Michael Small

• B.Sc.Hons (UWA), Ph.D (UWA), SnrMIEEE, MAustMS
• Chair at The University of Western Australia

Most previous studies on eigenspectral analysis of synchronization have focused on static multilayer networks with pairwise interactions. In this work, we extend the analysis to time-varying multilayer networks with higher-order interactions. Specifically, we consider two types of multilayer connections, namely, multiplex and interconnected network...

The Earth, a temporal complex system, is witnessing a shift in research on its coordinate system, moving away from conventional static positioning toward embracing dynamic modeling. Early positioning concentrates on static natural geographic features, with the emergence of geographic information systems introducing a growing demand for spatial data...

Link prediction aims to estimate the likelihood of connections between pairs of nodes in complex networks, which is beneficial to many applications from friend recommendation to metabolic network reconstruction. Traditional heuristic-based methodologies in the field of complex networks typically depend on predefined assumptions about node connectiv...

Community detection plays a crucial role in understanding the structural organization of complex networks. Previous methods, particularly those from statistical physics, primarily focus on the analysis of mesoscopic network structures and often struggle to integrate fine-grained node similarities. To address this limitation, we propose a low-comple...

While the assumption that dynamical systems are stationary is common for modeling purposes, in reality, this is rarely the case. Rather, these systems can change over time, a phenomenon referred to as concept drift in the modeling community. While there exist numerous statistics-based methods for concept drift detection on stochastic processes, app...

We propose a universal method based on deep reinforcement learning (specifically, soft actor–critic) to control the chimera state in the coupled oscillators. The policy for control is learned by maximizing the expectation of the cumulative reward in the reinforcement learning framework. With the aid of the local order parameter, we design a class o...

We examine the family of ordinal First Return Maps (FRMs) of a dynamical system time series to model the system’s dynamics. We consider two distinct modeling approaches using the same modeling method and compare their outcomes to ascertain the prerequisites for each to function and which approach is more effective in different circumstances. The fi...

When synchronizing two continuous typical chaotic systems, the state variables of the response system are usually bounded and satisfy the Lipschitz condition. This permits a universal synchronization method. In the synchronization of two high-dimensional discrete chaotic systems such as the coupled map lattice systems, the state variables of the re...

Continuous-state network spreading models provide critical numerical and analytic insights into transmission processes in epidemiology, rumor propagation, knowledge dissemination, and many other areas. Most of these models reflect only local features such as adjacency, degree, and transitivity, so can exhibit substantial error in the presence of gl...

Car following model is an important part in traffic modelling and has attracted a lot of attentions in the literature. As the proposed car following models become more complex with more components, reliably estimating their parameters becomes crucial to enhance model predictive performance. While most studies adopt an optimisation-based approach fo...

Estimating the size and density of fine particle aggregates in suspension is challenging, often involving analysing 2D images captured during settling tests. This study explores methods to better estimate drag and to derive size parameters, aiming to reduce calculation errors when characterizing complex aggregate structures. We compare 81 models fo...

Cascade prediction aims to estimate the popularity of information diffusion in complex networks, which is beneficial to many applications from identifying viral marketing to fake news propagation in social media, estimating the scientific impact (citations) of a new publication, and so on. How to effectively predict cascade growth size has become a...

The reservoir computing approach utilizes a time series of measurements as input to a high-dimensional dynamical system known as a reservoir. However, the approach relies on sampling a random matrix to define its underlying reservoir layer, which leads to numerous hyperparameters that need to be optimized. Here, we propose a nonlocally coupled pend...

A common approach to monitoring the status of physical and biological systems is through the regular measurement of various system parameters. Changes in a system’s underlying dynamics manifest as changes in the behaviour of the observed time series. For example, the transition from healthy cardiac activity to ventricular fibrillation results in er...

We present a novel SIRS model on scale-free networks that takes into account behavioral memory and time delayto depict an adaptive behavioral feedback mechanism, which can better characterize the actual spread of epidemics.We conduct rigorous analysis on the dynamics of the model, including the basic reproduction number R0, uniformpersistence and t...

A common approach of monitoring the status of physical and biological systems is through the regular measurement of various system parameters. Changes in a system's underlying dynamics manifest as changes in the behaviour of the observed time series. For example, the transition from healthy cardiac activity to ventricular fibrillation results in er...

Data that is collected at the individual-level from mobile phones is typically aggregated to the population-level for privacy reasons. If we are interested in answering questions regarding the mean, or working with groups appropriately modeled by a continuum, then this data is immediately informative. However, coupling such data regarding a populat...

Reliable assessment of suicide and self-harm risk in emergency medicine is critical for effective intervention and treatment of patients affected by mental health disorders. Teams of clinicians are faced with the challenge of rapidly integrating medical history, wide-ranging psychosocial factors, and real-time patient observations to inform diagnos...

Searching for key nodes and edges in a network is a long-standing problem. Recently cycle structure in a network has received more attention. Is it possible to propose a ranking algorithm for cycle importance? We address the problem of identifying the key cycles of a network. First, we provide a more concrete definition of importance—in terms of Fi...

We propose a robust algorithm for constructing first return maps of dynamical systems from time series without the need for embedding. A first return map is typically constructed using a convenient heuristic (maxima or zero-crossings of the time series, for example) or a computationally nuanced geometric approach (explicitly constructing a Poincaré...

Information dissemination and the associated change of individual behavior can significantly slow the spread of an epidemic. However, major social events which attract public attention will disturb information spread and affect epidemic transmission in ways that have not been readily quantified. We investigate the interplay between disease spreadin...

Network correlation dimension governs the distribution of network distance in terms of a power-law model and profoundly impacts both structural properties and dynamical processes. We develop new maximum likelihood methods which allow us robustly and objectively to identify network correlation dimension and a bounded interval of distances over which...

Single cell RNA sequencing is an ubiquitous method for studying changes in cellular states within and across conditions. Differential expression (DE) analysis may miss subtle differ- ences, especially where transcriptional variability is not unique to a specific condition, but shared across multiple conditions or phenotypes. Here, we present CDR-g...

We propose a robust and computationally efficient algorithm to generically construct first return maps of dynamical systems from time series without the need for embedding. Typically, a first return map is constructed using a heuristic convenience (maxima or zero-crossings of the time series, for example) or a computationally delicate geometric app...

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 optimize the selection of parameters such as embedding lag. This paper aims to provide a comprehen...

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 comprehen...

Dynamical networks are versatile models that describe a variety of behaviours such as synchronisation and feedback in networks of coupled dynamical components. However, applying these models in real systems is difficult as prior information of the connectivity structure or local dynamics is often unknown and must be inferred from node state observa...

Dynamical networks are a framework commonly used to model large networks of interacting time-varying components such as power grids and epidemic disease networks. The connectivity structure of dynamical networks play a key role in enabling many interesting behaviours such as synchronisation and chimeras. However, dynamical networks can also be vuln...

When working with time series, it is often beneficial to have an idea as to how complex the signal is. Periodic, chaotic and random signals (from least to most complex) may each be approached in different ways, and knowing when a signal can be identified as belonging to one of these categories can reveal a lot about the underlying system. In the fi...

The ongoing COVID-19 pandemic has inflicted tremendous economic and societal losses. In the absence of pharmaceutical interventions, the population behavioral response, including situational awareness and adherence to non-pharmaceutical intervention policies, has a significant impact on contagion dynamics. Game-theoretic models have been used to re...

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 stat...

Chaotic systems are ubiquitous in the real world, but often analytical models remain inaccessible. We find that a machine-learning method known as “reservoir computing” provides an alternative feasible way for modeling chaotic systems rather than conventional dynamical equations. Specifically, we show that recurrence in temporal and spatial scales...

Dimension governs dynamical processes on networks. The social and technological networks which we encounter in everyday life span a wide range of dimensions, but studies of spreading on finite-dimensional networks are usually restricted to one or two dimensions. To facilitate investigation of the impact of dimension on spreading processes, we defin...

Non-recurrent congestion disrupts normal traffic operations and lowers travel time (TT) reliability, which leads to many negative consequences such as difficulties in trip planning, missed appointments, loss in productivity, and driver frustration. Traffic incidents are one of the six causes of non-recurrent congestion. Early and accurate detection...

While reservoir computing (RC) has demonstrated astonishing performance in many practical scenarios, the understanding of its capability for generalization on previously unseen data is limited. To address this issue, we propose a novel generalization bound for RC based on the empirical Rademacher complexity under the probably approximately correct...

Topographic maps are a brain structure connecting pre-synpatic and post-synaptic brain regions. Topographic development is dependent on Hebbian-based plasticity mechanisms working in conjunction with spontaneous patterns of neural activity generated in the pre-synaptic regions. Studies performed in mouse have shown that these spontaneous patterns c...

We present the idea of reservoir time series analysis (RTSA), a method by which the state space representation generated by a reservoir computing (RC) model can be used for time series analysis. We discuss the motivation for this with reference to the characteristics of RC and present three ad hoc methods for generating representative features from...

Link prediction is the problem of predicting the uncertain relationship between a pair of nodes from observed structural information of a network. Link prediction algorithms are useful in gaining insight into different network structures from partial observation of exemplars. Existing local and quasilocal link prediction algorithms with low computa...

The maturation of the autonomic nervous system (ANS) starts in the gestation period and it is completed after birth in a variable time, reaching its peak in adulthood. However, the development of ANS maturation is not entirely understood in newborns. Clinically, the ANS condition is evaluated with monitoring of gestational age, Apgar score, heart r...

An essential requirement in any data analysis is to have a response variable representing the aim of the analysis. Much academic work is based on laboratory or simulated data, where the experiment is controlled, and the ground truth clearly defined. This is seldom the reality for equipment performance in an industrial environment and it is common t...

Modelling of 3D domain boundaries using information from drill holes is a standard procedure in mineral exploration and mining. Manual logging of drill holes can be difficult to exploit as the results may not be comparable between holes due to the subjective nature of geological logging. Exploration and mining companies commonly collect geochemical...

The maturation of the autonomic nervous system (ANS) starts in the gestation period and it is completed after birth in a variable time, reaching its peak in adulthood. However, the development of ANS maturation is not entirely understood in newborns. Clinically, the ANS condition is evaluated with monitoring of gestational age, Apgar score, heart r...

Assessing model accuracy for complex and chaotic systems is a non-trivial task that often relies on the calculation of dynamical invariants, such as Lyapunov exponents and correlation dimensions. Well-performing models are able to replicate the long-term dynamics and ergodic properties of the desired system. We term this phenomenon “dynamics learni...

We study the propagation and distribution of information-carrying signals injected in dynamical systems serving as reservoir computers. Through different combinations of repeated input signals, a multivariate correlation analysis reveals measures known as the consistency spectrum and consistency capacity. These are high-dimensional portraits of the...

Experienced process plant personnel observe that corrective maintenance work on one asset may often be followed by corrective work on the same asset or connected assets within a short amount of time. This problem is referred to as a cascading failure. Confirming if these events are chronic is difficult given the number of assets and the volume of m...

Topographic maps are a brain structure connecting pre-synpatic and post-synaptic brain regions. Topographic development is dependent on Hebbian-based plasticity mechanisms working in conjunction with spontaneous patterns of neural activity generated in the pre-synaptic regions. Studies performed in mouse have shown that these spontaneous patterns c...

We study the propagation and distribution of information-carrying signals injected in dynamical systems serving as a reservoir computers. A multivariate correlation analysis in tailored replica tests reveals consistency spectra and capacities of a reservoir. These measures provide a high-dimensional portrait of the nonlinear functional dependence o...

The rate of successfully acquiring knowledge depends on whether the individual has previously held that knowledge. In an earlier work, we represented this phenomenon by dividing the dynamical process of knowledge transmission into initial and retransmission stages, and applied mean field theory to identify an approximate condition for knowledge sur...

Reservoir computing (RC) is an attractive area of research by virtue of its potential for hardware implementation and low training cost. An intriguing research direction in this field is to interpret the underlying dynamics of an RC model by analyzing its short-term memory property, which can be quantified by the global index: memory capacity (MC)....

We study swarms as dynamical systems for reservoir computing (RC). By example of a modified Reynolds boids model, the specific symmetries and dynamical properties of a swarm are explored with respect to a nonlinear time-series prediction task. Specifically, we seek to extract meaningful information about a predator-like driving signal from the swar...

We study the task of determining parameters of dynamical systems from their time series using variations of reservoir computing. Averages of reservoir activations yield a static set of random features that allows us to separate different parameter values. We study such random feature models in the time and frequency domain. For the Lorenz and Rössl...

We propose a computationally simple and efficient network-based method for approximating topological entropy of low-dimensional chaotic systems. This approach relies on the notion of an ordinal partition. The proposed methodology is compared to the three existing techniques based on counting ordinal patterns—all of which derive from collecting stat...

Many modern institutions seek to be inclusive, but the quantitative benefits of this goal are not always communicated effectively to stakeholders. To facilitate this important dialogue, we propose a simple model with which to grow, in the presence of a given level of inclusivity, networks which represent the structure of organisations. The model pr...

Complex networks are a useful method to model many real-world systems from society to biology. Spreading dynamics of complex networks has attracted more and more attention and is currently an area of intense interest. In this study, by applying a perturbation approach to an individual-based susceptible–infected–susceptible (SIS) model, we derive an...

We propose a new paradigm for describing complex networks in terms of the spectrum of the adjacency matrix and its submatrices. We show that a variety of basic node information, such as degree, clique, and subgraph centrality, can be calculated analytically. Moreover, we find that energy of spectrum series can uncover randomness and complexity of n...

We are now witnessing a dramatic growth of heterogeneous data, consisting of a complex set of cross-media content, such as texts, images, videos, audio, graphics, spatio-temporal data, and multivariate time series. The inception of modern techniques from computer science have offered very robust and hi-tech solutions for data and information analys...

Structural changes in a network representation of a system, due to different experimental conditions, different connectivity across layers, or to its time evolution, can provide insight on its organization, function, and on how it responds to external perturbations. The deeper understanding of how gene networks cope with diseases and treatments is...

Networks offer a powerful language with which to describe and study pairwise interaction. However, in many contexts, these rich collective phenomena require a higher-order approach to encode dynamical processes — for example in idea integration and information transmission (co-publication is a particularly familiar example). Here we introduce a nov...

Cell-to-cell communication is mainly triggered by ligand-receptor activities. Through ligandreceptor pairs, cells coordinate complex processes such as development, homeostasis, and immune response. In this work, we model the ligand-receptor-mediated cell-to-cell communication network as a weighted directed hypergraph. In this mathematical model, co...

One of the challenges faced by companies in the oil and gas industry is the difficulty in assessing and quantifying subsurface uncertainties when planning for hydrocarbon exploitation. A commonly employed approach is to use available exploration and appraisal data to produce a range of possible subsurface realisations, through which hydrocarbon produ...

We study the consistency property in reservoir computers with noise. Consistency quantifies the functional dependence of a driven dynamical system on its input via replica tests. We characterise the high-dimensional profile of consistency in typical reservoirs subject to intrinsic and measurement noise. An integral of the consistency is introduced...

Significant advances have recently been made in modeling chaotic systems with the reservoir computing approach, especially for prediction. We find that although state prediction of the trained reservoir computer will gradually deviate from the actual trajectory of the original system, the associated geometric features remain invariant. Specifically...

The dynamic behavior of many physical, biological, and other systems, are organized according to the synchronization of chaotic oscillators. In this paper, we have proposed a new method with low sensitivity to noise for detecting synchronization by mapping time series to complex networks, called the ordinal partition network, and calculating the pe...

Structural changes in a network representation of a system (e.g.,different experimental conditions, time evolution), can provide insight on its organization, function and on how it responds to external perturbations. The deeper understanding of how gene networks cope with diseases and treatments is maybe the most incisive demonstration of the gains...

The COVID-19 Pandemic has been described as the global challenge of our time, an enormous human tragedy with dramatic economic impacts. This paper describes the response and expected recovery process for Western Australia, where a rapid and effective response was implemented. This has enabled an early transition into an expected recovery both in he...

Many models and real systems possess tipping points at which the state of the model or real system shifts dramatically. The ability to find any early-warnings in the vicinity of tipping points is of great importance to estimate how far the system is away from the critical point. Meanwhile, among the many schemes to convert time series into complex...

We develop an agent-based model of disease transmission in remote communities in Western Australia. Despite extreme isolation, we show that the movement of people amongst a large number of small but isolated communities has the effect of causing transmission to spread quickly. Significant movement between remote communities, and regional and urban...

We show that precise knowledge of epidemic transmission parameters is not required to build an informative model of the spread of disease. We propose a detailed model of the topology of the contact network under various external control regimes and demonstrate that this is sufficient to capture the salient dynamical characteristics and to inform de...

Evolution and popularity are two keys of the (Barabasi-Albert) BA model, which generate a power law distribution of network degree. Evolving network generation models are important as they offer an explanation of both how and why complex networks (and scale free networks in particular) are ubiquitous. We adopt the evolution principle then propose a...

We show that precise knowledge of epidemic transmission parameters is not required to build an informative model of the spread of disease. We propose a detailed model of the topology of the contact network under various control regimes and demonstrate that this is sufficient to capture the salient dynamical characteristics and to inform decisions....

Detection of dense communities has recently attracted increasing attention within network science and various metrics for detection of such communities have been proposed. The most popular metric-modularity-is based on the rule that the links within communities are denser than external links among communities. However, the principle of this metric...

Aggregation within particle suspensions is often sought to enhance settling. Aggregate settling velocity and density predictions are directly related to the drag coefficient. Despite extensive studies on aggregate drag forces, there remains a lack of explicit correlations suitable across a range of properties and flow conditions; most employ implic...

We analyze melodies of classical music by stochastic modeling and prediction, analogous to symbolic time series from a nonlinear dynamical system. The performance in a one-step prediction task indicates the capabilities of the models, given by Markov chains of different orders, to preserve prominent patterns of the compositions. We use cross-predic...

We study laminar chaos in an electronic experiment. A two-diode nonlinear circuit with delayed feedback shows chaotic dynamics similar to the Mackey-Glass or Ikeda delay systems. Clock modulation of a single delay line leads to a conservative variable delay, which with a second delay line is augmented to dissipative delays, leading to laminar chaot...

Various transformations from time series to complex networks have recently gained significant attention. These transformations provide an alternative perspective to better investigate complex systems. We present a transformation from multivariate time series to multilayer networks for their reciprocal characterization. This transformation ensures t...

Mapping time series to complex networks to analyze observables has recently become popular, both at the theoretical and the practitioner's level. The intent is to use network metrics to characterize the dynamics of the underlying system. Applications cover a wide range of problems, from geoscientific measurements to biomedical data and financial ti...

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 updati...

Short course on nonlinear time series analysis and deterministic chaos - an applied mathematics perspective, delivered at HIT.