Probability Theory Research Articles

Plasma profile reconstruction supported by kinetic modeling

Combining the analysis of multiple diagnostics and well-chosen prior information in the framework of Bayesian probability theory, the Integrated Data Analysis code (IDA Fischer et al 2010 Fusion Sci. Technol. 58 675–84) can provide density and temperature radial profiles of fusion plasmas. These IDA-fitted measurements are then used for further analysis, such as discharge simulations and other experimental data analysis. Since IDA considers measurement data, which is frequently fragmentary, with statistical and systematic uncertainties, which are often difficult to quantify, from a heterogeneous set of diagnostics, the fitted profiles and their gradients may be in contradiction to well-established expectations from transport theory. Using the modeling suite ASTRA coupled with the quasi-linear transport solver TGLF, we have created a loop in which simulated profiles and their uncertainties are fed back into IDA as an additional prior, thus providing constraints about the physically reasonable parameter space. We apply this physics-motivated prior to several different plasma scenarios and find improved heat flux match, while still matching the experimental data. This work feeds into a broader effort to make IDA more robust against measurement uncertainties or lack of measurements by combining multiple transport solvers with different levels of complexity and computing costs in a multi-fidelity approach.

Structural reliability analysis under stochastic seismic excitations and multidimensional limit state based on gamma mixture model and copula function

A novel method for analyzing the reliability of structures under non-stationary stochastic seismic excitations, considering the combined effect of multiple structural demand extreme values, is proposed. The spectral representation method is employed to establish a non-stationary stochastic seismic excitation model, and based on the theory of first-passage probability, multiple integral formulas for seismic reliability under multidimensional limit states are derived. The extreme value distribution is established using the Gamma mixture model (GMM). The equations for estimating the model parameters are derived based on both fractional moments and moment-generating functions, while the determination of the number of gamma distribution components is guided by the probability distribution and statistical characteristics of the samples. The joint probability density function (JPDF) for multiple demand extreme values is established by incorporating copula functions to account for correlation, and the fitting accuracy of different copula functions is assessed. The proposed method is illustrated using reinforced concrete (RC) frame structures. The results demonstrate that the fitting accuracy of extreme value distribution can be enhanced by adjusting the number of gamma distribution components in the GMM, which exhibits high accuracy in fitting both the main and tail regions. The presence of correlation can induce variations in the JPDF, thereby exerting an influence on the failure probability. Consequently, disregarding correlation is not conducive to reliability analysis.

The signaling dimension in generalized probabilistic theories

The signaling dimension of a given physical system quantifies the minimum dimension of a classical system required to reproduce all input/output correlations of the given system. Thus, unlike other dimension measures - such as the dimension of the linear space or the maximum number of (jointly or pairwise) perfectly discriminable states - which examine the correlation space only along a single direction, the signaling dimension does not depend on the arbitrary choice of a specific operational task. In this sense, the signaling dimension summarizes the structure of the entire set of input/output correlations consistent with a given system in a single scalar quantity. For quantum theory, it was recently proved by Frenkel and Weiner in a seminal result that the signaling dimension coincides with the Hilbert space dimension. Here, we derive analytical and algorithmic techniques to compute the signaling dimension for any given system of any given generalized probabilistic theory. We prove that it suffices to consider extremal measurements with ray-extremal effects, and we bound the number of elements of any such measurement in terms of the linear dimension. For systems with a finite number of extremal effects, we recast the problem of characterizing the extremal measurements with ray-extremal effects as the problem of deriving the vertex description of a polytope given its face description, which can be conveniently solved by standard techniques such as the double description algorithm. For each such measurement, we recast the computation of the signaling dimension as a linear program, and we propose a combinatorial branch and bound algorithm to reduce its size. We apply our results to derive the extremal measurements with ray-extremal effects of a composition of two square bits (or squits) and prove that their signaling dimension is five, even though each squit has a signaling dimension equal to two.

The Philosophy of Probability Value Behavior: Fractions and Composite Probability Functions in the Continuous Case

This paper focuses on probability value behavior in the case of continuous sample space by employing fractions intervals and composite functions. The study evaluates value behavior rather than finding values directly, which involves utilization of some concepts from continuity, geometric probability, and measure theory. This paper primarily uses an experiment that contains two major events, head H and tail T, in all their occurrence phases. This spread in infinite and uncountable fractions by a continuous motion within intervals and in the predominant circumstances where events are probabilistic values. As a result, every circumstance reflects many important characteristics of probability theory. Among the main results, this paper provides proven propositions that help design experiments upon understanding the case nature, with some explanations to the existing relation between probability value and the case nature. Also, this paper provides a proven corollary that allows visualizing negative probability values as a particular trial. This in turn proposes necessary uses for the composite probability function P_j 〖(p〗_i). Moreover, this paper provides numerical explanations of limits, which can demonstrate the nature of P_j 〖(p〗_i), alongside some techniques. Also, this paper considered conditional probability through some corollaries and the possibility of using the non-negative function of the interval i, alongside many important results in form of discussions.

RatHole: Authentication Algorithm for Controling Access to Mobile Phone File Management System

Millions of Naira are being laundered by criminals through internet fraud, which deceives the victim with a false presentation, or hacking, which involves breaking information system security to steal financial information or data. Cybercrime, more specifically internet fraud, has become a common problem facing the world. In any case, this only occurred if the attacker was able to obtain the victim's account privileges (bank account, credit card information, or login credentials). This work presented an authentication technique that can be inexpensively implemented and used to create a secure architecture that is hard to breach. It can also reduce the amount of overhead that is placed on the authentication server during an attempt at authentication. The possibility of breaking the authentication technique was calculated using probability theory, and the mobile-based authentication algorithm was implemented using Android Studio. The result of this research shows the implementations of RatHole algorithm using android operating system which is file management android app that is being protected with RatHole algorithm and the probability of breaking down the algorithm for 1 to 10 authentication method keeps reducing by averagely 0.12. The implemented Rat-Hole on android devices also consumed 20 to 30 megabytes of data very less than memory consumption of recent research based on block chain solution which consumed 1 gigabyte to 50 gigabyte of memory.

What if the Covid-19 Pandemic Never Happened Estimation of the Tourist Arrivals for 2020 Via Levenberg-Marquardt Optimization and K-Star (K ) Machine Learning Algorithms

Based on the probability theory, which is used to model uncertainty and randomness in real-world situations, the study aims to understand the impact of uncertain conditions, such as the Covid-19 pandemic, on the accuracy of the algorithms and the resulting losses to a country's tourism industry. The contribution of this paper to the international body of knowledge is twofold: firstly, it advances theoretical understanding of the use of probability theory in modelling real-world problems; and secondly, it offers a methodological approach for estimating tourist arrivals that accounts for the impact of extreme events. To achieve these aims, the Levenberg-Marquardt optimization was first applied to determine the optimal coefficients of the exponential function for estimating tourist arrivals from 1950 to 2020. Next, the K-Star machine learning algorithm was applied to the dataset with and without Covid-19 cases to estimate tourist arrivals.

A mathematical modeling approach to analyzing and addressing customer service inefficiencies in an international company

This paper presents a novel and in-depth mathematical approach to analyzing the inefficiencies and shortcomings of customer service in an international company based in China. By employing advanced mathematical concepts such as set theory, graph theory, probability theory, and stochastic processes, we develop a comprehensive and multi-faceted model that captures the various aspects of customer service, including unfairness, bureaucracy, failure to perform duties, irresponsibility, untruthfulness, and untrustworthiness. Our findings suggest that these issues are deeply rooted in the company's organizational structure and culture, and we propose potential solutions to address these problems. We also introduce new mathematical techniques, such as the use of hypergraphs and multi-objective optimization, to provide a more nuanced understanding of the complex dynamics at play within the customer service department.

2023년 민법(물권법 및 채권법) 중요 판례 평석

In this paper, among the major precedents of the Supreme Court on civil matters in the year of 2023, I analyzed the meaning and contents of 7 important decisions (focused on the law of real rights and claims). The Supreme Court explicitly ruled for the first time that in the so-called ‘mutual deprivation of the possession of his/her property,’ the claim for recovery of possession by the preceding encroacher could not be allowed. The Supreme Court repeatedly has held that claims by road site owners to local governments for land handover, road demolition, and traffic closures are, in principle, an abuse of rights. With respect to the claims of unjust enrichment, the Supreme Court also repeatedly states the legal principles of abandoning the exclusive right to use and profit. Although the legal principle is controversial in academia, in practice, it is firmly established as a useful legal principle in determining whether a claim for return of unjust enrichment is accept or not between the road site owners and the local governments. The Supreme Court explicitly ruled for the first time that a third party who acquired ownership after the unauthorized rental act by a person having a right of retention can also exercise the right to demand the extinction of the right of retention. In the past three years, there have been three Supreme Court rulings, including the target judgment in 2023, on issues that have been mainly disputed in academic fields regarding the right to demand the extinction of the right of retention, and it seems that many of the major issues regarding the right to demand the extinction of the right of retention have been settled through precedents. For the second time since 2017, the Supreme Court applied the ‘high probability theory with respect to obligee’s right of revocation’ to determine whether a claim based on continuous product supply contract arising after a fraudulent transfer is a claim protected by the law of revocation of the fraudulent transfer.

Bayesian neural networks to reduce accidents while tower crane operations

The subject of the article is methods of preventing and reducing the risk of an accident during the operation of a tower crane. The research focuses on the method when the Bayesian approach is integrated with an artificial neural network to determine probability distribution function of tower crane accident. The goal of the study isto provide the rational reasons why using a Bayesian neural network could reduce the level of accident risk while tower crane operating. To achieve the goal of the research were performed: review and analysis of the methods used in modern conditions to assess the level of accident risk when operating a tower crane; identified the reasons why these methods need improvements; proposed and provided justifications why Bayesian neural network could be a powerful method in preventing tower crane accident. During review and analysis were used: Bayes theorem, theory of probability and mathematical statistics, theory of artificial neural networks. The summary from the results of conducted analysis of modern methods which are used to estimate accident risk level for tower crane included that some methods are based on expert judgements only which are not possible to verify so the risk’s estimates obtained from those methods could be biased; other methods are good in estimation of the probability of happening of tower crane accident, however could not be used to prevent the accident to happen. In order to eliminated disadvantages of the used methods it is proposed to use Bayesian neural network to determine probability distribution function and use it to determine threshold value for risk factors which could provoke an accident’s event happens during tower crane operation.

A probabilistic identification of the buckling resistance of imperfect cylindrical shells in axial compression

The buckling resistance of imperfect circular cylindrical shells of elastic and isotropic material subject to axial compression is studied focusing on initial geometric imperfections. Considering the imperfections as a random field, the suggested probabilistic representation of the buckling resistance parallels the deterministic dependence of buckling loads on the size and shape of imperfections. It derives from the probability density function of an imperfection size measure and the conditional probability density functions of the resistance confined to the realizations of imperfections given their size levels. The separated representation of the buckling resistance allows: (1) supplementary checking the accuracy of the random field representation, (2) classifying measured and simulated imperfections by their size and shape effects on buckling loads, (3) prospective delimiting the range of working imperfections for fabrication tolerance classes, and (4) defining the characteristic imperfection for the semi-probabilistic design. Introductory calculations illustrate the dependence of the normalized buckling loads of a shell on the shape and size of imperfections.

Методика определения потерь участковой скорости движения грузовых поездов в границах железной дороги

Purpose: to develop a methodology for estimating the total losses of the local speed of freight trains, which, unlike existing methods based on calculating losses caused by the influence of individual operational factors, will be based on the use of statistical data, and take into account the entire range of operational factors that influence the implementation of the indicator under consideration. Methods: formation of a statistical database of railway operational parameters and conducting research on its basis using the tools of probability theory and mathematical statistics: assessing the distribution of the quantities under consideration, correlation and regression analysis. Results: it was established that 75 % of the variability in the local speed of freight trains is explained by changes in the size of the operating fleet of freight cars. Based on this, a methodology has been developed for estimating losses in the local speed of freight trains through the size of the working fleet of freight cars on the railway. A graphical and analytical method for determining these losses is proposed. Practical significance: it is shown that the developed methodology, in contrast to existing ones, makes it possible to more accurately estimate the loss of local speed of freight trains. Its use makes it possible to plan and analyze the implementation of the local speed of freight trains, taking into account the evolving operational work on the railway.

The Application of Mathematical Analysis in Investment Planning

Investment serves as a means to cultivate assets and secure long-term profits. However, inadequate investment planning poses a substantial risk of significant losses. Consequently, precise analysis becomes imperative for making intelligent investment decisions. One effective analytical approach involves the application of mathematical concepts in investment planning. This article conducts a comprehensive review of existing literature pertaining to the utilization of mathematical analysis in investment planning. Common mathematical concepts employed in investment analysis encompass probability theory, statistics, portfolio theory, and options theory. Probability theory and statistics aid investors in comprehending and forecasting potential gains and losses from specific investments. The primary objective of investment planning is profit maximization through effective risk management, necessitating a mature and structured analysis. Mathematical analysis emerges as a valuable method, and its application in investment planning yields more accurate and efficient results. Techniques such as statistical analysis, portfolio theory, and probability analysis contribute to risk minimization and return maximization by considering factors like asset correlation and risk levels. Thus, the incorporation of mathematical analysis proves crucial for well-structured and successful investment planning. The fifth entry in the bibliography emphasizes the importance of careful and planned analysis in making investment decisions. Economic and financial factors affecting market and investment performance are explored, along with portfolio risk diversification techniques and investment control. The article underscores the significance of understanding investment objectives and investor profiles while discussing various investment instruments such as stocks, bonds, and mutual funds. Overall, the article provides insights into managing investment portfolios effectively for optimal profitability.

Probabilistically coherent credences despite opacity

Abstract Real human agents, even when they are rational by everyday standards, sometimes assign different credences to objectively equivalent statements, such as ‘Orwell is a writer’ and ‘E.A. Blair is a writer’, or credences less than 1 to necessarily true statements, such as not-yet-proven theorems of arithmetic. Anna Mahtani calls this the phenomenon of ‘opacity’. Opaque credences seem probabilistically incoherent, which goes against a key modelling assumption of probability theory. I sketch a modelling strategy for capturing opaque credence assignments without abandoning probabilistic coherence. I draw on ideas from judgement-aggregation theory, where we face similar challenges of defining the ‘objects of judgement’.

Development of a Probability-Based In Vitro Eye Irritation Screening Platform.

Traditional eye irritation assessments, which rely on animal models or ex vivo tissues, face limitations due to ethical concerns, costs, and low throughput. Although numerous in vitro tests have been developed, none have successfully reconciled the need for high experimental throughput with the accurate prediction of irritation potential, attributable to the complexity of irritation mechanisms. Simple cell models, while suitable for high-throughput screening, offer limited mechanistic insights, contrasting with more physiologically relevant but less scalable complex organotypic corneal tissue constructs. This study presents a novel strategy to enhance the predictive accuracy of screening-compatible simple cell models in eye irritation testing. Our method combines the results of two in vitro assays-cell apoptosis and nociceptor (TRPV1) activation-using micropatterned chips to partition human corneal epithelial cells into numerous discrete small populations. Following exposure to test compounds, we measure apoptosis and nociceptor activation responses. The large datasets collected from the cell micropatterns facilitate binarization and statistical fitting to calculate a mathematical probability, which assesses the compound's potential to cause eye irritation. This method potentially enables the amalgamation of multiple mechanistic readouts into a singular index, providing a more accurate and reliable prediction of eye irritation potential in a format amenable to high-throughput screening.

Teaching Reform of “Probability Theory and Mathematical Statistics” Under the Background of New Engineering

Probability theory and mathematical statistics are fundamental courses for various majors in science and engineering. In response to the current teaching situation, we should integrate theory with practice, implement teaching reform, and carry out teaching innovation. The article carries out blended teaching with deep integration of online and offline modes and within and outside of class, constructing innovative measures of “four integrations and four reshaping.” The article conducts diversified evaluations to stimulate learning motivation and help achieve talent cultivation goals. Through the close integration of probability theory and mathematical statistics course teaching with professional education and practical application, the “three-in-one” teaching goal of value shaping, ability cultivation, and knowledge exploration is achieved. The fundamental task of “cultivating morality and talents” is implemented.

Neural Network Approximators for Marginal MAP in Probabilistic Circuits

Probabilistic circuits (PCs) such as sum-product networks efficiently represent large multi-variate probability distributions. They are preferred in practice over other probabilistic representations, such as Bayesian and Markov networks, because PCs can solve marginal inference (MAR) tasks in time that scales linearly in the size of the network. Unfortunately, the most probable explanation (MPE) task and its generalization, the marginal maximum-a-posteriori (MMAP) inference task remain NP-hard in these models. Inspired by the recent work on using neural networks for generating near-optimal solutions to optimization problems such as integer linear programming, we propose an approach that uses neural networks to approximate MMAP inference in PCs. The key idea in our approach is to approximate the cost of an assignment to the query variables using a continuous multilinear function and then use the latter as a loss function. The two main benefits of our new method are that it is self-supervised, and after the neural network is learned, it requires only linear time to output a solution. We evaluate our new approach on several benchmark datasets and show that it outperforms three competing linear time approximations: max-product inference, max-marginal inference, and sequential estimation, which are used in practice to solve MMAP tasks in PCs.

Decomposing Constraint Networks for Calculating c-Representations

It is well-known from probability theory that network-based methods like Bayesian networks constitute remarkable frameworks for efficient probabilistic reasoning. In this paper, we focus on qualitative default reasoning based on Spohn’s ranking functions for which network-based methods have not yet been studied satisfactorily. With constraint networks, we develop a framework for iterative calculations of c-representations, a family of ranking models of conditional belief bases which show outstanding properties from a commonsense and formal point of view, that are characterized by assigning possible worlds a degree of implausibility via penalizing the falsification of conditionals. Constraint networks unveil the dependencies among these penalty points (and hence among the conditionals) and make it possible to compute the penalty points locally on so-called safe sub-bases. As an application of our framework, we show that skeptical c-inferences can be drawn locally from safe sub-bases without losing validity.

Structured Probabilistic Coding

This paper presents a new supervised representation learning framework, namely structured probabilistic coding (SPC), to learn compact and informative representations from input related to the target task. SPC is an encoder-only probabilistic coding technology with a structured regularization from the target space. It can enhance the generalization ability of pre-trained language models for better language understanding. Specifically, our probabilistic coding simultaneously performs information encoding and task prediction in one module to more fully utilize the effective information from input data. It uses variational inference in the output space to reduce randomness and uncertainty. Besides, to better control the learning process of probabilistic representations, a structured regularization is proposed to promote uniformity across classes in the latent space. With the regularization term, SPC can preserve the Gaussian structure of the latent code and achieve better coverage of the hidden space with class uniformly. Experimental results on 12 natural language understanding tasks demonstrate that our SPC effectively improves the performance of pre-trained language models for classification and regression. Extensive experiments show that SPC can enhance the generalization capability, robustness to label noise, and clustering quality of output representations.

Numerical study of raceway behaviours of a slow-moving packed bed solid fuel gasifier

The moving-bed gasifier of solid fuels (e.g., coal or biomass) is a key chemical reactor to convert coal or biomass to clean fuel, where the profile of the raceway cavity and its flow-thermal-chemical behaviours can affect the performance of the gasifier, however, they are not well understood because of the process complexity and modelling challenge. In this study, an advanced 3D multi-fluid model, based on the Eulerian-Eulerian method, coupled with heat transfer and heterogenous reactions, is developed to describe the reacting flow behaviours inside and around the raceways. It is found that raceways inside the slow-moving packed bed gasifier are of balloon-like shapes; they are built in just a few seconds after issuing the jet from gas entry, and then both the average velocity for gas and particle are relatively stable. The gauge pressure conditions are not isobaric, and high temperatures, small gas densities and high reaction rates are observed near the raceway “shell”. Besides, it is found the raceway behaviours on horizontal cross-section feature more symmetry compared to those on other directions. In addition, probability theory and statistics are used to analyse the quantitative raceway results, and possibilities related to the distributions of gas properties, momentum and species are discussed. This model provides an effective tool to systematically study and optimise raceway behaviours inside a slow-moving packed bed solid fuel gasifier.

Ideology of Urban Road Transport Chaos and Accident Risk Management for Sustainable Transport Systems

Transport systems are complex systems present in modern cities. The sustainability of all other urban systems depends on the sustainable functioning of urban transport. Various processes occur within transport systems. Road traffic is one of them. At the same time, road traffic is a rather complex process to manage, which is explained by the influence of many different internal and external environmental factors. The unpredictable and chaotic behavior of each vehicle in a traffic flow complicates predicting the transport situation and traffic management. This problem gave rise to several unsolved problems, including traffic congestion and road accident rates. The solution to these problems is connected with sustainably managing transport systems in terms of road traffic. However, numerous regularities between elements within the system should be understood in order to implement the management process. Unfortunately, the results of many previous studies often reflect only partial regularities and have limited functionality. Therefore, a new approach to urban traffic management is needed. As opposed to the existing solutions, the authors of this paper propose to implement management based on the regularities of changes in the chaos of the transport system. In this regard, the purpose of this research is to establish the relationship between road traffic chaos and road accident rates. The general methodological basis of this research is the system approach and its methods: analysis and synthesis. The theoretical studies were mostly based on the theories of chaos, dynamic systems, and traffic flows. The experimental studies were based on the theories of experimental design, probability, and mathematical statistics. To achieve this goal, a profound analysis covered studies on the sustainability of transport and dynamic systems, sociodynamics, and traffic. The authors proposed considering the relative entropy of lane occupancy at signal-controlled intersections as a measure for assessing traffic flow chaos and sustainability. Notably, as the main conclusions, the authors established regularities for the influence of entropy on the kinetic energy of traffic flows and injury risk. It also makes sense to emphasize that the initial data for the experiment were collected via real-time processing of video images using neural network technologies. These technologies will further allow for the implementation of traffic management and real-time forecasting of various events. Ultimately, the authors identified changes in injury risk depending on the level of road chaos. According to the authors, the obtained results can be used to improve the sustainability of urban transport systems. The research identified changes in injury risk depending on the level of road chaos, which could have significant implications for urban traffic management strategies.