Probability Theory Research Articles

Derivation of stainless steel material factors for European and U.S. design standards

Modern structural design standards are based on the Limit State Design (LSD) philosophy, also known as Load and Resistance Factor Design (LRFD), which involves the use of resistance functions with accompanying safety factors that are based on a statistical evaluation of relevant experimental data, carried out within the framework of a probabilistic reliability theory. This paper presents the derivation of material factors for the yield strength and ultimate tensile strength of austenitic, duplex and ferritic stainless steels, and their associated coefficients of variation (COV) for use in evaluating the safety factors for the European design code EN 1993-1-4 and the American design codes Specification for Structural Stainless Steel Buildings (ANSI/AISC 370–21) and Specification for the Design of Cold-Formed Stainless Steel Structural Members (ASCE/SEI 8–22). Separate material factors and associated COV values are required for the U.S. and European design codes due to the different minimum specified strength values that are given in the respective product standards. The material factors were derived by analysing a large amount of material data provided by different stainless steel producers, which encompassed a wide range of stainless steels and material thicknesses.

Study of optimization for material processing parameters by means of probabilistic methodology for multi-objective optimization

Optimization for material processing parameters is a typical problem of multi-objective optimization, therefore selection and use of proper multi-objective optimization approach is indispensible. The inherent characteristic of newly proposed probabilistic methodology for multi-objective optimization is that it is with the feature of optimization of multiple objectives at the same time in viewpoint of system theory and in spirit of probability theory. In the present paper, the probabilistic methodology is employed to perform the designs of materials processing for improving quality and cost saving at the same time. The laser welding process of ANSI 304 austenitic stainless steel by using a pulsed Nd: YAG laser welding system and thin-wall machining of milling aluminum alloy 2024-T351 are taken as two examples. The quantitative optimum design of materials processing is performed equitably by conducting the assessment of preferable probability of each alternative. The studies indicate that: (1). the optimized parametric combination for the laser welding process of 2 mm thickness ANSI 304 austenitic stainless steel by using a pulsed Nd: YAG laser welding system is at laser parameters of 2.7 kW peak power, welding speed of 2 cm/min and pulse duration of 4 ms; (2). the optimized combination parameter for the thin-wall machining of milling aluminum alloy 2024-T351 is at tool diameter of 8 mm, feed per tooth of 0.06 mm/z, axial cut depth of 24 mm and radial cut depth of 0.625 mm. The optimal configurations guarantee the comprehensive quality of product and reducing energy consumption.

Method of information protection based on the integration of probabilistic encryption and noise immune coding

The subject matter of this article is the processes of increasing information security in communication systems to solve applied problems that are critical in the transmission of confidential data. The goal is to develop a multi-stage method for protecting information from unauthorized access, based on probabilistic encryption integration, error-correcting code, and error decorrelation. The tasks to be solved are as follows: to develop a probabilistic encryption algorithm that considers the entropy of the characters’ appearance in a message; to implement iterative coding with variable parameters of the information bits matrix; and to implement error decorrelation based on the generated matrix by interleaving information and check bits according to a given algorithm. Methodology: theory of signal communication and signal processing, theory of cryptography, theory of noise-resistant codes, probability theory, statistical analysis. The following results were obtained: a multi-stage method for protecting information from unauthorized access was proposed, in which at each step of data conversion, information secrecy is increased; probabilistic encryption was implemented, which considers the entropy of a discrete source of information when forming a space of random combinations; based on an iterative code with specified matrix parameters, an additional increase in the space of random combinations was implemented; error decorrelation reduces the multiplicity of errors in codewords and ensures mixing of bits according to a predetermined law. Conclusions. The scientific novelty of the results obtained is as follows: 1) an improved method of information protection from unauthorized access is proposed, based on probabilistic encryption integration, interference-resistant coding, and error decorrelation; 2) increasing information concealment is realized by eliminating the main shortcomings of probabilistic encryption, which did not take into account the entropy of the symbols of the open message; 3) it is proposed to form the space of random combinations taking into account the average probability of the appearance of a symbol in open texts, which will allow the output of a probabilistic cipher to form a stream of random combinations, which, according to its statistical properties, is close to the uniform distribution law; 4) further development of information protection methods based on interference-resistant coding and error decorrelation with encryption functions is received; 5) a further development of the statistical encryption method is the use of all redundant elements for both probabilistic encryption and interference-resistant coding.

Bosonic Representation of Matrices and Angular Momentum Probabilistic Representation of Cyclic States.

The Jordan-Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions. We illustrate this general scheme by examples of qubit states (spin-1/2 su(2)-group states) and even and odd Schrödinger cat states related to the other representation of su(2)-algebra (spin-j representation). The two-mode coherent-state superpositions associated with cyclic groups are studied, using the Jordan-Schwinger map. This map allows us to visualize and compare different properties of the mentioned states. For this, the su(2) coherent states for different angular momenta j are used to define a Husimi-like Q representation. Some properties of these states are explicitly presented for the cyclic groups C2 and C3. Also, their use in quantum information and computing is mentioned.

Causality: Using Math to Understand the Science of Cause and Effect

Some people say mathematics is the most important subject in science because it is the language of nature. In this article, we provide examples for this by explaining causality. Causality is an important concept because it influences essentially all areas of science and society. In simple terms, causality is the principle that examines the link between a “cause” and an “effect”. This allows us to study important practical questions. For instance, in medicine, biology or law, one can ask “What medication can be used to treat this disease?” “What protein activates a certain gene?” or “What criminal act caused the harm?” To answer these and similar questions, methods from probability, statistics, and graph theory are needed to quantify the meaning of causality. In this article, we provide an overview of this fascinating topic.

Detecting system defects of digital devices in the course of malfunction imitation using fuzzing

Aim. The paper proposes approaches to the organisation of testing of digital systems through malfunction imitation for the purpose of ensuring compliance of international and Russian failure and fault resistance standards for the purpose of efficient (in terms of time) detection of software defects as part of mass production of products. The paper proposes a structure and operating algorithm of a hardware and software test bed for malfunction simulation intended for testing a system’s devices. The test bed collects and processes data for fuzzing, hardware error identification, as well as defines the scope of testing.Methods. The paper used basic systems approach, classical methods of the probability theory and mathematical statistics, decision theory, methods of hardware and software testing and development, mathematical theory of fuzzy sets and fuzzy logic.Results. Malfunction simulation algorithms were developed for the purpose of testing hardware and software systems using fuzzing that ensure probabilistic estimation of the termination time of testing with a specified accuracy.Conclusions. The above set of algorithms allows detecting system defects in the process of software and hardware integration into a single system that cause new malfunctions (emergence) that cannot be taken into consideration at the design stage.

Analysis of the Impact of Curriculum Civics on Students’ Quality Cultivation Based on Bayesian Networks

Abstract This paper first analyzes the Bayesian network model based on probabilistic reasoning to study and explore the random phenomenon law of curriculum thinking. Secondly, probability theory and graph theory are utilized to deal with uncertain information and reduce the meta-multiplicity of the analysis of uncertain knowledge. Then, the Bayesian network structure learning problem is analyzed, and a constraint-based structure learning method is proposed to score students’ qualities by a given scoring function, and using a search algorithm, the best scoring network structure is searched. Finally, in order to analyze the influence of the Civics curriculum on the quality of students in college A, we should analyze the impact of the curriculum. The results show that from the innovative quality of students, the distribution density of innovative habit and innovative ability scores in the interval of 70~75 is (0.02, 0.035), and the distribution density of innovative consciousness scores in the interval of 70~86.25 is (0.005, 0.07). The data show that curriculum Civics can effectively promote the cultivation of innovative talents and the construction of an innovative country by internalizing the quality of innovation in the heart and externalizing it in the form of cultivating students’ innovative habits, improving their innovative consciousness and enhancing their innovative ability.

Стратегічні можливості підприємства та їх оцінювання

Assessment of strategic opportunities is an important stage of strategic planning for the develop-ment of an enterprise and an important component of its strategic management system. The study of the strategic level of the enterprise, its strategic potential will make it possible to analyze the features and determine the prospects of its development for the future. The evaluation of the level of effectiveness of the strategy chosen by the enterprise, which characterizes the direction of its strategic development, will allow to effectively influence the current state of economic activity and the dynamics of changes in this state, to identify more important factors that caused the specified changes, to forecast and plan such changes. A characteristic of strategic development in the process of such an assessment is the company's ability to achieve strategic goals and planned strategic results of its activities during the planned time period. At the same time, the availability and efficiency of the use of the appropriate resources necessary for the imple-mentation of the strategy, the ability to adapt the strategy to changes occurring under the influence of internal and external environmental factors, as well as the ability to obtain significant competitive ad-vantages due to the choice of the appropriate strategy, etc., also become important. The results of the analysis of these and other parameters specified in the study indicate the strategic capabilities of the en-terprise, that is, its ability to take advantage of the positive influence of external factors for its develop-ment and counteract the influence of negative factors, or minimize their influence on its activities. The article proposes a methodology for assessing the strategic capabilities of enterprises using the theory of probability, which will make it possible to take into account both the parameters of their internal environment, which determine the effectiveness of the chosen strategy, and the features of the external environment, which in today's complex conditions is characterized by a significant level of instability and unpredictability. The advantages and disadvantages of using this method during the development, selection and evaluation of enterprise strategies are considered, the peculiarities of its application in certain situa-tions are considered, the probability of the enterprise realizing its opportunities under various types of certainty and variability of the external environment is investigated, which will contribute to increasing the objectivity of assessing the gap between strategic the goals of enterprises and their capabilities and will help identify directions for reducing this gap in the long-term perspective.

Recent progress on limit theorems for large stochastic particle systems

This article presents a selection of recent results in the mathematical study of physical systems described by a large number of particles, with various types of interactions (mean-field, moderate, nearest-neighbor). Limit theorems are obtained concerning either the large-scale or the long-time behavior of these systems. These results rely on the use of a large range of mathematical tools, arising from both probability theory and the analysis of partial differential equations, and thereby illustrate fruitful interactions between these two disciplines.

Totality, Regularity, and Cardinality in Probability Theory

Abstract Recent developments in generalized probability theory have renewed a debate about whether regularity (i.e., the constraint that only logical contradictions get assigned probability $0$ ) should be a necessary feature of both chances and credences. Crucial to this debate, however, are some mathematical facts regarding the interplay between the existence of regular generalized probability measures and various cardinality assumptions. We improve on several known results in the literature regarding the existence of regular generalized probability measures. In particular, we give necessary and sufficient conditions for the existence of regular generalized probability measures defined on the whole powerset of any sample space.

Probabilistic Game Theory and Stochastic Model Predictive Control-Based Decision Making and Motion Planning in Uncontrolled Intersections for Autonomous Driving

Probabilistic Game Theory and Stochastic Model Predictive Control-Based Decision Making and Motion Planning in Uncontrolled Intersections for Autonomous Driving

Over-limit risk assessment method of integrated energy system considering source-load correlation

In an integrated energy system, source-load multiple uncertainties and correlations lead to an over-limit risk in operating state, including voltage, temperature, and pressure over-limit. Therefore, efficient probabilistic energy flow calculation methods and risk assessment theories applicable to integrated energy systems are crucial. This study proposed a probabilistic energy flow calculation method based on polynomial chaos expansion for an electric-heat-gas integrated energy system. The method accurately and efficiently calculated the over-limit probability of the system state variables, considering the coupling conditions of electricity, heat, and gas, as well as uncertainties and correlations in renewable energy unit outputs and multiple types of loads. To further evaluate and quantify the impact of uncertainty factors on the over-limit risk, a global sensitivity analysis method for the integrated energy system based on the analysis of covariance theory is proposed. This method considered the source-load correlation and aimed to identify the key uncertainty factors that influence stable operation. Simulation results demonstrated that the proposed method achieved accuracy to that of the Monte Carlo method while significantly reducing calculation time. It effectively quantified the over-limit risk under the presence of multiple source-load uncertainties.

Performance evaluation of cosmic ray muon trajectory estimation algorithms

Muons, being elementary particles with minimal interaction with nuclear materials and abundant at sea level, have sparked interest in utilizing them for imaging various applications, such as mining [Borselli et al., Sci. Rep. 12, 22329 (2022)], volcano imaging [Nagamine et al., Nucl. Instrum. Meth. A, 356, 585(1995)], and underground tunnel detection [Guardincerri et al., Pure Appl. Geophys. 174, 2133 (2017)]. Recently, their use in nuclear nonproliferation and safeguard verification has gained attention, particularly in cargo screening for nuclear waste smuggling [Baesso et al., J. Instrum. 9, C10041 (2014)], source localization [L. J. Schultz et al., Nucl. Instrum. Meth. A 519, 687 (2004)], and locating nuclear fuel debris in reactors [Borozdin et al., Phys. Rev. Let. 109, 152501 (2012)]. However, the resolution of muon image reconstruction techniques is limited due to multiple Coulomb scattering (MCS) within the target object. To achieve robust muon tomography, it is crucial to develop efficient and flexible physics-based algorithms that can model the MCS process accurately and estimate the most probable trajectory of muons as they pass through the target object. To address this limitation, in this study, a novel algorithmic approach utilizing the Bayesian probability theory and Gaussian approximation of MCS is chosen. Different energy levels, materials, and target sizes were considered in the evaluations. The results demonstrate that the Generalized Muon Trajectory Estimation (GMTE) algorithm offers significant improvements over currently used algorithms. Across all test scenarios, the GMTE algorithm demonstrated ∼50% and 38% increase in precision compared to Straight Line Path (SLP) and Point of Closest Approach (PoCA) algorithms, respectively. Furthermore, it exhibited 10%–35% and 10%–15% increases in muon flux utilization for high and medium Z materials, respectively, compared to the PoCA algorithm. In conclusion, the extensive simulations confirm the enhanced performance and efficiency of the GMTE algorithm, offering improved resolution and reduced measurement time for cosmic ray muon imaging compared to the current SLP and PoCA algorithms.

Von Mises-Fisher Elliptical Distribution.

Modern probabilistic learning systems mainly assume symmetric distributions, however, real-world data typically obey skewed distributions and are thus not adequately modeled through symmetric distributions. To address this issue, a generalization of symmetric distributions called elliptical distributions are increasingly used, together with further improvements based on skewed elliptical distributions. However, existing approaches are either hard to estimate or have complicated and abstract representations. To this end, we propose a novel approach based on the von-Mises-Fisher (vMF) distribution to obtain an explicit and simple probability representation of skewed elliptical distributions. The analysis shows that this not only allows us to design and implement nonsymmetric learning systems but also provides a physically meaningful and intuitive way of generalizing skewed distributions. For rigor, the proposed framework is proven to share important and desirable properties with its symmetric counterpart. The proposed vMF distribution is demonstrated to be easy to generate and stable to estimate, both theoretically and through examples.

Model predicting the onset of antiepileptic drug resistance in women of reproductive age with epilepsy: analytical study

Introduction. In attempt to find an answer regarding the possible scenarios of epilepsy evolution in women of reproductive age (e.g. worsening, remission, antiepileptic drug resistance, status epilepticus occurence), preferably - objective, based on simple, replicable, observable indicators that can be included in a mathematical probability estimation model, could significantly improve their quality of life and increase the effectiveness of prescribed treatments. Materials and methods. Bidirectional, cohort, descriptive-analytical study, conducted between 2016-2020. Primary data were collected in the Diomid Gherman Institute of Neurology and Neurosurgery, the State Hospital of Republic of Moldova and the Excellence Private Medical Institution. Out of 366 unique parameters, which were recorded in the 159 patients enrolled in the study at each visit (total, 4 documentation visits over 5 years period), 10 parameters were selected for multivariate analysis, considered relevant for predicting clinically significant outcomes. Criteria for parameter relevance were: reaching p≤0.1 in univariate analysis, easy documentation. Subsequently, testing for multicollinearity (calculation of variance inflation factor) and the contribution of each parameter in the formula was performed using the Akaike informativeness criteria. The performance of the developed predictive models was expressed by the area under the ROC curve, positive and negative prognostic power. Statistical analysis: GraphPad Prism, v. 9 trial (Graph Pad Software, Boston, USA). Results. Age at onset of the disease 14.0±6.3 years; age at first referral to specialist 24.0±7.2 years. The developed predictive model, based on 3 parameters (depressive state, annual frequency of seizures, presence of brain lesions on MRI) has a positive predictive value of 83%, negative of 62%, with an area under the ROC curve of 0.72 (95%CI = 0.56 to 0.88) and a probability of occurrence of 96%. Conclusions. Depressed patients with documented structural lesions on MRI and a high frequency of epileptic seizures have a progressive, significant risk (an OR of 5.3-24.0) of developing resistance to antiepileptic drugs.

Depression- and anxiety-associated disrupted brain structural networks revealed by probabilistic tractography in thyroid associated ophthalmopathy

BackgroundPatients with thyroid-associated opthalmopathy (TAO) have widespread white matter (WM) abnormalities in the emotional and cognitive functional regions. However, the topological representation of these WM abnormalities and the network-level structural aberrations underlying TAO and concomitant affective disorders are still unclear. MethodsWe used probabilistic diffusion tractography and graph theory to investigate brain network topology in 37 active, 35 inactive TAO patients and 23 healthy controls. Then, we evaluated the partial correlations between network topological metrics and clinical parameters. ResultsFor global topology, only active TAO patients exhibited significantly decreased global (Eglob) and local (Eloc) efficiency compared with controls, while no significant difference was observed between active and inactive TAO patients. For regional topology, we found a significantly decreased nodal efficiency in the left orbital superior frontal gyrus (ORBsup), medial orbital superior frontal gyrus (ORBsupmed), hippocampus and amygdala in active TAO patients compared with inactive ones. Intriguingly, Eglob, Eloc, and nodal efficiency of left ORBsup, ORBsupmed, olfactory cortex, gyrus rectus, hippocampus, right parahippocampal gyrus and amygdala had significantly positive correlations with anxiety/depression scores, bilateral exophthalmos and intraocular pressure in active TAO patients, while no significant correlation was observed in inactive TAO patients. LimitationsNo longitudinal follow-up. ConclusionsWM networks of TAO are characterized by decreased local specialization and global integration in the active phase, and decreased nodal efficiency highly related to anxiety and depression in the emotional and cognitive regions. Our findings provide new insight regarding the neurobiological mechanisms of TAO and contribute to the treatment of concomitant affective disorders.

Principle and application of random walk simulation: Multilayer networks, predation and stock market

Given the probabilities (which remain unchanged at each step) of travelling a certain distance in a certain direction, a random walk is a method used in probability theory to determine the likely position of a point depending on random movements. Markov processes, in which future behavior is independent of previous behavior, include random walks as an illustration. This study will mainly pay attention to three different applications of random walks in aspects of multilayer networks, predation and stock market. A real and intricate network could be solved by a mathematical equation depending on a random walk model. There are totally four different types of random walks that properly represent the motion of an animal searching for preys. Among these four types, CCRW is the best explanation for the route of a predator. Nevertheless, by analyzing the panel unit root tests, random walks fail to simulation the variability of share prices. This study promotes scholars to come up with an idea of the principle and application of random walks, and therefore realize the significance of such simulations.

Navigating the realm of noncommutative probability: Historical perspectives and future directionsstorical perspectives and future directions

This review article provides a comprehensive overview of the fascinating field of noncommutative probability theory, tracing its evolution from its inception in the early 1980s by Romanian-American mathematician Dan Voiculescu to its current state of prominence in mathematics. Through a meticulous examination of seminal works and recent advancements, we explore the key concepts, methodologies, and significant developments in this field, emphasizing the combinatorial aspects of noncommutative probability spaces, including non-crossing partitions and linked partitions. This exploration encompasses various aspects, including analytical methods, operator algebras, random matrices, and combinatorial structures. Additionally, it concludes with the current understanding and potential directions for future research.

Incorporating Multidimensional Data Analysis Methods for Probability Theory and Mathematical Statistics Teaching Reform and Practical Exploration

Abstract Based on the new curriculum reform and big data technology, this paper uses the radial function and RBF neural network algorithm in the multidimensional data analysis method to obtain the center, variance and output layer power of the neurons of Probability Theory and Mathematical Statistics. Construct the teaching evaluation model of Probability Theory and Mathematical Statistics according to the RBF neural network algorithm and screen 25 secondary indicators from the three aspects of teachers, students, and course content, thus forming the teaching evaluation index system of Probability Theory and Mathematical Statistics. Determine the evaluators and evaluation methods, according to the specific implementation of the evaluation. The evaluation model of “Teaching Probability Theory and Mathematical Statistics” based on the RBF neural network is tested for reliability and validity. The results show that the evaluation values of 25 indicators in the indicator system of the RBF-based evaluation model for the teaching of Probability Theory and Mathematical Statistics are all out of the range of 8.010-9.0, and |u 1| = 16.392≥2.241, |u 2| = 10.052≥2.241 in the examination scores of Probability Theory and Mathematical Statistics from the second semester of the academic year 2018/2019 to the second semester of the academic year 2020/2021, i.e., the examination scores of the course for the five semesters as a whole do not obey a normal distribution. This study enables students to better master the theoretical knowledge of Probability Theory and Mathematical Statistics, which is of great significance to the educational reform and practical exploration of Probability Theory and Mathematical Statistics in colleges and universities.

Wind damage vulnerability analysis of narrow base tower for distribution line based on probabilistic reliability

Steel narrowbase tower has been widely used in distribution network in recent years because that it covers an area smaller than the conventional tower, and has stronger wind resistance than concrete pole. In order to fully understand the wind resistance performance of narrow base tower, a vulnerability performance of narrow base tower under different wind speeds was analyzed based on probabilistic reliability theory. According to the damage characteristics of narrow base tower and the corresponding tall structure specification, wind performance level indexes of narrow base tower were established. When calculating the effect of wind load on narrow base tower, the randomness of wind load, material properties and dimensions were considered. The probability of the narrow base tower appearing different degrees of damage under different wind speeds was calculated, and subsequently a wind vulnerability curve of the narrow base tower was drawn. It is found that the severe damage probability of narrow base tower is about 5% when the wind speed is 23.6m/s. And in the case of severe damage probability is 95%, the wind speed reaches 80m/s. Narrow base tower has good resistance to wind disaster.