414 research outputs found
Graph Theory and Networks in Biology
In this paper, we present a survey of the use of graph theoretical techniques
in Biology. In particular, we discuss recent work on identifying and modelling
the structure of bio-molecular networks, as well as the application of
centrality measures to interaction networks and research on the hierarchical
structure of such networks and network motifs. Work on the link between
structural network properties and dynamics is also described, with emphasis on
synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape
Temporal Networks
A great variety of systems in nature, society and technology -- from the web
of sexual contacts to the Internet, from the nervous system to power grids --
can be modeled as graphs of vertices coupled by edges. The network structure,
describing how the graph is wired, helps us understand, predict and optimize
the behavior of dynamical systems. In many cases, however, the edges are not
continuously active. As an example, in networks of communication via email,
text messages, or phone calls, edges represent sequences of instantaneous or
practically instantaneous contacts. In some cases, edges are active for
non-negligible periods of time: e.g., the proximity patterns of inpatients at
hospitals can be represented by a graph where an edge between two individuals
is on throughout the time they are at the same ward. Like network topology, the
temporal structure of edge activations can affect dynamics of systems
interacting through the network, from disease contagion on the network of
patients to information diffusion over an e-mail network. In this review, we
present the emergent field of temporal networks, and discuss methods for
analyzing topological and temporal structure and models for elucidating their
relation to the behavior of dynamical systems. In the light of traditional
network theory, one can see this framework as moving the information of when
things happen from the dynamical system on the network, to the network itself.
Since fundamental properties, such as the transitivity of edges, do not
necessarily hold in temporal networks, many of these methods need to be quite
different from those for static networks
Network Approaches to Understand Individual Differences in Brain Connectivity: Opportunities for Personality Neuroscience
Over the past decade, advances in the interdisciplinary field of network science have provided a framework for understanding the intrinsic structure and function of human brain networks. A particularly fruitful area of this work has focused on patterns of functional connectivity derived from noninvasive neuroimaging techniques such as functional magnetic resonance imaging (fMRI). An important subset of these efforts has bridged the computational approaches of network science with the rich empirical data and biological hypotheses of neuroscience, and this research has begun to identify features of brain networks that explain individual differences in social, emotional, and cognitive functioning. The most common approach estimates connections assuming a single configuration of edges that is stable across the experimental session. In the literature, this is referred to as a static network approach, and researchers measure static brain networks while a subject is either at rest or performing a cognitively demanding task. Research on social and emotional functioning has primarily focused on linking static brain networks with individual differences, but recent advances have extended this work to examine temporal fluctuations in dynamic brain networks. Mounting evidence suggests that both the strength and flexibility of time-evolving brain networks influence individual differences in executive function, attention, working memory, and learning. In this review, we first examine the current evidence for brain networks involved in cognitive functioning. Then we review some preliminary evidence linking static network properties to individual differences in social and emotional functioning. We then discuss the applicability of emerging dynamic network methods for examining individual differences in social and emotional functioning. We close with an outline of important frontiers at the intersection between network science and neuroscience that will enhance our understanding of the neurobiological underpinnings of social behavior
Brain Rhythms Reveal a Hierarchical Network Organization
Recordings of ongoing neural activity with EEG and MEG exhibit oscillations of specific frequencies over a non-oscillatory background. The oscillations appear in the power spectrum as a collection of frequency bands that are evenly spaced on a logarithmic scale, thereby preventing mutual entrainment and cross-talk. Over the last few years, experimental, computational and theoretical studies have made substantial progress on our understanding of the biophysical mechanisms underlying the generation of network oscillations and their interactions, with emphasis on the role of neuronal synchronization. In this paper we ask a very different question. Rather than investigating how brain rhythms emerge, or whether they are necessary for neural function, we focus on what they tell us about functional brain connectivity. We hypothesized that if we were able to construct abstract networks, or “virtual brains”, whose dynamics were similar to EEG/MEG recordings, those networks would share structural features among themselves, and also with real brains. Applying mathematical techniques for inverse problems, we have reverse-engineered network architectures that generate characteristic dynamics of actual brains, including spindles and sharp waves, which appear in the power spectrum as frequency bands superimposed on a non-oscillatory background dominated by low frequencies. We show that all reconstructed networks display similar topological features (e.g. structural motifs) and dynamics. We have also reverse-engineered putative diseased brains (epileptic and schizophrenic), in which the oscillatory activity is altered in different ways, as reported in clinical studies. These reconstructed networks show consistent alterations of functional connectivity and dynamics. In particular, we show that the complexity of the network, quantified as proposed by Tononi, Sporns and Edelman, is a good indicator of brain fitness, since virtual brains modeling diseased states display lower complexity than virtual brains modeling normal neural function. We finally discuss the implications of our results for the neurobiology of health and disease
Data-Based And Theory-Based Network Models Of Perturbations To Neural Dynamics
Much of neuroscience is centered on uncovering simple principles that constrain the behavior of the brain. When considering the formation of neural architectures, similar structures can be recreated following the principles of minimizing wiring and maximizing topological complexity. However, a similar understanding of neural dynamics on top of these structural connections has not yet been achieved. One promising strategy for identifying underlying principles of neural dynamics is quantifying and modeling the response of neural systems to perturbation. Here, we use a spectrum of data- and theory-based network models to characterize the response of neural systems to different types of perturbations. We report how functional networks change in the context of pathological epileptic activity and brain-computer interface control. We also specifically test one possible principle: that activity is constrained to spread along connections in both the context of brain-computer interfaces and direct electrical stimulation. In the first study, we demonstrate across a wide variety of functional connectivity metrics and frequency bands that epileptic activity increases amplitude-based functional interactions, an observation that can now be incorporated into future theory-based models. In a second study, we determine that modeling activity that is constrained to spread along connections suggests why certain connections are important for brain-computer interface learning; specifically, these connections support sustained activity in attention regions. In our third study, we demonstrate that modeling activity changes from direct electrical stimulation using white matter connectivity explains more variance than models with rewired connections. This model generates testable predictions about which individuals, regions, and time points would lead to successful applications of direct electrical stimulation. Overall, this work demonstrates the potential uses of a range of data- and theory-based models for uncovering simple guiding principles that determine the behavior of a system. It also uses one specific principle - that activity is constrained to spread along connections - to understand the role of specific connections that may support learning, and provide a method to optimize individually tailored stimulation therapies for a specific outcome
Multilayer Networks
In most natural and engineered systems, a set of entities interact with each
other in complicated patterns that can encompass multiple types of
relationships, change in time, and include other types of complications. Such
systems include multiple subsystems and layers of connectivity, and it is
important to take such "multilayer" features into account to try to improve our
understanding of complex systems. Consequently, it is necessary to generalize
"traditional" network theory by developing (and validating) a framework and
associated tools to study multilayer systems in a comprehensive fashion. The
origins of such efforts date back several decades and arose in multiple
disciplines, and now the study of multilayer networks has become one of the
most important directions in network science. In this paper, we discuss the
history of multilayer networks (and related concepts) and review the exploding
body of work on such networks. To unify the disparate terminology in the large
body of recent work, we discuss a general framework for multilayer networks,
construct a dictionary of terminology to relate the numerous existing concepts
to each other, and provide a thorough discussion that compares, contrasts, and
translates between related notions such as multilayer networks, multiplex
networks, interdependent networks, networks of networks, and many others. We
also survey and discuss existing data sets that can be represented as
multilayer networks. We review attempts to generalize single-layer-network
diagnostics to multilayer networks. We also discuss the rapidly expanding
research on multilayer-network models and notions like community structure,
connected components, tensor decompositions, and various types of dynamical
processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure
Centralized and distributed cognitive task processing in the human connectome
A key question in modern neuroscience is how cognitive changes in a human
brain can be quantified and captured by functional connectomes (FC) . A
systematic approach to measure pairwise functional distance at different brain
states is lacking. This would provide a straight-forward way to quantify
differences in cognitive processing across tasks; also, it would help in
relating these differences in task-based FCs to the underlying structural
network. Here we propose a framework, based on the concept of Jensen-Shannon
divergence, to map the task-rest connectivity distance between tasks and
resting-state FC. We show how this information theoretical measure allows for
quantifying connectivity changes in distributed and centralized processing in
functional networks. We study resting-state and seven tasks from the Human
Connectome Project dataset to obtain the most distant links across tasks. We
investigate how these changes are associated to different functional brain
networks, and use the proposed measure to infer changes in the information
processing regimes. Furthermore, we show how the FC distance from resting state
is shaped by structural connectivity, and to what extent this relationship
depends on the task. This framework provides a well grounded mathematical
quantification of connectivity changes associated to cognitive processing in
large-scale brain networks.Comment: 22 pages main, 6 pages supplementary, 6 figures, 5 supplementary
figures, 1 table, 1 supplementary table. arXiv admin note: text overlap with
arXiv:1710.0219
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