Comparison of UK paediatric SARS-CoV-2 admissions across the first and second pandemic waves.

BACKGROUND: We hypothesised that the clinical characteristics of hospitalised children and young people (CYP) with SARS-CoV-2 in the UK second wave (W2) would differ from the first wave (W1) due to the alpha variant (B.1.1.7), school reopening and relaxation of shielding. METHODS: Prospective multicentre observational cohort study of patients <19 years hospitalised in the UK with SARS-CoV-2 between 17/01/20 and 31/01/21. Clinical characteristics were compared between W1 and W2 (W1 = 17/01/20-31/07/20,W2 = 01/08/20-31/01/21). RESULTS: 2044 CYP < 19 years from 187 hospitals. 427/2044 (20.6%) with asymptomatic/incidental SARS-CoV-2 were excluded from main analysis. 16.0% (248/1548) of symptomatic CYP were admitted to critical care and 0.8% (12/1504) died. 5.6% (91/1617) of symptomatic CYP had Multisystem Inflammatory Syndrome in Children (MIS-C). After excluding CYP with MIS-C, patients in W2 had lower Paediatric Early Warning Scores (PEWS, composite vital sign score), lower antibiotic use and less respiratory and cardiovascular support than W1. The proportion of CYP admitted to critical care was unchanged. 58.0% (938/1617) of symptomatic CYP had no reported comorbidity. Patients without co-morbidities were younger (42.4%, 398/938, <1 year), had lower PEWS, shorter length of stay and less respiratory support. CONCLUSIONS: We found no evidence of increased disease severity in W2 vs W1. A large proportion of hospitalised CYP had no comorbidity. IMPACT: No evidence of increased severity of COVID-19 admissions amongst children and young people (CYP) in the second vs first wave in the UK, despite changes in variant, relaxation of shielding and return to face-to-face schooling. CYP with no comorbidities made up a significant proportion of those admitted. However, they had shorter length of stays and lower treatment requirements than CYP with comorbidities once those with MIS-C were excluded. At least 20% of CYP admitted in this cohort had asymptomatic/incidental SARS-CoV-2 infection. This paper was presented to SAGE to inform CYP vaccination policy in the UK.

Characterisation of in-hospital complications associated with COVID-19 using the ISARIC WHO Clinical Characterisation Protocol UK: a prospective, multicentre cohort study.

BACKGROUND: COVID-19 is a multisystem disease and patients who survive might have in-hospital complications. These complications are likely to have important short-term and long-term consequences for patients, health-care utilisation, health-care system preparedness, and society amidst the ongoing COVID-19 pandemic. Our aim was to characterise the extent and effect of COVID-19 complications, particularly in those who survive, using the International Severe Acute Respiratory and Emerging Infections Consortium WHO Clinical Characterisation Protocol UK. METHODS: We did a prospective, multicentre cohort study in 302 UK health-care facilities. Adult patients aged 19 years or older, with confirmed or highly suspected SARS-CoV-2 infection leading to COVID-19 were included in the study. The primary outcome of this study was the incidence of in-hospital complications, defined as organ-specific diagnoses occurring alone or in addition to any hallmarks of COVID-19 illness. We used multilevel logistic regression and survival models to explore associations between these outcomes and in-hospital complications, age, and pre-existing comorbidities. FINDINGS: Between Jan 17 and Aug 4, 2020, 80 388 patients were included in the study. Of the patients admitted to hospital for management of COVID-19, 49·7% (36 367 of 73 197) had at least one complication. The mean age of our cohort was 71·1 years (SD 18·7), with 56·0% (41 025 of 73 197) being male and 81·0% (59 289 of 73 197) having at least one comorbidity. Males and those aged older than 60 years were most likely to have a complication (aged ≥60 years: 54·5% [16 579 of 30 416] in males and 48·2% [11 707 of 24 288] in females; aged <60 years: 48·8% [5179 of 10 609] in males and 36·6% [2814 of 7689] in females). Renal (24·3%, 17 752 of 73 197), complex respiratory (18·4%, 13 486 of 73 197), and systemic (16·3%, 11 895 of 73 197) complications were the most frequent. Cardiovascular (12·3%, 8973 of 73 197), neurological (4·3%, 3115 of 73 197), and gastrointestinal or liver (0·8%, 7901 of 73 197) complications were also reported. INTERPRETATION: Complications and worse functional outcomes in patients admitted to hospital with COVID-19 are high, even in young, previously healthy individuals. Acute complications are associated with reduced ability to self-care at discharge, with neurological complications being associated with the worst functional outcomes. COVID-19 complications are likely to cause a substantial strain on health and social care in the coming years. These data will help in the design and provision of services aimed at the post-hospitalisation care of patients with COVID-19. FUNDING: National Institute for Health Research and the UK Medical Research Council.

Parallel Machine Learning for Forecasting the Dynamics of Complex Networks.

Forecasting the dynamics of large, complex, sparse networks from previous time series data is important in a wide range of contexts. Here we present a machine learning scheme for this task using a parallel architecture that mimics the topology of the network of interest. We demonstrate the utility and scalability of our method implemented using reservoir computing on a chaotic network of oscillators. Two levels of prior knowledge are considered: (i) the network links are known, and (ii) the network links are unknown and inferred via a data-driven approach to approximately optimize prediction.

Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity.

We develop and test machine learning techniques for successfully using past state time series data and knowledge of a time-dependent system parameter to predict the evolution of the "climate" associated with the long-term behavior of a non-stationary dynamical system, where the non-stationary dynamical system is itself unknown. By the term climate, we mean the statistical properties of orbits rather than their precise trajectories in time. By the term non-stationary, we refer to systems that are, themselves, varying with time. We show that our methods perform well on test systems predicting both continuous gradual climate evolution as well as relatively sudden climate changes (which we refer to as "regime transitions"). We consider not only noiseless (i.e., deterministic) non-stationary dynamical systems, but also climate prediction for non-stationary dynamical systems subject to stochastic forcing (i.e., dynamical noise), and we develop a method for handling this latter case. The main conclusion of this paper is that machine learning has great promise as a new and highly effective approach to accomplishing data driven prediction of non-stationary systems.

Using data assimilation to train a hybrid forecast system that combines machine-learning and knowledge-based components.

We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data are in the form of noisy partial measurements of the past and present state of the dynamical system. Recently, there have been several promising data-driven approaches to forecasting of chaotic dynamical systems using machine learning. Particularly promising among these are hybrid approaches that combine machine learning with a knowledge-based model, where a machine-learning technique is used to correct the imperfections in the knowledge-based model. Such imperfections may be due to incomplete understanding and/or limited resolution of the physical processes in the underlying dynamical system, e.g., the atmosphere or the ocean. Previously proposed data-driven forecasting approaches tend to require, for training, measurements of all the variables that are intended to be forecast. We describe a way to relax this assumption by combining data assimilation with machine learning. We demonstrate this technique using the Ensemble Transform Kalman Filter to assimilate synthetic data for the three-variable Lorenz 1963 system and for the Kuramoto-Sivashinsky system, simulating a model error in each case by a misspecified parameter value. We show that by using partial measurements of the state of the dynamical system, we can train a machine-learning model to improve predictions made by an imperfect knowledge-based model.

Separation of chaotic signals by reservoir computing.

We demonstrate the utility of machine learning in the separation of superimposed chaotic signals using a technique called reservoir computing. We assume no knowledge of the dynamical equations that produce the signals and require only training data consisting of finite-time samples of the component signals. We test our method on signals that are formed as linear combinations of signals from two Lorenz systems with different parameters. Comparing our nonlinear method with the optimal linear solution to the separation problem, the Wiener filter, we find that our method significantly outperforms the Wiener filter in all the scenarios we study. Furthermore, this difference is particularly striking when the component signals have similar frequency spectra. Indeed, our method works well when the component frequency spectra are indistinguishable-a case where a Wiener filter performs essentially no separation.

Combining machine learning with knowledge-based modeling for scalable forecasting and subgrid-scale closure of large, complex, spatiotemporal systems.

We consider the commonly encountered situation (e.g., in weather forecast) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous system states and an imperfect model of the full system dynamics. Specifically, we attempt to utilize machine learning as the essential tool for integrating the use of past data into predictions. In order to facilitate scalability to the common scenario of interest where the spatiotemporally chaotic system is very large and complex, we propose combining two approaches: (i) a parallel machine learning prediction scheme and (ii) a hybrid technique for a composite prediction system composed of a knowledge-based component and a machine learning-based component. We demonstrate that not only can this method combining (i) and (ii) be scaled to give excellent performance for very large systems but also that the length of time series data needed to train our multiple, parallel machine learning components is dramatically less than that necessary without parallelization. Furthermore, considering cases where computational realization of the knowledge-based component does not resolve subgrid-scale processes, our scheme is able to use training data to incorporate the effect of the unresolved short-scale dynamics upon the resolved longer-scale dynamics (subgrid-scale closure).

Complexity reduction ansatz for systems of interacting orientable agents: Beyond the Kuramoto model.

Previous results have shown that a large class of complex systems consisting of many interacting heterogeneous phase oscillators exhibit an attracting invariant manifold. This result has enabled reduced analytic system descriptions from which all the long term dynamics of these systems can be calculated. Although very useful, these previous results are limited by the restriction that the individual interacting system components have one-dimensional dynamics, with states described by a single, scalar, angle-like variable (e.g., the Kuramoto model). In this paper, we consider a generalization to an appropriate class of coupled agents with higher-dimensional dynamics. For this generalized class of model systems, we demonstrate that the dynamics again contain an invariant manifold, hence enabling previously inaccessible analysis and improved numerical study, allowing a similar simplified description of these systems. We also discuss examples illustrating the potential utility of our results for a wide range of interesting situations.

Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach.

We demonstrate the effectiveness of using machine learning for model-free prediction of spatiotemporally chaotic systems of arbitrarily large spatial extent and attractor dimension purely from observations of the system's past evolution. We present a parallel scheme with an example implementation based on the reservoir computing paradigm and demonstrate the scalability of our scheme using the Kuramoto-Sivashinsky equation as an example of a spatiotemporally chaotic system.

Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model.

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the mechanistic processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have demonstrated promising results for forecasting chaotic systems purely from past time series measurements of system state variables (training data), without prior knowledge of the system dynamics. The motivation for this paper is the potential of machine learning for filling in the gaps in our underlying mechanistic knowledge that cause widely-used knowledge-based models to be inaccurate. Thus, we here propose a general method that leverages the advantages of these two approaches by combining a knowledge-based model and a machine learning technique to build a hybrid forecasting scheme. Potential applications for such an approach are numerous (e.g., improving weather forecasting). We demonstrate and test the utility of this approach using a particular illustrative version of a machine learning known as reservoir computing, and we apply the resulting hybrid forecaster to a low-dimensional chaotic system, as well as to a high-dimensional spatiotemporal chaotic system. These tests yield extremely promising results in that our hybrid technique is able to accurately predict for a much longer period of time than either its machine-learning component or its model-based component alone.

Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data.

We use recent advances in the machine learning area known as "reservoir computing" to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of measurements as input to a high-dimensional dynamical system called a "reservoir." After the reservoir's response to the data is recorded, linear regression is used to learn a large set of parameters, called the "output weights." The learned output weights are then used to form a modified autonomous reservoir designed to be capable of producing an arbitrarily long time series whose ergodic properties approximate those of the input signal. When successful, we say that the autonomous reservoir reproduces the attractor's "climate." Since the reservoir equations and output weights are known, we can compute the derivatives needed to determine the Lyapunov exponents of the autonomous reservoir, which we then use as estimates of the Lyapunov exponents for the original input generating system. We illustrate the effectiveness of our technique with two examples, the Lorenz system and the Kuramoto-Sivashinsky (KS) equation. In the case of the KS equation, we note that the high dimensional nature of the system and the large number of Lyapunov exponents yield a challenging test of our method, which we find the method successfully passes.

Reservoir observers: Model-free inference of unmeasured variables in chaotic systems.

Deducing the state of a dynamical system as a function of time from a limited number of concurrent system state measurements is an important problem of great practical utility. A scheme that accomplishes this is called an "observer." We consider the case in which a model of the system is unavailable or insufficiently accurate, but "training" time series data of the desired state variables are available for a short period of time, and a limited number of other system variables are continually measured. We propose a solution to this problem using networks of neuron-like units known as "reservoir computers." The measurements that are continually available are input to the network, which is trained with the limited-time data to output estimates of the desired state variables. We demonstrate our method, which we call a "reservoir observer," using the Rössler system, the Lorenz system, and the spatiotemporally chaotic Kuramoto-Sivashinsky equation. Subject to the condition of observability (i.e., whether it is in principle possible, by any means, to infer the desired unmeasured variables from the measured variables), we show that the reservoir observer can be a very effective and versatile tool for robustly reconstructing unmeasured dynamical system variables.

Modeling the network dynamics of pulse-coupled neurons.

We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions and degree correlations (assortativity). Using the ansatz of Ott and Antonsen [Chaos 18, 037113 (2008)], we obtain a reduced system of ordinary differential equations describing the mean-field dynamics, with significantly lower dimensionality compared with the complete set of dynamical equations for the system. We find that, for sufficiently large networks and degrees, the dynamical behavior of the reduced system agrees well with that of the full network. This dimensional reduction allows for an efficient characterization of system phase transitions and attractors. For networks with tightly peaked degree distributions, the macroscopic behavior closely resembles that of fully connected networks previously studied by others. In contrast, networks with highly skewed degree distributions exhibit different macroscopic dynamics due to the emergence of degree dependent behavior of different oscillators. For nonassortative networks (i.e., networks without degree correlations), we observe the presence of a synchronously firing phase that can be suppressed by the presence of either assortativity or disassortativity in the network. We show that the results derived here can be used to analyze the effects of network topology on macroscopic behavior in neuronal networks in a computationally efficient fashion.

Finding New Order in Biological Functions from the Network Structure of Gene Annotations.

The Gene Ontology (GO) provides biologists with a controlled terminology that describes how genes are associated with functions and how functional terms are related to one another. These term-term relationships encode how scientists conceive the organization of biological functions, and they take the form of a directed acyclic graph (DAG). Here, we propose that the network structure of gene-term annotations made using GO can be employed to establish an alternative approach for grouping functional terms that captures intrinsic functional relationships that are not evident in the hierarchical structure established in the GO DAG. Instead of relying on an externally defined organization for biological functions, our approach connects biological functions together if they are performed by the same genes, as indicated in a compendium of gene annotation data from numerous different sources. We show that grouping terms by this alternate scheme provides a new framework with which to describe and predict the functions of experimentally identified sets of genes.

Resynchronization of circadian oscillators and the east-west asymmetry of jet-lag.

Cells in the brain's Suprachiasmatic Nucleus (SCN) are known to regulate circadian rhythms in mammals. We model synchronization of SCN cells using the forced Kuramoto model, which consists of a large population of coupled phase oscillators (modeling individual SCN cells) with heterogeneous intrinsic frequencies and external periodic forcing. Here, the periodic forcing models diurnally varying external inputs such as sunrise, sunset, and alarm clocks. We reduce the dimensionality of the system using the ansatz of Ott and Antonsen and then study the effect of a sudden change of clock phase to simulate cross-time-zone travel. We estimate model parameters from previous biological experiments. By examining the phase space dynamics of the model, we study the mechanism leading to the difference typically experienced in the severity of jet-lag resulting from eastward and westward travel.

Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states.

In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

Consequences of anomalous diffusion in disordered systems under cyclic forcing.

We study the particle scale response of a 2D frictionless disk system to bulk forcing via cyclic shear with reversal amplitude γ_{r}. We find a subdiffusive γ_{r}-dependent regime, which is consistent with models of anomalous diffusion with scale-invariant cage dynamics, and a crossover to diffusive grain motion at high γ_{r}. Analysis of local displacements of a particle relative to its cage of neighbors reveals a key distinction from thermal systems. Particles are moved by fluctuations of their cage of neighbors rather than rattling in their cage, indicating a distinct cage-breaking mechanism.

Stabilizing machine learning prediction of dynamics: Novel noise-inspired regularization tested with reservoir computing.

Recent work has shown that machine learning (ML) models can skillfully forecast the dynamics of unknown chaotic systems. Short-term predictions of the state evolution and long-term predictions of the statistical patterns of the dynamics ("climate") can be produced by employing a feedback loop, whereby the model is trained to predict forward only one time step, then the model output is used as input for multiple time steps. In the absence of mitigating techniques, however, this feedback can result in artificially rapid error growth ("instability"). One established mitigating technique is to add noise to the ML model training input. Based on this technique, we formulate a new penalty term in the loss function for ML models with memory of past inputs that deterministically approximates the effect of many small, independent noise realizations added to the model input during training. We refer to this penalty and the resulting regularization as Linearized Multi-Noise Training (LMNT). We systematically examine the effect of LMNT, input noise, and other established regularization techniques in a case study using reservoir computing, a machine learning method using recurrent neural networks, to predict the spatiotemporal chaotic Kuramoto-Sivashinsky equation. We find that reservoir computers trained with noise or with LMNT produce climate predictions that appear to be indefinitely stable and have a climate very similar to the true system, while the short-term forecasts are substantially more accurate than those trained with other regularization techniques. Finally, we show the deterministic aspect of our LMNT regularization facilitates fast reservoir computer regularization hyperparameter tuning.