Toroidal topology of population activity in grid cells

The medial entorhinal cortex is part of a neural system for mapping the position of an individual within a physical environment1. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations2, and are organized in modules3 that collectively form a population code for the animal’s allocentric position1. The invariance of the correlation structure of this population code across environments4,5 and behavioural states6,7, independent of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern1,8–11. However, whether grid cell networks show continuous attractor dynamics, and how they interface with inputs from the environment, has remained unclear owing to the small samples of cells obtained so far. Here, using simultaneous recordings from many hundreds of grid cells and subsequent topological data analysis, we show that the joint activity of grid cells from an individual module resides on a toroidal manifold, as expected in a two-dimensional CAN. Positions on the torus correspond to positions of the moving animal in the environment. Individual cells are preferentially active at singular positions on the torus. Their positions are maintained between environments and from wakefulness to sleep, as predicted by CAN models for grid cells but not by alternative feedforward models12. This demonstration of network dynamics on a toroidal manifold provides a population-level visualization of CAN dynamics in grid cells.

Synthesis of a comprehensive population code for contextual features in the awake sensory cortex

How cortical circuits build representations of complex objects is poorly understood. Individual neurons must integrate broadly over space, yet simultaneously obtain sharp tuning to specific global stimulus features. Groups of neurons identifying different global features must then assemble into a population that forms a comprehensive code for these global stimulus properties. Although the logic for how single neurons summate over their spatial inputs has been well-explored in anesthetized animals, how large groups of neurons compose a flexible population code of higher order features in awake animals is not known. To address this question, we probed the integration and population coding of higher order stimuli in the somatosensory and visual cortices of awake mice using two-photon calcium imaging across cortical layers. We developed a novel tactile stimulator that allowed the precise measurement of spatial summation even in actively whisking mice. Using this system, we found a sparse but comprehensive population code for higher order tactile features that depends on a heterogeneous and neuron-specific logic of spatial summation beyond the receptive field. Different somatosensory cortical neurons summed specific combinations of sensory inputs supra-linearly, but integrated other inputs sub-linearly, leading to selective responses to higher order features. Visual cortical populations employed a nearly identical scheme to generate a comprehensive population code for contextual stimuli. These results suggest that a heterogeneous logic of input-specific supra-linear summation may represent a widespread cortical mechanism for the synthesis of sparse higher order feature codes in neural populations. This may explain how the brain exploits the thalamocortical expansion of dimensionality to encode arbitrary complex features of sensory stimuli.

STAR FORMATION HISTORIES OF BRIGHTEST CLUSTER GALAXIES WITH INTERMEDIATE CENTRAL AGES

This work is devoted to the study of the star formation histories (SFHs) of the brightest cluster galaxies (BCGs) with intermediate central ages (from 5 to 10Gyr), to confirm if BCGs with these ages represent different accretion histories or simply a stochastic effect. The sample is composed of 6 BCGs with intermediate central ages and 3 BCGs with old central ages (> 12Gyr) as comparison galaxies. The galaxies were observed with the integrated field spectrograph VIMOS installed in the Very Large Telescope (VLT). The SFHs were obtained with the full spectrum fitting technique using the star population code STARLIGHT. The BCGs of intermediate central age analyzed formed almost 100% of their stars at z > 2 and their SFHs are similar to the SFHs of BCGs of old central ages and elliptical galaxies of similar mass (MDyn > 1011 Mʘ); therefore, these BCGs do not represent different SFHs.

Distinct population code for movement kinematics and changes of ongoing movements in human subthalamic nucleus

The subthalamic nucleus (STN) is theorized to globally suppress movement through connections with downstream basal ganglia structures. Current theories are supported by increased STN activity when subjects withhold an uninitiated action plan, but a critical test of these theories requires studying STN responses when an ongoing action is replaced with an alternative. We perform this test in subjects with Parkinson's disease using an extended reaching task where the movement trajectory changes mid-action. We show that STN activity decreases during action switches, contrary to prevalent theories. Further, beta oscillations in the STN local field potential, which are associated with movement inhibition, do not show increased power or spiking entrainment during switches. We report an inhomogeneous population neural code in STN, with one sub-population encoding movement kinematics and direction and another encoding unexpected action switches. We suggest an elaborate neural code in STN that contributes to planning actions and changing the plans.

Rapid synaptic plasticity contributes to a learned conjunctive code of position and choice-related information in the hippocampus

To successfully perform goal-directed navigation, animals must know where they are and what they are doing, e.g., looking for water, bringing food back to the nest, or escaping from a predator. Hippocampal neurons code for these critical variables conjunctively, but little is known about how this where/what code is formed or flexibly routed to other brain regions. To address these questions, we performed intracellular whole-cell recordings in mouse CA1 during a cued, two-choice virtual navigation task. We demonstrate that plateau potentials in CA1 pyramidal neurons rapidly strengthen synaptic inputs carrying conjunctive information about position and choice. Plasticity-induced response fields were modulated by cues only in animals previously trained to collect rewards based on these cues. Thus, we reveal that gradual learning is required for the formation of a conjunctive population code, upstream of CA1, while plateau-potential-induced synaptic plasticity in CA1 enables flexible routing of the code to downstream brain regions.

A phenomenological spiking model for octopus cells in the posterior–ventral cochlear nucleus

Octopus cells in the posteroventral cochlear nucleus exhibit characteristic onset responses to broad band transients but are little investigated in response to more complex sound stimuli. In this paper, we propose a phenomenological, but biophysically motivated, modeling approach that allows to simulate responses of large populations of octopus cells to arbitrary sound pressure waves. The model depends on only few parameters and reproduces basic physiological characteristics like onset firing and phase locking to amplitude modulations. Simulated responses to speech stimuli suggest that octopus cells are particularly sensitive to high-frequency transients in natural sounds and their sustained firing to phonemes provides a population code for sound level.

The Geometry of Information Coding in Correlated Neural Populations

Neurons in the brain represent information in their collective activity. The fidelity of this neural population code depends on whether and how variability in the response of one neuron is shared with other neurons. Two decades of studies have investigated the influence of these noise correlations on the properties of neural coding. We provide an overview of the theoretical developments on the topic. Using simple, qualitative, and general arguments, we discuss, categorize, and relate the various published results. We emphasize the relevance of the fine structure of noise correlation, and we present a new approach to the issue. Throughout this review, we emphasize a geometrical picture of how noise correlations impact the neural code. Expected final online publication date for the Annual Review of Neuroscience, Volume 44 is July 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Population Codes Enable Learning from Few Examples By Shaping Inductive Bias

The brain can learn from a limited number of experiences, an ability which requires suitable built in assumptions about the nature of the tasks which must be learned, or inductive biases. While inductive biases are central components of intelligence, how they are reflected in and shaped by population codes are not well-understood. To address this question, we consider biologically-plausible reading out of an arbitrary stimulus-response pattern from an arbitrary population code, and develop an analytical theory that predicts the generalization error of the readout as a function of the number of samples. We find that learning performance is controlled by the eigenspectrum of the population code's inner-product kernel, which measures the similarity of neural responses to two different input stimuli. Many different codes can realize the same kernel; by analyzing recordings from the mouse primary visual cortex, we demonstrate that biological codes are metabolically more efficient than other codes with identical kernels. We demonstrate that the spectral properties of the kernel introduce an inductive bias toward explaining stimulus-response samples with simple functions and determine compatibility of the population code with learning task, and hence the sample-efficiency of learning. While the tail of the spectrum is important for large sample size behavior of learning, for small sample sizes, the bulk of the spectrum governs generalization. We apply our theory to experimental recordings of mouse primary visual cortex neural responses, elucidating a bias towards sample-efficient learning of low frequency orientation discrimination tasks. We demonstrate this emergence of this bias in a simple model of primary visual cortex, and further show how invariances in the code to stimulus variations affect learning performance. Finally, we demonstrate that our methods are applicable to time-dependent neural codes. Overall, our study suggests sample-efficient learning as a general normative coding principle.