Random Moments Research Articles

Low-voltage and high-contrast polymer dispersed liquid crystals enabled by ferroelectric fluoro-copolymer doped polyimide film

Smart windows incorporating polymer dispersed liquid crystal (PDLC) technology provide user-friendly operation and play a significant role in intelligent buildings and building energy conservation. Long standing issues of the PDLCs such as high driving voltage, low contrast ratio, and narrow viewing angle hinder their applications. Here PDLCs are sandwiched between the hybrid substrates composed of the ferroelectric polyvinylidene fluoride trifluoroethylene (P(VDF-TrFE)) copolymer and the homogeneous polyimide. The high dielectric constant and ion-trapping ability of ferroelectric copolymers increase the effective voltage drop in the PDLCs. Concurrently, the local electric field created by large dipole moment of ferroelectric copolymers triggers the alignment of liquid crystals (LCs) along the applied field. These synergistic effects contribute to a substantial decrease in the driving voltage of PDLCs. In the opaque state, the random dipole moments in ferroelectric copolymers disrupt the LC orientations near hybrid substrates, thereby increasing the light scattering and reducing the transmission of PDLCs. Consequently, the proposed PDLCs exhibit a contrast ratio ∼2× higher compared to the conventional PDLCs at normal incident. Moreover, the proposed PDLCs demonstrate a wider viewing angle in the transparent state compared to conventional PDLCs. This development promises energy-efficient, eco-friendly, and cost-effective smart windows.

Results From a Psychometric Validation Study: Patients With Irritable Bowel Syndrome Report Higher Symptom Burden Using End-of-Day Vs Real-Time Assessment.

Real-time assessment of gastrointestinal (GI) symptoms in irritable bowel syndrome (IBS) using the experience sampling method (ESM) is suggested as a more appropriate approach than currently used end-of-day or end-of-week reports. This psychometric evaluation study assesses the validity and reliability of a previously developed ESM-based patient-reported outcome measure (PROM) for real-time GI symptom assessment in IBS. This multicenter validation study included 230 Rome IV patients with IBS (80% female; mean age 41.2 years) in 3 European countries. Patients completed the electronic ESM-PROM (up to 10 random moments daily, with a weekly minimum completion rate of 33%) and an end-of-day symptom diary for 7 consecutive days. End-of-week questionnaires (Gastrointestinal Symptom Rating Scale for IBS, IBS Severity Scoring System, Patient Health Questionnaire-9, and Generalized Anxiety Disorder-7) were completed at the end of the 7-day period. The ESM assessment had a mean completion rate of 71%. Strong and significant correlations (0.651-0.956) with moderate-to-good consistency (intra-class correlation coefficients 0.580-0.779) were observed between ESM and end-of-day scores. However, end-of-day scores were significantly higher (Δ0.790-1.758, P < 0.001) than mean daily ESM scores. Differences with end-of-week scores were more pronounced, with weaker correlations (Pearson's r 0.393-0.802). ESM-PROM exhibited moderate-to-good internal consistency (Cronbach's α 0.585-0.887) across 5 symptom domains. First and second half-week scores demonstrated good-to-excellent consistency (intraclass correlation coefficients 0.871-0.958). Psychometric evaluation demonstrated strong validity and reliability of the ESM-PROM for real-time GI symptom assessment in IBS. In addition, the ESM-PROM provides a precise and reliable ascertainment of individual symptom pattern and trigger interactions, without the bias of peak reporting when compared with retrospective methods. This highlights its potential as a valuable tool for personalized healthcare in monitoring disease course and treatment response in patients with IBS.

Synthetic ground motions in heterogeneous geologies from various sources: the HEMEWS-3D database

Abstract. The ever-improving performances of physics-based simulations and the rapid developments of deep learning are offering new perspectives to study earthquake-induced ground motion. Due to the large amount of data required to train deep neural networks, applications have so far been limited to recorded data or two-dimensional (2D) simulations. To bridge the gap between deep learning and high-fidelity numerical simulations, this work introduces a new database of physics-based earthquake simulations. The HEterogeneous Materials and Elastic Waves with Source variability in 3D (HEMEWS-3D) database comprises 30 000 simulations of elastic wave propagation in 3D geological domains. Each domain is parametrized by a different geological model built from a random arrangement of layers augmented by random fields that represent heterogeneities. Elastic waves originate from a randomly located pointwise source parametrized by a random moment tensor. For each simulation, ground motion is synthesized at the surface by a grid of virtual sensors. The high frequency of waveforms (fmax⁡=5 Hz) allows for extensive analyses of surface ground motion. Existing and foreseen applications range from statistical analyses of the ground motion variability and machine learning methods on geological models to deep-learning-based predictions of ground motion that depend on 3D heterogeneous geologies and source properties. Data are available at https://doi.org/10.57745/LAI6YU (Lehmann, 2023).

Hybrid uncertainty propagation analysis of nonlinear systems in the frequency domain based on multi-scale random interval moment method

To quantify the impact of hybrid uncertainty (random and interval parameters) on the frequency-domain nonlinear dynamic response, the multi-scale method (MSM) and the random interval moment method (RIMM) are combined to establish a new uncertainty propagation analysis method, called the multi-scale random interval moment method (MS-RIMM). RIMM is used to describe the hybrid uncertainty, while MSM is used to determine the frequency-domain nonlinear dynamic response. The statistical characteristics (i.e., the expectation value and variance) of the amplitude-frequency response of the nonlinear system with hybrid uncertainties are derived. Furthermore, the accuracy and effectiveness of the proposed method are verified by comparing the results with those obtained using the multi-scale Monte Carlo simulation method (MS-MCSM). Overall, the results of this study can serve as a useful reference for the hybrid uncertainty propagation analysis of nonlinear systems and for predicting the frequency-domain nonlinear dynamic response.

Surrogate models for seismic and pushover response prediction of steel special moment resisting frames

For structural engineers, existing surrogate models of buildings present challenges due to inadequate datasets, exclusion of significant input variables impacting nonlinear building response, and failure to consider uncertainties associated with input parameters. Moreover, there are no surrogate models for the prediction of both pushover and nonlinear time history analysis (NLTHA) outputs. To overcome these challenges, the present study proposes a novel framework for surrogate modelling of steel structures, considering crucial structural factors impacting engineering demand parameters (EDPs). The first phase involves the development of a process by which 30,000 random steel special moment resisting frames (SMRFs) for low to high-rise buildings are generated, considering the material and geometrical uncertainties embedded in the design of structures. In the second phase, a surrogate model is developed to predict the seismic EDPs of SMRFs when exposed to various earthquake levels. This is accomplished by leveraging the results obtained from phase one. Moreover, separate surrogate models are developed for the prediction of SMRFs’ essential pushover parameters. Various machine learning (ML) methods are examined, and the outcomes are presented as user-friendly GUI tools. The findings highlighted the substantial influence of pushover parameters as well as beams and columns’ plastic hinges properties on the prediction of NLTHA, factors that have been overlooked in prior studies. Moreover, CatBoost has been acknowledged as the superior ML technique for predicting both pushover and NLTHA parameters for all buildings. This framework offers engineers the ability to estimate building responses without the necessity of conducting NLTHA, pushover, or even modal analysis which is computationally intensive.

Quasi-integrability and nonlinear resonances in cold atoms under modulation.

Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix Hamiltonian. The dynamics is shown to evolve on two coupled potential energy surfaces (PESs): one of them is binding, while the other one is scattering type. The dynamics is shown to be quasi-integrable with nonlinear resonances. The bounded dynamics with intermittent scattering at random moments presents a scenario reminiscent of Anderson and dynamical localization. We believe that a careful analytical investigation of a multi-component system that is classically non-integrable is relevant to many other fields, including quantum computation with multi-qubit systems.

Enhancement of Classifier Performance with Adam and RanAdam Hyper-Parameter Tuning for Lung Cancer Detection from Microarray Data-In Pursuit of Precision.

Microarray gene expression analysis is a powerful technique used in cancer classification and research to identify and understand gene expression patterns that can differentiate between different cancer types, subtypes, and stages. However, microarray databases are highly redundant, inherently nonlinear, and noisy. Therefore, extracting meaningful information from such a huge database is a challenging one. The paper adopts the Fast Fourier Transform (FFT) and Mixture Model (MM) for dimensionality reduction and utilises the Dragonfly optimisation algorithm as the feature selection technique. The classifiers employed in this research are Nonlinear Regression, Naïve Bayes, Decision Tree, Random Forest and SVM (RBF). The classifiers' performances are analysed with and without feature selection methods. Finally, Adaptive Moment Estimation (Adam) and Random Adaptive Moment Estimation (RanAdam) hyper-parameter tuning techniques are used as improvisation techniques for classifiers. The SVM (RBF) classifier with the Fast Fourier Transform Dimensionality Reduction method and Dragonfly feature selection achieved the highest accuracy of 98.343% with RanAdam hyper-parameter tuning compared to other classifiers.

Tracking Molecular Fragmentation in Electron-Ionization Mass Spectrometry with Ultrafast Time Resolution.

ConspectusMass spectrometry is a powerful analytical method capable of identifying compounds given a minute amount of material. The fragmentation pattern that results following molecular activation serves as a fingerprint that can be matched to a database compound for identification. Over the past half century, studies have addressed and, in many cases, named the chemical reactions that lead to some of the principal fragment ions. Theories have been developed to predict the observed fragmentation patterns, many of which assume that energy redistributes prior to dissociation. However, the existence of rearrangements and nonergodic processes complicates the prediction of fragmentation patterns and the identification of compounds that have yet to be entered into a curated database. To date, very few studies have addressed the time-dependent nature of the fragmentation of radical cations and, in particular, processes occurring with picosecond or shorter time scales where one expects to find nonergodic reactions.This Account focuses on a novel approach that enables tracking of molecular fragmentation in electron-ionization mass spectrometry with ultrafast time resolution. The two challenges that have prevented the time-resolved studies following electron ionization are the random impact parameter and moment of ionization of each molecule. In addition, medium-sized molecules can produce fragmentation patterns with tens if not hundreds of product ions. Spectroscopically interrogating all of these ions as a function of time is another major challenge. We describe strong field disruptive probing, a method that ionizes molecules on a femtosecond time scale and allows us to track in time the formation of all fragment ions simultaneously.Molecular fragmentation following ionization can occur on a very wide range of time scales. Metastable ions can survive from nanoseconds to microseconds; reactions that depend on vibrational energy redistribution can take picoseconds to nanoseconds; and direct dissociation processes and some rearrangements can take place in femtoseconds to picoseconds. All of these processes depend on the dynamics that occur during attoseconds and femtoseconds following the ionization process. Following a discussion of these time scales, we provide three examples of fragmentations that have been studied with femtosecond time resolution. Each of these examples include unforeseen reaction dynamics that involve a nonergodic process, highlighting the importance of time resolution in mass spectrometry. Finally, we explore future challenges and unresolved questions in mass spectrometry and, more broadly, in the domain of electron-initiated chemical reactions.

Combinatorial aspects of weighted free Poisson random variables

This paper will be devoted to the study of weighted (deformed) free Poisson random variables from the viewpoint of orthogonal polynomials and statistics of non-crossing partitions. A family of weighted (deformed) free Poisson random variables will be defined in a sense by the sum of weighted (deformed) free creation, annihilation, scalar, and intermediate operators with certain parameters on a weighted (deformed) free Fock space together with the vacuum expectation. We shall provide a combinatorial moment formula of non-commutative Poisson random variables. This formula gives us a very nice combinatorial interpretation to two parameters of weights. One can see that the deformation treated in this paper interpolates free and boolean Poisson random variables, their distributions and moments, and yields some conditionally free Poisson distribution by taking limit of the parameter.

A Mathematical Model for Assessing the Stability of the Functioning of an Element of the Information Infrastructure of an Automated Control System Exposed to Threats to Information Security

The problem of assessing the stability of an element of the information infrastructure of the automated control system to single impacts of threats to information security is considered. For the solution, it is proposed to reduce the problem of stability estimation to the problem of constructing the survivability function of the element under study and determining its extreme values. Functional analysis methods were used to solve the problem. The problem is solved subject to the adoption of exponential laws of distribution of random moments of exposure time and moments of recovery time of the element's function. Recommendations are given on the formation of initial data for modeling, the results of test modeling in the form of graphs of the survivability function. A computational experiment with a mathematical model was carried out, aimed at investigating the effectiveness of the proposed model. A mathematical model can be used to construct a survivability function with a single impact and restore the functionality of an element exposed to threats. The novelty of the result lies in the concretization of general and particular mathematical models designed to assess the stability of functioning under conditions of repeated exposure to threats, which makes it possible to significantly simplify the model with acceptable reliability of the result obtained.

THE MULTI-PARAMETER FRACTAL–FRACTIONAL INEQUALITIES FOR FRACTAL (P,m)-CONVEX FUNCTIONS

Local fractional calculus theory and parameterized method have greatly assisted in the advancement of the field of inequalities. To continue its enrichment, this study investigates the multi-parameter fractal–fractional integral inequalities containing the fractal [Formula: see text]-convex functions. Initially, we formulate the new conception of the fractal [Formula: see text]-convex functions and work on a variety of properties. Through the assistance of the fractal–fractional integrals, the [Formula: see text]-fractal identity with multiple parameters is established, and from that, integral inequalities are inferred regarding twice fractal differentiable functions which are fractal [Formula: see text]-convex. Furthermore, a few typical and novel outcomes are discussed and visualized for specific parameter values, separately. It concludes with some applications in respect of the special means, the quadrature formulas and random variable moments, respectively.

Transient characteristics and sites of pre‐breakdown in spark conditioning for high‐voltage vacuum interrupter under power frequency voltage

AbstractThe objective of this paper is to determine the transient characteristics and sites of the pre‐breakdown (pre‐BD) in the spark conditioning under power frequency voltage (PFV) in vacuum. A multi‐angle optical path system was designed and made the determination of the pre‐BD sites in spark conditioning possible, through one camera at two viewing angles. The experimental results indicate that, in the spark conditioning under PFV, the pre‐BDs continuously occurred at a random moment. Within several half‐waves, the number of the pre‐BDs could reach dozens of times, which was the key for the treatment of the electrode surface in conditioning. Under the application of PFV, the single pre‐BD occurred at a random moment, in which it would last for several microseconds and the peak value of the current would reach several amperes. Moreover, the pre‐BD sites randomly distributed in the surface of the electrode and almost covered the whole surface of the electrode. The pre‐BDs took place independently in both time and space, in which there should be no effect between each other of two sequential pre‐BDs. To sum up, the transient characteristics and the sites of the pre‐BDs determined in this paper could reveal the physical mechanism of the pre‐BD on the treatment of electrode surface in the conditioning process, which is quite significant to improve the BD voltage of vacuum interrupter.

Use of the experience sampling method in adolescents with Duchenne muscular dystrophy: a feasibility study

Experience sampling methods (ESM) using mobile health (mHealth) technology with a smartphone application are increasingly used in clinical practice and research. Still, recommendations are limited in young people, and adaptations may be necessary. Patients with Duchenne muscular dystrophy (DMD) are chronically treated with steroids from a young age. However, the impact of intermittent treatment schedules on fluctuations in somatic, cognitive and behavioural symptoms is poorly investigated. Existing studies are often cross-sectional and occur in controlled clinical settings, which do not provide sufficiently detailed insights into possible correlations. ESM might alleviate these problems. ESM innovates data collection with a smartphone application, which repeatedly assesses specific symptoms and contextual factors at random moments in daily life. We aimed to evaluate its feasibility in adolescents with DMD. In three (without/with/without steroids) 4-day periods of ESM, that were nested in 10/10 or 11/9 day on/off-medication periods, we evaluated its user-friendliness and compliance, and explored its ability to objectify fluctuations in somatic, cognitive and behavioural symptom severity and their relationship with contextual factors in seven DMD patients (age range 12–18 years) using intermittent corticosteroid treatment (dosage range 0.3–0.6 mg/kg/day). Patients reported that ESM was convenient and user-friendly. We were able to capture extensive intra-individual symptom fluctuations during intermittent corticosteroid treatment that were not revealed by routine clinical assessment. Implementing ESM to evaluate symptom fluctuation patterns in relation to treatment effects shows promise in adolescents with DMD. Optimization in further research is needed.

Two Different Solution Techniques for an Optimal Control Problem with a Stochastic Switching Time

In optimal control theory, strategic decision making requires the consideration of unforeseen disruptions that may arise within a predetermined time horizon. In this context, we introduce the concept of ”stochastic switching time” as a random moment in time at which a sudden, irreversible alteration takes place in the system’s dynamics or in the payoff function. To address optimal decision-making under such uncertain conditions, the literature presents two prominent methodologies: the ”backward” approach and the ”heterogeneous” approach. In this study, we offer an exposition and a comparative analysis of these two approaches. Finally, we present an illustrative example to show, in a detailed context, the advantages and disadvantages associated with these two solution strategies.

Algorithm for Calculating Noise Immunity of Cognitive Dynamic Systems in the State Space

The research method consists in applying the state space method, widely used in the study of automatic dynamical systems, to describe the behavior of cognitive systems. It is assumed, that at the input of the cognitive system, there is a signal and interference described by Poisson point processes, modeling the amount of information, the amount of emotional stress, etc., corresponding to each event. The cognitive properties of the system in the paper are taken into account by two circumstances. Firstly, events localized in time are characterized in the paper not only by the Poisson distribution of the times of their occurrence, but also by some random variables that characterize the importance (significance) events for the system. A typical example is the attribution of a certain amount of information to each event, if an information processing system is modeled. Another example is the emotional reaction of a person to the appearance of stress, described in a classic work on psychology. In this case, the point is the event that causes stress, and the effects of stress on the system are modeled by the relative magnitude of stress in accordance with the Holmes and Rahe scale. Secondly, the cognitive system processes, assimilates, adapts to the impact that each event has on it with its inherent speed. In this paper, this phenomenon is modeled as the passage of a point process through a dynamic system described by differential equations. Such processes are called filtered point processes. Examples of impacts are given and, for simplicity, an assumption is made about the magnitude of the impact as the amount of information received by the system when an event occurs. Thus, the model of a cognitive system is a dynamic system described by a differential equation in the state space, at the input of which messages with a certain information load appear at random discrete moments of time.As for any technical system, the cognitive system faces the task of evaluating the quality of its work. In this regard, the paper substantiates the use of a convenient quality index from an engineering point of view and an appropriate criterion in the form of a signal – interference ratio. The new results are differential equations in the state space for the mathematical expectations of the signal and interference, as well as an algorithm for calculating the noise immunity of the cognitive system. As an example, a graph of the noise immunity of a particular cognitive system is calculated and presented, confirming an intuitive idea of its behavior.In conclusion, it is noted that the main result of the paper is an algorithm for calculating the noise immunity of cognitive systems using differential equations that allow calculating the behavior of non-stationary cognitive systems under any point impacts described by a non-stationary function of the intensities of the appearance of points. The equations of behavior of the mathematical expectation of the processed information are reduced to a canonical form, which allows them to be applied to a variety of practical tasks, for example, to the description of hierarchical cognitive structures when the output of one level is the input of another.

The correlates of flow in the L2 classroom: Linking basic L2 task features to learner flow experiences

AbstractFlow is an intrinsic motivational state associated with full task engagement, positive affect, and enhanced performance. While research has examined how different language tasks interact with flow experiences, no study has examined learner flow experiences in a wide range of tasks using an experience sampling method to determine how universal basic task features (e.g., modality, participant structure, information distribution, and targeted skills) interact with flow. The present study aims to respond to this gap in the research. Participants were 13 teachers and 327 students from 18 intact French L2 classes in a Canadian postsecondary school. Teachers selected and implemented an average of six tasks from their personal repertoires at random moments throughout the semester. Immediately following each task, learners anonymously completed a flow experience questionnaire (N = 1408; α = 0.91), and teachers a task description questionnaire containing 17 basic task features (N = 81). Statistical analyses show that 10 of the 17 variables significantly interacted with learners’ flow experiences. The results not only validate a frequently used flow measurement and establish norms for future research but also outline a framework language teachers can use to evaluate and modify practices to improve learners’ subjective classroom experience.

The group behaviour modelling of workers in the labor market

Abstract We describe the mathematical modelling of the group behaviour of workers in the labor market. The worker receives the salary and seeks to improve his qualifications in order to receive higher wages. The worker enlarges his qualification by the investments in human capital. At a random moment of time, a vacancy appears that provides a jump in the worker’s salary. The mathematical model of the worker’s behaviour in the labor market is presented as an optimal control problem on an infinite time horizon. The paper presents the derivation of the Kolmogorov–Fokker–Planck equation for the Lévy process, which describes the behaviour of a large amount of workers within a social layer. The numerical solution of the Kolmogorov–Fokker–Planck equation and the calculation results are presented.

Motion analysis and power output optimization design of wave energy device

Wave energy is an essential marine renewable energy. Improving the energy conversion efficiency of wave energy devices is the key aspect of wave energy utilization research. This paper deals with the movement status of the wave energy device and its power optimization. Depending on Newton’s second law, the second-order ordinary differential equation model is established for the float and oscillator respectively. According to whether the damping coefficient is constant, the pending method coefficient is utilized to solve the general second-order solution ordinary differential equation model, and the drooping displacement and velocity graphs under different damping coefficients are obtained. The analysis shows that the oscillating wave energy device improved by the second-order ordinary differential equation model could become stable within a very short time. The motion displacement and velocity of the wave energy device at five random moments were taken to check the accuracy of the model, and the results show that the model has an excellent promoting effect on the motion state of the wave energy device at sea and reduces the depletion of the device in terms of accuracy of motion displacement and velocity.

Some stability results on non-linear singular differential systems with random impulsive moments

This paper studies the exponential stability for random impulsive non-linear singular differential systems. We established some new sufficient conditions for the proposed singular differential system by using the Lyapunov function method with random impulsive time points. Further, to validate the theoretical results' effectiveness, we finally gave two numerical examples that study with graphical illustration and an additional example involving matrices with complex entries, proving the results to be true in that case as well.

Magneto-structural characterization of different kinds of magnetic nanoparticles

Using well-established measurement techniques like transmission electron microscopy (TEM), dynamic light scattering (DLS), small and wide angle X-ray scattering (SAXS, WAXS), susceptometry, and magnetorelaxometry, the distribution of the physical and magnetic size (magnetic moments) and magnetic anisotropy of a variety of structurally different magnetic nanoparticle samples (MNPs) is analyzed and compared. A term which accounts for the presence of weak magnetic areas (WMAs) within the MNPs was introduced to the widespread analysis model for M(H) data, enabling a consistent interpretation of the data in most of the systems. A comparison of the size distributions as obtained for the physical and the magnetic diameter suggests a multidomain structure for three single core systems under investigation, in all probability evoked by the presence of a wustite phase, as identified by WAXS.Analyzing the relationship d < dm < dc between the average single core diameter d, the effective magnetic (domain) size dm and the cluster diameter dc quantitatively, two qualitatively different magnetic structures in multicore MNP (MCMNP) systems were identified: (i) The magnetic moments of single cores within the MCMNP of fluidMAG tend to build flux closure structures, driven by dipole–dipole interaction. (ii) The magnetic behavior of Resovist® was attributed to the presence of domain sizes of about 12 nm within MCMNP, exceeding the single core diameters of 5 nm. Thereby, WAXS revealed a bimodal crystallite size distribution suggesting a crystallite merging process within the MCMNP. The value of the effective magnetic moment of these MCMNP could be explained within the presented “random moment cluster model” (RMCM).We conclude that the combination of physical and magnetic structure parameters obtained from complementary measurement methods allows a reliable assessment of the magnetic structure of single and multicore MNPs.