69 research outputs found
Dynamics of stochastic integrate-and-fire networks
The neural dynamics generating sensory, motor, and cognitive functions are
commonly understood through field theories for neural population activity.
Classic neural field theories are derived from highly simplified models of
individual neurons, while biological neurons are highly complex cells.
Integrate-and-fire neuron models balance biophysical detail and analytical
tractability. Here, we develop a statistical field theory for networks of
integrate-and-fire neurons with stochastic spike emission. This reveals an
exact mapping to a self-consistent renewal process and a new mean field theory
for the activity in these networks. The mean field theory has a rate-dependent
leak, approximating the spike-driven resets of the membrane voltage. This gives
rise to bistability between quiescent and active states in homogenous and
excitatory-inhibitory pulse-coupled networks. The field-theoretic framework
also exposes fluctuation corrections to the mean field theory. We find that due
to the spike reset, fluctuations suppress activity. We then examine the roles
of spike resets and recurrent inhibition in stabilizing network activity. We
calculate the phase diagram for inhibitory stabilization and find that an
inhibition-stabilized regime occurs in wide regions of parameter space,
consistent with experimental reports of inhibitory stabilization in diverse
brain regions. Fluctuations narrow the region of inhibitory stabilization,
consistent with their role in suppressing activity through spike resets.Comment: A previous version of this article, now retracted
(https://journals.aps.org/prx/abstract/10.1103/ PhysRevX.12.041007),
contained errors described in the retraction notice
(https://journals.aps.org/prx/ abstract/10.1103/PhysRevX.13.029904). These
errors have been corrected in the current article, which was re-reviewed and
accepted back at Phys. Rev.
Tensor decompositions of higher-order correlations by nonlinear Hebbian learning
Biological synaptic plasticity exhibits nonlinearities that are not accounted for by
classic Hebbian learning rules. Here, we introduce a simple family of generalized
nonlinear Hebbian learning rules. We study the computations implemented by their
dynamics in the simple setting of a neuron receiving feedforward inputs. These
nonlinear Hebbian rules allow a neuron to learn tensor decompositions of its higher-order
input correlations. The particular input correlation decomposed and the form
of the decomposition depend on the location of nonlinearities in the plasticity
rule. For simple, biologically motivated parameters, the neuron learns eigenvectors
of higher-order input correlation tensors. We prove that tensor eigenvectors are
attractors and determine their basins of attraction. We calculate the volume of those
basins, showing that the dominant eigenvector has the largest basin of attraction.
We then study arbitrary learning rules and find that any learning rule that admits a
finite Taylor expansion into the neural input and output also has stable equilibria at
generalized eigenvectors of higher-order input correlation tensors. Nonlinearities
in synaptic plasticity thus allow a neuron to encode higher-order input correlations
in a simple fashion.https://proceedings.neurips.cc/paper/2021/hash/5e34a2b4c23f4de585fb09a7f546f527-Abstract.htm
The NANOGrav 15-year Data Set: Search for Anisotropy in the Gravitational-Wave Background
The North American Nanohertz Observatory for Gravitational Waves (NANOGrav)
has reported evidence for the presence of an isotropic nanohertz gravitational
wave background (GWB) in its 15 yr dataset. However, if the GWB is produced by
a population of inspiraling supermassive black hole binary (SMBHB) systems,
then the background is predicted to be anisotropic, depending on the
distribution of these systems in the local Universe and the statistical
properties of the SMBHB population. In this work, we search for anisotropy in
the GWB using multiple methods and bases to describe the distribution of the
GWB power on the sky. We do not find significant evidence of anisotropy, and
place a Bayesian upper limit on the level of broadband anisotropy such
that . We also derive conservative estimates on the
anisotropy expected from a random distribution of SMBHB systems using
astrophysical simulations conditioned on the isotropic GWB inferred in the
15-yr dataset, and show that this dataset has sufficient sensitivity to probe a
large fraction of the predicted level of anisotropy. We end by highlighting the
opportunities and challenges in searching for anisotropy in pulsar timing array
data.Comment: 19 pages, 11 figures; submitted to Astrophysical Journal Letters as
part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave
Background. For questions or comments, please email [email protected]
The NANOGrav 12.5 yr Data Set: A Computationally Efficient Eccentric Binary Search Pipeline and Constraints on an Eccentric Supermassive Binary Candidate in 3C 66B
The radio galaxy 3C 66B has been hypothesized to host a supermassive black hole binary (SMBHB) at its center based on electromagnetic observations. Its apparent 1.05 yr period and low redshift (∼0.02) make it an interesting testbed to search for low-frequency gravitational waves (GWs) using pulsar timing array (PTA) experiments. This source has been subjected to multiple searches for continuous GWs from a circular SMBHB, resulting in progressively more stringent constraints on its GW amplitude and chirp mass. In this paper, we develop a pipeline for performing Bayesian targeted searches for eccentric SMBHBs in PTA data sets, and test its efficacy by applying it to simulated data sets with varying injected signal strengths. We also search for a realistic eccentric SMBHB source in 3C 66B using the NANOGrav 12.5 yr data set employing PTA signal models containing Earth term-only as well as Earth+pulsar term contributions using this pipeline. Due to limitations in our PTA signal model, we get meaningful results only when the initial eccentricity e 0 < 0.5 and the symmetric mass ratio η > 0.1. We find no evidence for an eccentric SMBHB signal in our data, and therefore place 95% upper limits on the PTA signal amplitude of 88.1 ± 3.7 ns for the Earth term-only and 81.74 ± 0.86 ns for the Earth+pulsar term searches for e 0 < 0.5 and η > 0.1. Similar 95% upper limits on the chirp mass are (1.98 ± 0.05) × 109 and (1.81 ± 0.01) × 109 M ☉. These upper limits, while less stringent than those calculated from a circular binary search in the NANOGrav 12.5 yr data set, are consistent with the SMBHB model of 3C 66B developed from electromagnetic observations
The NANOGrav 15-Year Data Set: Detector Characterization and Noise Budget
Pulsar timing arrays (PTAs) are galactic-scale gravitational wave detectors.
Each individual arm, composed of a millisecond pulsar, a radio telescope, and a
kiloparsecs-long path, differs in its properties but, in aggregate, can be used
to extract low-frequency gravitational wave (GW) signals. We present a noise
and sensitivity analysis to accompany the NANOGrav 15-year data release and
associated papers, along with an in-depth introduction to PTA noise models. As
a first step in our analysis, we characterize each individual pulsar data set
with three types of white noise parameters and two red noise parameters. These
parameters, along with the timing model and, particularly, a piecewise-constant
model for the time-variable dispersion measure, determine the sensitivity curve
over the low-frequency GW band we are searching. We tabulate information for
all of the pulsars in this data release and present some representative
sensitivity curves. We then combine the individual pulsar sensitivities using a
signal-to-noise-ratio statistic to calculate the global sensitivity of the PTA
to a stochastic background of GWs, obtaining a minimum noise characteristic
strain of at 5 nHz. A power law-integrated analysis shows
rough agreement with the amplitudes recovered in NANOGrav's 15-year GW
background analysis. While our phenomenological noise model does not model all
known physical effects explicitly, it provides an accurate characterization of
the noise in the data while preserving sensitivity to multiple classes of GW
signals.Comment: 67 pages, 73 figures, 3 tables; published in Astrophysical Journal
Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational
Wave Background. For questions or comments, please email
[email protected]
The NANOGrav 12.5 yr Data Set: Search for Gravitational Wave Memory
We present the results of a Bayesian search for gravitational wave (GW) memory in the NANOGrav 12.5 yr data set. We find no convincing evidence for any gravitational wave memory signals in this data set. We find a Bayes factor of 2.8 in favor of a model that includes a memory signal and common spatially uncorrelated red noise (CURN) compared to a model including only a CURN. However, further investigation shows that a disproportionate amount of support for the memory signal comes from three dubious pulsars. Using a more flexible red-noise model in these pulsars reduces the Bayes factor to 1.3. Having found no compelling evidence, we go on to place upper limits on the strain amplitude of GW memory events as a function of sky location and event epoch. These upper limits are computed using a signal model that assumes the existence of a common, spatially uncorrelated red noise in addition to a GW memory signal. The median strain upper limit as a function of sky position is approximately 3.3 × 10−14. We also find that there are some differences in the upper limits as a function of sky position centered around PSR J0613−0200. This suggests that this pulsar has some excess noise that can be confounded with GW memory. Finally, the upper limits as a function of burst epoch continue to improve at later epochs. This improvement is attributable to the continued growth of the pulsar timing array
The NANOGrav 15-year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries
Evidence for a low-frequency stochastic gravitational wave background has
recently been reported based on analyses of pulsar timing array data. The most
likely source of such a background is a population of supermassive black hole
binaries, the loudest of which may be individually detected in these datasets.
Here we present the search for individual supermassive black hole binaries in
the NANOGrav 15-year dataset. We introduce several new techniques, which
enhance the efficiency and modeling accuracy of the analysis. The search
uncovered weak evidence for two candidate signals, one with a
gravitational-wave frequency of 4 nHz, and another at 170 nHz. The
significance of the low-frequency candidate was greatly diminished when
Hellings-Downs correlations were included in the background model. The
high-frequency candidate was discounted due to the lack of a plausible host
galaxy, the unlikely astrophysical prior odds of finding such a source, and
since most of its support comes from a single pulsar with a commensurate binary
period. Finding no compelling evidence for signals from individual binary
systems, we place upper limits on the strain amplitude of gravitational waves
emitted by such systems.Comment: 23 pages, 13 figures, 2 tables. Accepted for publication in
Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set
and the Gravitational Wave Background. For questions or comments, please
email [email protected]
The NANOGrav 15-year Data Set: Observations and Timing of 68 Millisecond Pulsars
We present observations and timing analyses of 68 millisecond pulsars (MSPs)
comprising the 15-year data set of the North American Nanohertz Observatory for
Gravitational Waves (NANOGrav). NANOGrav is a pulsar timing array (PTA)
experiment that is sensitive to low-frequency gravitational waves. This is
NANOGrav's fifth public data release, including both "narrowband" and
"wideband" time-of-arrival (TOA) measurements and corresponding pulsar timing
models. We have added 21 MSPs and extended our timing baselines by three years,
now spanning nearly 16 years for some of our sources. The data were collected
using the Arecibo Observatory, the Green Bank Telescope, and the Very Large
Array between frequencies of 327 MHz and 3 GHz, with most sources observed
approximately monthly. A number of notable methodological and procedural
changes were made compared to our previous data sets. These improve the overall
quality of the TOA data set and are part of the transition to new pulsar timing
and PTA analysis software packages. For the first time, our data products are
accompanied by a full suite of software to reproduce data reduction, analysis,
and results. Our timing models include a variety of newly detected astrometric
and binary pulsar parameters, including several significant improvements to
pulsar mass constraints. We find that the time series of 23 pulsars contain
detectable levels of red noise, 10 of which are new measurements. In this data
set, we find evidence for a stochastic gravitational-wave background.Comment: 90 pages, 74 figures, 6 tables; published in Astrophysical Journal
Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational
Wave Background. For questions or comments, please email
[email protected]
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