between studies, replication of studies, as well as enhancing study participant safety. We systematically reviewed the existing tVNS literature to evaluate current reporting practices. Based on this review, and consensus among participating authors, we propose a set of minimal reporting items to guide future tVNS studies. The suggested items address specific technical aspects of the device and stimulation parameters. We also cover general recommendations including inclusion and exclusion criteria for participants, outcome parameters and the detailed reporting of side effects. Furthermore, we review strategies used to identify the optimal stimulation parameters for a given research setting and summarize ongoing developments in animal research with potential implications for the application of tVNS in humans. Finally, we discuss the potential of tVNS in future research as well as the associated challenges across several disciplines in research and clinical practice

Transcutaneous vagus nerve stimulation facilitates effort invigoration

Introduction: Anhedonia is a core symptom in many mental disorders such as major depression. Generally defined as the 'inability to experience pleasure', recent debates push towards a conceptual revision emphasizing an understanding of anhedonia as a motivational deficit to work for rewards. Emerging evidence suggests that the vagus nerve affects dopaminergic circuits and metabolic signaling. Therefore, we expected transcutaneous vagus nerve stimulation (tVNS) to enhance the motivation to exert effort for rewards by modulating the effect of costs and benefits on instrumental behavior. Methods: In this study we applied tVNS/sham stimulation in a randomized crossover design to healthy subjects. They completed two sessions of a modified effort allocation task (EAT) and had to maintain a varying proportion of their individual maximum button press frequency to gain rewards. Results: Preliminary results in 24 participants indicate that the EAT tracks important aspects of costs and benefits of action as reflected in significant effects of reward magnitude, t(23) = 3.310, p = .003, and task difficulty, t(23) = -2.721, p = .012, on average button press frequency. Moreover, we found that higher reward magnitude increased effort invigoration by 8%, t(23) = 4.131, p < .001. Critically, the stimulation increased the invigoration by an additional 6%, t(22) = 3.042, p = .006. However, tVNS-effects on effort maintenance were modulated by session order and not significant at the group level, t(22) = 0.274, p = .787. Discussion: These findings confirm the suitability of the EAT to study effort-based decision making over time. We found that effort invigoration, but not maintenance was facilitated by tVNS. Nevertheless, more data is needed to assess whether the absence of tVNS effects on effort maintenance is due to a carry-over effect. To conclude, anti-depressant effects of the stimulation could be explained by an enhanced incentive value conferred by rewards

Transcutaneous vagus nerve stimulation facilitates invigoration of effort

Introduction: Anhedonia is a core symptom in many mental disorders such as major depressive disorder (MDD). Generally defined as the 'inability to experience pleasure', recent debates push towards a conceptual revision emphasizing an understanding of anhedonia as a motivational deficit to work for rewards [1]. Moreover, MDD is associated with changes in body weight, but the underlying mechanisms are not well understood. Vagus nerve stimulation is a promising novel therapy of treatment-resistant MDD [2], as well as treatment-resistant obesity [3]. However, the exact mechanisms behind the treatment effects are largely unknown. Intriguingly, emerging evidence suggests that the vagus nerve affects dopaminergic circuits and metabolic signaling [4]. Therefore, we expected non-invasive transcutaneous vagus nerve stimulation (tVNS) to enhance the motivation to exert effort for rewards by modulating the effect of costs and benefits on instrumental behavior. Methods: We applied tVNS/sham stimulation in a randomized crossover design to healthy normal- to overweight participants (N=24) after an overnight fast. As part of an ongoing study, they completed two morning sessions of a modified effort allocation task (EAT) [5]. Participants had to maintain a varying proportion of their individual maximum button press frequency in order to gain monetary and food rewards. The task comprises of 48 trials, in which we manipulated the reward magnitude, type and the difficulty to obtain the reward. We performed hierarchical linear regression analyses as implemented in HLM7 to investigate the impact of the stimulation on the invigoration and maintenance of behavior. Results: We found that the EAT tracks important aspects of costs and benefits of action as reflected in significant effects of reward magnitude, t(23)=3.310, p=0.003, and task difficulty, t(23)= -2.721, p=0.012, on average button press frequency. Moreover, we found that higher reward magnitude increased effort invigoration by 8%, t(23)=4.131, p<0.001. Critically, the stimulation increased the invigoration by an additional 6% relative to baseline, t(22)=3.042, p=0.006, but did not have a significant impact on the maintenance of behavior, t(22)=0.274, p=0.787, even if maintenance was corrected for day-to-day differences in baseline performance, t(23)=1.60, p=0.124. Discussion: Our findings confirm the suitability of the EAT to study effort-based decision-making over time. We found that effort invigoration, but not maintenance was facilitated by tVNS. Notably, the effect of stimulation on invigoration is almost as strong as the drive elicited by a tenfold increase of the reward magnitude at stake. Nevertheless, more data is needed to assess whether the absence of tVNS effects on effort maintenance is partly due to a carry-over effect. To conclude, the preliminary results point towards an influence of tVNS on dopaminergic signaling. Therefore, anti-depressant and weight-loss effects of the stimulation could be explained by an enhanced incentive value conferred by rewards