522 research outputs found
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
Clustering and Community Detection in Directed Networks: A Survey
Networks (or graphs) appear as dominant structures in diverse domains,
including sociology, biology, neuroscience and computer science. In most of the
aforementioned cases graphs are directed - in the sense that there is
directionality on the edges, making the semantics of the edges non symmetric.
An interesting feature that real networks present is the clustering or
community structure property, under which the graph topology is organized into
modules commonly called communities or clusters. The essence here is that nodes
of the same community are highly similar while on the contrary, nodes across
communities present low similarity. Revealing the underlying community
structure of directed complex networks has become a crucial and
interdisciplinary topic with a plethora of applications. Therefore, naturally
there is a recent wealth of research production in the area of mining directed
graphs - with clustering being the primary method and tool for community
detection and evaluation. The goal of this paper is to offer an in-depth review
of the methods presented so far for clustering directed networks along with the
relevant necessary methodological background and also related applications. The
survey commences by offering a concise review of the fundamental concepts and
methodological base on which graph clustering algorithms capitalize on. Then we
present the relevant work along two orthogonal classifications. The first one
is mostly concerned with the methodological principles of the clustering
algorithms, while the second one approaches the methods from the viewpoint
regarding the properties of a good cluster in a directed network. Further, we
present methods and metrics for evaluating graph clustering results,
demonstrate interesting application domains and provide promising future
research directions.Comment: 86 pages, 17 figures. Physics Reports Journal (To Appear
Modern temporal network theory: A colloquium
The power of any kind of network approach lies in the ability to simplify a
complex system so that one can better understand its function as a whole.
Sometimes it is beneficial, however, to include more information than in a
simple graph of only nodes and links. Adding information about times of
interactions can make predictions and mechanistic understanding more accurate.
The drawback, however, is that there are not so many methods available, partly
because temporal networks is a relatively young field, partly because it more
difficult to develop such methods compared to for static networks. In this
colloquium, we review the methods to analyze and model temporal networks and
processes taking place on them, focusing mainly on the last three years. This
includes the spreading of infectious disease, opinions, rumors, in social
networks; information packets in computer networks; various types of signaling
in biology, and more. We also discuss future directions.Comment: Final accepted versio
Network Geometry
Networks are finite metric spaces, with distances defined by the shortest paths between nodes. However, this is not the only form of network geometry: two others are the geometry of latent spaces underlying many networks and the effective geometry induced by dynamical processes in networks. These three approaches to network geometry are intimately related, and all three of them have been found to be exceptionally efficient in discovering fractality, scale invariance, self-similarity and other forms of fundamental symmetries in networks. Network geometry is also of great use in a variety of practical applications, from understanding how the brain works to routing in the Internet. We review the most important theoretical and practical developments dealing with these approaches to network geometry and offer perspectives on future research directions and challenges in this frontier in the study of complexity
TEMPORAL CONNECTIVITY AS A MEASURE OF ROBUSTNESS IN NONORTHOGONAL MULTIPLE ACCESS WIRELESS NETWORKS
Supplementary Material has been provided, but is not yet published.Nonorthogonal multiple access (NOMA) is recognized as an important technology to meet the performance requirements of fifth generation (5G) and beyond 5G (B5G) wireless networks. Through the technique of overloading, NOMA has the potential to support higher connection densities, increased spectral efficiency, and lower latency than orthogonal multiple access. The role of NOMA in 5G/B5G wireless networks necessitates a clear understanding of how overloading variability affects network robustness. This dissertation considers the relationship between variable overloading and network robustness through the lens of temporal network theory, where robustness is measured through the evolution of temporal connectivity between network devices (ND). We develop a NOMA temporal graph model and stochastic temporal component framework to characterize time-varying network connectivity as a function of NOMA overloading. The analysis is extended to derive stochastic expressions and probability mass functions for unidirectional connectivity, bidirectional connectivity, the inter-event time between unidirectional connectivity, and the minimum time required for bidirectional connectivity between all NDs. We test the accuracy of our analytical results through numerical simulations. Our results provide an overloading-based characterization of time-varying network robustness that is generalizable to any underlying NOMA implementation.National Security Agency, Fort George G. Meade, MD 20775Major, United States Marine CorpsApproved for public release. Distribution is unlimited
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