Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes-flexibility and selection-must operate over multiple temporal scales as performance of a skill changes from being slow and challenging to being fast and automatic. Such selective adaptability is naturally provided by modular structure, which plays a critical role in evolution, development, and optimal network function. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we investigate the role of modularity in human learning by identifying dynamic changes of modular organization spanning multiple temporal scales. Our results indicate that flexibility, which we measure by the allegiance of nodes to modules, in one experimental session predicts the relative amount of learning in a future session. We also develop a general statistical framework for the identification of modular architectures in evolving systems, which is broadly applicable to disciplines where network adaptability is crucial to the understanding of system performance.complex network | time-dependent network | fMRI | motor learning | community structure T he brain is a complex system, composed of many interacting parts, which dynamically adapts to a continually changing environment over multiple temporal scales. Over relatively short temporal scales, rapid adaptation and continuous evolution of those interactions or connections form the neurophysiological basis for behavioral adaptation or learning. At small spatial scales, stable neurophysiological signatures of learning have been best demonstrated in animal systems at the level of individual synapses between neurons (1-3). At a larger spatial scale, it is also well-known that specific regional changes in brain activity and effective connectivity accompany many forms of learning in humans-including the acquisition of motor skills (4, 5).Learning-associated adaptability is thought to stem from the principle of cortical modularity (6). Modular, or nearly decomposable (7), structures are aggregates of small subsystems (modules) that can perform specific functions without perturbing the remainder of the system. Such structure provides a combination of compartmentalization and redundancy, which reduces the interdependence of components, enhances robustness, and facilitates behavioral adaptation (8, 9). Modular organization also confers evolvability on a system by reducing constraints on change (8,(10)(11)(12). Indeed, a putative relationship between modularity and adaptability in the context of human neuroscience has recently been posited (13,14). To date, however, the existence of modularity in large-scale cortical connectivity during learning has not been tested directly.Based on the aforementioned theoretical and empirical grounds, we hypothesized that the principle of modularity would characterize the fundamental organiz...

Fire is a worldwide phenomenon that appears in the geological record soon after the appearance of terrestrial plants. Fire influences global ecosystem patterns and processes, including vegetation distribution and structure, the carbon cycle, and climate. Although humans and fire have always coexisted, our capacity to manage fire remains imperfect and may become more difficult in the future as climate change alters fire regimes. This risk is difficult to assess, however, because fires are still poorly represented in global models. Here, we discuss some of the most important issues involved in developing a better understanding of the role of fire in the Earth system.

We describe techniques for the robust detection of community structure in some classes of timedependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural modules in semi-decomposable systems. Null models play an important role both in the optimization of quality functions such as modularity and in the subsequent assessment of the statistical validity of identified community structure. We examine the sensitivity of such methods to model parameters and show how comparisons to null models can help identify system scales. By considering a large number of optimizations, we quantify the variance of network diagnostics over optimizations ("optimization variance") and over randomizations of network structure ("randomization variance"). Because the modularity quality function typically has a large number of nearly degenerate local optima for networks constructed using real data, we develop a method to construct representative partitions that uses a null model to correct for statistical noise in sets of partitions. To illustrate our results, we employ ensembles of time-dependent networks extracted from both nonlinear oscillators and empirical neuroscience data. Many social, physical, technological, and biological systems can be modeled as networks composed of numerous interacting parts. 1 As an increasing amount of time-resolved data has become available, it has become increasingly important to develop methods to quantify and characterize dynamic properties of temporal networks. 2 Generalizing the study of static networks, which are typically represented using graphs, to temporal networks entails the consideration of nodes (representing entities) and/or edges (representing ties between entities) that vary in time. As one considers data with more complicated structures, the appropriate network analyses must become increasingly nuanced. In the present paper, we discuss methods for algorithmic detection of dense clusters of nodes (i.e., communities) by optimizing quality functions on multilayer network representations of temporal networks. 3,4 We emphasize the development and analysis of different types of null-model networks, whose appropriateness depends on the structure of the networks one is studying as well as the construction of representative partitions that take advantage of a multilayer network framework. To illustrate our ideas, we use ensembles of time-dependent networks from the human brain and human behavior.

SignificanceAll animals have associated microbial communities called microbiomes that influence the physiology and fitness of their host. It is unclear to what extent individual microbial species versus interactions between them influence the host. Here, we mapped all possible interactions between individual species of bacteria against Drosophila melanogaster fruit fly fitness traits. Our approach revealed that the same bacterial interactions that shape microbiome abundances also shape host fitness traits. The fitness traits of lifespan and fecundity showed a life history tradeoff, where equal total fitness can be gotten by either high fecundity over a short life or low fecundity over a long life. The microbiome interactions are as important as the individual species in shaping these fundamental aspects of fly physiology.

Magnetic resonance imaging enables the noninvasive mapping of both anatomical white matter connectivity and dynamic patterns of neural activity in the human brain. We examine the relationship between the structural properties of white matter streamlines (structural connectivity) and the functional properties of correlations in neural activity (functional connectivity) within 84 healthy human subjects both at rest and during the performance of attention-and memory-demanding tasks. We show that structural properties, including the length, number, and spatial location of white matter streamlines, are indicative of and can be inferred from the strength of resting-state and task-based functional correlations between brain regions. These results, which are both representative of the entire set of subjects and consistently observed within individual subjects, uncover robust links between structural and functional connectivity in the human brain.uman cognitive function is supported by large-scale interactions between different regions of the brain. The anatomical scaffolding that mediates these interactions can be described by a structural connectome that maps the spatial layout of white matter (1). Structural connectivity (SC), defined by the physical properties of these direct anatomical connections, supports the relay of electrical signals between brain regions. Neurophysiological events can similarly be described by a functional connectome that maps coordinated changes in neuronal activity, field potentials, blood flow, or energy consumption (2). Functional connectivity (FC), defined by temporal correlations in such neurophysiological events, reflects the resting-state and task-dependent strengths of correlated activity in different brain regions (3-5). The estimation of structural and functional connectivity from different experimental techniques raises two complementary questions about the quantitative relationships between structural and functional connectomes: (i) to what extent can the resting-state and task-dependent strengths of functional correlations between brain regions be inferred from structural connectomes, and (ii) to what extent can the physical properties of anatomical connections be inferred from functional connectomes?Connectomes, whether examined at the neural or systems level, are networks whose structural properties, such as the length and number of connections, can differentially impact functional properties, such as local or global correlations in temporal dynamics. Whereas the length and density of anatomical connections are thought to impact functional processes such as information segregation and integration (6, 7), the extent to which such relationships are robustly observed in the human brain is not well understood. Previous studies have been limited in scope to specific anatomical connections and brain regions, small sample sizes, and resting-state neural activity (8-13) and have consequently left several fundamental questions unanswered. How do variations in structural features, such a...