Inference Of Dynamics Research Articles

Correlations in microbial abundance data reveal host-bacteria and bacteria-bacteria interactions jointly shaping the C. elegans microbiome

Compositional structure of host-associated microbiomes is potentially affected by interactions among the microbes and between the microbes and the host. To quantify the relative importance of these contributions to the microbiome composition and variation, here we analyze absolute abundance (count) data for a minimal eight-species native microbiome in the intestine. We find that a simple neutral model only considering migration, birth, death, and competition for space among the bacteria can capture the means and variances of bacterial abundance, but not the experimental bacteria-bacteria covariances. We find that either bacteria-bacteria interactions or correlations among bacterial population dynamics parameters induced by the host can qualitatively recapitulate the observed correlations among bacterial taxa. However, both models are underdetermined and not unique, and the combination of both mechanisms likely contributes. This highlights that single time-point measurements on their own are not sufficient to distinguish between two distinct biological mechanisms. Further, we observe that different interactions are required to explain (co)variance data in microbiota associated with different host genotypes, suggesting different community dynamics associated with these host types. Finally, we find that many of these signals are obscured when data are converted to proportions from counts, consistent with a growing literature on the limitations of compositional data for inference of population dynamics. We end with a discussion of the limitations of Lotka-Volterra type assumptions for microbial community data analysis revealed by our results. Published by the American Physical Society 2024

Taking cues from ecological and evolutionary theories to expand the landscape of disgust.

Behavioural avoidance of parasites in the environment generates what is known as the 'landscape of disgust' (analogous to the predator-induced 'landscape of fear'). Despite the potential for improving our inference of host-parasite dynamics, three limitations of the landscape of disgust restrict the insight that is gained from current research: (i) many host-parasite systems will not be appropriate for invoking the landscape of disgust framework; (ii) existing research has primarily focused on immediate choices made by hosts on small scales, limiting predictive power, generalizability, and the value of the insight obtained; and (iii) relevant ecological and evolutionary theory has yet to be integrated into the framework, challenging our ability to interpret the landscape of disgust within the context of most host-parasite systems. In this review, we explore the specific requirements for implementing a landscape of disgust framework in empirical systems. We also propose greater integration of habitat selection and evolutionary theories, aiming to generate novel insight, by exploring how the landscape of disgust varies within and across generations, presenting opportunities for future research. Despite interest in the impacts of parasitism on animal movement and behaviour, many unanswered questions remain.

Deep neural networks for endemic measles dynamics: Comparative analysis and integration with mechanistic models.

Measles is an important infectious disease system both for its burden on public health and as an opportunity for studying nonlinear spatio-temporal disease dynamics. Traditional mechanistic models often struggle to fully capture the complex nonlinear spatio-temporal dynamics inherent in measles outbreaks. In this paper, we first develop a high-dimensional feed-forward neural network model with spatial features (SFNN) to forecast endemic measles outbreaks and systematically compare its predictive power with that of a classical mechanistic model (TSIR). We illustrate the utility of our model using England and Wales measles data from 1944-1965. These data present multiple modeling challenges due to the interplay between metapopulations, seasonal trends, and nonlinear dynamics related to demographic changes. Our results show that while the TSIR model yields similarly performant short-term (1 to 2 biweeks ahead) forecasts for highly populous cities, our neural network model (SFNN) consistently achieves lower root mean squared error (RMSE) across other forecasting windows. Furthermore, we show that our spatial-feature neural network model, without imposing mechanistic assumptions a priori, can uncover gravity-model-like spatial hierarchy of measles spread in which major cities play an important role in driving regional outbreaks. We then turn our attention to integrative approaches that combine mechanistic and machine learning models. Specifically, we investigate how the TSIR can be utilized to improve a state-of-the-art approach known as Physics-Informed-Neural-Networks (PINN) which explicitly combines compartmental models and neural networks. Our results show that the TSIR can facilitate the reconstruction of latent susceptible dynamics, thereby enhancing both forecasts in terms of mean absolute error (MAE) and parameter inference of measles dynamics within the PINN. In summary, our results show that appropriately designed neural network-based models can outperform traditional mechanistic models for short to long-term forecasts, while simultaneously providing mechanistic interpretability. Our work also provides valuable insights into more effectively integrating machine learning models with mechanistic models to enhance public health responses to measles and similar infectious disease systems.

Dynamical Counterfactual Inference under Time-series Model for Waterflooding Oilfield

The performances of numerical simulation and machine learning in production forecasting are severely dependent on precise geological modeling and high-quality history matching. To address these challenges, causal inference is an effective methodology since it can provide a causality for formalizing causality in history, not statistical dependence. In this paper, to dynamically predict oil production from causality existed in waterflooding oilfield, a dynamical counterfactual inference framework is built to predict oil production. The proposed framework can forecast the oil production under non-observation of engineering factors, i.e., counterfactual, and provide the causal effect of engineering factors impacting on oil production. Meanwhile, combining with the practice exploitation in engineering factor impacting on production, a counterfactual experiment is designed to execute counterfactual prediction. Compared with general machine learning and statistical models, our results not only show better performance in oil production flooding but also guide the specific optimization in improving production, which holds more practical application significance.

Accounting for cellular-level variation in lysis: implications for virus-host dynamics.

Viral impacts on microbial populations depend on interaction phenotypes-including viral traits spanning the adsorption rate, latent period, and burst size. The latent period is a key viral trait in lytic infections. Defined as the time from viral adsorption to viral progeny release, the latent period of bacteriophage is conventionally inferred via one-step growth curves in which the accumulation of free virus is measured over time in a population of infected cells. Developed more than 80 years ago, one-step growth curves do not account for cellular-level variability in the timing of lysis, potentially biasing inference of viral traits. Here, we use nonlinear dynamical models to understand how individual-level variation of the latent period impacts virus-host dynamics. Our modeling approach shows that inference of the latent period via one-step growth curves is systematically biased-generating estimates of shorter latent periods than the underlying population-level mean. The bias arises because variability in lysis timing at the cellular level leads to a fraction of early burst events, which are interpreted, artefactually, as an earlier mean time of viral release. We develop a computational framework to estimate latent period variability from joint measurements of host and free virus populations. Our computational framework recovers both the mean and variance of the latent period within simulated infections including realistic measurement noise. This work suggests that reframing the latent period as a distribution to account for variability in the population will improve the study of viral traits and their role in shaping microbial populations.IMPORTANCEQuantifying viral traits-including the adsorption rate, burst size, and latent period-is critical to characterize viral infection dynamics and develop predictive models of viral impacts across scales from cells to ecosystems. Here, we revisit the gold standard of viral trait estimation-the one-step growth curve-to assess the extent to which assumptions at the core of viral infection dynamics lead to ongoing and systematic biases in inferences of viral traits. We show that latent period estimates obtained via one-step growth curves systematically underestimate the mean latent period and, in turn, overestimate the rate of viral killing at population scales. By explicitly incorporating trait variability into a dynamical inference framework that leverages both virus and host time series, we provide a practical route to improve estimates of the mean and variance of viral traits across diverse virus-microbe systems.

Machine Learning Approaches for 3D Motion Synthesis and Musculoskeletal Dynamics Estimation: A Survey.

The inference of 3D motion and dynamics of the human musculoskeletal system has traditionally been solved using physics-based methods that exploit physical parameters to provide realistic simulations. Yet, such methods suffer from computational complexity and reduced stability, hindering their use in computer graphics applications that require real-time performance. With the recent explosion of data capture (mocap, video) machine learning (ML) has started to become popular as it is able to create surrogate models harnessing the huge amount of data stemming from various sources, minimizing computational time (instead of resource usage), and most importantly, approximate real-time solutions. The main purpose of this paper is to provide a review and classification of the most recent works regarding motion prediction, motion synthesis as well as musculoskeletal dynamics estimation problems using ML techniques, in order to offer sufficient insight into the state-of-the-art and draw new research directions. While the study of motion may appear distinct to musculoskeletal dynamics, these application domains provide jointly the link for more natural computer graphics character animation, since ML-based musculoskeletal dynamics estimation enables modeling of more long-term, temporally evolving, ergonomic effects, while offering automated and fast solutions. Overall, our review offers an in-depth presentation and classification of ML applications in human motion analysis, unlike previous survey articles focusing on specific aspects of motion prediction.

B-BIND: Biophysical Bayesian Inference for Neurodegenerative Dynamics.

Throughout an organism's life, a multitude of complex and interdependent biological systems transition through biophysical processes that serve as indicators of the underlying biological states. Inferring these latent, unobserved states is a goal of modern biology and neuroscience. However, in many experimental setups, we can at best obtain discrete snapshots of the system at different times and for different individuals. This challenge is particularly relevant in the study of Alzheimer's Disease (AD) progression, where we observe the aggregation of pathology in brain donors, but the underlying disease state is unknown. This paper proposes a biophysically motivated Bayesian framework (B-BIND: Biophysical Bayesian Inference for Neurodegenerative Dynamics), where the disease state is modeled and continuously inferred from observed quantifications of multiple AD pathological proteins. Inspired by biophysical models, we describe pathological burden as an exponential process. The progression of AD is modeled by assigning a latent score, termed pseudotime, to each pathological state, creating a pseudotemporal order of donors based on their pathological burden. We study the theoretical properties of the model using linearization to reveal convergence and identifiability properties. We provide Markov chain Monte Carlo estimation algorithms, illustrating the effectiveness of our approach with multiple simulation studies across various data conditions. Applying this methodology to data from the Seattle Alzheimer's Disease Brain Cell Atlas, we infer the pseudotime ordering of donors. Finally, we analyze the information within each pathological feature to refine the model, focusing on the most informative pathologies. This framework lays the groundwork for continuous pseudotime modeling in the analysis of neurodegenerative diseases.

Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees

The growing time-series data make it possible to glimpse the hidden dynamics in various fields. However, developing a computational toolbox with high interpretability to unveil the interaction dynamics from data remains a crucial challenge. Here, we propose a new computational approach called automated dynamical model inference based on expression trees (ADMIET), in which the machine learning algorithm, the numerical integration of ordinary differential equations and the interpretability from prior knowledge are embedded into the symbolic learning scheme to establish a general framework for revealing the hidden dynamics in time-series data. ADMIET takes full advantage of both machine learning algorithm and expression tree. Firstly, we translate the prior knowledge into constraints on the structure of expression tree, reducing the search space and enhancing the interpretability. Secondly, we utilize the proposed adaptive penalty function to ensure the convergence of gradient descent algorithm and the selection of the symbols. Compared to gene expression programming, ADMIET exhibits its remarkable capability in function fitting with higher accuracy and broader applicability. Moreover, ADMIET can better fit parameters in nonlinear forms compared to regression methods. Furthermore, we apply ADMIET to two typical biological systems and one real data with different prior knowledge to infer the dynamical equations. The results indicate that ADMIET can not only discover the interaction relationships but also provide accurate estimates of the parameters in the equations. These results demonstrate ADMIET’s superiority in revealing interpretable dynamics from time-series biological data.

Deep learning accelerated numerical simulation for three-dimensional compressible fluids

Numerical simulation of fluid flow is a long-standing challenge across many physical application domains, including engineering, climate, and the physical science. There has been a surge of interest in high order schemes aimed at improving simulation accuracy on coarse grids. However, for high-dimensional fluids, the computational cost escalates with the number of dimensions involved. In this paper, we propose a deep learning-based approach to accelerate the numerical computation and further improve the accuracy in simulating three-dimensional (3D) compressible fluids which can be described by Eulerian equations. The proposed work utilizes 3D Euler transformer networks to learn the interpolation coefficients for cell boundaries, which are applied to approximate the boundary fluxes of fluid on coarser grids. Benefiting from learning features of high-resolution fluid flow, our learned interpolation method yields finer performance on coarse grids, thereby accelerating the fluid simulations and improving the numerical accuracy. The numerical experiments confirm that the proposed method improves performance in inference of coarse-grained dynamics.

Semiparametric inference of effective reproduction number dynamics from wastewater pathogen surveillance data.

Concentrations of pathogen genomes measured in wastewater have recently become available as a new data source to use when modeling the spread of infectious diseases. One promising use for this data source is inference of the effective reproduction number, the average number of individuals a newly infected person will infect. We propose a model where new infections arrive according to a time-varying immigration rate which can be interpreted as an average number of secondary infections produced by one infectious individual per unit time. This model allows us to estimate the effective reproduction number from concentrations of pathogen genomes, while avoiding difficulty to verify assumptions about the dynamics of the susceptible population. As a byproduct of our primary goal, we also produce a new model for estimating the effective reproduction number from case data using the same framework. We test this modeling framework in an agent-based simulation study with a realistic data generating mechanism which accounts for the time-varying dynamics of pathogen shedding. Finally, we apply our new model to estimating the effective reproduction number of SARS-CoV-2, the causative agent of COVID-19, in Los Angeles, CA, using pathogen RNA concentrations collected from a large wastewater treatment facility.

The Inverse of Exact Renormalization Group Flows as Statistical Inference.

We build on the view of the Exact Renormalization Group (ERG) as an instantiation of Optimal Transport described by a functional convection-diffusion equation. We provide a new information-theoretic perspective for understanding the ERG through the intermediary of Bayesian Statistical Inference. This connection is facilitated by the Dynamical Bayesian Inference scheme, which encodes Bayesian inference in the form of a one-parameter family of probability distributions solving an integro-differential equation derived from Bayes' law. In this note, we demonstrate how the Dynamical Bayesian Inference equation is, itself, equivalent to a diffusion equation, which we dub Bayesian Diffusion. By identifying the features that define Bayesian Diffusion and mapping them onto the features that define the ERG, we obtain a dictionary outlining how renormalization can be understood as the inverse of statistical inference.

Exact Inference for Continuous-Time Gaussian Process Dynamics

Many physical systems can be described as a continuous-time dynamical system. In practice, the true system is often unknown and has to be learned from measurement data. Since data is typically collected in discrete time, e.g. by sensors, most methods in Gaussian process (GP) dynamics model learning are trained on one-step ahead predictions. While this scheme is mathematically tempting, it can become problematic in several scenarios, e.g. if measurements are provided at irregularly-sampled time steps or physical system properties have to be conserved. Thus, we aim for a GP model of the true continuous-time dynamics. We tackle this task by leveraging higher-order numerical integrators. These integrators provide the necessary tools to discretize dynamical systems with arbitrary accuracy. However, most higher-order integrators require dynamics evaluations at intermediate time steps, making exact GP inference intractable. In previous work, this problem is often addressed by approximate inference techniques. However, exact GP inference is preferable in many scenarios, e.g. due to its mathematical guarantees. In order to enable direct inference, we propose to leverage multistep and Taylor integrators. We demonstrate how exact inference schemes can be derived for these types of integrators. Further, we derive tailored sampling schemes that allow one to draw consistent dynamics functions from the posterior. The learned model can thus be integrated with arbitrary integrators, just like a standard dynamical system. We show empirically and theoretically that our approach yields an accurate representation of the continuous-time system.

Dynamical flexible inference of nonlinear latent factors and structures in neural population activity.

Modelling the spatiotemporal dynamics in the activity of neural populations while also enabling their flexible inference is hindered by the complexity and noisiness of neural observations. Here we show that the lower-dimensional nonlinear latent factors and latent structures can be computationally modelled in a manner that allows for flexible inference causally, non-causally and in the presence of missing neural observations. To enable flexible inference, we developed a neural network that separates the model into jointly trained manifold and dynamic latent factors such that nonlinearity is captured through the manifold factors and the dynamics can be modelled in tractable linear form on this nonlinear manifold. We show that the model, which we named 'DFINE' (for 'dynamical flexible inference for nonlinear embeddings') achieves flexible inference in simulations of nonlinear dynamics and across neural datasets representing a diversity of brain regions and behaviours. Compared with earlier neural-network models, DFINE enables flexible inference, better predicts neural activity and behaviour, and better captures the latent neural manifold structure. DFINE may advance the development of neurotechnology and investigations in neuroscience.

Inference of transmission dynamics and retrospective forecast of invasive meningococcal disease.

The pathogenic bacteria Neisseria meningitidis, which causes invasive meningococcal disease (IMD), predominantly colonizes humans asymptomatically; however, invasive disease occurs in a small proportion of the population. Here, we explore the seasonality of IMD and develop and validate a suite of models for simulating and forecasting disease outcomes in the United States. We combine the models into multi-model ensembles (MME) based on the past performance of the individual models, as well as a naive equally weighted aggregation, and compare the retrospective forecast performance over a six-month forecast horizon. Deployment of the complete vaccination regimen, introduced in 2011, coincided with a change in the periodicity of IMD, suggesting altered transmission dynamics. We found that a model forced with the period obtained by local power wavelet decomposition best fit and forecast observations. In addition, the MME performed the best across the entire study period. Finally, our study included US-level data until 2022, allowing study of a possible IMD rebound after relaxation of non-pharmaceutical interventions imposed in response to the COVID-19 pandemic; however, no evidence of a rebound was found. Our findings demonstrate the ability of process-based models to retrospectively forecast IMD and provide a first analysis of the seasonality of IMD before and after the complete vaccination regimen.

Bayesian inference of polymerase dynamics over the exclusion process.

Transcription is a complex phenomenon that permits the conversion of genetic information into phenotype by means of an enzyme called RNA polymerase, which erratically moves along and scans the DNA template. We perform Bayesian inference over a paradigmatic mechanistic model of non-equilibrium statistical physics, i.e. the asymmetric exclusion processes in the hydrodynamic limit, assuming a Gaussian process prior for the polymerase progression rate as a latent variable. Our framework allows us to infer the speed of polymerases during transcription given their spatial distribution, while avoiding the explicit inversion of the system's dynamics. The results, which show processing rates strongly varying with genomic position and minor role of traffic-like congestion, may have strong implications for the understanding of gene expression.

ScTour: a deep learning architecture for robust inference and accurate prediction of cellular dynamics

Despite the continued efforts, a batch-insensitive tool that can both infer and predict the developmental dynamics using single-cell genomics is lacking. Here, I present scTour, a novel deep learning architecture to perform robust inference and accurate prediction of cellular dynamics with minimal influence from batch effects. For inference, scTour simultaneously estimates the developmental pseudotime, delineates the vector field, and maps the transcriptomic latent space under a single, integrated framework. For prediction, scTour precisely reconstructs the underlying dynamics of unseen cellular states or a new independent dataset. scTour’s functionalities are demonstrated in a variety of biological processes from 19 datasets.

Single-cell Ca2+ parameter inference reveals how transcriptional states inform dynamic cell responses.

Single-cell genomic technologies offer vast new resources with which to study cells, but their potential to inform parameter inference of cell dynamics has yet to be fully realized. Here we develop methods for Bayesian parameter inference with data that jointly measure gene expression and Ca2+ dynamics in single cells. We propose to share information between cells via transfer learning: for a sequence of cells, the posterior distribution of one cell is used to inform the prior distribution of the next. In application to intracellular Ca2+ signalling dynamics, we fit the parameters of a dynamical model for thousands of cells with variable single-cell responses. We show that transfer learning accelerates inference with sequences of cells regardless of how the cells are ordered. However, only by ordering cells based on their transcriptional similarity can we distinguish Ca2+ dynamic profiles and associated marker genes from the posterior distributions. Inference results reveal complex and competing sources of cell heterogeneity: parameter covariation can diverge between the intracellular and intercellular contexts. Overall, we discuss the extent to which single-cell parameter inference informed by transcriptional similarity can quantify relationships between gene expression states and signalling dynamics in single cells.

Neural Cross-Frequency Coupling Functions in Sleep

The human brain presents a heavily connected complex system. From a relatively fixed anatomy, it can enable a vast repertoire of functions. One important brain function is the process of natural sleep, which alters consciousness and voluntary muscle activity. On neural level, these alterations are accompanied by changes of the brain connectivity. In order to reveal the changes of connectivity associated with sleep, we present a methodological framework for reconstruction and assessment of functional interaction mechanisms. By analyzing EEG (electroencephalogram) recordings from human whole night sleep, first, we applied a time–frequency wavelet transform to study the existence and strength of brainwave oscillations. Then we applied a dynamical Bayesian inference on the phase dynamics in the presence of noise. With this method we reconstructed the cross-frequency coupling functions, which revealed the mechanism of how the interactions occur and manifest. We focus our analysis on the delta-alpha coupling function and observe how this cross-frequency coupling changes during the different sleep stages. The results demonstrated that the delta-alpha coupling function was increasing gradually from Awake to NREM3 (non-rapid eye movement), but only during NREM2 and NREM3 deep sleep it was significant in respect of surrogate data testing. The analysis on the spatially distributed connections showed that this significance is strong only for within the single electrode region and in the front-to-back direction. The presented methodological framework is for the whole-night sleep recordings, but it also carries general implications for other global neural states.

Dynamic models for musical rhythm perception and coordination.

Rhythmicity permeates large parts of human experience. Humans generate various motor and brain rhythms spanning a range of frequencies. We also experience and synchronize to externally imposed rhythmicity, for example from music and song or from the 24-h light-dark cycles of the sun. In the context of music, humans have the ability to perceive, generate, and anticipate rhythmic structures, for example, "the beat." Experimental and behavioral studies offer clues about the biophysical and neural mechanisms that underlie our rhythmic abilities, and about different brain areas that are involved but many open questions remain. In this paper, we review several theoretical and computational approaches, each centered at different levels of description, that address specific aspects of musical rhythmic generation, perception, attention, perception-action coordination, and learning. We survey methods and results from applications of dynamical systems theory, neuro-mechanistic modeling, and Bayesian inference. Some frameworks rely on synchronization of intrinsic brain rhythms that span the relevant frequency range; some formulations involve real-time adaptation schemes for error-correction to align the phase and frequency of a dedicated circuit; others involve learning and dynamically adjusting expectations to make rhythm tracking predictions. Each of the approaches, while initially designed to answer specific questions, offers the possibility of being integrated into a larger framework that provides insights into our ability to perceive and generate rhythmic patterns.

Non-invasive monitoring of tomato graft dynamics using thermography and fluorescence quantum yields measurements.

Grafting involves a sequence of modifications that may vary according to genotypes, grafting techniques and growing conditions. This process is often monitored using destructive methods, precluding the possibility of monitoring the entire process in the same grafted plant. The aim of this study was to test the effectiveness of two non-invasive methods -thermographic inference of transpiration and determination of chlorophyll quantum yields- for monitoring graft dynamics in tomato (Solanum lycopersicum L.) autografts, and to compare the results with other reliable measures: mechanical resistance parameters and xylem water potential. The mechanical resistance of grafted plants steadily increased from 6 days after grafting (DAG), 4.90±0.57 N/mm, to reach values similar to non-grafted plants at 16 DAG, 8.40±1.78 N/mm. Water potential showed an early decrease (from -0.34±0.16 MPa in non-grafted plants to -0.88±0.07 MPa at 2 DAG), recovering at 4 DAG to reach pre-grafting values at 12-16 DAG. Thermographic inference of transpiration dynamics displayed comparable changes. Monitoring maximum and effective quantum yield in functional grafts showed a comparable pattern: an initial decline, followed by recovery from 6 DAG onwards. Correlation analyses revealed a significant correlation between variation in temperature (thermographic monitoring of transpiration), water potential (r = 0.87; p = 0.02) and maximum tensile force (r = 0.75; p = 0.05). Additionally, we found a significant correlation between maximum quantum yield and some mechanical parameters. In conclusion, thermography monitoring, and to a lesser extent maximum quantum yield measurements, accurately depict changes in key parameters in grafted plants and serve as potential timing indicators of graft regeneration, rendering them valuable tools for monitoring graft functionality.