The field of neuroscience is facing an unprecedented expanse in the volume and diversity of available data. Traditionally, network models have provided key insights into the structure and function of the brain. With the advent of big data in neuroscience, both more sophisticated models capable of characterizing the increasing complexity of the data and novel methods of quantitative analysis are needed. Recently multilayer networks, a mathematical extension of traditional networks, have gained increasing popularity in neuroscience due to their ability to capture the full information of multi-model, multi-scale, spatiotemporal data sets. Here, we review multilayer networks and their applications in neuroscience, showing how incorporating the multilayer framework into network neuroscience analysis has uncovered previously hidden features of brain networks. We specifically highlight the use of multilayer networks to model disease, structure-function relationships, network evolution, and link multi-scale data. Finally, we close with a discussion of promising new directions of multilayer network neuroscience research and propose a modified definition of multilayer networks designed to unite and clarify the use of the multilayer formalism in describing real-world systems. some other measured unit [1,2]. Edges of the network represent the strength of connection between two units, and are typically chosen to measure either physical connections (structural networks) or statistical relationships between nodal dynamics (functional networks) [3]. The rich theory of networks has been successfully utilized in studying the brain by quantifying network structure though the calculation of descriptive and inferential network statistics which expose otherwise hidden phenomenon. Measures of centrality, degree distribution, clustering, small-worldness, and more [4,5,6] have been used to study disease, task, learning, behavior, and structure [7,3,8,9,2].The success of network theory in uncovering the complex organization of the human brain is not without limits, however, as traditional networks capture only a single mode of interaction between units.Recording technologies such as functional magnetic resonance imaging (fMRI), magnetoencephalography (MEG), and electroencephalogram (EEG) capture brain dynamics across time and across multiple frequency bands, and it is important to retain the information of the full frequency spectrum [10,11,12,13,14,15] or the full temporal profile [16,17,18,19] of such recordings. In addition to measuring functional interactions through fMRI or EEG, structural recording techniques such as diffusion weighted imaging (DWI) measure the presence and strength of physical connections between the various regions of the brain. The emergence of such increasingly large and multi-modal data sets therefore necessitates a quantitative model that is rich and flexible enough to both describe interactions between multiple scales and modalities and allow for meaningful analysis of the data to provide new and powerful ins...

Recurrent seizures, which define epilepsy, are transient abnormalities in the electrical activity of the brain. The mechanistic basis of seizure initiation, and the contribution of defined neuronal subtypes to seizure pathophysiology, remains poorly understood. We performedin vivotwo-photon calcium imaging in neocortex during temperature-induced seizures in male and female Dravet syndrome (Scn1a+/−) mice, a neurodevelopmental disorder with prominent temperature-sensitive epilepsy. Mean activity of both putative principal cells and parvalbumin-positive interneurons (PV-INs) was higher inScn1a+/− relative to wild-type controls during quiet wakefulness at baseline and at elevated core body temperature. However, wild-type PV-INs showed a progressive synchronization in response to temperature elevation that was absent in PV-INs fromScn1a+/− mice. Hence, PV-IN activity remains intact interictally inScn1a+/− mice, yet exhibits decreased synchrony immediately before seizure onset. We suggest that impaired PV-IN synchronization may contribute to the transition to the ictal state during temperature-induced seizures in Dravet syndrome.SIGNIFICANCE STATEMENTEpilepsy is a common neurological disorder defined by recurrent, unprovoked seizures. However, basic mechanisms of seizure initiation and propagation remain poorly understood. We performedin vivotwo-photon calcium imaging in an experimental model of Dravet syndrome (Scn1a+/− mice)—a severe neurodevelopmental disorder defined by temperature-sensitive, treatment-resistant epilepsy—and record activity of putative excitatory neurons and parvalbumin-positive GABAergic neocortical interneurons (PV-INs) during naturalistic seizures induced by increased core body temperature. PV-IN activity was higher inScn1a+/− relative to wild-type controls during quiet wakefulness. However, wild-type PV-INs showed progressive synchronization in response to temperature elevation that was absent in PV-INs fromScn1a+/− mice before seizure onset. Hence, impaired PV-IN synchronization may contribute to transition to seizure in Dravet syndrome.

Dynamic community detection provides a coherent description of network clusters over time, allowing one to track the growth and death of communities as the network evolves. However, modularity maximization, a popular method for performing multilayer community detection, requires the specification of an appropriate null model as well as resolution and interlayer coupling parameters. Importantly, the ability of the algorithm to accurately detect community evolution * smuldoon@buffalo.edu Networks are excellent data structures for capturing the pairwise interactions between a collection of objects, but when these interactions are dynamic, traditional network approaches require some form of data reduction to reduce the full range of interactions to a single summary. As a result, the final network may or may not be a good representative of the underlying system. A more suitable data structure for dynamic interactions is a temporal network [1, 2], which is a time ordered collection of networks organized into layers together with interlayer edges connecting nodes between layers. Temporal networks are increasingly being used to model time dependent properties of complex systems since no data loss is incurred as in the case of static networks [3][4][5][6][7]. A particularly important class of temporal networks are functional networks [8], in which nodes represent a dynamic unit and edges are given by a measure of functional similarity (see Fig. 1). For example, in brain networks nodes may represent neurons and edges are measured via synchronization between temporal spiking activity patterns [9].Since the nodes in a functional temporal network are themselves dynamic, the system may exhibit state changes where nodes switch between functional states. Such a state change is depicted in Fig. 1 and occurs between time layers 2 and 3. These state changes effect the properties and structure of the network, and it is important to develop network measures that are maximally sensitive to such changes [10]. Intuitively, one would expect interlayer edges to play a major role in temporal networks, as they model the strength of connections between nodes through time. However, it is typically assumed that interlayer edges exist only between a node and itself in the next layer, representing a self-identity link through time, and more importantly, the standard assumption is that interlayer edge weights are all set to the same constant value through time [3,[11][12][13]. While the latter assumption has made temporal networks easier to deploy in practice (since tuning a single parameter for interlayer edge weights is significantly easier than tuning all possible edge weights individually), it is insufficient at properly modeling functional networks that exhibit state changes where the properties of a node change over time and the similarity of a node to itself in the previous layer is not always constant.One important property of a functional temporal network that is especially sensitive

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