Limiting empirical spectral distribution for the non-backtracking matrix of an Erd\H{o}s-R\'enyi random graph

In this note, we give a precise description of the limiting empirical spectral distribution (ESD) for the non-backtracking matrices for an Erd\H{o}s-R\'{e}nyi graph assuming $np/\log n$ tends to infinity. We show that derandomizing part of the non-backtracking random matrix simplifies the spectrum considerably, and then we use Tao and Vu's replacement principle and the Bauer-Fike theorem to show that the partly derandomized spectrum is, in fact, very close to the original spectrum.Comment: 19 pages, 1 figure. Adjusted the figure in the new versio

First-order phase transition and fate of false vacuum remnants

False vacuum remnants in first-order phase transitions in the early Universe can form compact objects which may constitute dark matter. Such remnants form because particles develop large mass gaps between the two phases and become trapped in the old phase. We focus on remnants generated in a class of models with trapped dark sector particles, trace their development, and determine their ultimate fate. Depending on model and phase transition parameters, the evolutionary endpoint of these remnants can be primordial black holes, Fermi-balls, Q-balls, or thermal balls, and they all have the potential to constitute some portion or the whole of dark matter within a broad mass range. Notably, dark sector thermal balls can remain at high temperatures until the present day and are a new compact dark matter candidate which derives its energy from the thermal energy of internal particles instead of their mass or quantum pressure

Aggregating multiple body sensors for analysis in sports

Real time monitoring of the wellness of sportspersons, during their sporting activity and training, is important in order to maximise performance during the sporting event itself and during training, as well as being important for the health of the sportsperson overall. We have combined a suite of common, off-the-shelf sensors with specialist body sensing technology we are developing ourselves and constructed a software system for recording, analysing and presenting sensed data gathered from a single player during a sporting activity, a football match. We gather readings for heart rate, galvanic skin response, motion, heat flux, respiration, and location (GPS) using on-body sensors, while simultaneously tracking player activity using a combination of a playercam video and pitch-wide video recording. We have aggregated all this sensed data into a single overview of player performance and activity which can be reviewed, post-event. We are currently working on integrating other non-invasive methods for real-time on-body monitoring of sweat electrolytes and pH via a textile-based sweat sampling and analysis platform. Our work is heading in two directions; firstly from post-event data aggregation to real-time monitoring, and secondly, to convert raw sensor readings into performance indicators that are meaningful to practitioners in the field

The regulator of G protein signaling (RGS) domain of G protein-coupled receptor kinase 5 (GRK5) regulates plasma membrane localization and function.

The G protein-coupled receptor (GPCR) kinases (GRKs) phosphorylate activated GPCRs at the plasma membrane (PM). Here GRK5/GRK4 chimeras and point mutations in GRK5 identify a short sequence within the regulator of G protein signaling (RGS) domain in GRK5 that is critical for GRK5 PM localization. This region of the RGS domain of GRK5 coincides with a region of GRK6 and GRK1 shown to form a hydrophobic dimeric interface (HDI) in crystal structures. Coimmunoprecipitation (coIP) and acceptor photobleaching fluorescence resonance energy transfer assays show that expressed GRK5 self-associates in cells, whereas GRK5-M165E/F166E (GRK5-EE), containing hydrophilic mutations in the HDI region of the RGS domain, displays greatly decreased coIP interactions. Both forcing dimerization of GRK5-EE, via fusion to leucine zipper motifs, and appending an extra C-terminal membrane-binding region to GRK5-EE (GRK5-EE-CT) recover PM localization. In addition, GRK5-EE displays a decreased ability to inhibit PAR1-induced calcium release compared with GRK5 wild type (wt). In contrast, PM-localized GRK5-EE-CaaX (appending a C-terminal prenylation and polybasic motif from K-ras) or GRK5-EE-CT shows comparable ability to GRK5 wt to inhibit PAR1-induced calcium release. The results suggest a novel model in which GRK5 dimerization is important for its plasma membrane localization and function