arXiv subjects

Thomas Stemler

Publications and source records attributed to Thomas Stemler.

17 recordsLinked to original sources

arXiv2024

A Selfish Herd with a Target

One of the most striking phenomena in biological systems is the tendency for biological agents to spatially aggregate, and subsequently display further collective behaviours such as rotational motion. One prominent explanation for why agents tend to aggregate is known as the selfish herd hypothesis (SHH). The SHH proposes that each agent has a "domain of danger" whose area is proportional to the risk of predation. The SHH proposes that aggregation occurs as a result of agents seeking to minimise the area of their domain. Subsequent attempts to model the SHH have had varying success in displaying aggregation, and have mostly been unable to exhibit further collective behaviours, such as aligned motion or milling. Here, we introduce a model that seeks to generalise the principles of previous SHH models, by allowing agents to aim for domains of a specific (possibly non-minimal) area or a range of areas and study the resulting collective dynamics. Moreover, the model incorporates the lack of information that biological agents have by limiting the range of movement and vision of the agents. The model shows that the possibility of further collective motion is heavily dependent on the domain area the agents aim for - with several distinct phases of collective behaviour.

q-bio.QM↗

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

Model Calibration and Validation From A Statistical Inference Perspective

Despite the general consensus in transport research community that model calibration and validation are necessary to enhance model predictive performance, there exist significant inconsistencies in the literature. This is primarily due to a lack of consistent definitions, and a unified and statistically sound framework. In this paper, we provide a general and rigorous formulation of the model calibration and validation problem, and highlight its relation to statistical inference. We also conduct a comprehensive review of the steps and challenges involved, as well as point out inconsistencies, before providing suggestions on improving the current practices. This paper is intended to help the practitioners better understand the nature of model calibration and validation, and to promote statistically rigorous and correct practices. Although the examples are drawn from a transport research background - and that is our target audience - the content in this paper is equally applicable to other modelling contexts.

stat.ME↗

arXiv2023

Exploring Model Misspecification in Statistical Finite Elements via Shallow Water Equations

The abundance of observed data in recent years has increased the number of statistical augmentations to complex models across science and engineering. By augmentation we mean coherent statistical methods that incorporate measurements upon arrival and adjust the model accordingly. However, in this research area methodological developments tend to be central, with important assessments of model fidelity often taking second place. Recently, the statistical finite element method (statFEM) has been posited as a potential solution to the problem of model misspecification when the data are believed to be generated from an underlying partial differential equation system. Bayes nonlinear filtering permits data driven finite element discretised solutions that are updated to give a posterior distribution which quantifies the uncertainty over model solutions. The statFEM has shown great promise in systems subject to mild misspecification but its ability to handle scenarios of severe model misspecification has not yet been presented. In this paper we fill this gap, studying statFEM in the context of shallow water equations chosen for their oceanographic relevance. By deliberately misspecifying the governing equations, via linearisation, viscosity, and bathymetry, we systematically analyse misspecification through studying how the resultant approximate posterior distribution is affected, under additional regimes of decreasing spatiotemporal observational frequency. Results show that statFEM performs well with reasonable accuracy, as measured by theoretically sound proper scoring rules.

physics.data-an↗

arXiv2023

Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology

Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, the selection of embedding parameters can have a big impact on the resulting analysis. This has led to the creation of a large number of methods to optimise the selection of parameters such as embedding lag. This paper aims to provide a comprehensive overview of the fundamentals of embedding theory for readers who are new to the subject. We outline a collection of existing methods for selecting embedding lag in both uniform and non-uniform delay embedding cases. Highlighting the poor dynamical explainability of existing methods of selecting non-uniform lags, we provide an alternative method of selecting embedding lags that includes a mixture of both dynamical and topological arguments. The proposed method, {\em Significant Times on Persistent Strands} (SToPS), uses persistent homology to construct a characteristic time spectrum that quantifies the relative dynamical significance of each time lag. We test our method on periodic, chaotic and fast-slow time series and find that our method performs similar to existing automated non-uniform embedding methods. Additionally, $n$-step predictors trained on embeddings constructed with SToPS was found to outperform other embedding methods when predicting fast-slow time series.

math.DS↗

arXiv2022

Backpropagation on Dynamical Networks

Dynamical networks are versatile models that can describe a variety of behaviours such as synchronisation and feedback. However, applying these models in real world contexts is difficult as prior information pertaining to the connectivity structure or local dynamics is often unknown and must be inferred from time series observations of network states. Additionally, the influence of coupling interactions between nodes further complicates the isolation of local node dynamics. Given the architectural similarities between dynamical networks and recurrent neural networks (RNN), we propose a network inference method based on the backpropagation through time (BPTT) algorithm commonly used to train recurrent neural networks. This method aims to simultaneously infer both the connectivity structure and local node dynamics purely from observation of node states. An approximation of local node dynamics is first constructed using a neural network. This is alternated with an adapted BPTT algorithm to regress corresponding network weights by minimising prediction errors of the dynamical network based on the previously constructed local models until convergence is achieved. This method was found to be succesful in identifying the connectivity structure for coupled networks of Lorenz, Chua and FitzHugh-Nagumo oscillators. Freerun prediction performance with the resulting local models and weights was found to be comparable to the true system with noisy initial conditions. The method is also extended to non-conventional network couplings such as asymmetric negative coupling.

math.DS↗

arXiv2021

Low-rank statistical finite elements for scalable model-data synthesis

Statistical learning additions to physically derived mathematical models are gaining traction in the literature. A recent approach has been to augment the underlying physics of the governing equations with data driven Bayesian statistical methodology. Coined statFEM, the method acknowledges a priori model misspecification, by embedding stochastic forcing within the governing equations. Upon receipt of additional data, the posterior distribution of the discretised finite element solution is updated using classical Bayesian filtering techniques. The resultant posterior jointly quantifies uncertainty associated with the ubiquitous problem of model misspecification and the data intended to represent the true process of interest. Despite this appeal, computational scalability is a challenge to statFEM's application to high-dimensional problems typically experienced in physical and industrial contexts. This article overcomes this hurdle by embedding a low-rank approximation of the underlying dense covariance matrix, obtained from the leading order modes of the full-rank alternative. Demonstrated on a series of reaction-diffusion problems of increasing dimension, using experimental and simulated data, the method reconstructs the sparsely observed data-generating processes with minimal loss of information, in both the posterior mean and variance, paving the way for further integration of physical and probabilistic approaches to complex systems.

stat.ME↗

arXiv2019

Consistency in Echo-State Networks

Consistency is an extension to generalized synchronization which quantifies the degree of functional dependency of a driven nonlinear system to its input. We apply this concept to echo-state networks, which are an artificial-neural network version of reservoir computing. Through a replica test we measure the consistency levels of the high-dimensional response, yielding a comprehensive portrait of the echo-state property.

math.DS↗

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↗

arXiv2016

Tweaking Synchronisation by Link Addition

Natural and man-made networks often possess locally tree-like sub-structures. Taking such tree networks as our starting point, we show how the addition of links changes the synchronization properties of the network. We focus on two different methods of link addition. The first method adds single links that create cycles of a well-defined length. Following a topological approach we introduce cycles of varying length and analyze how this feature, as well as the position in the network, alters the synchronous behaviour. We show that in particular short cycles can lead to a maximum change of the Laplacian's eigenvalue spectrum, dictating the synchronization properties of such networks. The second method connects a certain proportion of the initially unconnected nodes. We simulate dynamical systems on these network topologies, with the nodes' local dynamics being either a discrete or continuous. Here our main result is that a certain amount of additional links, with the relative position in the network being crucial, can be beneficial to ensure stable synchronization.

nlin.CD↗

arXiv2015

Transient coupling relationships of the Holocene Australian monsoon

The northwest Australian summer monsoon owes a notable degree of its interannual variability to interactions with other regional monsoon systems. Therefore, changes in the nature of these relationships may contribute to variability in monsoon strength over longer time scales. Previous attempts to evaluate how proxy records from the Indonesian-Australian monsoon region correspond to other records from the Indian and East Asian monsoon regions, as well as to El Niño-related proxy records, have been qualitiative, relying on `curve-fitting' methods. Here, we seek a quantitative approach for identifying coupling relationships between paleoclimate proxy records, employing statistical techniques to compute the interdependence of two paleoclimate time series. We verify the use of complex networks to identify coupling relationships between modern climate indices. This method is then extended to a set of paleoclimate proxy records from the Asian, Australasian and South American regions spanning the past 9,000 years. The resulting networks demonstrate the existence of coupling relationships between regional monsoon systems on millennial time scales, but also highlight the transient nature of teleconnections during this period. In the context of the northwest Australian summer monsoon, we recognise a shift in coupling relationships from strong interhemispheric links with East Asian and ITCZ-related proxy records in the mid-Holocene to significantly weaker coupling in the later Holocene. Although the identified links cannot explain the underlying physical processes leading to coupling between regional monsoon systems, this method provides a step towards understanding the role that changes in teleconnections play in millennial- to orbital-scale climate variability.

physics.ao-ph↗

arXiv2015

Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. Firstly we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the Rössler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures -- thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length and network diameter are highly sensitive to the interior crisis captured in this particular data set.

nlin.CD↗

arXiv2014

Super-star networks: Growing optimal scale-free networks via likelihood

Preferential attachment --- by which new nodes attach to existing nodes with probability proportional to the existing nodes' degree --- has become the standard growth model for scale-free networks, where the asymptotic probability of a node having degree $k$ is proportional to $k^{-γ}$. However, the motivation for this model is entirely ad hoc. We use exact likelihood arguments and show that the optimal way to build a scale-free network is to attach most new links to nodes of low degree. Curiously, this leads to a scale-free networks with a single dominant hub: a star-like structure we call a super-star network. Asymptotically, the optimal strategy is to attach each new node to one of the nodes of degree $k$ with probability proportional to $\frac{1}{N+ζ(γ)(k+1)^γ}$ (in a $N$ node network) --- a stronger bias toward high degree nodes than exhibited by standard preferential attachment. Our algorithm generates optimally scale-free networks (the super-star networks) as well as randomly sampling the space of all scale-free networks with a given degree exponent $γ$. We generate viable realisation with finite $N$ for $1\ll γ<2$ as well as $γ>2$. We observe an apparently discontinuous transition at $γ\approx 2$ between so-called super-star networks and more tree-like realisations. Gradually increasing $γ$ further leads to re-emergence of a super-star hub. To quantify these structural features we derive a new analytic expression for the expected degree exponent of a pure preferential attachment process, and introduce alternative measures of network entropy. Our approach is generic and may also be applied to an arbitrary degree distribution.

nlin.AO↗

arXiv2013

A surrogate for networks -- How scale-free is my scale-free network?

Complex networks are now being studied in a wide range of disciplines across science and technology. In this paper we propose a method by which one can probe the properties of experimentally obtained network data. Rather than just measuring properties of a network inferred from data, we aim to ask how typical is that network? What properties of the observed network are typical of all such scale free networks, and which are peculiar? To do this we propose a series of methods that can be used to generate statistically likely complex networks which are both similar to the observed data and also consistent with an underlying null-hypothesis -- for example a particular degree distribution. There is a direct analogy between the approach we propose here and the surrogate data methods applied to nonlinear time series data.

physics.soc-ph↗

arXiv2013

What exactly are the properties of scale-free and other networks?

The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools and procedures to analyse the statistical properties of networks defined by arbitrary degree distributions and other constraints. Doing so reveals the highly likely properties, and some unrecognised richness, of scale-free networks, and casts doubt on some previously claimed properties being due to a scale-free characteristic.

nlin.AO↗

arXiv2012

The stability of networks --- towards a structural dynamical systems theory

The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle this problem have been made and all focus on either the controllability or synchronisability of the network --- usually analyzed by way of the master stability function, or the graph Laplacian. We take a different approach. Using the basic tools from dynamical systems theory we show that the dynamical stability of a network can easily be defined in terms of the eigenvalues of an homologue of the network adjacency matrix. This allows us to compute the stability of a network (a quantity derived from the eigenspectrum of the adjacency matrix). Numerical experiments show that this quantity is very closely related too, and can even be predicted from, the standard structural network properties. Following from this we show that the stability of large network systems can be understood via an analytic study of the eigenvalues of their fixed points --- even for a very large number of fixed points.

nlin.CD↗

arXiv2004

Noise reduction in chaotic time series by a local projection with nonlinear constraints

On the basis of a local-projective (LP) approach we develop a method of noise reduction in time series that makes use of nonlinear constraints appearing due to the deterministic character of the underlying dynamical system. The Delaunay triangulation approach is used to find the optimal nearest neighboring points in time series. The efficiency of our method is comparable to standard LP methods but our method is more robust to the input parameter estimation. The approach has been successfully applied for separating a signal from noise in the chaotic Henon and Lorenz models as well as for noisy experimental data obtained from an electronic Chua circuit. The method works properly for a mixture of additive and dynamical noise and can be used for the noise-level detection.

cond-mat.stat-mech↗