Massless Scalar Field Propagator in a Quantized Space-Time

We consider in detail the analytic behaviour of the non-interacting massless scalar field two-point function in H.S. Snyder's discretized non-commuting spacetime. The propagator we find is purely real on the Euclidean side of the complex $p^2$ plane and goes like $1/p^2$ as $p^2\to 0$ from either the Euclidean or Minkowski side. The real part of the propagator goes smoothly to zero as $p^2$ increases to the discretization scale $1/a^2$ and remains zero for $p^2>1/a^2$. This behaviour is consistent with the termination of single-particle propagation on the ultraviolet side of the discretization scale. The imaginary part of the propagator, consistent with a multiparticle-production branch discontinuity, is finite and continuous on the Minkowski side, slowly falling to zero when $1/a^2<p^2<\infty$. Finally, we argue that the spectral function for the multiparticle states appears to saturate as $p^2$ probes just beyond the $1/a^2$ discretization scale. We speculate on the cosmological consequences of such a spectral function.Comment: 6 pages, 1 eps figure embedded in manuscrip

Flows on Graphs with Random Capacities

We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold that depends on the distribution of capacities. We then examine the maximal total flux from the root to the leaves. Our methods generalize to simple graphs with loops, e.g., to hierarchical lattices and to complete graphs.Comment: 8 pages, 6 figure

Computing singularities of perturbation series

Many properties of current \emph{ab initio} approaches to the quantum many-body problem, both perturbational or otherwise, are related to the singularity structure of Rayleigh--Schr\"odinger perturbation theory. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the perturbed Hamiltonian on a vector, and does not rely on the terms in the perturbation series. Some illustrative model problems are studied, including a Helium-like model with $\delta$-function interactions for which M{\o}ller--Plesset perturbation theory is considered and the radius of convergence found.Comment: 11 figures, submitte

The Type IIP SN 2007od in UGC 12846: from a bright maximum to dust formation in the nebular phase

Ultraviolet (UV), optical and near infrared (NIR) observations of the type IIP supernova (SN) 2007od are presented, covering from the maximum light to the late phase, allowing to investigate in detail different physical phenomena in the expanding ejecta. These data turn this object into one of the most peculiar IIP ever studied. The early light curve of SN 2007od is similar to that of a bright IIPs with a short plateau, a bright peak (MV = -18 mag), but a very faint optical light curve at late time. However, with the inclusion of mid infrared (MIR) observations during the radioactive decay we have estimate a M(56Ni) ~ 2\times10^-2 M\odot. Modeling the bolometric light curve, ejecta expansion velocities and black-body temperature, we estimate a total ejected mass was 5 - 7.5 M\odot with a kinetic energy of at least 0.5 \times 10^51 erg. The early spectra reveal a boxy H{\alpha} profile and high velocities features of the Balmer series that suggest interaction between the ejecta and a close circum-stellar matter (CSM). SN 2007od may be, therefore, an intermediate case between a Type IIn SN and a typical Type IIP SN. Also late spectra show a clear evidence of CSM and the presence of dust formed inside the ejecta. The episodes of mass loss short before explosion, the bright plateau, along with the relatively small amount of 56Ni and the faint [O I] observed in the nebular spectra are consistent with a super-asympthotic giant branch (super-AGB) progenitor (M~9.7 - 11 M\odot).Comment: V2, some test added and three figures changed from the first version. 21 pages, 18 figures, accepted for publication in MNRAS on May 24, 201

Moderately Luminous type II Supernovae

Core-collapse Supernovae (CC-SNe) descend from progenitors more massive than about 8 Msun. Because of the young age of the progenitors, the ejecta may eventually interact with the circumstellar medium (CSM) via highly energetic processes detectable in the radio, X-ray, ultraviolet (UV) and, sometimes, in the optical domains. In this paper we present ultraviolet, optical and near infrared observations of five type II SNe, namely SNe 2009dd, 2007pk, 2010aj, 1995ad, and 1996W. Together with few other SNe they form a group of moderately luminous type II events. We collected photometry and spectroscopy with several telescopes in order to construct well-sampled light curves and spectral evolutions from the photospheric to the nebular phases. Both photometry and spectroscopy indicate a degree of heterogeneity in this sample. The light curves have luminous peak magnitudes ($-16.95<M_{B}<-18.70$). The ejected masses of ^56\ni for three SNe span a wide range of values ($2.8\times10^{-2}$Msun$<$M(\ni)$<1.4\times10^{-1}$Msun), while for a fourth (SN2010aj) we could determine a stringent upper limit ($7\times10^{-3}$Msun). Clues of interaction, such as the presence of high velocity (HV) features of the Balmer lines, are visible in the photospheric spectra of SNe 2009dd and 1996W. For SN2007pk we observe a spectral transition from a type IIn to a standard type II SN. Modelling the observations of SNe 2009dd, 2010aj and 1995ad with radiation hydrodynamics codes, we infer kinetic plus thermal energies of about 0.2-0.5 foe, initial radii of 2-5$\times10^{13}$ cm and ejected masses of $\sim$5.0-9.5 Msun. These values suggest moderate-mass, super-asymptotic giant branch (SAGB) or red super-giants (RSG) stars as SN precursors, in analogy with other luminous type IIP SNe 2007od and 2009bw.Comment: 28 pages, 27 fig, accepted by A&A, 3 pages of online material, abstract abridged. revised significantly with respect to the previous versio

Supervised Learning in Multilayer Spiking Neural Networks

The current article introduces a supervised learning algorithm for multilayer spiking neural networks. The algorithm presented here overcomes some limitations of existing learning algorithms as it can be applied to neurons firing multiple spikes and it can in principle be applied to any linearisable neuron model. The algorithm is applied successfully to various benchmarks, such as the XOR problem and the Iris data set, as well as complex classifications problems. The simulations also show the flexibility of this supervised learning algorithm which permits different encodings of the spike timing patterns, including precise spike trains encoding.Comment: 38 pages, 4 figure

Associations of sNfL with clinico-radiological measures in a large MS population

OBJECTIVE: Evaluation of serum neurofilament light chain (sNfL), measured using high-throughput assays on widely accessible platforms in large, real-world MS populations, is a critical step for sNfL to be utilized in clinical practice. METHODS: Multiple Sclerosis Partners Advancing Technology and Health Solutions (MS PATHS) is a network of healthcare institutions in the United States and Europe collecting standardized clinical/imaging data and biospecimens during routine clinic visits. sNfL was measured in 6974 MS and 201 healthy control (HC) participants, using a high-throughput, scalable immunoassay. RESULTS: Elevated sNfL levels for age (sNfL-E) were found in 1238 MS participants (17.8%). Factors associated with sNfL-E included male sex, younger age, progressive disease subtype, diabetes mellitus, impaired renal function, and active smoking. Higher body mass index (BMI) was associated with lower odds of elevated sNfL. Active treatment with disease-modifying therapy was associated with lower odds of sNfL-E. MS participants with sNfL-E exhibited worse neurological function (patient-reported disability, walking speed, manual dexterity, and cognitive processing speed), lower brain parenchymal fraction, and higher T2 lesion volume. Longitudinal analyses revealed accelerated short-term rates of whole brain atrophy in sNfL-E participants and higher odds of new T2 lesion development, although both MS participants with or without sNfL-E exhibited faster rates of whole brain atrophy compared to HC. Findings were consistent in analyses examining age-normative sNfL Z-scores as a continuous variable. INTERPRETATION: Elevated sNfL is associated with clinical disability, inflammatory disease activity, and whole brain atrophy in MS, but interpretation needs to account for comorbidities including impaired renal function, diabetes, and smoking