arXiv subjects

Deniz Eroglu

Publications and source records attributed to Deniz Eroglu.

At least 19 recordsLinked to original sources

arXiv2025

Physics for the environment and sustainable development

A reliable understanding of the Earth system is essential for the life quality of modern society. Natural hazards are the cause of most life and resource losses. The ability to define the conditions for a sustainable development of humankind, to keep the Earth system within the boundaries of habitable states, or to predict critical transitions and events in the dynamics of the Earth system are crucial to mitigate and adapt to Earth system related events and changes (e.g., volcanic eruptions, earthquakes, climate change) and to avert the disastrous consequences of natural hazards. In this chapter, we discuss key concepts from nonlinear physics and show that they enable us to treat challenging problems of Earth sciences which cannot be solved by classic methods. In particular, the concepts of multi-scaling, recurrence, synchronization, and complex networks have become crucial in the very last decades for a substantially more profound understanding of the dynamics of earthquakes, landslides, or (palaeo-)climate. They can even provide a significantly improved prediction of several high-impact extreme events. Additionally, crucial open challenges in the realm of methodological nature and applications to Earth sciences are given.

nlin.CD↗

arXiv2024

Machine learning for cerebral blood vessels' malformations

Cerebral aneurysms and arteriovenous malformations are life-threatening hemodynamic pathologies of the brain. While surgical intervention is often essential to prevent fatal outcomes, it carries significant risks both during the procedure and in the postoperative period, making the management of these conditions highly challenging. Parameters of cerebral blood flow, routinely monitored during medical interventions or with modern noninvasive high-resolution imaging methods, could potentially be utilized in machine learning-assisted protocols for risk assessment and therapeutic prognosis. To this end, we developed a linear oscillatory model of blood velocity and pressure for clinical data acquired from neurosurgical operations. Using the method of Sparse Identification of Nonlinear Dynamics (SINDy), the parameters of our model can be reconstructed online within milliseconds from a short time series of the hemodynamic variables. The identified parameter values enable automated classification of the blood-flow pathologies by means of logistic regression, achieving an accuracy of 73 \%}. Our results demonstrate the potential of this model for both diagnostic and prognostic applications, providing a robust and interpretable framework for assessing cerebral blood vessel conditions.

cs.LG↗

arXiv2024

Mathematical Modeling of the Role of Imitation in Crime Dynamics

Crime remains one of the significant problems that countries are grappling with globally. With shrinking economies and increasing poverty, crime has been on the rise in many countries. In this paper, we propose a system of non-linear ordinary differential equations to model crime dynamics in the presence of imitation. The model consists of four independent compartments: individuals who are not at risk of committing a crime, individuals at risk of committing a crime, individuals committing a crime, and individuals convicted and jailed for a crime. The model is analyzed using the basic reproduction number. The analysis shows the system has a locally asymptotically stable crime-free equilibrium when the basic reproduction number is less than unity. The model exhibits a backward bifurcation in which two endemic equilibria coexist with the crime-free equilibrium. When the basic reproduction number exceeds unity, the system has a locally asymptotically stable endemic equilibrium, and the crime-free becomes unstable. Numerical simulations are carried out to verify the analytical results. The sensitivity analysis shows that the relapse rate highly influences the basic reproduction number of our model. This indicates that the proportion of individuals leaving prisons and becoming criminals should be minimized to minimize crime.

math.DS↗

arXiv2024

Cycle-Star Motifs: Network Response to Link Modifications

Understanding efficient modifications to improve network functionality is a fundamental problem of scientific and industrial interest. We study the response of network dynamics against link modifications on a weakly connected directed graph consisting of two strongly connected components: an undirected star and an undirected cycle. We assume that there are directed edges starting from the cycle and ending at the star (master-slave formalism). We modify the graph by adding directed edges of arbitrarily large weights starting from the star and ending at the cycle (opposite direction of the cutset). We provide criteria (based on the sizes of the star and cycle, the coupling structure, and the weights of cutset and modification edges) that determine how the modification affects the spectral gap of the Laplacian matrix. We apply our approach to understand the modifications that either enhance or hinder synchronization in networks of chaotic Lorenz systems as well as R\"ossler. Our results show that the hindrance of collective dynamics due to link additions is not atypical as previously anticipated by modification analysis and thus allows for better control of collective properties.

nlin.CD↗

arXiv2024

Fourier's law breakdown for the planar-rotor chain with long-range coupling

The thermal conductivity, $\kappa$, of a homogeneous chain of generically-ranged interacting planar rotors, more precisely the inertial $\alpha-XY$ model, is numerically studied with the coupling constant decaying as $r^{-\alpha}$. The conductance ($\sigma\equiv \kappa/L$) is calculated for typical values of $\alpha$, temperature $T$ and lattice size $L$. For large $L$, the results can be collapsed into an universal $q$-stretched exponential form, namely $L^{\delta_{\alpha}} \sigma \propto e_{q_{\alpha}}^{-B_{\alpha}(L^{\gamma_{\alpha}}T)^{\eta_{\alpha}}}$, where $e_q^z\equiv [1+ (1-q)z]^{1/(1-q)}$. The parameters $(\gamma_{\alpha},\delta_{\alpha},B_{\alpha}, \eta_{\alpha})$ are $\alpha$-dependent, and $q_{\alpha}$ is the index of the $q$-stretched exponential. This form is achievable due to the ratio $\eta_{\alpha}/(q-1)$ being almost constant with respect to the lattice size $L$. Two distinct regimes are identified: for $0 \le \alpha < 2$, the Fourier law is violated, whereas for $\alpha\ge 2$, it is satisfied. These findings provide significant insights into heat conduction mechanisms in systems with long-range interactions.

cond-mat.stat-mech↗

arXiv2024

Regime change detection in irregularly sampled time series

Irregular sampling is a common problem in palaeoclimate studies. We propose a method that provides regularly sampled time series and at the same time a difference filtering of the data. The differences between successive time instances are derived by a transformation costs procedure. A subsequent recurrence analysis is used to investigate regime transitions. This approach is applied on speleothem based palaeoclimate proxy data from the Indonesian-Australian monsoon region. We can clearly identify Heinrich events in the palaeoclimate as characteristic changes in the dynamics.

physics.data-an↗

arXiv2023

Reconstructing Network Dynamics of Coupled Discrete Chaotic Units from Data

Reconstructing network dynamics from data is crucial for predicting the changes in the dynamics of complex systems such as neuron networks; however, previous research has shown that the reconstruction is possible under strong constraints such as the need for lengthy data or small system size. Here, we present a recovery scheme blending theoretical model reduction and sparse recovery to identify the governing equations and the interactions of weakly coupled chaotic maps on complex networks, easing unrealistic constraints for real-world applications. Learning dynamics and connectivity lead to detecting critical transitions for parameter changes. We apply our technique to realistic neuronal systems with and without noise on a real mouse neocortex and artificial networks.

math.DS↗

arXiv2023

First-principle validation of Fourier's law in d=1,2,3 classical systems

We numerically study the thermal transport in the classical inertial nearest-neighbor XY ferromagnet in $d=1,2,3$, the total number of sites being given by $N=L^d$, where $L$ is the linear size of the system. For the thermal conductance $σ$, we obtain $σ(T,L)\, L^{δ(d)} = A(d)\, e_{q(d)}^{- B(d)\,[L^{γ(d)}T]^{η(d)}}$ (with $e_q^z \equiv [1+(1-q)z]^{1/(1-q)};\,e_1^z=e^z;\,A(d)>0;\,B(d)>0;\,q(d)>1;\,η(d)>2;\,δ\ge 0; \,γ(d)>0)$, for all values of $L^{γ(d)}T$ for $d=1,2,3$. In the $L\to\infty$ limit, we have $σ\propto 1/L^{ρ_σ(d)}$ with $ρ_σ(d)= δ(d)+ γ(d) η(d)/[q(d)-1]$. The material conductivity is given by $κ=σL^d \propto 1/L^{ρ_κ(d)}$ ($L\to\infty$) with $ρ_κ(d)=ρ_σ(d)-d$. Our numerical results are consistent with 'conspiratory' $d$-dependences of $(q,η,δ,γ)$, which comply with normal thermal conductivity (Fourier law) for all dimensions.

cond-mat.stat-mech↗

arXiv2022

Emergent hypernetworks in weakly coupled oscillators

Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among oscillators, in spite that such models were originally defined as oscillator networks with pairwise interactions. Here, we show that hypernetworks can spontaneously emerge even in the presence of pairwise albeit nonlinear coupling given certain triplet frequency resonance conditions. The results are demonstrated in experiments with electrochemical oscillators and in simulations with integrate-and-fire neurons. By developing a comprehensive theory, we uncover the mechanism for emergent hypernetworks by identifying appearing and forbidden frequency resonant conditions. Furthermore, it is shown that microscopic linear (difference) coupling among units results in coupled mean fields, which have sufficient nonlinearity to facilitate hypernetworks. Our findings shed light on the apparent abundance of hypernetworks and provide a constructive way to predict and engineer their emergence.

math.DS↗

arXiv2022

Network structural origin of instabilities in large complex systems

A central issue in the study of large complex network systems, such as power grids, financial networks, and ecological systems, is to understand their response to dynamical perturbations. Recent studies recognize that many real networks show nonnormality and that nonnormality can give rise to reactivity--the capacity of a linearly stable system to amplify its response to perturbations, oftentimes exciting nonlinear instabilities. Here, we identify network structural properties underlying the pervasiveness of nonnormality and reactivity in real directed networks, which we establish using the most extensive data set of such networks studied in this context to date. The identified properties are imbalances between incoming and outgoing network links and paths at each node. Based on this characterization, we develop a theory that quantitatively predicts nonnormality and reactivity and explains the observed pervasiveness. We suggest that these results can be used to design, upgrade, control, and manage networks to avoid or promote network instabilities.

nlin.AO↗

arXiv2022

Transformation cost spectrum for irregularly sampled time series

Irregularly sampled time series analysis is a common problem in various disciplines. Since conventional methods are not directly applicable to irregularly sampled time series, a common interpolation approach is used; however, this causes data distortion and consequently biases further analyses. We propose a method that yields a regularly sampled time series spectrum of costs with minimum information loss. Each time series in this spectrum is a stationary series and acts as a difference filter. The transformation costs approach derives the differences between consecutive and arbitrarily sized segments. After obtaining regular sampling, recurrence plot analysis is performed to distinguish regime transitions. The approach is applied to a prototypical model to validate its performance and to different palaeoclimate proxy data sets located around Africa to identify critical climate transition periods during the last 5 million years and their characteristic properties.

stat.AP↗

arXiv2021

Sampling rate-corrected analysis of irregularly sampled time series

The analysis of irregularly sampled time series remains a challenging task requiring methods that account for continuous and abrupt changes of sampling resolution without introducing additional biases. The edit-distance is an effective metric to quantitatively compare time series segments of unequal length by computing the cost of transforming one segment into the other. We show that transformation costs generally exhibit a non-trivial relationship with local sampling rate. If the sampling resolution undergoes strong variations, this effect impedes unbiased comparison between different time episodes. We study the impact of this effect on recurrence quantification analysis, a framework that is well-suited for identifying regime shifts in nonlinear time series. A constrained randomization approach is put forward to correct for the biased recurrence quantification measures. This strategy involves the generation of a novel type of time series and time axis surrogates which we call sampling rate constrained (SRC) surrogates. We demonstrate the effectiveness of the proposed approach with a synthetic example and an irregularly sampled speleothem proxy record from Niue island in the central tropical Pacific. Application of the proposed correction scheme identifies a spurious transition that is solely imposed by an abrupt shift in sampling rate and uncovers periods of reduced seasonal rainfall predictability associated with enhanced ENSO and tropical cyclone activity.

stat.ME↗

arXiv2021

Revealing dynamics, communities and criticality from data

Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the dynamics of these networks, known as critical transitions, from data is important to avert disastrous consequences of major disruptions. Predicting such changes is a major challenge as it requires forecasting the behaviour for parameter ranges for which no data on the system is available. We address this issue for networks with weak individual interactions and chaotic local dynamics. We do this by building a model network, termed an {\em effective network}, consisting of the underlying local dynamics and a statistical description of their interactions. We show that behaviour of such networks can be decomposed in terms of an emergent deterministic component and a {\em fluctuation} term. Traditionally, such fluctuations are filtered out. However, as we show, they are key to accessing the interaction structure.

nlin.AO↗

arXiv2020

Multiplex Recurrence Networks

We have introduced a novel multiplex recurrence network (MRN) approach by combining recurrence networks with the multiplex network approach in order to investigate multivariate time series. The potential use of this approach is demonstrated on coupled map lattices and a typical example from palaeobotany research. In both examples, topological changes in the multiplex recurrence networks allow for the detection of regime changes in their dynamics. The method goes beyond classical interpretation of pollen records by considering the vegetation as a whole and using the intrinsic similarity in the dynamics of the different regional vegetation elements. We find that the different vegetation types behave more similar when one environmental factor acts as the dominant driving force.

physics.data-an↗

arXiv2019

Collective dynamics of random Janus oscillator networks

Janus oscillators have been recently introduced as a remarkably simple phase oscillator model that exhibits non-trivial dynamical patterns -- such as chimeras, explosive transitions, and asymmetry-induced synchronization -- that once were only observed in specifically tailored models. Here we study ensembles of Janus oscillators coupled on large homogeneous and heterogeneous networks. By virtue of the Ott-Antonsen reduction scheme, we find that the rich dynamics of Janus oscillators persists in the thermodynamic limit of random regular, Erdős-Rényi and scale-free random networks. We uncover for all these networks the coexistence between partially synchronized state and a multitude of states displaying global oscillations. Furthermore, abrupt transitions of the global and local order parameters are observed for all topologies considered. Interestingly, only for scale-free networks, it is found that states displaying global oscillations vanish in the thermodynamic limit.

nlin.AO↗

arXiv2019

Effective networks: a model to predict network structure and critical transitions from datasets

Real-world complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in network behaviour, known as critical transitions, from data is important to avert disastrous consequences of major disruptions. Predicting such changes is a major challenge as it requires forecasting the behaviour for parameter ranges for which no data on the system is available. In this paper, we address this issue for networks with weak individual interactions and chaotic local dynamics. We do this by building a model network, termed an effective network, consisting of the underlying local dynamics at each node and a statistical description of their interactions. We illustrate this approach by reconstructing the dynamics and structure of realistic neuronal interaction networks of the cat cerebral cortex. We reconstruct the community structure by analysing the stochastic fluctuations generated by the network and predict critical transitions for coupling parameters outside the observed range.

nlin.AO↗

arXiv2019

Multifaceted dynamics of Janus oscillator networks

Recent research has led to the discovery of fundamental new phenomena in network synchronization, including chimera states, explosive synchronization, and asymmetry-induced synchronization. Each of these phenomena has thus far been observed only in systems designed to exhibit that one phenomenon, which raises the questions of whether they are mutually compatible and, if so, under what conditions they co-occur. Here, we introduce a class of remarkably simple oscillator networks that concurrently exhibit all of these phenomena. The dynamical units consist of pairs of nonidentical phase oscillators, which we refer to as Janus oscillators by analogy with Janus particles and the mythological figure from which their name is derived. In contrast to previous studies, these networks exhibit (i) explosive synchronization with identical oscillators; (ii) extreme multistability of chimera states, including traveling, intermittent, and bouncing chimeras; and (iii) asymmetry-induced synchronization in which synchronization is promoted by random oscillator heterogeneity. These networks also exhibit the previously unobserved possibility of inverted synchronization transitions, in which a transition to a more synchronous state is induced by a reduction rather than an increase in the coupling strength. These various phenomena are shown to emerge under rather parsimonious conditions, and even in locally connected ring topologies, which has the potential to facilitate their use to control and manipulate synchronization in experiments.

nlin.AO↗

arXiv2018

Prediction of flow dynamics using point processes

Describing a time series parsimoniously is the first step to study the underlying dynamics. For a time-discrete system, a generating partition provides a compact description such that a time series and a symbolic sequence are one-to-one. But, for a time-continuous system, such a compact description does not have a solid basis. Here, we propose to describe a time-continuous time series using a local cross section and the times when the orbit crosses the local cross section. We show that if such a series of crossing times and some past observations are given, we can predict the system's dynamics with fine accuracy. This reconstructability neither depends strongly on the size nor the placement of the local cross section if we have a sufficiently long database. We demonstrate the proposed method using the Lorenz model as well as the actual measurement of wind speed.

physics.data-an↗