Low-dimensional Model Research Articles

Patterns of reported infection and reinfection of SARS-CoV-2 in England

One of the key features of any infectious disease is whether infection generates long-lasting immunity or whether repeated reinfection is common. In the former, the long-term dynamics are driven by the birth of susceptible individuals while in the latter the dynamics are governed by the speed of waning immunity. Between these two extremes a range of scenarios is possible. During the early waves of SARS-CoV-2, the underlying paradigm was for long-lasting immunity, but more recent data and in particular the 2022 Omicron waves have shown that reinfection can be relatively common. Here we investigate reported SARS-CoV-2 cases in England, partitioning the data into four main waves, and consider the temporal distribution of first and second reports of infection. We show that a simple low-dimensional statistical model of random (but scaled) reinfection captures much of the observed dynamics, with the value of this scaling, k, providing information of underlying epidemiological patterns. We conclude that there is considerable heterogeneity in risk of reporting reinfection by wave, age-group and location. The high levels of reinfection in the Omicron wave (we estimate that 18% of all Omicron cases had been previously infected, although not necessarily previously reported infection) point to reinfection events dominating future COVID-19 dynamics. This manuscript was submitted as part of a theme issue on “Modelling COVID-19 and Preparedness for Future Pandemics”.

A three-dimensional model to describe complete human corneal oxygenation during contact lens wear.

We perform a novel 3D study to quantify the corneal oxygen consumption and diffusion in each part of the cornea with different contact lens materials. The oxygen profile is calculated as a function of oxygen tension at the cornea-tear interface and the oxygen transmissibility of the lens, with values used in previous studies. We aim to determine the influence of a detailed geometry of the cornea in their modeling compared to previous low dimensional models used in the literature. To this end, a 3-D study based on an axisymmetric volume element analysis model was applied to different contact lenses currently on the market. We have obtained that the model provides a valuable tool for understanding the flux and cornea oxygen profiles through the epithelium, stroma, and endothelium. The most important results are related to the dependence of the oxygen flux through the cornea-lens system on the contact lens thickness and geometry. Both parameters play an important role in the corneal flux and oxygen tension distribution. The decline in oxygen consumption experienced by the cornea takes place just inside the epithelium, where the oxygen tension falls to between 95 and 16 mmHg under open eye conditions, and 30 to 0.3 mmHg under closed eye conditions, depending on the contact lens worn. This helps to understand the physiological response of the corneal tissue under conditions of daily and overnight contact lens wear, and the importance of detailed geometry of the cornea in the modeling of diffusion for oxygen and other species.

Supercritical and subcritical rotating convection in a horizontally periodic box with no-slip walls at the top and bottom

The study of instabilities in the convection of rotating fluids is one of the classical topics of research. However, in spite of more than five decades of research, the instabilities and related transition scenarios near the onset of rotating convection of low Prandtl number fluids are not well understood. Here, we investigate the transition scenario in rotating Rayleigh–Bénard convection with no-slip boundary conditions by performing 3D direct numerical simulations (DNS) and low-dimensional modeling. The governing parameters, namely, the Taylor number (Ta), Rayleigh number (Ra), and Prandtl number (Pr), are varied in the ranges 0<Ta≤8×103, 0<Ra<1×104, and 0<Pr≤0.35, where convection appears as a stationary cellular pattern. In DNS, for Pr<0.31, the supercritical or subcritical onset of convection appears, according as Ta>Tac(Pr) or Ta<Tac(Pr), where Tac(Pr) is a Pr dependent threshold of Ta. On the other hand, only supercritical onset of convection is observed for Pr≥0.31. At the subcritical onset, both finite amplitude stationary and time dependent solutions are manifested. The origin of these solutions are explained using a low dimensional model. DNS show that as Ra is increased beyond the onset of convection, the system becomes time dependent and depending on Pr, standing and traveling wave solutions are observed. For very small Pr (≤0.045), interestingly, finite amplitude time dependent solutions are manifested at the onset for higher Ta.

SNR Enhancement for Multi-TE MRSI Using Joint Low-Dimensional Model and Spatial Constraints.

We present a novel method to enhance the SNR for multi-TE MR spectroscopic imaging (MRSI) data by integrating learned nonlinear low-dimensional model and spatial constraints. A deep complex convolutional autoencoder (DCCAE) was developed to learn a nonlinear low-dimensional representation of the high-dimensional multi-TE 1H spectroscopy signals. The learned model significantly reduces the data dimension thus serving as an effective constraint for noise reduction. A reconstruction formulation was proposed to integrate the spatiospectral encoding model, the learned model, and a spatial constraint for an SNR-enhancing reconstruction from multi-TE data. The proposed method has been evaluated using both numerical simulations and in vivo brain MRSI experiments. The superior denoising performance of the proposed over alternative methods was demonstrated, both qualitatively and quantitatively. In vivo multi-TE data was used to assess the improved metabolite quantification reproducibility and accuracy achieved by the proposed method. We expect the proposed SNR-enhancing reconstruction to enable faster and/or higher-resolution multi-TE 1H-MRSI of the brain, potentially useful for various clinical applications.

Low-Dimensional Vector Representation Learning for Text Visualization Using Task-Oriented Dialogue Dataset

Text visualization is a complex technique that helps in data understanding and insight, and may lead to loss of information. Through the proposed low-dimensional vector representation learning method, deep learning and visualization through low-dimensional vector space construction were simultaneously performed. This method can transform a task-oriented dialogue dataset into low-dimensional coordinates, and based on this, a deep learning vector space can be constructed. The low-dimensional vector representation deep learning model found the intent of a sentence within a dataset and predicted the sentence components well in 3 out of 5 datasets. In addition, by checking the prediction results in the low-dimensional vector space, it was possible to improve the understanding of the data, such as identifying the structure or errors in the data.

Low-dimensional high-fidelity kinetic models for NOX formation by a compute intensification method

A novel compute intensification methodology to the construction of low-dimensional, high-fidelity “compact” kinetic models for NOX formation is designed and demonstrated. The method adapts the data intensive Machine Learned Optimisation of Chemical Kinetics (MLOCK) algorithm for compact model generation by the use of a combinatorial Latin Square method for virtual reaction network generation. A set of logical rules are defined which construct a minimally sized virtual reaction network comprising three additional nodes (N, NO, NO2). This NOX virtual reaction network is appended to a pre-existing compact model for methane combustion comprising fifteen nodes.The resulting eighteen node virtual reaction network is processed by the MLOCK coded algorithm to produce a plethora of compact model candidates for NOX formation during methane combustion. MLOCK automatically; populates the terms of the virtual reaction network with candidate inputs; measures the success of the resulting compact model candidates (in reproducing a broad set of gas turbine industry-defined performance targets); selects regions of input parameters space showing models of best performance; refines the input parameters to give better performance; and makes an ultimate selection of the best performing model or models.By this method, it is shown that a number of compact model candidates exist that show fidelities in excess of 75% in reproducing industry defined performance targets, with one model valid to >75% across fuel/air equivalence ratios of 0.5–1.0. However, to meet the full fuel/air equivalence ratio performance envelope defined by industry, we show that with this minimal virtual reaction network, two further compact models are required.

Do periods of decayless kink oscillations of solar coronal loops depend on noise?

ABSTRACT Decayless kink oscillations of solar coronal loops are studied in terms of a low-dimensional model based on a randomly driven Rayleigh oscillator with coefficients experiencing random fluctuations. The model considers kink oscillations as natural modes of coronal loops, decaying by linear resonant absorption. The damping is counteracted by random motions of the loop footpoints and the interaction of the loop with external quasi-steady flows with random fluctuations. In other words, the model combines the self-oscillatory and randomly driven mechanisms for the decayless behaviour. The random signals are taken to be of the stationary red noise nature. In the noiseless case, the model has an asymptotically stationary oscillatory solution, i.e. a kink self-oscillation. It is established that the kink oscillation period is practically independent of noise. This finding justifies the seismological estimations of the kink and Alfvén speeds, and the magnetic field in an oscillating loop by kink oscillations, based on the observed oscillation period. The oscillatory patterns are found to be almost harmonic. Noisy fluctuations of external flows modulate the amplitude of the almost monochromatic oscillatory pattern symmetrically, while random motions of the loop footpoints cause antisymmetric amplitude modulation. Such modulations are also consistent with the observed behaviour.

Committor Functions for Climate Phenomena at the Predictability Margin: The Example of El Niño–Southern Oscillation in the Jin and Timmermann Model

Abstract Many atmosphere and climate phenomena lie in the gray zone between weather and climate: they are not amenable to deterministic forecast, but they still depend on the initial condition. A natural example is medium-range forecasting, which is inherently probabilistic because it lies beyond the deterministic predictability time of the atmosphere, but for which statistically significant prediction can be made, which depends on the current state of the system. Similarly, one may ask the probability of occurrence of an El Niño event several months ahead of time. We introduce a quantity that corresponds precisely to this type of prediction problem: the committor function is the probability that an event takes place within a given time window, as a function of the initial condition. We compute it in the case of a low-dimensional stochastic model for El Niño, the Jin and Timmermann model. In this context, we show that the ability to predict the probability of occurrence of the event of interest may differ strongly depending on the initial state. The main result is the new distinction between probabilistic predictability (when the committor function is smooth and probability can be computed, which does not depend sensitively on the initial condition) and probabilistic unpredictability (when the committor function depends sensitively on the initial condition). We also demonstrate that the Jin and Timmermann model might be the first example of a stochastic differential equation with weak noise for which transition between attractors does not follow the Arrhenius law, which is expected based on large deviation theory and generic hypothesis. Significance Statement A key problem for atmospheric and climate phenomena is to predict events beyond the time scale over which deterministic weather forecast is possible. In a simple model of El Niño, we demonstrate the existence of two regimes, depending on initial conditions. For initial conditions in the “probabilistic predictability” regime, the system is unpredictable deterministically because of chaos, but the probability of occurrence of the event can still be predicted because it depends only weakly on the initial condition. In the “probabilistic unpredictability” regime, even predicting probabilities is difficult, because the probability depends strongly on initial conditions. These new concepts of probabilistic predictability and unpredictability should be key in understanding the predictability potential for rare events in climate problems, as well as in other complex dynamics.

The first International Conference on Mechanical System Dynamics grandly convened in Nanjing, China

The first International Conference on Mechanical System Dynamics grandly convened in Nanjing, China

A non-knotty inflation risk premium model

ABSTRACT In this article, I estimate the inflation risk premium (IRP) using a low-dimensional arbitrage-free dynamic model through a novel strategy. Instead of modelling the nominal and real yields jointly, I make assumptions about the short-term inflation rate. More specifically, I assume it follows a Gaussian process. This framework has a closed-form expression for IRP. Since inflation yields are not observed, to estimate the model parameters I approximate them by the break-even inflation rate. This approximation works well because the convexity correction is very small. I find that the estimated IRP is strongly correlated with those obtained using surveys or more complex models. Therefore, I provide an easier procedure to obtain IRP, avoiding the cumbersome estimation process of high-order models.

Three-dimensional fully coupled hydro-mechanical-chemical model for solute transport under mechanical and osmotic loading conditions

Mechanical deformation and chemico-osmotic consolidation of clay liners can change its intrinsic transport properties in all direction and can alter fluid and solute transport processes in the entire model domain. These phenomena are described inadequately by lower-dimensional models. Based on the Biot’s consolidation theory, fluid and solute mass conservation equations, a three-dimensional (3D) fully-coupled hydro-mechanical-chemical (HMC) model has been proposed in this study. The impacts of mechanical consolidation and chemico-osmotic consolidation on permeability, hydrodynamic dispersion, solute sorption, membrane efficiency, and chemical osmosis are considered in the model. The model is applied to evaluate performances of a single compacted clay liner (CCL) and a damaged geomembrane-compacted clay composite liner (GMB/CCL) to contain a generic landfill contaminant. Effect of model dimensionality on solute spread for CCL is found to be marginal, but for GMB/CCL the effect is significantly large. After 50-year simulation period, solute concentration at the half-length of the GMB/CCL liner is predicted to be 40% of the source concentration during 1D simulation, which is only 6% during the 3D simulation. The results revealed approximately 74% over-estimation of liner settlement in 1D simulation than that of the 3D for GMB/CL system. Solute spread accelerates (over-estimates) vertically than horizontally since overburden load and consequent mechanical loading-induced solute convection occurs in the same direction. However, in homogeneous and isotropic soils, horizontal spread retards the overall migration of contaminants, and it highlights the importance of 3D models to study solute transports under mechanical and chemico-osmotic loading conditions in semi-permeable clays, especially, for damaged geomembrane-clay liners. The results show the utility of geomembranes to reduce soil settlement, undulation, and restriction of solute migration. Furthermore, application of geomembrane can inhibit development of elevated negative excess pore water pressure at deeper portion of a clay liner.

Using scientific machine learning for experimental bifurcation analysis of dynamic systems

Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is a novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and reality through measurement data. Our exploratory study focuses on training universal differential equation (UDE) models for physical nonlinear dynamical systems with limit cycles: an aerofoil undergoing flutter oscillations and an electrodynamic nonlinear oscillator. We consider examples where training data is generated by numerical simulations, whereas we also employ the proposed modelling concept to physical experiments allowing us to investigate problems with a wide range of complexity. To collect the training data, the method of control-based continuation is used as it captures not just the stable but also the unstable limit cycles of the observed system. This feature makes it possible to extract more information about the observed system than the open-loop approach (surveying the steady state response by parameter sweeps without using control) would allow. We use both neural networks and Gaussian processes as universal approximators alongside the mechanistic models to give a critical assessment of the accuracy and robustness of the UDE modelling approach. We also highlight the potential issues one may run into during the training procedure indicating the limits of the current modelling framework.

Universal dynamics of heavy operators in boundary CFT2

We derive a universal asymptotic formula for generic boundary conditions for the average value of the bulk-to-boundary and boundary Operator Product Expansion coefficients of any unitary, compact two-dimensional Boundary CFT (BCFT) with c > 1. The asymptotic limit consists of taking one or more boundary primary operators — which transform under a single copy of the Virasoro algebra — to have parametrically large conformal dimension for fixed central charge. In particular, we find a single universal expression that interpolates between distinct heavy regimes, exactly as in the case of bulk OPE asymptotics [1]. The expression depends universally on the boundary entropy and the central charge, and not on any other details of the theory. We derive these asymptotics by studying crossing symmetry of various correlation functions on higher genus Riemann surfaces with open boundaries. Essential in the derivation is the use of the irrational versions of the crossing kernels that relate holomorphic Virasoro blocks in different channels. Our results strongly suggest an extended version of the Eigenstate Thermalization Hypothesis for boundary OPE coefficients, where the hierarchy between the diagonal and non-diagonal term in the ansatz is further controlled by the boundary entropy. We finally comment on the applications of our results in the context of AdS3/BCFT2, as well as on the recent relation of BCFTs with lower dimensional models of evaporating black holes.

Combining the neural mass model and Hodgkin–Huxley formalism: Neuronal dynamics modelling

Epilepsy is a neurological disorder that affects the nervous system and is characterized by recurrent seizures. Experimental data shows that increase in the extracellular potassium concentration can support the generation of seizures and that the T-type calcium channel antagonists can be effective as anti-epileptic drugs. To investigate these two phenomena in detail, we combine microscopic level modelling using Hodgkin–Huxley formalism and a macroscopic level approach using a neural mass model. The microscopic level approach describes the initiation of action potentials in individual neurons using conductance-based model. The macroscopic (neural mass model) approach is a low-dimensional phenomenological model that describes the activity of a large population of neurons. The neural mass model replicated the interactions between inhibitory and excitatory neuronal populations by using a sigmoidal function that converts neuronal postsynaptic potential into the average spiking rate of a given population. This sigmoidal function links two levels of modelling: microscopic and macroscopic. Our results are in agreement with experimental data and show that an increase in the extracellular potassium concentration or an increase in the T-type calcium conductance can cause brain network transitions from normal background to pathological seizure-like dynamics. In addition, the results show that these transitions only happen for a limited range of network parameters and that the slow-inhibitory synaptic gain has a stronger effect on network dynamics during transitions than the fast-inhibitory synaptic gain.

Development and Validation of a Novel Control-Volume Model for the Injection Flow in a Variable Cycle Engine

The variable area bypass injector (VABI) plays a crucial role in variable cycle engines by regulating the flow mixing process in complex bypass ducts, and low-dimensional theoretical models are the key to revealing its working mechanism while estimating its aerodynamic performance. An improved VABI model using the control volume method is established, through which the feature parameters that determine the VABI aerodynamic performance are summarized. To acquire an accurate prediction of the injection ratio, a calibration item is introduced to the governing equations to consider the static pressure discrepancy on the mixing plane, and a numerical database is developed to obtain the calibration item. Results show that the aerodynamic parameters that determine the VABI performance include the bypass total pressure ratio, bypass backpressure, and the injection ratio, while the injection angle and the VABI opening area also influence the injection flow characteristics. The injection ratio is increased by reducing the bypass total pressure ratio, decreasing the bypass backpressure, and closing the VABI. Numerical validation shows that the calculation error of the improved model is generally below 3%. The improved VABI model is then validated by a well-arranged experiment, for which the annular flow is simplified into a rectangular duct flow with an error of less than 5%. The experimental validation also proves the accuracy of the model.

DC conductance and memory in 3D gravity

Transport properties are investigated in the two-dimensional dual dynamics of AdS3 gravity. By providing boundary conditions that deform the ADM lapse and shift functions, we construct a lower dimensional model comprising two copies of chiral boson excitations with anisotropic scaling symmetry. Using bosonization, an electric current is identified. By means of the Kubo formula, we find a DC conductance depending on the level of the theory and the dynamical exponents. The bulk realization of the linear response is related to a type of gravitational memory emerging in the context of near-horizon boundary conditions. The process is adiabatic and represents a permanent spacetime deformation parametrized by anisotropic chiral bosons through a large gauge transformation.

Electron heating in 2D: Combining Fermi–Ulam acceleration and magnetic-moment non-adiabaticity in a mirror-configuration plasma

We analyze a new mechanism for the creation and confinement of energetic electrons in a mirror-configuration plasma. A Fermi–Ulam-type process, driven by end-localized coherent electrostatic oscillations, provides axial acceleration, while a natural non-adiabaticity of μ provides phase decorrelation and energy isotropization. This novel 2D combination causes the electron energy distribution function, calculated with a diffusive-loss model, to assume a Maxwellian shape with the μ non-adiabaticity, reducing loss-cone escape and annulling the absolute-barrier energy-limiting Chirikov criterion of lower dimensional models. The theoretical predictions are compared with data from an experiment.

Characteristics of Earthquake Cycles: A Cross-Dimensional Comparison of 0D to 3D Numerical Models.

High‐resolution computer simulations of earthquake sequences in three or even two dimensions pose great demands on time and energy, making lower‐cost simplifications a competitive alternative. We systematically study the advantages and limitations of simplifications that eliminate spatial dimensions in quasi‐dynamic earthquake sequence models, from 3D models with a 2D fault plane down to 0D or 1D models with a 0D fault point. We demonstrate that, when 2D or 3D models produce quasi‐periodic characteristic earthquakes, their behavior is qualitatively similar to lower‐dimension models. Certain coseismic characteristics like stress drop and fracture energy are largely controlled by frictional parameters and are thus largely comparable. However, other observations are quantitatively clearly affected by dimension reduction. We find corresponding increases in recurrence interval, coseismic slip, peak slip velocity, and rupture speed. These changes are to a large extent explained by the elimination of velocity‐strengthening patches that transmit tectonic loading onto the velocity‐weakening fault patch, thereby reducing the interseismic stress rate and enhancing the slip deficit. This explanation is supported by a concise theoretical framework, which explains some of these findings quantitatively and effectively estimates recurrence interval and slip. Through accounting for an equivalent stressing rate at the nucleation size h* into 2D and 3D models, 0D or 1D models can also effectively simulate these earthquake cycle parameters. Given the computational efficiency of lower‐dimensional models that run more than a million times faster, this paper aims to provide qualitative and quantitative guidance on economical model design and interpretation of modeling studies.

A reliability analysis method based on adaptive Kriging and partial least squares

In recent years, reliability analysis based on adaptive Kriging (AK) has been extensively studied. However, constructing the Kriging model of high-dimensional systems during adaptive learning faces huge computational challenges. This paper combines partial least squares (PLS) with AK to develop an efficient method for reliability analysis of high-dimensional systems, which is named as PLS-AK. The proposed method takes PLS algorithm as the dimensionality reduction (DR) technique of high-dimensional input variables. Then, in the reduced space of input principal components (PCs), a low-dimensional Kriging model is constructed with U learning function for reliability analysis. Since PLS usually requires adequate samples to determine the latent relationship between input and output variables, using too many initial samples before adaptive learning will weaken the advantages of AK. To avoid this problem, this paper also proposes a synchronous updating method for both the projection direction and AK model. In this way, only a few initial samples are required to determine the initial input projection, and the input projection will be updated and converge gradually as the number of training samples increases. At last, three examples can prove the effectiveness of the proposed PLS-AK method.

Contextuality in infinite one-dimensional translation-invariant local Hamiltonians

In recent years there has been a growing interest in treating many-body systems as Bell scenarios, where lattice sites play the role of distant parties and only near-neighbor statistics are accessible. We investigate contextuality arising from three Bell scenarios in infinite, translation-invariant 1D models: nearest-neighbor with two dichotomic observables per site; nearest- and next-to-nearest neighbor with two dichotomic observables per site, and nearest-neighbor with three dichotomic observables per site. For the first scenario, we give strong evidence that it cannot exhibit contextuality, not even in non-signaling physical theories beyond quantum mechanics. For the second one, we identify several low-dimensional models that reach the ultimate quantum limits, paving the way for self-testing ground states of quantum many-body systems. For the last scenario, which generalizes the Heisenberg model, we give strong evidence that, in order to exhibit contextuality, the dimension of the local quantum system must be at least 3.