A variant-dependent molecular clock with anomalous diffusion models SARS-CoV-2 evolution in humans.

The evolution of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in humans has been monitored at an unprecedented level due to the public health crisis, yet the stochastic dynamics underlying such a process is dubious. Here, considering the number of acquired mutations as the displacement of the viral particle from the origin, we performed biostatistical analyses from numerous whole genome sequences on the basis of a time-dependent probabilistic mathematical model. We showed that a model with a constant variant-dependent evolution rate and nonlinear mutational variance with time (i.e., anomalous diffusion) explained the SARS-CoV-2 evolutionary motion in humans during the first 120 wk of the pandemic in the United Kingdom. In particular, we found subdiffusion patterns for the Primal, Alpha, and Omicron variants but a weak superdiffusion pattern for the Delta variant. Our findings indicate that non-Brownian evolutionary motions occur in nature, thereby providing insight for viral phylodynamics.

Modelling the dynamics of mammalian gut homeostasis.

Homeostatic balance in the intestinal epithelium relies on a fast cellular turnover, which is coordinated by an intricate interplay between biochemical signalling, mechanical forces and organ geometry. We review recent modelling approaches that have been developed to understand different facets of this remarkable homeostatic equilibrium. Existing models offer different, albeit complementary, perspectives on the problem. First, biomechanical models aim to explain the local and global mechanical stresses driving cell renewal as well as tissue shape maintenance. Second, compartmental models provide insights into the conditions necessary to keep a constant flow of cells with well-defined ratios of cell types, and how perturbations can lead to an unbalance of relative compartment sizes. A third family of models address, at the cellular level, the nature and regulation of stem fate choices that are necessary to fuel cellular turnover. We also review how these different approaches are starting to be integrated together across scales, to provide quantitative predictions and new conceptual frameworks to think about the dynamics of cell renewal in complex tissues.

Effective vaccination strategies for human papillomavirus (HPV) infection and cervical cancer based on the mathematical model with a stochastic process.

Human papillomavirus (HPV) infection poses a significant risk to women's health by causing cervical cancer. In addition to HPV, cervical cancer incidence rates can be influenced by various factors, including human immunodeficiency virus and herpes, as well as screening policy. In this study, a mathematical model with stochastic processes was developed to analyze HPV transmission between genders and its subsequent impact on cervical cancer incidence. The model simulations suggest that both-gender vaccination is far more effective than female-only vaccination in preventing an increase in cervical cancer incidence. With increasing stochasticity, the difference between the number of patients in the vaccinated group and the number in the nonvaccinated group diminishes. To distinguish the patient population distribution of the vaccinated from the nonvaccinated, we calculated effect size (Cohen's distance) in addition to Student's t-test. The model analysis suggests a threshold vaccination rate for both genders for a clear reduction of cancer incidence when significant stochastic factors are present.

Optimal subsampling for semi-parametric accelerated failure time models with massive survival data using a rank-based approach.

Subsampling is a practical strategy for analyzing vast survival data, which are progressively encountered across diverse research domains. While the optimal subsampling method has been applied to inferences for Cox models and parametric accelerated failure time (AFT) models, its application to semi-parametric AFT models with rank-based estimation have received limited attention. The challenges arise from the non-smooth estimating function for regression coefficients and the seemingly zero contribution from censored observations in estimating functions in the commonly seen form. To address these challenges, we develop optimal subsampling probabilities for both event and censored observations by expressing the estimating functions through a well-defined stochastic process. Meanwhile, we apply an induced smoothing procedure to the non-smooth estimating functions. As the optimal subsampling probabilities depend on the unknown regression coefficients, we employ a two-step procedure to obtain a feasible estimation method. An additional benefit of the method is its ability to resolve the issue of underestimation of the variance when the subsample size approaches the full sample size. We validate the performance of our estimators through a simulation study and apply the methods to analyze the survival time of lymphoma patients in the surveillance, epidemiology, and end results program.

Electronic health record data is unable to effectively characterize measurement error from pulse oximetry: a simulation study.

Large data sets from electronic health records (EHR) have been used in journal articles to demonstrate race-based imprecision in pulse oximetry (SpO2) measurements. These articles do not appear to recognize the impact of the variability of the SpO2 values with respect to time ("deviation time"). This manuscript seeks to demonstrate that due to this variability, EHR data should not be used to quantify SpO2 error. Using the MIMIC-IV Waveform dataset, SpO2 values are sampled from 198 patients admitted to an intensive care unit and used as reference samples. The error derived from the EHR data is simulated using a set of deviation times. The laboratory oxygen saturation measurements are also simulated such that the performance of three simulated pulse oximeter devices will produce an average root mean squared (ARMS) error of 2%. An analysis is then undertaken to reproduce a medical device submission to a regulatory body by quantifying the mean error, the standard deviation of the error, and the ARMS error. Bland-Altman plots were also generated with their Limits of Agreements. Each analysis was repeated to evaluate whether the measurement errors were affected by increasing the deviation time. All error values increased linearly with respect to the logarithm of the time deviation. At 10 min, the ARMS error increased from a baseline of 2% to over 4%. EHR data cannot be reliably used to quantify SpO2 error. Caution should be used in interpreting prior manuscripts that rely on EHR data.

Community assembly of ectomycorrhizal fungal communities in pure and mixed Pinus massoniana forests.

Ectomycorrhizal (EcM) fungi play an important role in nutrient cycling and community ecological dynamics and are widely acknowledged as important components of forest ecosystems. However, little information is available regarding EcM fungal community structure or the possible relationship between EcM fungi, soil properties, and forestry activities in Pinus massoniana forests. In this study, we evaluated soil properties, extracellular enzyme activities, and fungal diversity and community composition in root and soil samples from pure Pinus massoniana natural forests, pure P. massoniana plantations, and P. massoniana and Liquidambar gracilipes mixed forests. The mixed forest showed the highest EcM fungal diversity in both root and bulk soil samples. Community composition and co-occurrence network structures differed significantly between forest types. Variation in the EcM fungal community was significantly correlated with the activities of ß-glucuronidase and ß-1,4-N-acetylglucosaminidase, whereas non-EcM fungal community characteristics were significantly correlated with ß-1,4-glucosidase and ß-glucuronidase activities. Furthermore, stochastic processes predominantly drove the assembly of both EcM and non-EcM fungal communities, while deterministic processes exerted greater influence on soil fungal communities in mixed forests compared to pure forests. Our findings may inform a deeper understanding of how the assembly processes and environmental roles of subterranean fungal communities differ between mixed and pure plantations and may provide insights for how to promote forest sustainability in subtropical areas.

Sensorless Speed Estimation of Induction Motors through Signal Analysis Based on Chaos Using Density of Maxima.

Three-phase induction motors are widely used in various industrial sectors and are responsible for a significant portion of the total electrical energy consumed. To ensure their efficient operation, it is necessary to apply control systems with specific algorithms able to estimate rotation speed accurately and with an adequate response time. However, the angular speed sensors used in induction motors are generally expensive and unreliable, and they may be unsuitable for use in hostile environments. This paper presents an algorithm for speed estimation in three-phase induction motors using the chaotic variable of maximum density. The technique used in this work analyzes the current signals from the motor power supply without invasive sensors on its structure. The results show that speed estimation is achieved with a response time lower than that obtained by classical techniques based on the Fourier Transform. This technique allows for the provision of motor shaft speed values when operated under variable load.

Topological analysis of vertebrate phylogenetic trees utilizing Horton's first law.

Phylogenetic trees visually represent evolution and diversification. While many studies have focused on the number and length of edges (branches), topological properties, such as edge connection patterns, are also important. In this study, the topological properties of phylogenetic trees were quantified, focusing on edge connection patterns. Horton's first law was applied to quantify the overall, rather than local, topological properties of phylogenetic trees. The topological properties of vertebrate phylogenetic trees for spiny-rayed fishes, Amphibians, turtles, Squamata, Aves, and placental mammals were analyzed. The topological features discussed herein include the number of first-order edges, maximum order, and bifurcation ratio. The average bifurcation ratio of all trees was approximately 3, suggesting that phylogenetic trees for different taxa have a common mechanism of evolution. Vertebrate phylogenetic trees were compared with artificial branching objects created from neutral stochastic branching model simulations. The topological properties of the actual vertebrate phylogenetic trees agreed with those of the artificial branching objects. Our study suggests that evolutionary events do not change the overall topological properties of actual phylogenetic trees, even if the number and length of the edges change. Specifically, non-neutral events (e.g., environmental changes and mass extinction) are not main factors associated with topological properties. The results instead demonstrate a relationship between the bifurcation ratio and symmetricity in the context of temporal changes of topological properties. When the number of first-order edges increased and the maximum order remained constant, the bifurcation ratio increased and symmetricity decreased. When the number of first-order edges increased and the maximum order increased by one, the bifurcation ratio decreased and symmetricity increased.

Grouped data with survey revision.

INTRODUCTION: Surveys are common research tools, and questionnaires revisions are a common occurrence in longitudinal studies. Revisions can, at times, introduce systematic shifts in measures of interest. We formulate that questionnaire revision are a stochastic process with transition matrices. Thus, revision shifts can be reduced by first estimating these transition matrices, which can be utilized in estimation of interested measures. MATERIALS AND METHOD: An ideal survey response model is defined by mapping between the true value of a participant's response to an interval in the grouped data type scale. A population completed surveys multiple times, as modeled with multiple stochastic process. This included stochastic processes related to true values and intervals. While multiple factors contribute to changes in survey responses, here, we explored the method that can mitigate the effects of questionnaire revision. We proposed the Version Alignment Method (VAM), a data preprocessing tool, which can separate the transitions according to revisions from all transitions via solving an optimization problem and using the revision-related transitions to remove the revision effect. To verify VAM, we used simulation data to study the estimation error and a real life MJ dataset containing large amounts of long-term questionnaire responses with several questionnaire revisions to study its feasibility. RESULT: We compared the difference of the annual average between consecutive years. Without adjustment, the difference is 0.593 when the revision occurred, while VAM brought it down to 0.115, where difference between years without revision was in the 0.005, 0.125 range. Furthermore, our method rendered the responses to the same set of intervals, thus comparing the relative frequency of items before and after revisions became possible. The average estimation error in L infinity was 0.0044 which occupied the 95% CI which was constructed by bootstrap analysis. CONCLUSION: Questionnaire revisions can induce different response bias and information loss, thus causing inconsistencies in the estimated measures. Conventional methods can only partly remedy this issue. Our proposal, VAM, can estimate the aggregate difference of all revision-related systematic errors and can reduce the differences, thus reducing inconsistencies in the final estimations of longitudinal studies.

Abundant and Rare Taxa of Planktonic Fungal Community Exhibit Distinct Assembly Patterns Along Coastal Eutrophication Gradient.

Revealing planktonic fungal ecology under coastal eutrophication is crucial to our understanding of microbial community shift in marine pollution background. We investigated the diversity, putative interspecies interactions, assembly processes and environmental responses of abundant and rare planktonic fungal communities along a eutrophication gradient present in the Beibu Gulf. The results showed that Dothideomycetes and Agaricomycetes were the predominant classes of abundant and rare fungi, respectively. We found that eutrophication significantly altered the planktonic fungal communities and affected the abundant taxa more than the rare taxa. The abundant and rare taxa were keystone members in the co-occurrence networks, and their interaction was enhanced with increasing nutrient concentrations. Stochastic processes dominated the community assembly of both abundant and rare planktonic fungi across the eutrophication gradient. Heterogeneous selection affected abundant taxa more than rare taxa, whereas homogenizing dispersal had a greater influence on rare taxa. Influences of environmental factors involving selection processes were detected, we found that abundant fungi were mainly influenced by carbon compounds, whereas rare taxa were simultaneously affected by carbon, nitrogen and phosphorus compounds in the Beibu Gulf. Overall, these findings highlight the distinct ecological adaptations of abundant and rare fungal communities to marine eutrophication.

Functional Guilds, Community Assembly, and Co-occurrence Patterns of Fungi in Metalliferous Mine Tailings Ponds in Mainland China.

Metalliferous mine tailings ponds are generally characterized by low levels of nutrient elements, sustained acidic conditions, and high contents of toxic metals. They represent one kind of extreme environments that are believed to resemble the Earth's early environmental conditions. There is increasing evidence that the diversity of fungi inhabiting mine tailings ponds is much higher than previously thought. However, little is known about functional guilds, community assembly, and co-occurrence patterns of fungi in such habitats. As a first attempt to address this critical knowledge gap, we employed high-throughput sequencing to characterize fungal communities in 33 mine tailings ponds distributed across 18 provinces of mainland China. A total of 5842 fungal phylotypes were identified, with saprotrophic fungi being the major functional guild. The predictors of fungal diversity in whole community and sub-communities differed considerably. Community assembly of the whole fungal community and individual functional guilds were primarily governed by stochastic processes. Total soil nitrogen and total phosphorus mediated the balance between stochastic and deterministic processes of the fungal community assembly. Co-occurrence network analysis uncovered a high modularity of the whole fungal community. The observed main modules largely consisted of saprotrophic fungi as well as various phylotypes that could not be assigned to known functional guilds. The richness of core fungal phylotypes, occupying vital positions in co-occurrence network, was positively correlated with edaphic properties such as soil enzyme activity. This indicates the important roles of core fungal phylotypes in soil organic matter decomposition and nutrient cycling. These findings improve our understanding of fungal ecology of extreme environments.

Quantifying Stochastic Processes in Shaping Dissolved Organic Matter Pool with High-Resolution Mass Spectrometry.

Natural dissolved organic matter (DOM) represents a ubiquitous molecular mixture, progressively characterized by spatiotemporal resolution. However, an inadequate comprehension of DOM molecular dynamics, especially the stochastic processes involved, hinders carbon cycling predictions. This study employs ecological principles to introduce a neutral theory to elucidate the fundamental processes involving molecular generation, degradation, and migration. A neutral model is thus formulated to assess the probability distribution of DOM molecules, whose frequencies and abundances follow a ß-distribution relationship. The neutral model is subsequently validated with high-resolution mass spectrometry (HRMS) data from various waterbodies, including lakes, rivers, and seas. The model fitting highlights the prevalence of molecular neutral distribution and quantifies the stochasticity within DOM molecular dynamics. Furthermore, the model identifies deviations of HRMS observations from neutral expectations in photochemical and microbial experiments, revealing nonrandom molecular transformations. The ecological null model further validates the neutral modeling results, demonstrating that photodegradation reduces molecular stochastic dynamics at the surface of an acidic pit lake, while random distribution intensifies at the river surface compared with the porewater. Taken together, the DOM molecular neutral model emphasizes the significance of stochastic processes in shaping a natural DOM pool, offering a potential theoretical framework for DOM molecular dynamics in aquatic and other ecosystems.

Precision quality control: a dynamic model for risk-based analysis of analytical quality.

OBJECTIVES: There is continuing pressure to improve the cost effectiveness of quality control (QC) for clinical laboratory testing. Risk-based approaches are promising but recent research has uncovered problems in some common methods. There is a need for improvements in risk-based methods for quality control. METHODS: We provide an overview of a dynamic model for assay behavior. We demonstrate the practical application of the model using simulation and compare the performance of simple Shewhart QC monitoring against Westgard rules. We also demonstrate the utility of trade-off curves for analysis of QC performance. RESULTS: Westgard rules outperform simple Shewhart control over a narrow range of the trade-off curve of false-positive and false negative risk. The risk trade-off can be visualized in terms of risk, risk vs. cost, or in terms of cost. Risk trade-off curves can be "smoothed" by log transformation. CONCLUSIONS: Dynamic risk-models may provide advantages relative to static models for risk-based QC analysis.

A time variant uncertainty propagation method for high-dimensional dynamic structural system via K-L expansion and Bayesian deep neural network.

In this paper, a time variant uncertainty propagation (TUP) method for dynamic structural system with high-dimensional input variables is proposed. Firstly, an arbitrary stochastic process simulation (ASPS) method based on Karhunen-Loève (K-L) expansion and numerical integration is developed, expressing the stochastic process as the combination of its marginal distributions and eigen functions at several discrete time points. Secondly, the iterative sorting method is implemented to the statistic samples of marginal distributions for matching the constraints of covariance function. Since marginal distributions are directly used to express the stochastic process, the proposed ASPS is suitable for stationary or non-stationary stochastic processes with arbitrary marginal distributions. Thirdly, the high-dimensional TUP problem is converted into several high-dimensional static uncertainty propagation (UP) problems after implementing ASPS. Then, the Bayesian deep neural network based UP method is used to compute the marginal distributions as well as the eigen functions of dynamic system response, the high-dimensional TUP problem can thus be solved. Finally, several numerical examples are used to validate the effectiveness of the proposed method. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

Inferring microbial community assembly in an urban river basin through geo-multi-omics and phylogenetic bin-based null-model analysis of surface water.

Understanding the community assembly process is a central issue in microbial ecology. In this study, we analyzed the community assembly of particle-associated (PA) and free-living (FL) surface water microbiomes in 54 sites from the headstream to the river mouth of an urban river in Japan, the river basin of which has the highest human population density in the country. Analyses were conducted from two perspectives: (1) analysis of deterministic processes considering only environmental factors using a geo-multi-omics dataset and (2) analysis of deterministic and stochastic processes to estimate the contributions of heterogeneous selection (HeS), homogeneous selection (HoS), dispersal limitation (DL), homogenizing dispersal (HD), and drift (DR) as community assembly processes using a phylogenetic bin-based null model. The variation in microbiomes was successfully explained from a deterministic perspective by environmental factors, such as organic matter-related, nitrogen metabolism, and salinity-related parameters, using multivariate statistical analysis, network analysis, and habitat prediction. In addition, we demonstrated the dominance of stochastic processes (DL, HD, and DR) over deterministic processes (HeS and HoS) in community assembly from both deterministic and stochastic perspectives. Our analysis revealed that as the distance between two sites increased, the effect of HoS sharply decreased while the effect of HeS increased, particularly between upstream and estuary sites, indicating that the salinity gradient could potentially enhance the contribution of HeS to community assembly. Our study highlights the importance of both stochastic and deterministic processes in community assembly of PA and FL surface water microbiomes in urban riverine ecosystems.

Temporal and Probabilistic Comparisons of Epidemic Interventions.

Forecasting disease spread is a critical tool to help public health officials design and plan public health interventions. However, the expected future state of an epidemic is not necessarily well defined as disease spread is inherently stochastic, contact patterns within a population are heterogeneous, and behaviors change. In this work, we use time-dependent probability generating functions (PGFs) to capture these characteristics by modeling a stochastic branching process of the spread of a disease over a network of contacts in which public health interventions are introduced over time. To achieve this, we define a general transmissibility equation to account for varying transmission rates (e.g. masking), recovery rates (e.g. treatment), contact patterns (e.g. social distancing) and percentage of the population immunized (e.g. vaccination). The resulting framework allows for a temporal and probabilistic analysis of an intervention's impact on disease spread, which match continuous-time stochastic simulations that are much more computationally expensive. To aid policy making, we then define several metrics over which temporal and probabilistic intervention forecasts can be compared: Looking at the expected number of cases and the worst-case scenario over time, as well as the probability of reaching a critical level of cases and of not seeing any improvement following an intervention. Given that epidemics do not always follow their average expected trajectories and that the underlying dynamics can change over time, our work paves the way for more detailed short-term forecasts of disease spread and more informed comparison of intervention strategies.

Under-reported time-varying MINAR(1) process for modeling multivariate count series.

A time-varying multivariate integer-valued autoregressive of order one (tvMINAR(1)) model is introduced for the non-stationary time series of correlated counts when under-reporting is likely present. A non-diagonal autoregression probability network is structured to preserve the cross-correlation of multivariate series, provide a necessary condition to ease model-fittings computations, and derive the full likelihood using the Viterbi algorithm. The motivating construction applies to fully under-reported counts that rely on a mixture presentation of the random thinning operator. Simulation studies are conducted to examine the proposed model, and the analysis of COVID-19 daily cases is accomplished to highlight its usefulness in applications. Finally, the comparison of models is presented using the posterior predictive checking method.

Reed restoration decreased nutrients in wetlands with dredged sediments: Microbial community assembly and function in rhizosphere.

Using dredged sediments as substrate for aquatic plants is a low-cost and ecological friendly way for in situ aquatic ecological restoration. However, the limited information available about how aquatic plant restoration affects the microbial ecology and nutrients in dredged sediments. In this study, nutrient contents, enzyme activities, and bacterial and archaeal communities in vertical sediment layers were determined in bulk and reed zones of wetlands constructed with dredged sediments in west Lake Taihu for three years. Reed restoration significantly decreased total nitrogen, total phosphorus, and organic carbon contents and increased alkaline phosphatase, urease, and sucrase activities compared to bulk area. Bacterial communities in vertical sediment layers had higher similarity in reed zone in comparison to bulk zone, and many bacterial and archaeal genera were only detected in reed rhizosphere zones. Compared with the bulk zone, the reed restoration area has a higher abundance of phylum Actinobacteriota, Hydrothermarchaeota, and class α-proteobacteria. The assembly process of the bacterial and archaeal communities was primarily shaped by dispersal limitation (67.03% and 32.97%, respectively), and stochastic processes were enhanced in the reed recovery area. Network analysis show that there were more complicated interactions among bacteria and archaea and low-abundance taxa were crucial in maintaining the microbial community stability in rhizosphere of reed zone. PICRUST2 analysis demonstrate that reed restoration promotes metabolic pathways related to C and N cycle in dredged sediments. These data highlight that using dredged sediments as substrates for aquatic plants can transform waste material into a valuable resource, enhancing the benefits to the environment.

Mathematical model of the cell signaling pathway based on the extended Boolean network model with a stochastic process.

BACKGROUND: In cell signaling pathways, proteins interact with each other to determine cell fate in response to either cell-extrinsic (micro-environmental) or intrinsic cues. One of the well-studied pathways, the mitogen-activated protein kinase (MAPK) signaling pathway, regulates cell processes such as differentiation, proliferation, apoptosis, and survival in response to various micro-environmental stimuli in eukaryotes. Upon micro-environmental stimulus, receptors on the cell membrane become activated. Activated receptors initiate a cascade of protein activation in the MAPK pathway. This activation involves protein binding, creating scaffold proteins, which are known to facilitate effective MAPK signaling transduction. RESULTS: This paper presents a novel mathematical model of a cell signaling pathway coordinated by protein scaffolding. The model is based on the extended Boolean network approach with stochastic processes. Protein production or decay in a cell was modeled considering the stochastic process, whereas the protein-protein interactions were modeled based on the extended Boolean network approach. Our model fills a gap in the binary set applied to previous models. The model simultaneously considers the stochastic process directly. Using the model, we simulated a simplified mitogen-activated protein kinase (MAPK) signaling pathway upon stimulation of both a single receptor at the initial time and multiple receptors at several time points. Our simulations showed that the signal is amplified as it travels down to the pathway from the receptor, generating substantially amplified downstream ERK activity. The noise generated by the stochastic process of protein self-activity in the model was also amplified as the signaling propagated through the pathway. CONCLUSIONS: The signaling transduction in a simplified MAPK signaling pathway could be explained by a mathematical model based on the extended Boolean network model with a stochastic process. The model simulations demonstrated signaling amplifications when it travels downstream, which was already observed in experimental settings. We also highlight the importance of stochastic activity in regulating protein inactivation.

Distinct Composition and Assembly Processes of Bacterial Communities in a River from the Arid Area: Ecotypes or Habitat Types?

The composition, function, and assembly mechanism of the bacterial community are the focus of microbial ecology. Unsupervised machine learning may be a better way to understand the characteristics of bacterial metacommunities compared to the empirical habitat types. In this study, the composition, potential function, and assembly mechanism of the bacterial community in the arid river were analysed. The Dirichlet multinomial mixture method recognised four ecotypes across the three habitats (biofilm, water, and sediment). The bacterial communities in water are more sensitive to human activities. Bacterial diversity and richness in water decreased as the intensity of human activities increased from the region of water II to water I. Significant differences in the composition and potential function profile of bacterial communities between water ecotypes were also observed, such as higher relative abundance in the taxonomic composition of Firmicutes and potential function of plastic degradation in water I than those in water II. Habitat filtering may play a more critical role in the assembly of bacterial communities in the river biofilm, while stochastic processes dominate the assembly process of bacterial communities in water and sediment. In water I, salinity and mean annual precipitation were the main drivers shaping the biogeography of taxonomic structure, while mean annual temperature, total organic carbon, and ammonium nitrogen were the main environmental factors influencing the taxonomic structure in water II. These results would provide conceptual frameworks about choosing habitat types or ecotypes for the research of microbial communities among different niches in the aquatic environment.