Probability Theory Approach Research Articles

A Probability Theory Approach to Stability Analysis of Networked Sampled-Data Systems With Consecutive Packet Dropouts

In this brief note, a probability theory approach is proposed to investigate the stability analysis issue for a class of networked sampled-data systems with packet dropouts. The continuous-time linear system under consideration is first transformed into a discrete-time system, where the system matrix of the discrete-time system is characterized by stochastic characteristic. Then, by the matrix exponential computation, an equivalent discrete-time stochastic system is established. Based on this, a controller is designed by the law of total expectation, which guarantees the stochastic stability of the closed-loop stochastic system. Finally, a numerical example and an example using power grid with IEEE 4-bus line are used to verify the effectiveness and applicability of the proposed design algorithm.

A probabilistic evaluation of the argument of correction in affirmative action

Objective: The issue of affirmative action is a major point of discussion in distributive justice and allocation of scarce resources such as job-offerings or college seats. Philosophical arguments around this focus on diversity, historical justice and correction. The objective of this study is to examine the argument of correction in relation to affirmative action, which states that affirmative action helps correct biases in metrics used to measure merit. Method: We develop of a stochastic formulation of the argument of correction and analyse it using a probability-theory approach. Result: We find with the help of two counterexamples that the argument of correction is not generally valid, when we admit the stochastic nature of the problem. Conclusion: Though the argument of correction may be valid in some special cases, its general lack of validity presents a major challenge to this dominant argument widely used in the literature. Keywords: Affirmative action; distributive Justice; allocation of resources

Can Shiozawa’s, Morioka’s and Taniuchi’s Microfoundations for Evolutionary Economics (2019) Serve As the Microfoundations for “… Post-Keynesian Economics “ (2019, p.vii)? The Answer Is Definitely Yes if Post –Keynesians Can Break Away From Joan Robinson’s Anti-Mathematical, Anti-Formalist Views

Can Shiozawa’s, Morioka’s and Taniuchi’s Microfoundations for Evolutionary Economics (2019) Serve As the Microfoundations for “… Post-Keynesian Economics “ (2019, p.vii)? The Answer Is Definitely Yes if Post –Keynesians Can Break Away From Joan Robinson’s Anti-Mathematical, Anti-Formalist Views

РЕГЛАМЕНТАЦИЯ ПАРАМЕТРОВ ШЕРОХОВАТОСТИ ФУНКЦИОНАЛЬНЫХ ПОВЕРХНОСТЕЙ ДЕТАЛЕЙ МАШИН В ТЕХНОЛОГИЧЕСКОЙ ДОКУМЕНТАЦИИ

On the basis of the probability theory approach to the formation of surface roughness parameters in machinery during machining there is offered an algorithmic solution of an urgent problem of the regulations of roughness parameters for machinery functional surfaces in technological documentation. The algorithmic solutions for the following parameter versions are developed (RSS 2.309-73): the highest value; the smallest value; a value range; a rated value with ultimate deviations; an indication of two and more parameters. The theoretical investigation results may serve as a starting point for the further development of theory and practice for the technological support of roughness parameters in machinery functional surfaces with the required reliability. 
 Foe a wide actual realization of investigation results the solution of a number of problems is needed: 1) the development of standards or guide information on the regulations in technological documentation of required technological values of roughness parameters; 2) the further development of investigations in the field of technological support reliability of quality parame-ters (including roughness) of blank surfaces in the course of machining in technologically flexible systems.

Randomness vs. fuzziness in managerial decision-making

Managers often deal with uncertainty of a different nature in their decision processes. They can encounter uncertainty in terms of randomness or fuzziness (i.e., mist, obscurity, inaccuracy or vagueness). In the first case (randomness), it can be described, for example, by probability distribution, in the second case (fuzziness) it cannot be characterized in such a way. The methodological part of the paper presents basic tools for dealing with the uncertainty of both of these types, which are techniques of probability theory and fuzzy approach technique. The original contribution of the theoretical part is the interpretation of these different techniques based on the existence of fundamental analogies between them. These techniques are then applied to the problem of the project valuation with its “internal” value. In the first case, the solution is the point value of the statistical E[PV], in the second case the triangular fuzzy number of the subjective E[PV]. The comparison of the results of both techniques shows that the fuzzy approach extends the standard outcome of a series useful information. This informative “superstructure” of the fuzzy approach compared to the standard solution is another original benefit of the paper.

Statistical description of transport in multimode fibers with mode-dependent loss

We analyze coherent wave transport in a new physical setting associated with multimode wave systems where reflection is completely suppressed and mode-dependent losses together with mode mixing are dictating the wave propagation. An additional physical constraint is the fact that in realistic circumstances the access to the scattering (or transmission) matrix is incomplete. We have addressed all these challenges by providing a statistical description of wave transport which fuses together a free probability theory approach with a filtered random matrix ensemble. Our theoretical predictions have been tested successfully against experimental data of light transport in multimode fibers.

Risk-based determination of heat demand for central and district heating by a probability theory approach

One of the most important design tasks related to the establishment and operation of heat supply systems involve design heat demand of a required reliability level. Determination of heat demand for central and district heating is set out in standards in the practice of both Hungary and most European countries. Methodologies reflect a deterministic tendency. The uncertainty of heat demand for heating so specified is not analyzed: values are not associated with reliability, probability and confidence interval figures. Our article presents the method of risk-based determination of heat demand for central and district heating by probability theory approach.

Special Issue: Modeling & Simulation for Cyber Security of Autonomous Vehicle Systems

The transportation and information gathering needs of our world are changing. Transportation systems are becoming more vital for our society and also more congested. Networking holds out the hope for more efficient use of multiple autonomous systems but also opens the door for increased risk exposure to failures and malicious attacks. Developments in internet technologies, online auctions and games, social networks, high-technology engineered systems with multiple dynamic components, and elsewhere motivate new advancements for decision, interaction, and control in cyberphysical systems (CPS) with autonomous dynamical subsystems. Examples of vehicle CPS can be found in areas as diverse as automobiles, air transportation, civil infrastructure, trains, and surface and subsurface water vehicles. Information Assurance must provide authentic, accurate, secure, reliable, and timely information to vehicle decision and control systems in order to achieve information dominance, mission performance, and survivability in risky changing environments. Computing and information processes must be carried out over distributed and heterogeneous networked systems for resilience to minimize single point of failure to malicious attacks. Recent advances in autonomous cyberphysical systems show promise for improved reconnaissance, surveillance, and security in foreign and domestic conflicts. However, CPS also present new and unevaluated sets of attack surfaces in communications and controls. As such, the modeling and simulation of cyber security in autonomous systems is a critical research area that will ultimately dictate the ways these systems should interact with people and each other. Thus, the goal of this Special Issue is collect a comprehensive body of descriptive and prescriptive approaches to modeling and simulating cyber security threats, defense techniques, and overall frameworks in highly dynamic and hostile environments. This special issue is composed of five papers that show the current state of modeling, simulation, decision, and control in some important areas of cyberphysical systems. The paper by Yagdereli, Gemci, and Aktas x presents a study on cyber security of unmanned vehicles, including cars, civilian unmanned aircraft, trains, and boats. Types of cyber-attacks are characterized, including passive and active attacks. Potential vulnerabilities of autonomous vehicles are detailed. Metrics for cybersecurity are proposed. A framework for mitigation strategies based on modeling and simulation is presented. The paper by Bergin presents a cyber-attack and simulation framework based on a live-virtual-constructive (LVC) environment. The focus is on wireless mobile network interfaces for military autonomous vehicles. LVC offers opportunities for training and assessment of humanin-the loop performance. Security threats and vulnerabilities are discussed, and attack techniques are outlined including denial of service, passive attack, and malicious agents. A cyber-attack and simulation framework is detailed including methods of data modeling, storage, and transfer. The paper by Cavagnaro and Tiller presents a framework for risk assessment of force allocation and countermeasures in autonomous vehicle air operations. A probability theory approach is used to define tipping points to quantify game outcomes that represent mission success. Probability distributions are presented for risk assessment, and random walks are employed to yield a distribution of outcome results. Based on these tools, the Tiller software wargame simulation Modern Air Power has been developed and is applied in this paper to force allocation and countermeasures based on game-changing capabilities.

Geometric Series via Probability

We describe a probability theory approach to find the sum of a convergent geometric series.

Cancellous bone fast and slow waves obtained with Bayesian probability theory correlate with porosity from computed tomography

A Bayesian probability theory approach for separating overlapping ultrasonic fast and slow waves in cancellous bone has been previously introduced. The goals of this study were to investigate whether the fast and slow waves obtained from Bayesian separation of an apparently single mode signal individually correlate with porosity and to isolate the fast and slow waves from medial-lateral insonification of the calcaneus. The Bayesian technique was applied to trabecular bone data from eight human calcanei insonified in the medial-lateral direction. The phase velocity, slope of attenuation (nBUA), and amplitude were determined for both the fast and slow waves. The porosity was assessed by micro-computed tomography (microCT) and ranged from 78.7% to 94.1%. The method successfully separated the fast and slow waves from medial-lateral insonification of the calcaneus. The phase velocity for both the fast and slow wave modes showed an inverse correlation with porosity (R(2) = 0.73 and R(2) = 0.86, respectively). The slope of attenuation for both wave modes also had a negative correlation with porosity (fast wave: R(2) = 0.73, slow wave: R(2) = 0.53). The fast wave amplitude decreased with increasing porosity (R(2) = 0.66). Conversely, the slow wave amplitude modestly increased with increasing porosity (R(2) = 0.39).

Human reliability analysis (HRA) emanating from use of technology for ships navigating within coastal area

The traditional approach to the study of human factors in the maritime field involves the analysis of accidents without considering human factors reliability analysis. The main approach being use to analyze human errors are statistical approach and probability theory approach. Another suitable approach to the study of human factors in the maritime industry is the quasi-experimental field study where variations in performance (for example attention) can be observed as a function of natural variations in performance shaping factors. This paper analyzes result of modeling human error and human reliability emanating from the use of technology on board ship navigation in coastal water area by using qualitative and quantitative tools. Accident reports from marine department are used as empirical material for quantitative analysis. The literature on safety is based on common themes of accidents, the influence of human error resulting from technology usage design, accident report from MAIB and interventions information are use for qualitative assessment. Human reliability assessment involves analysis of accident in waterways, emanating from human-technology factors interface. This paper report an enhancement requirement of the methodological issues with previous research study, monitoring and deduce recommendations for technology modification of the human factors necessary to improve maritime safety performance. The result presented can contribute to rule making, and safety management leading for development of guideline and standards for human reliability risk management for ship navigating within inland and coastal waters.

Effects of Sampling on Measuring Galaxy Count Probabilities

We investigate in detail the effects of sampling on our ability to accurately reconstruct the distribution of galaxies from galaxy surveys. We use a simple probability theory approach, Bayesian classifier theory and Bayesian transition probabilities. We find the best Bayesian estimator for the case of low sampling rates, and show that even in the optimal case certain higher order characteristics of the distribution are irretrievably washed out by sparse sampling: we illustrate this by a simple model for cluster selection. We show that even choosing an optimal threshold, there are nonzero numbers for both misidentified clusters and true clusters missed. The introduction of sampling has an effect on the distribution function that is similar to convolution. Deconvolution is possible and given in the paper, although it might become unstable as sampling rates become low. These findings have important consequences on planning and strategies of future galaxy surveys.

Application Using VLSI Hardware Realization of Self–Learning Recursive Fuzzy Model

This paper presents a hardware application of a self—learning fuzzy logic controller on industrial gas furnace data. The fuzzy algorithm is based upon a unique probability theory approach to fuzzy identification and estimation. This method was chosen because of an inherent filtering operation making it highly immune to noise. In the past the majority of fuzzy inference processors have been designed as application-specific circuits or custom IC’s. Using semi—custom programmable IC’s resolves the problems of development costs, adaptability of designs and execution speed.

VLSI Hardware Realization of Self-Learning Recursive Fuzzy Model for Dynamic Systems

This paper presents a hardware realization of a self-learning fuzzy logic controller, based upon a unique probability theory approach to fuzzy identification and estimation. This method was chosen because of an inherent filtering operation making it highly immune to noise. A method of overcoming the limitations of application specific fuzzy hardware systems, by using programmable logic cell array le's, is also presented. In the past the majority of fuzzy inference processors have been designed as application-specific circuits or custom IC's. Using semi-custom programmable IC's resolves both the problems of development costs and that of adaptability of designs.

Is Probability Theory Relevant for Uncertainty? A Post Keynesian Perspective

Mainstream perspectives involving uncertainty presume that expectations are based on either a statistical analysis of past data, with market signals providing information about objective probabilities, or on subjective perceptions of these probabilities founded on the axioms of expected utility theory. Post Keynesians, following Keynes, have developed a different perspective, where probability distributions are not the basis for comprehending real world behavior under uncertainty. According to this analysis, there are many important situations where “true” uncertainty exists regarding future consequences of today's choices. Whenever conditions of true uncertainty prevail, human behavior may differ systematically from what is implied by the standard expected utility perspective. This paper explains how the Post Keynesian perspective differs from the orthodox probability theory approach, thereby providing a more general theory which can explain long-run decisions regarding liquidity demands, investment decisions, the existence of long period underemployment equilibrium, the long-run nonneutrality of money, and the unique and important role Keynes assigned to nominal contracts and especially the money wage contract.

The effective volumes of atomic-molecular systems and the correlation of electrons

The probability-theory approach to the study of the states of atoms and molecules makes it possible to interpret the information on the effective volumes of atoms and molecules, contained in the wave function. This approach also makes it possible to estimate the electron correlation.

Twin concordance: A set theoretic and probability theory approach

The concepts and assumptions used in twin concordance studies are made explicit with a mathematical treatment. The logic connecting those assumptions to the usual interpretations of twin studies is substantiated in a rigorous manner through the use of elementary set and probability theory.