Probability Distribution Theory Research Articles

A novel method for linguistic steganography by English translation using attention mechanism and probability distribution theory.

To enhance our ability to model long-range semantical dependencies, we introduce a novel approach for linguistic steganography through English translation. This method leverages attention mechanisms and probability distribution theory, known as NMT-stega (Neural Machine Translation-steganography). Specifically, to optimize translation accuracy and make full use of valuable source text information, we employ an attention-based NMT model as our translation technique. To address potential issues related to the degradation of text quality due to secret information embedding, we have devised a dynamic word pick policy based on probability variance. This policy adaptively constructs an alternative set and dynamically adjusts embedding capacity at each time step, guided by variance thresholds. Additionally, we have incorporated prior knowledge into the model by introducing a hyper-parameter that balances the contributions of the source and target text when predicting the embedded words. Extensive ablation experiments and comparative analyses, conducted on a large-scale Chinese-English corpus, validate the effectiveness of the proposed method across several critical aspects, including embedding rate, text quality, anti-steganography, and semantical distance. Notably, our numerical results demonstrate that the NMT-stega method outperforms alternative approaches in anti-steganography tasks, achieving the highest scores in two steganalysis models, NFZ-WDA (with score of 53) and LS-CNN (with score of 56.4). This underscores the superiority of NMT-stega in the anti-steganography attack task. Furthermore, even when generating longer sentences, with average lengths reaching 47 words, our method maintains strong semantical relationships, as evidenced by a semantic distance of 87.916. Moreover, we evaluate the proposed method using two metrics, Bilingual Evaluation Understudy and Perplexity, and achieve impressive scores of 42.103 and 23.592, respectively, highlighting its exceptional performance in the machine translation task.

Prediction model for sandstone strength based on Weibull distribution of micro-element strength and power-law distribution of crack length

It is of the great significance to construct the strength prediction model that considers the influence of the macro and micro defects in the rock in an overall manner to ensure the construction of smart mines and the safety of underground personnel and equipment. Based on the Weibull distribution of rock micro-element strength and the power-law distribution of crack length and the discrete element calculation model, the prediction model for strength of damaged rock specimens were established by numerical simulation and theoretical derivation respectively. Then the rationality of the model was verified by the calculated results. The results show that: 1) The weibull distribution of the micro-element strength and the power-law distribution of the crack length in the PFC2D calculation model are realized by programming, and the quantitative corresponding relationship between the macro, micro and micro damage in the rock and the corresponding distribution parameters is analyzed. 2) 400 sandstone specimens with macro, micro and micro damage are numerically established and loaded to achieve statistical analysis of the relationship between micro element strength, pre-crack information and rock strength. According to the simulation results, the four-dimensional space scatter points of uniaxial compressive strength of sandstone specimens are constructed, and the flow law of compressive strength of sandstone specimens under the influence of multiple damage parameters is obtained. 3) Combined with Mori Tanaka method and rock damage probability distribution theory, a 12 parameter rock strength prediction model is established. The model can both describe the influence of the micro-element strength and macroscopic crack information on the rock strength, and the model calculation results are highly consistent with the simulated results, with the correlation coefficient up to 0.991.

Permeable pavement hydraulic optimization by using an analytical-probabilistic model

Abstract On-source storage controls are a sustainable solution for stormwater management in a scenario of continuous urban area growth. Structures that manage storage volumes through infiltration include extra environmental benefits, such as groundwater recharge, evapotranspiration, and pollutant load removal. Permeable pavement systems are among these controls and can easily integrate into dense urban areas, resulting in paved surfaces contributing to stormwater management. The shift toward on-source strategies is encouraged through regulations, policies, incentives, and awareness campaigns, which are substantially increasing their dissemination. Optimizing the design of on-source storage controls with infiltration, such as permeable pavement systems, through robust methodologies can reduce reservoir depth, reducing environmental impact and costs without impact on reliability. The analytical-probabilistic (AP) method using derived probability distribution theory from rainfall event characteristics and the mathematical description of hydrologic processes within the permeable pavement systems provides an analytical equation that can be used as a design tool, proving robustness analogous with continuous simulations. Results obtained with the AP method were compared with traditional event-based methodologies and continuous simulation, assessing the reliability of the proposed method in optimizing permeable pavement systems' reservoir depth.

Normal Distribution on Energy Saving Problem for the Wireless Sensor Network Life on the Vacation Period

Based on math operations, we can do some analytic approaches for the energy saving for the WSN life. We will study the vacation period time using numerical methods for studding the energy saving mechanism in analytic models. Several research papers have reported that the normal distribution of a random variable has an enormous contribution in analyzing and comparing the data with each other, making the process easier according to methods used or observing the tendencies of numerous occurrences in life applications. This paper focuses on analyzing two problems: the first one is the normal distribution and its special cases by solving real problems of WSN node operations and the second one is the application of standard normal distribution relate to saving energy during vacation time in a certain time interval. The goal of our work is to obtain the appropriate algorithm to minimize the risk of data loss during the network vacation period, which is associated with the organization of network node structures after this period time, and to maximize the battery life of individual sensors. For that, we will use math methods and based on probability distribution theory, we derive some distributions of the processing period duration from an arbitrary fixed time up to a variable time t. The analytic approach based on the conception of Laplace transform and the Lagrange method performs better than the previous results. We continue by examining them through detailed calculations and graphs. We compare the predicted energy saving and the average real energy.

ОБ ИННОВАЦИОННЫХ МЕТОДАХ УСРЕДНЕНИЯ ЧИСЛОВЫХ ДАННЫХ

Numerical data refers to any finite set of data in the form of numbers, vectors, functions, matrices representing the results of an experiment or field observations. Averaging of deterministic, random variables and matrices is considered from a single point of view as a minimization of a function in the form of a generalized least squares problem. A new definition of the mean is given. Three generalizations of averages are obtained as solutions to the minimization problem. If the known averages are harmonic, geometric, arithmetic and quadratic averages and, perhaps, some other averages, then the first generalization of averages has already given an uncountable set of averages. Two new averages are derived from the first generalization. For particular types of averages arising from the first generalization, their interpretations are given in terms of absolute and relative deviations (errors). A sufficient condition of the mean is proved for all averages. Inequalities for six averages are proved. The law of nine numbers has been discovered. The concept of a complex average is given. The concept of optimal mean is introduced. New definitions of mathematical expectation and variance and their generalizations are proposed. In the family of mathematical expectations obtained, only the classical mathematical expectation turned out to be linear. The application of generalized mathematical expectation has led to the discovery of two new distributions in probability theory, namely, the harmonic and relative distributions of a continuous random variable are determined and analytically presented.

A measure of variability within parametric families of continuous distributions

A new approach to theory of continuous probability distributions, based on scalar-valued score functions, offers the score mean as a finite typical value of distributions including the heavy-tailed ones. In the article, we define the score variance as a finite measure of variability of distributions with respect to the typical value and discuss its properties and methods of its estimation. By means of the square root of the score variance we introduce a generalized Rao distance in the sample space.

A Systematic Investigation on the Damage Characteristics of Fish in Axial Flow Pumps

An axial flow pump is a kind of high-specific revolution vane pump that has the characteristics of large flow, low head, and high efficiency. Due to its unique properties, it is widely used in large water diversion projects, such as the South-to-North Water Diversion Project. However, during the operation of the pump, some fish enter the axial flow pump together with the water flow through the screen before the entrance of the pump station. Consequently, some fish are inevitably damaged or even die in the process of traversing through the pump. Meanwhile, the decay of dead fish directly affects the quality of water, hence, posing serious ecological pollution and destabilizing the ecological balance. Therefore, understanding the dynamics of axial flow pumps in relation to fish species in water bodies for biodiversity and ecosystem services remain vital for nature conservation. In this paper, the impact of damage of the model pump on fish is exhaustively investigated according to the theory of blade impact model, impact probability, impact mortality, and mortality distribution under different working conditions. Through the simulation of the flow state inside the impeller, the areas that are lower than the pressure threshold, higher than the shear strain rate threshold, and higher than the pressure gradient threshold in the impeller at different flow rates are analyzed. Based on the unsteady results, the volume fluctuation characteristics of the three damage mechanisms in the impeller are analyzed. Furthermore, Powell vortex acoustic equation is used to locate the high noise source region of the axial flow pump. After extensive comparison of the dipole sound source intensity, it is revealed that the dipole noise source in the impeller and guide vane is dominant. In conclusion, this study provides a holistic perspective for evaluating fish damage caused by the flow in the impeller of the axial flow pump. Furthermore, it will proffer significant references to the construction of ecological water conservancy projects.

A Comparative Study of Goodness-of-Fit Tests for the Laplace Distribution

The Laplace distribution is one of the earliest distributions in probability theory and is a frequently used distribution in many fields. Consequently, various goodness-of-fit tests for the Laplace distribution have been thoroughly derived in theliterature. The purpose of this paper is to carry out a comparative study of these tests as well as a new one we develop. Power comparisons of all such tests are performed via Monte Carlo simulations of sample data generatedfrom twenty seven alternatives distributions. Despite the fact that no single test was found to be most powerful in all situations, several useful recommendations however are made.

An extension of Apostol type of Hermite-Genocchi polynomials and their probabilistic representation

The main purpose of this paper is to introduce and investigate the various properties of a new generalization of Apostol Hermite-Genocchi polynomials. We derive many useful results involving new generalized Apostol Hermite-Genocchi polynomials. We also consider some statistical applications of the new family in probability distribution theory and reliability.

A New Neutrosophic Negative Binomial Distribution: Properties and Applications

Many problems in real life exist that are full of confusion, vagueness, and ambiguity. The quantification of such issues in a scientific way is the need of time. The negative binomial distribution is an important discrete probability distribution from the account of classical probability distribution theory. The distribution was used to study the chance of kth success in n trials before n − 1 failures for crisp data. The literature lacks in dealing with the situations for interval-valued data under negative binomial distribution. In this research, the neutrosophic negative binomial distribution is proposed to generalize the classical negative binomial distribution. The generalized proposed distribution considers the indeterminacy and crisp form from interval-valued. Several properties of the proposed distribution, such as moment generating function, characteristic function, and probability generating function, are also derived. Furthermore, the derivation of reliability analysis properties such as survival, hazard rate, reversed hazard rate, cumulative hazard rate, mills ratio, and odds ratio are also presented. In addition, order statistics for the proposed distribution, including w th , joint, median, minimum, and maximum order statistics are part of the paper. The proposed distribution is discussed from the real data applications perspective by considering the different case studies. This research opens the way to deal with the problems that follow conventional conveyances and include nonprecisely determined details simultaneously.

NONLINEAR STRUCTURAL ESTIMATION OF LOCALIZED NETWORK USING HOMOTOPHIC TOPOLOGICAL (2(N)+1) DIMENSIONAL FOR DISTANCE THEORY (HTD-DT)

A Nonlinear Structural Equation Model (NLSEM) is formed on the basis of various dimension in normal mutual estimation depending on Distance Estimation Theory (DET) and its complex networks structure. The homotophy linear topography analyze the dimension of formal network in hidden paths to consider the linear structure. However, dimension theory is a linear dependence between the variables for observation is problem in nature of distance estimation along the node and these approaches have limitations to form shortest communication. This paper proposes the Nonlinear structural estimation of localized network using homotphic topological (2 (n)+1) dimensional for distance theory Structure equation model based on the Probability distribution theory of evaluation model (PDTE) that compensates for the potential innumerable dependencies between network points. For this unstructural reason, network densities are provided to take advantage of the lower specific margins of density that are present in most real-world networks. The Gambier IV order $(y \frac{d^2 y}{dt^2} (\alpha, \beta)$, complex constant) is used to optimize the Painleve I order $(X’=X’^{(dy/dt)}y^2 + t)$ equation to derive the neighborhood singularities to estimate the distance. This computational provides an efficient integration to the diagonal gradient algorithm has been developed to estimate the SEM coefficients of polymorphic formation and therefore infer the edge structures on distance estimation. Preliminary testing of simulated data demonstrates the effectiveness of the new approach produce high estimation with lower redundancy steps of mathematical solvation.

Carbon oxides emissions from lithium-ion batteries under thermal runaway from measurements and predictive model

A concentration test device was set up to study and analyze the thermal runaway gas production process in lithium-ion batteries. The experimental conditions for the research were determined by the influence of different external environments and gas flow rates on the thermal runaway process. Gas measurement and analysis of CO and CO2 generated in thermal runaway process under different states of charge (SOCs), different ambient temperatures and different electric heating power were conducted. The following results were obtained. Under different SOCs, the concentrations of CO and CO2 decreased as the charge capacity of the lithium-ion batteries decreased. Under different ambient temperatures, the concentration of CO2 decreased with the decrease of the ambient temperature. However, the concentration of CO at the ambient temperature of 180 °C was higher than that at the ambient temperature of 220 °C. Under different electric heating power, the concentrations of CO and CO2 decreased with the decrease of the electric heating power. Besides, Bayesian prior probability distribution theory was adopted to analyze the variations of CO concentration relative to time in the thermal runaway process, the results of which can predict thermal runaway state of lithium-ion batteries. The findings can serve to provide reference for accident prevention and control of thermal runaway of lithium-ion batteries.

A NEW APPROACH TO ASSESSING THE OPERATIONAL SAFETY OF COMPOSITE MATERIALS AND PARTS OF COMPLEX STRUCTURES BASED ON ARTIFICIAL INTELLIGENCE METHODS AS A PART OF NEURAL NETWORKS AND DEEP RESULTS OF MULTI-CRITERIA COMPLEX NON-DESTRUCTIVE TESTING

The article proposes a new approach to assessing the operational safety of materials and parts of complex structures based on artificial intelligence methods based on artificial neural networks and multi-criteria complex non-destructive testing, and special mathematical and algorithmic support for systems for evaluating operational safety and predicting residual life under external influences. A method of morphological analysis of the procedures for using measurement tools for heterogeneous information with different a priori information, both about the type of characteristics and the distribution of errors in the input and output signals, has been developed. The classification of problems of measuring parameters for the integration of heterogeneous information is proposed. A macromodel of error is obtained that can be used for research purposes to minimize errors in the developed equipment or for the purpose of correcting errors during operation. A classification of methods for measuring heterogeneous information from the standpoint of probability distribution theory is proposed. Experimental testing of developed algorithms tailored aggregation of information non-destructive testing and adaptation to poorly formalized parameters, which confirmed the effectiveness of the developed methods and algorithms for assessment of structures and resource forecasting their operational reliability was carried out.

The Properties and Application of Poisson Distribution

Poisson distribution is not only a very important distribution in probability theory, but also a useful tool to study the random events. Firstly, this paper gives a simple introduction of Poisson distribution and some characteristics of the Poisson distribution. Secondly, some properties of Poisson distribution are introduced and proved. In the end, some application of Poisson distribution are introduced, such as the application in the rare event and in daily life. We also do some analysis about the application of Poisson distribution.

Patent Keyword Analysis of Disaster Artificial Intelligence Using Bayesian Network Modeling and Factor Analysis

At present, artificial intelligence (AI) contributes to most technological fields. AI has also been introduced in the disaster area to replace humans and contribute to the prevention of disasters and the minimization of damages. So, it is necessary to analyze disaster AI in order to effectively make use of it. In this paper, we analyze the patent documents related to disaster AI technology. We propose Bayesian network modeling and factor analysis for the technology analysis of disaster AI. This is based on probability distribution and graph theory. It is also a statistical model that depends on multivariate data analysis. In order to show how the proposed model can be applied to a real problem, we carried out a case study to collect and analyze the patent data related to disaster AI.

Recursive Calculation Model for a Special Multivariate Normal Probability of First-Order Stationary Sequence

The consecutive hit probability of antiaircraft artillery corresponds to the multivariate normal probability distribution. The computational complexity depends on the length of the firing error sequence (i.e., the integral dimension may exceed 100). The traditional numerical integration and the Monte Carlo method are too slow for this calculation. This paper established the state equation of the firing error sequence, which was the bridge between the multivariate normal probability distribution and stochastic process theory. The recursive calculation model was given after the rigorous derivation process. The accuracy and computational complexity of the model were quantified by theoretical analysis and expressed intuitively by examples. The model shows the upper bound for the absolute error, and the computational efficiency is significantly improved.

Optical detection of contamination event in water distribution system using online Bayesian method with UV–Vis spectrometry

The detection of contamination events in water distribution systems remains a major concern to public health. However, much of the contaminant detection methods are supervised learning which cannot adapt to the complex environment in practical applications. In this work, a contaminant detection method using ultraviolet–visible spectroscopy technique was developed to achieve a goal of real-time detection on online acquisition of absorbance spectra. This method combined the advantages of probability distribution, message-passing algorithm and Bayesian theory. Message-passing algorithm was used to achieve a goal of online detection on noisy UV–Vis spectra signals. The proposed Bayesian algorithm organized the message passing schedule and helped to extract sequential patterns for event classification, which can avoid extreme conclusions. In addition, parameters were set up based on reasonable prior, by which the detection model was dynamically updated. Pilot scale experiment was conducted for long-term online monitoring of the water distribution system. And the experiment results showed improved performances in its ability to detect contamination events with higher probabilities, compared to previous studies.

A modified firefly algorithm for optimizing a multi stage supply chain network with stochastic demand and fuzzy production capacity

Production-distribution network (PDN) design is among complex problems with dynamic relationships that cause substantial amount of uncertainty including customers’ demands, production capacity and others. This paper addresses a multi stage production–distribution planning (PDP) problem with multi suppliers, producers, potential entrepots, potential retailers and inland and outland customers under uncertain environment. A mixed integer linear programming (MILP) model is presented to describe the purpose problem for optimizing the integrated total cost of the system. The proposed model considers operational risks involving uncertainties related to producers’ capacity and customers’ demand with applying probability distribution and fuzzy set theory. Commercial software cannot solve large sized instances in a reasonable run time. So, we presented a novel heuristic based on firefly algorithm (FA) called selective firefly algorithm (SFA) to solve the large sized problems. In the proposed SFA, each firefly identifies all fireflies with more brightness and evaluates its brightness change before moving, implicitly. Afterwards, the firefly that makes the best change is selected and initial firefly moves toward the selected firefly. Several numerical examples in both small and large sizes are applied to demonstrate the performance of the proposed heuristic.

Gamma mixture of generalized error distribution

A new symmetric heavy-tailed distribution, namely gamma mixture of generalized error distribution is defined by scaling generalized error distribution with gamma distribution, its probability density function, k-moment, skewness and kurtosis are derived. After tedious calculation, we also give the Fisher information matrix, moment estimators and maximum likelihood estimators for the parameters of gamma mixture of generalized error distribution. In order to evaluate the effectiveness of the point estimators and the stability of Fisher information matrix, extensive simulation experiments are carried out in three groups of parameters. Additionally, the new distribution is applied to Apple Inc. stock (AAPL) data and compared with normal distribution, F-S skewed standardized t distribution and generalized error distribution. It is found that the new distribution has better fitting effect on the data under the Akaike information criterion (AIC). To a certain extent, our results enrich the probability distribution theory and develop the scale mixture distribution, which will provide help and reference for financial data analysis.

Connectivity Analysis of a Highway With One Entry/Exit and Multiple Roadside Units

This paper studies the connectivity problem of vehicles moving on a highway road and considers a one-way road scenario where there exist one entry and exit, and multiple roadside units (RSUs) equidistantly deployed along the road. A connectivity analytical model is derived for analyzing the connectivity probability, taking into account the existence of the entry and exit and the deployment of multiple RSUs. In the considered road scenario, the entry and exit is uniformly distributed on the highway road. At the entry and exit, a vehicle may enter or exit from the road, or drive through the entry and exit with a certain probability. In deriving the connectivity analytical model, the highway road is divided into several segments and the connectivity probability of each segment is derived based on probability distribution theory. The connectivity probability of the highway road is then derived based on the connectivity probability on each sub-segment. Moreover, several parameters that may affect the connectivity of the road are taken into account, including a vehicle's arrival rate and moving speed, the number of RSUs deployed on the road, and a vehicle's driving-through probability at the entry and exit. The derived analytical model is justified based on simulation results. It can be used to investigate the effects of major parameters on the connectivity probability of a highway road, which is useful for the deployment of RSUs in such scenarios.