This paper compares three numerical schemes for Caputo fractional differential equations: the Shifted Chebyshev Tau Method (SCTM), the Shifted Chebyshev Collocation Method (SCCM), and the Haar Wavelet Collocation Method (HWCM). In the two Chebyshev schemes, the unknown solution is approximated by shifted Chebyshev polynomials, whereas the Haar formulation uses localized piecewise-constant basis functions and fractional integration matrices. Each method reduces the governing equation to a finite algebraic system. The original contribution is a controlled like-for-like comparison in which the three formulations use the same numbers of unknowns, common independent test grids, and the same accuracy, conditioning, sparsity, and timing diagnostics. Six benchmark problems with known exact solutions are examined using the balanced approximation sizes N = 4, 8, 16, 32. The first five examples have smooth polynomial solutions. SCTM and SCCM recover the exact profiles to the adopted working precision whenever the exact polynomial lies in the selected approximation space. The sixth example has the nonpolynomial solution u(x) = x 5/2, whose third derivative is unbounded at the left endpoint, and therefore provides a genuine low-regularity convergence test. At N = 32, the maximum errors of SCTM and SCCM are 4.39523 × 10−6 and 4.31475 × 10−6 , respectively, whereas HWCM gives 4.33493 × 10−2 . The results show that the Chebyshev methods provide the highest accuracy for the problems studied, SCCM generally achieves this accuracy with a lower assembly cost than SCTM, and HWCM produces better-conditioned and less dense systems with generally first-order-type convergence.
Nonlocal equations have emerged as a prominent research frontier in the field of nonlinear partial differential equations, while simultaneously posing pervasive challenges in theoretical modeling across disciplines including elastic vibrations and geometric analysis. To date, the academic community has developed a robust and comprehensive theoretical framework for such equations, with existing results encompassing both critical and supercritical nonlinearities. Nevertheless, when employing variational methods to investigate multiple positive solutions of nonlocal equations defined on the four-dimensional ball, the loss of embedding compactness induced by critical terms remains a core bottleneck hindering further progress. This paper explores multiple positive solutions of nonlocal equations with both critical and supercritical nonlinear terms on the four-dimensional spherical domain. To rigorously establish the existence of multiple positive solutions, we integrate the Nehari manifold framework with advanced variational techniques. We harness the Brézis–Lieb lemma to circumvent the compactness deficiency arising from critical nonlinearities, and draw upon potential function analysis to compensate for the failure of compactness conditions caused by supercritical terms, thereby rigorously proving the existence of k distinct positive solutions for the equation. This result not only generalizes some existing conclusions in the literature but also offers new insights for further research on high-dimensional nonlocal problems.
This paper develops a dynamic optimal-control framework for the coupled visitor-flow and energy-consumption processes of large-scale scenic destinations. Zone-level visitor density is modelled by nonlinear ordinary differential equations and facility loads by first-order linear equations with control inputs and occupancy disturbances, giving a single constrained plant for which we establish non-negativity, forward invariance of a compact set, and existence and uniqueness of solutions. For the associated finite-horizon problem, we prove that an optimal control exists and, applying Pontryagin's minimum principle, derive the costate equations and show that the optimal routing law is bang-bang with an explicit switching function. In contrast, the optimal energy law is saturated affine in the costate. A receding-horizon controller re-solves the problem online and, equipped with terminal ingredients, is recursively feasible and nominally asymptotically stable. An extended Kalman filter driven by an Internet of Things (IoT) sensor network supplies the state estimate, and its expected error covariance is proved uniformly bounded under Bernoulli sensor dropout. On a three-zone, nine-facility benchmark, the closed loop raises comfort compliance from 50% to 89% of slots, cuts mean waiting time by 57%, reduces total energy by 2.9% and load variance by 10%, and degrades gracefully at dropout rates up to 20%; a linear predictive variant proves competitive, so the nonlinear model's empirical advantage is not established. Robust stability under disturbance and distributed-parameter extensions remain open.
In this paper, we provide a rigorous mathematical justification for a simplified model of a piezoelectric plate stabilized around a steady state. Asymptotic analysis of a 3D piezoelectric materials model with linear feedback control laws is performed as the thickness h of the plate tends to zero. We derive a 2D piezoelectric plate model which is consistent and stable for an approximation of the 3D model, ensuring its validity for the design of thin electromechanical devices. The energy decay for the 2D and 3D systems is established. Such a dimension reduction is very important because, when the plate thickness is very small, it simplifies numerical calculations and, above all, avoids the numerical calculation problems caused by distortion between the plate dimensions. Furthermore, the study reveals that when the thickness of a piezoelectric plate is very small, we no longer need the restrictions to only eleven stabilizable types of piezoelectric materials. The core contribution of this work is the direct integration of this fully coupled dimensional reduction with control theory.
In this paper, we study the existence and uniqueness of solutions, Bielecki–Hyers–Ulam stability, and Bielecki–Hyers–Ulam–Rassias stability for non-linear fractional Volterra Fredholm Hammerstein integro-delay dynamic systems with instantaneous impulses on time scale. Such systems provide a unified framework that encompasses both continuous and discrete models, making them highly appropriate for describing complex real-world phenomena involving memory effects, hereditary properties, and sudden perturbations. Sufficient conditions are established for the existence and uniqueness of solutions to the considered systems. In particular, the Picard operator and the Banach fixed point theorem are utilized to prove the existence and uniqueness of solutions. Moreover, we analyze the qualitative behavior of solutions by proving Bielecki–Hyers–Ulam stability and Bielecki–Hyers–Ulam–Rassias stability. To obtain these stability results, Grönwall’s inequality on time scales is used as the main analytical tool. For our results, some suitable assumptions are imposed along with appropriate Lipschitz conditions on the nonlinear terms. By constructing appropriate contractive mappings in a suitably defined Bielecki-type normed space, we develop a unified and systematic framework to handle the combined effects of integral operators, fractional dynamics, delay arguments, and impulsive perturbations. Finally, an illustrative example is provided to demonstrate the effectiveness and applicability of the theoretical findings.
This study investigates the relationship between intellectual capital efficiency and the financial performance of Islamic banks in Malaysia by employing dynamic modeling and empirical panel analysis. In knowledge-driven financial systems, intellectual capital, which includes human capital, structural capital, and capital usage efficiency, has a significant impact on creating a long-term competitive edge. This study sets up a system of differential equations to anticipate how bank performance would change over time based on the parts of intellectual capital and how they are invested. Therefore, this captures both theoretical dynamics and real-world consequences. The theoretical model delineates equilibrium conditions and demonstrates the local asymptotic stability of the intellectual capital system. The study employs the Value-Added Intellectual Coefficient (VAIC) approach, examining an unbalanced panel dataset of 11 comprehensive Islamic banks in Malaysia from 2012 to 2023, resulting in 132 bank-year observations. To find out how intellectual capital affects financial success, we use fixed-effects panel regression with robust standard errors. We look at return on assets (ROA) and return on equity (ROE). The empirical findings demonstrate that the overall efficiency of intellectual capital exerts a positive and significant influence on bank profitability. When dispersed, human capital efficiency is found to be the most important factor affecting financial performance, followed by capital employed efficiency. Structural capital efficiency, on the other hand, has no statistically significant effect. The results are similar across different model setups and diagnostic tests. These results highlight the importance of knowledge resources and efficient capital deployment in enhancing the competitiveness and sustainability of Islamic banking institutions. This study contributes to the field by integrating dynamic system modeling intellectual capital.
Load Frequency Control (LFC) is a fundamental issue in modern power systems, aimed at maintaining system frequency at its nominal value (50/60 Hz) while ensuring accurate regulation of tie-line power exchanges in interconnected areas. This study develops a comprehensive state-space modeling framework for single-area, two-area, and three-area power systems to support dynamic analysis and controller design. Integral controllers and optimal control strategies based on the Riccati equation-namely, Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG)-are implemented to enhance system performance. These controllers effectively minimize frequency and voltage deviations under varying load conditions, thereby improving power quality. To achieve faster and more precise control, a Digital Deadbeat Controller (DDC) is also proposed, ensuring rapid convergence to steady-state conditions. A comparative analysis across different system configurations highlights the steady-state frequency deviations and overall performance improvements. The study also addresses persistent challenges caused by memory-dependent nonlinearities such as backlash/deadband, which induce limit cycle (LC) oscillations and degrade system stability. Backlash nonlinearity, inherent in speed governors used in LFC, plays a significant role in these oscillations. Two methods are proposed to mitigate LC behavior: signal stabilization using deterministic or random inputs. Simulation results obtained using MATLAB/Simulink demonstrate the effectiveness of these approaches. The findings confirm that both DDC and signal stabilization techniques achieve the desired performance (Delta f = 0, t -> 0), indicating robust and efficient control suitable for practical power system applications.
Based on an adaptive universe model, this perspective article presents a phenomenological framework that correlates the dark energy equation of state w with the cosmic growth index gamma via the linear relation w(a) = -1 + eta(gamma(a)-0.55). Recognizing that the coupling between dark energy and structure formation may evolve with cosmic time, the framework is extended to a redshift-dependent formulation: w(z) = -1 + eta(z)[gamma(z)-0.55] + Delta wbg(z), where eta(z) captures the structure-dependent coupling and Delta wbg(z) accounts for intrinsic background evolution. Several physically motivated parameterizations of eta(z) are proposed, including continuous forms (smooth transition and oscillatory) and a phenomenological piecewise model aligned with distinct phases of structure formation history. Built upon an interacting dark sector model that strictly conserves energy and momentum, the framework maintains the spacetime geometry of General Relativity while naturally addressing both the Hubble tension (via enhanced late-time expansion) and the S8 tension (via suppressed structure growth). A hierarchical Bayesian testing roadmap with Fisher forecasts demonstrates that upcoming surveys (DESI, Euclid, Roman) can decisively detect couplings of magnitude |eta|greater than or similar to 0.05 at high significance. The framework yields distinctive, testable predictions-including correlated w(z) and f sigma 8(z) evolution, a gravitational slip parameter eta slip = 1 that distinguishes it from modified gravity theories, and scale-dependent signatures in the nonlinear regime-providing a comprehensive path to either validate or falsify the hypothesized dark energy-structure growth connection.
This paper investigates the numerical computation of magnetic fields in a Hall thruster, a process governed by a nonlinear elliptic boundary value problem. The model rigorously accounts for the influence of ferromagnetic materials, where the relative permeability is defined as a magnetic field-dependent function exceeding unity in core regions and set to unity elsewhere. Consequently, the model equations are inherently nonlinear, and their coefficients exhibit discontinuity across material interfaces. To solve this complex system, the finite difference method is applied on a uniform staggered mesh to derive a system of nonlinear difference equations with discontinuous coefficients. An iterative algorithm featuring a nested loop structure is presented to tackle this nonlinearity: an inner loop computes the magnetic field for a fixed relative permeability, while an outer loop updates the permeability distribution based on the current field solution. A critical challenge in such simulations is the convergence difficulty under high excitation due to strong nonlinearity and magnetic saturation. To address this, we propose a robust nested iterative algorithm enhanced with Aitken extrapolation. The method is validated through numerical simulations on a miniature Hall thruster model across three distinct coil ampere-turn configurations. Results highlight a critical distinction: while the standard fixed-point iteration performs adequately under low-to-moderate excitation, it fails to converge under the high-excitation condition. In contrast, the proposed Aitken-accelerated algorithm achieves stable convergence across all test cases, successfully resolving the convergence bottleneck in high-field scenarios. This advancement provides a robust framework for the magnetic circuit design of high-power Hall thrusters.
This work presents a theoretical framework to study the non-Markovian dynamics of a two-level quantum emitter interacting with a broadband squeezed electromagnetic reservoir, and both one- and two-photon interaction processes are incorporated. Mathematical modeling uses a time-convolution less projection operator technique. This yields a time-local master equation. The coefficients of this equation are derived from integrals over the reservoir's squeezed correlation functions: and . The model is validated through rigorous numerical simulation of the resulting dynamical equations. Testing involves computing key physical observables: the transient emission spectrum and the field linear entropy . These predictions are systematically analyzed against variations in squeezing parameters , coupling strengths , and detector bandwidth . The results confirm that the model successfully captures phase-dependent decoherence, spectral modulation, and purity oscillations. Notably, two-photon processes suppress decoherence under strong squeezing. The consistency between analytical derivations and numerical outcomes validates the framework. It is established as a predictive tool for quantum optics in engineered nonclassical environments. This study directly connects engineered reservoir properties specifically its nonclassical photon statistics to observable, time-dependent quantum phenomena. The findings offer fundamental insights and a predictive tool for quantum control, sensing, and information processing in tailored electromagnetic environments.
The premise of blind image deblurring revolves around the restoration of a clear image from a blurred one without prior knowledge of the specific blur kernel employed. Within this realm, various image priors have been extensively investigated and applied to address this inherently challenging problem. Throughout the image deblurring process, ensuring the resulting image intensities remain strictly non-negative is often imperative. However, prevalent numerical methodologies utilized to solve this issue have shown instances where the outcomes are not consistently favorable, leading to undesirable negative intensities that contribute to significant areas of darkness in the restored images. This study introduces a novel model designed to tackle the blind image deblurring problem by leveraging mean curvature. The proposed model not only assures positive outcomes but also confines the upper limit of image intensity values, thereby maintaining them within a predefined range. Additionally, new numerical algorithms are introduced, which not only restore the image but also estimate the blur kernel. Comparative analyses between these proposed algorithms and existing numerical techniques have been conducted to showcase the effectiveness and feasibility of our suggested approach.
The selection of an AI-based radar system to detect drones is a multi-criteria decision-making (MCDM) problem with many conflicting criteria. Exchanges between positive and negative aspects of each radar system in uncertain and incomplete information should be assessed by decision-makers. The traditional MCDM models are usually not effective in dealing with such complexities, especially when both positive and negative aspects are involved, and comparative reasoning is needed (dominance). In order to address these shortcomings, this article suggests an advanced model using the bipolar fuzzy dominance rough set (BFDRS) approach. The suggested method combines fuzzy logic to deal with uncertainty, dominance-based rough sets to model preferences, and bipolar fuzzy sets to manage dual-natured assessments. In order to operationalize the framework, we propose two new aggregation operators, namely bipolar fuzzy dominance rough dombi averaging (BFDRDA) and bipolar fuzzy dominance rough dombi geometric (BFDRDG), to combine expert opinions in the context of multiple criteria successfully. After that, we develop an MCDM methodology, which is the WASPAS method, within the framework of BFDRS, to prioritize AI radar alternatives in the presence of uncertainty. An extensive case study proves the relevance of the suggested model, and a comparative analysis with the currently existing ones proves its strength and higher decision-support abilities in complex and contradictory environments.
Natural convection and thermal transport in a porous square cavity with a wavy cold wall and a localized heat source on the left sidewall are numerically examined in this work. The cavity is filled with a fluid-saturated porous medium and is governed by the Darcy model under steady, laminar flow conditions with the Boussinesq approximation. A heater of fixed length is mounted on the left sidewall at three different points, namely the lower, center, and upper positions, while the right sidewall is maintained at a constant cold temperature and modeled with varying waviness in terms of amplitude and number of undulations. The remaining walls are considered adiabatic. The governing dimensionless equations for energy and stream functions are discretized using the finite difference technique and solved iteratively for various heater positions, right sidewall waviness, and Darcy-Rayleigh values after transforming the physical wavy domain into a rectangular computational domain. Results are presented in the form of Nusselt numbers, isotherms, streamlines, and heatlines. The findings indicate that the heater position has a significant influence on the convection flow, and heat transfer performance. The averaged heat transmission rate is improved by the right sidewall's increased waviness. Among the heater placements, lower heating produces the highest averaged heat transfer for higher Darcy-Rayleigh numbers, whereas center heating is more effective under weak convection conditions. This study provides useful insight into the thermal design of porous systems involving non-uniform heating, such as solar air conditioning, ventilation, and heating systems.
In this paper, we present an operational matrix method for integrating fractional Riccati differential equations (FRDEs) based on Haar wavelets. The fractional derivative is considered in the sense of Atangana's beta derivative, which effectively captures the memory and nonlocal characteristics of complex dynamical systems. The proposed technique employs a truncated Haar wavelet series and an operational matrix of integration to convert the governing FRDEs into a system of algebraic equations. These equations are then formulated as objective functions, and the unknown Haar wavelet coefficients are determined using a random search optimization procedure. This transformation reduces the computational complexity and provides an efficient framework for handling nonlinear fractional-order problems. The convergence and validity of the proposed method are demonstrated using several illustrative examples. The numerical results obtained with the proposed approach are compared with those from the Adams-Bashforth method, and the results show that the present technique provides more accurate approximations. Furthermore, to assess the performance and reliability of the method, several error metrics were computed, including the mean absolute deviation, root mean square error, Theil's inequality coefficient, Nash-Sutcliffe efficiency (NSE), and variance account for (VAF), for different numbers of collocation points. The results confirm that the Haar wavelet operational matrix method is simple to implement, computationally efficient, and highly accurate for solving fractional Riccati differential equations.
In this paper, we develop a mathematical model that describes the within-host co-dynamics of two arboviruses, Zika virus (ZIKV) and Chikungunya virus (CHIKV). The model is also modified to investigate the impact of various treatment strategies. The model incorporates four cell types: uninfected target cells, latently infected cells, actively infected cells, and antibodies. The analysis establishes that all solutions remain nonnegative and bounded overtime. It further reveals the presence of four distinct steady states: the disease-free steady state, the ZIKV-only steady state, the CHIKV-only steady state, and the coexistence steady state representing co-infection. The next-generation matrix technique was applied to determine the reproduction numbers for the ZIKV-only model, the CHIKV-only model, and the ZIKV-CHIKV co-infection model (denoted by RLZ, RLC and RL0 = max{RLZ, RLC}, respectively) as well as the invasion reproduction numbers RL,inv Z and RL,inv C which determine whether a virus can successfully invade an existing infection state. We conducted a mathematical analysis to determine the existence of equilibrium points and to establish the criteria for their global stability. Global stability is verified through the application of suitably constructed Lyapunov functions. The effects of four therapeutic strategies are included: (i) antiviral therapy that prevents viral infection of target cells, (ii) antiviral therapy that suppresses viral production, (iii) immune-stimulating treatment, and (iv) therapy that increases the rate of antibody circulation. Simulations show antivirals outperform immune-boosting strategies in clearing co-infection, while combining both offers synergy by suppressing replication and enhancing host defenses. The proposed model, along with the theoretical analysis, is new and offers a useful framework for studying viral co-infections.
To study system fault evolution using multi-modal data, multi-modal data are associated with multiple factors, and a mapping and superposition method for multi-modal data flows and factors is established. Multi-modal data and their characteristics are discussed. The mapping between multi-modal data flows and factors and the superposition of mapping results are investigated. The robustness of superposition operators, dynamic system modeling of factor evolution, and denoising performance of the mapping-superposition strategy are theoretically analyzed. The function of mapping in system fault evolution is explained, and a case study is provided. Results show that disaster data exhibit multi-modal characteristics. A multi-modal data flow consists of multiple single-modal data flows, which can be further subdivided into multifactor value data flows. These establish a mapping relationship between factors and time calibration and form a factor mapping model for single-/multi-modal data flows. It is necessary to consider the superposition forms of multi-factor value data flows mapped to the same factor, including scalar, vector, and max-min superposition forms, with corresponding mathematical models and superposition processes provided. The framework is embedded into a continuous-time dynamic model based on differential equations, supporting state estimation and optimal control. The proposed method is applied to analyze the fault process of an unmanned monitoring aircraft. The case is modeled with linear differential equations to simulate factor state trajectories and fault events. The results can provide a multi-dimensional data interface for the study of system fault processes, facilitating the analysis, prediction, early warning, and intervention of system faults.
At present, there are some shortcomings in the dynamic adaptability and subjectivity of coal mine safety performance evaluation, and it is difficult to realize the short-term safety performance evaluation with full staff participation. In this study, based on the Analytic Network Process-Technique for Order Preference by Similarity to an Ideal Solution (ANP-TOPSIS), a coal mine safety performance evaluation index system was constructed, and the evaluation index was optimized by a particle swarm optimization algorithm to improve the accuracy of dynamic index weight allocation. Emotional processing analysis technology is introduced, and the survey evaluation form is designed to quantify the subjective emotional tendency. Statistical methods such as the intra-group correlation coefficient, consistency test and regression model are used to improve the reliability of expert scoring data and quantitatively analyze individual subjective differences. Using the random forest classification method, combined with the term frequency-inverse document frequency (TF-IDF) to vectorize the text data, a bottom-up dynamic evaluation method of employee safety performance based on machine learning is established. The random forest model achieved an average F1-score of 0.929, with all six safety dimensions scoring above 0.8. The example shows that the scientific decision support for improving the coal mine safety performance level.
Addressing the challenge of quantitatively identifying deep thief zones in mature oilfields during the high water-cut stage, this study proposes a robust quantitative characterization model for thief channels based on the non-Euclidean, meshless Connection Element Method (CEM) to directly guide in-depth fluid diversion and integrated profile control and flooding treatments through automated flow path tracking rooted in a directed-graph depth-first search algorithm. To systematically capture the complex subsurface topological network, a comprehensive multi-parameter connectivity parameter system was constructed by integrating key dynamic indicators, including connection conductivity, connection volume, and path splitting coefficients. By dynamically coupling these parameters with the field-wide Lorentz coefficient, a dimensionless channeling factor was defined to establish a rigorous four-level quantitative standard—ranging from extreme channeling to matrix seepage—thereby successfully advancing preferential pathway evaluation from qualitative inference to spatial grading and precise localization. Quantitative validation against conventional commercial grid-based compositional simulators demonstrates the superior fidelity and performance forecasting efficiency of the proposed method: the CEM framework achieves an exceptionally accurate water-cut prediction Root Mean Square Error (RMSE) of approximately 3.8%. Crucially, by abstracting continuous domains into streamlined networks, it drastically compresses structural degrees of freedom, successfully accelerating the operational execution runtime from 7.3 s to a mere 1.6 s. Ultimately, this work provides a computationally highly efficient, physically sound novel approach for the reliable mapping and graded quantification of deep dominant channeling pathways in mature heterogeneous oilfields.
In this paper, we examined the suitability of epidemic models on networks to assess their potential application for detecting malware propagation patterns in peer-to-peer (P2P) computer networks. We analyzed how the Susceptible-Infected (SI), Susceptible-Infected-Susceptible (SIS), and Susceptible-Infected-Recovered (SIR) models, which were originally developed for biological viruses, can be applied to digital viruses. Using the Gnutella network dataset as a representative topology of P2P networks, we simulated infection scenarios to evaluate how scale-free network properties and the presence of high-degree nodes acting as super-spreaders influence the propagation speed and network saturation. The obtained results show that the examined models can be used and provide valuable insight into epidemic dynamics. However, the existing models are not perfect, and the introduction of additional states, such as L for latency and Q for quarantine, is proposed, since these are relevant for digital devices and digital viruses. More precisely, the absence of latent (L) and quarantine (Q) components leads to an overestimation of infection speed and an inability to model strategic isolation. Accordingly, this study provides empirical evidence that standard biological models are not sufficient for accurate predictions in the field of cybersecurity in P2P environments, and that future modeling efforts should move from basic compartmental models toward more advanced frameworks, such as SEIR and SIQR, to realistically capture malware activation delays and the impact of active defense strategies.
Colorectal cancer liver metastasis (CRLM) remains a major determinant of long-term outcomes. Existing clinical models are typically static and single-modality, limiting early warning and individualized follow-up. We prospectively enrolled 300 treatment-na & iuml;ve colorectal cancer patients. We collected preoperative three-phase contrast-enhanced ultrasound (CEUS) dynamic sequences, longitudinal serum marker measurements (EZH2/CD10) from preoperation through 12 months, and 35 clinical-pathological variables. The proposed Dynamic Modality Alignment Network (DMA-Net) includes (i) an imaging encoder based on an enhanced 3D-ResNet18 to extract perfusion kinetics, (ii) a molecular encoder using BiLSTM with temporal attention to model serial biomarkers, and (iii) a clinical encoder (MLP) for structured variables. A dynamic alignment module and cross-modal attention fuse modalities, followed by a discrete-time survival head that outputs month-specific conditional hazards and cumulative risks. On the held-out test set, the tri-modal model achieved an area under the curve (AUC) of 0.918 at 12 months with favorable calibration (Brier score 0.123), outperforming a traditional Cox model built from clinical variables (AUC 0.782, Brier score 0.177). Time-dependent evaluation showed stable AUCs from 3 to 12 months (0.904-0.919). Ablation experiments indicated that imaging and molecular branches contributed most to discrimination, whereas clinical variables improved calibration. Multimodal dynamic modeling integrating CEUS perfusion, longitudinal biomarkers, and clinical variables improves early warning and risk stratification for CRLM, and provides a practical framework to support personalized surveillance.
