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With the in-depth development of social reforms, the scientificization of enterprise online examinations has become more and more urgent and important. The key to realizing scientific examinations is the automation and rationalization of propositions. Therefore, the construction and realization of the test question bank is also more important. In the realization of the entire test question database, how to select satisfactory test questions randomly from a large number of test questions through the selection of test questions so that the average difficulty, discriminability, and reliability of the test are satisfactory? These requirements are also more important. Among them, random selection of questions is an important difficulty in the realization of the test question bank. In order to solve the difficulties of random selection of these test questions, the author combines the experience of constructing the test question bank and uses the discrete binomial distribution to draw conclusions. Random variables established the first mathematical model for topic selection. By determining the form of the test questions and the distribution of the difficulty of the test questions and then making it use a random function to select questions, this will achieve better results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of exponential synchronization of semi-Markov jump stochastic complex dynamical networks using nonuniform sampled-data control with random delayed information exchanges among dynamical nodes are discussed. In particular, it is considered that random delayed information exchanges follow a Bernoulli distribution, in which stochastic variables are used to model randomness. To achieve exponential synchronization, we designed a nonuniform sampled-data control approach. By constructing an appropriate Lyapunov–Krasovskii functional and using the Wirtinger inequality, sufficient criteria were obtained in terms of linear matrix inequalities. Finally, numerical examples were implemented to demonstrate the effectiveness and superiority of the proposed design techniques. [ABSTRACT FROM AUTHOR]

This paper is concerned with the passivity problem of memristive bidirectional associative memory neural networks (MBAMNNs) with probabilistic and mixed time-varying delays. By applying random variables with Bernoulli distribution, the information of probability time-varying delays is taken into account. Furthermore, we consider the probability distribution of the variation and the extent of the delays; therefore, the results derived are less conservative than in the existing papers. In particular, the leakage delays as well as distributed delays are all taken into consideration. Based on appropriate Lyapunov-Krasovskii functionals (LKFs) and some useful inequalities, several conditions for passive performance are established in linear matrix inequalities (LMIs). Finally, numerical examples are given to demonstrate the feasibility of the presented theories, and the results reveal that the probabilistic and mixed time-varying delays have an unstable influence on the system and should not be ignored. [ABSTRACT FROM AUTHOR]

Introduction. Determining the prevalence of SARS-CoV-2 in blood donors makes the control of virus circulation possible in healthy people and helps implement strategies to reduce virus transmission. The purpose of the study was to examine the seroprevalence of COVID-19 in blood donors using systematic review and meta-analysis. Materials and Methods. The electronic databases PubMed, Scopus, Web of Science, and the Google Scholar search engine were searched using standard keywords up to 2022-04-26. The variance of each study was calculated according to the binomial distribution. Studies were combined according to the sample size and variance. Q Cochrane test and I2 index were used to examine the heterogeneity of the studies. Data analysis was performed in STATA 14 software, and the significance level of the tests was P < 0.05. Results. In the 28 papers examined with 227894 samples, the seroprevalence of COVID-19 in blood donors was 10% (95% CI: 9%, 11%), estimated 5% (95% CI: 4%, 7%) among men and 6% (95% CI: 4%, 7%) among women. This rate in different blood groups was as follows: A 12% (95% CI: 10%–14%), B 12% (95% CI: 10%–15%), AB 9% (95% CI: 7%–12%), and O 13% (95% CI: 11%–16%). The seroprevalence of COVID-19 in blood donors in North America 10%, Europe 7%, Asia 23%, South America 5%, and Africa was 4%; Moreover, the seroprevalence of IgG antibodies was estimated to be 23% (95% CI: 18%–29%) and IgM 29% (95% CI: 9%–49%). Conclusion. The highest prevalence of COVID-19 serum in women blood donors was among blood group O and Asia. The seroprevalence of IgG and IgM antibodies was high too. [ABSTRACT FROM AUTHOR]

High reliable street-level landmarks are the basis of IP geolocation, but landmark evaluation methods having been proposed cannot evaluate the street-level landmarks. Therefore, in this paper, a street-level landmark evaluation method based on nearest router is proposed. The location organization declared is regarded as an area not a point. Firstly, the declared location of preevaluated landmark is verified by IP location databases. Secondly, the preevaluated landmarks are grouped according to their nearest router. Then, the distance constraint is obtained using delay value between landmark and its nearest router by delay-distance correlation. And relation model is established among distance constraint, organization’s region radius, and distance between two landmarks. Finally, the reliability value of landmarks is calculated in each group based on relational model and binomial distribution. Landmarks evaluation experiment is taken based on 7082 preevaluated landmarks, and the results show that geolocation errors decrease obviously using evaluated landmarks. The mean error of 100 targets in Shanghai is reduced from 7.832km to 2.185km. [ABSTRACT FROM AUTHOR]

This paper concentrates on the event-triggered H ∞ filter design for the discrete-time Markovian jump neural networks under random missing measurements and cyber attacks. Considering that the controlled system and the filtering can exchange information over a shared communication network which is vulnerable to the cyber attacks and has limited bandwidth, the event-triggered mechanism is proposed to relieve the communication burden of data transmission. A variable conforming to Bernoulli distribution is exploited to describe the stochastic phenomenon since the missing measurements occur with random probability. Furthermore, seeing that the communication networks are vulnerable to external malicious attacks, the transferred information via the shared communication network may be changed by the injected false information from the attackers. Based on the above consideration, sufficient conditions for the filtering error system to maintain asymptotically stable are provided with predefined H ∞ performance. In the end, three numerical examples are given to verify the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Achieving both simplicity and efficiency in fully homomorphic encryption (FHE) schemes is important for practical applications. In the simple FHE scheme proposed by Ducas and Micciancio (DM), ciphertexts are refreshed after each homomorphic operation. And ciphertext refreshing has become a major bottleneck for the overall efficiency of the scheme. In this paper, we propose a more efficient FHE scheme with fewer ciphertext refreshings. Based on the DM scheme and another simple FHE scheme proposed by Gentry, Sahai, and Waters (GSW), ciphertext matrix operations and ciphertext vector additions are both applied in our scheme. Compared with the DM scheme, one more homomorphic NOT AND (NAND) operation can be performed on ciphertexts before ciphertext refreshing. Results show that, under the same security parameters, the computational cost of our scheme is obviously lower than that of GSW and DM schemes for a depth-2 binary circuit with NAND gates. And the error rate of our scheme is kept at a sufficiently low level. [ABSTRACT FROM AUTHOR]

In nonlife actuarial science, credibility models are one of the main methods of experience ratemaking. Bühlmann-Straub credibility model can be expressed as a special case of linear mixed models (LMMs) with the underlying assumption of normality. In this paper, we extend the assumption of Bühlmann-Straub model to include Poisson and negative binomial distributions as they are more appropriate for describing the distribution of a number of claims. By using the framework of generalized linear mixed models (GLMMs), we obtain the generalized credibility premiums that contain as particular cases another credibility premium in the literature. Compared to generalized linear mixed models, our extended credibility models also have an advantage in that the credibility factor falls into the range from 0 to 1. The performance of our models in comparison with an existing model in the literature is also evaluated through numerical studies, which shows that our approach produces premium estimates close to the optima. In addition, our proposed model can also be applied to the most commonly used ratemaking approach, namely, the net, the optimal Bonus-Malus system. [ABSTRACT FROM AUTHOR]

This paper applies a T-S fuzzy model to depict a class of nonlinear time-varying-delay singular systems and investigates the dissipative filtering problem for these systems under deception attacks. The measurement output is assumed to encounter random deception attacks during signal transmission, and a Bernoulli distribution is used to describe this random phenomena. In this case, the filtering error system modeled by a stochastic singular T-S fuzzy system is established and stochastic admissibility for this kind of system is defined firstly. Then, by combining some integral inequalities and using the Lyapunov–Krasovskii functional approach, sufficient delay-dependent conditions are presented based on linear matrix inequality techniques, where the system of filtering error can be stochastically admissible and strictly ℚ , S , ℝ -dissipative against randomly occurring deception attacks. Moreover, parameters of the desired filter can be obtained via the solutions of the established conditions. The validity of our work is illustrated through a mostly used example of the nonlinear system. [ABSTRACT FROM AUTHOR]

In this paper, a statistical simulation algorithm for the power series distribution, called the Max Erlang Binomial distribution, is proposed, analyzed, and tested for bladder cancer remission time data. In order to present the simulation technique, the EM algorithm for statistical estimation aimed at estimating the model parameters is described. [ABSTRACT FROM AUTHOR]

Tapering electromagnetic bandgap (EBG) structures is a common method in designing microstrip filters with different periodic structures. A novel technique for tapering EBG structures with the amplitude coefficients obtained from the sine function has been illustrated. This method deduces mellifluous coefficients that improves the performance with reasonable stopband width, preferable insertion loss level, and much-minimized passband ripples compared to similar designs with other tapering methods (e.g., binomial distribution, Chebyshev distribution, and conventional cosine tapering). It also offers tandem use of tapered EBG structures, leading to the novel meandered transmission line tandem design that significantly reduces the length of the filter; more than 40% is possible, compared to the uniform and conventional tapered designs. Size reduction on such a large scale will benefit the designers with the limited space issues. [ABSTRACT FROM AUTHOR]

Attribute data from high-quality processes can be monitored effectively by deciding on whether or not to stop at each time where r ≥ 1 failures have occurred. The smaller the degree of change in failure rate during out of control one wants to be optimally protected against, the larger the r should be. Under homogeneity, the distribution involved is negative binomial. However, in health care monitoring, (groups of) patients will often belong to different risk categories. In the present paper, we will show how information about category membership can be used to adjust the basic negative binomial charts to the actual risk incurred. Attention is also devoted to comparing such conditional charts to their unconditional counterparts. The latter do take possible heterogeneity into account but refrain from risk-adjustment. Note that in the risk adjusted case several parameters are involved, which will all be typically unknown. Hence, the potentially considerable estimation effects of the new charts will be investigated as well. [ABSTRACT FROM AUTHOR]

Culicoides are important vectors for livestock and human pathogens. Wild animals act as reservoirs for important orbiviruses such as bluetongue and African horse sickness viruses. There are only limited studies on the distribution of Culicoides species in forest habitats. In this study, we collected Culicoides from different wildlife sanctuaries and national parks of Karnataka. We collected and morphologically identified 8597 Culicoides. We found 18 species of Culicoides in different sites, with C. oxystoma and C. imicola being the predominant species across the sites. The sequence alignment and phylogenetic analysis of the Cox1 gene of Cuilicoides species revealed a huge level of sequence similarity and their wide distribution around the world. Most of the isolates from our study were closely related to Chinese isolates. The abundance of the species was analyzed using the Bayesian ordination method. We used a hierarchical joint distribution negative binomial regression model to detect the correlation between species owing to environmental covariates and residual correlation. The presence of potential vectors for important livestock pathogens in wild habitats in our study warrants further research on the detection of pathogens in Culicoides collected from forest habitats and adopt surveillance in wild animal habitats to prevent disease spread from wild animals to livestock and vice versa. [ABSTRACT FROM AUTHOR]

Networks are prevalent in real life, and the study of network evolution models is very important for understanding the nature and laws of real networks. The distribution of the initial degree of nodes in existing classical models is constant or uniform. The model we proposed shows binomial distribution, and it is consistent with real network data. The theoretical analysis shows that the proposed model is scale-free at different probability values and its clustering coefficients are adjustable, and the Barabasi-Albert model is a special case of p = 0 in our model. In addition, the analytical results of the clustering coefficients can be estimated using mean-field theory. The mean clustering coefficients calculated from the simulated data and the analytical results tend to be stable. The model also exhibits small-world characteristics and has good reproducibility for short distances of real networks. Our model combines three network characteristics, scale-free, high clustering coefficients, and small-world characteristics, which is a significant improvement over traditional models with only a single or two characteristics. The theoretical analysis procedure can be used as a theoretical reference for various network models to study the estimation of clustering coefficients. The existence of stable equilibrium points of the model explains the controversy of whether scale-free is universal or not, and this explanation provides a new way of thinking to understand the problem. [ABSTRACT FROM AUTHOR]

This paper addresses the least-squares centralized fusion estimation problem of discrete-time random signals from measured outputs, which are perturbed by correlated noises. These measurements are obtained by different sensors, which send their information to a processing center, where the complete set of data is combined to obtain the estimators. Due to random transmission failures, some of the data packets processed for the estimation may either contain only noise (uncertain observations), be delayed (randomly delayed observations), or even be definitely lost (random packet dropouts). These multiple random transmission uncertainties are modelled by sequences of independent Bernoulli random variables with different probabilities for the different sensors. By an innovation approach and using the last observation that successfully arrived when a packet is lost, a recursive algorithm is designed for the filtering estimation problem. The proposed algorithm is easily implemented and does not require knowledge of the signal evolution model, as only the first- and second-order moments of the processes involved are used. A numerical simulation example illustrates the feasibility of the proposed estimators and shows how the probabilities of the multiple random failures influence their performance. [ABSTRACT FROM AUTHOR]

Online tracking time-varying number of targets is a challenging issue due to measurement noise, target birth or death, and association uncertainty, especially when target number is large. In this paper, we propose an efficient approximation of the Labeled Multi-Bernoulli (LMB) filter to perform online multitarget state estimation and track maintenance efficiently. On the basis of the original LMB filer, we propose a target posterior approximation technique to use a weighted single Gaussian component representing each individual target. Moreover, we present the Gaussian mixture implementation of the proposed efficient approximation of the LMB filter under linear, Gaussian assumptions on the target dynamic model and measurement model. Numerical results verify that our proposed efficient approximation of the LMB filer achieves accurate tracking performance and runs several times faster than the original LMB filer. [ABSTRACT FROM AUTHOR]

The distribution of the spin directions of spiral galaxies in the Sloan Digital Sky Survey has been a topic of debate in the past two decades, with conflicting conclusions reported even in cases where the same data were used. Here, we follow one of the previous experiments by applying the SpArcFiRe algorithm to annotate the spin directions in an original dataset of Galaxy Zoo 1. The annotation of the galaxy spin directions is carried out after the first step of selecting the spiral galaxies in three different manners: manual analysis by Galaxy Zoo classifications, by a model-driven computer analysis, and with no selection of spiral galaxies. The results show that when spiral galaxies are selected by Galaxy Zoo volunteers, the distribution of their spin directions as determined by SpArcFiRe is not random, which agrees with previous reports. When selecting the spiral galaxies using a model-driven computer analysis or without selecting the spiral galaxies at all, the distribution is also not random. Simple binomial distribution analysis shows that the probability of the parity violation to occur by chance is lower than 0.01. Fitting the spin directions as observed from the Earth to cosine dependence exhibits a dipole axis with statistical strength of 2.33 σ to 3.97 σ. These experiments show that regardless of the selection mechanism and the analysis method, all experiments show similar conclusions. These results are aligned with previous reports using other methods and telescopes, suggesting that the spin directions of spiral galaxies as observed from the Earth exhibit a dipole axis formed by their spin directions. Possible explanations can be related to the large-scale structure of the universe or to the internal structure of galaxies. The catalogs of annotated galaxies generated as part of this study are available. [ABSTRACT FROM AUTHOR]

This paper investigates the nonfragile H∞ synchronization problem of complex dynamical networks with randomly occurring controller gain fluctuations and uncertainties. These randomly occurring phenomena are described by independent stochastic variables satisfying Bernoulli distributions, which are adopted to model more realistic dynamical behaviors of the complex networks. By applying the Lyapunov-Krasovskii method, delay-dependent criteria are established to ensure that the synchronization can be achieved with the prescribed H∞ disturbance attenuation. Moreover, the obtained results do not rely on the derivatives of time-varying delays. A set of nonfragile controllers are further designed in terms of linear matrix inequality (LMI) approach. Finally, a numerical example is given to illustrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal Kalman filtering problem for a class of discrete stochastic systems with multiplicative noises and random two-step sensor delays. Three Bernoulli distributed random variables with known conditional probabilities are introduced to characterize the phenomena of the random two-step sensor delays which may happen during the data transmission. By using the state augmentation approach and innovation analysis technique, an optimal Kalman filter is constructed for the augmented system in the sense of the minimum mean square error (MMSE). Subsequently, the optimal Kalman filtering is derived for corresponding augmented system in initial instants. Finally, a simulation example is provided to demonstrate the feasibility and effectiveness of the proposed filtering method. [ABSTRACT FROM AUTHOR]

In several experiments of survival analysis, the cause of death or failure of any subject may be characterized by more than one cause. Since the cause of failure may be dependent or independent, in this work, we discuss the competing risk lifetime model under progressive type-II censored where the removal follows a binomial distribution. We consider the Akshaya lifetime failure model under independent causes and the number of subjects removed at every failure time when the removal follows the binomial distribution with known parameters. The classical and Bayesian approaches are used to account for the point and interval estimation procedures for parameters and parametric functions. The Bayes estimate is obtained by using the Markov Chain Monte Carlo (MCMC) method under symmetric and asymmetric loss functions. We apply the Metropolis–Hasting algorithm to generate MCMC samples from the posterior density function. A simulated data set is applied to diagnose the performance of the two techniques applied here. The data represented the survival times of mice kept in a conventional germ-free environment, all of which were exposed to a fixed dose of radiation at the age of 5 to 6 weeks, which was used as a practice for the model discussed. There are 3 causes of death. In group 1, we considered thymic lymphoma to be the first cause and other causes to be the second. On the base of mice data, the survival mean time (cumulative incidence function) of mice of the second cause is higher than the first cause. [ABSTRACT FROM AUTHOR]

This paper studies the sampled-data based consensus of multiagent system with general linear time-invariant dynamics. It focuses on looking for a maximum allowable sampling period bound such that as long as the sampling period is less than this bound, there always exist linear consensus protocols solving the consensus problem. Both fixed and randomly switching topologies are considered. For systems under fixed topology, a necessary and sufficient sampling period bound is obtained for single-input multiagent systems, and a sufficient allowable bound is proposed for multi-input systems by solving the H∞ optimal control problem of certain system with uncertainty. For systems under randomly switchingtopologies, tree-type and complete broadcasting network with Bernoulli packet losses are discussed, and explicit allowable sampling period bounds are, respectively, given based on the unstable eigenvalues of agent's system matrix and packet loss probability. Numerical examples are given to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper investigates the H∞ fixed-lag fault estimator design for linear discrete time-varying (LDTV) systems with intermittent measurements, which is described by a Bernoulli distributed random variable. Through constructing a novel partially equivalent dynamic system, the fault estimator design is converted into a deterministic quadratic minimization problem. By applying the innovation reorganization technique and the projection formula in Krein space, a necessary and sufficient condition is obtained for the existence of the estimator. The parameter matrices of the estimator are derived by recursively solving two standard Riccati equations. An illustrative example is provided to show the effectiveness and applicability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper examines a discrete-time modified D-policy Geo/G/1 queue with Bernoulli feedback. Using a decomposition method, the steady-state system size distribution at epoch n+ is obtained. Moreover, the steady-state system size distributions at epochs n- and n are also derived. Two special cases are given. Finally, a wireless local area network is numerically presented to validate the applicability of steady-state system size distribution and its important application in system capacity design. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce and investigate a class of q-Bernoulli, q-Euler, and q-Genocchi polynomials. The q-analogues of well-known formulas are derived. In addition, the q-analogue of the Srivastava-Pintér theorem is obtained. Some new identities, involving q-polynomials, are proved. [ABSTRACT FROM AUTHOR]

This paper deals with the H∞ filtering problem for nonlinear systems with randomly occurring output degradation phenomenon. Such a phenomenon is described by a stochastic variable which obeys the Bernoulli distribution with probability known priorly. A sufficient condition is derived for the nonlinear system to reach the required H∞ performance. An iterative algorithm is then proposed to obtain the filter parameters recursively by solving the corresponding linear matrix inequality. A numerical example is presented to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with H∞ filter design problem for large-scale systems with missing measurements. The occurrence of missing measurements is assumed to be a Bernoulli distributed sequence with known probability. The new full-dimensional filter is designed to make the filter error system exponentially mean-square stable and achieve a prescribed H∞ performance. Sufficient conditions are derived in terms of linear matrix inequality (LMI) for the existence of the filter, and the parameters of filter are obtained by solving the LMI. Finally, the numerical simulation results illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper investigates the filtering problem for a class of network-based systems with random network-induced delays. The considered randomdelay between the sensor and the filter is assumed to be satisfying a certain stochastic characteristic. Considering the probability of the delay taking value in different intervals, a stochastic variable satisfying Bernoulli randombinary distribution is introduced and a new systemmodel is established by employing the information of the probability distribution. By using a properly constructed Lyapunov function, sufficient conditions for the existence of the H∞ filters are presented in terms of linear matrix inequalities, which are dependent on the occurrence probability of both the random communication delays. The filter parameter is then characterized by the solution to a set of LMIs. A simulation example is employed to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with observer-based feedback stabilization of networked control systems (NCSs) with random packet dropouts. Both sensor-to-controller (S/C) and controller-to-actuator (C/A) packet dropouts are considered, and their behavior is assumed to obey the Bernoulli randombinary distribution. Thehold-input strategy is adopted, in which the previous packet is used if the packet is lost. An observer-based feedback controller is designed, and sufficient conditions for stochastic stability are derived in the form of linear matrix inequalities (LMIs). A numerical example illustrates the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper deals with a robust H∞ deconvolution filtering problem for discrete-time nonlinear stochastic systems with randomly occurring sensor delays. The delayed measurements are assumed to occur in a random way characterized by a random variable sequence following the Bernoulli distribution with time-varying probability. The purpose is to design an H∞ deconvolution filter such that, for all the admissible randomly occurring sensor delays, nonlinear disturbances, and external noises, the input signal distorted by the transmission channel could be recovered to a specified extent. By utilizing the constructed Lyapunov functional relying on the time-varying probability parameters, the desired sufficient criteria are derived. The proposed H∞ deconvolution filter parameters include not only the fixed gains obtained by solving a convex optimization problem but also the online measurable timevarying probability. When the time-varying sensor delays occur randomly with a time-varying probability sequence, the proposed gain-scheduled filtering algorithm is very effective. The obtained design algorithm is finally verified in the light of simulation examples. [ABSTRACT FROM AUTHOR]

This paper considers the estimation problem for the Frèchet distribution under progressive Type II censoring with random removals, where the number of units removed at each failure time has a binomial distribution. We use the maximum likelihood method to obtain the estimators of parameters and derive the sampling distributions of the estimators, and we also construct the confidence intervals for the parameters and percentile of the failure time distribution. [ABSTRACT FROM AUTHOR]

This paper develops a distribution-free (or nonparametric) Shewhart-type statistical quality control chart for detecting a broad change in the probability distribution of a process. The proposed chart is designed for grouped observations, and it requires the availability of a reference (or training) sample of observations taken when the process was operating in-control. The charting statistic is a modified version of the two-sample Kolmogorov-Smirnov test statistic that allows the exact calculation of the conditional average run length using the binomial distribution. Unlike the traditional distribution-based control charts (such as the Shewhart X-Bar), the proposed chart maintains the same control limits and the in-control average run length over the class of all (symmetric or asymmetric) continuous probability distributions. The proposed chart aims at monitoring a broad, rather than a one-parameter, change in a process distribution. Simulation studies show that the chart is more robust against increased skewness and/or outliers in the process output. Further, the proposed chart is shown to be more efficient than the Shewhart X-Bar chart when the underlying process distribution has tails heavier than those of the normal distribution. [ABSTRACT FROM AUTHOR]

We study Kendall's tau and Spearman's rho concordance measures for discrete variables. We mainly provide their best bounds using positive dependence properties. These bounds are difficult to write down explicitly in general. Here, we give the explicit formula of the best bounds in a particular Fréchet space in order to understand the behavior of the ranges of these measures. Also, based on the empirical copula which is viewed as a discrete distribution, we propose a new estimator of the copula function. Finally, we give useful dependence properties of the bivariate Poisson distribution and show the relationship between parameters of the Poisson distribution and both tau and rho. [ABSTRACT FROM AUTHOR]

A statistical method is applied to predict the behaviour of a quantum model consisting of a qubit interacting with a single-mode cavity field. The qubit is prepared in excited state while the field starts from the binomial distribution state. The wave function of the proposed model is obtained. A von Neumann entropy is used to investigate the behaviour of the entanglement between the field and the qubits. Moreover, the atomic Q and Wigner functions are used to identify the behaviour of the distribution in a phase space. The simulation method is used to estimate the parameters of the proposed model to reach the best results. A numerical study is performed to estimate the specific dependency of the binomial distribution state. The results of entanglement were compared with the atomic Q and Wigner functions. The results showed that there are many maximum values of entanglement periodically. The results also confirmed a correlation between von Neumann entropy, the atomic Q , and Wigner functions. [ABSTRACT FROM AUTHOR]

In recent years, hashing learning has received increasing attention in supervised video retrieval. However, most existing supervised video hashing approaches design hash functions based on pairwise similarity or triple relationships and focus on local information, which results in low retrieval accuracy. In this work, we propose a novel supervised framework called discriminative codebook hashing (DCH) for large-scale video retrieval. The proposed DCH encourages samples within the same category to converge to the same code word and maximizes the mutual distances among different categories. Specifically, we first propose the discriminative codebook via a predefined distance among intercode words and Bernoulli distributions to handle each hash bit. Then, we use the composite Kullback–Leibler (KL) divergence to align the neighborhood structures between the high-dimensional space and the Hamming space. The proposed DCH is optimized via the gradient descent algorithm. Experimental results on three widely used video datasets verify that our proposed DCH performs better than several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Negation in general represents the contradiction and denial of anything. In classical logic, negation is identified as the logical connective that takes truthfulness to falsehood. However, there can be situations in which we have to deal with the possibility of any truth value besides true or false. The probability theory has been effective in modelling such situations. Therefore exploring the concept of probability functions from the negation point of view should be helpful in investigating new horizons related with a random phenomena. The negation of a probability distribution results from a transformation which reallocates the probability of each event equally among the other alternatives in a finite sample space. Proposed by Yager, this transformation possesses the maximum entropy allocation. Since any type of mixing increases the disorder(uncertainty) in a system, intuitively the uncertainty associated with the obtained negation must be greater than the uncertainty associated with the original probability distribution. A closer look at Yager's negation reveals that negation of probabilities are convex combinations of the probabilities in the original distribution and we have utilized this for estimating the unpredictability associated with the negation and the implications have been discussed in detail. Also, we have shown that the concept of negation can be helpful for estimation of symmetry and biasness in probability distributions. The binomial distribution has been taken as an example. An extension in case of Atanassov's intuitionistic fuzzy sets has also been discussed. [ABSTRACT FROM AUTHOR]

The study was conducted to assess key factors influencing suspected white spot syndrome virus ( WSSV) disease and associated shrimp production and economic performance in three contrasting black tiger shrimp ( P enaeus monodon) culture technologies promoted by the United States Agency for International Development funded Shrimp Quality Support Project ( SQSP) in Bangladesh. A total of 350 traditional, 315 Modified Traditional Technology1 ( MTT1), 36 MTT2 and 88 Closed System Technology ( CST) farmers from 10 sub-districts in three districts of Khulna division were surveyed following random sampling at the end of the project. Binomial probit regression analysis revealed that smaller newly constructed ponds (known locally as gher) were less susceptible to WSSV, provided aquatic weeds were controlled using chemicals. Removal of sludge from ghers also had a positive effect, irrespective of technology and location. It was also shown that stocking of screened shrimp postlarvae ( PL) does not guarantee protection against WSSV ( t = 1.39, P > 0.05). Higher shrimp production was obtained by farmers practicing CST, followed by those operating MTTs and traditional technology respectively. Farmers who adopted CST also gained higher profitability followed by those operating MTT1, MTT2 and traditional technology. [ABSTRACT FROM AUTHOR]

We discuss a new concept of the q -extension of Bernoulli measure. From those measures, we derive some interesting properties on the generalized q-Bernoulli numbers with weight α attached to X. [ABSTRACT FROM AUTHOR]

A family of generalized binomial probability distributions attached to Landau levels on the Riemann sphere is introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained explicitly. As an application, photon number statistics related to coherent states under consideration are discussed. [ABSTRACT FROM AUTHOR]

The least-squares quadratic estimation problem of signals from observations coming from multiple sensors is addressed when there is a nonzero probability that each observation does not contain the signal to be estimated. We assume that, at each sensor, the uncertainty about the signal being present or missing in the observation is modelled by correlated Bernoulli random variables, whose probabilities are not necessarily the same for all the sensors. A recursive algorithm is derived without requiring the knowledge of the signal state-space model but only the moments (up to the fourth-order ones) of the signal and observation noise, the uncertainty probabilities, and the correlation between the variables modelling the uncertainty. The estimators require the autocovariance and cross-covariance functions of the signal and their second-order powers in a semidegenerate kernel form. The recursive quadratic filtering algorithm is derived from a linear estimation algorithm for a suitably defined augmented system. [ABSTRACT FROM AUTHOR]

There are two types of master equations in describing nonequilibrium phenomena with memory effect: (i) the memory function type and (ii) the nonstationary type. A generalized Polya process is studied within the framework of a non-stationary type master equation approach. For a transitionrate with an arbitrary time-dependent relaxation function, the exact solution of a generalized Polya process is obtained. The characteristic features of temporal variation of the solution are displayed for some typical time-dependent relaxation functions reflecting memory in the systems. [ABSTRACT FROM AUTHOR]

We study the mean earnings of a lottery winner as a function of the number n of participants in the lottery and of the success probability p. We show, in particular, that, for fixed p, there exists an optimal value of n where the mean earnings are maximized. We also establish a relation with the inverse moments of a binomial distribution and suggest new formulas (exact and approximate) for them. [ABSTRACT FROM AUTHOR]

In this study, a stochastic diagnosis method based on the changing information of not only a linear correlation but also a higher-order nonlinear correlation is proposed in a form suitable for online signal processing in time domain by using a personal computer, especially in order to find minutely the mutual relationship between sound and vibration emitted from rotational machines. More specifically, a conditional probability hierarchically reflecting various types of correlation information is theoretically derived by introducing an expression on the multidimensional probability distribution in orthogonal expansion series form. The effectiveness of the proposed theory is experimentally confirmed by applying it to the observed data emitted from a rotational machine driven by an electric motor. [ABSTRACT FROM AUTHOR]

Conventional hole-patterned photonic bandgap structures (PBGSs) yield distinct and wide stopband, but suffer from a significant ripples in the passband beyond the optimized filling factor (FF) of 0.25. Binomial distribution in PBGSs can yield improved performance beyond this value. The optimum FF of binomially distributed PBGSs has been ivestigated at multifrequencies in the X-band, namely, at 9, 10.5, and 12 GHz. It can be seen that 0.4 may be considered as the optimum FF for binomially distributed PBGSs at different frequencies within X-band operations. Finally, binomially PBGSs with this optimium FF are applied in a bandpass filter (BPF) for suppresing the intrinsic spurious harmonics of a BPF. The various experimental investigations reveal that the variation in number of PBG elements and their locations affect the performance of harmonic suppression. Binomially distributed PBGSs are found to be potential candidate to suppress the harmonic signal and to improve the return- and insertion-loss bandwidths. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006. [ABSTRACT FROM AUTHOR]