We study the Patrol Security Game (PSG), a robotic patrolling problem formulated as an extensive-form Stackelberg game, in which the attacker strategically selects the timing, location, and duration of an attack. The defender’s goal is to compute an infinite-horizon patrolling policy that minimizes the attacker’s expected payoff. By restricting the defender’s strategy to a time-homogeneous first-order Markov chain, we show that PSG can be reformulated as a combinatorial minimax problem. We prove that the optimal strategy under zero-penalty scenarios corresponds to minimizing either the expected hitting time or return time, depending on the attacker’s visibility model. These optimal policies are closed-form and can be computed efficiently. On the other hand, in high-penalty cases, we observe that the patrolling schedule with high randomness can minimize the attacker’s expected gain. However, in general, the minimax objective becomes non-convex. To address this, we introduce a bi-criteria optimization framework that jointly considers the expected maximum reward (EMR) and entropy rate of the patrolling policy. We propose three graph-based algorithms and a deep reinforcement learning model to efficiently balance these two objectives. Each algorithm demonstrates distinct strengths under different configurations, such as varying penalty scales and cost function settings. The extensive experiments on both synthetic and real-world crime datasets validate the effectiveness of our approaches, demonstrating superior performance and scalability compared to state-of-the-art baselines.

Antibodies have emerged as central components of therapeutic strategies against viral infectious diseases, functioning as key effectors in both prevention and treatment. While traditional antibody discovery has relied heavily on high-throughput screening, the field is now shifting toward rational antibody design, which requires integrative insights into sequence-structure-function relationships. However, existing resources provide a valuable foundation but remain limited in scope, highlighting the need for a standardized and well-annotated antibody database that integrates multidimensional features to further support systematic exploration, cross-pathogen comparison, and rational antibody design. Here, we introduce the Multidimensional Antiviral Antibody Database (MAAD; http://www.raabmd.org/raab/index), a curated platform dedicated to antibody, nanobody and single-chain variable fragment targeting three high-impact RNA virus families, Coronaviridae (SARS-CoV-1, SARS-CoV-2, MERS-CoV), Orthomyxoviridae (influenza virus), and Pneumoviridae (respiratory syncytial virus, human metapneumovirus), which were selected due to the large, high-quality datasets accumulated in recent years. MAAD further incorporates a suite of interactive analysis modules, including CDR and germline annotation, similarity-based sequence analysis, sequence-based clustering and structure-guided identification of antigen-antibody interface residues, complemented by per-site entropy and mutation rate profiling. These features enable in-depth exploration of antibody sequence characteristics, thereby facilitating functional and structural insights for rational antibody design. Together, by bridging antibody sequence, structure and function, MAAD offers an open and standardized platform that advances comparative antiviral research and supports therapeutic antibody discovery.

Prenatal maternal stress (PS) is a risk factor for adverse offspring neurodevelopment. Heart rate variability (HRV) complexity provides a non-invasive marker of maternal autonomic regulation and may be influenced by mind–body interventions such as Yoga. In this quasi-randomized controlled trial, 28 chronically stressed pregnant women were followed from the second trimester until birth: 14 participated in weekly Hatha Yoga with electrocardiogram (ECG) recordings, and 14 received standard obstetric care with monthly ECGs. Group allocation was based on availability, with participants unaware of their assignment at enrollment. HRV complexity was assessed first with Sample Entropy and Entropy Rate and then expanded to 94 HRV metrics spanning temporal, frequency, nonlinear, and information-theoretical domains. All metrics were covariate-adjusted (maternal age, BMI, gestational age), standardized, and analyzed using timepoint-specific principal component analysis (PCA). From this, a unified HRV index was derived. Analyses revealed that HRV metric relationships changed dynamically across pregnancy, with PCA loadings shifting from frequency toward complexity measures in late gestation. The mixed effects model identified a significant time x group interaction effect (p = 0.041). These findings suggest a restructuring of HRV signal-analytical domains with advancing pregnancy attributable to Yoga and highlight the utility of advanced HRV analysis frameworks for future, larger trials.

Mass-balanced compartmental systems defy classical deterministic entropy measures since both metric and topological entropy vanish in dissipative dynamics. By interpreting open compartmental systems as absorbing continuous-time Markov chains that describe the random journey of a single representative particle, we allow established information-theoretic principles to be applied to this particular type of deterministic dynamical system. In particular, path entropy quantifies the uncertainty of complete trajectories, while entropy rates measure the average uncertainty of instantaneous transitions. Using Shannon’s information entropy, we derive closed-form expressions for these quantities in equilibrium and extend the maximum entropy principle (MaxEnt) to the problem of model selection in compartmental dynamics. This information-theoretic framework not only provides a systematic way to address equifinality but also reveals hidden structural properties of complex systems such as the global carbon cycle.

The exponential growth of digital data transmission and storage demands robust encryption mechanisms capable of securing sensitive multimedia content across diverse platforms. This comprehensive review examines the convergence of chaotic systems, DNA encoding techniques, and big data analytics in developing next-generation image encryption algorithms. Through systematic analysis of recent advances in chaos-based cryptographic methods, this paper evaluates the effectiveness of hybrid approaches combining chaotic maps, DNA computing, and machine learning techniques for multimedia security. The study synthesizes findings from 24 peer-reviewed publications spanning 2022-2024, highlighting breakthrough methodologies in bit-level encryption, visual cryptography, and real-time security applications. Our analysis reveals that DNA-chaos hybrid systems achieve superior entropy rates (>7.99), correlation coefficients approaching zero, and processing speeds suitable for real-time applications. The integration of big data analytics enhances key generation mechanisms and provides adaptive security frameworks capable of responding to evolving cyber threats. These findings contribute significantly to the development of quantum-resistant encryption protocols and establish foundational principles for secure communication in the era of big data.

Neural complexity, measured as the entropy of noninvasively recorded electrophysiological signals, evolves with age in early infancy, differentiates between typical and atypical development, and likely serves as a surrogate marker of brain maturation. However, the reason for this evolution of neural entropy in early infant development remains unclear. To understand this evolution, we measured the proportion of time that the infant brain spent in a bursting pattern of activity and related this activity pattern to the neural complexity (i.e., entropy or entropy rate). Additionally, we sought to predict neural complexity using each infant’s gestational age and to replicate sex-related complexity differences previously reported in age-equivalent fetuses. Four distinct complexity estimator algorithms – Lempel-Ziv (LZ) complexity, multiscale entropy (MSE), complexity via state-space entropy rate (CSER), and context tree weighting (CTW) – were applied to 8-channel infant electroencephalogram (EEG) recordings in 28 preterm infants (27–34 weeks gestational age). To explore factors influencing signal complexity, we modeled relationships between complexity estimates, on the one hand, and spontaneous activity transients, gestational age, and sex, on the other hand. We calculated channel-averages for each complexity estimate separately, as derived either from entire EEG recordings or separately from burst and interburst periods. Our results suggest that increased EEG signal continuity with maturation may drive increases in neural complexity as quiescent periods subside. Additionally, our results largely recapitulate previous findings linking neural complexity to biological sex in third-trimester fetuses. We also observed unexpected differences between entropy rate results obtained using CSER (a newer algorithm) and older algorithms. These findings support further research into neural complexity as a potential predictor of clinical outcomes in infants at high risk for neurodevelopmental disorders.

The exponential growth of digital data transmission and storage demands robust encryption mechanisms capable of securing sensitive multimedia content across diverse platforms. This comprehensive review examines the convergence of chaotic systems, DNA encoding techniques, and big data analytics in developing next-generation image encryption algorithms. Through systematic analysis of recent advances in chaos-based cryptographic methods, this paper evaluates the effectiveness of hybrid approaches combining chaotic maps, DNA computing, and machine learning techniques for multimedia security. The study synthesizes findings from 24 peer-reviewed publications spanning 2022-2024, highlighting breakthrough methodologies in bit-level encryption, visual cryptography, and real-time security applications. Our analysis reveals that DNA-chaos hybrid systems achieve superior entropy rates (>7.99), correlation coefficients approaching zero, and processing speeds suitable for real-time applications. The integration of big data analytics enhances key generation mechanisms and provides adaptive security frameworks capable of responding to evolving cyber threats. These findings contribute significantly to the development of quantum-resistant encryption protocols and establish foundational principles for secure communication in the era of big data.

Multiscale entropy rates: A study on different stochastic processes

Linear and nonlinear features of EEG microstate associated with insomnia.

New concepts of magnetohydrodynamics and entropy rate for radiative nanofluid flow invoking artificial neural network approach

Abstract Introduction : Radiomics quantify radiological data to correlate with clinical findings. Dyssynchrony, a proposed radiomic parameter measured via phase images, reflects the temporal discoordination of ventricular contraction, which can impair overall cardiac efficiency. This study assessed the consistency and reliability of dyssynchrony in laminar and turbulent flow compartments under varying image acquisition. It also evaluated the relationship between dyssynchrony and fluid dynamics alterations. Methods : The dataset included 64 dynamic images using gamma camera (128,000 frames) generated using an in-home phantom, representing combinations of flow velocity, count, and frame rates. Phase and amplitude images were generated and analyzed to calculate synchrony, entropy, approximate entropy (ApEn), and bounded-ApEn for different rotation directions. Entropy values were examined under parameter changes, with comparisons using Pearson’s test, ANOVA, logistic regression, and receiver operating characteristic (ROC) analysis. Results : Images were categorized by activity concentrations: Group 1 (37 MBq), Group 2 (29.5 MBq), and Group 3 (18.5 MBq). Group 1 showed a strong negative correlation between entropy and frame rates (r = −0.991, p < 0.001), while Group 3 displayed positive correlations between frame rate, ApEn, gray count, and pixel count. Logistic regression predicted turbulence (AUC = 0.93) and direction (AUC = 0.96) using bounded-ApEn. Regression analysis indicated ApEn and bounded-ApEn significantly predicted vortex parameters (R² = 93%). Conclusion : Dyssynchrony metrics, including entropy, ApEn, and bounded-ApEn, demonstrated consistent measurements across varying conditions. These findings highlight their potential for enhancing diagnostic accuracy and guiding personalized therapeutic strategies for conditions influenced by blood flow patterns

Unsupervised hyperspectral image (HSI) clustering is a fundamental yet challenging task due to high dimensionality and complex spectral–spatial characteristics. In this paper, we propose a novel and efficient clustering framework centered on adaptive and diverse anchor graph modeling. First, we introduce a parameter-free construction strategy that employs Entropy Rate Superpixel (ERS) segmentation to generate multiple anchor graphs of varying sizes from a single HSI, overcoming the limitation of fixed anchor quantities and enhancing structural expressiveness. Second, we propose an anchor-to-pixel label propagation mechanism to transfer anchor-level cluster labels back to the pixel level, reinforcing spatial coherence and spectral discriminability. Third, we perform clustering directly at the anchor level, which substantially reduces computational cost while retaining structure-aware accuracy. Extensive experiments on three benchmark datasets (Trento, Salinas, and Pavia Center) demonstrate the effectiveness and efficiency of our approach.

Secure autonomous secret key distillation (SKD) systems traditionally depend on external common randomness (CR) sources, which often suffer from instability and limited reliability over long-term operation. In this work, we propose a novel SKD architecture that synthesizes CR by combining a keystream of a shared-key keystream generator KSG(KG) with locally generated binary Bernoulli noise. This construction emulates the statistical properties of the classical Maurer satellite scenario while enabling deterministic control over key parameters such as bit error rate, entropy, and leakage rate (LR). We derive a closed-form lower bound on the equivocation of the shared-secret key KG from the viewpoint of an adversary with access to public reconciliation data. This allows us to define an admissible operational region in which the system guarantees long-term secrecy through periodic key refreshes, without relying on advantage distillation. We integrate the Winnow protocol as the information reconciliation mechanism, optimized for short block lengths (N=8), and analyze its performance in terms of efficiency, LR, and final key disagreement rate (KDR). The proposed system operates in two modes: ideal secrecy, achieving secret key rates up to 22% under stringent constraints (KDR < 10−5, LR < 10−10), and perfect secrecy mode, which approximately halves the key rate. Notably, these security guarantees are achieved autonomously, without reliance on advantage distillation or external CR sources. Theoretical findings are further supported by experimental verification demonstrating the practical viability of the proposed system under realistic conditions. This study introduces, for the first time, an autonomous CR-based SKD system with provable security performance independent of communication channels or external randomness, thus enhancing the practical viability of secure key distribution schemes.

Abstract In many fields, such as language acquisition, neuropsychology of language, the study of aging, and historical linguistics, corpora are used for estimating the diversity of grammatical structures that are produced during a period by an individual, community, or type of speakers. In these cases, treebanks are taken as representative samples of the syntactic structures that might be encountered. Generalizing the potential syntactic diversity from the structures documented in a small corpus requires careful extrapolation whose accuracy is constrained by the limited size of representative sub-corpora. In this article, I demonstrate—both theoretically and empirically—that a grammar’s derivational entropy and the mean length of the utterances (MLU) it generates are fundamentally linked, giving rise to a new measure, the derivational entropy rate. The mean length of utterances becomes the most practical index of syntactic complexity; I demonstrate that MLU is not a mere proxy, but a fundamental measure of syntactic diversity. In combination with the new derivational entropy rate measure, it provides a theory-free assessment of grammatical complexity. The derivational entropy rate indexes the rate at which different grammatical annotation frameworks determine the grammatical complexity of treebanks. I evaluate the Smoothed Induced Treebank Entropy (SITE) as a tool for estimating these measures accurately, even from very small treebanks. I conclude by discussing important implications of these results for both NLP and human language processing.

In existing linguistic decision-making (LDM) methods, individual decision maker generally evaluates alternatives through a single-round evaluation process, in which only preliminary cognition of individual decision maker can be excavated. This results in the evaluation provided by individual decision maker may not well reflect their integrated preference through the single-round evaluation process. To address this issue, a multi-round evaluation process should be designed, in which the decision maker can constantly renew his or her acquired cognition through previous rounds of evaluation and further updates his or her evaluation. In this paper, a cognitive-driven LDM method based on the multi-round evaluation process is proposed to overcome the insufficiency of existing methods in adequately exploring the decision maker comprehensive cognition. First, the transition process of linguistic term (LT) of the alternative induced by decision maker’s cognition renewal is modeled as a Markov chain. The transition probability from one state to another within the state space is then created to obtain the incomplete transition matrix, whose entropy rate is maximized to derive the complete transition matrix via the constructed convex optimization problem. The stable distributions of alternatives can be generated based on their complete transition matrices. The aggregated stable distributions of alternatives are obtained by minimizing the dissimilarity between them and the individual stable distributions of alternatives on the criteria. On this basis, the ranking order of alternatives can be generated. The proposed method is further applied to a diagnostic ultrasound system selection problem for demonstrating its applicability and effectiveness. The comparative experiment reveals the significance of considering decision maker’s renewal cognition in the multi-round decision-making process. This paper provides insights on improving decision-making quality through the modeling of decision maker's acquired cognition in the multi-round decision-making processes.

Generating random variates is a fundamental operation in diverse areas of computer science and is supported in almost all modern programming languages. Traditional software libraries for random variate generation are grounded in the idealized "Real-RAM" model of computation, where algorithms are assumed to be able to access uniformly distributed real numbers from the unit interval and compute with infinite-precision real arithmetic. These assumptions are unrealistic, as any software implementation of a Real-RAM algorithm on a physical computer can instead access a stream of individual random bits and computes with finite-precision arithmetic. As a result, existing libraries have few theoretical guarantees in practice. For example, the actual distribution of a random variate generator is generally unknown, intractable to quantify, and arbitrarily different from the desired distribution; causing runtime errors, unexpected behavior, and inconsistent APIs. This article introduces a new approach to principled and practical random variate generation with formal guarantees. The key idea is to first specify the desired probability distribution in terms of a finite-precision numerical program that defines its cumulative distribution function (CDF), and then generate exact random variates according to this CDF. We present a universal and fully automated method to synthesize exact random variate generators given any numerical CDF implemented in any binary number format, such as floating-point, fixed-point, and posits. The method is guaranteed to operate with the same precision used to specify the CDF, does not overflow, avoids expensive arbitrary-precision arithmetic, and exposes a consistent API. The method rests on a novel space-time optimal implementation for the class of generators that attain the information-theoretically optimal Knuth and Yao entropy rate, consuming the least possible number of input random bits per output variate. We develop a random variate generation library using our method in C and evaluate it on a diverse set of "continuous" and "discrete" distributions, showing competitive runtime with the state-of-the-art GNU Scientific Library while delivering higher accuracy, entropy efficiency, and automation.

AI-based personalized real-time risk prediction for behavioral management in psychiatric wards using multimodal data.

Heat transfer in the transportation of nanoparticles has a significant impact on raising the efficiency of various devices in industrial and technological fields. Here we investigated heat transfer and entropy generation rate for Darcy-Forchheimer stagnation point fluid flow toward a stretched surface in the presence of two types of nanofluids (Al 2 O 3 +water) and (Al 2 O 3 +kerosene oil). In the modeling of energy expression, we utilized the impact of radiative heat flux, internal heat generation, and viscous dissipation. Slip and thermal stratification effects are also present. By employing appropriate transformations, a nonlinear partial differential system can be converted into an ordinary differential system. For solutions computations, a numerical scheme ND-Solve, along with shooting techniques, is implemented. The outcomes of variables that have an impact on temperature and velocity are analyzed. Entropy rate and Bejan number for the considered model are discussed. A physical description of entropy generation against various sundry variables is presented. From the results, it is observed that with greater values of both inverse Darcy number ( D a − 1 ) and slip parameter ( β 3 ) velocity field shows decreasing trend and temperature field intensifies for higher radiation parameter ( R d * ) and heat generation parameter ( δ ^ ). Entropy rate rises for all flow parameters of both nanofluids while Bejan number decreases for inverse Darcy number ( D a − 1 ) and Eckert number ( Ec ). Heat transfer rate boosted for radiation parameter ( R d * ) and surface drag reduces for convection parameter ( β 2 ).

Bots have become increasingly prevalent in the digital sphere and have taken up a proactive role in shaping democratic processes. While previous studies have focused on their influence at the individual level, their potential macro-level impact on communication dynamics remains underexplored. This study adopts an information-theoretic approach from dynamical systems theory to examine the role of political bots shaping the dynamics of an online political discussion on Twitter. We quantify the components of this dynamic process in terms of its complexity, predictability, and its entropy rate, or the remaining uncertainty. Findings suggest that bot activity is associated with increased complexity and, simultaneously, with more uncertainty in the structural dynamics of online political communication. While our dataset features earlier-generation bots, findings foreshadow the possibility for even more complex and uncertain online politics in the age of sophisticated and autonomous generative AI agents. Our presented framework showcases how this can be studied with the use of information-theoretic measures from dynamical systems theory.

Natural landscapes are crucial resources for enhancing visitor experiences in ecotourism destinations. Previous research indicates that high temperatures may impact tourists' perception of landscapes and emotions. Still, the potential value of natural landscape perception in regulating tourists' emotions under high-temperature conditions remains unclear. In this study, we employed machine learning models such as LSTM-CNN, Hrnet, and XGBoost, combined with hotspot analysis and SHAP methods, to compare and reveal the potential impacts of natural landscape elements on tourists' emotions under different temperature conditions. The results indicate: (1) Emotion prediction and spatial analysis reveal a significant increase in the proportion of negative emotions under high-temperature conditions, reaching 30.1%, with negative emotion hotspots concentrated in the downtown area, whereas, under non-high temperature conditions, negative emotions accounted for 14.1%, with a more uniform spatial distribution. (2) Under non-high temperature conditions, the four most influential factors on tourists' emotions were Color complexity (0.73), Visual entropy (0.71), Greenness (0.68), and Aquatic rate (0.6). In contrast, under high-temperature conditions, the most influential factors were Greenness (0.6), Openness (0.56), Visual entropy (0.55), and Color complexity (0.55). (3) Compared to non-high temperature conditions, high temperatures enhanced the positive effects of environmental perception on emotions, with Greenness (0.94), Color complexity (0.84), and Enclosure (0.71) showing stable positive impacts. Additionally, aquatic elements under high-temperature conditions had a significant emotional regulation effect (contribution of 1.05), effectively improving the overall visitor experience. This study provides a data foundation for optimizing natural landscapes in ecotourism destinations, integrating the advantages of various machine learning methods, and proposing a framework for data collection, comparison, and evaluation of natural landscape perception under different temperature conditions. It thoroughly explores the potential of natural landscapes to enhance visitor experiences under various temperature conditions and provides sustainable planning recommendations for the sustainable conservation of natural ecosystems and ecotourism.