Lucille Calmon, Juan G. Restrepo, Joaquín J. Torres, Ginestra Bianconi
Topological signals defined on nodes, links and higher dimensional simplices define the dynamical state of a network or of a simplicial complex. As such, topological signals are attracting increasing attention in network theory, dynamical systems, signal processing and machine learning. Topological signals defined on the nodes are typically studied in network dynamics, while topological signals defined on links are much less explored. Here we investigate topological synchronization describing locally coupled topological signals defined on the nodes and on the links of a network. The dynamics of signals defined on the nodes is affected by a phase lag depending on the dynamical state of nearby links and vice versa, the dynamics of topological signals defined on the links is affected by a phase lag depending on the dynamical state of nearby nodes. We show that topological synchronization on a fully connected network is explosive and leads to a discontinuous forward transition and a continuous backward transition. The analytical investigation of the phase diagram provides an analytical expression for the critical threshold of the discontinuous explosive synchronization. The model also displays an exotic coherent synchronized phase, also called rhythmic phase, characterized by having non-stationary order parameters which can shed light on topological mechanisms for the emergence of brain rhythms.

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Mitochondria appear to communicate and cooperate with one another, both within and between cells. Biologists are only just beginning to understand how and why.

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Heiko Hamann and Andreagiovanni Reina (2021) Scalability in Computing and Robotics. IEEE Transactions on Computers.
https://doi.org/10.1109/TC.2021.3089044
https://arxiv.org/abs/2006.04969

Efficient engineered systems require scalability. A scalable system has increasing performance with increasing system size. In an ideal situation, the increase in performance (e.g., speedup) corresponds to the number of units (e.g., processors, robots, users) that are added to the system (e.g., three times the number of processors in a computer would lead to three times faster computations). However, if multiple units work on the same task, then coordination among these units is required. This coordination can introduce overheads with an impact on system performance. The coordination costs can lead to sublinear improvement or even diminishing performance with increasing system size. However, there are also systems that implement efficient coordination and exploit collaboration of units to attain superlinear improvement. Modeling the scalability dynamics is key to understanding and engineering efficient systems. Known laws of scalability, such as Amdahl’s law, Gustafson’s law, and Gunther’s Universal Scalability Law, are minimalistic phenomenological models that explain a rich variety of system behaviors through concise equations. While useful to gain general insights, the phenomenological nature of these models may limit the understanding of the underlying dynamics, as they are detached from first principles that could explain coordination overheads or synergies among units. Through a decentralized system approach, we propose a general model based on generic interactions between units that is able to describe, as specific cases, any general pattern of scalability included by previously reported laws. The proposed general model of scalability has the advantage of being built on first principles, or at least on a microscopic description of interaction between units, and therefore has the potential to contribute to a better understanding of system behavior and scalability. We show that this generic model can be applied to a diverse set of systems, such as parallel supercomputers, robot swarms, or wireless sensor networks, therefore creating a unified view on interdisciplinary design for scalability.

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Jake M. Hofman, Duncan J. Watts, Susan Athey, Filiz Garip, Thomas L. Griffiths, Jon Kleinberg, Helen Margetts, Sendhil Mullainathan, Matthew J. Salganik, Simine Vazire, Alessandro Vespignani & Tal Yarkoni
Nature (2021)

Computational social science is more than just large repositories of digital data and the computational methods needed to construct and analyse them. It also represents a convergence of different fields with different ways of thinking about and doing science. The goal of this Perspective is to provide some clarity around how these approaches differ from one another and to propose how they might be productively integrated. Towards this end we make two contributions. The first is a schema for thinking about research activities along two dimensions—the extent to which work is explanatory, focusing on identifying and estimating causal effects, and the degree of consideration given to testing predictions of outcomes—and how these two priorities can complement, rather than compete with, one another. Our second contribution is to advocate that computational social scientists devote more attention to combining prediction and explanation, which we call integrative modelling, and to outline some practical suggestions for realizing this goal.

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