Branching processes, the max-plus algebra and network calculus

Branching processes can describe the dynamics of various queueing systems, peer-to-peer systems, delay tolerant networks, etc. In this paper we study the basic stochastic recursion of multitype branching processes, but in two non-standard contexts. First, we consider this recursion in the max-plus algebra where branching corresponds to finding the maximal offspring of the current generation. Secondly, we consider network-calculus-type deterministic bounds as introduced by Cruz, which we extend to handle branching-type processes. The paper provides both qualitative and quantitative results and introduces various applications of (max-plus) branching processes in queueing theory

On the Resolution of the Time-Like Singularities in Reissner-Nordstrom and Negative-Mass Schwarzschild

Certain time-like singularities are shown to be resolved already in classical General Relativity once one passes from particle probes to scalar waves. The time evolution can be defined uniquely and some general conditions for that are formulated. The Reissner-Nordstrom singularity allows for communication through the singularity and can be termed "beam splitter" since the transmission probability of a suitably prepared high energy wave packet is 25%. The high frequency dependence of the cross section is w^{-4/3}. However, smooth geometries arbitrarily close to the singular one require a finite amount of negative energy matter. The negative-mass Schwarzschild has a qualitatively different resolution interpreted to be fully reflecting. These 4d results are similar to the 2d black hole and are generalized to an arbitrary dimension d>4.Comment: 47 pages, 5 figures. v2: See end of introduction for an important note adde

Introduction to Holographic Superconductors

These lectures give an introduction to the theory of holographic superconductors. These are superconductors that have a dual gravitational description using gauge/gravity duality. After introducing a suitable gravitational theory, we discuss its properties in various regimes: the probe limit, the effects of backreaction, the zero temperature limit, and the addition of magnetic fields. Using the gauge/gravity dictionary, these properties reproduce many of the standard features of superconductors. Some familiarity with gauge/gravity duality is assumed. A list of open problems is included at the end.Comment: 34 pages, 10 figures, to appear in the proceedings of the 5th Aegean Summer School, "From Gravity to Thermal Gauge Theories: the AdS/CFT Correspondence"; v2: references adde

Theory of Magneto--Acoustic Transport in Modulated Quantum Hall Systems Near ν=1/2\nu=1/2

Motivated by the experimental results of Willett et al [Phys.Rev. Lett., {\bf 78}, 4478 (1997)] we develop a magneto-transport theory for the response of a two dimensional electron gas (2DEG) in the Fractional Quantum Hall Regime near Landau level filling factor $\nu = 1/2$ to the surface acoustic wave (SAW) in the presence of an added periodic density modulation. We assume there exists a Composite Fermion Fermi Surface (CF-FS) at $\nu = 1/2$, and we show that the deformation of the (CF-FS) due to the density modulation can be at the origin of the observed transport anomalies for the experimental conditions. Our analysis is carried out particularly for the non-local case which corresponds to the SAW experiments. We introduce a new model of a deformed CF-FS. The model permits us to explain anomalous features of the response of the modulated 2DEG to the SAW near $\nu = 1/2:$ namely the nonlinear wave vector dependence of the electron conductivity, the appearance of peaks in the SAW velocity shift and attenuation and the anisotropy of the effect, all of which originate from contributions to the conductivity tensor due to the regions of the CF-FS which are flattened by the applied modulation.Comment: 13 pages, 4 figures, the published versio

The calibration of the Sudbury Neutrino Observatory using uniformly distributed radioactive sources

The production and analysis of distributed sources of 24Na and 222Rn in the Sudbury Neutrino Observatory (SNO) are described. These unique sources provided accurate calibrations of the response to neutrons, produced through photodisintegration of the deuterons in the heavy water target, and to low energy betas and gammas. The application of these sources in determining the neutron detection efficiency and response of the 3He proportional counter array, and the characteristics of background Cherenkov light from trace amounts of natural radioactivity is described.Comment: 24 pages, 13 figure

Holographic mesons in various dimensions

We calculate the spectrum of fluctuations of a probe Dk-brane in the background of N Dp-branes, for k=p,p+2,p+4 and p< 5. The result corresponds to the mesonic spectrum of a (p+1)-dimensional super-Yang-Mills (SYM) theory coupled to `dynamical quarks', i.e., fields in the fundamental representation -- the latter are confined to a defect for k=p and p+2. We find a universal behaviour where the spectrum is discrete and the mesons are deeply bound. The mass gap and spectrum are set by the scale M ~ m_q/g_{eff}(m_q), where m_q is the mass of the fundamental fields and g_{eff}(m_q) is the effective coupling evaluated at the quark mass, i.e. g_{eff}^2(m_q)=g_{ym}^2 N m_q^{p-3}. We consider the evolution of the meson spectra into the far infrared of three-dimensional SYM, where the gravity dual lifts to M-theory. We also argue that the mass scale appearing in the meson spectra is dictated by holography.Comment: 44 pages, 2 figures; v2: typos corrected, references adde

Clustered mutations in the GRIK2 kainate receptor subunit gene underlie diverse neurodevelopmental disorders

Kainate receptors (KARs) are glutamate-gated cation channels with diverse roles in the central nervous system. Bi-allelic loss of function of the KAR-encoding gene GRIK2 causes a nonsyndromic neurodevelopmental disorder (NDD) with intellectual disability and developmental delay as core features. The extent to which mono-allelic variants in GRIK2 also underlie NDDs is less understood because only a single individual has been reported previously. Here, we describe an additional eleven individuals with heterozygous de novo variants in GRIK2 causative for neurodevelopmental deficits that include intellectual disability. Five children harbored recurrent de novo variants (three encoding p.Thr660Lys and two p.Thr660Arg), and four children and one adult were homozygous for a previously reported variant (c.1969G>A [p.Ala657Thr]). Individuals with shared variants had some overlapping behavioral and neurological dysfunction, suggesting that the GRIK2 variants are likely pathogenic. Analogous mutations introduced into recombinant GluK2 KAR subunits at sites within the M3 transmembrane domain (encoding p.Ala657Thr, p.Thr660Lys, and p.Thr660Arg) and the M3-S2 linker domain (encoding p.Ile668Thr) had complex effects on functional properties and membrane localization of homomeric and heteromeric KARs. Both p.Thr660Lys and p.Thr660Arg mutant KARs exhibited markedly slowed gating kinetics, similar to p.Ala657Thr-containing receptors. Moreover, we observed emerging genotype-phenotype correlations, including the presence of severe epilepsy in individuals with the p.Thr660Lys variant and hypomyelination in individuals with either the p.Thr660Lys or p.Thr660Arg variant. Collectively, these results demonstrate that human GRIK2 variants predicted to alter channel function are causative for early childhood development disorders and further emphasize the importance of clarifying the role of KARs in early nervous system development.Genetics of disease, diagnosis and treatmen

Clustered mutations in the GRIK2 kainate receptor subunit gene underlie diverse neurodevelopmental disorders (vol 108, pg 1692, 2021)

Neurolog

Measurement of the νe and total 8B solar neutrino fluxes with the Sudbury Neutrino Observatory phase-III data set

This paper details the solar neutrino analysis of the 385.17-day phase-III data set acquired by the Sudbury Neutrino Observatory (SNO). An array of 3He proportional counters was installed in the heavy-water target to measure precisely the rate of neutrino-deuteron neutral-current interactions. This technique to determine the total active 8B solar neutrino flux was largely independent of the methods employed in previous phases. The total flux of active neutrinos was measured to be 5.54-0.31+0.33(stat.)-0.34+0.36(syst.)×106 cm-2 s-1, consistent with previous measurements and standard solar models. A global analysis of solar and reactor neutrino mixing parameters yielded the best-fit values of Δm2=7.59-0.21+0.19×10 -5eV2 and θ=34.4-1.2+1.3degrees