Mapping clinical interactions in an Australian tertiary hospital emergency department for patients presenting with risk of suicide or self-harm: Network modeling from observational data.

BACKGROUND: 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 face the challenge of rapidly integrating medical history, wide-ranging psychosocial factors, and real-time patient observations to inform diagnosis, treatment, and referral decisions. Patient outcomes therefore depend on the reliable flow of information through networks of clinical staff and information systems. This study aimed to develop a quantitative data-driven research framework for the analysis of information flow in emergency healthcare settings to evaluate clinical practice and operational models for emergency psychiatric care. METHODS AND FINDINGS: We deployed 2 observers in a tertiary hospital emergency department during 2018 for a total of 118.5 h to record clinical interactions along patient trajectories for presentations with risk of self-harm or suicide (n = 272 interactions for n = 43 patient trajectories). The study population was reflective of a naturalistic sample of patients presenting to a tertiary emergency department in a metropolitan Australian city. Using the observational data, we constructed a clinical interaction network to model the flow of clinical information at a systems level. Community detection via modularity maximization revealed communities in the network closely aligned with the underlying clinical team structure. The Psychiatric Liaison Nurse (PLN) was identified as the most important agent in the network as quantified by node degree, closeness centrality, and betweenness centrality. Betweenness centrality of the PLN was significantly higher than expected by chance (>95th percentile compared with randomly shuffled networks) and removing the PLN from the network reduced both the global efficiency of the model and the closeness centrality of all doctors. This indicated a potential vulnerability in the system that could negatively impact patient care if the function of the PLN was compromised. We developed an algorithmic strategy to mitigate this risk by targeted strengthening of links between clinical teams using greedy cumulative addition of network edges in the model. Finally, we identified specific interactions along patient trajectories which were most likely to precipitate a psychiatric referral using a machine learning model trained on features from dynamically constructed clinical interaction networks. The main limitation of this study is the use of nonclinical information only (i.e., modeling is based on timing of interactions and agents involved, but not the content or quantity of information transferred during interactions). CONCLUSIONS: This study demonstrates a data-driven research framework, new to the best of our knowledge, to assess and reinforce important information pathways that guide clinical decision processes and provide complementary insights for improving clinical practice and operational models in emergency medicine for patients at risk of suicide or self-harm. Our findings suggest that PLNs can play a crucial role in clinical communication, but overreliance on PLNs may pose risks to reliable information flow. Operational models that utilize PLNs may be made more robust to these risks by improving interdisciplinary communication between doctors. Our research framework could also be applied more broadly to investigate service delivery in different healthcare settings or for other medical specialties, patient groups, or demographics.

Network Spreading from Network Dimension.

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 global correlations typical of empirical networks. Here, we propose mitigating this limitation via a network property ideally suited to capturing spreading. This is the network correlation dimension, which characterizes how the number of nodes within range of a source typically scales with distance. Applying the approach to susceptible-infected-recovered processes leads to a spreading model which, for a wide range of networks and epidemic parameters, can provide more accurate predictions of the early stages of a spreading process than important established models of substantially higher complexity. In addition, the proposed model leads to a basic reproduction number that provides information about the final state not available from popular established models.

Searching for Key Cycles in a Complex Network.

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 Fiedler value (the second smallest Laplacian eigenvalue). Key cycles are those that contribute most substantially to the dynamical behavior of the network. Second, by comparing the sensitivity of Fiedler value to different cycles, a neat index for ranking cycles is provided. Numerical examples are given to show the effectiveness of this method.

Ordinal Poincaré sections: Reconstructing the first return map from an ordinal segmentation of time series.

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 section from a hyper-surface normal to the flow and then interpolating to determine intersections with trajectories). Our method is based on ordinal partitions of the time series, and the first return map is constructed from successive intersections with specific ordinal sequences. We can obtain distinct first return maps for each ordinal sequence in general. We define entropy-based measures to guide our selection of the ordinal sequence for a "good" first return map and show that this method can robustly be applied to time series from classical chaotic systems to extract the underlying first return map dynamics. The results are shown for several well-known dynamical systems (Lorenz, Rössler, and Mackey-Glass in chaotic regimes).

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 optimize 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, 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 were found to outperform other embedding methods when predicting fast-slow time series.

A tighter generalization bound for reservoir computing.

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 learning framework. Note that the generalization bound for the RC is derived in terms of the model hyperparameters. For this reason, it can explore the dependencies of the generalization bound for RC on its hyperparameters. Compared with the existing generalization bound, our generalization bound for RC is tighter, which is verified by numerical experiments. Furthermore, we study the generalization bound for the RC corresponding to different reservoir graphs, including directed acyclic graph (DAG) and Erdos-R e´nyi undirected random graph (ER graph). Specifically, the generalization bound for the RC whose reservoir graph is designated as a DAG can be refined by leveraging the structural property (i.e., the longest path length) of the DAG. Finally, both theoretical and experimental findings confirm that the generalization bound for the RC of a DAG is lower and less sensitive to the model hyperparameters than that for the RC of an ER graph.

Reservoir time series analysis: Using the response of complex dynamical systems as a universal indicator of change.

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 the reservoir state space. We then develop and implement a hypothesis test to assess the capacity of these features to distinguish signals from systems with varying parameters. In comparison to a number of benchmark approaches (statistical, Fourier, phase space, and recurrence analysis), we are able to show significant, generalized accuracy across the proposed RTSA features that surpasses the benchmark methods. Finally, we briefly present an application for bearing fault distinction to motivate the use of RTSA in application.

Multilayer networks with higher-order interaction reveal the impact of collective behavior on epidemic dynamics.

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 reproduce the concurrent evolution of behavioral responses and disease contagion, and social networks are critical platforms on which behavior imitation between social contacts, even dispersed in distant communities, takes place. Such joint contagion dynamics has not been sufficiently explored, which poses a challenge for policies aimed at containing the infection. In this study, we present a multi-layer network model to study contagion dynamics and behavioral adaptation. It comprises two physical layers that mimic the two solitary communities, and one social layer that encapsulates the social influence of agents from these two communities. Moreover, we adopt high-order interactions in the form of simplicial complexes on the social influence layer to delineate the behavior imitation of individual agents. This model offers a novel platform to articulate the interaction between physically isolated communities and the ensuing coevolution of behavioral change and spreading dynamics. The analytical insights harnessed therefrom provide compelling guidelines on coordinated policy design to enhance the preparedness for future pandemics.

Multiple Sensors Data Integration for Traffic Incident Detection Using the Quadrant Scan.

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 helps reduce incident duration, but it remains a challenge due to the limitation of current sensor technologies. In this paper, we employ a recurrence-based technique, the Quadrant Scan, to analyse time series traffic volume data for incident detection. The data is recorded by multiple sensors along a section of urban highway. The results show that the proposed method can detect incidents better by integrating data from the multiple sensors in each direction, compared to using them individually. It can also distinguish non-recurrent traffic congestion caused by incidents from recurrent congestion. The results show that the Quadrant Scan is a promising algorithm for real-time traffic incident detection with a short delay. It could also be extended to other non-recurrent congestion types.

Epidemic dynamics on higher-dimensional small world networks.

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 define a flexible higher-dimensional small world network model and characterize the dependence of its structural properties on dimension. Subsequently, we derive mean field, pair approximation, intertwined continuous Markov chain and probabilistic discrete Markov chain models of a COVID-19-inspired susceptible-exposed-infected-removed (SEIR) epidemic process with quarantine and isolation strategies, and for each model identify the basic reproduction number R 0 , which determines whether an introduced infinitesimal level of infection in an initially susceptible population will shrink or grow. We apply these four continuous state models, together with discrete state Monte Carlo simulations, to analyse how spreading varies with model parameters. Both network properties and the outcome of Monte Carlo simulations vary substantially with dimension or rewiring rate, but predictions of continuous state models change only slightly. A different trend appears for epidemic model parameters: as these vary, the outcomes of Monte Carlo change less than those of continuous state methods. Furthermore, under a wide range of conditions, the four continuous state approximations present similar deviations from the outcome of Monte Carlo simulations. This bias is usually least when using the pair approximation model, varies only slightly with network size, and decreases with dimension or rewiring rate. Finally, we characterize the discrepancies between Monte Carlo and continuous state models by simultaneously considering network efficiency and network size.

Parameter extraction with reservoir computing: Nonlinear time series analysis and application to industrial maintenance.

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 Rössler systems throughout stable and chaotic regimes, we achieve accurate and robust parameter extraction. For vibration data of centrifugal pumps, we find a significant ability to recover the operating regime. While the time domain models achieve higher performance for the numerical systems, the frequency domain models are superior in the application context.

Revisiting the memory capacity in reservoir computing of directed acyclic network.

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). In this paper, the global MC of the RC whose reservoir network is specified as a directed acyclic network (DAN) is examined, and first we give that its global MC is theoretically bounded by the length of the longest path of the reservoir DAN. Since the global MC is technically influenced by the model hyperparameters, the dependency of the MC on the hyperparameters of this RC is then explored in detail. In the further study, we employ the improved conventional network embedding method (i.e., struc2vec) to mine the underlying memory community in the reservoir DAN, which can be regarded as the cluster of reservoir nodes with the same memory profile. Experimental results demonstrate that such a memory community structure can provide a concrete interpretation of the global MC of this RC. Finally, the clustered RC is proposed by exploiting the detected memory community structure of DAN, where its prediction performance is verified to be enhanced with lower training cost compared with other RC models on several chaotic time series benchmarks.

Grading your models: Assessing dynamics learning of models using persistent homology.

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 learning." However, existing estimates based on dynamical invariants, such as Lyapunov exponents and correlation dimensions, are not unique to each system, not necessarily robust to noise, and struggle with detecting pathological errors, such as errors in the manifold density distribution. This can make meaningful and accurate model assessment difficult. We explore the use of a topological data analysis technique, persistent homology, applied to uniformly sampled trajectories from constructed reservoir models of the Lorenz system to assess the learning quality of a model. A proposed persistent homology point summary, conformance, was able to identify models with successful dynamics learning and detect discrepancies in the manifold density distribution.

Reservoir computing with swarms.

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 swarm's response to that signal. We find that the naïve implementation of a swarm for computation is very inefficient, as permutation symmetry of the individual agents reduces the computational capacity. To circumvent this, we distinguish between the computational substrate of the swarm and a separate observation layer, in which the swarm's response is measured for use in the task. We demonstrate the implementation of a radial basis-localized observation layer for this task. The behavior of the swarm is characterized by order parameters and measures of consistency and related to the performance of the swarm as a reservoir. The relationship between RC performance and swarm behavior demonstrates that optimal computational properties are obtained near a phase transition regime.

Reciprocal characterization from multivariate time series to multilayer complex networks.

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 that the underlying geometrical features of time series are preserved in their network counterparts. We identify underlying dynamical transitions of the time series through statistics of the structure of the corresponding networks. Meanwhile, this allows us to propose the concept of interlayer entropy to measure the coupling strength between the layers of a network. Specifically, we prove that under mild conditions, for the given transformation method, the application of interlayer entropy in networks is equivalent to transfer entropy in time series. Interlayer entropy is utilized to describe the information flow in a multilayer network.

Growing networks with communities: A distributive link model.

Evolution and popularity are two keys of the Barabasi-Albert model, which generates a power law distribution of network degrees. 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 and then propose a very simple and intuitive new model for network growth, which naturally evolves modular networks with multiple communities. The number and size of the communities evolve over time and are primarily subjected to a single free parameter. Surprisingly, under some circumstances, our framework can construct a tree-like network with clear community structures-branches and leaves of a tree. Results also show that new communities will absorb a link resource to weaken the degree growth of hub nodes. Our models have a common explanation for the community of regular and tree-like networks and also breaks the tyranny of the early adopter; unlike the standard popularity principle, newer nodes and communities will come to dominance over time. Importantly, our model can fit well with the construction of the SARS-Cov-2 haplotype evolutionary network.

The active selfish herd.

The selfish herd hypothesis provides an explanation for group aggregation via the selfish avoidance of predators. Conceptually, and as was first proposed, this movement should aim to minimise the danger domain of each individual. Whilst many reasonable proxies have been proposed, none have directly sought to reduce the danger domain. In this work we present a two dimensional stochastic model that actively optimises these domains. The individuals' dynamics are determined by sampling the space surrounding them and moving to achieve the largest possible domain reduction. Two variants of this idea are investigated with sampling occurring either locally or globally. We simulate our models and two of the previously proposed benchmark selfish herd models: k-nearest neighbours (kNN); and local crowded horizon (LCH). The resulting positions are analysed to determine the benefit to the individual and the group's ability to form a compact group. To do this, the group level metric of packing fraction and individual level metric of domain size are observed over time for a range of noise levels. With these measures we show a clear stratification of the four models when noise is not included. kNN never resulted in centrally compacted herd, while the local active selfish model and LCH did so with varying levels of success. The most centralised groups were achieved with our global active selfish herd model. The inclusion of noise improved aggregation in all models. This was particularly so with the local active selfish model with a change to ordering of performance so that it marginally outperformed LCH in aggregation. By more closely following Hamilton's original conception and aligning the individual's goal of a reduced danger domain with the movement it makes increased cohesion is observed, thus confirming his hypothesis, however, these findings are dependent on noise. Moreover, many features originally conjectured by Hamilton are also observed in our simulations.

Quadrant scan for multi-scale transition detection.

Transition detection in temporal and nontemporal signals is a problem encountered in various disciplines. We investigate the quadrant scan technique to analyze recurrence plots to identify tipping points of a dynamical system. We define two types of transition, state-transition and dynamic-transition, and prove analytically the ability of quadrant scans to detect both types. We then provide an extension by considering a weighting scheme to overcome limitations of the standard scheme. We further highlight the merits of the quadrant scan and our extension by studying several applications. The ability of the quadrant scan and its extension to deal with nontemporal, multivariate, or large data sets as well as their capability to classify multiscale transitions are demonstrated in detail through several examples and settings.

The reservoir's perspective on generalized synchronization.

We employ reservoir computing for a reconstruction task in coupled chaotic systems, across a range of dynamical relationships including generalized synchronization. For a drive-response setup, a temporal representation of the synchronized state is discussed as an alternative to the known instantaneous form. The reservoir has access to both representations through its fading memory property, each with advantages in different dynamical regimes. We also extract signatures of the maximal conditional Lyapunov exponent in the performance of variations of the reservoir topology. Moreover, the reservoir model reproduces different levels of consistency where there is no synchronization. In a bidirectional coupling setup, high reconstruction accuracy is achieved despite poor observability and independent of generalized synchronization.

Learned emergence in selfish collective motion.

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 the specific case of many selfish individuals simultaneously optimizing 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, with an appropriate representation of input and output states, this selfish movement can be learned. This suggests that a more sophisticated neural network, such as a brain, could also learn this behavior and provides an avenue to further the search for realistic movement rules in systems of autonomous individuals.