Phantom oscillations in principal component analysis.

Principal component analysis (PCA) is a dimensionality reduction method that is known for being simple and easy to interpret. Principal components are often interpreted as low-dimensional patterns in high-dimensional space. However, this simple interpretation fails for timeseries, spatial maps, and other continuous data. In these cases, nonoscillatory data may have oscillatory principal components. Here, we show that two common properties of data cause oscillatory principal components: smoothness and shifts in time or space. These two properties implicate almost all neuroscience data. We show how the oscillations produced by PCA, which we call "phantom oscillations," impact data analysis. We also show that traditional cross-validation does not detect phantom oscillations, so we suggest procedures that do. Our findings are supported by a collection of mathematical proofs. Collectively, our work demonstrates that patterns which emerge from high-dimensional data analysis may not faithfully represent the underlying data.

Functional brain networks reflect spatial and temporal autocorrelation.

High-throughput experimental methods in neuroscience have led to an explosion of techniques for measuring complex interactions and multi-dimensional patterns. However, whether sophisticated measures of emergent phenomena can be traced back to simpler, low-dimensional statistics is largely unknown. To explore this question, we examined resting-state functional magnetic resonance imaging (rs-fMRI) data using complex topology measures from network neuroscience. Here we show that spatial and temporal autocorrelation are reliable statistics that explain numerous measures of network topology. Surrogate time series with subject-matched spatial and temporal autocorrelation capture nearly all reliable individual and regional variation in these topology measures. Network topology changes during aging are driven by spatial autocorrelation, and multiple serotonergic drugs causally induce the same topographic change in temporal autocorrelation. This reductionistic interpretation of widely used complexity measures may help link them to neurobiology.

A transcriptomic axis predicts state modulation of cortical interneurons.

Transcriptomics has revealed that cortical inhibitory neurons exhibit a great diversity of fine molecular subtypes1-6, but it is not known whether these subtypes have correspondingly diverse patterns of activity in the living brain. Here we show that inhibitory subtypes in primary visual cortex (V1) have diverse correlates with brain state, which are organized by a single factor: position along the main axis of transcriptomic variation. We combined in vivo two-photon calcium imaging of mouse V1 with a transcriptomic method to identify mRNA for 72 selected genes in ex vivo slices. We classified inhibitory neurons imaged in layers 1-3 into a three-level hierarchy of 5 subclasses, 11 types and 35 subtypes using previously defined transcriptomic clusters3. Responses to visual stimuli differed significantly only between subclasses, with cells in the Sncg subclass uniformly suppressed, and cells in the other subclasses predominantly excited. Modulation by brain state differed at all hierarchical levels but could be largely predicted from the first transcriptomic principal component, which also predicted correlations with simultaneously recorded cells. Inhibitory subtypes that fired more in resting, oscillatory brain states had a smaller fraction of their axonal projections in layer 1, narrower spikes, lower input resistance and weaker adaptation as determined in vitro7, and expressed more inhibitory cholinergic receptors. Subtypes that fired more during arousal had the opposite properties. Thus, a simple principle may largely explain how diverse inhibitory V1 subtypes shape state-dependent cortical processing.

Transient neuronal suppression for exploitation of new sensory evidence.

In noisy but stationary environments, decisions should be based on the temporal integration of sequentially sampled evidence. This strategy has been supported by many behavioral studies and is qualitatively consistent with neural activity in multiple brain areas. By contrast, decision-making in the face of non-stationary sensory evidence remains poorly understood. Here, we trained monkeys to identify and respond via saccade to the dominant color of a dynamically refreshed bicolor patch that becomes informative after a variable delay. Animals' behavioral responses were briefly suppressed after evidence changes, and many neurons in the frontal eye field displayed a corresponding dip in activity at this time, similar to that frequently observed after stimulus onset but sensitive to stimulus strength. Generalized drift-diffusion models revealed consistency of behavior and neural activity with brief suppression of motor output, but not with pausing or resetting of evidence accumulation. These results suggest that momentary arrest of motor preparation is important for dynamic perceptual decision making.

Confluence of Timing and Reward Biases in Perceptual Decision-Making Dynamics.

Although the decisions of our daily lives often occur in the context of temporal and reward structures, the impact of such regularities on decision-making strategy is poorly understood. Here, to explore how temporal and reward context modulate strategy, we trained 2 male rhesus monkeys to perform a novel perceptual decision-making task with asymmetric rewards and time-varying evidence reliability. To model the choice and response time patterns, we developed a computational framework for fitting generalized drift-diffusion models, which flexibly accommodate diverse evidence accumulation strategies. We found that a dynamic urgency signal and leaky integration, in combination with two independent forms of reward biases, best capture behavior. We also tested how temporal structure influences urgency by systematically manipulating the temporal structure of sensory evidence, and found that the time course of urgency was affected by temporal context. Overall, our approach identified key components of cognitive mechanisms for incorporating temporal and reward structure into decisions.SIGNIFICANCE STATEMENT In everyday life, decisions are influenced by many factors, including reward structures and stimulus timing. While reward and timing have been characterized in isolation, ecologically valid decision-making involves a multiplicity of factors acting simultaneously. This raises questions about whether the same decision-making strategy is used when these two factors are concurrently manipulated. To address these questions, we trained rhesus monkeys to perform a novel decision-making task with both reward asymmetry and temporal uncertainty. In order to understand their strategy and hint at its neural mechanisms, we used the new generalized drift diffusion modeling framework to model both reward and timing mechanisms. We found two of each reward and timing mechanisms are necessary to explain our data.

A flexible framework for simulating and fitting generalized drift-diffusion models.

The drift-diffusion model (DDM) is an important decision-making model in cognitive neuroscience. However, innovations in model form have been limited by methodological challenges. Here, we introduce the generalized drift-diffusion model (GDDM) framework for building and fitting DDM extensions, and provide a software package which implements the framework. The GDDM framework augments traditional DDM parameters through arbitrary user-defined functions. Models are solved numerically by directly solving the Fokker-Planck equation using efficient numerical methods, yielding a 100-fold or greater speedup over standard methodology. This speed allows GDDMs to be fit to data using maximum likelihood on the full response time (RT) distribution. We demonstrate fitting of GDDMs within our framework to both animal and human datasets from perceptual decision-making tasks, with better accuracy and fewer parameters than several DDMs implemented using the latest methodology, to test hypothesized decision-making mechanisms. Overall, our framework will allow for decision-making model innovation and novel experimental designs.

Generative modeling of brain maps with spatial autocorrelation.

Studies of large-scale brain organization have revealed interesting relationships between spatial gradients in brain maps across multiple modalities. Evaluating the significance of these findings requires establishing statistical expectations under a null hypothesis of interest. Through generative modeling of synthetic data that instantiate a specific null hypothesis, quantitative benchmarks can be derived for arbitrarily complex statistical measures. Here, we present a generative null model, provided as an open-access software platform, that generates surrogate maps with spatial autocorrelation (SA) matched to SA of a target brain map. SA is a prominent and ubiquitous property of brain maps that violates assumptions of independence in conventional statistical tests. Our method can simulate surrogate brain maps, constrained by empirical data, that preserve the SA of cortical, subcortical, parcellated, and dense brain maps. We characterize how SA impacts p-values in pairwise brain map comparisons. Furthermore, we demonstrate how SA-preserving surrogate maps can be used in gene set enrichment analyses to test hypotheses of interest related to brain map topography. Our findings demonstrate the utility of SA-preserving surrogate maps for hypothesis testing in complex statistical analyses, and underscore the need to disambiguate meaningful relationships from chance associations in studies of large-scale brain organization.

Adolescent Tuning of Association Cortex in Human Structural Brain Networks.

Motivated by prior data on local cortical shrinkage and intracortical myelination, we predicted age-related changes in topological organization of cortical structural networks during adolescence. We estimated structural correlation from magnetic resonance imaging measures of cortical thickness at 308 regions in a sample of N = 297 healthy participants, aged 14-24 years. We used a novel sliding-window analysis to measure age-related changes in network attributes globally, locally and in the context of several community partitions of the network. We found that the strength of structural correlation generally decreased as a function of age. Association cortical regions demonstrated a sharp decrease in nodal degree (hubness) from 14 years, reaching a minimum at approximately 19 years, and then levelling off or even slightly increasing until 24 years. Greater and more prolonged age-related changes in degree of cortical regions within the brain network were associated with faster rates of adolescent cortical myelination and shrinkage. The brain regions that demonstrated the greatest age-related changes were concentrated within prefrontal modules. We conclude that human adolescence is associated with biologically plausible changes in structural imaging markers of brain network organization, consistent with the concept of tuning or consolidating anatomical connectivity between frontal cortex and the rest of the connectome.

Morphometric Similarity Networks Detect Microscale Cortical Organization and Predict Inter-Individual Cognitive Variation.

Macroscopic cortical networks are important for cognitive function, but it remains challenging to construct anatomically plausible individual structural connectomes from human neuroimaging. We introduce a new technique for cortical network mapping based on inter-regional similarity of multiple morphometric parameters measured using multimodal MRI. In three cohorts (two human, one macaque), we find that the resulting morphometric similarity networks (MSNs) have a complex topological organization comprising modules and high-degree hubs. Human MSN modules recapitulate known cortical cytoarchitectonic divisions, and greater inter-regional morphometric similarity was associated with stronger inter-regional co-expression of genes enriched for neuronal terms. Comparing macaque MSNs with tract-tracing data confirmed that morphometric similarity was related to axonal connectivity. Finally, variation in the degree of human MSN nodes accounted for about 40% of between-subject variability in IQ. Morphometric similarity mapping provides a novel, robust, and biologically plausible approach to understanding how human cortical networks underpin individual differences in psychological functions.

Structural covariance networks are coupled to expression of genes enriched in supragranular layers of the human cortex.

Complex network topology is characteristic of many biological systems, including anatomical and functional brain networks (connectomes). Here, we first constructed a structural covariance network from MRI measures of cortical thickness on 296 healthy volunteers, aged 14-24 years. Next, we designed a new algorithm for matching sample locations from the Allen Brain Atlas to the nodes of the SCN. Subsequently we used this to define, transcriptomic brain networks by estimating gene co-expression between pairs of cortical regions. Finally, we explored the hypothesis that transcriptional networks and structural MRI connectomes are coupled. A transcriptional brain network (TBN) and a structural covariance network (SCN) were correlated across connection weights and showed qualitatively similar complex topological properties: assortativity, small-worldness, modularity, and a rich-club. In both networks, the weight of an edge was inversely related to the anatomical (Euclidean) distance between regions. There were differences between networks in degree and distance distributions: the transcriptional network had a less fat-tailed degree distribution and a less positively skewed distance distribution than the SCN. However, cortical areas connected to each other within modules of the SCN had significantly higher levels of whole genome co-expression than expected by chance. Nodes connected in the SCN had especially high levels of expression and co-expression of a human supragranular enriched (HSE) gene set that has been specifically located to supragranular layers of human cerebral cortex and is known to be important for large-scale, long-distance cortico-cortical connectivity. This coupling of brain transcriptome and connectome topologies was largely but not entirely accounted for by the common constraint of physical distance on both networks.

Versatility of nodal affiliation to communities.

Graph theoretical analysis of the community structure of networks attempts to identify the communities (or modules) to which each node affiliates. However, this is in most cases an ill-posed problem, as the affiliation of a node to a single community is often ambiguous. Previous solutions have attempted to identify all of the communities to which each node affiliates. Instead of taking this approach, we introduce versatility, V, as a novel metric of nodal affiliation: V ≈ 0 means that a node is consistently assigned to a specific community; V >> 0 means it is inconsistently assigned to different communities. Versatility works in conjunction with existing community detection algorithms, and it satisfies many theoretically desirable properties in idealised networks designed to maximise ambiguity of modular decomposition. The local minima of global mean versatility identified the resolution parameters of a hierarchical community detection algorithm that least ambiguously decomposed the community structure of a social (karate club) network and the mouse brain connectome. Our results suggest that nodal versatility is useful in quantifying the inherent ambiguity of modular decomposition.

Mean-field equations for neuronal networks with arbitrary degree distributions.

The emergent dynamics in networks of recurrently coupled spiking neurons depends on the interplay between single-cell dynamics and network topology. Most theoretical studies on network dynamics have assumed simple topologies, such as connections that are made randomly and independently with a fixed probability (Erdös-Rényi network) (ER) or all-to-all connected networks. However, recent findings from slice experiments suggest that the actual patterns of connectivity between cortical neurons are more structured than in the ER random network. Here we explore how introducing additional higher-order statistical structure into the connectivity can affect the dynamics in neuronal networks. Specifically, we consider networks in which the number of presynaptic and postsynaptic contacts for each neuron, the degrees, are drawn from a joint degree distribution. We derive mean-field equations for a single population of homogeneous neurons and for a network of excitatory and inhibitory neurons, where the neurons can have arbitrary degree distributions. Through analysis of the mean-field equations and simulation of networks of integrate-and-fire neurons, we show that such networks have potentially much richer dynamics than an equivalent ER network. Finally, we relate the degree distributions to so-called cortical motifs.