arXiv subjects

Sean P. Cornelius

Publications and source records attributed to Sean P. Cornelius.

17 recordsLinked to original sources

arXiv2025

Tempological Control of Network Dynamics

Feedback control is an effective strategy for stabilizing a desired state and has been widely adopted in maintaining the stability of systems such as flying birds and power grids. By default, this framework requires continuous control input to offset deviations from the desired state, which can be invasive and cost a considerable amount of energy. Here, we introduce tempological (temporal + topological) control -- a novel, noninvasive strategy that harnesses the inherent flexibility of time-varying networks to control the dynamics of a general nonlinear system. By strategically switching network topology on-the-fly based on the current states of the nodes, we show how it is possible to drive a system to a desired state or even stabilize otherwise unstable states, all in the absence of external forcing. We demonstrate the utility of our approach using networks of Kuramoto and Stuart-Landau oscillators, achieving synchronization out of sets of unsynchronizable networks. Finally, we develop a statistical theory that explains why tempological control will almost always succeed in the limit of large and diverse temporal networks, with diversity of network configurations overcoming the deficiencies of any snapshot in isolation.

nlin.AO↗

arXiv2025

How more data can hurt: Instability and regularization in next-generation reservoir computing

It has been found recently that more data can, counter-intuitively, hurt the performance of deep neural networks. Here, we show that a more extreme version of the phenomenon occurs in data-driven models of dynamical systems. To elucidate the underlying mechanism, we focus on next-generation reservoir computing (NGRC) -- a popular framework for learning dynamics from data. We find that, despite learning a better representation of the flow map with more training data, NGRC can adopt an ill-conditioned ``integrator'' and lose stability. We link this data-induced instability to the auxiliary dimensions created by the delayed states in NGRC. Based on these findings, we propose simple strategies to mitigate the instability, either by increasing regularization strength in tandem with data size, or by carefully introducing noise during training. Our results highlight the importance of proper regularization in data-driven modeling of dynamical systems.

cs.LG↗

arXiv2025

Personalised strategy of allocating social goods in structured populations

Cooperation underlies many aspects of the evolution of human and animal societies, where cooperators produce social goods to benefit others. Explaining the emergence of cooperation among selfish individuals has become a major research interest in evolutionary dynamics. Previous studies typically use complex networks to capture the interactions between individuals, and assume that cooperators distribute benefits equally to their neighbors. In practice, the distribution of social goods is often non-uniform, and individuals may selectively provide benefits to those they interact with based on their personal preferences. Here, we develop an efficient algorithm to optimize the placement of donation structure in any given network to minimize the threshold for the emergence of cooperation. We find when cooperators allocate the benefits preferentially compared to the traditional settings of donating to all neighbors, cooperation tends to be maximally promoted. Furthermore, the optimal donation structure is strongly disassortative -- the low-degree nodes tend to donate to high-degree ones preferentially and vice versa. Based on this finding, we offer a local heuristic strategy based on degree thresholds for personalizing the allocation of social goods and choosing each cooperator's recipient, which we use to prove its effectiveness in empirical datasets. Our findings advance the understanding of mechanisms for promoting cooperation with strategic allocations of social goods.

physics.soc-ph↗

arXiv2023

Catch-22s of reservoir computing

Reservoir Computing (RC) is a simple and efficient model-free framework for forecasting the behavior of nonlinear dynamical systems from data. Here, we show that there exist commonly-studied systems for which leading RC frameworks struggle to learn the dynamics unless key information about the underlying system is already known. We focus on the important problem of basin prediction -- determining which attractor a system will converge to from its initial conditions. First, we show that the predictions of standard RC models (echo state networks) depend critically on warm-up time, requiring a warm-up trajectory containing almost the entire transient in order to identify the correct attractor. Accordingly, we turn to Next-Generation Reservoir Computing (NGRC), an attractive variant of RC that requires negligible warm-up time. By incorporating the exact nonlinearities in the original equations, we show that NGRC can accurately reconstruct intricate and high-dimensional basins of attraction, even with sparse training data (e.g., a single transient trajectory). Yet, a tiny uncertainty in the exact nonlinearity can render prediction accuracy no better than chance. Our results highlight the challenges faced by data-driven methods in learning the dynamics of multistable systems and suggest potential avenues to make these approaches more robust.

cs.LG↗

arXiv2023

Doubly heterogeneous networks facilitate the emergence of collective cooperation

There is growing recognition that the network structures arising from interactions between different entities in physical, social and biological systems fundamentally alter the evolutionary outcomes. Previous paradigm exploring evolutionary game dynamics has assumed that individuals update their strategies at an identical rate, reporting that structurally heterogeneous networks -- despite their ubiquity in real systems -- generally hinder the emergence of collective cooperation compared to their homogeneous counterparts. Here we solve this paradox by creating a new paradigm where individuals on arbitrary networks are allowed to update strategies at arbitrary, personalized rates, and provide the precise condition under which universal collective cooperation is favored. We find that when individuals' update rates vary inversely with their number of connections, heterogeneous networks actually outperform homogeneous ones in promoting cooperation. This surprising property of such "doubly heterogeneous" networks cautions against the conventional wisdom that heterogeneous networks are antagonistic to cooperation. We further develop an efficient protocol for optimizing the promotion of cooperation by tuning individuals' update rates in any structure. Our findings highlight that personalized interaction dynamics, beyond structure, in complex networks are fundamental to understanding and promoting collective cooperation.

physics.soc-ph↗

arXiv2023

Mastering Percolation-like Games with Deep Learning

Though robustness of networks to random attacks has been widely studied, intentional destruction by an intelligent agent is not tractable with previous methods. Here we devise a single-player game on a lattice that mimics the logic of an attacker attempting to destroy a network. The objective of the game is to disable all nodes in the fewest number of steps. We develop a reinforcement learning approach using deep Q-learning that is capable of learning to play this game successfully, and in so doing, to optimally attack a network. Because the learning algorithm is universal, we train agents on different definitions of robustness and compare the learned strategies. We find that superficially similar definitions of robustness induce different strategies in the trained agent, implying that optimally attacking or defending a network is sensitive the particular objective. Our method provides a new approach to understand network robustness, with potential applications to other discrete processes in disordered systems.

cs.LG↗

arXiv2020

High-resolution human mobility data reveal race and wealth disparities in disaster evacuation patterns

Major disasters such as extreme weather events can magnify and exacerbate pre-existing social disparities, with disadvantaged populations bearing disproportionate costs. Despite the implications for equity and emergency planning, we lack a quantitative understanding of how these social fault lines translate to different behaviors in large-scale emergency contexts. Here we investigate this problem in the context of Hurricane Harvey, using over 30 million anonymized GPS records from over 150,000 opted-in users in the Greater Houston Area to quantify patterns of disaster-inflicted relocation activities before, during, and after the shock. We show that evacuation distance is highly homogenous across individuals from different types of neighborhoods classified by race and wealth, obeying a truncated power-law distribution. Yet here the similarities end: we find that both race and wealth strongly impact evacuation patterns, with disadvantaged minority populations less likely to evacuate than wealthier white residents. Finally, there are considerable discrepancies in terms of departure and return times by race and wealth, with strong social cohesion among evacuees from advantaged neighborhoods in their destination choices. These empirical findings bring new insights into mobility and evacuations, providing policy recommendations for residents, decision makers, and disaster managers alike.

physics.soc-ph↗

arXiv2017

Control energy scaling in temporal networks

In practical terms, controlling a network requires manipulating a large number of nodes with a comparatively small number of external inputs, a process that is facilitated by paths that broadcast the influence of the (directly-controlled) driver nodes to the rest of the network. Recent work has shown that surprisingly, temporal networks can enjoy tremendous control advantages over their static counterparts despite the fact that in temporal networks such paths are seldom instantaneously available. To understand the underlying reasons, here we systematically analyze the scaling behavior of a key control cost for temporal networks--the control energy. We show that the energy costs of controlling temporal networks are determined solely by the spectral properties of an "effective" Gramian matrix, analogous to the static network case. Surprisingly, we find that this scaling is largely dictated by the first and the last network snapshot in the temporal sequence, independent of the number of intervening snapshots, the initial and final states, and the number of driver nodes. Our results uncover the intrinsic laws governing why and when temporal networks save considerable control energy over their static counterparts.

nlin.AO↗

arXiv2016

Evolution of Cooperation on Temporal Networks

The structure of social networks is a key determinant in fostering cooperation and other altruistic behavior among naturally selfish individuals. However, most real social interactions are temporal, being both finite in duration and spread out over time. This raises the question of whether stable cooperation can form despite an intrinsically fragmented social fabric. Here we develop a framework to study the evolution of cooperation on temporal networks in the setting of the classic Prisoner's Dilemma. By analyzing both real and synthetic datasets, we find that temporal networks generally facilitate the evolution of cooperation compared to their static counterparts. More interestingly, we find that the intrinsic human interactive pattern like bursty behavior impedes the evolution of cooperation. Finally, we introduce a measure to quantify the temporality present in networks and demonstrate that there is an intermediate level of temporality that boosts cooperation most. Our results open a new avenue for investigating the evolution of cooperation in more realistic structured populations.

physics.soc-ph↗

arXiv2016

Controllability of multiplex, multi-timescale networks

The paradigm of layered networks is used to describe many real-world systems -- from biological networks, to social organizations and transportation systems. Recently there has been much progress in understanding the general properties of multilayer networks, our understanding of how to control such systems remains limited. One aspect that makes this endeavor challenging is that each layer can operate at a different timescale, thus we cannot directly apply standard ideas from structural control theory of individual networks. Here we address the problem of controlling multilayer and multi-timescale networks focusing on two-layer multiplex networks with one-to-one interlayer coupling. We investigate the case when the control signal is applied to the nodes of one layer. We develop a theory based on disjoint path covers to determine the minimum number of inputs ($N_\T i$) necessary for full control. We show that if both layers operate on the same timescale then the network structure of both layers equally affect controllability. In the presence of timescale separation, controllability is enhanced if the controller interacts with the faster layer: $N_\T i$ decreases as the timescale difference increases up to a critical timescale difference, above which $N_\T i$ remains constant and is completely determined by the faster layer. In contrast, control becomes increasingly difficult if the controller interacts with the layer operating on the slower timescale and increasing timescale separation leads to increased $N_\T i$, again up to a critical value, above which $N_\T i$ still depends on the structure of both layers. By identifying the underlying mechanisms that connect timescale difference and controllability for a simplified model, we provide insight into disentangling how our ability to control real interacting complex systems is affected by a variety of sources of complexity.

physics.soc-ph↗

arXiv2016

The fundamental advantages of temporal networks

Despite the traditional focus of network science on static networks, most networked systems of scientific interest are characterized by temporal links. By disrupting the paths, link temporality has been shown to frustrate many dynamical processes on networks, from information spreading to accessibility. Considering the ubiquity of temporal networks in nature, we must ask: Are there any advantages of the networks' temporality? Here we develop an analytical framework to explore the control properties of temporal networks, arriving at the counterintuitive conclusion that temporal networks, compared to their static (i.e. aggregated) counterparts, reach controllability faster, demand orders of magnitude less control energy, and the control trajectories, through which the system reaches its final states, are significantly more compact than those characterizing their static counterparts. The combination of analytical, numerical and empirical results demonstrates that temporality ensures a degree of flexibility that would be unattainable in static networks, significantly enhancing our ability to control them.

nlin.AO↗

arXiv2015

Regularity underlies erratic population abundances in marine ecosystems

The abundance of a species' population in an ecosystem is rarely stationary, often exhibiting large fluctuations over time. Using historical data on marine species, we show that the year-to-year fluctuations of population growth rate obey a well-defined double-exponential (Laplace) distribution. This striking regularity allows us to devise a stochastic model despite seemingly irregular variations in population abundances. The model identifies the effect of reduced growth at low population density as a key factor missed in current approaches of population variability analysis and without which extinction risks are severely underestimated. The model also allows us to separate the effect of demographic stochasticity and show that single-species growth rates are dominantly determined by stochasticity common to all species. This dominance---and the implications it has for interspecies correlations, including co-extinctions---emphasizes the need of ecosystem-level management approaches to reduce the extinction risk of the individual species themselves.

nlin.AO↗

arXiv2013

NECO - A scalable algorithm for NEtwork COntrol

We present an algorithm for the control of complex networks and other nonlinear, high-dimensional dynamical systems. The computational approach is based on the recently-introduced concept of compensatory perturbations -- intentional alterations to the state of a complex system that can drive it to a desired target state even when there are constraints on the perturbations that forbid reaching the target state directly. Included here is ready-to-use software that can be applied to identify eligible control interventions in a general system described by coupled ordinary differential equations, whose specific form can be specified by the user. The algorithm is highly scalable, with the computational cost scaling as the number of dynamical variables to the power 2.5.

math.OC↗

arXiv2013

Realistic Control of Network Dynamics

The control of complex networks is of paramount importance in areas as diverse as ecosystem management, emergency response, and cell reprogramming. A fundamental property of networks is that perturbations to one node can affect other nodes, potentially causing the entire system to change behavior or fail. Here, we show that it is possible to exploit the same principle to control network behavior. Our approach accounts for the nonlinear dynamics inherent to real systems, and allows bringing the system to a desired target state even when this state is not directly accessible due to constraints that limit the allowed interventions. Applications show that this framework permits reprogramming a network to a desired task as well as rescuing networks from the brink of failure---which we illustrate through the mitigation of cascading failures in a power-grid network and the identification of potential drug targets in a signaling network of human cancer.

cond-mat.dis-nn↗

arXiv2011

Comment on "Controllability of Complex Networks with Nonlinear Dynamics"

The recent paper by W.-X. Wang, Y.-C. Lai, J. Ren, B. Li & C. Grebogi [arXiv:1107.2177v1] proposed a method for the control of complex networks with nonlinear dynamics based on linearizing the system around a finite number of local desired states. The authors purport that any bidirectional network with one-dimensional intrinsic node dynamics can be fully controlled by a single driver node, which can be any node in the network, regardless of the network topology. According to this result, a network with an arbitrarily large number of nodes (a million, a billion, or even more) could be controlled by a single node. Here we show, however, that this result is specious and that it does not hold true even for networks with only two nodes. We demonstrate that the erroneous results are a consequence of a fundamental flaw in the proposed method, namely, that reaching a local desired state using the proposed linearization procedure generally requires a nonlocal trajectory, which grossly violates the linear approximation. Their further conclusion that network systems with nonlinear dynamics are more controllable than those with linear dynamics is a known fact presented as novel based on a flawed argument. A central problem underlying the authors' argument is that their formulation is entirely based on the number of driver nodes required to reach a desired state---even when this number is one, keeping the system at that desired state generally requires directly controlling all nodes in the network. When this is taken into account, the conclusion that nonlinear dynamics can facilitate network control was already anticipated in S.P. Cornelius, W.L. Kath & A.E. Motter [arXiv:1105.3726v1], which is not referenced in their paper. If one insists on using the authors' formulation, then, in contradiction to their claim, nonlinear systems would never be more controllable than linear ones because...

cond-mat.dis-nn↗

arXiv2011

Controlling Complex Networks with Compensatory Perturbations

The response of complex networks to perturbations is of utmost importance in areas as diverse as ecosystem management, emergency response, and cell reprogramming. A fundamental property of networks is that the perturbation of one node can affect other nodes, in a process that may cause the entire or substantial part of the system to change behavior and possibly collapse. Recent research in metabolic and food-web networks has demonstrated the concept that network damage caused by external perturbations can often be mitigated or reversed by the application of compensatory perturbations. Compensatory perturbations are constrained to be physically admissible and amenable to implementation on the network. However, the systematic identification of compensatory perturbations that conform to these constraints remains an open problem. Here, we present a method to construct compensatory perturbations that can control the fate of general networks under such constraints. Our approach accounts for the full nonlinear behavior of real complex networks and can bring the system to a desirable target state even when this state is not directly accessible. Applications to genetic networks show that compensatory perturbations are effective even when limited to a small fraction of all nodes in the network and that they are far more effective when limited to the highest-degree nodes. The approach is conceptually simple and computationally efficient, making it suitable for the rescue, control, and reprogramming of large complex networks in various domains.

q-bio.MN↗

arXiv2011

Dispensability of Escherichia coli's latent pathways

Gene-knockout experiments on single-cell organisms have established that expression of a substantial fraction of genes is not needed for optimal growth. This problem acquired a new dimension with the recent discovery that environmental and genetic perturbations of the bacterium Escherichia coli are followed by the temporary activation of a large number of latent metabolic pathways, which suggests the hypothesis that temporarily activated reactions impact growth and hence facilitate adaptation in the presence of perturbations. Here we test this hypothesis computationally and find, surprisingly, that the availability of latent pathways consistently offers no growth advantage, and tends in fact to inhibit growth after genetic perturbations. This is shown to be true even for latent pathways with a known function in alternate conditions, thus extending the significance of this adverse effect beyond apparently nonessential genes. These findings raise the possibility that latent pathway activation is in fact derivative of another, potentially suboptimal, adaptive response.

q-bio.MN↗