The Moments of the Hydrogen Atom by the Method of Brackets

Expectation values of powers of the radial coordinate in arbitrary hydrogen states are given, in the quantum case, by an integral involving the associated Laguerre function. The method of brackets is used to evaluate the integral in closed-form and to produce an expression for this average value as a finite sum

Molecular basis of class III ligand recognition by PDZ3 in murine protein tyrosine phosphatase PTPN13

Protein tyrosine phosphatase PTPN13, also known as PTP-BL in mice, represents a large multi-domain non-transmembrane scaffolding protein that contains five consecutive PDZ domains. Here, we report the solution structures of the extended murine PTPN13 PDZ3 domain in its apo form and in complex with its physiological ligand, the carboxy-terminus of protein kinase C-related kinase-2 (PRK2), determined by multidimensional NMR spectroscopy. Both in its ligand-free state and when complexed to PRK2, PDZ3 of PTPN13 adopts the classical compact, globular D/E fold. PDZ3 of PTPN13 binds five carboxy-terminal amino acids of PRK2 via a groove located between the EB-strand and the DB-helix. The PRK2 peptide resides in the canonical PDZ3 binding cleft in an elongated manner and the amino acid side chains in position P0 and P-2, cysteine and aspartate, of the ligand face the groove between EB-strand and DB-helix, whereas the PRK2 side chains of tryptophan and alanine located in position P-1 and P-3 point away from the binding cleft. These structures are rare examples of selective class III ligand recognition by a PDZ domain and now provide a basis for the detailed structural investigation of the promiscuous interaction between the PDZ domains of PTPN13 and their ligands. They will also lead to a better understanding of the proposed scaffolding function of these domains in multi-protein complexes assembled by PTPN13 and could ultimately contribute to low molecular weight antagonists that might even act on the PRK2 signaling pathway to modulate rearrangements of the actin cytoskeleton

Open-source, Python-based, hardware and software for controlling behavioural neuroscience experiments

Laboratory behavioural tasks are an essential research tool. As questions asked of behaviour and brain activity become more sophisticated, the ability to specify and run richly structured tasks becomes more important. An increasing focus on reproducibility also necessitates accurate communication of task logic to other researchers. To these ends, we developed pyControl, a system of open-source hardware and software for controlling behavioural experiments comprising a simple yet flexible Python-based syntax for specifying tasks as extended state machines, hardware modules for building behavioural setups, and a graphical user interface designed for efficiently running high-throughput experiments on many setups in parallel, all with extensive online documentation. These tools make it quicker, easier, and cheaper to implement rich behavioural tasks at scale. As important, pyControl facilitates communication and reproducibility of behavioural experiments through a highly readable task definition syntax and self-documenting features. Here, we outline the system’s design and rationale, present validation experiments characterising system performance, and demonstrate example applications in freely moving and head-fixed mouse behaviour

Report of the Quark Flavor Physics Working Group

This report represents the response of the Intensity Frontier Quark Flavor Physics Working Group to the Snowmass charge. We summarize the current status of quark flavor physics and identify many exciting future opportunities for studying the properties of strange, charm, and bottom quarks. The ability of these studies to reveal the effects of new physics at high mass scales make them an essential ingredient in a well-balanced experimental particle physics program.This report represents the response of the Intensity Frontier Quark Flavor Physics Working Group to the Snowmass charge. We summarize the current status of quark flavor physics and identify many exciting future opportunities for studying the properties of strange, charm, and bottom quarks. The ability of these studies to reveal the effects of new physics at high mass scales make them an essential ingredient in a well-balanced experimental particle physics program