A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons

Corrigendum to: “Measurement of the tt ̄ production cross-section using eμ events with b-tagged jets in pp collisions at √s = 13 TeV with the ATLAS detector” [Phys. Lett. B 761 (2016) 136–157]

This paper describes a measurement of the inclusive top quark pair production cross-section (sigma(t (t) over bar)) with a data sample of 3.2fb(-1)of proton-proton collisions at a centre-of-mass energy of root s= 13TeV, collected in 2015 by the ATLAS detector at the LHC. This measurement uses events with an opposite-charge electron-muon pair in the final state. Jets containing b-quarks are tagged using an algorithm based on track impact parameters and reconstructed secondary vertices. The numbers of events with exactly one and exactly two b-tagged jets are counted and used to determine simultaneously sigma(t (t) over bar) and the efficiency to reconstruct and b-tag a jet from a top quark decay, thereby minimising the associated systematic uncertainties. The cross-section is measured to be:sigma(t (t) over bar) = 818 +/- 8 (stat) +/- 27 (syst) +/- 19 (lumi) +/- 12 (beam) pb,where the four uncertainties arise from data statistics, experimental and theoretical systematic effects, the integrated luminosity and the LHC beam energy, giving a total relative uncertainty of 4.4%. The result is consistent with theoretical QCD calculations at next-to-next-to-leading order. A fiducial measurement corresponding to the experimental acceptance of the leptons is also presented

Measurement of the nuclear modification factor for muons from charm and bottom hadrons in Pb+Pb collisions at 5.02 TeV with the ATLAS detector

Heavy-flavour hadron production provides information about the transport properties and microscopic structure of the quark-gluon plasma created in ultra-relativistic heavy-ion collisions. A measurement of the muons from semileptonic decays of charm and bottom hadrons produced in Pb+Pb and pp collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV with the ATLAS detector at the Large Hadron Collider is presented. The Pb+Pb data were collected in 2015 and 2018 with sampled integrated luminosities of 208 mu b(-1) and 38 mu b(-1), respectively, and pp data with a sampled integrated luminosity of 1.17 pb(-1) were collected in 2017. Muons from heavy-flavour semileptonic decays are separated from the light-flavour hadronic background using the momentum imbalance between the inner detector and muon spectrometer measurements, and muons originating from charm and bottom decays are further separated via the muon track's transverse impact parameter. Differential yields in Pb+Pb collisions and differential cross sections in pp collisions for such muons are measured as a function of muon transverse momentum from 4 GeV to 30 GeV in the absolute pseudorapidity interval vertical bar eta vertical bar < 2. Nuclear modification factors for charm and bottom muons are presented as a function of muon transverse momentum in intervals of Pb+Pb collision centrality. The bottom muon results are the most precise measurement of b quark nuclear modification at low transverse momentum where reconstruction of B hadrons is challenging. The measured nuclear modification factors quantify a significant suppression of the yields of muons from decays of charm and bottom hadrons, with stronger effects for muons from charm hadron decays

A search for an unexpected asymmetry in the production of e+μ− and e−μ+ pairs in proton-proton collisions recorded by the ATLAS detector at root s = 13 TeV

This search, a type not previously performed at ATLAS, uses a comparison of the production cross sections for e(+)mu(-) and e(-)mu(+) pairs to constrain physics processes beyond the Standard Model. It uses 139 fb(-1) of proton-proton collision data recorded at root s = 13 TeV at the LHC. Targeting sources of new physics which prefer final states containing e(+)mu(-) and e(-)mu(+), the search contains two broad signal regions which are used to provide model-independent constraints on the ratio of cross sections at the 2% level. The search also has two special selections targeting supersymmetric models and leptoquark signatures. Observations using one of these selections are able to exclude, at 95% confidence level, singly produced smuons with masses up to 640 GeV in a model in which the only other light sparticle is a neutralino when the R-parity-violating coupling lambda(23)(1)' is close to unity. Observations using the other selection exclude scalar leptoquarks with masses below 1880 GeV when g(1R)(eu) = g(1R)(mu c) = 1, at 95% confidence level. The limit on the coupling reduces to g(1R)(eu) = g(1R)(mu c) = 0.46 for a mass of 1420 GeV

Measurements of photo-nuclear jet production in Pb plus Pb collisions with ATLAS

Ultra-peripheral heavy ion collisions provide a unique opportunity to study the parton distributions in the colliding nuclei via the measurement of photo-nuclear jet production. An analysis of jet production in ultra-peripheral Pb+Pb collisions at √sNN = 5.02 TeV performed using data collected with the ATLAS detector in 2015 is described. The data set corresponds to a total Pb+Pb integrated luminosity of 0.38 nb−1. The ultra-peripheral collisions are selected using a combination of forward neutron and rapidity gap requirements. The cross-sections, not unfolded for detector response, are compared to results from Pythia Monte Carlo simulations re-weighted to match a photon spectrum obtained from the STARlight model. Qualitative agreement between data and these simulations is observed over a broad kinematic range suggesting that using these collisions to measure nuclear parton distributions is experimentally realisable

Measurements of photo-nuclear jet production in Pb + Pb collisions with ATLAS

Ultra-peripheral heavy ion collisions provide a unique opportunity to study the parton distributions in the colliding nuclei via the measurement of photo-nuclear jet production. An analysis of jet production in ultra-peripheral Pb+Pb collisions at √sNN = 5.02 TeV performed using data collected with the ATLAS detector in 2015 is described. The data set corresponds to a total Pb+Pb integrated luminosity of 0.38 nb⁻¹. The ultra-peripheral collisions are selected using a combination of forward neutron and rapidity gap requirements. The cross-sections, not unfolded for detector response, are compared to results from Pythia Monte Carlo simulations re-weighted to match a photon spectrum obtained from the STARlight model. Qualitative agreement between data and these simulations is observed over a broad kinematic range suggesting that using these collisions to measure nuclear parton distributions is experimentally realisable

Visual-Vestibular Dissociation: Differential Sensitivity To Acceleration And Velocity

Vision contributes to balance, and vision is thought to dominate vestibular (or inertial) information in the perception of linear self-motion (Lishman & Lee, 1973; Mittelstaedt & Mittelstaedt, 2001). Is the visual system more sensitive to linear whole-field accelerations than are inertial systems? This would be surprising because the visual system is regarded as being much less sensitive to local acceleration signals than to local velocity signals (e.g., Eagle, 1996). We measured discrimination thresholds (JNDs) for peak velocity and for peak acceleration using immersive whole-field visual signals for linear motion (in an HMD) as well as non-visual whole-body inertial experiences (on a motorized cart). In both modalities, motion stimuli were developed in which peak acceleration and peak velocity were decoupled. The initial acceleration profiles in each case were roughly Gaussian, while the resulting velocity profiles were S-shaped. Acceleration duration was varied between 1 and 1.5 seconds, so that peak velocity could not be used to substitute for peak acceleration, nor could acceleration substitute for velocity without precise temporal integration. In a 2 X 2 design, stimuli were either visual (virtual hallway presented in a 60 deg FOV HMD) or inertial (on a computer-controlled cart), and judgments were either of peak velocity or peak acceleration. Observers made comparisons to an internal standard, with feedback. Despite the feedback, observers in the inertial experiments confounded velocity with acceleration, and JNDs for peak velocity discrimination from inertial senses were about 10% of the standard, whereas JNDs for peak acceleration were about 5%. Conversely JNDs for peak visual velocity were about 5% of the standard, while those for acceleration were about 10%. Evidently, visual superiority is limited to the perception of velocity. Visual and vestibular sensitivities may be complementary in perceiving accelerative and non-accelerative phases of self-motion

Comparison of the phase portraits of excitatory-inhibitory networks.

<p><b>A.</b> Architecture of the large network of spiking neurons. <b>B.</b> Architecture of the network of two complex-valued firing-rate units. <b>C–E.</b> A sparse, randomly-connected network of QIF, EIF, or LIF neurons, respectively. For each connection strength, 50 ms of the firing rate of the excitatory population is shown in black. Stability diagram of the corresponding two-unit complex-valued rate-model network is superimposed on each panel, where orange indicates a stable limit-cycle, and white a stable fixed-point. A constant external input was also included with mean and variance set to produce a baseline firing rate of 50 Hz and a CV of 0.1 when and were zero. <b>F.</b> Sample excitatory (top, red) and inhibitory (bottom, blue) dynamics from both the spiking (dark) and rate (light) EIF networks with and (green square in D). An exemplary spike raster of 50 neurons from each population (excitatory/inhibitory, respectively) is overlaid on the firing rate curves of both networks. Horizontal scale bar = 10 ms. Vertical scale bar = 10 Hz. <b>G.</b> Power spectra of excitatory (top) and inhibitory (bottom) units from both networks, with spiking network in darker shades and rate network in lighter shades, as in F. Both networks have a dominant frequency near 50 Hz. Curves represent mean power spectra from all parameters in D for which both networks are oscillatory (standard error comparable to line width). <b>H.</b> Cross-correlation between excitatory and inhibitory units for EIF spiking (dark purple) and rate (light purple) networks. Both networks exhibit maximal correlation at a small positive phase shift, indicating that inhibitory oscillations follow closely behind excitatory oscillations. As in G, curves represent means over all parameters producing oscillations in D, with standard error smaller than line width.</p

Parameters of the integrate-and-fire models.

<p>Parameters of the integrate-and-fire models.</p

Rate model accuracy as a function of input noise.

<p>The response of each rate model is compared to a spiking population receiving an input with fluctuating common term and constant variance. The common input is composed of a baseline level and a fluctuating component composed of equal-amplitude sinusoidal oscillations with random phases and frequencies of 61, 50, 33, 13.1, and 7.9 Hz. <b>A–B.</b> Response of EIF population and both rate models to input with a CV of either 0.1 (A) or 0.8 (B). Top, middle, and bottom panels are as described in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003301#pcbi-1003301-g001" target="_blank">Figure 1</a>. <b>C.</b> For each spiking model and each CV value, the maximum of the shifted correlation coefficient is computed between the trial-averaged firing rate of the spiking population and each rate model. The trial-averaged firing rate of a spiking population is computed from 300 repetitions of the same common input and different instantiations of noise. Each point in C represents the mean standard error of 10 different instantiations of the random phase shifts in the common input. In most cases, error bars are smaller than the marker. The maximal shifted correlation coefficient between the complex-valued rate model and the EIF, QIF, and LIF are shown in cyan, green, and blue, respectively. The same comparisons between the EIF and the classic rate model either optimized for each CV value or just to CV = 0.8 are shown in red and dark red, respectively. Classic rate model comparisons to the LIF and QIF produce similar results but are omitted for clarity.</p