arXiv subjects

Jordan Snyder

Publications and source records attributed to Jordan Snyder.

7 recordsLinked to original sources

arXiv2021

Data-driven stochastic modeling of coarse-grained dynamics with finite-size effects using Langevin regression

Obtaining coarse-grained models that accurately incorporate finite-size effects is an important open challenge in the study of complex, multi-scale systems. We apply Langevin regression, a recently developed method for finding stochastic differential equation (SDE) descriptions of realistically-sampled time series data, to understand finite-size effects in the Kuramoto model of coupled oscillators. We find that across the entire bifurcation diagram, the dynamics of the Kuramoto order parameter are statistically consistent with an SDE whose drift term has the form predicted by the Ott-Antonsen ansatz in the $N\to \infty$ limit. We find that the diffusion term is nearly independent of the bifurcation parameter, and has a magnitude decaying as $N^{-1/2}$, consistent with the central limit theorem. This shows that the diverging fluctuations of the order parameter near the critical point are driven by a bifurcation in the underlying drift term, rather than increased stochastic forcing.

nlin.AO↗

arXiv2021

Quantifying the Global Support Network for Non-State Armed Groups (NAGs)

Human history has been shaped by armed conflicts. Rather than large-scale interstate wars, low-intensity attacks have been more prevalent in the post-World War era. These attacks are often carried out by non-state armed groups (NAGs), which are supported by host states (HSs). We analyze the global bipartite network of NAG-HS support and its evolution over the period of 1945-2010. We find striking parallels to ecological networks such as mutualistic and parasitic forms of support, and a nested and modular network architecture. The nestedness emerges from preferential behaviors: highly connected players are more likely to both gain and lose connections. Long-persisting major modules are identified, reflecting both regional and trans-regional interests, which show significant turnover in their membership, contrary to the transitory ones. Revealing this architecture further enables the identification of actor's roles and provide insights for effective intervention strategies.

cs.SI↗

arXiv2020

Data-driven Selection of Coarse-Grained Models of Coupled Oscillators

Systematic discovery of reduced-order closure models for multi-scale processes remains an important open problem in complex dynamical systems. Even when an effective lower-dimensional representation exists, reduced models are difficult to obtain using solely analytical methods. Rigorous methodologies for finding such coarse-grained representations of multi-scale phenomena would enable accelerated computational simulations and provide fundamental insights into the complex dynamics of interest. We focus on a heterogeneous population of oscillators of Kuramoto type as a canonical model of complex dynamics, and develop a data-driven approach for inferring its coarse-grained description. Our method is based on a numerical optimization of the coefficients in a general equation of motion informed by analytical derivations in the thermodynamic limit. We show that certain assumptions are required to obtain an autonomous coarse-grained equation of motion. However, optimizing coefficient values enables coarse-grained models with conceptually disparate functional forms, yet comparable quality of representation, to provide accurate reduced-order descriptions of the underlying system.

nlin.AO↗

arXiv2020

Thresholding normally distributed data creates complex networks

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 model for correlated 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 the correlated data, even though the underlying data are not "complex". In particular, we observe heavy-tailed degree distributions, a large numbers of triangles, and short path lengths, while we do not observe non-vanishing clustering or community structure.

cs.SI↗

arXiv2020

Degree-targeted cascades in modular, degree-heterogeneous networks

The dynamics of cascading activation, such as rapid changes in public opinion and the outbreak of disease epidemics, have a crucial dependence on the connectivity patterns among the agents. We study cascading dynamics in modular, degree-heterogeneous networks, and consider the impact of intra-module seeding strategy on inter-module spread. Specifically, we establish that although activating the highest-degree nodes is more effective than random selection at growing a cascade locally, there is a critical level of inter-module connectivity required for a cascade to cross from one module to another, irrespective of the seeding strategy. We present an analytical proof of this statement for the case that each module has the same degree distribution and all module pairs have the same inter-module connectivity, while our simulation results suggest its validity for more general situations, including a ring of modules. Interestingly, we find that on a network comprised of two modules, this critical level is primarily determined by the degree distribution of the \emph{alter} module, as opposed to the seed module. Our analytical approach extends a method developed by Gleeson, but is able to capture different seeding strategies using only one dynamical variable per module, namely the conditional exposure probability. Our work shows that the possibility of a global cascade depends sensitively on inter-module connectivity, and less on the intra-module seeding strategy. This suggests, for example, that slight changes to inter-module connectivity can be a feasible intervention strategy to promote or inhibit global cascades.

physics.soc-ph↗

arXiv2018

A Dynamic Niche Model for the Emergence and Evolution of Mutualistic Network Structures

Mutualistic interactions are vital constituents of ecological and socio-economic systems. Empirical studies have found that the patterns of reciprocal relations among the participants often shows the salient features of being simultaneously nested and modular. Whether and how these two structural properties of mutualistic networks can emerge out of a common mechanism however remains unclear. We propose a unified dynamic model based on the adaptation of niche relations that gives rise to both structural features. We apply Hutchinson's concept of niche interaction to networked cooperative species. Their niche relation evolves under the assumption of fitness maximization. Modularity and nestedness emerge concurrently through the accumulated local advantages in the structural and demographic distribution. A rich ensemble of key dynamical behaviors are unveiled in the dynamical framework. We demonstrate that mutualism can exhibit either a stabilizing or destabilizing effect on the evolved network, which undergoes a drastic transition with the overall competition level. Most strikingly, the adaptive network may exhibit a profound nature of history-dependency in response to environmental changes, allowing it to be found in alternative stable structures. The adaptive nature of niche interactions, as captured in our framework, can underlie a broad class of ecological relations and also socio-economic networks that engage in bipartite cooperation.

q-bio.PE↗

arXiv2017

Stability of entrainment of a continuum of coupled oscillators

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 free-running coupled oscillators.

nlin.AO↗