Entropy Metrics Research Articles

Analyzing boron oxide networks through Shannon entropy and Pearson correlation coefficient

In the current age of chemical science, chemical graph theory has significantly advanced our understanding of the characteristics of chemical compounds. To simulate the mathematical, chemical, and physical aspects of networks, a topological index, a numerical measure obtained from the graph of a chemical network, employed. Recent work has explored the topological properties of boron oxide using chemical graph theory. In this work, we conduct a Pearson correlation analysis of boron oxide to assess the correlations between the Van and S indices and entropy metrics. We analyze the Pearson correlation coefficients between the entropy values and the calculated indices using a heatmap. In this article, a significant positive correlation between the Van, and S indices, and entropy values, which is represented by the heatmap of the strong linear correlations. To avoid duplication, a dimensionality reduction technique should be used for highly connected variables. Additionally, this study gives a detailed explanation of the link between the indices and entropy, which will form the basis of further statistical investigations.

Implementation of Chaotic Neural Key Generation Algorithm For IoT Devices

This paper presents a new method for generating encryption keys for Internet of Things (IoT) devices. This method combines chaos theory with neural networks to create secure and efficient keys. We use the Lorenz chaotic system to generate complex patterns and a Convolutional Neural Network (CNN) to learn and predict these patterns. This approach is designed to address the unique security challenges of IoT devices, which often have limited computing power. We tested our method with different key sizes and evaluated its performance using accuracy, loss, entropy, and correlation metrics. The results show that key sizes between 256 and 512 bits offer the best balance between model performance and security for IoT devices. We also conducted Diehard statistical tests, which our key generation method passed successfully, demonstrating its ability to produce high-quality random keys.

Unraveling the spatio-temporal trajectories of urban growth in Asansol city, West Bengal: A geospatial exploration of the emerging urbanlandscape

The rapid urban growth of Asansol City has led to the rise of unplanned built-up areas, disrupting natural land covers and posing challenges to sustainable resource management. Hence, this study aims to quantify spatio-temporal trajectories of urban growth in Asansol City during 1991–2021, using integrated remote sensing and GIS-based techniques. Landsat 5 TM and 8 OLI/TIRS satellite imageries were used to delineate built-up and non-built-up areas using a random forest machine-learning algorithm. The study utilized the gradient approach, urban sprawl typologies, urban expansion indices, shannon’s entropy, and landscape fragmentation metrics to analyze the pattern, direction, intensity and dynamics of urban expansion in a space-time context. The findings showed that built-up growth increased significantly from 25.49 sq. km. to 57.18 sq. km. between 1991 and 2021, with the highest growth observed in the westward direction and within 3 km from the CBD. The study highlighted the prevalence of edge expansion and scatter development as dominant typologies of urban growth. Urban expansion indices, shannon's entropy and landscape fragmentation metrics analysis revealed the increasing urban sprawl towards the periphery and the formation of clustered built-up areas near the CBD. The outcomes of this study provide a basis for sustainable urban development by quantifying spatio-temporal trajectories and highlighting challenges from unrestrained growth of Asansol municipal corporation.

Foundation model for efficient biological discovery in single-molecule data.

Modern data-intensive techniques offer ever deeper insights into biology, but render the process of discovery increasingly complex. For example, exploiting the unique ability of single-molecule fluorescence microscopy (SMFM)1-5. to uncover rare but critical intermediates often demands manual inspection of time traces and iterative ad hoc approaches that are difficult to systematize. To facilitate systematic and efficient discovery from SMFM data, we introduce META-SiM, a transformer-based foundation model pre-trained on diverse SMFM analysis tasks. META-SiM achieves high performance-rivaling best-in-class algorithms-on a broad range of analysis tasks including trace selection, classification, segmentation, idealization, and stepwise photobleaching analysis. Additionally, the model produces high-dimensional embedding vectors that encapsulate detailed information about each trace, which the web-based META-SiM Projector (https://www.simol-projector.org) casts into lower-dimensional space for efficient whole-dataset visualization, labeling, comparison, and sharing. Combining this Projector with the objective metric of Local Shannon Entropy enables rapid identification of condition-specific behaviors, even if rare or subtle. As a result, by applying META-SiM to an existing single-molecule Förster resonance energy transfer (smFRET) dataset6, we discover a previously unobserved intermediate state in pre-mRNA splicing. META-SiM thus removes bottlenecks, improves objectivity, and both systematizes and accelerates biological discovery in complex single-molecule data.

Block-based color image encryption algorithm by a novel memristor chaotic system and new RNA computation

The security of images is closely related to the protection of information privacy. We proposed a novel 5D memory resistive chaotic system (5D-MRCS), which exhibits good chaotic characteristics. Therefore, we employed it to design an image encryption algorithm aimed at ensuring secure image transmission. To further enhance the complexity of the algorithm and obtain more chaotic sequences, we combine the 5D-MRCS with the Hodgkin-Huxley (HH) model and use this combination in algorithm design. Initially, we combine the plain image with the hash function SHA-384 to devise and generate the secret key. Subsequently, the algorithm determines whether to pad the plain image based on different block size requirements. Then, we use multiple chaotic sequences generated by the 5D-MRCS and HH model to perform the global image permutation operation. Our designed permutation algorithm includes two parts: Block-based permutation and a new pixel-level permutation. Next, the scrambled image undergoes block-based random RNA diffusion, incorporating two newly proposed methods in the RNA operations, ultimately resulting in the ciphertext image. The algorithm’s NPCR, UACI, information entropy, and other security performance metrics are very close to the ideal values, and it possess characteristics such as resistance to differential, cutting, chosen plaintext, and noise attacks. Compared with other algorithms, it still has some advantages across multiple images and demonstrates excellent image encryption performance.

Exploring topological indices and entropy measure via rational curve fitting models for calcium hydroxide network

This work uses rational curve fitting models to investigate the complex link between topological indices and entropy metrics in calcium hydroxide (Ca(OH)2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Ca(OH)_{2})$$\\end{document} networks. Entropy measurements shed light on the complexity and disorder of these networks, whereas topological indices are essential instruments for comprehending the structural characteristics of chemical substances. Our goal is to find new patterns and connections by merging these two fields, improving materials science’s prediction capacity. We calculate many topological indices, such as the Randic, Balaban, and Zagreb indices, and examine the relationship between them and entropy measurements obtained from (Ca(OH)2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Ca(OH)_{2})$$\\end{document} structural arrangement.

Potential Benefits and Challenges of Quantifying Pseudoreplication in Genomic Data with Entropy Statistics.

Generating vast arrays of genetic markers for evolutionary ecology studies has become routine and cost-effective. However, analyzing data from large numbers of loci associated with a small number of finite chromosomes introduces a challenge: loci on the same chromosome do not assort independently, leading to pseudoreplication. Previous studies have demonstrated that pseudoreplication can substantially reduce precision of genetic analyses (and make confidence intervals wider), such as FST and linkage disequilibrium (LD) measures between pairs of loci. In LD analyses, another type of dependency (overlapping pairs of the same loci) also creates pseudoreplication. Building on previous work, we explore the potential of entropy metrics to improve the status quo, particularly total correlation (TC), to assess pseudoreplication in LD studies. Our simulations, performed on a monoecious population with a range of effective population sizes (Ne) and numbers of loci, attempted to isolate the overlapping-pairs-of-loci effect by considering unlinked loci and using entropy to quantify inter-locus relationships. We hypothesized a positive correlation between TC and the number of loci (L), and a negative correlation between TC and Ne. Results from our statistical models predicting TC demonstrate a strong effect of the number of loci, and muted effects of Ne and other predictors, adding support to the use of entropy-based metrics as a tool for estimating the statistical information of complex genetic datasets. Our results also highlight a challenge regarding scalability; computational limitations arise as the number of loci grows, making our current approach limited to smaller datasets. Despite these challenges, this work further refines our understanding of entropy measures, and offers insights into the complex dynamics of genetic information in evolutionary ecology research.

An accurate and efficient forecast framework for fine PM2.5 maps using spatiotemporal recurrent neural networks

Commonly used numerical prediction models for PM2.5 maps suffer from low accuracy and high computation cost, which cannot meet the requirements for fine-scale air pollution control. In this study, we propose a framework based on the spatiotemporal recurrent neural network (PredRNN) to efficiently generate accurate 3-h and 6-km PM2.5 maps with a lead time of 5 days. In this framework, two PredRNN networks are initially utilized to forecast PM2.5 concentration at ground monitoring sites and the spatial distribution of aerosol optical depth (AOD) by assimilating the output of numerical prediction model. Subsequently, the 3-h and 6-km PM2.5 forecasted maps with a lead time of 5 days can be inferred by establishing the regression links between the forecasted results of PM2.5 concentration at ground sites and AOD maps. We evaluate the proposed framework in the Beijing-Tianjin-Hebei urban agglomeration region during 2017–2020. Compared with the numerical prediction products of the Copernicus Atmosphere Monitoring Service, the proposed framework achieves higher accuracy, with R2 of 0.83 at the forecast base time and 0.70 at the fifth day. The spatial information richness is also enhanced by approximately 15.67% according to the information entropy metrics. Notably, the proposed framework only requires 1 min for forecasting 5-days PM2.5 maps. These results demonstrate that our framework can efficiently generate accurate and fine PM2.5 maps with a lead time of 5 days.

The impact of controlled breathing on autonomic nervous system modulation: analysis using phase-rectified signal averaging, entropy and heart rate variability

Objective.The present study investigated how breathing stimuli affect both non-linear and linear metrics of the autonomic nervous system (ANS).Approach.The analysed dataset consisted of 70 young, healthy volunteers, in whom arterial blood pressure (ABP) was measured noninvasively during 5 min sessions of controlled breathing at three different frequencies: 6, 10 and 15 breaths min-1. CO2concentration and respiratory rate were continuously monitored throughout the controlled breathing sessions. The ANS was characterized using non-linear methods, including phase-rectified signal averaging (PRSA) for estimating heart acceleration and deceleration capacity (AC, DC), multiscale entropy, approximate entropy, sample entropy, and fuzzy entropy, as well as time and frequency-domain measures (low frequency, LF; high-frequency, HF; total power, TP) of heart rate variability (HRV).Main results.Higher breathing rates resulted in a significant decrease in end-tidal CO2concentration (p< 0.001), accompanied by increases in both ABP (p <0.001) and heart rate (HR,p <0.001). A strong, linear decline in AC and DC (p <0.001 for both) was observed with increasing breathing rate. All entropy metrics increased with breathing frequency (p <0.001). In the time-domain, HRV metrics significantly decreased with breathing frequency (p <0.01 for all). In the frequency-domain, HRV LF and HRV HF decreased (p= 0.038 andp= 0.040, respectively), although these changes were modest. There was no significant change in HRV TP with breathing frequencies.Significance.Alterations in CO2levels, a potent chemoreceptor trigger, and changes in HR most likely modulate ANS metrics. Non-linear PRSA and entropy appear to be more sensitive to breathing stimuli compared to frequency-dependent HRV metrics. Further research involving a larger cohort of healthy subjects is needed to validate our observations.

Assessment of alternative metrics in the application of infrared thermography to detect muscle damage in sports.

Objective.The association between muscle damage and skin temperature is controversial. We hypothesize that including metrics that are more sensitive to individual responses by considering variability and regions representative of higher temperature could influence skin temperature outcomes. Here, the objective of the study was to determine whether using alternative metrics (TMAX, entropy, and pixelgraphy) leads to different results than mean, maximum, minimum, and standard deviation (SD) skin temperature when addressing muscle damage using infrared thermography.Approach.Thermal images from four previous investigations measuring skin temperature before and after muscle damage in the anterior thigh and the posterior lower leg were used. The TMAX, entropy, and pixelgraphy (percentage of pixels above 33 °C) metrics were applied.Main results.On 48 h after running a marathon or half-marathon, no differences were found in skin temperature when applying any metric. Mean, minimum, maximum, TMAX, and pixelgraphy were lower 48 h after than at basal condition following quadriceps muscle damage (p< 0.05). Maximum skin temperature and pixelgraphy were lower 48 h after than the basal condition following muscle damage to the triceps sural (p< 0.05). Overall, TMAX strongly correlated with mean (r= 0.85) and maximum temperatures (r= 0.99) and moderately with minimum (r= 0.66) and pixelgraphy parameter (r= 0.64). Entropy strongly correlates with SD (r= 0.94) and inversely moderately with minimum temperature (r= -0.53). The pixelgraphy moderately correlated with mean (r= 0.68), maximum (r= 0.62), minimum (r= 0.58), and TMAX (r= 0.64).Significance.Using alternative metrics does not change skin temperature outcomes following muscle damage of lower extremity muscle groups.

Energy-Efficient Anomaly Detection and Chaoticity in Electric Vehicle Driving Behavior.

Detection of abnormal situations in mobile systems not only provides predictions about risky situations but also has the potential to increase energy efficiency. In this study, two real-world drives of a battery electric vehicle and unsupervised hybrid anomaly detection approaches were developed. The anomaly detection performances of hybrid models created with the combination of Long Short-Term Memory (LSTM)-Autoencoder, the Local Outlier Factor (LOF), and the Mahalanobis distance were evaluated with the silhouette score, Davies-Bouldin index, and Calinski-Harabasz index, and the potential energy recovery rates were also determined. Two driving datasets were evaluated in terms of chaotic aspects using the Lyapunov exponent, Kolmogorov-Sinai entropy, and fractal dimension metrics. The developed hybrid models are superior to the sub-methods in anomaly detection. Hybrid Model-2 had 2.92% more successful results in anomaly detection compared to Hybrid Model-1. In terms of potential energy saving, Hybrid Model-1 provided 31.26% superiority, while Hybrid Model-2 provided 31.48%. It was also observed that there is a close relationship between anomaly and chaoticity. In the literature where cyber security and visual sources dominate in anomaly detection, a strategy was developed that provides energy efficiency-based anomaly detection and chaotic analysis from data obtained without additional sensor data.

Foundation model for efficient biological discovery in single-molecule data.

Modern data-intensive techniques offer ever deeper insights into biology, but render the process of discovery increasingly complex. For example, exploiting the unique ability of single-molecule fluorescence microscopy (SMFM)1-5. to uncover rare but critical intermediates often demands manual inspection of time traces and iterative ad hoc approaches that are difficult to systematize. To facilitate systematic and efficient discovery from SMFM data, we introduce META-SiM, a transformer-based foundation model pre-trained on diverse SMFM analysis tasks. META-SiM achieves high performance-rivaling best-in-class algorithms-on a broad range of analysis tasks including trace selection, classification, segmentation, idealization, and stepwise photobleaching analysis. Additionally, the model produces high-dimensional embedding vectors that encapsulate detailed information about each trace, which the web-based META-SiM Projector (https://www.simol-projector.org) casts into lower-dimensional space for efficient whole-dataset visualization, labeling, comparison, and sharing. Combining this Projector with the objective metric of Local Shannon Entropy enables rapid identification of condition-specific behaviors, even if rare or subtle. As a result, by applying META-SiM to an existing single-molecule Förster resonance energy transfer (smFRET) dataset6, we discover a previously unobserved intermediate state in pre-mRNA splicing. META-SiM thus removes bottlenecks, improves objectivity, and both systematizes and accelerates biological discovery in complex single-molecule data.

Analysis of longitudinal patterns and predictors of medicine use in residential aged care using group-based trajectory modelling: The MEDTRAC-Polypharmacy longitudinal cohort study.

Polypharmacy serves as a quality indicator in residential aged care facilities (RACFs) due to concerns about inappropriate medication use. However, aggregated polypharmacy rates at a single time offer limited value. Longitudinal analysis of polypharmacy patterns provides valuable insights into identifying potential overuse of medicines. We aimed to determine long-term trajectories of polypharmacy (≥9 medicines) and factors associated with each polypharmacy trajectory group. This was a longitudinal cohort study using electronic data from 30 RACFs in New South Wales, Australia. We conducted group-based trajectory modelling to identify and characterize polypharmacy trajectories over 3 years. We evaluated the model fitness using the Bayesian Information Criterion, entropy (with a value of ≥0.8 considered ideal) and several other metrics. The study included 2837 permanent residents (median age = 86 years, 61.7% female and 47.4% had dementia). We identified five polypharmacy trajectory groups: group 1 (no polypharmacy, 46.0%); group 2 (increasing polypharmacy, 9.4%); group 3 (decreasing polypharmacy, 9.2%); group 4 (increasing-then decreasing polypharmacy, 10.0%), and group 5 (persistent polypharmacy, 25.4%). The model showed excellent performance (e.g., entropy = 0.9). Multinomial logistic regressions revealed the profile of each trajectory group (e.g., group 5 residents had higher odds of chronic respiratory disease compared with group 1). Our study identified five polypharmacy trajectory groups, including one with over a quarter of residents following a persistently high trajectory, signalling concerning medication overuse. Quality indicator programs should adopt tailored metrics to monitor diverse polypharmacy trajectory groups, moving beyond the current one-size-fits-all approach and better capturing the evolving dynamics of residents' medication regimens.

A quantum information theoretic analysis of reinforcement learning-assisted quantum architecture search

In the field of quantum computing, variational quantum algorithms (VQAs) represent a pivotal category of quantum solutions across a broad spectrum of applications. These algorithms demonstrate significant potential for realising quantum computational advantage. A fundamental aspect of VQAs involves formulating expressive and efficient quantum circuits (namely ansatz), and automating the search of such ansatz is known as quantum architecture search (QAS). Recently reinforcement learning (RL) techniques is utilized to automate the search for ansatzes, know as RL-QAS. This study investigates RL-QAS for crafting ansatz tailored to the variational quantum state diagonalisation problem. Our investigation includes a comprehensive analysis of various dimensions, such as the entanglement thresholds of the resultant states, the impact of initial conditions on the performance of RL-agent, the phase transition behaviour of correlation in concurrence bounds, and the discrete contributions of qubits in deducing eigenvalues through conditional entropy metrics. We leverage these insights to devise an entanglement-guided admissible ansatz in QAS to diagonalise random quantum states using optimal resources. Furthermore, the methodologies presented herein offer a generalised framework for constructing reward functions within RL-QAS applicable to variational quantum algorithms.

Multidecadal Changes of the Seasonal Potential Predictability of Winter PNA and Associated Circulation Anomalies

Abstract Utilizing ensemble hindcast data from the Community Earth System Model (CESM) spanning the years 1900–2014, the multidecadal changes in the seasonal potential predictability of the winter Pacific–North American (PNA) teleconnection pattern and associated circulation anomalies have been investigated by using an information-based metric of relative entropy and the method of the most predictable component analysis. Results show that the seasonal potential predictability of winter PNA has significant multidecadal changes, with values much higher at the two ends of the twentieth century and much lower in between particularly in the 1930s and 1940s. The changes in the seasonal potential predictability of winter PNA are mostly reflected by the temporal evolutions of PNA rather than the location changes of active centers. Further, the changes are mostly contributed by the external forcing of El Niño–Southern Oscillation (ENSO)-related sea surface temperature anomalies in tropical central and eastern Pacific. In particular, the combined effects of lower amplitudes, reduced persistence, and a more eastward shift in warming centers lead to the reduced seasonal potential predictability of PNA and associated circulation changes in the 1930s and 1940s. Significance Statement Seasonal prediction of the winter Pacific–North American (PNA) teleconnection pattern and associated circulation anomalies is very important due to its profound climate impacts. Understanding the multidecadal fluctuations and its driving sources of the potential predictability of winter PNA and associated circulation anomalies are meaningful for skillful seasonal prediction of winter PNA and circulation anomalies as well as related climate variations. This study for the first time shows that the multidecadal fluctuations of the potential predictability of winter PNA are quite significant and the changes are mostly reflected by its temporal evolutions rather than spatial shifts of active centers. Furthermore, this study shows that the strength, persistence, and warming center locations of ENSO-related sea surface temperatures in tropical Pacific play a crucial role on the multidecadal changes of the potential predictability of winter PNA and associated circulation anomalies.

China’s New Housing Security Model: Evaluation of the Job–Housing Balance in Affordable Rental Housing, Shanghai

The Chinese government’s recent low-income housing scheme aims to tackle housing challenges faced by the urban floating population. A notable shift in this initiative is the focus on the job–housing balance. This study proposes that the spatial interaction between land designated for affordable rental housing and land for commercial facilities serves as a fundamental metric for evaluating this equilibrium, providing insights into the effectiveness of China’s nascent affordable housing efforts. Drawing on post-2021 data, when China’s revamped affordable housing policy took effect, our research examines the spatial distribution of affordable rental housing and commercial service land in Shanghai. By employing coupled coordination models and local entropy metrics, we delve into the supply equilibrium and pragmatic interrelation of these land types. Our findings reveal localized clustering in the spatial arrangement of rental and commercial land within Shanghai. Zones in the urban core exhibit a supply balance, while the peripheries display diminishing accessibility between these land types. Core urban areas have a lower supply balance but higher accessibility, whereas urban fringes face both low supply balance and low accessibility. These study outcomes have significant implications for strategic planning and the construction of affordable rental housing.

Optimized dispersion Higuchi fractal dimension and its refined composite multi-scale version for signal analysis

Higuchi fractal dimension (HFD), as a classic nonlinear dynamic metric, which is commonly used to detect signal dynamic changes. However, it is difficult for HFD to process signal outliers. To address this issue, dispersion HFD (DHFD) is proposed, which improves the signal complexity representation ability of HFD by introducing the normal cumulative distribution function and round function in dispersion entropy. Nevertheless, the parameter selection of DHFD can affect the complexity value. Therefore, an optimized dispersion HFD (ODHFD) is proposed, which solves the threshold selection problem of DHFD and can more effectively reflect the complexity of the signal. In addition, an optimized refined composite DHFD (ORCMDHFD) has been proposed, which can more comprehensively reflect the complexity information for the signal at multiple scales. The simulation experiment results show that DHFD has a smaller standard deviation than HFD when calculating white noise signal complexity, and DHFD have the least dependence on signal length compared to other metrics, as well as RCMDHFD has the best separability for simulated noise signals. Actual experiments have shown that ODHFD and ORCMDHFD is superior to other entropy and fractal dimension metrics in distinguishing ship radiated noise and mechanical fault signals, and has broad application prospects in the field of signal analysis.

Entropy-based syntactic tree analysis for text classification: a novel approach to distinguishing between original and translated Chinese texts

Abstract This research focuses on classifying translated and non-translated Chinese texts by analyzing syntactic rule features, using an integrated approach of machine learning and entropy analysis. The methodology employs information entropy to gauge the complexity of syntactic rules in both text types. The methodology is based on the concept of information entropy, which serves as a quantitative measure for the complexity inherent in syntactic rules as manifested from tree-based annotations. The goal of the study is to explore whether translated Chinese texts demonstrate syntactic characteristics that are significantly different from those of non-translated texts, thereby permitting a reliable classification between the two. To do this, the research calculates information entropy values for syntactic rules in two comparable corpora, one of translated and the other of non-translated Chinese texts. Then, various machine learning models are applied to these entropy metrics to identify any significant differences between the two groups. The results show significant differences in the syntactic structures. Translated texts have a higher degree of entropy, indicating more complex syntactic constructs compared to non-translated texts. These findings contribute to our understanding of the effect of translation on language syntax, with implications for text classification and translation studies.

Quantum entropic exchange at avoided crossings due to laser–atom interaction

In the present study, we detail the entropic characteristics of a dressed atom, wherein the atom undergoes an interaction with a monochromatic laser beam. Our investigation of the laser–atom interplay employs a well-established non-perturbative quasi-energy methodology, allowing us to discern the dressed wavefunctions and quasi-energies of the laser-dressed atom. Utilizing these dressed wavefunctions as a foundation, we systematically examine various entropic measures, observing their behaviour for laser frequency and intensity. The selection of levels within the system adheres to the criteria dictated by the selection rules governing transitions between these levels. Our exploration focuses on the interplay between Shannon entropy and other entropic metrics, with their fluctuations intricately tied to the phenomenon of avoided crossings. As the laser amplitude intensifies, the AC Stark effect takes centre stage, exerting influence over the sharp or smooth variations in Shannon entropy at these avoided crossings. Furthermore, we delineate the correlation between the number of levels considered and the identification of avoided crossings. Our present analysis sheds light on the intricate dynamics in the dressed atom system, enhancing our understanding of the interplay between laser-induced dressing and entropic measures.

On an Aggregated Estimate for Human Mobility Regularities through Movement Trends and Population Density.

This article introduces an analytical framework that interprets individual measures of entropy-based mobility derived from mobile phone data. We explore and analyze two widely recognized entropy metrics: random entropy and uncorrelated Shannon entropy. These metrics are estimated through collective variables of human mobility, including movement trends and population density. By employing a collisional model, we establish statistical relationships between entropy measures and mobility variables. Furthermore, our research addresses three primary objectives: firstly, validating the model; secondly, exploring correlations between aggregated mobility and entropy measures in comparison to five economic indicators; and finally, demonstrating the utility of entropy measures. Specifically, we provide an effective population density estimate that offers a more realistic understanding of social interactions. This estimation takes into account both movement regularities and intensity, utilizing real-time data analysis conducted during the peak period of the COVID-19 pandemic.