A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

The physiological variability of channel density in hippocampal CA1 pyramidal cells and interneurons explored using a unified data-driven modeling workflow

Every neuron is part of a network, exerting its function by transforming multiple spatiotemporal synaptic input patterns into a single spiking output. This function is specified by the particular shape and passive electrical properties of the neuronal membrane, and the composition and spatial distribution of ion channels across its processes. For a variety of physiological or pathological reasons, the intrinsic input/output function may change during a neuron’s lifetime. This process results in high variability in the peak specific conductance of ion channels in individual neurons. The mechanisms responsible for this variability are not well understood, although there are clear indications from experiment and modeling that degeneracy and correlation among multiple channels may be involved. Here, we studied this issue in biophysical models of hippocampal CA1 pyramidal neurons and interneurons. Using a unified data-driven simulation workflow and starting from a set of experimental recordings and morphological reconstructions obtained from rats, we built and analyzed several ensembles of morphologically and biophysically accurate single cell models with intrinsic electrophysiological properties consistent with experimental findings. The results suggest that the set of conductances expressed in any given hippocampal neuron may be considered as belonging to two groups: one subset is responsible for the major characteristics of the firing behavior in each population and the other responsible for a robust degeneracy. Analysis of the model neurons suggests several experimentally testable predictions related to the combination and relative proportion of the different conductances that should be expressed on the membrane of different types of neurons for them to fulfill their role in the hippocampus circuitry

Encoding and retrieval in a CA1 microcircuit model of the hippocampus

Recent years have witnessed a dramatic accumulation of knowledge about the morphological, physiological and molecular characteristics, as well as connectivity and synaptic properties of neurons in the mammalian hippocampus. Despite these advances, very little insight has been gained into the computational function of the different neuronal classes; in particular, the role of the various inhibitory interneurons in encoding and retrieval of information remains elusive. Mathematical and computational models of microcircuits play an instrumental role in exploring microcircuit functions and facilitate the dissection of operations performed by diverse inhibitory interneurons. A model of the CA1 microcircuitry is presented using biophysical representations of its major cell types: pyramidal, basket, axo-axonic, bistratified and oriens lacunosummoleculare cells. Computer simulations explore the biophysical mechanisms by which encoding and retrieval of spatio-temporal input patterns are achieved by the CA1 microcircuitry. The model proposes functional roles for the different classes of inhibitory interneurons in the encoding and retrieval cycles

Escaping from cycles through a glass transition

A random walk is performed over a disordered media composed of $N$ sites random and uniformly distributed inside a $d$-dimensional hypercube. The walker cannot remain in the same site and hops to one of its $n$ neighboring sites with a transition probability that depends on the distance $D$ between sites according to a cost function $E(D)$. The stochasticity level is parametrized by a formal temperature $T$. In the case $T = 0$, the walk is deterministic and ergodicity is broken: the phase space is divided in a ${\cal O}(N)$ number of attractor basins of two-cycles that trap the walker. For $d = 1$, analytic results indicate the existence of a glass transition at $T_1 = 1/2$ as $N \to \infty$. Below $T_1$, the average trapping time in two-cycles diverges and out-of-equilibrium behavior appears. Similar glass transitions occur in higher dimensions choosing a proper cost function. We also present some results for the statistics of distances for Poisson spatial point processes.Comment: 11 pages, 4 figure

Spatial Representation and Navigation in a Bio-inspired Robot

A biologically inspired computational model of rodent repre-sentation?based (locale) navigation is presented. The model combines visual input in the form of realistic two dimensional grey-scale images and odometer signals to drive the firing of simulated place and head direction cells via Hebbian synapses. The space representation is built incrementally and on-line without any prior information about the environment and consists of a large population of location-sensitive units (place cells) with overlapping receptive fields. Goal navigation is performed using reinforcement learning in continuous state and action spaces, where the state space is represented by population activity of the place cells. The model is able to reproduce a number of behavioral and neuro-physiological data on rodents. Performance of the model was tested on both simulated and real mobile Khepera robots in a set of behavioral tasks and is comparable to the performance of animals in similar tasks

Relationship between nerve fiber layer hemorrhages and outcomes in central retinal vein occlusion

PURPOSE. To evaluate the depth and pattern of retinal hemorrhage in acute central retinal vein occlusion (CRVO) and to correlate these with visual and anatomic outcomes. METHODS. Retinal hemorrhages were evaluated with color fundus photography and fluorescein angiography at baseline and follow-up. Snellen visual acuity (VA), central foveal thickness (CFT), extent of retinal ischemia, and development of neovascularization were analyzed. RESULTS. 108 eyes from 108 patients were evaluated. Mean age was 63.6 ± 16.1 years with a predilection for the right eye (73.1). Average follow-up was 17.2 ± 19.2 months. Mean VA at baseline was 20/126 and 20/80 at final follow-up. Baseline (P = 0.005) and final VA (P = 0.02) in eyes with perivascular nerve fiber layer (NFL) hemorrhages were significantly worse than in eyes with deep hemorrhages alone. Baseline CFT was greater in the group with perivascular hemorrhages (826 ± 394 μm) compared to the group with deep hemorrhages alone (455 ± 273 μm, P < 0.001). The 10 disc areas of retinal ischemia was more common in patients with perivascular (80.0) and peripapillary (31.3) versus deep hemorrhages alone (16.1, P < 0.001). Neovascularization of the iris was more common, although this differrence was not significant, in the groups with peripapillary (14.3) and perivascular (2.0) NFL versus deep hemorrhages alone (0.0). CONCLUSIONS. NFL retinal hemorrhages at baseline correlate with more severe forms of CRVO, with greater macular edema, poorer visual outcomes, and greater risk of ischemia and neovascularization. This may be related to the organization of the retinal capillary plexus. The depth and pattern of distribution of retinal hemorrhages in CRVO may provide an easily identifiable early biomarker of CRVO prognosis. Copyright 2020 The Author

Search for the Zγ decay mode of new high-mass resonances in pp collisions at √s = 13 TeV with the ATLAS detector

This letter presents a search for narrow, high-mass resonances in the Zγ final state with the Z boson decaying into a pair of electrons or muons. The √s = 13 TeV pp collision data were recorded by the ATLAS detector at the CERN Large Hadron Collider and have an integrated luminosity of 140 fb−1. The data are found to be in agreement with the Standard Model background expectation. Upper limits are set on the resonance production cross section times the decay branching ratio into Zγ. For spin-0 resonances produced via gluon–gluon fusion, the observed limits at 95% confidence level vary between 65.5 fb and 0.6 fb, while for spin-2 resonances produced via gluon–gluon fusion (or quark–antiquark initial states) limits vary between 77.4 (76.1) fb and 0.6 (0.5) fb, for the mass range from 220 GeV to 3400 GeV

Search for lepton-favour violation in high-mass dilepton final states using 139 fb−1 of pp collisions at √s = 13 TeV with the ATLAS detector

A search is performed for a heavy particle decaying into different-flavour, dilepton final states, using 139 fb−1 of proton-proton collision data at √s = 13 TeV collected in 2015–2018 by the ATLAS detector at the Large Hadron Collider. Final states with electrons, muons and hadronically decaying tau leptons are considered (eμ, eτ or μτ). No significant excess over the Standard Model predictions is observed. Upper limits on the production cross-section are set as a function of the mass of a Z′ boson, a supersymmetric τ-sneutrino, and a quantum black-hole. The observed 95% CL lower mass limits obtained on a typical benchmark model Z′ boson are 5.0 TeV (eμ), 4.0 TeV (eτ), and 3.9 TeV (μτ), respectively

Search for third-generation vector-like leptons in pp collisions at s√ = 13 TeV with the ATLAS detector

A search for vector-like leptons in multilepton (two, three, or four-or-more electrons plus muons) final states with zero or more hadronic τ-lepton decays is presented. The search is performed using a dataset corresponding to an integrated luminosity of 139 fb−1 of proton-proton collisions at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector at the LHC. To maximize the separation of signal and background, a machine-learning classifier is used. No excess of events is observed beyond the Standard Model expectation. Using a doublet vector-like lepton model, vector-like leptons coupling to third-generation Standard Model leptons are excluded in the mass range from 130 GeV to 900 GeV at the 95% confidence level, while the highest excluded mass is expected to be 970 GeV

Search for heavy Higgs bosons with flavour-violating couplings in multi-lepton plus b-jets final states in pp collisions at 13 TeV with the ATLAS detector

A search for new heavy scalars with flavour-violating decays in final states with multiple leptons and b-tagged jets is presented. The results are interpreted in terms of a general two-Higgs-doublet model involving an additional scalar with couplings to the top-quark and the three up-type quarks (ρtt, ρtc, and ρtu). The targeted signals lead to final states with either a same-sign top-quark pair, three top-quarks, or four top-quarks. The search is based on a data sample of proton-proton collisions at √s = 13 TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb−1. Events are categorised depending on the multiplicity of light charged leptons (electrons or muons), total lepton charge, and a deep-neural-network output to enhance the purity of each of the signals. Masses of an additional scalar boson mH between 200 − 630 GeV with couplings ρtt = 0.4, ρtc = 0.2, and ρtu = 0.2 are excluded at 95% confidence level. Additional interpretations are provided in models of R-parity violating supersymmetry, motivated by the recent flavour and (g − 2)μ anomalies