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

In the context of tightening sustainability regulations and rising demands for transparent and responsible capital allocation, understanding how digital financial innovations influence market efficiency has become increasingly important. This study examines the impact of Financial Technology (FinTech) solutions and crowdfunding platforms on sustainable market efficiency, volatility dynamics, and risk structures in the United Kingdom. Using weekly data for the Financial Times Stock Exchange 100 (FTSE 100) index from January 2010 to June 2025, the analysis applies the Lo–MacKinlay variance ratio test to assess compliance with the Random Walk Hypothesis as a proxy for informational efficiency. Firm-level proxies for FinTech and crowdfunding activity are constructed using the Nomenclature of Economic Activities (NACE) and Standard Industrial Classification (SIC) systems. The empirical results indicate substantial deviations from random-walk behavior in crowdfunding-related market segments, where persistent positive autocorrelation and elevated volatility reflect liquidity constraints and informational frictions. By contrast, FinTech-dominated segments display milder inefficiencies and faster information absorption, pointing to more stable price-adjustment mechanisms. After controlling for structural distortions through heteroskedasticity-consistent corrections and volatility adjustments, variance ratios converge toward unity, suggesting a restoration of informational efficiency. The results provide relevant insights for investors, regulators, and policymakers seeking to align financial innovation with the objectives of sustainable financial systems.

Sea level rise, a critical consequence of global climate change, poses significant challenges to coastal communities worldwide. While long-term trends in sealevel rise garner considerable attention, understanding and predicting interannual variability fluctuations are equally crucial for effective coastal management and adaptation. This research investigates detrended annual variability of adjusted sea level data, focusing on the unpredictable fluctuations superimposed on long-term trends. By employing Autoregressive Integrated Moving Average (ARIMA) modeling, this study aims to quantify and forecast these interannual variations, providing a statistical baseline that underscores the challenge of interannual variability prediction for coastal management. Utilizing adjusted annual sea level measurements from the National Oceanic and Atmospheric Administration spanning 1993-2019, this research isolates residual interannual fluctuations by removing the influence of long-term trends and other components through data adjustment. This adjustment process, typically incorporating corrections for factors like glacial isostatic adjustment and vertical land motion, enables a focused analysis of the residual fluctuations. The adjusted sea level data was imported into the Minitab web platform for analysis. The "Forecast with Best ARIMA Model" tool within Minitab's "Stat" menu was employed to automatically identify, fit and diagnose the most appropriate ARIMA model. This tool explores a range of potential ARIMA models, varying the order of autoregressive (AR), integrated (I) and moving average (MA) components, using the Akaike Information Criterion with correction (AICc) to select the best-fitting model while penalizing complexity. The results of this analysis reveal that, after an extensive screening of the ARIMA parameter space, the ARIMA(0,1,0) model, also known as the random walk with drift, emerged as the optimal representation of the adjusted sea level data. This suggests that the residual interannual variability, after accounting for factors removed during data adjustment, is largely unpredictable within the ARIMA framework. The selected model was then used to generate 100-year forecasts, from 2020-2119, along with 95% confidence intervals to quantify forecast uncertainty. The standard error of the forecasts was also analyzed, revealing a clear increase in uncertainty with longer forecast horizons. In conclusion, this research demonstrates that while the adjusted sea level exhibits significant annual variability, this variability is largely unpredictable using ARIMA models. This finding underscores the importance of separating the analysis of these kinds of fluctuations from the long-term sea level rise trend, which must be modeled using different approaches. The 100-year forecasts and associated confidence intervals provide valuable information for coastal communities to better prepare for and manage the risks associated with interannual sea level fluctuations, even if precise predictions are not possible. Concurrence of AICc, AIC and BIC provides strong support for validity of the model, reinforces the principle of parsimony, suggests genuine random walk behavior in the adjusted sea level data and increases confidence in the interpretation of the results. While the ARIMA(0,1,0) serves as a robust baseline for understanding the inherent unpredictability of adjusted sea level variations, future research could explore the potential of incorporating predictors, such as climate indices or employing non-linear time series models to further refine understanding and predictive capabilities concerning interannual sealevel changes.

ABSTRACTThe Allee effect is an important ecological process that has implications for extinction of endangered species and for assisting the management of invasive species. Few instances of Allee effects have been quantified in nature due to the adaptive resilience of species and the difficulty in empirically linking ecological mechanisms to population change. While Allee effects could theoretically assist with invasive species eradications, the mechanism by which a management intervention could achieve both component and demographic Allee effects has not been tested. We developed an individual‐based simulation model to explore whether the intentional disruption of animal behaviour could elicit a mate‐finding Allee effect to facilitate the eradication of an invasive mammal. We used stoats (Mustela erminea) as a test species and generalised the results by examining the sensitivity of Allee effects to a range of biological attributes and management scenarios. The ecological challenge was to turn the colonising adaptations (high mobility, olfactory communication and delayed placental implantation) into vulnerabilities for Allee effects. Following an initial population reduction through trapping, reproductive pheromone decoys were deployed to disrupt mate finding. When key ecological, management and technological conditions were met during the deployment of decoys, an increase in the probability of eradication demonstrated a demographic Allee effect. The mate‐finding Allee threshold occurred only at very low densities, indicating the importance of population control. The Allee effect increased with increasing number of deployed decoys and attractiveness to divert movement direction away from potential mates. Increasing the bias in random walk behaviour towards nearby decoys reduced mate finding, whereas low‐biased random walk induced by detection of multiple scents increased reproduction. Increasing survival rates increased longevity and the time for individuals to find mates, which decreased the probability of an Allee effect. The modest increased probability of eradication under optimal biological and management conditions demonstrated the resilience of species to mate‐finding Allee effects.

This study analyses Italy’s monthly data about health expenditure from January 2012 to October 2022, sourced from International Financial Statistics (IMF). Augmented Dickey-Fuller (ADF) tests confirm the series is non-stationary at levels, exhibiting random walk behaviour, but achieves stationarity after first differencing, indicating integration of order one [Et ~ I(1)]. Regression analysis reveals a significant 12-month lagged effect, where a 1% increase in prior health expenditure growth raises the current growth rate by 0.19%, reflecting annual seasonality (e.g., fiscal budgets, winter health costs). The constant term indicates a robust 4.26% monthly growth rate, driven by Italy’s aging population, rising medical costs, and universal healthcare system (SSN), consistent with 8–9% of GDP spending. ARIMA forecasting shows a 0.284% increase in current growth per 1% prior growth, while GARCH(1,1) modelling indicates a marginally significant 0.169% effect from 5-month lagged growth and persistent volatility from shocks like COVID-19. The small value of R2 and insignificant F-stat. value suggested unmodeled factors (e.g., GDP, inflation) drive variability. The 2012–2022 period, marked by economic recovery and the pandemic, underscores volatility, necessitating refined models and flexible budgeting for Italy’s healthcare system.

This paper investigates the informational efficiency and cross-correlations among the five largest African stock markets—Johannesburg, Casablanca, Botswana, Nigerian, and Egyptian—using Multifractal Detrended Cross-Correlation Analysis (MF-DCCA). Spanning the period from January 30, 2012, to August 8, 2024, with nearly 3,050 observations, the study explores the multifractal characteristics and complex interdependencies among these markets. Initial results from the Cross-Correlation Significance Test indicate statistically significant relationships across most index pairs. Further analysis using MF-DCCA components—Generalized Hurst exponents, Rényi exponents, and the Hölder Singularity Spectrum—reveals persistent long-range cross-correlations and strong multifractal behavior. The application of surrogate and shuffling procedures confirms that both long-memory effects and heavy-tailed distributions contribute to the observed multifractality. These findings suggest the presence of informational inefficiencies within and between African stock markets, as evidenced by deviations from random-walk behavior. The study provides new insights into market dynamics in emerging economies, with practical implications for investors, portfolio managers, and policymakers.

High-frequency data offers unparalleled insights into market dynamics, facilitating the analysis of statistical properties, dynamic correlations, and scaling behaviours with a precision previously unattainable. These Statistical Properties are essential framework for understanding and modelling the interactions between global financial markets over time. The aim of this study was to investigate the dynamic conditional correlations and scaling behaviour of high-frequency data from January,1 2010 to December 31, 2020. Using the S&P 500, FTSE 100, Nikkei 225, HKEX and DAX as sampled financial markets, the results revealed significant differences in correlation patterns across the markets, as well as fractal-like scaling behaviour. The relationship between the S&P 500-FTSE 100 and S&P 500-DAX supports trend-following strategies, while the Nikkei 225-HKEX and Nikkei 225-FTSE 100 may be closer to random-walk behaviour. This study advances the frontier of knowledge on high-frequency data and offers insights into the temporal relationships and scaling properties between financial markets.

This paper studies the eigentime and related issues in the fractal network corresponding to the Sierpiński fractal antenna. The access time or hitting time H (i, j) is the expected number of steps before node j is visited, starting from node i . The eigentime of G is the expectation of H (i, j) for all i, j ∈G . Classical eigenvalue method let H (i, i) =0. However, when studying the random walk behavior. of electrons in fractal networks corresponding to fractal antennas, it is necessary to consider the time when electrons leave a certain node and first return to that node (self return time) . This paper adopts two research methods-the eigenvalue method based on spectral theory and the Markov chain method based on stochastic process theory-to obtain the modified intrinsic time, and demonstrates through an example that the difference between the classical intrinsic time and the modified intrinsic time is precisely due to the self return time. This paper shows the applications of fractal networks in modern communications. The research results are expected to provide a theoretical basis for the design and performance optimization of fractal antennas.

This study examines whether Large Language Models (LLMs) can support momentum-based breakout strategies for retail investors by analysing technical charts and validating statistical patterns. We analysed 3,621 price charts (2023–2025) to assess LLMs’ ability to identify trading setups and deviations from random walk behaviour. 13,624 tests were run on 1,204 trades using various statistical tests. While 70% of patterns conformed to random walk behaviour in the short term (7–15 days), momentum signals rose to 26.42% over longer periods (50–250 days). Complex prompting produced both higher random walk classification (72.41% vs. 69.29%) and better returns than single-shot prompting. Incorporating Gamma Exposure (GEX) improved caution but reduced return rates. Discrepancies of up to 20% between JavaScript and Python implementations underscored LLMs’ current limitations in statistical precision. Overall, LLMs may democratise technical analysis but still require human oversight, structured prompting, and validation through traditional methods.

ABSTRACT The proposed Random Walk‐based Improved GOOSE (IGOOSE) search algorithm is a novel population‐based meta‐heuristic algorithm inspired by the collective movement patterns of geese and the stochastic nature of random walks. This algorithm includes the inherent balance between exploration and exploitation by integrating random walk behavior with local search strategies. In this paper, the IGOOSE search algorithm has been rigorously tested across 23 benchmark functions where 13 benchmarks are with varying dimensions (10, 30, 50, and 100 dimensions). These benchmarks provide a diverse range of optimization landscapes, enabling comprehensive evaluation of IGOOSE algorithm performance under different problem complexities. The algorithm is tested by various parameters such as convergence speed, magnitude of solution, and robustness for different dimensions. Further, IGOOSE algorithm is applied to optimize eight distinct engineering problems, showcasing its versatility and effectiveness in real‐world scenarios. The results of these evaluations highlight IGOOSE algorithm as a competitive optimization tool, offering promising performance across both standard benchmarks and complex structural engineering problems. Its ability to balance exploration and exploitation effectively, combined with its ability to deal with different problems, positions IGOOSE algorithm as a valuable tool.

Scattering phenomena offer significant application potential in fields such as high-resolution imaging, sensing, material characterization, and photonic computing due to their random-walk behavior and intricate spatial intensity statistics. A key to enhanced performance is to generate or reconfigure scattered light with tailored statistics to meet the specific requirements of various applications. Existing methods for reconfiguring scattering often rely on spatial light modulators and computational tools, which invariably involve complex algorithms and are constrained by limited spatial resolution and lack of control over polarization responses. In this work, we investigate the modulation of scattering statistics with a liquid crystal–polymer composite (LCPC) under varying applied voltages. By leveraging the electro-optic properties of LCPCs, the morphology and types of the reconfigured speckles can be dynamically adjusted between Rayleigh and non-Rayleigh with good stability. In addition, the polarization characteristics of the reconfigured speckles can be modulated, introducing another degree of freedom in scattering reconfiguration. These findings underscore the potential of LCPCs as a promising platform for reconfiguring scattering, offering new possibilities in adaptive optics, neuromorphic computing, and imaging-related applications.

Learning integrated inflation forecasts in a simple multi-agent macroeconomic model

This contribution presents a Kalman filtering strategy for space-frequency reconstruction of mechanical sources. The proposed approach is based on the definition of an appropriate state-space model, where the state equation assumes that the force vector follows a random walk behavior, while the observation equation is the classical linear relationship between the force and the measured response through the transfer function matrix of the considered structure. One of the main challenges of the proposed approach is the fine-tuning of the covariance matrix associated with the process noise. In this work, it is estimated and adapted at each frequency during the filtering procedure. A numerical experiment is performed on a simply supported beam excited by a broadband point mechanical force to evaluate the reconstruction performance of the proposed approach. Further comparisons with other regularization strategies are also proposed to provide a fair overview of the results obtained.

Source: created by the researcher using Eviews v.13 and the results of the statistical analysis The variance ratio has been employed for various slowdown periods 2, 4, 8, and 16 in order to apply the Variance Ratio Test to the primary EGX indices and qualitative sector indices in the Egyptian market. 16 EGX30 Z.Stat.

This study employs multifractal detrended fluctuation analysis to investigate the impact of fuel cell introduction in the Korean electricity market via the lens of multifractal scaling behavior. Using multifractal analysis, the research delineates discrepancies between peak and off-peak hours, accounting for the daily cyclicity of the electricity market, and proposes a crossover point detection method based on the Chow test. Furthermore, the impacts of fuel cell introduction are evidenced through various methods that encompass multifractal spectra and market efficiency. The findings initially indicate a higher degree of multifractality during off-peak hours relative to peak hours. In particular, the crossover points emerged solely during off-peak hours, unveiling short- and long-term dynamics predicated on a near-annual cycle. Additionally, the average Hurst exponent for the short-term was 0.542, while the average for the long-term was 0.098, representing a notable discrepancy. The introduction of fuel cells attenuated the heterogeneity in the scaling behavior, which is potentially attributable to the decreased volatility in both the supply and demand spectra. Remarkably, after the introduction of fuel cells, there was a discernible decrease in the influence of long-range correlation within multifractality, and the market exhibited an increased propensity toward random-walk behavior. This phenomenon was also detected in the market deficiency measure, from an average of 0.536, prior to the introduction, to an average of 0.267, following the introduction, signifying an improvement in market efficiency. This implies that the introduction of fuel cells into the market engendered increased supply stability and a consistent increase in demand, mitigating volatility on both the supply and demand sides, thus increasing market efficiency.

Abstract This research holds significance for advancing financial forecasting methodologies by shifting the focus from traditional sentiment analysis of individual tweets to exploring intricate semantic relationships within news tweets from top-followed news channels on Twitter. Addressing a notable research gap in financial forecasting, often dominated by sentiment analysis, our study endeavors to fill the void left by the underexplored intricate relationships within news entities and their dynamic semantic evolution. Motivated by the inherent challenges in predicting the random walk behavior of stock prices, we contend that incorporating longitudinal data derived from the semantic relationships between news entities can enhance the accuracy of stock market forecasts. The study pioneers a twelve-year exploration, encompassing data from 55 leading news channels on Twitter, boasting a collective following of 714 million users. The approach employs natural language processing (NLP) to extract two million unique entities, whose semantics are analyzed through complex network analysis, laying the foundation for the forecasting model. Finally, this research introduces a model linked to the dynamic semantic structure of news flow. The predictive model considers the impact of exogenous variables influenced by the evolving relationships among news entities. The results offer a proof of concept, highlighting the potential of utilizing dynamic semantic relationships among news entities for financial prediction. On average, the model demonstrates an improvement in accuracy of 40.3% across ten different stock price predictions. These findings are expounded through relevant theories, offering a theoretical foundation for observed patterns and indicating a promising direction for future research in this domain.

We compute tree level scattering amplitudes involving more than one highly excited states and tachyons in bosonic string theory. We use these amplitudes to understand the chaotic and thermal aspects of the excited string states lending support to the Susskind-Horowitz-Polchinski correspondence principle. The unaveraged amplitudes exhibit chaos in the resonance distribution as a function of the kinematic parameters, which can be described by random matrix theory. Upon coarse-graining, these amplitudes are shown to exponentiate, and capture various thermal features, including features of a stringy version of the eigenstate thermalization hypothesis as well as notions of typicality. Further, we compute the effective string form factor corresponding to the highly excited states, and argue for the random walk behaviour of the long strings.

This paper presents a trajectory control system design for a quadcopter, an unmanned aerial vehicle (UAV), which is based on estimated parameters that are assumed to exhibit random walk behavior. Initially, the rotational dynamic model of the UAV is formulated using the Newton Euler method in terms of angular velocity about the x, y, and z axes. This model is then simplified into three separated-first-order linear differential equations, with coefficients derived from the combined effects of inertia, aerodynamic drag, and gyroscopic effects, referred to as lumped parameters. A Proportional-Integral (PI) controller with feed-forward design is then developed to control this simplified model. To adapt the controller to the lumped parameters that exhibit random walk behavior, each simplified equation is restructured into a processing and measurement model. The states of these models are estimated by using the Unscented Kalman Filter (UKF). These estimated values are then utilized to adjust the PI gains and compensate the signal of the designed angular velocity controller, transforming it into an adaptive controller. The entire UAV controller comprises two main parts, an inner loop for adaptive angular rate control and an outer loop serving as an attitude-thrust controller. The proposed controller is simulated using Simulink, with circular and square trajectories. The simulation results demonstrate that the quadcopter successfully follows the desired circular and square paths. The steady-state error for the x and y axes in the square trajectory is less than 0.05 meters within 5 seconds, and for the z axis, it is less than 0.02 meters within 2.5 seconds. The controller gains do not require adjustment when changing trajectories. Moreover, the estimated parameters remain nearly constant at steady state.

Purpose — The current study seeks to understand whether individual stock returns exhibit random movement and are not dependent (efficient at weak form) on fourteen out of sixteen actively traded Arab stock markets in the Middle East and North Africa (MENA) region, based on the size of the market value.Method — Various non-parametric methods, including autocorrelation test, variance ratio test, Phillips-Perron unit root test, and runs test, are used to assess the random walk hypothesis for daily data following the Covid-19 vaccination program. This analysis covers the period from January 3, 2021, to March 28, 2023.Result — The study results present evidence that all individual stock returns deviate from random walk behavior. However, only Kuwait, Jordan, and Palestine stock returns follow the random walk based on the run test results at a significance level of 10%. Therefore, it can be concluded that all stock returns are inefficient at the weak-form, suggesting that investors have opportunities for unexpected gains.Practical implications — The findings of this study suggest that investors in the MENA region may have opportunities for unexpected gains, as individual stock returns deviate from random walk behavior, highlighting the importance of considering market dynamics and employing informed investment strategies. Additionally, policymakers could benefit from understanding the inefficiencies in stock returns to implement measures that promote market stability and efficiency.

The objectives of the study was to examine whether the broad market indices of NEPSE is weak-form efficient empirically and to investigate whether there are any anomalies or inefficiencies in the market that can be exploited for profit. The study aims to determine the relationship between NEPSE indices. By collecting historical data and analyzing correlations, the research seeks to assess the degree of market efficiency in the NEPSE, examining if prices fully reflect available information and exhibit random walk behavior. The findings will contribute to understanding the NEPSE's market efficiency and provide insights into the applicability of the EMH in the context of Nepal's stock market. The study found that the EMH is not fully supported in the Nepal Stock Exchange, as evidenced by the rejection of the null hypothesis for the banking sub-index and the hotels and tourism index. The critical t-values were used to determine the significance of the results, with lower t-values indicating greater evidence against the null hypothesis. The results suggest that past observations of the NEPSE indices can be used to predict future values with some accuracy, indicating a violation of the weak form of the EMH. This research delves into the efficiency of the Nepalese stock market, which remains relatively underexplored in academic literature compared to more prominent global exchanges. Keywords: Nepal Stock Exchange, efficient market hypothesis, broad market indices, market efficiency, random walk hypothesis