Enriched Lawvere Theories for Operational Semantics

Enriched Lawvere theories are a generalization of Lawvere theories that allow us to describe the operational semantics of formal systems. For example, a graph enriched Lawvere theory describes structures that have a graph of operations of each arity, where the vertices are operations and the edges are rewrites between operations. Enriched theories can be used to equip systems with operational semantics, and maps between enriching categories can serve to translate between different forms of operational and denotational semantics. The Grothendieck construction lets us study all models of all enriched theories in all contexts in a single category. We illustrate these ideas with the SKI-combinator calculus, a variable-free version of the lambda calculus.Comment: In Proceedings ACT 2019, arXiv:2009.0633

Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation

We investigate masses of light mesons from a coupled system of Dyson--Schwinger (DSE) and Bethe--Salpeter equations (BSE), taking into account dominant non-Abelian, sub-leading Abelian, and dominant pion cloud contributions to the dressed quark-gluon vertex. The axial-vector Ward-Takahashi identity preserving Bethe-Salpeter kernel is constructed and the spectrum of light mesons calculated. Our model goes significantly beyond the rainbow-ladder. We find that sub-leading Abelian corrections are further dynamically suppressed, and that our results supersede early qualitative predictions from simple truncation schemes.Comment: 4 pages, 3 figures, 1 table. Talk given at the 5-th Int. Conf. on Quarks and Nuclear Physics, Beijing, September 21-26,200

Examination of Methylation Sites for Forensic Age Determination from Semen

Methylation Sensitive High-Resolution Melt (MS-HRM) is based on quantitating the melt curve from an experimental sample against a standard of known methylation levels. Whereas most applications of age prediction using methylation markers are based upon pyrosequencing or SNaPshot technologies, these analysis methods are both cost and instrumentation prohibitive. This study sought to use to the varied methylation status of the ELOVL2 and FHL2 alleles, both having known correlation with age (Hamano et. al.), in a labor and time efficient manner to develop an age prediction model. A non-linear regression and standard curve was compiled from the methylation status in a sample (n=7) of extracted semen samples and compared to chronological age. The methylation status of ELVOL2 and FHL2 from each sample was obtained, with the conclusion that no correlation in methylation percentage and biological age existed for this sample of individuals aged 20-33. The principal objective of this study, to expand the application of MS-HRM age prediction from blood to other body fluids, will need further testing using larger sample sizes and broader age ranges prior to application in forensic casework.https://scholarscompass.vcu.edu/uresposters/1281/thumbnail.jp

Mass spectra and Regge trajectories of light mesons in the Bethe-Salpeter approach

We extend the calculation of relativistic bound-states of a fermion anti-fermion pair in the Bethe-Salpeter formalism to the case of total angular momentum $J=3$. Together with results for $J \le 2$ this allows for the investigation of Regge trajectories in this approach. We exemplify such a study for ground and excited states of light unflavored mesons as well as strange mesons within the rainbow-ladder approximation. For the $\rho$- and $\phi$-meson we find a linear Regge trajectory within numerical accuracy. Discrepancies with experiment in other channels highlight the need to go beyond rainbow-ladder and to consider effects such as state mixing and more sophisticated quark-antiquark interaction kernels.Comment: 11 pages, 8 figures, 2 tables. Minor typos corrected; accepted in EPJ

The role of momentum dependent dressing functions and vector meson dominance in hadronic light-by-light contributions to the muon g-2

We present a refined calculation of the quark-loop contribution to hadronic light-by-light scatter- ing that focuses upon the impact of the transverse components of the quark-photon vertex. These structures are compared and contrasted with those found within the extended NJL-models. We discuss similarities and differences between the two approaches and further clarify the important role of momentum dependent dressing functions. As expected we find that the transverse structures of the quark-photon vertex lead to a suppression of the quark-loop contribution to the anomalous magnetic moment of the muon. However, we find evidence that this suppression is overestimated within models with simple approximations for the quark-photon interaction.Comment: 13 pages, 5 figures, v2: typos corrected, references added, version submitted to PR