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Our goal is to model and measure functional and effective (directional) connectivity in multichannel brain physiological signals (e.g., electroencephalograms, local field potentials). The difficulties from analyzing these data mainly come from two aspects: first, there are major statistical and computational challenges for modeling and analyzing high-dimensional multichannel brain signals; second, there is no set of universally agreed measures for characterizing connectivity. To model multichannel brain signals, our approach is to fit a vector autoregressive (VAR) model with potentially high lag order so that complex lead-lag temporal dynamics between the channels can be captured. Estimates of the VAR model will be obtained by our proposed hybrid LASSLE (LASSO + LSE) method which combines regularization (to control for sparsity) and least squares estimation (to improve bias and mean-squared error). Then we employ some measures of connectivity but put an emphasis on partial directed coherence (PDC) which can capture the directional connectivity between channels. PDC is a frequency-specific measure that explains the extent to which the present oscillatory activity in a sender channel influences the future oscillatory activity in a specific receiver channel relative to all possible receivers in the network. The proposed modeling approach provided key insights into potential functional relationships among simultaneously recorded sites during performance of a complex memory task. Specifically, this novel method was successful in quantifying patterns of effective connectivity across electrode locations, and in capturing how these patterns varied across trial epochs and trial types.

The standard approach to analyzing brain electrical activity is to examine the spectral density function (SDF) and identify frequency bands, defined a priori, that have the most substantial relative contributions to the overall variance of the signal. However, a limitation of this approach is that the precise frequency and bandwidth of oscillations are not uniform across different cognitive demands. Thus, these bands should not be arbitrarily set in any analysis. To overcome this limitation, the Bayesian mixture auto-regressive decomposition (BMARD) method is proposed, as a data-driven approach that identifies (i) the number of prominent spectral peaks, (ii) the frequency peak locations, and (iii) their corresponding bandwidths (or spread of power around the peaks). Using the BMARD method, the standardized SDF is represented as a Dirichlet process mixture based on a kernel derived from second-order auto-regressive processes which completely characterize the location (peak) and scale (bandwidth) parameters. A Metropolis-Hastings within the Gibbs algorithm is developed for sampling the posterior distribution of the mixture parameters. Simulations demonstrate the robust performance of the proposed method. Finally, the BMARD method is applied to analyze local field potential (LFP) activity from the hippocampus of laboratory rats across different conditions in a non-spatial sequence memory experiment, to identify the most prominent frequency bands and examine the link between specific patterns of brain oscillatory activity and trial-specific cognitive demands.

The hippocampus is known to play a critical role in processing information about temporal context. However, it remains unclear how hippocampal oscillations are involved, and how their functional organization is influenced by connectivity gradients. We examined local field potential activity in CA1 as rats performed a nonspatial odor sequence memory task. We found that odor sequence processing epochs were characterized by distinct spectral profiles and proximodistal CA1 gradients of theta and 20-40 Hz power than track running epochs. We also discovered that 20-40 Hz power was predictive of sequence memory performance, particularly in proximal CA1 and during the plateau of high power observed in trials in which animals had to maintain their decision until instructed to respond. Altogether, these results provide evidence that dynamics of 20-40 Hz power along the CA1 axis are linked to trial-specific processing of nonspatial information critical to order judgments and are consistent with a role for 20-40 Hz power in gating information processing., Competing Interests: SG, GE, JJ, MY, NF No competing interests declared, (© 2022, Gattas et al.)

The hippocampus is critical to the temporal organization of our experiences. Although this fundamental capacity is conserved across modalities and species, its underlying neuronal mechanisms remain unclear. Here we recorded hippocampal activity as rats remembered an extended sequence of nonspatial events unfolding over several seconds, as in daily life episodes in humans. We then developed statistical machine learning methods to analyze the ensemble activity and discovered forms of sequential organization and coding important for order memory judgments. Specifically, we found that hippocampal ensembles provide significant temporal coding throughout nonspatial event sequences, differentiate distinct types of task-critical information sequentially within events, and exhibit theta-associated reactivation of the sequential relationships among events. We also demonstrate that nonspatial event representations are sequentially organized within individual theta cycles and precess across successive cycles. These findings suggest a fundamental function of the hippocampal network is to encode, preserve, and predict the sequential order of experiences., (© 2022. The Author(s).)

We propose a novel regularized mixture model for clustering matrix-valued data. The proposed method assumes a separable covariance structure for each cluster and imposes a sparsity structure (eg, low rankness, spatial sparsity) for the mean signal of each cluster. We formulate the problem as a finite mixture model of matrix-normal distributions with regularization terms, and then develop an expectation maximization type of algorithm for efficient computation. In theory, we show that the proposed estimators are strongly consistent for various choices of penalty functions. Simulation and two applications on brain signal studies confirm the excellent performance of the proposed method including a better prediction accuracy than the competitors and the scientific interpretability of the solution., (© 2020 The International Biometric Society.)

Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices and propose a novel Bayesian framework based on modeling the correlations as products of unit vectors. By specifying a wide range of distributions on a sphere (e.g. the squared-Dirichlet distribution), the proposed approach induces flexible prior distributions for covariance matrices (that go beyond the commonly used inverse-Wishart prior). For modeling real-life spatio-temporal processes with complex dependence structures, we extend our method to dynamic cases and introduce unit-vector Gaussian process priors in order to capture the evolution of correlation among components of a multivariate time series. To handle the intractability of the resulting posterior, we introduce the adaptive Δ-Spherical Hamiltonian Monte Carlo. We demonstrate the validity and flexibility of our proposed framework in a simulation study of periodic processes and an analysis of rat's local field potential activity in a complex sequence memory task.

There is a strong interest in the neuroscience community to measure brain connectivity and develop methods that can differentiate connectivity across patient groups and across different experimental stimuli. The development of such statistical tools is critical to understand the dynamics of functional relationships among brain structures supporting memory encoding and retrieval. However, the challenge comes from the need to incorporate within-condition similarity with between-conditions heterogeneity in modeling connectivity, as well as how to provide a natural way to conduct trial- and condition-level inference on effective connectivity. A Bayesian hierarchical vector autoregressive (BH-VAR) model is proposed to characterize brain connectivity and infer differences in connectivity across conditions. Within-condition connectivity similarity and between-conditions connectivity heterogeneity are accounted for by the priors on trial-specific models. In addition to the fully Bayesian framework, an alternative two-stage computation approach is also proposed which still allows straightforward uncertainty quantification of between-trial conditions via MCMC posterior sampling, but provides a fast approximate procedure for the estimation of trial-specific VAR parameters. A novel aspect of the approach is the use of a frequency-specific measure, partial directed coherence (PDC), to characterize effective connectivity under the Bayesian framework. More specifically, PDC allows inferring directionality and explaining the extent to which the present oscillatory activity at a certain frequency in a sender channel influences the future oscillatory activity in a specific receiver channel relative to all possible receivers in the brain network. The proposed model is applied to a large electrophysiological dataset collected as rats performed a complex sequence memory task. This unique dataset includes local field potentials (LFPs) activity recorded from an array of electrodes across hippocampal region CA1 while animals were presented with multiple trials from two main conditions. The proposed modeling approach provided novel insights into hippocampal connectivity during memory performance. Specifically, it separated CA1 into two functional units, a lateral and a medial segment, each showing stronger functional connectivity to itself than to the other. This approach also revealed that information primarily flowed in a lateral-to-medial direction across trials (within-condition), and suggested this effect was stronger on one trial condition than the other (between-conditions effect). Collectively, these results indicate that the proposed model is a promising approach to quantify the variation of functional connectivity, both within- and between-conditions, and thus should have broad applications in neuroscience research.

We propose an evolutionary state space model (E-SSM) for analyzing high dimensional brain signals whose statistical properties evolve over the course of a non-spatial memory experiment. Under E-SSM, brain signals are modeled as mixtures of components (e.g., AR(2) process) with oscillatory activity at pre-defined frequency bands. To account for the potential non-stationarity of these components (since the brain responses could vary throughout the entire experiment), the parameters are allowed to vary over epochs. Compared with classical approaches such as independent component analysis and filtering, the proposed method accounts for the entire temporal correlation of the components and accommodates non-stationarity. For inference purpose, we propose a novel computational algorithm based upon using Kalman smoother, maximum likelihood and blocked resampling. The E-SSM model is applied to simulation studies and an application to a multi-epoch local field potentials (LFP) signal data collected from a non-spatial (olfactory) sequence memory task study. The results confirm that our method captures the evolution of the power for different components across different phases in the experiment and identifies clusters of electrodes that behave similarly with respect to the decomposition of different sources. These findings suggest that the activity of different electrodes does change over the course of an experiment in practice; treating these epoch recordings as realizations of an identical process could lead to misleading results. In summary, the proposed method underscores the importance of capturing the evolution in brain responses over the study period.

Considerable research in rodents and humans indicates the hippocampus and prefrontal cortex are essential for remembering temporal relationships among stimuli, and accumulating evidence suggests the perirhinal cortex may also be involved. However, experimental parameters differ substantially across studies, which limits our ability to fully understand the fundamental contributions of these structures. In fact, previous studies vary in the type of temporal memory they emphasize (e.g., order, sequence, or separation in time), the stimuli and responses they use (e.g., trial-unique or repeated sequences, and incidental or rewarded behavior), and the degree to which they control for potential confounding factors (e.g., primary and recency effects, or order memory deficits secondary to item memory impairments). To help integrate these findings, we developed a new paradigm testing incidental memory for trial-unique series of events, and concurrently assessed order and item memory in animals with damage to the hippocampus, prefrontal cortex, or perirhinal cortex. We found that this new approach led to robust order and item memory, and that hippocampal, prefrontal and perirhinal damage selectively impaired order memory. These findings suggest the hippocampus, prefrontal cortex and perirhinal cortex are part of a broad network of structures essential for incidentally learning the order of events in episodic memory., (Copyright © 2019 Elsevier B.V. All rights reserved.)

The hippocampus plays a critical role in the memory for sequences of events, a defining feature of episodic memory. To shed light on the fundamental mechanisms supporting this capacity, we recently recorded neural activity in CA1 as rats performed a nonspatial odor sequence memory task. Our main finding was that, while the animals' location and behavior remained constant, a proportion of CA1 neurons fired differentially to odors depending on whether they were presented in or out of sequence (sequence cells). Here, we further examined if such sequence coding varied along the distal-to-proximal axis of the dorsal CA1 region (distal: toward subiculum; proximal: toward CA3). Differences in information processing along this axis have been suggested by recent anatomical and electrophysiological evidence that odor information may be more strongly represented in the distal segment, whereas spatial information may be more strongly represented in the proximal segment. Recorded neurons were grouped into four arbitrary sections of dorsal CA1, ranging from distal to proximal. We found that, although sequence cell coding was observed across the distal-to-proximal extent of CA1 from which we recorded, it was significantly higher in intermediate CA1, a region with more balanced anatomical input from lateral and medial entorhinal regions. More specifically, in that particular segment of CA1, we observed a significant increase in the magnitude of sequence coding of all cells, as well as in the sequential information content of sequence cells. Importantly, a different pattern was observed when examining the distribution of spatial coding from the same electrodes. Consistent with previous reports, our results suggest that spatial information was more strongly represented in the proximal section of CA1 (higher proportion of cells with place fields). These findings indicate that nonspatial sequence memory coding is not uniformly distributed along the transverse axis of CA1, and that this distribution does not simply follow the expected gradient based on the stimulus modality or the degree of spatial selectivity. Instead, the observed distribution suggests this form of sequence coding may be associated with convergent input from lateral and medial entorhinal regions, which is present throughout the proximodistal axis but greater in intermediate CA1., (Copyright © 2017 Elsevier B.V. All rights reserved.)

The hippocampus is critical to the memory for sequences of events, a defining feature of episodic memory. However, the fundamental neuronal mechanisms underlying this capacity remain elusive. While considerable research indicates hippocampal neurons can represent sequences of locations, direct evidence of coding for the memory of sequential relationships among nonspatial events remains lacking. To address this important issue, we recorded neural activity in CA1 as rats performed a hippocampus-dependent sequence-memory task. Briefly, the task involves the presentation of repeated sequences of odors at a single port and requires rats to identify each item as "in sequence" or "out of sequence". We report that, while the animals' location and behavior remained constant, hippocampal activity differed depending on the temporal context of items-in this case, whether they were presented in or out of sequence. Some neurons showed this effect across items or sequence positions (general sequence cells), while others exhibited selectivity for specific conjunctions of item and sequence position information (conjunctive sequence cells) or for specific probe types (probe-specific sequence cells). We also found that the temporal context of individual trials could be accurately decoded from the activity of neuronal ensembles, that sequence coding at the single-cell and ensemble level was linked to sequence memory performance, and that slow-gamma oscillations (20-40 Hz) were more strongly modulated by temporal context and performance than theta oscillations (4-12 Hz). These findings provide compelling evidence that sequence coding extends beyond the domain of spatial trajectories and is thus a fundamental function of the hippocampus., Significance Statement: The ability to remember the order of life events depends on the hippocampus, but the underlying neural mechanisms remain poorly understood. Here we addressed this issue by recording neural activity in hippocampal region CA1 while rats performed a nonspatial sequence memory task. We found that hippocampal neurons code for the temporal context of items (whether odors were presented in the correct or incorrect sequential position) and that this activity is linked with memory performance. The discovery of this novel form of temporal coding in hippocampal neurons advances our fundamental understanding of the neurobiology of episodic memory and will serve as a foundation for our cross-species, multitechnique approach aimed at elucidating the neural mechanisms underlying memory impairments in aging and dementia., (Copyright © 2016 Allen et al.)

Typical aging is associated with diminished episodic memory performance. To improve our understanding of the fundamental mechanisms underlying this age-related memory deficit, we previously developed an integrated, cross-species approach to link converging evidence from human and animal research. This novel approach focuses on the ability to remember sequences of events, an important feature of episodic memory. Unlike existing paradigms, this task is nonspatial, nonverbal, and can be used to isolate different cognitive processes that may be differentially affected in aging. Here, we used this task to make a comprehensive comparison of sequence memory performance between younger (18-22 yr) and older adults (62-86 yr). Specifically, participants viewed repeated sequences of six colored, fractal images and indicated whether each item was presented "in sequence" or "out of sequence." Several out of sequence probe trials were used to provide a detailed assessment of sequence memory, including: (i) repeating an item from earlier in the sequence ("Repeats"; e.g., AB A: DEF), (ii) skipping ahead in the sequence ("Skips"; e.g., AB D: DEF), and (iii) inserting an item from a different sequence into the same ordinal position ("Ordinal Transfers"; e.g., AB 3: DEF). We found that older adults performed as well as younger controls when tested on well-known and predictable sequences, but were severely impaired when tested using novel sequences. Importantly, overall sequence memory performance in older adults steadily declined with age, a decline not detected with other measures (RAVLT or BPS-O). We further characterized this deficit by showing that performance of older adults was severely impaired on specific probe trials that required detailed knowledge of the sequence (Skips and Ordinal Transfers), and was associated with a shift in their underlying mnemonic representation of the sequences. Collectively, these findings provide unambiguous evidence that the capacity to remember sequences of events is fundamentally affected by typical aging., (© 2015 Allen et al.; Published by Cold Spring Harbor Laboratory Press.)

A critical feature of episodic memory is the ability to remember the order of events as they occurred in time, a capacity shared across species including humans, nonhuman primates, and rodents. Accumulating evidence suggests that this capacity depends on a network of structures including the hippocampus and the prefrontal cortex, but their respective contributions remain poorly understood. As addressing this important issue will require converging evidence from complementary investigative techniques, we developed a cross-species, nonspatial sequence memory task suitable for behavioral and neurophysiological studies in rodents and in humans. The task involves the repeated presentation of sequences of items (odors in rats and images in humans) and requires subjects to make a judgment as to whether each item is presented "in sequence" or "out of sequence." To shed light on the cognitive processes and sequence representations supporting performance, different types of "out of sequence" probe trials were used including: (i) repeating an item from earlier in the sequence (Repeats; e.g., ABAD), (ii) skipping ahead in the sequence (Skips; e.g., ABD), and (iii) inserting an item from a different sequence into the same ordinal position (Ordinal Transfers; e.g., A2CD). We found a remarkable similarity in the performance of rats and humans, particularly in the pattern of results across probe trial types. Thus, the results suggest that rats and humans not only remember the sequences of events, but also use similar underlying cognitive processes and mnemonic representations. This strong cross-species correspondence validates this task for use in future basic and clinical interdisciplinary studies aimed at examining the neural mechanisms underlying episodic memory., (© 2014 Wiley Periodicals, Inc.)