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Project management requires the chaotic but important task of estimating software development effort. Several soft computing approaches have been proposed to increase estimation accuracy, and optimization techniques are utilized to concentrate on key aspects. However, a majority of works use data processing that has been found to be unreliable, time-consuming and typically leads to greater error rates. Therefore, the research proposes an efficient software development effort prediction model employing unique deep learning technology to alleviate the existing limitations. Data collection, pre-processing, feature selection and software development effort prediction are only a few of the varied phases of the proposed objective. After data collection, the data are pre-processed, including data cleaning, normalization, missing values and imputation. The expanded archer fish optimization method (Ext_AFO) is used to choose the best features from the pre-processed data. The Multilayer Perceptron Assisted Honey Bidirectional Gated Recurrent Feed Forward Network (Multi-HBiG) is built into this research work to provide an intelligent prediction model for software development effort estimation. The model parameters are adjusted using the Adaptive Honey Badger Optimisation Algorithm (A-Hba) to improve the overall estimation performance. The Albrecht dataset, China dataset, Desharnais dataset, Kemerer dataset, Maxwell dataset, Kitchenham dataset and Cocomos81 dataset are the datasets used in this study. The proposed approach surpassed other models when compared against Mean Relative Error (MRE), Mean Magnitude of Relative Error (MMRE), Mean Balanced Relative Error (MBRE) and Mean Inverted Balanced Relative Error (MIBRE) in the results section. The proposed model was assessed in this study using the MAE in each dataset, and it achieved 0.0753 for the China dataset, 0.0763 for the Cocomos81 dataset, 0.0737 for the Desharnais dataset, 0.0754 for the Kemerer dataset, 0.0759 for the Kitchenham dataset, 0.0734 for the Maxwell dataset and 0.0737 for the Albrecht dataset, respectively. [ABSTRACT FROM AUTHOR]

The simultaneous presence of uncertain data delays and data loss in a network control system complicates the state estimation problem and its solution. This paper redesigns the Kalman filter (KF) algorithm for systems with k-step random delayed data and data loss to improve estimation accuracy. A binary Bernoulli distribution is employed in the modified KF algorithm to model the received data with the knowledge of data delay and loss probabilities. Besides, the distribution of the non-Gaussian noise in the measurement system will degrade the performance of the conventional KF algorithm based on the minimum mean square error. Therefore, the modified KF algorithm is extended to the maximum correntropy Kalman filter (MCKF) algorithm to overcome the effect of non-Gaussian noise. The estimation accuracy of the modified KF and MCKF algorithms are experimentally compared under Gaussian and non-Gaussian noises, respectively. The simulation results demonstrate the excellent estimation performance of the proposed modified KF and MCKF algorithms under Gaussian and non-Gaussian noises, respectively. [ABSTRACT FROM AUTHOR]

In this paper, event-triggered control for uncertain delayed neural networks (DNNs) with actuator saturation against deception attack is discussed. We propose a novel framework into which an event-triggered mechanism (ETM), actuator saturation, system uncertainty, and deception attack are combined. In the framework, the discrete ETM is employed to determine whether the sampled signal should be transmitted to controller so as to save network bandwidth, a random occurrence deception attack model satisfying Bernoulli distribution is introduced to construct the system robust, and actuator saturation is considered due to the actual complex network environment. Based on the framework, we discussed the stochastic stability of a novel delayed neural network model in a closed-loop system. By resorting to the appropriate Lyapunov–Krasovskii functional (LKF), we derive some new sufficient conditions for the stochastically stable of the system and obtain the gain of the system controller using efficient linear matrix inequality (LMI) method. Finally, a numerical example, in the end, demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This study addresses $\mathcal {H}_{\infty }$ filtering against DoS attacks within the framework of singular Markov jump systems. To provide a more comprehensive depiction of the issue pertaining to cyber security, DoS attacks are perceived as occurring in an unpredictable manner and can be represented by a collection of a random variable that follows the Bernoulli distribution. Consequently, the corresponding filter error system is formulated. Utilizing a set of viable linear matrix inequalities, this research establishes criteria of stochastically admissible for filter error system, ensuring a specified $\mathcal {H}_{\infty }$ performance. A filter design method under DoS attacks is proposed. Finally, the effectiveness of this method is demonstrated through a practical example involving a tunnel diode model.

This paper considers the problem of randomly varying trial lengths of a class of two-dimensional (2D) linear systems represented by Roesser model, and two new iterative learning control (ILC) schemes are proposed. One is a conventional P-type control rule with a modified tracking error; the other is an ILC law with an iteration-average operator. Both learning control schemes are developed by a 2D stochastic variable to describe varying trial lengths. Under the Bernoulli distribution assumption and the initial state conditions, the convergence analysis is performed rigorously in the probability sense. Finally, illustrative examples have been provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract This paper aims to establish distribution-free concentration inequalities for the log-likelihood function of Bernoulli variables, which means that the tail bounds are independent of the parameters. Moreover, Bernstein’s and Bennett’s inequalities with optimal constants are obtained. The simulation study shows significant improvements over the previous results.

This paper aims to establish distribution-free concentration inequalities for the log-likelihood function of Bernoulli variables, which means that the tail bounds are independent of the parameters. Moreover, Bernstein's and Bennett's inequalities with optimal constants are obtained. The simulation study shows significant improvements over the previous results. [ABSTRACT FROM AUTHOR]

Several studies deal with the development of advanced statistical methods for predicting football match results. These predictions are then used to construct profitable betting strategies. Even if the most popular bets are based on whether one expects that a team will win, lose, or draw in the next game, nowadays a variety of other outcomes are available for betting purposes. While some of these events are binary in nature (e.g. the red cards occurrence), others can be seen as binary outcomes. In this paper we propose a simple framework, based on score-driven models, able to obtain accurate forecasts for binary outcomes in soccer matches. To show the usefulness of the proposed statistical approach, two experiments to the English Premier League and to the Italian Serie A are provided for predicting red cards occurrence, Under/Over and Goal/No Goal events. [ABSTRACT FROM AUTHOR]

This paper is devoted to analyzing Fixed/Preassigned-time synchronization of T–S fuzzy complex networks (TSFCNs) with stochastic effects. Unlike the existing results, partial information communication and complete information communication are all considered according to a Bernoulli distribution. Furthermore, different controllers with quantization are structured to realize our synchronization goal, and one of control parameters can switch based on the error information. Besides, we derive sufficient conditions to guarantee Fixed-time(FDT) and Preassigned-time(PAT) synchronization of TSFCNs, and analyze the difference of FDT and PAT synchronization. Finally, numerical examples and comparisons show that our results are valid. • Both successful communication and unsuccessful communication are considered by using Bernoulli random variable. • Quantized fuzzy controllers are designed, and one of control parameters can switch with the error information of systems. • Sufficient conditions of fixed-time and preassigned-time synchronization are derived for the stochastic T-S fuzzy complex networks. [ABSTRACT FROM AUTHOR]

The continuous Bernoulli distribution is defined on the unit interval and has a unique property related to fractiles. A fractile is a position on a probability density function where the corresponding surface is a fixed proportion. This article presents the derivation of properties of the continuous Bernoulli distribution and formulates a fractile or quantile regression model for a unit response using the exponentiated continuous Bernoulli distribution. Monte Carlo simulation studies evaluate the performance of point and interval estimators for both the continuous Bernoulli distribution and the fractile regression model. Real-world datasets from science and education are analyzed to illustrate the modeling abilities of the continuous Bernoulli distribution and the exponentiated continuous Bernoulli quantile regression model. [ABSTRACT FROM AUTHOR]

In this paper, an underwater robot system with nonlinear characteristics is studied by a backstepping method. Based on the state preservation problem of an Autonomous Underwater Vehicle (AUV), this paper applies the backstepping probabilistic gain controller to the nonlinear system of the AUV for the first time. Under the comprehensive influence of underwater resistance, turbulence, and driving force, the motion of the AUV has strong coupling, strong nonlinearity, and an unpredictable state. At this time, the system's output feedback can solve the problem of an unmeasurable state. In order to achieve a good control effect and extend the cruising range of the AUV, first, this paper will select the state error to make it a new control objective. The system's control is transformed into the selection of system parameters, which greatly simplifies the degree of calculation. Second, this paper introduces the concept of a stochastic backstepping control strategy, in which the robot's actuators work discontinuously. The actuator works only when there is a random disturbance, and the control effect is not diminished. Finally, the backstepping probabilistic gain controller is designed according to the nonlinear system applied to the simulation model for verification, and the final result confirms the effect of the controller design. [ABSTRACT FROM AUTHOR]

Multiregional clinical trials have a hierarchical data structure because several regions form a patient population and individual patients are nested within their own regions. Data are obtained from two different levels: regions and patients. To incorporate such a hierarchical structure, hierarchical linear models were proposed for the response variables following a normal distribution by Kim and Kang. In this article, we extend the hierarchical linear models to propose hierarchical generalized linear models (HGLMs) so that the response variables can follow the exponential family. We describe the details of the model when the response variable follows the Bernoulli distribution and the Poisson distribution. Simulation studies show that the empirical powers of the HGLM are greater than random effects model when region-level covariates are incorporated. [ABSTRACT FROM AUTHOR]

Due to a colossal soccer market, soccer analysis has attracted considerable attention from industry and academia. In-game outcome prediction has great potential in various applications such as game broadcasting, tactical decision making, and betting. In some sports, the method of directly predicting in-game outcomes based on the ongoing game state is already being used as a statistical tool. However, soccer is a sport with low-scoring games and frequent draws, which makes in-game prediction challenging. Most existing studies focus on pre-game prediction instead. This paper, however, proposes a two-stage method for soccer in-game outcome prediction, namely in-game outcome prediction (IGSOP). When the full length of a soccer game is divided into sufficiently small time frames, the goal scored by each team in each time frame can be modeled as a random variable following the Bernoulli distribution. In the first stage, IGSOP adopts state-based machine learning to predict the probability of a scoring goal in each future time frame. In the second stage, IGSOP simulates the remainder of the game to estimate the outcome of a game. This two-stage approach effectively captures the dynamic situation after a goal and the uncertainty in the late phase of a game. Chinese Super League data have been used for algorithm training and evaluation, and the results demonstrate that IGSOP outperforms existing methods, especially in predicting draws and prediction during final moments of games. IGSOP provides a novel perspective to solve the problem of in-game outcome prediction in soccer, which has a potential ripple effect on related research. [ABSTRACT FROM AUTHOR]

The continuous Bernoulli distribution is defined on the unit interval and has a unique property related to fractiles. A fractile is a position on a probability density function where the corresponding surface is a fixed proportion. This article presents the derivation of properties of the continuous Bernoulli distribution and formulates a fractile or quantile regression model for a unit response using the exponentiated continuous Bernoulli distribution. Monte Carlo simulation studies evaluate the performance of point and interval estimators for both the continuous Bernoulli distribution and the fractile regression model. Real-world datasets from science and education are analyzed to illustrate the modeling abilities of the continuous Bernoulli distribution and the exponentiated continuous Bernoulli quantile regression model.

A diagnosing method for phased antenna array element failures is proposed. The element excitation amplitudes and phases are reconstructed by a compressed sensing based approach, in which the radiated electric fields of the array are sampled by a single fixed receiving antenna. The diagnosing can be processed when the phased array is still in service. Particularly, it can be specialized for detecting faults only. Element excitation phases are designed to follow Bernoulli distribution, which is difficult to be realized in conventional geometric sampling methods. It is capable to provide effective and simultaneous detection for different types of failures with phase control means that are simpler comparing with other methods in which excitation phase adjustment is required. Especially, a two-step detection strategy is proposed to effectively detect phase failures due to faultily short-circuited phase shifters. Numerical results illustrate the effective sensing range of a single receiving antenna. Full-wave simulations validate the diagnosing performance in the presence of mutual couplings between array elements.

In this paper, maximal prefix codes with constant average length are investigated. This class of codes is a generalized class of thin codes. Some basic properties of the class of codes are given in this paper. This class of codes is shown to be closed under two operations "product of languages" and "composition of codes". Finite maximal prefix codes over binary alphabets with constant average length n = 3 are completely determined (the cases n = 1 and 2 are trivial). There are infinitely many such codes which can be classified into 9 series. [ABSTRACT FROM AUTHOR]

In this paper, an underwater robot system with nonlinear characteristics is studied by a backstepping method. Based on the state preservation problem of an Autonomous Underwater Vehicle (AUV), this paper applies the backstepping probabilistic gain controller to the nonlinear system of the AUV for the first time. Under the comprehensive influence of underwater resistance, turbulence, and driving force, the motion of the AUV has strong coupling, strong nonlinearity, and an unpredictable state. At this time, the system’s output feedback can solve the problem of an unmeasurable state. In order to achieve a good control effect and extend the cruising range of the AUV, first, this paper will select the state error to make it a new control objective. The system’s control is transformed into the selection of system parameters, which greatly simplifies the degree of calculation. Second, this paper introduces the concept of a stochastic backstepping control strategy, in which the robot’s actuators work discontinuously. The actuator works only when there is a random disturbance, and the control effect is not diminished. Finally, the backstepping probabilistic gain controller is designed according to the nonlinear system applied to the simulation model for verification, and the final result confirms the effect of the controller design.

It is known that due to uncertain delays and missing data wireless sensor networks (WSNs) may incur a significant loss in performance. In this work, we solve the problem in discrete-time state-space by developing the unbiased finite impulse response (UFIR) filter, Kalman filter (KF), and game theory H ∞ filter for systems with randomly delayed data and packet dropouts. The binary Bernoulli distribution is adopted for WSN channels to model the arrival data with supposedly known delay-time probability. The effectiveness of the UFIR filter, KF, and H ∞ filter is compared experimentally in terms of accuracy and robustness employing the GPS-measured vehicle coordinates transmitted with latency over WSN. [ABSTRACT FROM AUTHOR]

Milling chatter seriously affects workpiece surface quality and production efficiency. It is very important to accurately identify the milling stability domain for suppressing chatter and improving production efficiency. At present, the stability of the milling system is generally judged according to the fact that the spectral radius for eigenvalues of the state transition matrix is less than 1. However, there are random errors in both milling and hammering tests, which will inevitably cause errors in the attribute parameters of the milling system. The error of attribute parameters seriously affects the judgment result of milling stability. Therefore, the probabilistic characteristics of milling stability are studied to establish a correction method of stability lobe diagram (SLD) based on the optimization of attribute parameters. Firstly, in combination with Floquet theory, Newton-Cotes numerical integration is relied on to deduce a milling stability judgment model. Secondly, the stability judgment model is equivalently represented as a probability function of the Bernoulli distribution. The pre-correction function of attribute parameters is proposed as well as the re-correction function according to Bernoulli distribution of stability judgment results. Finally, a neural network between the attribute parameters and the spectral radius is established for every group of milling parameters to obtain higher computer efficiency. Because only the natural frequency affects the left and right positions of SLD, the golden section optimization method is presented for the natural frequency whereas the genetic algorithm is suggested to find the optimal other parameters. The experimental results show that the proposed method can improve the stability judgment accuracy of a single SLD lobe from 70% to 98%. Moreover, the whole SLD can be improved from 74% of the stability judgment accuracy to 89%. [ABSTRACT FROM AUTHOR]

In real-life applications, we often do not have population data but we can collect several samples from a large sample size of data. In this paper, we propose a median-based machine-learning approach and algorithm to predict the parameter of the Bernoulli distribution. We illustrate the proposed median approach by generating various sample datasets from Bernoulli population distribution to validate the accuracy of the proposed approach. We also analyze the effectiveness of the median methods using machine-learning techniques including correction method and logistic regression. Our results show that the median-based measure outperforms the mean measure in the applications of machine learning using sampling distribution approaches.

Due to a colossal soccer market, soccer analysis has attracted considerable attention from industry and academia. In-game outcome prediction has great potential in various applications such as game broadcasting, tactical decision making, and betting. In some sports, the method of directly predicting in-game outcomes based on the ongoing game state is already being used as a statistical tool. However, soccer is a sport with low-scoring games and frequent draws, which makes in-game prediction challenging. Most existing studies focus on pre-game prediction instead. This paper, however, proposes a two-stage method for soccer in-game outcome prediction, namely in-game outcome prediction (IGSOP). When the full length of a soccer game is divided into sufficiently small time frames, the goal scored by each team in each time frame can be modeled as a random variable following the Bernoulli distribution. In the first stage, IGSOP adopts state-based machine learning to predict the probability of a scoring goal in each future time frame. In the second stage, IGSOP simulates the remainder of the game to estimate the outcome of a game. This two-stage approach effectively captures the dynamic situation after a goal and the uncertainty in the late phase of a game. Chinese Super League data have been used for algorithm training and evaluation, and the results demonstrate that IGSOP outperforms existing methods, especially in predicting draws and prediction during final moments of games. IGSOP provides a novel perspective to solve the problem of in-game outcome prediction in soccer, which has a potential ripple effect on related research.

Finite mixture models are an important tool in the statistical analysis of data, for example in data clustering. The optimal parameters of a mixture model are usually computed by maximizing the log-likelihood functional via the Expectation-Maximization algorithm. We propose an alternative approach based on the theory of Mean Field Games, a class of differential games with an infinite number of agents. We show that the solution of a finite state space multi-population Mean Field Games system characterizes the critical points of the log-likelihood functional for a Bernoulli mixture. The approach is then generalized to mixture models of categorical distributions. Hence, the Mean Field Games approach provides a method to compute the parameters of the mixture model, and we show its application to some standard examples in cluster analysis. [ABSTRACT FROM AUTHOR]

Parametric yield estimation over multiple process corners plays an important role in robust circuit design. In this article, we propose a novel Bayesian inference method based on Bernoulli distribution (BI-BD) to efficiently estimate the multicorner yields for binary output circuit. The key idea is to encode the circuit performance correlation among different corners as our prior knowledge. Consequently, after combining a few simulation samples, the yield estimation over all corners can be calibrated via Bayesian inference based on iterative reweighted least squares (IRLS) and expectation maximization (EM). A circuit example demonstrates that the proposed BI-BD method can achieve up to 2.0 × cost reduction over the conventional Monte Carlo method without surrendering any accuracy. [ABSTRACT FROM AUTHOR]

This paper concerns the structure and the properties of a special class of combinatorial systems called minimal linear grammars. The role of unambiguous minimal linear grammars is investigated in the framework of the information transmission and coding problem and some related issues. [ABSTRACT FROM AUTHOR]

Radiation-induced single transient faults (STFs) are expected to evolve into multiple transient faults (MTFs) at nanoscale CMOS technology nodes. For this reason, the reliability evaluation of logic circuits in the presence of MTFs is becoming an important aspect of the design process of deep submicron and nanoscale systems. However, an accurate evaluation of the reliability of large-scale and very large-scale circuits is both very complex and time-consuming. Accordingly, this paper presents a novel soft error reliability calculation approach for logic circuits based on a probability distribution model. The correctness or incorrectness of individual logic elements are regarded as random events obeying Bernoulli distribution. Subsequently, logic element conversion-based fault simulation experiments are conducted to analyze the logical masking effects of the circuit when one logic element fails or when two elements fail simultaneously. On this basis, the reliability boundaries of the logic circuits can efficiently be calculated using the proposed probability model and fault simulation results. The proposed solution can obtain an accurate reliability range through single fault and double faults simulations with small sample sizes, and also scales well with the variation of the error rate of the circuit element. To validate the proposed approach, we have calculated the reliability boundaries of ISCAS'85, ISCAS'89, and ITC'99 benchmark circuits. Statistical analysis and experimental results demonstrate that our method is effective and scalable, while also maintaining sufficiently close accuracy. [ABSTRACT FROM AUTHOR]

• Given an alphabet A , and an (anti-)automorphism θ , a set L ⊆ A ⁎ is θ -invariant if θ (L) = L. • In the framework of θ -invariant sets, a defect effect is highlighted. • Several non-trivial examples of finite complete θ -invariant codes are presented. • Over a finite alphabet, any regular non complete θ -invariant code can be embedded into a complete one. • Given a thin θ -invariant code, being a maximal code, or being maximal in the family of θ -invariant codes, or being complete are equivalent properties. Let A be an arbitrary alphabet and let θ be an (anti-)automorphism of A ⁎ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under θ (θ -invariant for short) that is, languages L satisfying θ (L) ⊆ L. We establish an extension of the famous defect theorem. With regard to the so-called notion of completeness, we provide a series of examples of finite complete θ -invariant codes. Moreover, we establish a formula which allows to embed any non-complete θ -invariant code into a complete one. As a consequence, in the family of the so-called thin θ -invariant codes, maximality and completeness are two equivalent notions. [ABSTRACT FROM AUTHOR]

Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean independent entries. More precisely, we show that, under some moment conditions, such random matrices are asymptotically η -diagonal and Boolean independent from each other. This paper also gives a combinatorial condition under which such matrices are asymptotically Boolean independent from the matrix obtained by permuting the entries (thus extending a recent result in Boolean probability). In particular, we show that the random matrices considered are asymptotically Boolean independent from some of their partial transposes. The main results of the paper are based on combinatorial techniques. [ABSTRACT FROM AUTHOR]

The unscented Kalman filtering problem is investigated for a class of non‐linear discrete‐time stochastic systems subject to random packet dropout. Here, a random variable, which obeys Bernoulli distribution with known conditional probability, is introduced to depict the phenomenon of packet dropout occurring in a stochastic way. Based on the compensation technology of packet dropout, the one‐step prediction value of observer instead of zero‐input is used as a compensator when packet dropout occurs. Owing to taking the phenomenon of random packet dropout into account, the authors need to compute parameters to reduce the effects of the compensator. Then, based on the minimum mean square error principle, a new unscented Kalman filtering algorithm is proposed such that, for the random packet dropout, the filtering error is minimised. By solving the recursive matrix equations, the filter gain matrices and error covariance matrices can be obtained and the proposed results can be easily verified by using the standard numerical software. They finally provide two examples, one is a numerical example to show the performance of the proposed approach, and the other is to solve the problem of target estimation for a tracking system with random packet dropout. [ABSTRACT FROM AUTHOR]

The paper is concerned with sets of Bernoulli distributions which are closed under substitutions of independent random variables into Boolean functions from a given set (an algebra of Bernoulli distributions). A description of all finite algebras of Bernoulli distributions is given. [ABSTRACT FROM AUTHOR]

The central limit theorem indicates that when the sample size goes to infinite, the sampling distribution of means tends to follow a normal distribution; it is the basis for the most usual confidence interval and sample size formulas. This study analyzes what sample size is large enough to assume that the distribution of the estimator of a proportion follows a Normal distribution. Also, we propose the use of a correction factor in sample size formulas to ensure a confidence level even when the central limit theorem does not apply for these distributions. [ABSTRACT FROM AUTHOR]