Stochastic Threshold Research Articles

A GENERALIZATION OF THRESHOLD-BASED AND PROBABILITY-BASED MODELS OF INFORMATION DIFFUSION

Diffusion of information through complex networks is of interest in studies such as propagation prediction and influence maximization, both of which have applications in viral marketing and rumor controlling. There are a variety of information diffusion models, all of which simulate the adoption and spread of information over time. However, there is a lack of understanding of whether, despite their conceptual differences, these models represent the same underlying generative structures. For instance, if two different models utilize different conceptual mechanisms, but generate the same results, does the choice of model matter? A classification of diffusion of information models is developed based on the neighbor knowledge of the model infection requirement and the stochasticity of the model. This classification allows for the identification of models that fall into each respective category. The study involves the analysis of the following agent-based models on directed scale-free networks: (1) a linear absolute threshold model (LATM), (2) a linear fractional threshold model (LTFM), (3) the independent cascade model (ICM), (4) Bass-Rand-Rust model (BRRM) (5) a stochastic linear absolute threshold model (SLATM) (6) a stochastic fractional threshold model (SLFTM), and (7) Dodds–Watts model (DWM). Through the execution of simulations and analysis of the experimental results, the distinctive properties of each model are identified. Our analysis reveals that similarity in conceptual design does not imply similarity in behavior concerning speed, final state of nodes and edges, and sensitivity to parameters. Therefore, we highlight the importance of considering the unique behavioral characteristics of each model when selecting a suitable information diffusion model for a particular application.

A generalized stochastic SIRS epidemic model incorporating mean-reverting Ornstein–Uhlenbeck process

The aim of this work is to study a new stochastic SIRS epidemic model that includes the mean-reverting Ornstein–Uhlenbeck process and a general incidence rate. First, we prove the global existence and positivity of the solution by using Lyapunov functions. Second, we analytically make out the stochastic epidemic threshold T̃0S which pilots the extinction and persistence in mean of the disease. We have proven that the disease extinguishes when T̃0S<1. Otherwise, if T̃0S>1, then disease is persistent in mean. For the critical case T̃0S=1, we have shown that the disease dies out by using an approach involving some appropriate stopping times. Finally, we present a series of numerical simulations to confirm the feasibility and correctness of the theoretical analysis results.

Modeling cryptosporidiosis in humans and cattle: Deterministic and stochastic approaches

Cryptosporidiosis is a zoonotic disease caused by Cryptosporidium. The disease poses a public and veterinary health problem worldwide. A deterministic model and its corresponding continuous time Markov chain (CTMC) stochastic model are developed and analyzed to investigate cryptosporidiosis transmission dynamics in humans and cattle. The basic reproduction number R0 for the deterministic model and stochastic threshold for the CTMC stochastic model are computed by the next generation matrix method and multitype branching process, respectively. The normalized forward sensitivity index method is used to determine the sensitivity index for each parameter in R0. Per capita birth rate of cattle, the rate of cattle to acquire cryptosporidiosis infection from the environment and the rate at which infected cattle shed Cryptosporidium oocysts in the environment play an important role in the persistence of the disease whereas Cryptosporidium oocysts natural death rate, cattle recovery rate and cattle natural death rate are most negative sensitive parameters in the dynamics of cryptosporidiosis. Numerical results for CTMC stochastic model show that the likelihood of cryptosporidiosis extinction is high when it arises from an infected human. However, there is a major outbreak if cryptosporidiosis emerges either from infected cattle or from Cryptosporidium oocysts in the environment or when it emerges from all three infectious compartments. Therefore to control the disease, control measures should focus on maintaining personal and cattle farm hygiene and decontaminating the environment to destroy Cryptosporidium oocysts.

The Galton–Watson branching process for TB dynamics: The potential for disease persistence or extinction

Tuberculosis is a critical problem particularly in developing countries of Africa that has resulted in a high mortality rate. The disease is transmitted through air when a susceptible individual inhales Mycobacterium tuberculosis bacteria that have been released by an infected person during coughing, sneezing, singing or speaking. In this work, we formulate and analyze a deterministic model and its corresponding continuous time Markov chain (CTMC) stochastic model to study the dynamics of tuberculosis in humans. The Galton–Watson multitype branching process is adopted to compute the stochastic threshold ρ(M) and determine the possibility of tuberculosis persistence or extinction. The next generation method is employed to find the basic reproduction number R0 and the partial rank correlation coefficient method is used to determine the most sensitive parameters in the spread of tuberculosis. Sensitivity analysis shows that the probability of TB infection, the fraction of individuals who progress to pulmonary TB, pulmonary TB induced death and human recruitment rate influence the transmission of TB disease. If the basic reproduction number R0<1 and the stochastic threshold ρ(M)<1 then tuberculosis clears in human population. If R0>1 then tuberculosis persists in the population. However, there is a possibility of tuberculosis to persist or clear if ρ(M)>1 depending on the number of infectious agents at the beginning of the tuberculosis outbreak. Results reveal that the probability of tuberculosis extinction is small if TB emerges from individuals with pulmonary TB and it is large if TB emerges from individuals with latent TB. If TB emerges from individuals with extra-pulmonary TB, then the disease clears in the population. These results suggest that it is essential to treat humans with pulmonary tuberculosis particularly at the beginning of the disease outbreak so as to control human TB.

Threshold dynamics of a stochastic general SIRS epidemic model with migration.

In this study, a stochastic SIRS epidemic model that features constant immigration and general incidence rate is investigated. Our findings show that the dynamical behaviors of the stochastic system can be predicted using the stochastic threshold $ R_0^S $. If $ R_0^S < 1 $, the disease will become extinct with certainty, given additional conditions. Conversely, if $ R_0^S > 1 $, the disease has the potential to persist. Moreover, the necessary conditions for the existence of the stationary distribution of positive solution in the event of disease persistence is determined. Our theoretical findings are validated through numerical simulations.

Stringency of environmental policy in China: When pollution drives bribery

This study provides a political economy explanation for the recently increased stringency of China's environmental policy. Specifically, we argue that prior to 2009, bribery from polluting firms was relatively successful in persuading local regulators to implement weak environmental policies. Since that time, pollution has reached a threshold that significantly changed regulators' objectives, leading them to refuse bribes, hence strengthening environmental policy. Thus, we built a theoretical general equilibrium model (with uncertainty about a pollution-induced catastrophe) in order to investigate the decision-making of local regulators. Using pollution and bribery data from China, we empirically confirmed the existence of a threshold for PM2.5 and calibrated our theoretical model. We showed that the current pollution level is higher than the optimal level of 9 μg/m 3 that a forward-looking regulator would target (with a 1.5% risk of facing a pollution catastrophe). This suggests that the current pro-environmental activities of Chinese firms have been triggered by the changing behaviors of local regulators. • The current more stringent environmental policy in China is attributed to less bribery. • The reduction in bribery in China is due to a stochastic pollution threshold. • The stochastic pollution threshold was reached in China between 2009 and 2016. • Forward-looking local regulators should choose a steady-state with low pollution. • China's severe pollution in the past is attributed to myopic local regulators.

Efficient Gradient Support Pursuit With Less Hard Thresholding for Cardinality-Constrained Learning.

Recently, stochastic hard thresholding (HT) optimization methods [e.g., stochastic variance reduced gradient hard thresholding (SVRGHT)] are becoming more attractive for solving large-scale sparsity/rank-constrained problems. However, they have much higher HT oracle complexities, especially for high-dimensional data or large-scale matrices. To address this issue and inspired by the well-known Gradient Support Pursuit (GraSP) method, this article proposes a new Relaxed Gradient Support Pursuit (RGraSP) framework. Unlike GraSP, RGraSP only requires to yield an approximation solution at each iteration. Based on the property of RGraSP, we also present an efficient stochastic variance reduction-gradient support pursuit algorithm and its fast version (called stochastic variance reduced gradient support pursuit (SVRGSP+). We prove that the gradient oracle complexity of both our algorithms is two times less than that of SVRGHT. In particular, their HT complexity is about κ∧s times less than that of SVRGHT, where κ∧s is the restricted condition number. Moreover, we prove that our algorithms enjoy fast linear convergence to an approximately global optimum, and also present an asynchronous parallel variant to deal with very high-dimensional and sparse data. Experimental results on both synthetic and real-world datasets show that our algorithms yield superior results than the state-of-the-art gradient HT methods.

Approximation and Analysis of Natural Data Based on NARX Neural Networks Involving Wavelet Filtering

Recurrent neural network (RNN) models continue the theory of the autoregression integrated moving average (ARIMA) model class. In this paper, we consider the architecture of the RNN with embedded memory—«Process of Nonlinear Autoregressive Exogenous Model» (NARX). Though it is known that NN is a universal approximator, certain difficulties and restrictions in different NN applications are still topical and call for new approaches and methods. In particular, it is difficult for an NN to model noisy and significantly nonstationary time series. The paper suggests optimizing the modeling process for a complicated-structure time series by NARX networks involving wavelet filtering. The developed procedure of wavelet filtering includes the application of the construction of wavelet packets and stochastic thresholds. A method to estimate the thresholds to obtain a solution with a defined confidence level is also developed. We introduce the algorithm of wavelet filtering. It is shown that the proposed wavelet filtering makes it possible to obtain a more accurate NARX model and improves the efficiency of the forecasting process for a natural time series of a complicated structure. Compared to ARIMA, the suggested method allows us to obtain a more adequate model of a nonstationary time series of complex nonlinear structure. The advantage of the method, compared to RNN, is the higher quality of data approximation for smaller computation efforts at the stages of network training and functioning that provides the solution to the problem of long-term dependencies. Moreover, we develop a scheme of approach realization for the task of data modeling based on NARX and anomaly detection. The necessity of anomaly detection arises in different application areas. Anomaly detection is of particular relevance in the problems of geophysical monitoring and requires method accuracy and efficiency. The effectiveness of the suggested method is illustrated in the example of processing of ionospheric parameter time series. We also present the results for the problem of ionospheric anomaly detection. The approach can be applied in space weather forecasting to predict ionospheric parameters and to detect ionospheric anomalies.

An online stochastic MPC-based fault-tolerant optimization for microgrids

Due to the current energy dependence of society, the availability and correct functioning of microgrids are strategic issues to be dealt with. Currently, energy management systems are very focused on achieving systems that present a remarkable optimization of demand as well as a high degree of fault tolerance. This paper presents a novel Control Reconfiguration framework to manage faults based on Model Predictive Control (MPC). The proposal comprises fault detection, isolation and reconfiguration. The Fault Detection and Isolation method identifies the faults based on parity equations, structured residuals and stochastic thresholds, while the reconfiguration is focused on adapting the control law to the faulty scenario. Therefore, two different model predictive controllers are involved: MPC-1 drives the microgrid to the correct values and MPC-2 carries out the control reconfiguration, optimizing a multi-criteria objective function where outputs are the values of criteria. The new decision variables of the fault reconfiguration are the selection of mitigation actions to be performed to reduce the effects of faults. A novel formulation of this problem is provided. Experiments have been carried out on a real microgrid located in the laboratory to show the benefits of the method.

A dynamic spike threshold with correlated noise predicts observed patterns of negative interval correlations in neuronal spike trains

Negative correlations in the sequential evolution of interspike intervals (ISIs) are a signature of memory in neuronal spike-trains. They provide coding benefits including firing-rate stabilization, improved detectability of weak sensory signals, and enhanced transmission of information by improving signal-to-noise ratio. Primary electrosensory afferent spike-trains in weakly electric fish fall into two categories based on the pattern of ISI correlations: non-bursting units have negative correlations which remain negative but decay to zero with increasing lags (Type I ISI correlations), and bursting units have oscillatory (alternating sign) correlation which damp to zero with increasing lags (Type II ISI correlations). Here, we predict and match observed ISI correlations in these afferents using a stochastic dynamic threshold model. We determine the ISI correlation function as a function of an arbitrary discrete noise correlation function {{,mathrm{mathbf {R}},}}_k, where k is a multiple of the mean ISI. The function permits forward and inverse calculations of the correlation function. Both types of correlation functions can be generated by adding colored noise to the spike threshold with Type I correlations generated with slow noise and Type II correlations generated with fast noise. A first-order autoregressive (AR) process with a single parameter is sufficient to predict and accurately match both types of afferent ISI correlation functions, with the type being determined by the sign of the AR parameter. The predicted and experimentally observed correlations are in geometric progression. The theory predicts that the limiting sum of ISI correlations is -0.5 yielding a perfect DC-block in the power spectrum of the spike train. Observed ISI correlations from afferents have a limiting sum that is slightly larger at -0.475 pm 0.04 (text {mean} pm text {s.d.}). We conclude that the underlying process for generating ISIs may be a simple combination of low-order AR and moving average processes and discuss the results from the perspective of optimal coding.

Effects of Random Environmental Perturbation on the Dynamics of a Nutrient–Phytoplankton–Zooplankton Model with Nutrient Recycling

A stochastic nutrient–phytoplankton–zooplankton model with instantaneous nutrient recycling is proposed and analyzed in this paper. When the nutrient uptake function and the grazing function are linear and the ingested phytoplankton is completely absorbed by the zooplankton, we establish two stochastic thresholds R0S and R1S, which completely determine the persistence and extinction of the plankton. That is, if R0S&lt;1, both the phytoplankton and the zooplankton eventually are eliminated; if R0S&gt;1 and R1S&lt;1, the phytoplankton is persistent in mean but the zooplankton is extinct; while for R1S&gt;1, the entire system is persistent in mean. Furthermore, sufficient criteria for the existence of ergodic stationary distribution of the model are obtained and the persistent levels of the plankton are estimated. Numeric simulations are carried out to illustrate the theoretical results and to conclude our study. Our results suggest that environmental noise may cause the local bloom of phytoplankton, which surprisingly can be used to explain the formation of algal blooms to some extent. Moreover, we find that the nonlinear nutrient uptake function and grazing function may take credit for the periodic succession of blooms regardless of whether they are in the absence or presence of the environmental noises.

Calculation and implementation of sample-wide stochastic thresholds for forensic genetic analysis of STRs and SNPs for massively parallel sequencing platforms

Capillary electrophoresis (CE) analysis of short tandem repeats (STRs) and single nucleotide polymorphisms (SNPs) use a stochastic threshold to consider the possibility of missing alleles (dropouts) or detecting additional alleles (drop-ins). In CE, this threshold may be approximately 200 RFU, and peak heights are assessed relative to this threshold. In next generation sequencing (NGS), also known as massively parallel sequencing (MPS), STRs are identified by their sequence, and specific alleles are identified by their repeat number and intra-allelic variation. Abundance is approximated by the number of sequence reads for each allele. The total number of reads generated for each marker in a sample depends on factors such as the numbers of samples pooled for sequencing, the number of markers in the assay, the integrity and quantity of the input DNA sample, and the inter-locus balance of the assay. For multiplexes that contain both autosomal and sex-linked markers, the biological sex of the sample also influences total reads per locus. To normalize these variables and better establish a robust stochastic threshold, a sample-wide metric is proposed for estimating the possibility of dropouts or drop-ins based on the variance of the inter-locus balance of the markers across a sample. The intuition is that samples with variable allele balance globally are more likely to have noisier data and therefore require more stringent read count thresholds. This method is robust to sequencing multiplexity, biological sex and manufacturing lot variation.

Traveling salesperson problem with unique pricing and stochastic thresholds

In this variant of traveling salesperson person problem, only the customers who accept to pay a unique service fee are serviced. Each customer has a random price acceptance threshold and accepts to pay any fee lower than this threshold. To address this issue, a chance-constrained stochastic model is developed and two exact methods, one based on a Branch & Cut scheme, and the other on Logic Based Benders Decomposition, are built. Numerical tests show that, on small instances both methods are efficient but on larger instances with 100 customers, Logic Based Benders Decomposition dominates clearly the Branch & Cut method.

Impact of Levy noise on a stochastic Norovirus epidemic model with information intervention

In this article, we study the dynamics of Norovirus infection by developing a stochastic epidemic model having Levy noise. The study shows that Levy noise and informative interventions have more influence on the said dynamics. Firstly, we show that the model has a unique global positive solution. After this, we formulated a stochastic threshold value as a necessary condition for the extinction and persistence in the mean of the proposed epidemic model. Finally, numerical simulation are drawn to verify our obtained results of the dynamics. The perturbed stochastic approach may affect the dynamical properties of the model and large noises will be greatly significant to minimize its transmission.

Comparison of the Efficiency of GlobalfilerTM IQC PCR Amplification Kit and Powerplex® Fusion 6C System with Half-Volume Reactions for Forensic Trace DNA Testing

Two major challenges in daily and routinely forensic genetics test are samples with low or very low quantitiesof DNA and high cost of processing. To overcome these obstacles, a reduction in reaction volume to half wouldoffer a substantial benefit, but even so it should provide complete genetic profiles without conceding the qualityof the results. The aim of this study is to test the robustness of two commercially available kits, GlobalFilerTMIQC PCR Amplification Kit (GF-IQC) and PowerPlex® Fusion 6C System (P-6C), with half volume reaction inaccordance with SGWDAM guidelines. GF-IQC showed minimum and stochastic threshold of 45 and 610 RFU,while P-6C demonstrated 60 and 670 RFU of those values respectively. The P-6C can tolerate to many inhibitorsincluding melanin, hematin, and humic acid. Both kits showed the same performance on case work profiling andthe sensitivity of allele detection of P-6C was not significantly different from that of GF-IQC (p=0.144). The resultsof this study demonstrated that GF-IQC and P-6C with half volume reaction can produce good quality profiles andcould be applied for forensic DNA examination.

Impact of information and Lévy noise on stochastic COVID-19 epidemic model under real statistical data

In this paper, we consider the dynamical behaviour of a stochastic coronavirus (COVID-19) susceptible-infected-removed epidemic model with the inclusion of the influence of information intervention and Lévy noise. The existence and uniqueness of the model positive solution are proved. Then, we establish a stochastic threshold as a sufficient condition for the extinction and persistence in mean of the disease. Based on the available COVID-19 data, the parameters of the model were estimated and we fit the model with real statistics. Finally, numerical simulations are presented to support our theoretical results.

Outbreak or extinction of bovine cysticercosis and human taeniasis: A Stochastic modelling approach

Bovine cysticercosis and human taeniasis are neglected food-borne infections that pose challenges to food safety, peoples’ health and the economy of rural farmers who depend on livestock keeping. In this paper, the continuous time Markov chain (CTMC) stochastic model is formulated based on its corresponding deterministic model and rigorously analyzed to study the dynamics of cysticercosis in cattle and taeniasis in humans. The multitype branching process is adopted to compute the stochastic threshold and numerical simulations for the CTMC model with 10,000 sample paths are used to compute probabilities of diseases’ extinction when initial conditions for infected classes are varied. The results show that when there is disease outbreak, the solutions of CTMC stochastic model are relatively close to deterministic model solutions. The analytical and numerical results for probability of diseases’ extinction are in good agreement when initially there is no infectious human. Some variations in probability of diseases’ extinction are due to infectious beef being considered a discrete number in CTMC model. The results show further that the diseases' extinction probability is high when the diseases emerge from a small number of T. saginata eggs or from infected cattle. However, the probability becomes low when there is at least an infectious beef at the beginning of the diseases' outbreak.

Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network

This paper aims at analyzing the dynamical behavior of a SIR hepatitis B epidemic stochastic model via a novel approach by incorporating the effect of information interventions and random perturbations. Initially, we demonstrate the positivity and global existence of the solutions. Afterward, we derive the stochastic threshold parameter mathbf {R_s}, followed by the fact that this number concludes the transmission of hepatitis B from the population. By increasing the intensity of noise, we get mathbf {R_s} less than one, inferring that ultimately hepatitis B will lapse. While decreasing the intensity of noise to a sufficient level, we have mathbf {R_s} > 1. For the case mathbf {R_s} > 1, adequate results for the presence of stationary distribution are achieved, showing the prevalence of hepatitis B. The present study also involves the derivation of the necessary conditions for the persistence of the epidemic. Finally, the main theoretical solutions are plotted through simulations. Discussion on theoretical and numerical results shows that utilizing random perturbations and information interventions have a pronounced impact on the syndrome’s dynamics. Furthermore, since most communities interact with each other, and the disease spread rate is affected by this factor, a new variable-order fractional network of the stochastic hepatitis B model is offered. Subsequently, this study will provide a robust theoretical basis for comprehending worldwide SIR stochastic and variable-order fractional network-related case studies.

Thresholding process on the dissimilarities between probability models for change detection on remote sensing data

Change detection comprises a very important application in environmental studies involving multitemporal data obtained by remote sensing. Developing more accurate change detection methods is an ongoing challenge. Our study presents a new, unsupervised change detection method based on the concepts of stochastic distances and thresholding. To prove the effectiveness of the method, a study was carried out involving a region in southeastern Brazil, from 1999 to 2018, which underwent a high rate of environmental degradation caused by urban, industrial, and sand mining expansion. In this investigation, images obtained by thematic mapper and operational land imager sensors aboard the Landsat-5 and -8 satellites were used. Comparisons with the change vector analysis (CVA) method are included in the analyses. Results showed that the proposed method is capable of providing more accurate results in relation to the CVA method, after adequate parameterization, providing more realistic mappings with greater precision.

The threshold dynamics of a stochastic two-patch brucellosis model

Brucellosis is one of the major infective and contagious bacterial diseases among animals in pastoral areas of some countries. In this paper, we introduce the effect of environment white noise in the spatial propagation process of brucellosis, and consider a stochastic two-patch brucellosis model. On one hand, we get existence and uniqueness of the global positive solution to the stochastic systems. On the other hand, by using the stochastic Lyapunov function theory we obtain a series of stochastic threshold dynamics results, incorporating extinction of the disease, existence of a unique ergodic stationary distribution of the positive solutions to systems in both patch 1 and patch 2. Furthermore, we find that stochastic perturbation is contribute to extinction of the disease to some extent by numerical simulations.