Abstract: In order to monitor and predict complex phenomena, such as traffic on a large region of road network, operators often use theory-driven simulation models, which have the advantage of extensibility and interpretability when compared to machine learning methods. However, the optimisation of these models is often restricted to a "black-box" approach, due to high complexity and difficulty in measuring the parameters in the real world (assuming the model parameters correspond to their physical counterparts at all). In this seminar I will discuss the optimisation of driver behaviour parameters for an agent-based simulation covering an extended region of the Perth network. This model is employed in real-time for the prediction of the next hour of traffic. The key challenges in optimising this model arise from its high-dimensional nature, the presence of noise, computational limitations, as well as the assumption that the optimal parameters themselves are dynamic. In order to address these issues we use techniques and shortcuts to reduce the scale of the problem, such as Bayesian optimisation and a nearest neighbour method that efficiently reuses simulation outputs for multiple tasks. Finally, I will discuss attempts at model emulation, which have been unsuccessful so far, but could be used for true real-time optimisation.

Abstract: One of the major advances in the field of nonlinear time series analysis was the formalisation of the embedding theorems of Whitney and Takens, applied to dynamical systems theory. In its simplest form, these theorems show that one can reconstruct (up to a diffeomorphism) the multidimensional dynamics of a system using only observed scalar time series. The dominant in which this is achieved is via the uniform delay embedding approach, which requires the selection of two parameters: a delay lag, and an embedding dimension. However, in most real-world applications it is not always clear how one should go about selecting the delay lag. This has led to the proposal of many several heuristical and statistical approaches. Furthermore, one can also consider a more general form a delay embedding with nonuniform lags, which is better suited for describing dynamics with disparate time and spatial scales. This generalisation comes at the expense of further exacerbating the selection of optimal embedding parameters. In this talk, I will provide a brief overview on the heuristics and methods used to select delays lags for embedding reconstruction. This will be followed by a topological data analysis method, Significant Times on Persistent Strands, that aims to characterise the importance of different time scales that may be used to inform the selection of nonunifrom delay lags. I will also briefly discuss the relationship between signal autocorrelation and lag selection, and provide a potential new nonlinear approach to quantifying correlations using ideas from machine learning.

Abstract: Reservoir computing (RC) is a machine learning framework designed to utilise a dynamical system as the central processing unit to facilitate efficient computation. Since its inception at the turn of the century the framework has shown impressive results on a range of supervised learning tasks from time series forecasting to classification. Despite a well-developed understanding of how these methods work and a history of successful results, little work has looked to extend the methods encapsulated in RC to unsupervised contexts. In this talk I will discuss the work from my PhD thesis that looks at bridging the gap from RC to unsupervised learning tasks. I will specifically address two distinct problems; what does unsupervised RC entail, and how can these ideas be utilised in practice. I address the first point through the introduction of reservoir time series analysis (RTSA), a novel analysis field which encapsulates methods that leverage the state space representation generated by a RC model for generalised time series analysis tasks. As part of this I will propose a number of methods for extracting features under the framework, and position RTSA within the current understanding of both the RC and nonlinear time series analysis (NTSA) communities. I then address the second point by applying these novel RTSA methods to unsupervised learning tasks, specifically signal distinction, recurrence preservation and concept drift detection. I consider both synthetic and experimental data to demonstrate potential use cases of RTSA on real-world problems, as well as a range of NTSA methods as comparisons to benchmark RTSA performance. The RTSA methods demonstrate strong performance across these tasks, both generally and with respect to existing NTSA methods, which encourages further development of the RTSA field in the future

Abstract: Modeling and inference in multivariate time series is central in statistics, signal processing, and machine learning. A fundamental question when analyzing multivariate sequences is the search for relationships between their entries (or the modeled hidden states), especially when the inherent structure is a directed (causal) graph. In such context, graphical modeling combined with sparsity constraints allows to limit the proliferation of parameters and enables a compact data representation which is easier to interpret in applications, e.g., in inferring causal relationships of physical processes in a Granger sense. In this talk, we present a novel perspective consisting on state-space models being interpreted as graphs. Then, we propose novel algorithms that exploit this new perspective for the estimation of the linear matrix operator and also the covariance matrix in the state equation of a linear-Gaussian state-space model. Finally, we discuss the extension of this perspective for the estimation of other model parameters in more complicated models.

Abstract: We delve into the applications of Network Analysis on Malaysian datasets, covering a spectrum of topics. These include devising Covid-19 reopening strategies, examining company relationships within Bursa Malaysia, and finding the ‘Kevin Bacon’ of the Malay language film industry.

Abstract: With a simple betting game we discover that:

- it's possible to make a profit by repeatedly playing some kinds of unprofitable games (Shannon's daemon);

- it's easy to lose by repeatedly playing a profitable game, unless you're smart like Kelly.

The first strategy, called Shannon's daemon, volatility pumping or any of several other names, is akin to picking pennies off the freeway, but is useful to sophisticated investors. For those who are more risk averse, it may be better to try to overcome volatility drag, which is what causes the losses in the second case. For our simple game, we discover that

- if there are many players, taxation can increase everybody's wealth;

- a solo player can make a profit from repeated plays of a profitable game by the magic of constant rebalancing.

The simplest kind of constant rebalancing, the Kelly criterion, has been used in practice, both in casinos and in the stock market, but it requires accurate knowledge of the odds. We look at how a variant of constant rebalancing of a basket of stocks can work asymptotically better than the best one in the basket. Surprisingly, this works without assumptions about the statistical properties of the prices. The canonical approach is Cover's universal portfolio, which only assumes that the prices are bounded.

Abstract: Suicide is a leading cause of death and has profound and lasting impacts on survivors. Repeated non-suicidal self-injury increases the capability for individuals to attempt and commit suicide, and over the long term reduces the predictability of suicidal behaviour. Predictive modelling is employed at a Perth based psychiatric hospital (Perth Clinic), to identify who is at most risk of committing self-harm and when. These predictions can be used to inform when and where clinical interventions are needed. Patient background information is collected at admission to the hospital. Patients also complete a daily questionnaire which aims to assess psychological distress, vulnerability, and resilience. This data is used to predict self-harm risk. The model previously used accurately predicts those patients who are at risk. Of the patients who are predicted to be at heighted risk of self-harm however, 9 out of 10 do not require self-harm interventions (area under curve 0.9, positive predictive value 0.1). Improvements in predictive performance will allow limited resources to be more efficiently deployed for preventing adverse mental health outcomes. The aim of the current project is to find alternate predictive methods for determining when inpatients are at heightened risk of self-harm.

Abstract: The partitioning of dynamical systems is necessary to apply a symbolic dynamics analysis. While many partitioning schemes exist, in practice an ordinal partition is frequently used. We are interested in identifying possible alternatives to ordinal partitioning, however, there is currently no generalised method for assessing the performance of a partitioning scheme on a given system. We approach this problem by proposing a metric that measures the mutual information between each point's symbol history under a coarse partition (one with few partitions), and its partition assignment under a fine partition (one with many partitions). We apply this metric to a set of test systems and partitions, and find that it is likely suitable as it generally displays the expected behaviour. Using this metric, results suggest that among the tested partitions, the ordinal partition is indeed a high-information partitioning scheme because of its use of previous values to assign partitions.

Abstract: Speaker: Daniel Claassen , Department of Mathematics and Statistics, UWA

Topic: Statistical Finite Element Modelling for Misspecified SST Simulation and Inversion

Abstract:

With the increasing abundance of data made available to both mathematical and statistical modellers, the problem of data synthesis and then resultant model error can often be neglected through model generalisations and assumptions. This can be responsible for larger issues in certain fields- for example, the continued struggle in Oceanography to identify the physical characteristics of processes such as upwelling, or cooling from cloud cover. In this work, we present the ongoing development of a method to tackle this general problem of uncertainty by using a limited, deliberately misspecified model for sea surface temperature (SST) on the Nino 3.4 region and simulating forward with additive noise via a Gaussian Process in a Statistical Finite Element Method (StatFEM). Physical model parameters are driven via re-analysis data, and an ensemble output from the model is filtered via an Ensemble Kalman Filter (EnKF). Inversion is to be performed inside the filtering process to identify the characteristics of some of the latent parameters of the model. The result is a posterior distribution over solutions for given temperature profile states that quantifies uncertainty in a number of ways, from the SST profile itself to the model's parameters.

Abstract: The use of knowledge graphs for natural language processing tasks, including question answering, has been gaining traction in recent years. However, existing approaches often need help to capture temporal information, which is critical in industry data as it is naturally time variant. Industry data presents a unique opportunity to explore temporal knowledge graphs, where the head entity represents an event, and the tail entity is a time-variant state. For example, Engine X (head entity) was observed leaking oil (tail) with a start-time (temporal point) and an optional end-time (temporal point). Sirui will introduce existing question-answering systems over temporal knowledge graphs, and she will present an approach under development. The proposed approach enables accurate retrieval of time-sensitive information from large-scale knowledge repositories. It leverages a neural network architecture that integrates temporal information with question-and-answer embeddings, allowing the system to reason over the temporal structure of the graph to generate accurate answers. Incorporating temporal aspects into question answering enables the system to effectively handle time-dependent queries, gain valuable insights into historical trends, and support informed decision-making through temporal knowledge graph analysis.

Abstract: Herein we study a weighted multilayered socio-ecological network system in sustainability,in which a policy reform is applied to one or more layers of the network. We investigate the knock-on effect from this reform and the influence of centrality of nodes in spreading the reform. Our model highlights the properties allowing to reach a positive density of reformed nodes inside a layer and across the layers. The system stability is contingent on the synchronization across the multiplex network. Our results suggest that sustainability may be best achieved when the central nodes are the greatest propagators of an essential reform. In terms of policy-making, in particular on the management and governance of natural resources, our framework offers a brand new perspective on the polycentric governance; it even enriches it through new attributes. 

Abstract: 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 and dimension.  This task is made more challenging for nonuniform embedding cases where multiple time lags need to be selected. In this research, we explore an alternative approach of selecting embedding lags that includes a mixture of both dynamical and topological arguments. The proposed method, 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. These characteristic times can then be used to inform the selection of non-uniform time lags. 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.

2022 V. Afraimovich Award Lecture, 29 September 2022.

Abstract: Applied mathematics involves building models of the real world. When those models consist of differential equations (as they very often do) one can seek to do one of two things: (1) make approximations that allow those models to be solved on a restricted, but still useful, domain; or (2) study thos equations and offer a descriptive understanding of the dynamics of the underlying system. Increasingly, our ability to collect data is exceeding our skill at constructing viable and interesting systems of equations. I will describe the situation where we have a stream of observed time series data but insufficient expertise to write down an appropriate generating set of equations. From that stream of data, I will describe methods that we have been working on that offers a descriptive understanding of the dynamics that is equivalent to what might’ve been obtained from the equations. That is, for chaotic systems, we seek to estimate quantities such as Lyapunov exponents, (unstable) periodic orbits, symbolic dynamics, correlation dimension, and attractor topology directly from the data. This allows us to describe the behaviour of the underlying system from observed data, and - importantly for practical applications - quantify change in that behaviour.

Abstract: Functional brain networks exhibits high level of temporal variability even in resting-state. This dynamic property is closely related to higher-order cognitive function and cognitive flexibility. In this talk I will report several of our works on dynamic brain networks, which address the dynamics of brain networks over multiple spatial scales, including nodal and hemispheric level, and showed that dynamic changes are associated with higher cognitive functions in humans like IQ, creativity, language function and cognitive flexibility. Based on the world’s largest multi-scale database of brain science, such as the American Brain Project HCP, the British Biobank, and Allen Brain, we also investigated genetic underpinnings of the dynamic changes of brain networks. Our work demonstrated the functional significance of the dynamic changes of brain networks and may provide insights into the inner workings of the brain.

Abstract: All models are lies. Some lies are useful.
Everybody knows that reconstructionism, the building of models from data by universal approximation methods, isn't really science. It gives us at best a house built of straw, as opposed to the solid brick houses built by mathematics and physics.
In this talk I hope to cast some doubt on what everybody knows, and perhaps even to engender a suspicion that the brick houses are merely cleverly painted straw ones.  

Abstract: Dynamical networks are versatile models that can describe a variety of interesting behaviours such as synchronisation and feedback. However, applying these models to 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 also 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 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. Following this, an adapted BPTT algorithm is used to regress corresponding network weights by minimising prediction errors of the dynamical network based on the previously constructed local model. These two steps are alternated until convergence in the predicted trajectories and network weights is achieved.  

Preliminary results of this method applied to coupled networks of a variety of chaotic oscillators is presented showing partial success in identifying connectivity structure. Free run 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 negative coupling and hidden node detection.

Abstract: Since the start of 2020, mathematical epidemiology is suddenly sexy again (probably the last time it was had something to do with a bloke named John Snow – no, not *that* John Snow). Despite their success, continuum compartmental models of disease transmission are very good at doing one thing – predicting exponential growth in well mixed populations. Compartmental models do not deal well with populations that are heterogenous, spatially diffuse and in which disease is relatively rare. Conversely, computational resources are now cheap enough and data sufficiently plentiful that any fool with an online python coding course under their belt can implement an agent-based model.  

Despite the cynicism expressed in the first paragraph, I would like to talk about what we’ve been doing to model the spread of covid-19 and how this might be useful for the unique challenges (and opportunities) that present themselves to Western Australia. While the methods I employ will be largely agent-based simulations, I will emphasise that one still needs to observe good modelling practise - simple enough to be useful, but no simpler. The emphasis is on robust models with few parameters that nonetheless capture the salient features of the system. The specific focus of this talk will be on addressing transmission to remote regions of Western Australia and negotiating the current wave as WA opens up. In particular, I will discuss the effect that heterogeneity of vaccine distribution may have on disease propagation. Or, does assortativity of vaccine coverage affect transmission? Are the (wilfully) unvaccinated a liability to themselves and a risk to the rest of the population or just an entertaining diversion in the online comment sections of our newspapers? 

Abstract: The aim of the following work is to model the maintenance of ecological networks in forest environments, built from bioreserves, patches and corridors, when these grids are subject to random processes such as extreme natural events. The management plan consists in providing both temporary and sustainable habitats to migratory species. It also aims at ensuring connectivity between the natural areas without interruption. After presenting the random graph-theoretic framework, we apply the stochastic optimal control to the graph dynamics. Our results show that the preservation of the network architecture cannot be achieved, under stochastic control, over the entire duration. It can only be accomplished, at the cost of sacrificing the links between the patches, by increasing usage of the control devices. This would have a negative effect on the species migration by causing congestion among the channels left at their disposal. The optimal scenario, in which the shadow price is at its lowest and all connections are well-preserved, occurs at half of the course, be it the only optimal stopping moment found on the stochastic optimal trajectories. The optimal forestry policy thus has to cut down the timing of the practices devoted to biodiversity protection by half.

Abstract: Topographic complexity on continental shelves is the catalyst that transforms the barotropic tide into the secondary and residual circulations that dominate vertical and cross-shelf mixing processes. Island wakes are one such example that are observed to significantly influence the transport and distribution of biological and physical scalars. Despite the importance of island wakes, to date, no sufficient, mechanistic description of the physical processes governing their development exists for the general case of unsteady tidal forcing. When the flow is shallow, the influence of bottom friction is significant, and when the flow is unsteady, the influence of bed friction is also transient and vertically confined to a benthic boundary layer. This seminar presents a body of work that examines the wake formation, temporal evolution and vertical transport in shallow island wakes for unsteady tidal forcing.

Laboratory experiments that can determine the unsteady, 3D velocity fields play an essential role in this quest and a simple circular island cross section is utilised in this fundamental experimental study of the characteristics of shallow island wakes.  Four archetypal wake forms are observed and studied in detail: (i) symmetric; (ii) asymmetric; (iii) unsteady bubble; and (iv) vortex shedding. The vertical structure of the wake governs the wake vortex topology and depends on three key parameters: i) the tidal excursion relative to the island diameter, ii) the bottom boundary layer thickness relative to the flow depth, and iii) the aspect ratio of the flow depth to the island diameter. The importance of secondary vortices in island wake upwelling is highlighted by local peaks in vertical velocity magnitude that exceed 40% of the peak external tidal velocity. A model of wake upwelling based on Ekman pumping from the bottom boundary layer is utilised to establish scaling laws for island wake circulation which, remarkably, is independent of the wake form. Finally, an intrinsic link between the dynamical eddy scales, predicted by the Ekman pumping model, and the island wake form and stability is demonstrated.  

The novel experimental measurements present a view of island wake upwelling where primary and secondary flow structures vigorously stir the water column over the full depth. This vigorous mixing has implications for the modelling of passive biological tracers and the time scales that determine productivity in topographically-complex continental shelf regions. 

Abstract: The deterministic Susceptible-Infected-Susceptible (SIS) bivirus network model explores how two viruses, for example two different strains of a disease, compete to spread across a meta-population network. Each node represents a large population, connected to other nodes on a two-layer network, with each layer describing the infection network of one of the viruses. We present a body of work on the bivirus network model, using a range of theoretical tools such as algebraic geometry, monotone systems theory, and control-theoretic perturbation arguments.

First, we show that almost all bivirus networks have a finite number of equilibria. We also prove that the typical limiting behaviour of a bivirus network is convergence to an equilibrium, among the finite set. Next, given the network layer of one virus, we show how to design the network layer of the second virus such that the overall network exhibits new and interesting dynamical phenomena. In the first result, we present a design procedure that yields a bivirus network with an infinite number of equilibria in a connected set. Second, we design a network where both viruses can win a survival of the fittest battle depending on the initial conditions. This last result significantly expands existing literature, which have only identified networks where a specific virus wins the battle irrespective of the initial conditions. 

Abstract: To deviate from the conventional research seminars, here I will discuss my personal experience transitioning out of academia last year. In November 2020, I changed from a research career with UWA and CSIRO to teaching physics and mathematics in high school through the Teach for Australia program, which connects talented individuals to secondary schools in low socio-economic areas. In this talk I will reflect on my experience 6 months into the program. What strengths did I, as a research applied mathematician, bring to the teaching role at my school? How did my tertiary teaching experience translate to secondary teaching? While my current pedagogical education is in the secondary context, what translatable skills could I bring back to tertiary education? As a personal reflection, why did I transition from academia into this program where I do far more work?

Abstract: Similar to living systems, self-propelled, i.e. active particles (APs) are able to arrange into collective states such as flocks or swarms. Opposed to living systems, however, currently available AP systems lack an essential feature, namely the possibility to control their motion on a single-particle level in response to their neighbours. In addition, interactions between APs are usually limited to mere physical forces opposed to much more complex social interactions dominating the response within animal groups. In our work, we present the first experimental realization of a laser-responsive AP system, which is able for controlled social interactions amongst each other. Inspired by so-called zonal models which were successful in reproducing the collective behavior of biological and social systems, our APs are able for non-reciprocal living-like interactions, i.e. they can align with neighbours, follow peers and avoid mutual collisions. Experimentally, we realize this with a feedback system where the positions and orientations of each AP are tracked in real time. This information is used to steer a laser beam to each particle such that its motion is controlled independently of each other. Exemplarily, we demonstrate the formation of cohesive swarms and rotating groups by application of relatively simple interaction rules and show their robustness against noise, misbehaving particles and the presence of obstacles. Furthermore, we provide evidence, that collective states are near a critical point as already suggested by living systems. Finally, we demonstrate how the motion of APs change in the presence of viscoelastic media, which provide the typical environment of microorganisms.

1. To Bäuerle, Robert C Löffler, and Clemens Bechinger, Nature Comm. 11 (1), 1 (2020).

2. C. Lozano, J.R. Gomez-Solano, and C. Bechinger, Nature Materials 18, 1118 (2019).

3. F. Lavergne, H. Wendehenne, T. Bäuerle, and C. Bechinger, Science 364, 70 (2019).

Abstract: The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation. For large-scale dynamical networks, it is extremely difficult or physically impossible to have enough sensor nodes to make the system fully observable. Even if the network system is in principle observable,  high-dimensionality poses fundamental limits on the computational tractability and performance of a full-state observer. To overcome the curse of dimensionality, we instead require the system to be functionally observable---i.e., a targeted subset of state variables can be reconstructed from the available measurements. Here, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to determine the minimal set of required sensors and to design the corresponding state observer with minimum order. Compared to the full-state observer, the proposed functional observer achieves the same estimation quality with substantially less sensing and computational resources, making it suitable for large-scale networks. We apply the proposed methods to the detection of cyber-attacks in power grids from limited phase measurement data and the inference of the prevalence rate of infection during an epidemic under limited testing conditions. The applications demonstrate that the functional observer can significantly scale up our ability to explore otherwise inaccessible dynamical processes on complex networks.

Abstract: Prediction and mitigation of chatter has become a prominent research field during the last decade due to its detrimental effect on cutting tool life and surface finish of the workpiece. Existing methods in the literature mainly rely on signal decomposition using standard tools such as Fast Fourier Transforms (FFT), Power Spectral Density (PSD), and Autocorrelation Functions (ACFs). More recently, Wavelet Packet Transform (WPT) and Ensemble Empirical Mode Decomposition (EEMD) were also combined with machine learning for chatter detection. However, current tools for chatter diagnosis have two main limitations that preclude their wide adoption on shop floors: they require careful manual preprocessing of data by experienced users, and the robustness of the resulting classifiers to variations between the training and the implementation environments has hardly been studied. In this talk, I describe two novel approaches that mitigate the need for manual preprocessing: one is based on extracting features using Topological Data Analysis (TDA), and the second is based on Dynamic Time Warping (DTW) similarity measures of time series combined with a kNN algorithm. We apply these approaches to identify chatter in tagged vibration signals obtained from a turning process performed with four different tool overhang lengths. We also study the transfer learning capability of each approach by training and testing on cutting configurations with different overhang lengths. For the TDA approach, we employ five different featurization methods for persistence diagrams—which constitute the flagship tool of TDA. We provide a comparison of the classification accuracy for all the different methods, and we comment on their transfer learning capabilities.

Abstract: Persistent homology, the flagship method of topological data analysis, can be used to provide a quantitative summary of the shape of data.  One way to pass data to this method is to start with a finite, discrete metric space (whether or not it arises from a Euclidean embedding) and to study the resulting filtration of the Rips complex.  In this talk, we will discuss several available methods for turning a time series into a a discrete metric space, including the Takens embedding, $k$-nearest neighbor networks, and ordinal partition networks.  Combined with persistent homology and machine learning methods, we show how this can be used to classify behavior in time series in both synthetic and experimental data.

Abstract: We propose network growth and restructuring models to show how the concept of inclusivity can be captured using random walks instead of arbitrary labels. Not only can the models capture realistic small world and scale-free properties, they also fix the mean degree and limiting degree distribution, and so allow the role of inclusivity to be isolated from these confounding factors. We find that inclusivity promotes network efficiency and robustness, but that increasing the mean degree reduces the dependence of these properties upon inclusivity.

Abstract: Link prediction is the problem of predicting the location of either unknown or fake links from uncertain structural information of a network. Link prediction algorithms are useful in gaining insight into different network structures from partial observations of exemplars. However, existing link prediction algorithms only focus on regular complex networks and are overly dependent on either the closed triangular structure of networks. The performance of these algorithms on tree-like networks is poor. Hence, we proposed a method that is based on the network heterogeneity. We test our algorithms for three real large sparse networks: a metropolitan water distribution network, a Twitter network, and a sexual contact network. We find that our method is effective and performs better than traditional algorithms, especially for the Twitter network. Moreover, previous studies shown that the internal links within communities are more predictable than external links. In the future, we will adopt the advantage of community structure to improve the accuracy of our methods.

Abstract: We study the task of determining parameters of dynamical systems from their time series, which we call parameter extraction. We present a series of models inspired by reservoir computing that generate a mapping from the original time series to some static, high dimensional vector or feature. These random (in the sense of arbitrarily selected) feature maps (RFM) allow us to separate different parameter values. We explore a number of RFM variations, presenting models in the time and frequency domain, as well as considering models with and without time series embedding. For the Lorenz and Rossler systems throughout stable and chaotic regimes we achieve accurate parameter extraction with significant robustness to key hyper-parameters of the models. As a final consideration, we assess the RFM performance on an engineering application; cavitation detection in centrifugal pumps from vibration data.

Abstract: The immune system acts as a dynamic network whose complexity rivals that of the nervous system. Modelling interactions between cells, as well as the functional changes triggered by these interactions, is a key step in understanding how the immune system responds to a particular challenge. In this talk, I will present our intended approach to unravelling the mechanistic processes behind a promising, but not yet understood, immunotherapy treatment in a melanoma mice model. Our aim is to generate prioritized predictions of potential therapeutic targets by building and utilizing a mathematical model that incorporates the inferred underlying cellular communication and transcriptional regulatory networks that govern the system.

Abstract: Models of physical systems as sets of particles interacting through generalised `forces' are common to a wide variety of sciences. While individual-based (microscopic) models of such systems are generally conceptually simple, they are often intractable analytically and computationally as most systems to be modelled contain an infeasibly large number of particles. It is common in such circumstances to derive a macroscopic continuum model, which tracks the evolution of population-averaged probability densities over an individual particle's phase space. In this talk we will explore approaches to deriving continuum models of second-order (kinetic) systems with short-ranged interaction forces using matched asymptotic expansion in the small interaction length parameter. As an archetypical example, we first show that this approach allows us to derive the Boltzmann equation as a continuum description of a low-density potential-force system. We then consider the Cucker-Smale individual-based model of collective behaviour and explore how our approach to deriving a corresponding macroscopic model has to be modified as a result of the system's clustering behaviour.

Abstract: It has been suggested that several subsystems oof the Earth system may respond abruptly to ongoing gradual increases of atmospheric greenhouse gas concentrations and temperatures. Key examples of these potential tipping elements are the polar ice sheets, the Amazon rainforest, and the Atlantic Meridional Overturning Circulation (AMOC). Here, we investigate these systems from a perspective combining paleoclimate proxies with modelling evidence and recent observations. Based on the theory of random dynamical systems, characteristic changes in the dynamics of systems approaching bifurcation-induced transitions have previously been introduced. We review these methods and introduce some modifications and extensions, before applying them to observations of Greenland Ice Sheet melt rates, Arctic sea ice extent, and fingerprints of the strength of the AMOC. Our results indicate that these three subsystems may indeed approaching bifurcation-induced abrupt transition in response to anthropogenic climate change. 

Abstract: The identification of sudden dynamical changes in time series is crucially impacted by the level of uncertainty in the data and by whether or not it is incorporated reliably in the analysis. We present here a new representation of time series that inherently take care of uncertainties in all subsequent analyses: Instead of considering a time series as a sequence of point-like objects (with or without additional error), we represent time series as a sequence of probability density functions. We show how this can be used to detect sudden changes in the time series using networks that encode the recurrence properties of the system.

Abstract: In the last few years, we have extensively studied consistency of driven dynamical systems, and applied the concept to reservoir computers in order to gain some understanding of their function. After summarising the basics of consistency, as well as recent developments together with reservoir computing, this talk will focus on our most recent work on consistency capacity. This capacity is a robust measure of how many independent degrees of freedom of a reservoir effectively respond to an input signal, and thus an indicator of the reservoir's potential for performance in a task. For multiple input channels, a set of replica experiments with combinations of the channels reveals a hierarchy of capacities at different levels of cross-channel dependence. For each channel, a modified replica experiment resolves capacity over time, leading to a nonlinear fading memory profile. The approach can be used for experimentation with numerical as well as physical reservoirs, potentially leading to improved reservoir design and enhanced understanding of information processing in nonlinear systems.

Abstract: Recently the product graphs are being used in a recursive manner to model the real world networks. The two examples of such product graphs are the Kronecker product and the Corona product. The former is being widely investigated as the deterministic and stochastic graphs while the latter are being investigated only for the $r$-regular deterministic graphs. Here we introduce a growing complex network model using generalized corona product of graphs defined by Erdos-Renyi graphs (GCG-ER). This model generates networks in which links that appear due to the definition of corona product are deterministic and all other links are generated with probability `p'. We investigate degree distribution, average path length, diameter, expected number of triangles and average clustering coefficient of GCG-ER. We introduce Pascal's triangle representation for GCG-ER in order to determine the shortest distance and paths between the nodes in a GCG-ER.

Abstract: We propose a model-free approach to analyse the movement of pedestrians in experiments and simulations. Using concepts from control and analysis of complex dynamical systems we set up a scheme which allows us to identify dynamical unstable signatures in pedestrian flows. These signatures are the building blocks for crowd control and soft management of people. Our approach is entirely data driven and we provide a proof of concept by field and laboratory experiments. In addition, our approach provides, based on experimental observations, quantitative benchmarks to judge the quality of mathematical models for pedestrian motion.

Abstract: Paleoclimate data is one of the most challenging to analyze due to uneven sampling, observational noise, and uncertainty in estimates. I will present a hybrid method that combines Recurrence Plots, Laplacian Eigenmaps, and Fisher Information metric and can be used reliably to identify dynamical transitions in a paleoclimate time series. An additional advantage of using this new scheme is that it provides a dynamical systems-based understanding of the underlying transitions. Furthermore, as a demonstration of the practical usefulness of the approach, I will apply it to a paleoclimate time series: a recently published speleothem oxygen isotope record from North India covering the past 5,700 years. This particular time series reconstructs the hydroclimate of the region and covers the period relevant to the evolution of the Indus Valley Civilization. My analysis of this series shows that potentially transitions in monsoon led to the demise of this bronze age civilization.

Abstract: There could be nonlinear stochastic systems everywhere, although such a system had not been identified explicitly. In the last three years, we have been developing a set of methods for identifying a nonlinear stochastic system using two independent hypothesis tests and analyzing its time series. We have found that we could employ permutations (ordinal patterns) and/or recurrence plots for this purpose. We present theorems as well as numerical examples, demonstrating that combinatorics helps us to establish rigorous methods for analyzing a time series generated from a nonlinear stochastic system.

Talk ID: MS12A

Speaker: İrem Topal (Kadir Has University)

Title: Sensing network dynamics of weakly coupled chaotic units

Abstract: Real-world complex systems are composed of units which interact through intricate networks. The ability to predict critical transitions in network behavior from data is important to avert the disastrous consequences of major disruptions. To predict such changes for a dynamical system from data, one first needs to reconstruct the governing equations of the system of interest. This is not a straightforward process for weakly interacting chaotic systems over a heterogeneous network. In this study, we approach this reconstruction problem by blending sparse regression techniques with dynamical systems’ theory to reveal rules which govern the local dynamics of each node and determine the topology of networks. As an application, we illustrate this approach by reconstructing the dynamics and structure of Hindmarsh-Rose neuronal model used to study bursting behavior of the membrane potential as isolated dynamics on different networked systems.

Talk ID: MS12B

Speaker: Shannon Algar (UWA)

Title: Learned emergence in selfish collective motion

Abstract: To understand the collective motion of many individuals, we often rely on agent-based models with rules that may be computationally complex and involved. For biologically inspired systems in particular, this raises questions about whether the imposed rules are necessarily an accurate reflection of what is being followed. The basic premise of updating one’s state according to some underlying motivation is well suited to the realm of reservoir computing; however, entire swarms of individuals are yet to be tasked with learning movement in this framework. This work focuses on many selfish individuals optimising their domains in a manner conducive to reducing their personal risk of predation. Using an echo state network and data generated from the agent-based model, we show that this selfish movement can be learned. This suggests that a more sophisticated neural network, such as a brain, could also learn this behaviour and provides an avenue to further the search for realistic movement rules in systems of autonomous individuals. 


Talk ID: MS12C

Speaker: Konstantinos Sakellariou (Nodes & Links)

Title: Estimating dynamical invariants using ordinal partition networks.

Abstract: Ordinal partition networks constitute a computationally simple method for analysing a scalar time series. This technique involves a mapping of the data to a network representation with the intent of using network metrics in order to characterise the underlying dynamics. A variety of time-series-to-network transforms have been proposed in the literature. It has been observed that different dynamical regimes produce networks with distinct topological features. However, estimating invariants, such as topological entropy or positive Lyapunov exponents, accurately remains an open problem for this class of techniques. In this talk we demonstrate that this particular network transform can be interpreted via a Markovian framework which allows us to exploit ergodic-theoretic ideas in order to estimate invariants on an ensemble of time series generated by nonlinear chaotic dynamics.

Talk ID: MS12D

Speaker: Francisco Rodrigues (University of São Paulo)

Title: A machine learning approach to predicting dynamical observables from network structure

Abstract: Estimating the outcome of a given dynamical process from structural features is a key unsolved challenge in network science. The goal is hindered by difficulties associated with nonlinearities, correlations and feedbacks between the structure and dynamics of complex systems. In this talk, we will present an approach based on machine learning algorithms that are shown to provide an answer to the previous challenge. Specifically, we will show that it is possible to estimate the outbreak size of disease starting from a single node as well as the degree of synchronicity of a system made up of Kuramoto oscillators. In doing so, we show which topological features of the network are key for this estimation and provide a rank of the importance of network metrics with higher accuracy than previously done. Our approach is general and can be applied to any dynamical process running on top of complex networks.

Maths is playing a pivotal role in the understanding and fight against epidemics. We will understand together how differential equations can be useful to predict the evolution of infectious diseases and to help governments in taking farsighted decisions.

What Can Networks Tell Us about Disease Transmission – in Cities and in the Outback?

Social networks are familiar to all of us: from our networks of friends and co-workers to Facebook and Instagram. Networks also provide a mechanism for modelling the transmission of information – or disease. In this talk I will describe how network science is being used to model the risk of transmission of coronavirus and the effect of various control strategies in cities like Perth. What is the risk posed by gathering 30,000 spectators in a football ground, and what is the benefit of working from home or installing COVIDSafe? In remote areas the challenges of infectious diseases are acute and very complex. We study the network of movement of people between these remote communities and find that they act like a large virtual city, highly vulnerable to infection.

Abstract: We will present ongoing work that explores the use of an agent-based swarm as a computational substrate in a reservoir computing framework. As a high-dimensional dynamical system with optional external forcing, the agent-based model is a candidate for reservoir computing. With the example of a modified Reynolds boids model, we discuss the matching of the specific symmetries and dynamical properties of the swarm with the requirements of the reservoir. Subjecting the swarm to a `predator’-like driving signal facilitates use of the group’s response in avoiding predation for a nonlinear time-series prediction task. We will demonstrate a relationship between the reservoir computer’s performance in this prediction task and the swarm’s behaviour and highlight a phase transition in the behaviour of the swarm where optimal computational properties are yielded in a critical regime.

Abstract: Driven dynamical systems are commonly characterised by their conditional Lyapunov exponents (CLE). If the maximum CLE is negative, the system is conditionally stable and its state is a function of the driving signal. If the maximum CLE is positive, the system is chaotic and thus its state depends also on initial conditions. The concept of consistency goes beyond this binary classification by measuring the degree of functional dependence between drive and response using a replica test [1]. Consistency allows for both numerical and experimental investigation of driven dynamical systems, and is more powerful than time series analysis without repeatedly driving the system. This talk will cover the basics and our recent advances in consistency theory, and its applications to reservoir computing [2].

[1] Uchida et al., Phys. Rev. Lett. 93, 244102 (2004)

[2] Lymburn et al., Chaos 29, 023118 (2019)

Abstract: The 2019 New Coronavirus Disease (COVID-19) outbreak began to occur and escalate in a special holiday period in China (about 20 days surrounding the Lunar New Year), during which a huge volume of intercity travel took place, resulting in outbreaks in multiple regions in China connected by an active transportation network. Thus, in order to understand the COVID-19 spreading process in China, it is essential to examine the human migration dynamics, especially between the epicentre Wuhan and other Chinese cities. A new Susceptible-Exposed-Infected-Confirmed-Removed (SEICR) model with consideration of intercity travel and active intervention is proposed for predicting the spreading progression of COVID-19. The model takes into account the known or reported number of infected cases being fewer than the actual number of infected individuals due to insufficient testing. The model integrates intercity travel data to track the movement of exposed and infected individuals among cities, and allows different levels of active intervention to be considered so that realistic prediction of the number of infected individuals can be performed. Data from over 500 cities/regions in China, Japan, South Korea, Italy, Iran, and USA are included in the study.

Abstract: In the minerals processing industry, it is common to separate tailings slurries into solid and liquid components. One method is by treatment with a polymer flocculant, which adsorbs onto the surface of multiple solid particles, binding them together. Large fractal-like aggregates are formed which rapidly settle out of quiescent fluid in a huge “gravity thickener”. The two main desired objectives are a high throughput or a clear fluid. There are many physical phenomena which affect the result of the flocculation process and we look to models for guidance. Population balance models (PBMs) describe how the distribution of aggregates (by size) evolves with time. Such models have a long history and have been adapted from simple coalescence models to accommodate fractal aggregates composed of many identical primary particles. Unfortunately, in our application the primary particles are polydisperse in size and far from identical. Here we propose a PBM framework based on the Gillespie algorithm that excels in describing the evolution of a polydisperse suspension of primary particles.

Abstract: If hard computational problems, e.g. NP-complete problems exist, then massive parallelism is necessary to solve them in practice. Attempts at this, including quantum computing and DNA computing have, however, struck diverse scalability barriers. Specifically, energy consumption, rather than computational time or memory, seems to be the universal bottleneck for algorithms implemented by physical means. On the other hand, a recently introduced computational technology – networks-based biocomputation – throws this emergent motif into question by appearing, on its surface, to be highly scalable. NBC uses motile, self-replicating, autonomous biological agents (like molecular motors or bacteria) to explore, in a massively parallel fashion, physical networks whose structure encodes the computational problem of interest, while the solutions can then be read out from the final positions of the agents. In this talk, I will attempt to resolve this dichotomy by reviewing recent progress in NBC, including its ability to experimentally solve increasingly large instances of NP-complete problems, the technological challenges faced in scaling it further as well as its potential theoretical limitations, derived from a computational, idealised model of NBC. Taken together, these recent results hint at a deep duality between computational complexity and physical laws. For instance, if NBC-like systems cannot solve NP-complete problems in polynomial time, then, in the context of Turing machines, there exist languages not in P/poly, with profound consequences (including P!=NP). More broadly, progress in this area may lead to a formal mathematical statement of a new law of physics, essentially setting model-independent, energetic limits on algorithmic processes.

Abstract: Disease spreading are ubiquitous processes in social networks. The modelling of the propagation of an infectious agent depends not only on the basic reproduction number, which gives the average number of secondary cases in a susceptible population, but also on the pattern of contact between subjects. In this talk, we will discuss the modelling of epidemic processes in networks, including rumour and disease propagation. We will introduce a model of epidemic spreading with awareness, where the disease and information are propagated in different layers with different time scales. We will show that the time scale determines whether the information awareness is beneficial or not to the disease spreading. Finally, we will show how machine learning can be applied to predict the capacity of propagation of each node and quantify how network properties influence the propagation of the infectious agent.

Abstract: Large complex projects have become the norm in several industries over the last few decades. However, only about 7% of all projects worldwide are delivered without schedule or cost overruns. Nodes & Links, a young tech start-up, aims at improving project performance by making use of the large amounts of data collected throughout the lifetime of complex projects. In this talk, I'll present a few real-world problems that arise within such large-scale projects and demonstrate how network science can be used to tackle these challenging issues and contribute to a project's successful delivery. In contrast to modern trends, the approach adopted at Nodes & Links employs complexity science rather than black-box-style artificial intelligence tools such as machine learning in order to analyse the data and reach useful conclusions for the practitioner.

Abstract: Real-world complex systems such as ecosystems and neuron networks appear in most aspects of our everyday life. These complex systems are often made up of components, called nodes, which interact through an intricate network. By observing past behavior of such complex systems, it may be possible to predict behavior for some time in the future. However, it is much harder to predict new behavior of such complex systems when parameters change to a new range. In this talk, I will address this challenge by building an effective network, that is, a faithful model of the network consisting of the underlying local dynamics at each node and an accurate statistical description of the interactions. An effective network makes it possible to predict sudden changes in behavior – also known as critical transitions – that can lead to major disruptions in the complex system. The construct of an effective network only requires observations of the states of a representative sample of nodes for a relatively short time window. To illustrate the power of this approach, we show how to reconstruct the dynamics and structure of real networks, such as neuronal interactions in the cat cerebral cortex. In such network we were even able to predict critical transitions for parameters outside the observed range. These findings raise the possibility of network control to anticipate malfunctions in advance of sudden changes in behavior.

Abstract: Networks of physically connected dynamical units can give rise to very different clustering structures of synchronized behaviour. In other words, network functional connectivity does not necessarily match the underlying physical connections. Here, we provide a framework to infer, in an automatic fashion, the functional connectivity of phase synchronized clusters. By using recent advances in multivariate singular spectrum analysis (MSSA) for phase synchronization, this approach has several advantages over other methods in the literature: (i) system-wise comparison of all data at the same time, as contrasted to pairwise or tripletwise comparisons; (ii) no need for any a priori phase or frequency definition, being adaptative to the specific structure of the data; (iii) highly robust against experimental noise. The approach is presented through numerical experiments with a network of coupled Rossler oscillators for an increasing coupling strength. Then, preliminary results will be shown to test the feasibility of using this framework to infer the functional connectivity of a fascinating dynamical system/network of oscillators: a reservoir computer - in a sense, this part is a sequel of my seminar last year, regarding the "soul and bones of a reservoir computer".

Abstract: At the time of the first novel coronavirus outbreak of the 21st century (Hong Kong, 2003), super-spreaders were unhelpfully defined as infected individuals with a greater than expected (that is, greater than the mean) number of secondary infections. A more useful definition would be to say that if a pathogen has numbers of secondary infections following a power-law distribution, then those instances in the tail are super-spreaders. There is now ample anecdotal evidence of super-spreader events associated with the 2020 coronavirus pandemic.  We will introduce a simple model of super-spreader events and discuss implications for transmission of coronaviruses (on, in fact, any respiratory pathogen and many other things besides). Our model indicate the unbounded nature of super-spreaders leads to super-exponential spread. We therefore conclude that it is unlikely that there will be any spectators at the next Western Derby.

Tutorial on ordinal network construction  methods, and closely related recurrence network method, for nonlinear time series analysis. Based on Seminar in the Complex Systems Seminar Series 22 May 2020, UWA.

Abstract: The process of natural selection has resulted in biological systems (including animals) that increase the chances of an animal surviving and reproducing in a continuously changing environment. For this talk, I will focus on thermoregulation: the homeostatic system that results in a relatively constant core body temperature in animals that thermoregulate, and how core body temperature responds to environmental change. First, I will discuss the predictability of environmental change and the responses of biological systems that help the animal to cope with these changes. Then, I will discuss the importance of “time” in adaptive biology using examples based on our current research. My concluding example will be the case of assessing animal welfare to illustrate how the analysis of complex systems can contribute to our understanding biological systems and predict the capacity of animals to respond to future challenges.

Abstract: This seminar will provide a brief overview of recent advances in the field of reservoir computing (RC), as well as our local approach, ideas, and future perspectives. We will discuss some aspects of the 'big picture' of RC, with a focus on the physical RC paradigm.