# Nonlinear Sciences - Adaptation and Self-Organizing Systems Publications (50)

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## Nonlinear Sciences - Adaptation and Self-Organizing Systems Publications

We study the loss of coherence of electrochemical oscillations on meso- and nanosized electrodes with numeric simulations of the electrochemical master equation for a prototypical electrochemical oscillator, the hydrogen peroxide reduction on Pt electrodes in the presence of halides. On nanoelectrodes, the electrode potential changes whenever a stochastic electron-transfer event takes place. Electrochemical reaction rate coefficients depend exponentially on the electrode potential and become thus fluctuating quantities as well. Read More

Investigation of social influence dynamics requires mathematical models that are "simple" enough to admit rigorous analysis, and yet sufficiently "rich" to capture salient features of social groups. Thus, the mechanism of iterative opinion pooling from (DeGroot, 1974), which can explain the generation of consensus, was elaborated in (Friedkin and Johnsen, 1999) to take into account individuals' ongoing attachments to their initial opinions, or prejudices. The "anchorage" of individuals to their prejudices may disable reaching consensus and cause disagreement in a social influence network. Read More

Earth system analysis is the study of the joint dynamics of biogeophysical, social and technological processes on our planet. To advance our understanding of possible future development pathways and identify management options for navigating to safe operating spaces while avoiding undesirable domains, computer models of the Earth system are developed and applied. These models hardly represent dynamical properties of technological processes despite their great planetary-scale influence on the biogeophysical components of the Earth system and the associated risks for human societies posed, e. Read More

One of the most compelling problems in science consists in understanding how living systems process information. After all, the way they process information defines their capacities to learning and adaptation. There is an increasing consensus in that living systems are not machines in any sense. Read More

Transformations to create more sustainable social-ecological systems are urgently needed. Structural change is a feature of transformations of social-ecological systems that is of critical importance but is little understood. Here, we propose a framework for conceptualising and modelling sustainability transformations based on adaptive networks. Read More

Game theory often assumes rational players that play equilibrium strategies. But when the players have to learn their strategies by playing the game repeatedly, how often do the strategies converge? We analyze generic two player games using a standard learning algorithm, and also study replicator dynamics, which is closely related. We show that the frequency with which strategies converge to a fixed point can be understood by analyzing the best reply structure of the payoff matrix. Read More

This paper outlines a methodological approach to generate adaptive agents driving themselves near points of criticality. Using a synthetic approach we construct a conceptual model that, instead of specifying mechanistic requirements to generate criticality, exploits the maintenance of an organizational structure capable of reproducing critical behavior. Our approach captures the well-known principle of universality that classifies critical phenomena inside a few universality classes of systems without relying on specific mechanisms or topologies. Read More

In this paper we investigate how so-called quorum-sensing networks can be de-synchronized. Such networks, which arise in many important application fields such as systems biology, are characterized by the fact that direct communication between network nodes is superimposed to communication with a shared, environmental, variable. In particular, we provide a new sufficient condition ensuring that the trajectories of these quorum-sensing networks diverge from their synchronous evolution. Read More

Imitation is widely observed in populations of decision-making agents. Using our recent convergence results for asynchronous imitation dynamics on networks, we consider how such networks can be efficiently driven to a desired equilibrium state by offering payoff incentives for using a certain strategy, either uniformly or targeted to individuals. In particular, if for each available strategy, agents playing that strategy receive maximum payoff when their neighbors play that same strategy, we show that providing incentives to agents in a network that is at equilibrium will result in convergence to a unique new equilibrium. Read More

We analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of the introduced order parameters capture all transitions from incoherence over phase locking to full synchrony for arbitrary, finite networks. We then introduce an alternative, universal order parameter that accurately tracks the degree of partial phase locking and synchronization, adapting the traditional definition to account for the network topology and its influence on the phase coherence of the oscillators. Read More

Optimization of the stability of synchronized states between a pair of symmetrically coupled reaction-diffusion systems exhibiting rhythmic spatiotemporal patterns is studied in the framework of the phase reduction theory. The optimal linear filter that maximizes the linear stability of the in-phase synchronized state is derived for the case where the two systems are linearly coupled. The nonlinear optimal interaction function that theoretically gives the largest linear stability of the in-phase synchronized state is also derived. Read More

We consider optimization of linear stability of synchronized states between a pair of weakly coupled limit-cycle oscillators with cross coupling, where different components of state variables of the oscillators are allowed to interact. On the basis of the phase reduction theory, the coupling matrix between different components of the oscillator states that maximizes the linear stability of the synchronized state under given constraints on overall coupling intensity and on stationary phase difference is derived. The improvement in the linear stability is illustrated by using several types of limit-cycle oscillators as examples. Read More

Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are often modeled as nonlinear limit-cycle oscillators. In this article, we briefly review phase reduction theory, which is a simple and powerful method for analyzing the synchronization properties of limit-cycle oscillators exhibiting rhythmic dynamics. Read More

The hierarchical product of networks represents a natural tool for building large networks out of two smaller networks. The hierarchical product is a generalization of the Cartesian product and results in less regular and therefore more heterogeneous network structures. Here we investigate the behaviors of two classical dynamical processes on hierarchical products: diffusion and synchronization of chaotic oscillators, both of which depend on the eigenvalue spectrum of the network Laplacian matrix. Read More

The observed spatio-temporal ciliary beat patterns on multiciliated epithelia are suspected to be the result of self-organizing processes on various levels. Here, we present an abstract epithelium model at the pluricellular level, which intends to make the self-organization of ciliary beating patterns as well as of the associated fluid transport across the airway epithelium plausible. Ciliated cells are modeled in terms of locally interacting oscillating two-state actuators. Read More

The Kuramoto model is a system of nonlinear differential equations that models networks of coupled oscillators and is often used to study synchronization among the oscillators. In this paper we study steady state solutions of the Kuramoto model by assigning to each steady state a tuple of integers which records how the state twists around the cycles in the network. We then use this new classification of steady states to obtain a "Weyl" type of asymptotic estimate for the number of steady states as the number of oscillators becomes arbitrarily large while preserving the cycle structure. Read More

We explore a new mechanism to explain polarization phenomena in opinion dynamics. The model is based on the idea that agents evaluate alternative views on the basis of the social feedback obtained on expressing them. A high support of the favored and therefore expressed opinion in the social environment, is treated as a positive social feedback which reinforces the value associated to this opinion. Read More

Linear optimal power flow (LOPF) algorithms use a linearization of the alternating current (AC) load flow equations to optimize generator dispatch in a network subject to the loading constraints of the network branches. Common algorithms use the voltage angles at the buses as optimization variables, but alternatives can be computationally advantageous. In this article we provide a review of existing methods and describe new formulations, which express the loading constraints directly in terms of the flows themselves, using a decomposition of the graph into a spanning tree and closed cycles. Read More

The notion of entropy is shared between statistics and thermodynamics, and is fundamental to both disciplines. This makes statistical problems particularly suitable for reaction network implementations. In this paper we show how to perform a statistical operation known as Information Projection or E projection with stochastic mass-action kinetics. Read More

Investigation of the critical levels and catastrophes in the complex systems of different nature is useful and perspective. Mathematical modeling and analysis is presented for revealing and investigation of the phenomena and critical levels in a development of complex systems for various natures associated with diverse complicated factors, in particular with shifted arguments of the system. Intensive research in this direction and developed techniques may optimize management of the complex systems in financial-economic, natural and other fields. Read More

This contribution reports an application of MultiFractal Detrended Fluctuation Analysis, MFDFA based novel feature extraction technique for automated detection of epilepsy. In fractal geometry, Multifractal Detrended Fluctuation Analysis MFDFA is a popular technique to examine the self-similarity of a nonlinear, chaotic and noisy time series. In the present research work, EEG signals representing healthy, interictal (seizure free) and ictal activities (seizure) are acquired from an existing available database. Read More

We consider a rotor made of two camphor disks glued below the ends of a plastic stripe. The disks are floating on a water surface and the plastic stripe does not touch the surface. The system can rotate around a vertical axis located at the center of the stripe. Read More

In previously identified forms of remote synchronization between two nodes, the intermediate portion of the network connecting the two nodes is not synchronized with them but generally exhibits some coherent dynamics. Here we report on a network phenomenon we call incoherence-mediated remote synchronization (IMRS), in which two non-contiguous parts of the network are identically synchronized while the dynamics of the intermediate part is statistically and information-theoretically incoherent. We identify mirror symmetry in the network structure as a mechanism allowing for such behavior, and show that IMRS is robust against dynamical noise as well as against parameter changes. Read More

We study the dynamics of overdamped Brownian particles diffusing in force fields and undergoing stochastic resetting to a given location with a generic {\em space-dependent} rate of resetting. We introduce a novel quantum mechanical approach that allows to calculate in a systematic way analytical expressions for a variety of statistics of the dynamics, such as (i) the propagator prior to first reset; (ii) the distribution of the first-reset time, and, most interestingly, (iii) the spatial distribution of the particle at long times. A key to our accomplishment is the derivation of an equality relating the transition probability prior to first reset with the propagator of a suitable quantum mechanical problem. Read More

In recent years, studies of long-range interacting (LRI) systems have taken centre stage in the arena of statistical mechanics and dynamical system studies, due to new theoretical developments involving tools from as diverse a field as kinetic theory, non-equilibrium statistical mechanics, and large deviation theory, but also due to new and exciting experimental realizations of LRI systems. In this invited contribution, we discuss the general features of long-range interactions, emphasizing in particular the main physical phenomenon of non-additivity, which leads to a plethora of distinct effects, both thermodynamic and dynamic, that are not observed with short-range interactions: Ensemble inequivalence, slow relaxation, broken ergodicity. We also discuss several physical systems with long-range interactions: mean-field spin systems, self-gravitating systems, Euler equations in two dimensions, Coulomb systems, one-component electron plasma, dipolar systems, free-electron lasers, atoms trapped in optical cavities. Read More

In 1979 Penrose hypothesized that the arrows of time are explained by the hypothesis that the fundamental laws are time irreversible. That is, our reversible laws, such as the standard model and general relativity are effective, and emerge from an underlying fundamental theory which is time irreversible. In Cort\^{e}s and Smolin (2014a, 2014b, 2016) we put forward a research program aiming at realizing just this. Read More

We discuss a novel microscopic model for collective decision-making interacting multi-agent systems. In particular we are interested in modeling a well known phenomena in the experimental literature called equality bias, where agents tend to behave in the same way as if they were as good, or as bad, as their partner. We analyze the introduced problem and we prove the suboptimality of the collective decision-making in the presence of equality bias. Read More

**Authors:**Yi Yang

^{1}, Stefan Bruns

^{2}, Melania Rogowska

^{3}, Sepideh S. Hakim

^{4}, Jörg U. Hammel

^{5}, Susan L. S. Stipp

^{6}, Henning O. Sørensen

^{7}

**Affiliations:**

^{1}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{2}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{3}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{4}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{5}Helmholtz-Zentrum Geesthacht, Germany,

^{6}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{7}Nano-Science Center, Department of Chemistry, University of Copenhagen

The dissolution of porous materials in a flow field shapes the morphologies of many geologic landscapes. Identifying the dissolution front, the interface between the reactive and the unreactive regions in a dissolving medium, is a prerequisite for studying dissolution kinetics. Despite its fundamental importance, the dynamics of a dissolution front in an evolving natural microstructure has never been reported. Read More

**Authors:**Y. Yang

^{1}, S. S. Hakim

^{2}, S. Bruns

^{3}, M. Rogowska

^{4}, S. Boehnert

^{5}, J. U. Hammel

^{6}, S. L. S. Stipp

^{7}, H. O. Sørensen

^{8}

**Affiliations:**

^{1}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{2}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{3}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{4}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{5}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{6}Helmholtz-Zentrum Geesthacht, Germany,

^{7}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{8}Nano-Science Center, Department of Chemistry, University of Copenhagen

The dissolution of porous media in a geologic formation induced by the injection of massive amounts of CO2 can undermine the mechanical stability of the formation structure before carbon mineralization takes place. The geomechanical impact of geologic carbon storage is therefore closely related to the structural sustainability of the chosen reservoir as well as the probability of buoyancy driven CO2 leakage through caprocks. Here we show, with a combination of ex situ nanotomography and in situ microtomography, that the presence of dissolved CO2 in water produces a homogeneous dissolution pattern in natural chalk microstructure. Read More

**Authors:**Y. Yang

^{1}, S. S. Hakim

^{2}, S. Bruns

^{3}, K. Uesugi

^{4}, K. N. Dalby

^{5}, S. L. S. Stipp

^{6}, H. O. Sørensen

^{7}

**Affiliations:**

^{1}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{2}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{3}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{4}SPring-8, Japan,

^{5}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{6}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{7}Nano-Science Center, Department of Chemistry, University of Copenhagen

Growth of wormholes in porous media can lead to self-organization of flow networks with an overwhelming geometric complexity. Despite decades of study, the mechanism by which a dominant wormhole develops its path during growth remains elusive. Here we show that the trajectory of a growing wormhole can be predicted by identifying the flowpath with a so-called minimum cumulative surface. Read More

The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have been for a long time a central focus of complexity science, and physics. Here, we introduce group-theoretic concepts to identify and enumerate the symmetric inputs, which result in irreversible system behaviors with undesired effects on many computational tasks. The concept of so-called configuration shift-symmetry is applied on two-dimensional cellular automata as an ideal model of computation. Read More

**Affiliations:**

^{1}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{2}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{3}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{4}Nano-Science Center, Department of Chemistry, University of Copenhagen

When reactive fluids flow through a dissolving porous medium, conductive channels form, leading to fluid breakthrough. This phenomenon is important in geologic carbon storage, where the dissolution of CO2 in water increases the acidity and produce microstructures significantly different from those in an intact reservoir. We demonstrate the controlling mechanism for the dissolution patterns in natural porous materials. Read More

**Affiliations:**

^{1}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{2}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{3}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{4}Nano-Science Center, Department of Chemistry, University of Copenhagen

Reactive infiltration instability (RII) drives the development of many natural and engineered flow systems. These are encountered e.g. Read More

**Affiliations:**

^{1}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{2}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{3}Nano-Science Center, Department of Chemistry, University of Copenhagen,

^{4}Nano-Science Center, Department of Chemistry, University of Copenhagen

The tendency of irreversible processes to generate entropy is the ultimate driving force for the evolution of nature. In engineering, entropy production is often used as a measure of usable energy losses. In this study we show that the analysis of the entropy production patterns can help understand the vastly diversified experimental observations of water-rock interactions in natural porous media. Read More

**Affiliations:**

^{1}MAMBA, LJLL

Collective motion of chemotactic bacteria as E. Coli relies, at the individual level, on a continuous reorientation by runs and tumbles. It has been established that the length of run is decided by a stiff response to temporal sensing of chemical cues along the pathway. Read More

We present an approach for reconstructing networks of pulse-coupled neuron-like oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases are instantaneously reset by incoming pulses. Using an iterative procedure, we recover the properties of all nodes, namely their phase response curves and natural frequencies, as well as strengths of all directed connections. Read More

Message-passing methods provide a powerful approach for calculating the expected size of cascades either on random networks (e.g., drawn from a configuration-model ensemble or its generalizations) asymptotically as the number $N$ of nodes becomes infinite or on specific finite-size networks. Read More

We demonstrate the application of the multiplex networks-approach for the analysis of various networks which connected individuals and communities in the politically highly fragmented late medieval Balkans (1204-1453 AD) within and across border zones. We present how we obtain relational data from our sources and the integration of these data into three different networks (of roads, state administration and ecclesiastical administration) of various topologies; then we calculate several indicators for influences and overlaps between these different networks which connect the same set of nodes (settlements). We analyse changes and continuities in the topologies of the various networks for three time-steps (1210, 1324 and 1380 CE) and demonstrate the role of these networks as frameworks for social interactions. Read More

Recently the dynamics of signed networks, where the ties among the agents can be both positive (attractive) or negative (repulsive) have attracted substantial attention of the research community. Examples of such networks are models of opinion dynamics over signed graphs, recently introduced by Altafini (2012,2013) and extended to discrete-time case by Meng et al. (2014). Read More

Many problems in industry --- and in the social, natural, information, and medical sciences --- involve discrete data and benefit from approaches from subjects such as network science, information theory, optimization, probability, and statistics. Because the study of networks is concerned explicitly with connectivity between different entities, it has become very prominent in industrial settings, and this importance has been accentuated further amidst the modern data deluge. In this article, we discuss the role of network analysis in industrial and applied mathematics, and we give several examples of network science in industry. Read More

The spider silk is one of the most interesting bio-materials investigated in the last years. One of the main reasons that brought scientists to study this organized system is its high level of resistance if compared to other artificial materials characterized by higher density. Subsequently, researchers discovered that the spider silk is a complex system formed by different kinds of proteins, organized (or disorganized) to guarantee the required resistance, which is function of the final application and of the environmental conditions. Read More

Many coordination phenomena in Nature are grounded on a synchronisation regime. In the case of brain dynamics, such self-organised process allows the neurons of particular brain regions to behave as a whole and thus directly controlling the neural activity, the muscles and finally the whole human body. However, not always such synchronised collective behaviour is the desired one, this is the case of neurodegenerative diseases such as Parkinson's or epilepsy where abnormal synchronisation induces undesired effects such as tremors and epileptic seizures. Read More

The vortices that appear repeatedly and suggest turbulent dynamics are crucial to the understanding of sheared turbulence. These vortices produce order out of chaos, benefiting the turbulence modelling that focuses only on statistically stable quantities. In three dimensions, the hairpin vortices play such a fundamental role in the transport of momentum and energy for wall bounded sheared turbulence. Read More

Spontaneous symmetry breaking (SSB) is an important phenomenon observed in various fields including physics and biology. In this connection, we here show that the trade-off between attractive and repulsive couplings can induce spontaneous symmetry breaking in a homogeneous system of coupled oscillators. With a simple model of a system of two coupled Stuart-Landau oscillators, we demonstrate how the tendency of attractive coupling in inducing in-phase synchronized (IPS) oscillations and the tendency of repulsive coupling in inducing out-of-phase synchronized (OPS) oscillations compete with each other and give rise to symmetry breaking oscillatory (SBO) states and interesting multistabilities. Read More

We propose a model of an adaptive network of spiking neurons that gives rise to a hypernetwork of its dynamic states at the upper level of description. Left to itself, the network exhibits a sequence of transient clustering which relates to a traffic in the hypernetwork in the form of a random walk. Receiving inputs the system is able to generate reproducible sequences corresponding to stimulus-specific paths in the hypernetwork. Read More

Phase response curve (PRC) is an extremely useful tool for studying the response of oscillatory systems, e.g. neurons, to sparse or weak stimulation. Read More

Avalanches of electrochemical activity in brain networks have been empirically reported to obey scale-invariant behavior --characterized by power-law distributions up to some upper cut-off-- both in vitro and in vivo. Elucidating whether such scaling laws stem from the underlying neural dynamics operating at the edge of a phase transition is a fascinating possibility, as systems poised at criticality have been argued to exhibit a number of important functional advantages. Here we employ a well-known model for neural dynamics with synaptic plasticity, to elucidate an alternative scenario in which neuronal avalanches can coexist, overlapping in time, but still remaining scale-free. Read More

Robustness of spatial pattern against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively investigated, little is known about a general mechanism for achieving robustness in reaction-diffusion systems. Here, we propose a buffered reaction-diffusion system, in which active states of chemicals mediated by buffer molecules contribute to reactions, and demonstrate that robustness of the pattern wavelength is achieved by the dynamics of the buffer molecule. Read More

Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre-synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory instantaneous post-synaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions. Read More

Living organisms, ecosystems, and social systems are examples of complex systems in which robustness against inclusion of new elements is an essential feature. A recently proposed simple model has revealed a general mechanism by which such systems can become robust against inclusion of elements with random interactions when the elements have a moderate number of links. This happens as a result of two opposing effects such that while the inclusion of elements with more interactions makes each individual element more robust against disturbances, it also increases the net impact of the loss of any element in the system. Read More