arXiv subjects

Adilson E. Motter

Publications and source records attributed to Adilson E. Motter.

At least 91 records · Page 5Linked to original sources

arXiv2016

Symmetric States Requiring System Asymmetry

Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the complete synchronization of the entire network is the state inheriting the system symmetry. As in other systems subject to symmetry breaking, such symmetric states are not always stable. Here we report on the discovery of the converse of symmetry breaking--the scenario in which complete synchronization is not stable for identically-coupled identical oscillators but becomes stable when, and only when, the oscillator parameters are judiciously tuned to nonidentical values, thereby breaking the system symmetry to preserve the state symmetry. Aside from demonstrating that diversity can facilitate and even be required for uniformity and consensus, this suggests a mechanism for convergent forms of pattern formation in which initially asymmetric patterns evolve into symmetric ones.

cond-mat.dis-nn↗

arXiv2016

Introduction to Focus Issue: Patterns of Network Synchronization

The study of synchronization of coupled systems is currently undergoing a major surge fueled by recent discoveries of new forms of collective dynamics and the development of techniques to characterize a myriad of new patterns of network synchronization. This includes chimera states, phenomena determined by symmetry, remote synchronization, and asymmetry-induced synchronization. This Focus Issue presents a selection of contributions at the forefront of these developments, to which this introduction is intended to offer an up-to-date foundation.

cond-mat.dis-nn↗

arXiv2015

Networkcontrology

An increasing number of complex systems are now modeled as networks of coupled dynamical entities. Nonlinearity and high-dimensionality are hallmarks of the dynamics of such networks but have generally been regarded as obstacles to control. Here I discuss recent advances on mathematical and computational approaches to control high-dimensional nonlinear network dynamics under general constraints on the admissible interventions. I also discuss the potential of network control to address pressing scientific problems in various disciplines.

cond-mat.dis-nn↗

arXiv2015

Control of stochastic and induced switching in biophysical networks

Noise caused by fluctuations at the molecular level is a fundamental part of intracellular processes. While the response of biological systems to noise has been studied extensively, there has been limited understanding of how to exploit it to induce a desired cell state. Here we present a scalable, quantitative method based on the Freidlin-Wentzell action to predict and control noise-induced switching between different states in genetic networks that, conveniently, can also control transitions between stable states in the absence of noise. We apply this methodology to models of cell differentiation and show how predicted manipulations of tunable factors can induce lineage changes, and further utilize it to identify new candidate strategies for cancer therapy in a cell death pathway model. This framework offers a systems approach to identifying the key factors for rationally manipulating biophysical dynamics, and should also find use in controlling other classes of noisy complex networks.

q-bio.MN↗

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↗

arXiv2015

Detecting structural breaks in seasonal time series by regularized optimization

Real-world systems are often complex, dynamic, and nonlinear. Understanding the dynamics of a system from its observed time series is key to the prediction and control of the system's behavior. While most existing techniques tacitly assume some form of stationarity or continuity, abrupt changes, which are often due to external disturbances or sudden changes in the intrinsic dynamics, are common in time series. Structural breaks, which are time points at which the statistical patterns of a time series change, pose considerable challenges to data analysis. Without identification of such break points, the same dynamic rule would be applied to the whole period of observation, whereas false identification of structural breaks may lead to overfitting. In this paper, we cast the problem of decomposing a time series into its trend and seasonal components as an optimization problem. This problem is ill-posed due to the arbitrariness in the number of parameters. To overcome this difficulty, we propose the addition of a penalty function (i.e., a regularization term) that accounts for the number of parameters. Our approach simultaneously identifies seasonality and trend without the need of iterations, and allows the reliable detection of structural breaks. The method is applied to recorded data on fish populations and sea surface temperature, where it detects structural breaks that would have been neglected otherwise. This suggests that our method can lead to a general approach for the monitoring, prediction, and prevention of structural changes in real systems.

stat.CO↗

arXiv2014

Inertial particle trapping in an open vortical flow

Recent numerical results on advection dynamics have shown that particles denser than the fluid can remain trapped indefinitely in a bounded region of an open fluid flow. Here, we investigate this counterintuitive phenomenon both numerically and analytically to establish the conditions under which the underlying particle-trapping attractors can form. We focus on a two-dimensional open flow composed of a pair of vortices and its specular image, which is a system we represent as a vortex pair plus a wall along the symmetry line. Considering particles that are much denser than the fluid, we show that two point attractors form in the neighborhood of the vortex pair provided that the particle Stokes number is smaller than a critical value of order unity. In the absence of the wall, the boundaries of the basins of the attracting points are smooth. When the wall is present, the point attractors describe counter-rotating ellipses in this frame, with a period equal to half the period of one isolated vortex pair. However, their boundaries are shown to become fractal if the distance to the wall is smaller than a critical distance that scales with the inverse square root of the Stokes number. This transformation is related to the breakdown of a separatrix that gives rise to a heteroclinic tangle close to the vortices, which we describe using a Melnikov function. For an even smaller distance to the wall, we demonstrate that a second separatrix breaks down and a new heteroclinic tangle forms farther away from the vortices. Particles released in the open part of the flow can approach the attractors and be trapped permanently provided that they cross the two separatrices. Furthermore, the trapping of heavy particles from the open flow is shown to be robust to the presence of gravity, viscosity, and noise.

physics.flu-dyn↗

arXiv2013

Doubly Transient Chaos: The Generic Form of Chaos in Autonomous Dissipative Systems

Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final state sensitivity observed in connection with fractal basin boundaries in conservative scattering systems and driven dissipative systems. Here we focus on the most prevalent case of undriven dissipative systems, whose transient dynamics fall outside the scope of previous studies since no time-dependent solutions can exist for asymptotically long times. We show that such systems can exhibit positive finite-time Lyapunov exponents and fractal-like basin boundaries which nevertheless have codimension one. In sharp contrast with its driven and conservative counterparts, the settling rate to the (fixed-point) attractors grows exponentially in time, meaning that the fraction of trajectories away from the attractors decays super-exponentially. While no invariant chaotic sets exist in such cases, the irregular behavior is governed by transient interactions with transient chaotic saddles, which act as effective, time-varying chaotic sets.

nlin.CD↗

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↗

arXiv2013

Chaos at Fifty

In 1963 Edward Lorenz revealed deterministic predictability to be an illusion and gave birth to a field that still thrives. This Feature Article discusses Lorenz's discovery and developments that followed from it.

nlin.CD↗

arXiv2013

Controllability transition and nonlocality in network control

A common goal in the control of a large network is to minimize the number of driver nodes or control inputs. Yet, the physical determination of control signals and the properties of the resulting control trajectories remain widely under-explored. Here we show that: (i) numerical control fails in practice even for linear systems if the controllability Gramian is ill-conditioned, which occurs frequently even when existing controllability criteria are satisfied unambiguously; (ii) the control trajectories are generally nonlocal in the phase space, and their lengths are strongly anti-correlated with the numerical success rate and number of control inputs; (iii) numerical success rate increases abruptly from zero to nearly one as the number of control inputs is increased, a transformation we term numerical controllability transition. This reveals a trade-off between nonlocality of the control trajectory in the phase space and nonlocality of the control inputs in the network itself. The failure of numerical control cannot be overcome in general by merely increasing numerical precision---successful control requires instead increasing the number of control inputs beyond the numerical controllability transition.

cond-mat.dis-nn↗

arXiv2013

Longitudinal inverted compressibility in super-strained metamaterials

We develop a statistical physics theory for solid-solid phase transitions in which a metamaterial undergoes longitudinal contraction in response to increase in external tension. Such transitions, which are forbidden in thermodynamic equilibrium, have recently been shown to be possible during the decay of metastable, super-strained states. We present a first-principles model to predict these transitions and validate it using molecular dynamics simulations. Aside from its immediate mechanical implications, our theory points to a wealth of analogous inverted responses, such as inverted susceptibility or heat-capacity transitions, allowed when considering realistic scales.

cond-mat.stat-mech↗

arXiv2013

Identifying trends in word frequency dynamics

The word-stock of a language is a complex dynamical system in which words can be created, evolve, and become extinct. Even more dynamic are the short-term fluctuations in word usage by individuals in a population. Building on the recent demonstration that word niche is a strong determinant of future rise or fall in word frequency, here we introduce a model that allows us to distinguish persistent from temporary increases in frequency. Our model is illustrated using a 10^8-word database from an online discussion group and a 10^11-word collection of digitized books. The model reveals a strong relation between changes in word dissemination and changes in frequency. Aside from their implications for short-term word frequency dynamics, these observations are potentially important for language evolution as new words must survive in the short term in order to survive in the long term.

physics.soc-ph↗

arXiv2013

Network Observability Transitions

In the modeling, monitoring, and control of complex networks, a fundamental problem concerns the comprehensive determination of the state of the system from limited measurements. Using power grids as example networks, we show that this problem leads to a new type of percolation transition, here termed a {\it network observability transition}, which we solve analytically for the configuration model. We also demonstrate a dual role of the network's community structure, which both facilitates optimal measurement placement and renders the networks substantially more sensitive to `observability attacks'. Aside from their immediate implications for the development of smart grids, these results provide insights into decentralized biological, social, and technological networks.

physics.soc-ph↗

arXiv2012

Mechanical Metamaterials with Negative Compressibility Transitions

When tensioned, ordinary materials expand along the direction of the applied force. Here, we explore network concepts to design metamaterials exhibiting negative compressibility transitions, during which a material undergoes contraction when tensioned (or expansion when pressured). Continuous contraction of a material in the same direction of an applied tension, and in response to this tension, is inherently unstable. The conceptually similar effect we demonstrate can be achieved, however, through destabilisations of (meta)stable equilibria of the constituents. These destabilisations give rise to a stress-induced solid-solid phase transition associated with a twisted hysteresis curve for the stress-strain relationship. The strain-driven counterpart of negative compressibility transitions is a force amplification phenomenon, where an increase in deformation induces a discontinuous increase in response force. We suggest that the proposed materials could be useful for the design of actuators, force amplifiers, micro-mechanical controls, and protective devices.

cond-mat.mtrl-sci↗

arXiv2012

Networks in Motion

Feature article on how networks that govern communication, growth, herd behavior, and other key processes in nature and society are becoming increasingly amenable to modeling, forecast, and control.

physics.soc-ph↗

arXiv2012

Why Optimal States Recruit Fewer Reactions in Metabolic Networks

The metabolic network of a living cell involves several hundreds or thousands of interconnected biochemical reactions. Previous research has shown that under realistic conditions only a fraction of these reactions is concurrently active in any given cell. This is partially determined by nutrient availability, but is also strongly dependent on the metabolic function and network structure. Here, we establish rigorous bounds showing that the fraction of active reactions is smaller (rather than larger) in metabolic networks evolved or engineered to optimize a specific metabolic task, and we show that this is largely determined by the presence of thermodynamically irreversible reactions in the network. We also show that the inactivation of a certain number of reactions determined by irreversibility can generate a cascade of secondary reaction inactivations that propagates through the network. The mathematical results are complemented with numerical simulations of the metabolic networks of the bacterium Escherichia coli and of human cells, which show, counterintuitively, that even the maximization of the total reaction flux in the network leads to a reduced number of active reactions.

q-bio.MN↗