Characterizing neuronal responses to natural stimuli remains a central goal in sensory neuroscience. In auditory cortical neurons, the stimulus selectivity of elicited spiking activity is summarized by a spectrotemporal receptive field (STRF) that relates neuronal responses to the stimulus spectrogram. Though effective in characterizing primary auditory cortical responses, STRFs of non-primary auditory neurons can be quite intricate, reflecting their mixed selectivity. The complexity of non-primary STRFs hence impedes understanding how acoustic stimulus representations are transformed along the auditory pathway. Here, we focus on the relationship between ferret primary auditory cortex (A1) and a secondary region, dorsal posterior ectosylvian gyrus (PEG). We propose estimating receptive fields in PEG with respect to a well-established high-dimensional computational model of primary-cortical stimulus representations. These "cortical receptive fields" (CortRF) are estimated greedily to identify the salient primary-cortical features modulating spiking responses and in turn related to corresponding spectrotemporal features. Hence, they provide biologically plausible hierarchical decompositions of STRFs in PEG. Such CortRF analysis was applied to PEG neuronal responses to speech and temporally orthogonal ripple combination (TORC) stimuli and, for comparison, to A1 neuronal responses. CortRFs of PEG neurons captured their selectivity to more complex spectrotemporal features than A1 neurons; moreover, CortRF models were more predictive of PEG (but not A1) responses to speech. Our results thus suggest that secondary-cortical stimulus representations can be computed as sparse combinations of primary-cortical features that facilitate encoding natural stimuli. Thus, by adding the primary-cortical representation, we can account for PEG single-unit responses to natural sounds better than bypassing it and considering as input the auditory spectrogram. These results confirm with explicit details the presumed hierarchical organization of the auditory cortex.

Optogenetic stimulation has opened up a new avenue to probe neuronal circuitry at high spatiotemporal resolutions. A key challenge in optogenetic stimulation is deciding which subset out of thousands of neurons should be stimulated to elicit a desired network activation or affect behavior. In this work, we introduce a reinforcement learning approach to adaptively narrow down the multitude of stimulation possibilities and robustly identify Granger causal networks that underlie neuronal activity. We use realistic simulations with different underlying circuitry to show the effectiveness of reinforcement learning in identifying an optimal policy for selecting stimulation targets.

Central in the study of population codes, coordinated ensemble spiking activity is widely observable in neural recordings with hypothesized roles in robust stimulus representation, interareal communication, and learning and memory formation. Model-free measures of synchrony characterize coherent pairwise activity but not higher-order interactions, a limitation transcended by statistical models of ensemble spiking activity. However, existing model-based analyses often impose assumptions about the relevance of higher-order interactions and require repeated trials to characterize dynamics in the correlational structure of ensemble activity. To address these shortcomings, we propose an adaptive greedy filtering algorithm based on a discretized mark point-process model of ensemble spiking and a corresponding statistical inference framework to identify significant higher-order coordination. In the course of developing a precise statistical test, we show that confidence intervals can be constructed for greedily estimated parameters. We demonstrate the utility of our proposed methods on simulated neuronal assemblies. Applied to multi-electrode recordings from human and rat cortical assemblies, our proposed methods provide new insights into the dynamics underlying localized population activity during transitions between brain states.

Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this methodology are: 1) over-fitting as a result of limited data duration, and 2) correlated process noise as a confounding factor, both leading to errors in identifying the causal influences. Sparse estimation via the LASSO has successfully addressed these challenges for parameter estimation. However, the classical statistical tests for Granger causality resort to asymptotic analysis of ordinary least squares, which require long data duration to be useful and are not immune to confounding effects. In this work, we address this disconnect by introducing a LASSO-based statistic and studying its non-asymptotic properties under the assumption that the true models admit sparse autoregressive representations. We establish fundamental limits for reliable identification of Granger causal influences using the proposed LASSO-based statistic. We further characterize the false positive error probability and test power of a simple thresholding rule for identifying Granger causal effects and provide two methods to set the threshold in a data-driven fashion. We present simulation studies and application to real data to compare the performance of our proposed method to ordinary least squares and existing LASSO-based methods in detecting Granger causal influences, which corroborate our theoretical results.

Coordinated ensemble spiking activity is widely observable in neural recordings and central in the study of population codes, with hypothesized roles including robust stimulus representation, interareal communication of neural information, and learning and memory formation. Model-free measures of synchrony characterize the coherence of pairwise activity, but not higher-order interactions; this limitation is transcended by statistical models of ensemble spiking activity. However, existing model-based analyses often impose assumptions about the relevance of higher-order interactions and require multiple repeated trials in order to characterize dynamics in the correlational structure of ensemble activity. To address these shortcomings, we propose an adaptive greedy filtering algorithm based on a discretized mark point-process model of ensemble spiking and a corresponding precise statistical inference framework to identify significant coordinated higher-order spiking activity. In the course of developing the statistical inference procedures, we also show that confidence intervals can be constructed for greedily estimated parameters. We demonstrate the utility of our proposed methods on simulated neuronal assemblies. Applied to multi-electrode recordings of human cortical ensembles, our proposed methods provide new insights into the dynamics underlying localized population activity during transitions between brain states.

Estimating the latent dynamics underlying biological processes is a central problem in computational biology. State-space models with Gaussian statistics are widely used for estimation of such latent dynamics and have been successfully utilized in the analysis of biological data. Gaussian statistics, however, fail to capture several key features of the dynamics of biological processes (e.g., brain dynamics) such as abrupt state changes and exogenous processes that affect the states in a structured fashion. Although Gaussian mixture process noise models have been considered as an alternative to capture such effects, data-driven inference of their parameters is not well-established in the literature. The objective of this paper is to develop efficient algorithms for inferring the parameters of a general class of Gaussian mixture process noise models from noisy and limited observations, and to utilize them in extracting the neural dynamics that underlie auditory processing from magnetoencephalography (MEG) data in a cocktail party setting. We develop an algorithm based on Expectation-Maximization to estimate the process noise parameters from state-space observations. We apply our algorithm to simulated and experimentally-recorded MEG data from auditory experiments in the cocktail party paradigm to estimate the underlying dynamic Temporal Response Functions (TRFs). Our simulation results show that the richer representation of the process noise as a Gaussian mixture significantly improves state estimation and capturing the heterogeneity of the TRF dynamics. Application to MEG data reveals improvements over existing TRF estimation techniques, and provides a reliable alternative to current approaches for probing neural dynamics in a cocktail party scenario, as well as attention decoding in emerging applications such as smart hearing aids. Our proposed methodology provides a framework for efficient inference of Gaussian mixture process noise models, with application to a wide range of biological data with underlying heterogeneous and latent dynamics.

We consider the problem of estimating the power spectral density of the neural covariates underlying the spiking of a neuronal population. We assume the spiking of the neuronal ensemble to be described by Bernoulli statistics. Furthermore, we consider the conditional intensity function to be the logistic map of a second-order stationary process with sparse frequency content. Using the binary spiking data recorded from the population, we calculate the maximum a posteriori estimate of the power spectral density of the process while enforcing sparsity-promoting priors on the estimate. Using both simulated and clinically recorded data, we show that our method outperforms the existing methods for extracting a frequency domain representation from the spiking data of a neuronal population.

Let A ∈ {-1,1}Na×n and B ∈ {-1,1}Nb×n be two matrices whose rows are drawn i.i.d. from the codewords of the binary codes Caand Cbof length n and dual distances d'aand d'b, respectively, under the mapping 0 → 1 and 1 → -1. It is proven that as n → ∞ with ya:=n/Na∈ (0,∞) and yb:=n/Nb∈ (0, ∞) fixed, the empirical spectral distribution of the matrix A B*/√{NaNb} resembles a universal distribution (closely related to the distribution function of the free multiplicative convolution of two members of the Marchenko-Pastur family of densities) in the sense of the Lévy distance, if the asymptotic dual distances of the underlying binary codes are large enough. Moreover, an explicit upper bound on the Lévy distance of the two distributions in terms of ya, yb, d'a, and d'bis given. Under mild conditions, the upper bound is strengthened to the Kolmogorov distance of the underlying distributions. Numerical studies on the empirical spectral distribution of the product of random matrices from BCH and Gold codes are provided, which verify the validity of this result.

In this paper, we study the problem of distributed spectrum allocation under a vertical spectrum sharing scenario in a cognitive radio network. The secondary users share the spectrum licensed to the primary user by observing the activity statistics of the primary users, and regulate their transmission strategy in order to abide by the spectrum sharing etiquette. When the primary user is inactive in a subset of the available frequency bands, the secondary users share the spectrum using the recently proposed GADIA algorithm [1]. In this paper, we present analytical and numerical results on the performance of the GADIA algorithm in conjunction with the above-mentioned vertical spectrum sharing scenario. These results reveal near-optimal performance guarantees for the overall vertical spectrum sharing scenario.

We consider the problem of recovering a sequence of vectors, $(x_k)_{k=0}^K$, for which the increments $x_k-x_{k-1}$ are $S_k$-sparse (with $S_k$ typically smaller than $S_1$), based on linear measurements $(y_k = A_k x_k + e_k)_{k=1}^K$, where $A_k$ and $e_k$ denote the measurement matrix and noise, respectively. Assuming each $A_k$ obeys the restricted isometry property (RIP) of a certain order---depending only on $S_k$---we show that in the absence of noise a convex program, which minimizes the weighted sum of the $\ell_1$-norm of successive differences subject to the linear measurement constraints, recovers the sequence $(x_k)_{k=1}^K$ \emph{exactly}. This is an interesting result because this convex program is equivalent to a standard compressive sensing problem with a highly-structured aggregate measurement matrix which does not satisfy the RIP requirements in the standard sense, and yet we can achieve exact recovery. In the presence of bounded noise, we propose a quadratically-constrained convex program for recovery and derive bounds on the reconstruction error of the sequence. We supplement our theoretical analysis with simulations and an application to real video data. These further support the validity of the proposed approach for acquisition and recovery of signals with time-varying sparsity.

LetCbe a binary linear block code of lengthn, dimensionkand minimum Hamming distancedover GF(2)n. Letd⊥denote the minimum Hamming distance of the dual code ofCover GF(2)n. Let ε:GF(2)n→{-1,1}nbe the component-wise mapping ε(vi):=(-1)vi, forv=(v1,v2,...,vn) ∈ GF(2)n. Finally, forpn, let \mmbΦCbe a p × n random matrix whose rows are obtained by mapping a uniformly drawn set of sizepof the codewords ofCunder ε. It is shown that ford⊥large enough andy:=p/n∈ (0,1) fixed, asn→∞ the empirical spectral distribution of the Gram matrix of [1/(√n)]\mmbΦCresembles that of a random i.i.d. Rademacher matrix (i.e., the Marchenko-Pastur distribution). Moreover, an explicit asymptotic uniform bound on the distance of the empirical spectral distribution of the Gram matrix of [1/(√n)]\mmbΦCto the Marchenko-Pastur distribution as a function ofyandd⊥is presented.

In this paper, the problem of distributed dynamic frequency allocation is considered for a canonical communication network, which spans several networks such as cognitive radio networks and digital subscriber lines (DSLs). A greedy asynchronous distributed interference avoidance (GADIA) algorithm for horizontal spectrum sharing has been proposed that achieves performance close to that of a centralized optimal algorithm. The convergence of the GADIA algorithm to a near-optimal frequency allocation strategy is proved and several asymptotic performance bounds have been established for various spatial configurations of the network nodes. Furthermore, the near-equilibrium dynamics of the GADIA algorithm has been studied using the Glauber dynamics, by identifying the problem with the antiferromagnetic inhomogeneous long-range Potts model. Using the near-equilibrium dynamics and methods from stochastic analysis, the robustness of the algorithm with respect to time variations in the activity of network nodes is studied. These analytic results along with simulation studies reveal that the performance is close to that of an optimum centralized frequency allocation algorithm. Further simulation studies confirm that our proposed algorithm outperforms the iterative water-filling algorithm in the low signal-to-interference-plus-noise ratio (SINR) regime, in terms of achieved sum rate, complexity, convergence rate, and robustness to time-varying node activities.