Posts by Collection

publications

Stability of entrainment of a continuum of coupled oscillators

Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017

Complex natural and engineered systems are ubiquitous, and their behavior is challenging to characterize and control. We examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can result in each oscillator attaining the frequency of the driving signal, with a phase offset determined by its natural frequency. We consider a special case of interacting oscillators in which the coupling tends to destabilize the phase configuration to which the driving signal would send the collection in the absence of coupling. In this setting, we derive stability results that characterize the trade-off between the effects of driving and coupling, and compare these results to the well-known Kuramoto model of a collection of freerunning coupled oscillators. Read more

Recommended citation: Jordan Snyder, Anatoly Zlotnik, Aric Hagberg, "Stability of entrainment of a continuum of coupled oscillators." Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017. http://aip.scitation.org/doi/10.1063/1.4994567

A Pulse-gated, Neural Implementation of the Backpropagation Algorithm

Published in Proceedings of the 7th Annual Neuro-inspired Computational Elements Workshop on - NICE '19, 2019

For some time, it has been thought that backpropagation of errors could not be implemented in biophysiologically realistic neural circuits. This belief was largely due to either 1) the need for symmetric replication of feedback and feedforward weights, 2) the need for differing forms of activation between forward and backward propagating sweeps, and 3) the need for a separate network for error gradient computation and storage, on the one hand, or 4) nonphysiological backpropagation through the forward propagating neurons themselves, on the other. In this paper, we present spiking neuron mechanisms for gating pulses to maintain short-term memories, controlling forward inference and backward error propagation, and coordinating learning of feedback and feedforward weights. These neural mechanisms are synthesized into a new backpropagation algorithm for neuromorphic circuits. Read more

Recommended citation: Andrew Sornborger, Louis Tao, Jordan Snyder, Anatoly Zlotnik, "A Pulse-gated, Neural Implementation of the Backpropagation Algorithm." Proceedings of the 7th Annual Neuro-inspired Computational Elements Workshop on - NICE '19, 2019. http://dl.acm.org/citation.cfm?doid=3320288.3320305

Thresholding normally distributed data creates complex networks

Published in arXiv, 2019

Network data sets are often constructed by some kind of thresholding procedure. The resulting networks frequently possess properties such as heavy-tailed degree distributions, clustering, large connected components and short average shortest path lengths. These properties are considered typical of complex networks and appear in many contexts, prompting consideration of their universality. Here we introduce a simple generative model for continuous valued relational data and study the network ensemble obtained by thresholding it. We find that some, but not all, of the properties associated with complex networks can be seen after thresholding, even though the underlying data is not "complex". In particular, we observe heavy-tailed degree distributions, large numbers of triangles, and short path lengths, while we do not observe non-vanishing clustering or community structure. Read more

Recommended citation: George Cantwell, Yanchen Liu, Benjamin Maier, Alice Schwarze, Carlos Serv{\'{a}}n, Jordan Snyder, Guillaume St-Onge, "Thresholding normally distributed data creates complex networks." arXiv, 2019. http://arxiv.org/abs/1902.08278

Degree-targeted cascades in modular, degree-heterogeneous networks

Published in arXiv, 2020

Many large scale phenomena, such as rapid changes in public opinion and the outbreak of disease epidemics, can be fruitfully modeled as cascades of activation on networks. This provides understanding of how various connectivity patterns among agents can influence the eventual extent of a cascade. We consider cascading dynamics on modular, degree-heterogeneous networks, as such features are observed in many real-world networks, and consider specifically the impact of the seeding strategy. We derive an analytic set of equations for the system by introducing a reduced description that extends a method developed by Gleeson that lets us accurately capture different seeding strategies using only one dynamical variable per module, namely the conditional exposure probability. We establish that activating the highest-degree nodes rather than random selection is more effective at growing a cascade locally, while the ability of a cascade to fully activate other modules is determined by the extent of large-scale interconnection between modules and is independent of how seed nodes are selected. Read more

Recommended citation: Jordan Snyder, Weiran Cai, Raissa D'Souza, "Degree-targeted cascades in modular, degree-heterogeneous networks." arXiv, 2020. http://arxiv.org/abs/2004.09316

Thresholding normally distributed data creates complex networks

Published in Physical Review E, 2020

Network data sets are often constructed by some kind of thresholding procedure. The resulting networks frequently possess properties such as heavy-tailed degree distributions, clustering, large connected components and short average shortest path lengths. These properties are considered typical of complex networks and appear in many contexts, prompting consideration of their universality. Here we introduce a simple generative model for continuous valued relational data and study the network ensemble obtained by thresholding it. We find that some, but not all, of the properties associated with complex networks can be seen after thresholding, even though the underlying data is not "complex". In particular, we observe heavy-tailed degree distributions, large numbers of triangles, and short path lengths, while we do not observe non-vanishing clustering or community structure. Read more

Recommended citation: George Cantwell, Yanchen Liu, Benjamin Maier, Alice Schwarze, Carlos Serv{\'{a}}n, Jordan Snyder, Guillaume St-Onge, "Thresholding normally distributed data creates complex networks." Physical Review E, 2020. https://link.aps.org/doi/10.1103/PhysRevE.101.062302

Mutualistic networks emerging from adaptive niche-based interactions

Published in Nature Communications, 2020

Mutualistic networks are vital ecological and social systems shaped by adaptation and evolution. They involve bipartite cooperation via the exchange of goods or services between actors of different types. Empirical observations of mutualistic networks across genres and geographic conditions reveal correlated nested and modular patterns. Yet, the underlying mechanism for the network assembly remains unclear. We propose a niche-based adaptive mechanism where both nestedness and modularity emerge simultaneously as complementary facets of an optimal niche structure. Key dynamical properties are revealed at different timescales. Foremost, mutualism can either enhance or reduce the network stability, depending on competition intensity. Moreover, structural adaptations are asymmetric, exhibiting strong hysteresis in response to environmental change. Finally, at the evolutionary timescale we show that the adaptive mechanism plays a crucial role in preserving the distinctive patterns of mutualism under species invasions and extinctions. Read more

Recommended citation: Weiran Cai, Jordan Snyder, Alan Hastings, Raissa D'Souza, "Mutualistic networks emerging from adaptive niche-based interactions." Nature Communications, 2020. http://dx.doi.org/10.1038/s41467-020-19154-5

talks

Computing Geometric Integrated Information

Published:

For decades, scientists across many disciplines, from biology to physics to mathematics, have been fascinated by emergent phenomena - complex behavior that arises from the interaction of many simple units. One approach to uncovering the underlying mechanisms behind emergence comes from information theory, which aims to quantitatively describe coordination between units in terms of production, transmission, and processing of information. In this talk, I will present a unified geometric interpretation of several different information measures intended to quantify causally-relevant information flow among components of a stochastic process, and calculate them on multi-layered primate social network data recorded by the McCowan lab at the California National Primate Research Center (CNPRC). Read more

Entrainment of Coupled Oscillators

Published:

Complex systems are ubiquitous, and often difficult to control. As a toy model for the control of a complex system, we take a system of coupled phase oscillators, all subject to the same periodic driving signal. It was shown by Anatoly Zlotnik and collaborators that in the absence of coupling, this can result in each oscillator attaining the frequency of the driving signal, with a phase offset determined by the oscillator’s natural frequency. We consider a special case in which the coupling tends to destabilize the phase configuration to which the driving signal would send the oscillators in the absence of coupling. In this setting we derive stability estimates that capture the trade-off between driving and coupling, and compare these results to the unforced version (i.e. the standard Kuramoto model). Read more

Modeling collective behavior in hierarchically-organized systems

Published:

Collective behavior is the organizing principle that has made existence anything more than a homogeneous expanse of mass and energy. Understanding how collective behavior emerges and operates is not only fascinating as a purely intellectual exercise, but compelling from an engineering perspective as well. In this talk I will describe how hierarchical structures arise naturally in systems that exhibit collective behavior, and describe two mathematical modeling projects aimed at giving a quantitative understanding of the building blocks of collective behavior in hierarchically organized systems. Read more

Coarse-graining for coupled oscillators: a case study in discovering low-dimensional dynamics

Published:

Numerical simulations form a backbone of modern science. We investigate the following question: given a simulation of some dynamical process, does there exist a good lower-dimensional representation? If so, finding such a representation may offer both computational speedup and fundamental insight into the dynamics of interest. To approach this question in the abstract, we infer coarse-grained equations of motion that describe a heterogeneous population of oscillators with a modular coupling structure. We choose this system because it is known to exhibit a transition from high- to low-dimensional behavior, and that low-dimensional behavior is well-described by equations of a known form. We conclude by exploring ways to move forward by systematically discarding several of the simplifying assumptions at play. Read more

teaching