A stochastic model for neural progenitor dynamics in the mouse cerebral cortex.

We have designed a stochastic model of embryonic neurogenesis in the mouse cerebral cortex, using the formalism of compound Poisson processes. The model accounts for the dynamics of different progenitor cell types and neurons. The expectation and variance of the cell number of each type are derived analytically and illustrated through numerical simulations. The effects of stochastic transition rates between cell types, and stochastic duration of the cell division cycle have been investigated sequentially. The model does not only predict the number of neurons, but also their spatial distribution into deeper and upper cortical layers. The model outputs are consistent with experimental data providing the number of neurons and intermediate progenitors according to embryonic age in control and mutant situations.

Epigenome-augmented eQTL-hotspots reveal genome-wide transcriptional programs in 36 human tissues.

Expression quantitative trait loci (eQTLs) are used to inform the mechanisms of transcriptional regulation in eukaryotic cells. However, the specificity of genome-wide eQTL identification is limited by stringent control for false discoveries. Here, we described a method based on the non-homogeneous Poisson process to identify 125 489 regions with highly frequent, multiple eQTL associations, or 'eQTL-hotspots', from the public database of 59 human tissues or cell types. We stratified the eQTL-hotspots into two classes with their distinct sequence and epigenomic characteristics. Based on these classifications, we developed a machine-learning model, E-SpotFinder, for augmented discovery of tissue- or cell-type-specific eQTL-hotspots. We applied this model to 36 tissues or cell types. Using augmented eQTL-hotspots, we recovered 655 402 eSNPs and reconstructed a comprehensive regulatory network of 2 725 380 cis-interactions among eQTL-hotspots. We further identified 52 012 modules representing transcriptional programs with unique functional backgrounds. In summary, our study provided a framework of epigenome-augmented eQTL analysis and thereby constructed comprehensive genome-wide networks of cis-regulations across diverse human tissues or cell types.

Enrollment Forecast for Clinical Trials at the Planning Phase with Study-Level Historical Data.

Given progressive developments and demands on clinical trials, accurate enrollment timeline forecasting is increasingly crucial for both strategic decision-making and trial execution excellence. Naïve approach assumes flat rates on enrollment using average of historical data, while traditional statistical approach applies simple Poisson-Gamma model using time-invariant rates for site activation and subject recruitment. Both of them are lack of non-trivial factors such as time and location. We propose a novel two-segment statistical approach based on Quasi-Poisson regression for subject accrual rate and Poisson process for subject enrollment and site activation. The input study-level data are publicly accessible and it can be integrated with historical study data from user's organization to prospectively predict enrollment timeline. The new framework is neat and accurate compared to preceding works. We validate the performance of our proposed enrollment model and compare the results with other frameworks on 7 curated studies.

Point process models for COVID-19 cases and deaths.

The study of events distributed over time which can be quantified as point processes has attracted much interest over the years due to its wide range of applications. It has recently gained new relevance due to the COVID-19 case and death processes associated with SARS-CoV-2 that characterize the COVID-19 pandemic and are observed across different countries. It is of interest to study the behavior of these point processes and how they may be related to covariates such as mobility restrictions, gross domestic product per capita, and fraction of population of older age. As infections and deaths in a region are intrinsically events that arrive at random times, a point process approach is natural for this setting. We adopt techniques for conditional functional point processes that target point processes as responses with vector covariates as predictors, to study the interaction and optimal transport between case and death processes and doubling times conditional on covariates.

Unifying incidence and prevalence under a time-varying general branching process.

Renewal equations are a popular approach used in modelling the number of new infections, i.e., incidence, in an outbreak. We develop a stochastic model of an outbreak based on a time-varying variant of the Crump-Mode-Jagers branching process. This model accommodates a time-varying reproduction number and a time-varying distribution for the generation interval. We then derive renewal-like integral equations for incidence, cumulative incidence and prevalence under this model. We show that the equations for incidence and prevalence are consistent with the so-called back-calculation relationship. We analyse two particular cases of these integral equations, one that arises from a Bellman-Harris process and one that arises from an inhomogeneous Poisson process model of transmission. We also show that the incidence integral equations that arise from both of these specific models agree with the renewal equation used ubiquitously in infectious disease modelling. We present a numerical discretisation scheme to solve these equations, and use this scheme to estimate rates of transmission from serological prevalence of SARS-CoV-2 in the UK and historical incidence data on Influenza, Measles, SARS and Smallpox.

Software reliability model for open-source software that considers the number of finite faults and dependent faults.

Software has become a vital factor in the fourth industrial revolution. Owing to the increase in demand for software products in various fields (big data, artificial intelligence, the Internet of Things, etc.), the software industry has expanded more than ever before. Therefore, software reliability has become very important, and efforts are being made to increase it. One of these efforts is the development of software reliability models (SRMs). SRMs have been studied for a long time as a model that predicts software reliability by using the number of software faults. Software failures can occur for several reasons, including independent software faults such as code errors and software hangs, as well as dependent cases where code errors lead to other software faults. Recently, due to the diversity of software operating environments, software faults are more likely to occur in a dependent manner, and, for this reason, they are likely to increase rapidly from the beginning and progress slowly to the maximum number thereafter. In addition, many large companies have focused on open-source software (OSS) development, and OSS is being developed by many users. In this study, we propose a new SRM that considers the number of finite faults and dependent faults, and examine the goodness-of-fit of a new SRM and other existing non-homogeneous Poisson process models based on the OSS datasets. Through numerical examples, the proposed model demonstrated a significantly better goodness-of-fit when compared to other existing models, and it also exhibited better results on the newly proposed integrated criteria.

Comprehensive evaluation of software system reliability based on component-based generalized G-O models.

The component-based software system has a core that is based on architecture design. Predicting the reliability growth trends of a software system in the early stages of the development process is conducive to reducing waste and loss caused by blind development. Restricted by the lack of information and data in the design and integration phase, it is difficult to implement reliability prediction research at this stage. In this article, we focus on a software system in which the reliability of each component follows the G-O model. First, two system-level parameters, which are the total number of system faults and the detection rate of the system faults, are defined. Then, by studying the relationship between the total number of faults and the detection rate of faults between the components and the system, the defined system parameters are calculated from the known component parameters. On this basis, and by incorporating the system parameters, we construct a reliability growth model for the software system, called the component-based generalized G-O model (CB-GGOM). Besides, two approximate models of CB-GGOM are proposed to facilitate reliability evaluation of the software system in the early and stable stages of the integration test. An engineering explanation of the proposed models is also provided, and their effectiveness is verified through simulation and with an authentic example. Since the proposed models are formulated without any integration test data, they are beneficial for developers to optimize test strategies of the software system and implement defect prevention in advance.

Scanning behaviour in ants: an interplay between random-rate processes and oscillators.

At the start of a journey home or to a foraging site, ants often stop, interrupting their forward movement, turn on the spot a number of times, and fixate in different directions. These scanning bouts are thought to provide visual information for choosing a path to travel. The temporal organization of such scanning bouts has implications about the neural organisation of navigational behaviour. We examined (1) the temporal distribution of the start of such scanning bouts and (2) the dynamics of saccadic body turns and fixations that compose a scanning bout in Australian desert ants, Melophorus bagoti, as they came out of a walled channel onto open field at the start of their homeward journey. Ants were caught when they neared their nest and displaced to different locations to start their journey home again. The observed parameters were mostly similar across familiar and unfamiliar locations. The turning angles of saccadic body turning to the right or left showed some stereotypy, with a peak just under 45°. The direction of such saccades appears to be determined by a slow oscillatory process as described in other insect species. In timing, however, both the distribution of inter-scanning-bout intervals and individual fixation durations showed exponential characteristics, the signature for a random-rate or Poisson process. Neurobiologically, therefore, there must be some process that switches behaviour (starting a scanning bout or ending a fixation) with equal probability at every moment in time. We discuss how chance events in the ant brain that occasionally reach a threshold for triggering such behaviours can generate the results.

Non-homogeneous continuous-time Markov chain with covariates: Applications to ambulatory hypertension monitoring.

Hypertension significantly increases the risk for many health conditions including heart disease and stroke. Hypertensive patients often have continuous measurements of their blood pressure to better understand how it fluctuates over the day. The continuous-time Markov chain (CTMC) is commonly used to study repeated measurements with categorical outcomes. However, the standard CTMC may be restrictive, because the rates of transitions between states are assumed to be constant through time, while the transition rates for describing the dynamics of hypertension are likely to be changing over time. In addition, the applications of CTMC rarely account for the effects of other covariates on state transitions. In this article, we considered a non-homogeneous continuous-time Markov chain with two states to analyze changes in hypertension while accounting for multiple covariates. The explicit formulas for the transition probability matrix as well as the corresponding likelihood function were derived. In addition, we proposed a maximum likelihood estimation algorithm for estimating the parameters in the time-dependent rate function. Lastly, the model performance was demonstrated through both a simulation study and application to ambulatory blood pressure data.

Multi-release software model based on testing coverage incorporating random effect (SDE).

In the past, various Software Reliability Growth Models (SRGMs) have been proposed using different parameters to improve software worthiness. Testing Coverage is one such parameter that has been studied in numerous models of software in the past and it has proved its influence on the reliability models. To sustain themselves in the market, software firms keep upgrading their software with new features or enhancements by rectifying previously reported faults. Also, there is an impact of the random effect on testing coverage during both the testing and operational phase. In this paper, we have proposed a Software reliability growth model based on testing coverage with random effect along with imperfect debugging. Later, the multi-release problem is presented for the proposed model. The proposed model is validated on the dataset from Tandem Computers. The results for each release of the models have been discussed based on the different performance criteria. The numerical results illustrate that models fit the failure data significantly.•The random effect in the testing coverage rate is handled using Stochastic Differential Equations (SDE).•Three testing coverage functions used are Exponential, Weibull, and S-shaped.•Four Releases of the software model has been presented.

Prediction of Bus Passenger Traffic using Gaussian Process Regression.

The paper summarizes the design and implementation of a passenger traffic prediction model, based on Gaussian Process Regression (GPR). Passenger traffic analysis is the present day requirement for proper bus scheduling and traffic management to improve the efficiency and passenger comfort. Bayesian analysis uses statistical modelling to recursively estimate new data from existing data. GPR is a fully Bayesian process model, which is developed using PyMC3 with Theano as backend. The passenger data is modelled as a Poisson process so that the prior for designing the GP regression model is a Gamma distributed function. It is observed that the proposed GP based regression method outperforms the existing methods like Student-t process model and Kernel Ridge Regression (KRR) process.

Analyzing recurrent and nonrecurrent terminal events data in discrete time.

Joint analysis of recurrent and nonrecurrent terminal events has attracted substantial attention in literature. However, there lacks formal methodology for such analysis when the event time data are on discrete scales, even though some modeling and inference strategies have been developed for discrete-time survival analysis. We propose a discrete-time joint modeling approach for the analysis of recurrent and terminal events where the two types of events may be correlated with each other. The proposed joint modeling assumes a shared frailty to account for the dependence among recurrent events and between the recurrent and the terminal terminal events. Also, the joint modeling allows for time-dependent covariates and rich families of transformation models for the recurrent and terminal events. A major advantage of our approach is that it does not assume a distribution for the frailty, nor does it assume a Poisson process for the analysis of the recurrent event. The utility of the proposed analysis is illustrated by simulation studies and two real applications, where the application to the biochemists' rank promotion data jointly analyzes the biochemists' citation numbers and times to rank promotion, and the application to the scleroderma lung study data jointly analyzes the adverse events and off-drug time among patients with the symptomatic scleroderma-related interstitial lung disease.

Earthquake pattern analysis using subsequence time series clustering.

In this paper, a subsequence time-series clustering algorithm is proposed to identify the strongly coupled aftershocks sequences and Poissonian background activity from earthquake catalogs of active regions. The proposed method considers the inter-event time statistics between the successive pair of events for characterizing the nature of temporal sequences and observing their relevance with earthquake epicenters and magnitude information simultaneously. This approach categorizes the long-earthquake time series into the finite meaningful temporal sequences and then applies the clustering mechanism to the selective sequences. The proposed approach is built on two phases: (1) a Gaussian kernel-based density estimation for finding the optimal subsequence of given earthquake time-series, and (2) inter-event time ( Δ t ) and distance-based observation of each subsequence for checking the presence of highly correlated aftershock sequences (hot-spots) in it. The existence of aftershocks is determined based on the coefficient of variation (COV). A sliding temporal window on Δ t with earthquake's magnitude M is applied on the selective subsequence to filter out the presence of time-correlated events and make the meaningful time stationary Poissonian subsequences. This proposed approach is applied to the regional Sumatra-Andaman (2000-2021) and worldwide ISC-GEM (2000-2016) earthquake catalog. Simulation results indicate that meaningful subsequences (background events) can be modeled by a homogeneous Poisson process after achieving a linear cumulative rate and time-independent λ in the exponential distribution of Δ t . The relations C O V a ( T ) > C O V o ( T ) > ( C O V b ( T ) ≈ 1 ) and C O V a ( d ) > C O V o ( d ) > C O V b ( d ) are achieved for both studied catalogs. Comparative analysis justifies the competitive performance of the proposed approach to the state-of-art approaches and recently introduced methods.

Statistical Analysis of Silicon Photomultiplier Output Signals.

Silicon photomultipliers are relatively new devices designed as a matrix of single-photon avalanche detectors, which have become popular for their miniature dimensions and low operating voltage. Their superior sensitivity allows detecting low-photon-count optical pulses, e.g., in ranging and LIDAR applications. The output signal of the photomultiplier is a non-stationary stochastic process, from which a weak periodic pulse can be extracted by means of statistical processing. Using the double-exponential approximation of output avalanche pulses the paper presents a simple analytical solution to the mean and variance of the stochastic process. It is shown that even for an ideal square optical pulse the rising edge of the statistically detected signal is longer than the edge of individual avalanche pulses. The knowledge of the detected waveform can be used to design an optimum laser pulse waveform or algorithms for estimating the time of arrival. The experimental section demonstrates the proposed procedure.

Detecting clusters of transcription factors based on a nonhomogeneous poisson process model.

BACKGROUND: Rapidly growing genome-wide ChIP-seq data have provided unprecedented opportunities to explore transcription factor (TF) binding under various cellular conditions. Despite the rich resources, development of analytical methods for studying the interaction among TFs in gene regulation still lags behind. RESULTS: In order to address cooperative TF binding and detect TF clusters with coordinative functions, we have developed novel computational methods based on clustering the sample paths of nonhomogeneous Poisson processes. Simulation studies demonstrated the capability of these methods to accurately detect TF clusters and uncover the hierarchy of TF interactions. A further application to the multiple-TF ChIP-seq data in mouse embryonic stem cells (ESCs) showed that our methods identified the cluster of core ESC regulators reported in the literature and provided new insights on functional implications of transcrisptional regulatory modules. CONCLUSIONS: Effective analytical tools are essential for studying protein-DNA relations. Information derived from this research will help us better understand the orchestration of transcription factors in gene regulation processes.

Statistical models of near-accident event and pedestrian behavior at non-signalized intersections.

This paper proposes an innovative framework of modeling the statistical properties of the near-accident event and pedestrian behavior at non-signalized intersections based on Poisson process and logistic regression. The first contribution of this study is that the predictive intensity model of the near-accident event is established by regarding the near-accident event as a Poisson process on space of the vehicle velocity, distance to the intersection and lateral distance to the pedestrian at the time when pedestrian appears. Besides, logistic regression is used to build the model which can predict the probability of pedestrian behavior. The two proposed models are validated in a generative simulation. The simulated pedestrian behavior data is generated by the proposed models and compared with the real data. The real data set is from the drive recorder data base of Smart Mobility Research Center (SMRC) at Tokyo University of Agriculture and Technology. Accident and near-accident data has been collected in the city streets with an image-captured drive recorder mounted on a taxi since 2006. The findings in this study are expected to be useful for constructions of traffic simulators or safety control design which considers the pedestrian-vehicle interaction.

Inference, Prediction, & Entropy-Rate Estimation of Continuous-Time, Discrete-Event Processes.

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide new methods for inferring, predicting, and estimating them. The methods rely on an extension of Bayesian structural inference that takes advantage of neural network's universal approximation power. Based on experiments with complex synthetic data, the methods are competitive with the state-of-the-art for prediction and entropy-rate estimation.

An intelligent spatial stream processing framework for digital forensics amid the COVID-19 outbreak.

In recent times, several strategies to minimize the spread of 2019 novel coronavirus disease (COVID-19) have been adopted. Some recent technological breakthroughs like the drone-based tracking systems have focused on devising specific dynamical approaches for administering public mobility and providing early detection of symptomatic patients. In this paper, a smart real-time image processing framework converged with a non-contact thermal temperature screening module was implemented. The proposed framework comprised of three modules v i z . , smart temperature screening system, tracking infection footprint, and monitoring social distancing policies. This was accomplished by employing Histogram of Oriented Gradients (HOG) transformation to identify infection hotspots. Further, Haar Cascade and local binary pattern histogram (LBPH) algorithms were used for real-time facial recognition and enforcing social distancing policies. In order to manage the redundant video frames generated at the local computing device, two holistic models, namely, event-triggered video framing (ETVF) and real-time video framing (RTVF) have been deduced, and their respective processing costs were studied for different arrival rates of the video frame. It was observed that the proposed ETVF approach outperforms the performance of RTVF by providing optimal processing costs resulting from the elimination of redundant data frames. Results corresponding to autocorrelation analysis have been presented for the case study of India pertaining to the number of confirmed COVID-19 cases, recovered cases, and deaths to obtain an understanding of epidemiological spread of the virus. Further, choropleth analysis was performed for indicating the magnitude of COVID-19 spread corresponding to different regions in India.

Forecasting COVID19 Reliability of the Countries by Using Non-Homogeneous Poisson Process Models.

Reliability is the probability that a system or a product fulfills its intended function without failure over a period of time and it is generally used to determine the reliability, release and testing stop time of the system. The primary objective of this study is to predict and forecast COVID19 reliabilities of the countries by utilizing this definition of the reliability. To our knowledge, this study is the first carried out in the direction of this objective. The major contribution of this study is to model the COVID19 data by considering the intensity functions with different types of functional shapes, including geometric, exponential, Weibull, gamma and identifying best fit (BF) model for each country, separately. To achieve the objective determined, cumulative number of confirmed cases are modelled by eight Non-Homogenous Poisson Process (NHPP) models. BF models are selected based on three comparison criteria, including Root Mean Square Error (RMSE), Normalized Root Mean Square Error (NRMSE), and Theil Statistics (TS). The results can be summarized as follows: S-shaped models provide better fit for 56 of 70 countries. Current outbreak may continue in 43 countries and a new outbreak may occur in 27 countries. 50 countries have the reliability smaller than 75%, 9 countries between 75% and 90%, and 11 countries a 90% or higher on 11 August 2021. Supplementary Information: The online version contains supplementary material available at 10.1007/s00354-022-00183-1.

Estimating the basic reproduction number from noisy daily data.

In this paper, we propose an easy to implement generalized linear models (GLM) methodology for estimating the basic reproduction number, R0, a major epidemic parameter for assessing the transmissibility of an infection. Our approach rests on well known qualitative properties of the classical SIR and SEIR systems for large populations. Moreover, we assume that information at the individual network level is not available. In inference we consider non homogeneous Poisson observation processes and mainly concentrate on epidemics that spread through a completely susceptible population. Further, we examine the performance of the estimator under various scenarios of relevance in practice, like partially observed data. We perform a detailed simulation study and illustrate our approach on Covid-19 Canadian data sets. Finally, we present extensions of our methodology and discuss its merits and practical limitations, in particular the challenges in estimating R0 when mitigation measures are applied.