On the Convergence of Population Protocols When Population Goes to Infinity

Population protocols have been introduced as a model of sensor networks consisting of very limited mobile agents with no control over their own movement. A population protocol corresponds to a collection of anonymous agents, modeled by finite automata, that interact with one another to carry out computations, by updating their states, using some rules. Their computational power has been investigated under several hypotheses but always when restricted to finite size populations. In particular, predicates stably computable in the original model have been characterized as those definable in Presburger arithmetic. We study mathematically the convergence of population protocols when the size of the population goes to infinity. We do so by giving general results, that we illustrate through the example of a particular population protocol for which we even obtain an asymptotic development. This example shows in particular that these protocols seem to have a rather different computational power when a huge population hypothesis is considered.Comment: Submitted to Applied Mathematics and Computation. 200

Discrete Morse theory and graph braid groups

If Gamma is any finite graph, then the unlabelled configuration space of n points on Gamma, denoted UC^n(Gamma), is the space of n-element subsets of Gamma. The braid group of Gamma on n strands is the fundamental group of UC^n(Gamma). We apply a discrete version of Morse theory to these UC^n(Gamma), for any n and any Gamma, and provide a clear description of the critical cells in every case. As a result, we can calculate a presentation for the braid group of any tree, for any number of strands. We also give a simple proof of a theorem due to Ghrist: the space UC^n(Gamma) strong deformation retracts onto a CW complex of dimension at most k, where k is the number of vertices in Gamma of degree at least 3 (and k is thus independent of n).Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-44.abs.htm

Spine intervertebral disc labeling using a fully convolutional redundant counting model

Labeling intervertebral discs is relevant as it notably enables clinicians to understand the relationship between a patient's symptoms (pain, paralysis) and the exact level of spinal cord injury. However manually labeling those discs is a tedious and user-biased task which would benefit from automated methods. While some automated methods already exist for MRI and CT-scan, they are either not publicly available, or fail to generalize across various imaging contrasts. In this paper we combine a Fully Convolutional Network (FCN) with inception modules to localize and label intervertebral discs. We demonstrate a proof-of-concept application in a publicly-available multi-center and multi-contrast MRI database (n=235 subjects). The code is publicly available at https://github.com/neuropoly/vertebral-labeling-deep-learning.Comment: MIDL 202

Nonrelativistic spatiotemporal quantum reference frames

Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special attention. Here, we introduce and analyze a nonrelativistic framework in which each system contains an internal clock in addition to its external (spatial) degree of freedom and, hence, can be used as a spatiotemporal quantum reference frame. We present expressions for expectation values and variances of relevant observables in different perspectives, as well as relations between these quantities in different perspectives in scenarios with no interactions. In particular, we show that even in these simple scenarios the relative uncertainty between clocks affects the relative spatial spread of the systems

Viral Load Monitoring of Antiretroviral Therapy, cohort viral load and HIV transmission in Southern Africa: A Mathematical Modelling Analysis

In low-income settings, treatment failure is often identified using CD4 cell count monitoring. Consequently, patients remain on a failing regimen, resulting in a higher risk of transmission. We investigated the benefit of routine viral load monitoring for reducing HIV transmission

Quantum memories based on engineered dissipation

Storing quantum information for long times without disruptions is a major requirement for most quantum information technologies. A very appealing approach is to use self-correcting Hamiltonians, i.e. tailoring local interactions among the qubits such that when the system is weakly coupled to a cold bath the thermalization process takes a long time. Here we propose an alternative but more powerful approach in which the coupling to a bath is engineered, so that dissipation protects the encoded qubit against more general kinds of errors. We show that the method can be implemented locally in four dimensional lattice geometries by means of a toric code, and propose a simple 2D set-up for proof of principle experiments.Comment: 6 +8 pages, 4 figures, Includes minor corrections updated references and aknowledgement

2-D Radiative Transfer in Protostellar Envelopes: II. An Evolutionary Sequence

We present model spectral energy distributions, colors, polarization, and images for an evolutionary sequence of a low-mass protostar from the early collapse stage (Class 0) to the remnant disk stage (Class III). We find a substantial overlap in colors and SEDs between protostars embedded in envelopes (Class 0-I) and T Tauri disks (Class II), especially at mid-IR wavelengths. Edge-on Class I-II sources show double-peaked spectral energy distributions, with a short-wavelength hump due to scattered light and the long-wavelength hump due to thermal emission. These are the bluest sources in mid-IR color-color diagrams. Since Class 0 and I sources are diffuse, the size of the aperture over which fluxes are integrated has a substantial effect on the computed colors, with larger aperture results showing significantly bluer colors. This causes overlap in color-color diagrams between all evolutionary states, especially in the mid-IR. However the near-IR polarization of the Class 0 sources is much higher than the Class I-II sources, providing a means to separate these evolutionary states. We varied the grain properties in the circumstellar envelope, allowing for larger grains in the disk midplane and smaller in the envelope. We find that grain growth in disks of Class I sources can be detected at wavelengths greater than 100 $\mu$m. Our image calculations predict that the diffuse emission from edge-on Class I and II sources should be detectable in the mid-IR with the Space Infrared Telescope Facility (SIRTF) in nearby star forming regions (out to several hundred parsecs).Comment: A version with high-resolution images is available at http://www.astro.wisc.edu/glimpse/glimpsepubs.htm

Absence of Magnetism in Hcp Iron-Nickel at 11 K

Synchrotron Mössbauer spectroscopy (SMS) was performed on an hcp-phase alloy of composition Fe92Ni8 at a pressure of 21 GPa and a temperature of 11 K. Density functional theoretical calculations predict antiferromagnetism in both hcp Fe and hcp Fe-Ni. For hcp Fe, these calculations predict no hyperfine magnetic field, consistent with previous experiments. For hcp Fe-Ni, however, substantial hyperfine magnetic fields are predicted, but these were not observed in the SMS spectra. Two possible explanations are suggested. First, small but significant errors in the generalized gradient approximation density functional may lead to an erroneous prediction of magnetic order or of erroneous hyperfine magnetic fields in antiferromagnetic hcp Fe-Ni. Alternately, quantum fluctuations with periods much shorter than the lifetime of the nuclear excited state would prohibit the detection of moments by SMS

The relationship between self‐reported received and perceived social support: A meta‐analytic review

Social support is broad term encompassing a variety of constructs, including support perceptions (perceived support) and receipt of supportive behaviors (received support). Of these constructs, only perceived support has been regarded as consistently linked to health, and researchers have offered differing assessments of the strength of the received‐perceived support relationship. An overall estimate of the received‐perceived support relationship would clearly further the dialogue on the relationship between received and perceived support and thus assist in the theoretical development of the field. This study evaluated all available studies using the Inventory of Socially Supportive Behaviors (ISSB; Barrera, Sandler, & Ramsey, 1981, American Journal of Community Psychology, 9, 435–447) and any measure of perceived social support. Using effect sizes from 23 studies, we found an average correlation of r = .35, p < .001. Implications of this estimate for further development of models of social support as well as interventions to enhance social support are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/117157/1/ajcp9100.pd