Random Phenomena Research Articles

Refraction Surface-Based Stellar Atmospheric Refraction Correction and Error Estimation for Terrestrial Star Tracker

Stellar atmospheric refraction imaging error, as the optical imaging variation of starlight before and after passing through Earth&#x2019;s atmosphere, is one of the key issues for terrestrial star trackers to obtain accurate attitude measurement results. To resolve the problem, a refraction surface-based stellar atmospheric refraction correction method is presented in this paper. Different from existing correction methods, a new atmospheric refraction feature, i.e., stellar atmospheric refraction surface, is proposed to represent the random irregular optical phenomena of starlight, and avoids the limitations of theoretical atmospheric models and empirical formulas. On the basis of the principles of &#x201C;collinear refraction surfaces&#x201D;, &#x201C;invariable refraction surface&#x201D;, the proposed model successfully realizes the accuracy atmospheric refraction correction by the sensor itself, without external atmospheric parameters. Then, by analyzing the error factors parallel and perpendicular to the atmospheric refraction surface, the atmospheric refraction correction error estimation model is established to forecast the attitude accuracy after correction. Numerical simulations and night sky experiments validate the reliability of our atmospheric refraction correction method and error estimation model. The average angular distance error of the test star tracker is reduced from <inline-formula> <tex-math notation="LaTeX">$31.1310''$ </tex-math></inline-formula> into <inline-formula> <tex-math notation="LaTeX">$1.7705''$ </tex-math></inline-formula>, which is significantly decreased by 94.31&#x0025;.

Does Population Size Drive Changes in Transatlantic Vagrancy for Gulls? A Study of Seven North Atlantic Species

European gulls Chroicocephalus ridibundus, Larus canus, and L. graellsii have dispersed to North America and C. ridibundus and L. graellsii have bred or attempted to breed. North American gulls L. delawarensis, Leucophaeus atricilla, Leucophaeus pipixcan, and Chroicocephalus philadelphia have dispersed to Europe, although no successful breeding by non-hybrid pairs has yet occurred. We hypothesized that as gull population sizes increase, the number of birds exploring potential new breeding sites also increases. To test our hypothesis, we compared the number of transatlantic vagrants to the population size on the previous year using generalized linear models. We found an increasing number of transatlantic vagrants moving in both directions, which suggests that vagrancy is not a random phenomenon driven by strong winds nor caused by reverse migration. Population size predicted transatlantic vagrancy in four of the seven species. However, our hypothesis that increases in population size drive increases in vagrancy was only supported in two of these instances. We further looked at sub-populations of L. delawarensis in North America and tested our hypothesis for each subpopulation. We found partial support for our hypothesis for these data. Even within one species, we observed multiple relationships between vagrancy and population size. Our results showed that size or trend in source population size—in some circumstances—is clearly a driver of vagrancy, but other factors must play an important role too. As anthropogenic development continues, and high-quality habitats become farther apart, it is important that we continue to investigate all drivers of vagrancy because the persistence of a species may depend crucially on its longest-distance dispersers.

Iterative learning guaranteed cost control based on two‐dimensional Roesser systems subject to denial‐of‐service attacks and fading measurements

AbstractIn this article, the network‐based iterative learning guaranteed cost control problem for the linear systems subject to denial‐of‐service (DoS) attacks at input and output (I/O) sides is studied via faded channels. First, the DoS attacks are modeled by independent Bernoulli sequences, where the expectation and variance are known. The fading measurements in I/O channels are described as independent Gaussian distributions with known expectations and variances respectively. Then, the repetitive system and the proposed ILC scheme involving both the iteration and time axes are transformed into a random two‐dimensional (2D) Roesser model by using the 2D system theory. The mean‐square asymptotic stability is introduced and followed by the definition of guaranteed cost function. Next, sufficient conditions that can not only ensure the asymptotic stability but also the cost index are derived. By applying the linear matrix inequality technology, the gain matrices and the upper bound of the control cost are further obtained. After exploring the adverse effect brought by the random fading phenomenon, a compensation algorithm is then designed and the analysis is strictly deduced. Finally, an injection molding process example is given to confirm the validity of the design.

Biology of the Extracellular Proteasome.

Proteasomes are traditionally considered intracellular complexes that play a critical role in maintaining proteostasis by degrading short-lived regulatory proteins and removing damaged proteins. Remarkably, in addition to these well-studied intracellular roles, accumulating data indicate that proteasomes are also present in extracellular body fluids. Not much is known about the origin, biological role, mode(s) of regulation or mechanisms of extracellular transport of these complexes. Nevertheless, emerging evidence indicates that the presence of proteasomes in the extracellular milieu is not a random phenomenon, but rather a regulated, coordinated physiological process. In this review, we provide an overview of the current understanding of extracellular proteasomes. To this end, we examine 143 proteomic datasets, leading us to the realization that 20S proteasome subunits are present in at least 25 different body fluids. Our analysis also indicates that while 19S subunits exist in some of those fluids, the dominant proteasome activator in these compartments is the PA28α/β complex. We also elaborate on the positive correlations that have been identified in plasma and extracellular vesicles, between 20S proteasome and activity levels to disease severity and treatment efficacy, suggesting the involvement of this understudied complex in pathophysiology. In addition, we address the considerations and practical experimental methods that should be taken when investigating extracellular proteasomes. Overall, we hope this review will stimulate new opportunities for investigation and thoughtful discussions on this exciting topic that will contribute to the maturation of the field.

Research on Data Analysis Literacy of High School Students in China

Data analysis is an important mathematical technique for studying random phenomena and a major method for mathematical applications in the era of big data. For students, the stage of high school is a critical period to form and develop their data analysis ability, so scholars have paid a lot of attention to the issue of education about data analysis literacy of high school students. However, there is a lack of systematic organization of the literature. In order to help researchers grasp the current status of research and promote further investigation, this paper summarizes relevant literature in China and analyzes the research results. The following conclusions are drawn from the summary and analysis of previous studies: 1. Previous studies on data analysis literacy of high school students have focused on five main aspects: basic connotation, cognitive status, influencing factors, cultivation strategies and evaluation methods; 2. Among them, cognitive status and cultivation strategies are the hot issues; 3. In terms of research methods, scholars mostly use pencil-and-paper tests, questionnaires or interviews to investigate cognitive status, and analyze the influencing factors and cultivation strategies just with theoretical thinking; 4. In previous studies, there are shortcomings of single research method and lack of empirical practice, while the previous researches on influencing factors are not systematic or comprehensive. The research conclusions on cultivation strategies lack feasibility or validity, and the researches on evaluation methods are relatively scarce. Therefore, scholars can start from the evaluation method to explore a reasonable and feasible evaluation system with high audience. It is necessary for scholars to further improve the research methods on the influencing factors and cultivation strategies in future studies, and to conduct more in-depth and systematic researches on the influencing factors of data analysis literacy from an empirical perspective, in order to find out more comprehensive influencing factors and more operable cultivation strategies.

Periodicity in ultrasonic atomization involving beads-fountain oscillations and mist generation: Effects of driving frequency

Ultrasonic atomization induced by high driving frequency, generally on the order of 1 MHz or higher, could involve a liquid fountain in the form of a corrugated jet, or a chain of “beads” of submillimeter diameter in contact. This study concerns dynamics/instability of such beads fountain, observed under lower input power density (≤ 6 W/cm2) of the “flat” ultrasound transducer with a “regulating” nozzle equipped, exhibiting time-varying characteristics with certain periodicity. High-speed, high-resolution images are processed for quantitative elucidation: frequency analysis (fast Fourier transform) and time–frequency analysis (discrete wavelet transform) are employed, respectively, to evaluate dominant frequencies of beads-surface oscillations and to reveal factor(s) triggering mist emergence. The resulting time variation in the measured (or apparent) fountain structure, associated with the recurring-beads size scalable to the ultrasound wavelength, subsumes periodic nature predictable from simple physical modeling as well as principle. It is further found that such dynamics in (time-series data for) the fountain structure at given height(s) along a series of beads would signal “bursting” of liquid droplets emanating out of a highly deformed bead often followed by a cloud of tiny droplets, or mist. In particular, the bursting appears to be not a completely random phenomenon but should concur with the fountain periodicity with a limited extent of probability.

A new random field on lattices

The risk of occurrence of atypical phenomena is a cross-cutting concern in several areas, such as engineering, climatology, finance, actuarial, among others. Extreme value theory is the natural tool to approach this theme. Many of these random phenomena carry variables defined in time and space, usually modeled through random fields. Thus, the study of random fields in the context of extreme values becomes imperative and has been developed especially in the last decade. In this work, we propose a new random field, called pMAX, designed for modeling extremes. We analyze its dependence and pre-asymptotic dependence structure through the corresponding bivariate tail dependence coefficients. Estimators for the model parameters are obtained and their finite sample properties analyzed. Examples with simulations illustrate the results.

How can a random phenomenon between particles be synchronized instantaneously and independently of the distance between said particles?

Entanglement is a random phenomenon that is instantly synchronized, regardless of the space that mediates between entangled particles. However, the instantaneous transmission of information using entanglement is impossible. This is because the instantaneity in the synchronization of non-local outcomes as a consequence of quantum measurement (after the distribution of the entangled pairs) cannot be used for an entanglement-based communication system to transmit information instantaneously. This impossibility stems from the following two reasons: (a) the difficulty of controlling non-local outcomes through local actions without the intervention of an auxiliary channel (classical), and (b) regardless of the previous point, no communication system based on entanglement can be instantaneous due to the distribution of an entangled pair at relativistic speeds, necessary to generate the quantum channel, each time a qubit must be transmitted. Three simple experiments help to clarify this controversial point. In fact, this study establishes what is truly responsible for the impossibility to transmit information instantaneously of any communication system based on entanglement. In this respect, functional models of the internal behavior of quantum measurement, and entanglement were developed, which allow analyzing the instantaneity post-distribution of entangled particles, before and after a quantum measurement, as well as the randomness in the results obtained from a quantum measurement of the entanglement. In this sense, this study establishes a debate about three possible responsible for the aforementioned randomness: the quantum measurement itself, entanglement, and the human intervention. Finally, homology between the entanglement and the double-slit experiment is presented.

Model-based estimation for population total under model misspecification using the balanced sampling scheme

A common assumption in the model-based inference is that the model which explains the behavior of the random phenomena being investigated is correctly specified. But if model is incorrect, it turns out that the inference can be affected and the predictions can be poor, which leads to increase the bias of an estimator. In this article, a balanced sampling technique is introduced for reducing the model misspecification bias in estimating the finite population total where working model is deviates from the underlying true model. Some special cases like homogeneous population model, linear population model and ratio population model are considered under the misspecified basis function regression model by utilizing the model relationship. Design-based efficiency comparisons of the proposed estimators to the existing ones are evaluated through simulation and a real data set. It is shown that the proposed estimators using the balancing scheme keep up the superiority in simple random sampling.

Method for Enhanced Accuracy in Machining Free-Form Surfaces on CNC Milling Machines

Abstract The present article describes a method for enhanced accuracy in machining free-form surfaces produced on CNC milling machines. In this method, surface patch machining programs are generated based on their nominal CAD model. After the pretreatment, coordinate control measurements are carried out. The obtained results of the measurements contain information on the values and distribution of observed machining deviations. These data, after appropriate processing, are used to build a corrected CAD model of the surface produced. This model, made using reverse engineering techniques, compensates for the observed machining deviations. After regeneration of machining programs, the object processing and control measurements are repeated. As a result of the conducted procedure, the accuracy of the manufacture of the surface object is increased. This article also proposes the introduction of a simple procedure for the filtration of measurement data. Its purpose is to minimise the effect of random phenomena on the final machining error correction. The final part of the article presents the effects of the proposed method of increasing the accuracy of manufacturing on ‘raw’ and filtered measurement data. In both cases, a significant improvement in the accuracy of the machining process was achieved, with better final results obtained from the filtered measurement data. The method proposed in the article has been verified for three-axis machining with a ball-end cutter.

Frequentist statistical inference without repeated sampling

Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random phenomena are interpreted as classical probabilities, and this interpretation of equally likely chance outcomes is applied to statistical inference using urn models. These are used to address Bayesian criticisms of frequentist methods. Recent descriptions of p-values, confidence intervals, and power are viewed through the lens of classical probability based on a single random sample from the population.

Event-triggered distributed filtering for a class of uncertain parameter systems over dynamic switching topologies networks subject to missing measurements

In this paper, the event-triggered distributed filtering (ETDF) problem is discussed for a class of uncertain parameter systems over dynamic switching topologies networks subject to missing measurements. The event-triggered communication mechanism is introduced to improve energy utilization of sensor network. The randomness phenomena of dynamic switching typologies and missing measurements are characterized by two sets of random variables satisfying Bernoulli distribution. By taking the influence of the parameter uncertainty of the system and the stochastic disturbance of the corresponding estimator gain into account, a novel optimal ETDF is constructed with a linear consistency strategy. Moreover, the estimator gain is obtained by minimizing the upper bound of the estimation error covariance. Finally, an illustrative simulation is provided to illustrate the effectiveness of the proposed algorithm.

Актуальность преподавания математики в медицинском вузе

Research relevance: the article discusses relevance of problem in teaching higher mathematics, considers examples from some sections of mathematics with medical interpretations. Unfortunately, despite the obvious importance of mathematical training for medical doctor profession, its necessity poorly understood not only by junior students, but also by some teachers of specialized departments in medical universities. Research objectives: to reveal the relevance and importance in teaching the mathematics subject in medical universities. Research materials and methods: development of mathematical methods, establishment of specific patterns inherent in random phenomena and the problems of probability theory for teaching mathematics in a medical university. Research results: students must learn to set mathematical problems in medical area and understand tools and how to apply in solving these problems. Conclusions: to improve the mathematics teaching quality to future doctors, a transition is required from the classical teaching of the discipline to teaching methods of technological application of mathematical methods in medical practice.

H[formula omitted] synchronization of semi-Markovian jump neural networks with random sensor nonlinearities via adaptive event-triggered output feedback control

In this paper, the H∞ synchronization problem of semi-Markovian jump neural networks (s-MJNNs) based on adaptive event-triggered scheme (AETS) output feedback control is studied. Also, the time-varying delay and leakage delay are considered in the system model. In order to solve the problems that the state of the system is not completely observable and limited network resources, an output feedback controller with AETS is designed. At the same time, in order to describe the performance of the sensor in the feedback link, the random nonlinear phenomenon of the sensor is described by the variable complying with Bernoulli probability distribution. A suitable Lyapunov–Krasovskii functional (LKF) is constructed and the bounds of integral terms are estimated by affine Bessel–Legendre inequality. Finally, sufficient conditions for asymptotic stability of the synchronization error system are obtained. And, two numerical examples show the feasibility of the research work.

A New Odd Fréchet Lehmann Type II–G Family of Distributions: A Power Function Distribution With Theory and Applications

Modeling complex random phenomena frequently observed in reliability engineering and medical science once thought to be an enigma. Scientists and practitioners agree that an appropriate but simple model is the best choice for this investigation. We contribute a new family referred to as an odd Fr&amp;eacute;chet Lehmann type-II (OFrLII) G family of distributions to address these issues. This new family has involved a shape parameter that modulated the tails of new models. Furthermore, we develop a list of eight new sub-models for a new family and a power function distribution (OFrLII&amp;ndash;PF) nominated for detailed discussion. We derive several complementary mathematical properties and explicit expressions for the moments, quantile function, and order statistics. We plot possible shapes of the density and the hazard rate functions over the particular choices of the model parameters. We follow a technique known as maximum likelihood estimation to estimate unknown model parameters and a simulation study established to assess the asymptotic behavior of these MLEs. The applicability of the OFrLII&amp;ndash;G family, is evaluated via OFrLII &amp;ndash;PF distribution. For this, we fit two engineering and one COVID&amp;ndash;19 pandemic dataset. Supportive results of OFrLII&amp;ndash;PF distribution declare it as a better fit model against the well-established competitor&amp;rsquo;s ones. A modified odd Fr&amp;eacute;chet Lehmann Type II&amp;ndash;G Family of Distributions: A Power Function Distribution with Theory and Applications

Simulation of non-Gaussian stochastic processes with prescribed rainflow cycle count using short-time Fourier transform

Random phenomena described by non-Gaussian processes are ubiquitous in many scientific fields. Properly understanding their characteristics is crucial in safety analysis, where the random occurrence of extreme values is often critical. In practice, the information available for fully characterizing a stochastic process is often limited by experimental constraints. Thus, prediction based on simulations comes as a valid alternative. Motivated by applications in structural fatigue assessment, this research presents a simulation method for non-Gaussian stochastic processes that is able to jointly reproduce a prescribed power spectral density and a rainflow cycle count. The main idea is to model non-Gaussian behavior by a frequency-dependent non-linearity in the short-time Fourier transform. As such, the power spectral density is directly imposed, while the non-linear model is optimized to match the rainflow cycle count. It is shown that the model is flexible enough to be interpolated between different operating points, so as to allow the simulation of stochastic processes at non-measured operating conditions. The full methodology is illustrated for assessing the fatigue assessment of a hydroelectric turbine runner.

Observer‐based guaranteed cost control for IT‐2 stochastic fuzzy coupled neural networks with Markov switching topology

SummaryThis study focuses on the guaranteed cost control problem for interval type‐2 stochastic fuzzy coupled neural networks (NNs) elicited by the observer framework with Markov switching topology, external disturbances, and quantization effect. In particular, the guaranteed cost controller is developed with an upper bound of the guaranteed cost function and also ensures stability of the addressed networks. Also, the integration of lower and upper membership functions are incorporated to relax the stability condition of the networks. Notably, the randomness phenomena are incorporated by the agency of stochastic variables that satisfies the Bernoulli distribution characteristics. Specifically, the state feedback controller considered with quantization effect is designed through undirected communication graph subject to Markov switching topology. In consequence with Lyapunov–Krasovskii‐functional and algebraic graph theory, sufficient conditions are established to assure the stochastic stabilization of the NNs with some specified cost value. Explicitly, the optimal upper bound of the guaranteed cost function and the controller gain fluctuations of the state and the observer are effectuated through the developed conditions. Finally, the reduced conservatism and efficiency of the proposed analytical design are demonstrated through a numerical example.

Extracting Governing Laws from Sample Path Data of Non-Gaussian Stochastic Dynamical Systems

Advances in data science are leading to new progresses in the analysis and understanding of complex dynamics for systems with experimental and observational data. With numerous physical phenomena exhibiting bursting, flights, hopping, and intermittent features, stochastic differential equations with non-Gaussian L\'evy noise are suitable to model these systems. Thus it is desirable and essential to infer such equations from available data to reasonably predict dynamical behaviors. In this work, we consider a data-driven method to extract stochastic dynamical systems with non-Gaussian asymmetric (rather than the symmetric) L\'evy process, as well as Gaussian Brownian motion. We establish a theoretical framework and design a numerical algorithm to compute the asymmetric L\'evy jump measure, drift and diffusion (i.e., nonlocal Kramers-Moyal formulas), hence obtaining the stochastic governing law, from noisy data. Numerical experiments on several prototypical examples confirm the efficacy and accuracy of this method. This method will become an effective tool in discovering the governing laws from available data sets and in understanding the mechanisms underlying complex random phenomena.

Strategic Design and reality levels: scenarios as prisms for creating possible futures

Strategic Design, when seen as a metaprojectual methodological approach, continuously expands its meaning effects, creating projects that intervene in systems for sociocultural transformation. It carries an open vision of design, permeated by the reflexive dominion (BENTZ, 2014), which welcomes the arbitrary character and the multiplicity of interactions, uncertainties, indeterminations and random phenomena (MORIN, 2015). Such intervention allows the creation of scenarios as a process guided by the imagination of other possible realities and contemplate the systems in the perspective of their openness. In this sense, the epistemological vision that integrates open systems, as well as the perspective of Strategic Design, joins the Transdisciplinarity method to discuss the elaboration of scenarios from the different reality levels. Guided by an abductive reasoning this method considers the existence of an invariable set of systems under the action of several General Laws, which constitutes more than one reality, without necessarily having a discontinuity separating them (NICOLESCU, 1999). Called the Principle of the Included Third, this conception permeated by the interdependence of simultaneous realities, leads to the elaboration of prismatic scenarios by their spectral character, and brings light to different but complementary perspectives, as well as the colors reflected in optical dispersive prisms.

Fraction-of-Time Probability: Advancing Beyond the Need for Stationarity and Ergodicity Assumptions

Time series arising from measurements in many fields of physics, engineering, chemistry, biology, and econometrics, are commonly modeled as sample paths from an ensemble which, together with a probability measure, is called a stochastic process. Stationarity and ergodicity assumptions about this model are generally made for analytical convenience and mathematical tractability of the model. In this article, it is shown that a dichotomy, which can be very misleading in practice, exists between the properties of a stochastic process and those of its individual sample paths. This dichotomy can be eliminated by adopting the fraction-of-time (FOT) probability approach reviewed in this article for which a probabilistic model is constructed from a single time series without introducing the abstraction of the stochastic process. Two FOT-probability models are reviewed. The first considers probabilistic functions that do not depend on time and employs the relative measure on the real line as a probability measure and the time average as an expectation operator. Such time series are called stationary signals. The second considers periodic, poly-periodic, and almost periodic probabilistic functions and employs the operator that extracts the finite-strength additive sine-wave components of its argument as an expectation operator. This latter model is appropriate for describing time series originating from phenomena involving a combination of periodic and random phenomena. Such time series are called cyclostationary, poly-cyclostationary, and almost cyclostationary signals. The FOT-probability alternative provides a means for circumventing two standard but undesirable practices: (1) Adopting the Kolmogorov stochastic process model by using its Axiom VI without being able to verify its validity for the specific application and (2) Assuming Birkhoff&#x2019;s ergodicity condition holds without being able to verify its validity for the specific application.