This paper addresses the existence of mild solutions and the approximate controllability of a class of higher-order Hilfer fractional semi-linear neutral stochastic differential equations with non-instantaneous impulses in Hilbert spaces. The system is driven by both fractional Brownian motion and Poisson jumps, thereby capturing long-range dependence as well as random discontinuities. By combining techniques from fractional calculus, stochastic analysis, and operator theory, we establish sufficient conditions for the existence of mild solutions. The analysis is carried out through the construction of suitable solution operator families and the application of Sadovskii’s fixed point theorem in an appropriate phase space framework. In addition, we investigate the controllability properties of the system and derive criteria ensuring approximate controllability of the underlying fractional neutral dynamics. The proposed approach relies on the structural properties of the higher-order Hilfer fractional derivative, estimates for stochastic integrals with respect to fractional Brownian motion, and compactness arguments adapted to non-instantaneous impulsive effects. The inclusion of Poisson jumps and neutral terms introduces significant analytical difficulties, which are overcome using refined resolvent operator techniques and fractional power estimates. An illustrative example is presented to demonstrate the applicability of the theoretical results. The results obtained generalize and unify several recent developments in the theory of fractional stochastic systems and provide a flexible framework for analyzing controlled dynamical models with memory, randomness, and impulsive behavior.

This study proposes a multi-scale damage correlation path to characterise the softening behaviour of soft rock under dry-wet cycles, based on multi-scale damage variables. By testing the mineral composition and internal structural changes of soft rocks under different dry-wet cycles, and based on the energy evolution mechanism and damage constitutive characteristics, the multi-scale correlation effects of soft rock softening under dry-wet cycles were analysed. The results indicate that as the number of dry-wet cycles increase, the mechanical properties of soft rock exhibit an exponential decay mode, and mineral particles exhibit Weibull-distributed random failure behaviour.

This article presents a new measure to analyze the random behavior in multivariate time series. This study extended the range of entropy choices from Shannon, Rényi and Tsallis to fractional case. Furthermore, it is proposed explicit expressions of the Mutual Information Matrix (MIM) based on fractional entropy to analyze the nonlinear interactions between time series. Fractional entropy depends on a fractional parameter, and it is more sensitive to temporal non-linear dynamics than other methods related to classical entropies. Additionally, the eigenvalues of MIM based on fractional entropy are used to obtain a global information measure, which it represents the total mutual information among the entire time series can be quantified. To illustrate the obtained results, four models (Poisson, sinusoidal, coupled logistic maps and controlled vector autoregressive) are simulated and results are discussed. Finally, Covid-19 pandemic data time series from various testing centers in Baghdad (Iraq) was used to validate the behavior of proposed measures. Results demonstrate that the proposed global measure is more effective in predicting the nature of Covid-19 spread, which may assist governments in planning for its containment.

We test the eigenstate thermalization hypothesis (ETH) in 1 + 1 -dimensional SU(2) lattice gauge theory (LGT) with one flavor of dynamical fermions. Using the loop-string-hadron framework of the LGT with a bosonic cutoff, we exactly diagonalize the Hamiltonian for finite size systems and calculate matrix elements (MEs) in the eigenbasis for both local and nonlocal operators. We analyze different indicators to identify the parameter space for quantum chaos at finite lattice sizes and investigate how the ETH behavior emerges in both the diagonal and off-diagonal MEs. Our investigations allow us to study various timescales of thermalization and the emergence of random matrix behavior, and highlight the interplays of the several diagnostics with each other. Furthermore, from the off-diagonal MEs, we extract a smooth function that is closely related to the spectral function for both local and nonlocal operators. We find numerical evidence of the spectral gap and the memory peak in the nonlocal operator case. Finally, we investigate aspects of subsystem ETH in the lattice gauge theory and identify certain features in the subsystem reduced density matrix that are unique to gauge theories.

HighlightsAdaptive filtering method based on change-point analysis for IC curve denoising.Dynamic extraction of degradation features from incomplete IC curves.Feature fragments are integrated into a two-dimensional hierarchical matrix.Designed CNN captures spatial–temporal degradation patterns.The framework achieves accurate lifetime prediction under real-world constraints.

Theoretical and experimental approaches for the motion characteristics of the cage considering ball-cage random collision behavior

In the above article [1], Fig. 5 was mistakenly placed. The correct one should be as follows:

This study provides an in-depth study of the spatial distribution and concentration of retail businesses in Faisalabad and Lahore Cities. In this study used grid cluster locations and graduated colour systems to analyse the spatial distribution of shops across several categories. The findings show systematic spatial patterns in the distribution of retail businesses, indicating the existence of relevant forces that go beyond random behaviour. The outcome of the study emphasizes the significant influence of geographic distribution on the economic structure of both cities. The use of grid cluster location maps, in conjunction with graduated colour schemes, provides an excellent representation of the spatial distribution of shops across different categories. By conducting a comprehensive examination, this study offers valuable insights into the densities and concentrations of clusters, thereby empowering stakeholders with the ability to make well-informed decisions. Statistical methodologies such as Moran's Index, z-scores and p-values serve to highlight the importance of spatial autocorrelation, a phenomenon that exerts significant effects on commercial strategies, public policies, and urban developmental plans. This study highlights the necessity for further investigation into the factors that contribute to the Distribution patterns. The present study analyses the Cost of running a business and the influence of varying shop sizes on retail shops, ranging from 125 to more than 300 square feet. This study thoroughly investigates the impact of different shop sizes on both customer experiences and financial aspects, including factors such as rent, utilities, taxes, and salaries. Pie charts to represent the expenditures across various shop sizes, offering detailed insights into several categories of retail stores. This study provides a comprehensive analysis of the study's findings, resulting in practical proposals. The suggested ideas are designed to address the needs and interests of many stakeholders, such as urban planners, entrepreneurs, and policymakers. In conclusion, this study provides useful insights into the geographical distribution of Retail shops in Faisalabad and Lahore. The observed non-random grouping patterns emphasize the essential role of deliberate choices in urban planning, economic growth, and business strategies. The guidance provided offers valuable insights for both individuals and organisations, advising them in making well-informed decisions and enhancing the economic conditions of both urban centers.

Mechanical metamaterials achieve multistep, programmable responses through sequential deformation driven by snapping instabilities, yet these sequences are typically governed by unavoidable imperfections, resulting in random and uncontrollable behavior. Here, we harness intra- and interlayer magnetic interactions coupled with elasticity to reprogram the ordering of sequential buckling instabilities in kirigami-inspired soft magnetic metamaterials. In single-layer systems, intralayer coupling among magnetized units produces random snapping sequences but generates strongly nonlinear-spiked force-displacement responses with pronounced hysteresis, in contrast to the simultaneous buckling of unmagnetized sheets. In multilayer assemblies, interlayer magnetic interactions trigger chain reaction-like propagation, transforming randomness into robust, directional snapping across structures. This mechanism establishes a paradigm for deterministic, multistep mechanical responses without continuously applied fields and opens avenues for adaptive materials in energy dissipation, waveguiding, reconfigurable soft robotics, and biomedical devices.

Modelling of ultrasonic velocity for measuring water holdup in vertical upward oil-water two-phase flow.

Currently, only a limited number of Mark-Houwink-Sakurada (MHS) equations are available for chitin, and their applicability is constrained by the narrow range of suitable solvent systems. The Mark-Houwink-Sakurada (MHS) equation is a widely used and practical approach for estimating polymer molecular weight from intrinsic viscosity measurements, particularly when chromatographic techniques are not readily accessible. This study aimed to establish new MHS equations for chitin to facilitate reliable molecular weight determination across different solvents and temperatures. Chitin samples with varying molecular weights were prepared via H2O2 degradation, and their weight-average molecular weights (Mw) were determined by high-performance size-exclusion chromatography (HPSEC). Intrinsic viscosity ([η]) was measured using a capillary viscometer at 25 and 30 °C in three solvent systems: 5% LiCl/N,N-dimethylacetamide (LiCl/DMAc), 8% NaOH/4% urea, and 10% NaOH/0.3% tannic acid (w/w). Double-logarithmic plots of Mw versus [η] were constructed to derive the corresponding MHS equations. At identical molecular weights and temperatures, intrinsic viscosity followed the order: LiCl/DMAc > NaOH/urea > NaOH/tannic acid. Increasing temperature led to higher intrinsic viscosity and conformation parameter (a) values. Chitin dissolved in LiCl/DMAc and NaOH/urea exhibited rod-like conformations, with a values ranging from 0.79 to 0.97, whereas chitin in NaOH/tannic acid displayed random coil behavior (a = 0.56-0.69). These established MHS equations expand the solvent applicability for chitin molecular weight determination and provide insights into its solution conformation under different chemical environments.

This study revisits the Efficient Markets Hypothesis by employing a GRU-D neural network to predict stock return distributions across global equity markets, accounting for missing and irregular data. It examines whether stock returns exhibit statistically significant departures from purely random behavior. By combining price, technical and fundamental inputs, it tests both weak and semi-strong market efficiency. We implement the GRU-D model on a global dataset of stock returns, where daily returns are classified into quartiles. Model performance is assessed using Micro-Average Area Under the Curve (AUC) and Relative Classifier Information (RCI). Robustness checks include sub-sample tests across countries and sectors, an examination of the COVID-19 sub-period, and a price-memory persistence analysis. The results reveal that the GRU-D model achieves a ranking accuracy of approximately 75% when classifying returns, with statistical significance at the 99.99% confidence level, and exhibits modest but robust deviations from strict market efficiency. These deviations persist for up to 200 trading days. Notably, the findings indicate that the GRU-D model is more robust during the COVID-19 period. These findings are consistent with the Adaptive Markets Hypothesis and underscore the relevance of machine-learning frameworks, particularly those designed for imperfect data environments, for identifying time-varying departures from strict market efficiency in global equity markets.

Laplacian spectrum and random walk behavior in a rounded knot network modeled on the helical structures in chemical and biological systems

Improved damage constitutive modeling of post-peak random failure behavior in quasi-brittle rocks

Abstract Geological materials have inherent uncertainties from variability in particle properties, such as inter‐particle friction. Traditional deterministic models overlook this variability, leading to inaccurate predictions of geophysical flow behavior. We developed a novel 3D discrete element method framework incorporating stochastic field theory, capturing granular materials' random flow behavior. Combined with ring shear tests and PFC, we also propose a virtual ring shear test. The effect of coefficient of variation (COV) and correlation distance of inter‐particle friction coefficient μ on particle mechanical properties is discussed. Monte Carlo simulations show ignoring μ uncertainty does not affect its strain softening and strengthening characteristics, but may overestimate shear strength. Under quasi‐static shear, shear stress‐shear displacement curves of heterogeneous samples with nearly identical particle arrangement but varied properties formed curve clusters of a certain width. The cluster width positively correlates with both and COV. Additionally, μ heterogeneity does not affect microscopic force chain's overall evolution trend, but significantly impacts its characteristic peak value. Specifically, as the average sliding friction coefficient decreases, the mean contact force reduces while the mean coordination number increases. Furthermore, we propose shear strength reduction coefficients for different confidence levels. These findings provide valuable insights into granular soil mechanical behavior during landslide evolution and hazard assessment.

This article addresses the lateral dynamics control problem for autonomous vehicle systems under randomly perturbed sampling (RPS) periods and the FlexRay communication protocol. To capture vehicle nonlinearities under variable-velocity conditions, a T-S fuzzy model is constructed using longitudinal velocity as the premise variable. The random sampling behavior caused by hardware aging and environmental disturbances is modeled as a Markovian process. Then, measured outputs are transmitted under the FlexRay protocol (FRP) that integrates both time-driven (static) and event-driven (dynamic) scheduling characteristics. By fully analyzing the situation of static and dynamic scheduling, a unified compensation strategy is employed to build a new switching output model reflecting the impact of the FRP on the measured outputs. Based on this output model, a sampling-mode-dependent fuzzy controller is designed to handle random sampling and hybrid scheduling issues, which results in a membership asynchronous phenomenon between the autonomous vehicle model and controller. By using the asynchronous constraint technique, sufficient conditions with low conservatism are derived to guarantee stochastic stability and $H_{\infty }$ performance of the closed-loop system. Furthermore, a comprehensive optimization problem (OP) is established, and a corresponding genetic algorithm (GA) is presented to provide a solution-solving scheme. Simulation results confirm the effectiveness and superiority of the proposed control strategy under complex communication environments.

The superparamagnetic tunnel junction (SP-MTJ) represents an attractive solution for stochastic computing applications, providing substantial advantages in terms of area efficiency over traditional complementary metal oxide semiconductor (CMOS) technologies. This study proposes an effective technique to enable SP-MTJ functionality by incorporating a molybdenum (Mo) insertion layer above the free layer using the standard spin-transfer-torque magnetoresistive random-access memory (STT-MRAM) structure. Through precise modulation of the Mo layer thickness, the perpendicular magnetic anisotropy (PMA) can be systematically controlled, resulting in intrinsic stochastic switching behavior. Consequently, the engineered SP-MTJ functions as an efficient, compact probabilistic bits (p-bits), demonstrating intrinsic random oscillatory behavior for implementing stochastic discrete Hopfield neural network (DHNN). Simulation results demonstrate the potential and effectiveness in addressing challenging combinatorial optimization problems (COPs).

With the rapid development of artificial intelligence (AI), a variety of attack techniques have emerged, threatening the data security. In this background, energy-efficient lightweight security primitives are required to guarantee the security of the Internet of Things (IoT). The conventional silicon-based true random number generator (TRNG) suffers from design complexity, high power consumption, and limited throughput, making it unsuitable for low-power and high-performance applications. Magnetic tunnel junctions (MTJs) can be used as a random source due to the random switching behaviors. However, most of the existing MTJ-based TRNG designs rely on reset–write–read operations, which limit throughput and energy efficiency. In this work, we propose a high-throughput TRNG based on the superparamagnetic tunnel junction (SMTJ). By reducing the thermal stability factor, SMTJ undergoes spontaneous random switching driven by thermal fluctuation, eliminating the need for costly reset and write operations. A compact spin-orbit torque (SOT)-controlled SMTJ model is developed and integrated by using the <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nand</small>-SPIN structure, achieving a TRNG design with low power, high throughput, and high randomness.

Accurate modeling of electric vehicle (EV) charging dynamics is essential for optimizing charging infrastructure and grid integration, especially when dealing with sparse data and random charging behavior. This paper proposes a unified load flow (ULF) model that captures the spatio-temporal evolution of charging behavior, incorporating EV arrival and departure dynamics as boundary conditions. A classical point optimization physics-informed neural network (PoPINN) is used to solve the ULF model, with a novel boundary condition design that ensures physical consistency during training. To enhance model consistency and robustness under stochastic and data-sparse conditions, a boundary-aware region-optimized PINN (RoPINN) is developed. This approach incorporates boundary information into regional optimization, enforcing arrival–departure consistency within local spatiotemporal regions and enabling reliable learning from incomplete data. The proposed framework provides a coherent data–physics integration strategy for modeling uncertain and incomplete EV charging information, enabling accurate prediction of charging power and load flow evolution. Simulation results on both synthetic and real-world datasets demonstrate the robustness, accuracy, and practical applicability of the proposed method for large-scale EV charging optimization and smart grid management.

Propagation of infra-slow and slow brain activities in electroencephalogram related to behavioral information processing.