Bernoulli Process Research Articles

Predicting Natural Gas Production in Various Nations Using a Fractional Grey Bernoulli Approach

Accurate forecasting of natural gas production is crucial for economic stability, environmental sustainability, and market investment. This study presents an advanced forecasting method using the fractional grey Bernoulli model, which combines fractional accumulation and Bernoulli processes to enhance the predictive accuracy for nonlinear datasets. The model’s versatility and flexibility allow it to adapt to various data characteristics and complexities, thereby outperforming traditional grey models in forecasting performance. To optimize the model parameters, this study employs the Particle Swarm Optimization (PSO) algorithm, further improving the model’s effectiveness. Empirical analysis of natural gas production data from Brazil, Italy, and Qatar demonstrates that the model exhibits significant advantages in both fitting and forecasting capabilities. The findings indicate that the fractional grey Bernoulli model achieves high accuracy and reliability in predicting natural gas production in these countries, providing a robust framework for strategic energy planning and investment decision-making. With average forecast errors of 1.9113%, 4.0353%, and 1.8902% for natural gas production in Brazil, Italy, and Qatar respectively, this study underscores the model’s effectiveness in enhancing forecast reliability and minimizing risk, providing valuable insights for sustainable energy development.

Closed-form solutions for Bernoulli and compound Poisson branching processes in random environments*

Abstract For branching processes, the generating functions for the limit distributions of the so-called ratios of probabilities of rare events satisfy Schröder-type integral–functional equations. With the exception of a few special cases, the corresponding equations cannot be solved analytically. I found a large class of Poisson-type offspring distributions for which the Schröder-type functional equations can be solved analytically. Moreover, for the asymptotics of limit distributions, the power and constant factors can be written explicitly. As a bonus, Bernoulli branching processes in random environments are treated. The beauty of this example is that the explicit formula for the generating function is unknown. Nevertheless, the closed-form expressions for the power and constant factors in the asymptotic can be written with the help of some effective techniques. The asymptotic expansion also contains oscillatory terms absent in the Poisson case. It is shown that at power three in the Bernoulli binomial kernels, short-phase discrete oscillations turn into long-phase continuous ones.

Refining current methods: Including comorbidity adjustment in burden of disease estimates

Abstract When quantifying years lost due to disability (YLD), a correction for multimorbidity (or comorbidity, COMO for short, in the Global Burden of Disease study) is necessary to avoid overestimating the morbidity-related burden of disease. Such an overestimation occurs if the calculation of disease frequencies does not consider that persons are counted more than once in a cross-sectional year. In such cases, the time spent with illness at an individual level can add up to a value of more than 1 year. To avoid this, a microsimulation is used that corrects the YLD to a maximum value of 1. A standard approach is to generate a synthetic data set by age, gender and region. Using prevalence estimates and based on (independent) Bernoulli experiments, a vector of diseases is randomly assigned to these (pseudo) individuals. The assignment is usually independent, which means that the presence of one disease has no influence on the presence of another disease. At this level, the individual YLD are then proportionally corrected (the maximum value is 1) and extrapolated to the population. However, there is evidence that disease clusters exist at the individual level. As part of the further development of such multimorbidity correction methods, a new approach will be tested and applied to generate a more realistic population of interest. This considers correlation patterns (1st step) between diseases when generating the synthetic data (2nd step) on the basis of Bernoulli experiments. For this purpose, the existing approaches need to be enriched by (pairwise) correlations between diseases, which requires the inclusion of additional epidemiological data sources. It is assumed that this will lead to an additional correction of the YLD, as they are still overestimated under an independent assignment.

Event‐Triggered Generalized Extended State Observer‐Based Control for Nonlinear Networked Systems Under Gain Variation and Multi‐Channel Attacks

ABSTRACTThis paper investigates the event‐triggered generalized extended state observer‐based estimation issue for a class of nonlinear networked control systems with unmodeled dynamics, external disturbances and multi‐channel attacks. In order to resist different forms of attack threats on multiple communication channels from sensors to the observer, Markov chain is introduced to describe the stochastic switching or jumping behavior between different attack modes. Considering the limited network resources, the measured outputs are transmitted to the observer only when the triggering conditions are met. Moreover, the parameters modeled by the Bernoulli process are adopted to help analyze potential random gain variations of the generalized extended state observer. By employing Lyapunov stability theory and stochastic systems analysis, sufficient conditions are derived to ensure that the augmented system is exponentially bounded in mean square, and the expected observer gains are further determined through linear matrix inequalities. Finally, a numerical example and a simulation related to the RLC series circuit system are conducted, illustrating the proposed method's effectiveness.

Cost Analysis of Fuzzy Discrete (s, S) Queueing Inventory System with Positive Lead Time and Optimization using Genetic Algorithm

In this article, a queueing inventory model with discrete time (DQIM) FGEOM/FGEOM/1 with (s, S) replenishment policy incorporating fuzzy numbers as input parameters is considered. The system has a fuzzy pentagonal number arrival rate according to a Bernoulli process and a fuzzy pentagonal number service rate that follows a geometric distribution. Here, S represents the highest level of stock where the process of replenishment is stopped, and s represents the lowest level of stock at which replenishment is started again. Using matrix geometric method, the steady-state solution is obtained followed by derivation of various fuzzy performance measures. Further, the total cost function is defined as a two-variable function of the minimum and maximum stock level. Genetic algorithm is employed to optimize the total cost. Various examples are presented to highlight the dependence of cost on input parameters. The use of PFN in DQIS and genetic algorithm in the optimization of DQIS is introduced in this paper for the first time. JEL Codes: C44, C61, C62, D11, D12, L89 Received: 17/07/2024. Accepted: 29/09/2024. Published: 04/10/24.

Long-Run Behavior Estimation of Temporal Boolean Networks With Multiple Data Losses.

This brief devotes to investigating the long-run behavior estimation of temporal Boolean networks (TBNs) with multiple data losses, especially the asymptotical stability. The information transmission is modeled by Bernoulli variables, based on which an augmented system is constructed to facilitate the analysis. A theorem guarantees that the asymptotical stability of the original system can be converted to that of the augmented system. Subsequently, one necessary and sufficient condition is obtained for asymptotical stability. Furthermore, an auxiliary system is derived to study the synchronization issue of the ideal TBNs with normal data transmission and TBNs with multiple data losses, as well as an effective criterion for verifying synchronization. Finally, numerical examples are given to illustrate the validity of the theoretical results.

Drought‐Rich Periods Are More Likely Than Flood‐Rich Periods in Brazil

AbstractStreamflow exhibits persistent decadal variability; however, it is unclear if the magnitude and spatial extent of these variabilities are symmetric for droughts and floods. Here, we examine drought‐rich and flood‐rich periods in 319 streamflow gauges in Brazil from 1940 to 2020. Drought‐ and flood‐rich periods are detected by computing annual streamflow minima and maxima time series and using scan statistics to verify if events exceeding a threshold follow a Bernoulli process. We contrast streamflow time clustering with rainfall, evaporation, water abstraction, the Atlantic Multidecadal Oscillation (AMO), and the Pacific Decadal Oscillation (PDO). We detected a higher spatial frequency of drought‐ than flood‐rich periods. For 5‐year return period thresholds, drought‐rich periods are observed in 81% of the basins, 16.7 times the false positive rate (4.8%) and 4.7 times flood‐rich periods (17%). This asymmetry is linked with sharp increases in water abstractions since the 1990s and a higher prevalence of rainfall‐poor periods (41% of gauges) compared to rainfall‐rich (22% of gauges), which we interpret as being further amplified into drought‐rich periods due to an interannual persistence of water storage deficits. Brazil experienced a dry period until the 1960s, extensive flooding in the 1980s, and record low flows from the 2000s onward. Drought and flood‐rich periods are well aligned with rainfall clustering, water abstractions, the AMO and PDO. Droughts‐rich periods are more frequent in shorter time scales (several years to one decade) and flood‐rich periods in longer time scales (a few decades). Our findings highlight the nonlinearity and asymmetry of drought and flood change at decadal scales.

Model for random internalization of nanoparticles by cells

We propose a stochastic model for the internalization of nanoparticles by cells formulating cellular uptake as a compound Poisson process with a random probability of success. This is an alternative approach to the one presented by Rees [] who explained overdispersion in nanoparticle uptake and associated negative binomial distribution by considering a Poisson distribution for particle arrival and a gamma-distributed cell area. In our stochastic model, the formation of new pits is represented by the Poisson process, whereas the capturing process and the population heterogeneity are described by a random Bernoulli process with a beta-distributed probability of success. The random probability of success generates ensemble-averaged conditional transition probabilities that increase with the number of newly formed pits (self-reinforcement). As a result, an ensemble-averaged nanoparticle uptake can be represented as a Polya process. We derive an explicit formula for the distribution of the random number of pits containing nanoparticles. In the limit of the fast nucleation and low probability of nanoparticle capture, we find the negative binomial distribution. Published by the American Physical Society 2024

Input-to-State Stability of Switched Network Control Systems Under Unknown Deception Attacks.

This article focuses on the stability issue of switched network control systems (SNCSs) under deception attacks described by a Bernoulli process with unknown probability distribution. The false information in deception attacks is unknown but bounded and may be state dependent or state independent. By means of the input-to-state stability (ISS) tool and the convex combination method, an improved lemma is first developed for SNCSs, which facilitates the derivations of our results. After that, some attack-independent sufficient conditions for the ISS of SNCSs are obtained for mode-dependent average dwell time switching and stochastic switching, respectively. Different from existing results, the concerned switching contributes to the stability of SNCSs, which benefits the ISS performance of SNCSs even though the unknown deception attacks cause all subsystems to be non-ISS. The proposed results provide an effective solution with strong robustness to deal with unknown deception attacks or denial-of-service attacks.

Line-of-sight Cox percolation on Poisson–Delaunay triangulation

In this work, percolation properties of device-to-device (D2D) networks in urban environments are investigated. On a street system modeled by a Poisson–Delaunay triangulation (PDT), users are of two types: given either by a Cox process supported by the edges of the PDT (i.e. on streets) or by a Bernoulli process on the vertices of the PDT (i.e. at crossroads). We state several percolation regimes for the resulting connectivity graph according to the parameters of the model. This work completes and specifies results of Le Gall et al. (2021). To do it, we take advantage of a percolation tool, inspired by enhancement techniques, used to our knowledge for the first time in the context of communication networks.

Explainable decomposition of nested dense subgraphs

Discovering dense regions in a graph is a popular tool for analyzing graphs. While useful, analyzing such decompositions may be difficult without additional information. Fortunately, many real-world networks have additional information, namely node labels. In this paper we focus on finding decompositions that have dense inner subgraphs and that can be explained using labels. More formally, we construct a binary tree T with labels on non-leaves that we use to partition the nodes in the input graph. To measure the quality of the tree, we model the edges in the shell and the cross edges to the inner shells as a Bernoulli variable. We reward the decompositions with the dense regions by requiring that the model parameters are non-increasing. We show that our problem is NP-hard, even inapproximable if we constrain the size of the tree. Consequently, we propose a greedy algorithm that iteratively finds the best split and applies it to the current tree. We demonstrate how we can efficiently compute the best split by maintaining certain counters. Our experiments show that our algorithm can process networks with over million edges in few minutes. Moreover, we show that the algorithm can find the ground truth in synthetic data and produces interpretable decompositions when applied to real world networks.

Receding horizon estimation for multi‐rate sampled data systems under component‐based event‐triggered mechanisms: Handling delayed and degraded measurements

AbstractThe purpose of this article is to develop the receding horizon (RH) estimation for multi‐rate sampled systems with measurement delays and packet losses in the measurements. An event‐triggered transmission scheme is introduced to remove measurements that are unnecessary for the design of the estimator. The stochastic diagonal matrixes are introduced to represent the phenomenon of packet losses, where each component is subject to an individual Bernoulli process. The original system is firstly transformed into a delay‐free one by using the reorganized observation method. Further, a batch form and an iterative form of RH estimation are proposed by minimizing a given cost function that includes some terminal weighting terms based on the new system. The stability of the proposed RH estimation is guaranteed by the natural assumptions and a simulation instance is given to verify the effectiveness of the proposed method.

Event‐triggered adaptive output feedback control of unmanned aerial vehicles under hybrid attacks

AbstractThis study addresses the adaptive dynamic output feedback (DOF) control for unmanned aerial vehicle systems subjected to hybrid attacks. These attacks are delineated by two Bernoulli variables, signifying denial‐of‐service (DoS) and deception attacks, respectively. In an effort to enhance energy efficiency and reduce communication costs in the presence of network delays, the study introduces an innovative probability event‐triggering mechanism (PETM). Subsequently, it crafts a DOF controller that operates based on the available measurement outputs. By harnessing Lyapunov stability theory, the study identifies sufficient conditions that guarantee the stability of the system's augmented dynamics. Finally, the efficacy and applicability of the proposed method are underscored through a case study on an unmanned aerial vehicle.

Probabilistic Fuzzy System for Evaluation and Classification in Failure Mode and Effect Analysis

Failure Mode and Effect Analysis (FMEA) is an essential risk analysis tool that is widely applicable in various industrial sectors. This structured technique allows us to identify and assign priority levels to potential failures that violate the reliability of a system or process. Failure evaluation occurs in a decision-making environment with uncertainty. This study proposes a probabilistic fuzzy system that integrates linguistic and stochastic uncertainty based on a Mamdani-type model to strengthen the FMEA technique. The system is based on analyzing the frequency of failures and obtaining the parameters to determine the probability of occurrence through the Poisson distribution. In addition, the severity and detection criteria were evaluated by the experts and modeled using the Binomial distribution. The evaluation result is a discrete value analogous to the process of obtaining the success or failure of the expert generating the evaluation of 10 Bernoulli experiments. Three fuzzy inference expert systems were developed to combine multiple experts’ opinions and reduce linguistic subjectivity. The case study was implemented in the knitting area of a textile company in the south of Guanajuato to validate the proposed approach. The potential failure of the knitting machinery, which compromises the top tension subsystem’s performance and the product’s quality, was analyzed. The proposed system, which is based on a robust mathematical model, allows for reliable fault evaluation with a simple scale. The classification performed by the system and the one performed by the experts has similar behavior. The results show that the proposed approach supports decision-making by prioritizing failure modes.

단수 휴가와 일량 제어정책을 갖는 이산시간 Geo/G/1 시스템의 대기시간 분석

In this paper, we derived the steady-state waiting time distribution of a discrete-time Geo/ G/1 queuing system under single vacation and D-policy. Customers such as WIP(work-in- process), parts, packets arrive at the system with Bernoulli process, and the server takes a single vacation with length of V when there are no more customers to service in the system. The restart condition is met when the total service time (workload, unfinished work) of customers waiting in the system at the end of vacation exceeds the workload threshold D. If the total amount of work in the system is less than or equal to D at the end of vacation, the server waits until the restart conditions are met and serves waiting customers. Otherwise, it starts to be busy as soon as the vacation ends. The average waiting time was also derived as a performance measure. Additionally, the computability of theoretical results was confirmed through a numerical example. The server control policy covered in this study can be applied in situations where it is desired to reduce operating costs per unit time due to high server restart costs (or energy consumption) in production and communication systems.

An improved gossip-based distributed control strategy of multi-objective combined economic emission dispatch in smart grids with stochastic communication link failures

This paper proposes a distributed control strategy, leveraging gossip-based communication, for combined economic emission dispatch (CEED) in smart grids. It optimizes economic dispatch while considering separate objectives for SO2, NOx, CO2 emissions. The network is modeled as a Bernoulli process to describe stochastic communication link failures. Utilizing the Analytic Hierarchy Process to determine the weights between multiple objectives in the CEED to aid decision-makers at thermal power plants in selecting appropriate solutions based on the actual conditions of power grid. Simulation results demonstrate the strategy effectiveness.

Finite region stability and networked predictive control for 2-D nonlinear time-delayed systems with quantization, packet dropouts and random disturbances

In this paper, we focus on the finite region stability (FRS) and networked predictive control (NPC) problems for two-dimensional (2-D) networked control systems (NCS) with time delays, quantization errors, packet losses and random disturbances described by the Roesser model. The random packet dropouts and disturbances are modeled as Bernoulli process, and the sufficient conditions of FRS and finite region boundedness (FRB) for 2-D NCS are obtained by using the expectation to process the Lyapunov function difference, so as to better study the transient performance of the systems. According to the recursive formula, an active compensation scheme for time delays of NPC is proposed, which takes into account quantization errors, packet losses, nonlinearity and interferences. Introducing FRS and FRB into 2-D NCS and considering the above factors in NPC scheme are new attempts made in this paper. An example is used to demonstrate the validity of the conclusions in the end.

Regression estimation for continuous-time functional data processes with missing at random response

In this paper, we are interested in nonparametric kernel estimation of a generalised regression function based on an incomplete sample ( X t , Y t , ζ t ) t ∈ [ 0 , T ] copies of a continuous-time stationary and ergodic process ( X , Y , ζ ) . The predictor X is valued in some infinite-dimensional space, whereas the real-valued process Y is observed when the Bernoulli process ζ = 1 and missing whenever ζ = 0 . Uniform almost sure consistency rate as well as the evaluation of the conditional bias and asymptotic mean square error are established. The asymptotic distribution of the estimator is provided with a discussion on its use in building asymptotic confidence intervals. To illustrate the performance of the proposed estimator, a first simulation is performed to compare the efficiency of discrete-time and continuous-time estimators. A second simulation is conducted to discuss the selection of the optimal sampling mesh in the continuous-time case. Then, a third simulation is considered to build asymptotic confidence intervals. An application to financial time series is used to study the performance of the proposed estimator in terms of point and interval prediction of the IBM asset price log-returns. Finally, a second application is introduced to discuss the usage of the initial estimator to impute missing household-level peak electricity demand.

An encoding approach for stable change point detection

Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis. We develop a structural subsampling procedure such that the observations are encoded into multiple sequences of Bernoulli variables. A maximum likelihood approach in conjunction with a newly developed searching algorithm is implemented to detect change points on each Bernoulli process separately. Then, aggregation statistics are proposed to collectively synthesize change-point results from all individual univariate time series into consistent and stable location estimations. We also study a weighting strategy to measure the degree of relevance for different subsampled groups. Simulation studies are conducted and shown that the proposed change-point methodology for multivariate time series has favorable performance comparing with currently available state-of-the-art nonparametric methods under various settings with different degrees of complexity. Real data analyses are finally performed on categorical, ordinal, and continuous time series taken from fields of genetics, climate, and finance.

Finite-time synchronization for coupled neural networks with time-delay jumping coupling

The finite-time synchronization problem is studied for coupled neural networks (CNNs) with time-delay jumping coupling. Markovian switching topologies, imprecise delay models, uncertain parameters and the unavailable of topology modes are considered in this work. A mode-dependent delay with pre-known conditional probability is built to handle the imprecise delay model problem. A hidden Markov model with uncertain parameters is introduced to describe the mode mismatch problem, and an asynchronous controller is designed. Besides, a set of Bernoulli processes models the random packet dropouts during data communication. Based on Markovian switching topologies, mode-dependent delays, uncertain probabilities and packet dropout, a sufficient condition that guarantees the CNNs reach finite-time synchronization (FTS) is derived. Finally, a numerical example is derived to demonstrate the efficiency of the proposed synchronous technique.