787 research outputs found
Inferring decoding strategy from choice probabilities in the presence of noise correlations
The activity of cortical neurons in sensory areas covaries with perceptual decisions, a relationship often quantified by choice probabilities. While choice probabilities have been measured extensively, their interpretation has remained fraught with difficulty. Here, we derive the mathematical relationship between choice probabilities, read-out weights and noise correlations within the standard neural decision making model. Our solution allows us to prove and generalize earlier observations based on numerical simulations, and to derive novel predictions. Importantly, we show how the read-out weight profile, or decoding strategy, can be inferred from experimentally measurable quantities. Furthermore, we present a test to decide whether the decoding weights of individual neurons are optimal, even without knowing the underlying noise correlations. We confirm the practical feasibility of our approach using simulated data from a realistic population model. Our work thus provides the theoretical foundation for a growing body of experimental results on choice probabilities and correlations
Common Input Explains Higher-Order Correlations and Entropy in a Simple Model of Neural Population Activity
Simultaneously recorded neurons exhibit correlations whose underlying causes are not known. Here, we use a population of threshold neurons receiving correlated inputs to model neural population recordings. We show analytically that small changes in second-order correlations can lead to large changes in higher-order redundancies, and that the resulting interactions have a strong impact on the entropy, sparsity, and statistical heat capacity of the population. Our findings for this simple model may explain some surprising effects recently observed in neural population recordings
Bands, resonances, edge singularities and excitons in core level spectroscopy investigated within the dynamical mean field theory
Using a recently developed impurity solver we exemplify how dynamical mean
field theory captures band excitations, resonances, edge singularities and
excitons in core level x-ray absorption (XAS) and core level photo electron
spectroscopy (cPES) on metals, correlated metals and Mott insulators. Comparing
XAS at different values of the core-valence interaction shows how the
quasiparticle peak in the absence of core-valence interactions evolves into a
resonance of similar shape, but different origin. Whereas XAS is rather
insensitive to the metal insulator transition, cPES can be used, due to
nonlocal screening, to measure the amount of local charge fluctuation
Coupled Cluster Channels in the Homogeneous Electron Gas
We discuss diagrammatic modifications to the coupled cluster doubles (CCD)
equations, wherein different groups of terms out of rings, ladders,
crossed-rings and mosaics can be removed to form approximations to the coupled
cluster method, of interest due to their similarity with various types of
random phase approximations. The finite uniform electron gas is benchmarked for
14- and 54-electron systems at the complete basis set limit over a wide density
range and performance of different flavours of CCD are determined. These
results confirm that rings generally overcorrelate and ladders generally
undercorrelate; mosaics-only CCD yields a result surprisingly close to CCD. We
use a recently developed numerical analysis [J. J. Shepherd and A. Gr\"uneis,
Phys. Rev. Lett. 110, 226401 (2013)] to study the behaviours of these methods
in the thermodynamic limit. We determine that the mosaics, on forming the
Brueckner Hamltonian, open a gap in the effective one-particle eigenvalues at
the Fermi energy. Numerical evidence is presented which shows that methods
based on this renormalisation have convergent energies in the thermodynamic
limit including mosaic-only CCD, which is just a renormalised MP2. All other
methods including only a single channel, namely ladder-only CCD, ring-only CCD
and crossed-ring-only CCD, appear to yield divergent energies; incorporation of
mosaic terms prevents this from happening.Comment: 9 pages, 4 figures, 1 table. Comments welcome: [email protected]
Bayesian estimation of orientation preference maps
Imaging techniques such as optical imaging of intrinsic signals, 2-photon calcium imaging and voltage sensitive dye imaging can be used to measure the functional organization of visual cortex across different spatial and temporal scales. Here, we present Bayesian methods based on Gaussian processes for extracting topographic maps from functional imaging data. In particular, we focus on the estimation of orientation preference maps (OPMs) from intrinsic signal imaging data. We model the underlying map as a bivariate Gaussian process, with a prior covariance function that reflects known properties of OPMs, and a noise covariance adjusted to the data. The posterior mean can be interpreted as an optimally smoothed estimate of the map, and can be used for model based interpolations of the map from sparse measurements. By sampling from the posterior distribution, we can get error bars on statistical properties such as preferred orientations, pinwheel locations or pinwheel counts. Finally, the use of an explicit probabilistic model facilitates interpretation of parameters and quantitative model comparisons. We demonstrate our model both on simulated data and on intrinsic signaling data from ferret visual cortex
Training deep neural density estimators to identify mechanistic models of neural dynamics
Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-- trained using model simulations-- to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features, and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics
Electronic depth profiles with atomic layer resolution from resonant soft x-ray reflectivity
The analysis of x-ray reflectivity data from artificial heterostructures
usually relies on the homogeneity of optical properties of the constituent
materials. However, when the x-ray energy is tuned to an absorption edge, this
homogeneity no longer exists. Within the same material, spatial regions
containing elements at resonance will have optical properties very different
from regions without resonating sites. In this situation, models assuming
homogeneous optical properties throughout the material can fail to describe the
reflectivity adequately. As we show here, resonant soft x-ray reflectivity is
sensitive to these variations, even though the wavelength is typically large as
compared to the atomic distances over which the optical properties vary. We
have therefore developed a scheme for analyzing resonant soft x-ray
reflectivity data, which takes the atomic structure of a material into account
by "slicing" it into atomic planes with characteristic optical properties.
Using LaSrMnO4 as an example, we discuss both the theoretical and experimental
implications of this approach. Our analysis not only allows to determine
important structural information such as interface terminations and stacking of
atomic layers, but also enables to extract depth-resolved spectroscopic
information with atomic resolution, thus enhancing the capability of the
technique to study emergent phenomena at surfaces and interfaces.Comment: Completely overhauled with respect to the previous version due to
peer revie
Quantitative determination of bond order and lattice distortions in nickel oxide heterostructures by resonant x-ray scattering
We present a combined study of Ni -edge resonant x-ray scattering and
density functional calculations to probe and distinguish electronically driven
ordering and lattice distortions in nickelate heterostructures. We demonstrate
that due to the low crystal symmetry, contributions from structural distortions
can contribute significantly to the energy-dependent Bragg peak intensities of
a bond-ordered NdNiO reference film. For a LaNiO-LaAlO superlattice
that exhibits magnetic order, we establish a rigorous upper bound on the
bond-order parameter. We thus conclusively confirm predictions of a dominant
spin density wave order parameter in metallic nickelates with a
quasi-two-dimensional electronic structure
Group equivariant neural posterior estimation
Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude
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