Search Results (741)

In compressed sensing, it is believed that the L₀ norm minimization is the best way to enforce a sparse solution. However, the L₀ norm is difficult to implement in a gradient-based iterative image reconstruction algorithm. The total variation (TV) norm minimization is considered a proper substitute for the L₀ norm minimization. This paper points out that the TV norm is not powerful enough to enforce a piecewise-constant image. This paper uses the limited-angle tomography to illustrate the possibility of using the L₀ norm to encourage a piecewise-constant image. However, one of the drawbacks of the L₀ norm is that its derivative is zero almost everywhere, making a gradient-based algorithm useless. Our novel idea is to replace the zero value of the L₀ norm derivative with a zero-mean random variable. Computer simulations show that the proposed L₀ norm minimization outperforms the TV minimization. The novelty of this paper is the introduction of some randomness in the gradient of the objective function when the gradient is zero. The quantitative evaluations indicate the improvements of the proposed method in terms of the structural similarity (SSIM) and the peak signal-to-noise ratio (PSNR). Full article

This study addresses the practical stability analysis of Riemann-Liouville fractional-order nonlinear systems with time delays. We first establish a rigorous formulation of initial conditions that aligns with the properties of Riemann-Liouville fractional derivatives. Subsequently, a generalized definition of practical stability is introduced, specifically tailored to accommodate the hybrid dynamics of fractional calculus and time-delay phenomena. By constructing appropriate Lyapunov-Krasovskii functionals and employing an enhanced Razumikhin-type technique, we derive sufficient conditions ensuring practical stability in the $L_p$-norm sense. The theoretical findings are validated through illustrative example for fractional order nonlinear systems with time delays. Full article

Suppose X and Y are Banach spaces, K is a compact Hausdorff space, and $C(K, X)$ is the Banach space of all continuous X-valued functions (with the supremum norm). We will study some strongly bounded operators $T:C(K, X)\to Y$ with representing measures $m:\Sigma \to L(X,Y)$, where $L(X,Y)$ is the Banach space of all operators $T:X\to Y$ and $\Sigma$ is the $\sigma$-algebra of Borel subsets of K. The classes of operators that we will discuss are the Grothendieck, p-limited, p-compact, limited, operators with completely continuous, unconditionally converging, and p-converging adjoints, compact, and absolutely summing. We give a characterization of the limited operators (resp. operators with completely continuous, unconditionally converging, p-convergent adjoints) in terms of their representing measures. Full article

In this paper, a linearized mixed finite volume element (MFVE) scheme is proposed to solve the nonlinear time fractional fourth-order reaction–diffusion models with the Riemann–Liouville time fractional derivative. By introducing an auxiliary variable $\sigma =\Delta u$, the original fourth-order model is reformulated into a lower-order coupled system. The first-order time derivative and the time fractional derivative are discretized by using the BDF2 formula and the weighted and shifted Grünwald difference (WSGD) formula, respectively. Then, a fully discrete MFVE scheme is constructed by using the primal and dual grids. The existence and uniqueness of a solution for the MFVE scheme are proven based on the matrix theories. The scheme’s unconditional stability is rigorously derived by using the Gronwall inequality in detail. Moreover, the optimal error estimates for u in the discrete $L^{\infty }\left(L^2(\Omega )\right)$ and $L^2\left(H^1(\Omega )\right)$ norms and for $\sigma$ in the discrete $L^2\left(L^2(\Omega )\right)$ norm are obtained. Finally, three numerical examples are given to confirm its feasibility and effectiveness. Full article

The prediction of reservoir and caprock thickness is important in geological evaluations for site selection for aquifer underground gas storage. Therefore, high-resolution seismic identification of reservoirs and caprocks is crucial. High-resolution time–frequency decomposition is one of the key methods for identifying sedimentary layers. Based on this, we propose a least squares constrained spectral analysis method using a greedy fast shrinkage algorithm. This method replaces the traditional Tikhonov regularization objective function with an L1-norm regularized objective function and employs a greedy fast shrinkage algorithm. By utilizing shorter window lengths to segment the data into more precise series, the method significantly improves the computational efficiency of spectral analysis while also enhancing its accuracy to a certain extent. Numerical models demonstrate that compared to the time–frequency spectra obtained using traditional methods such as wavelet transform, short-time Fourier transform, and generalized S-transform, the proposed method can achieve high-resolution extraction of the dominant frequencies of seismic waves, with superior noise resistance. Furthermore, its application in a research area in southern China shows that the method can effectively predict thicker sedimentary layers in low-frequency ranges and accurately identify thinner sedimentary layers in high-frequency ranges. Full article

In this short note, we focus on complete translating solitons with a bounded $L_f^n$-norm of the second fundamental form and obtain two results. First, based on a Sobolev-type inequality and a Simons-type inequality, we establish a rigidity theorem of complete translating solitons. Second, based on the same Sobolev-type inequality and a Bochner-type inequality, a vanishing theorem regarding $L_f^p$ weighted harmonic 1-forms is proved. Full article

The increasing complexity of financial reporting has enabled the implementation of innovative accounting practices that often obscure a company’s actual performance. This project seeks to uncover manipulative behaviours by constructing an anomaly detection model that utilises unsupervised machine learning techniques. We examined a dataset of 149,566 Slovak firms from 2016 to 2023, which included 12 financial parameters. Utilising TwoSteps and K-means clustering in IBM SPSS, we discerned patterns of normative financial activity and computed an abnormality index for each firm. Entities with the most significant deviation from cluster centroids were identified as suspicious. The model attained a silhouette score of 1.0, signifying outstanding clustering quality. We discovered a total of 231 anomalous firms, predominantly concentrated in sectors C (32.47%), G (13.42%), and L (7.36%). Our research indicates that anomaly-based models can markedly enhance the precision of fraud detection, especially in scenarios with scarce labelled data. The model integrates intricate data processing and delivers an exhaustive study of the regional and sectoral distribution of anomalies, thereby increasing its relevance in practical applications. Full article

This study presents an image inpainting model based on an energy functional that incorporates the $L^p$ norm of the fractional Laplacian operator as a regularization term and the $H^{-1}$ norm as a fidelity term. Using the properties of the fractional Laplacian operator, the $L^p$ norm is employed with an adjustable parameter p to enhance the operator’s ability to restore fine details in various types of images. The replacement of the conventional $L^2$ norm with the $H^{-1}$ norm enables better preservation of global structures in denoising and restoration tasks. This paper introduces a diffusion partial differential equation by adding an intermediate term and provides a theoretical proof of the existence and uniqueness of its solution in Sobolev spaces. Furthermore, it demonstrates that the solution converges to the minimizer of the energy functional as time approaches infinity. Numerical experiments that compare the proposed method with traditional and deep learning models validate its effectiveness in image inpainting tasks. Full article

We introduce a novel family of compactly supported basis functions, termed Legendre Delta-Shaped Functions (LDSFs), constructed using the eigenfunctions of the Legendre differential equation. We begin by proving that LDSFs form a basis for a Haar space. We then demonstrate that interpolation using classical Legendre polynomials is a special case of interpolation with the proposed Legendre Delta-Shaped Basis Functions (LDSBFs). To illustrate the potential of LDSBFs, we apply the corresponding series to approximate a rectangular pulse. The results reveal that Gibbs oscillations decay rapidly, resulting in significantly improved accuracy across smooth regions. This example underscores the effectiveness and novelty of our approach. Furthermore, LDSBFs are employed within the collocation framework to solve Poisson-type equations and systems of nonlinear differential equations arising in energy transfer problems. We also derive new error bounds for interpolation polynomials in a special case, expressed in both the discrete ${(L}_2)$ norm and the Sobolev $\left(H_p\right)$ norm. To validate the proposed method, we compare our results with those obtained using the Legendre pseudospectral method. Numerical experiments confirm that our approach is accurate, efficient, and highly competitive with existing techniques. Full article

This paper proposes a novel sparse twin parametric insensitive support vector regression (STPISVR) model, designed to enhance sparsity and improve generalization performance. Similar to twin parametric insensitive support vector regression (TPISVR), STPISVR constructs a pair of nonparallel parametric insensitive bound functions to indirectly determine the regression function. The optimization problems are reformulated as two sparse linear programming problems (LPPs), rather than traditional quadratic programming problems (QPPs). The two LPPs are originally derived from initial L1-norm regularization terms imposed on their respective dual variables, which are simplified to constants via the Karush–Kuhn–Tucker (KKT) conditions and consequently disappear. This simplification reduces model complexity, while the constraints constructed through the KKT conditions— particularly their geometric properties—effectively ensure sparsity. Moreover, a two-stage hybrid tuning strategy—combining grid search for coarse parameter space exploration and Bayesian optimization for fine-grained convergence—is proposed to precisely select the optimal parameters, reducing tuning time and improving accuracy compared to a singlemethod strategy. Experimental results on synthetic and benchmark datasets demonstrate that STPISVR significantly reduces the number of support vectors (SVs), thereby improving prediction speed and achieving a favorable trade-off among prediction accuracy, sparsity, and computational efficiency. Overall, STPISVR enhances generalization ability, promotes sparsity, and improves prediction efficiency, making it a competitive tool for regression tasks, especially in handling complex data structures. Full article

Traditional color vision tests lack the sensitivity to detect subtle differences in individuals with normal color vision. The Konan ColorDx Cone Contrast Threshold (CCT) HD test allows the quantitative measurement of color discrimination thresholds for each cone type. This cross-sectional study established normative values for L-, M-, and S-cone contrast sensitivities and evaluated the effects of age and sex on color discrimination thresholds. Participants aged 15–79 years with normal color vision were included (n = 216; 55% female). CCTs were measured monocularly using the Konan ColorDx CCT HD test under standardized conditions, and the influences of age and sex on L-, M-, and S-cone sensitivities were evaluated. In all groups, L-cone sensitivity was the highest, followed by the M- and S-cone sensitivities. Overall contrast sensitivity was significantly higher in females than in males (mean difference = −0.041), especially for adolescents and young adults (20–24 years). Young adults outperformed middle-aged and older adults, with age-related decline most pronounced for S-cone sensitivity in those over 60. The right and left eye sensitivities did not differ. This study provides age- and sex-stratified normative data for the Konan Color Dx CCT HD test, supporting its use for clinical and occupational assessments. Full article

In the context of climate change, it becomes of utmost importance to limit the negative impact of industrial activities on carbon emissions, water stress, biodiversity loss, and natural resources depletion. Whether we consider the situation from a product-centered perspective (life cycle, R&D&I process, tools, methods, design, production, etc.) or from a human-centered perspective (habits, practices, fixation, strategic orientations, emotional sensitivity, etc.), coming years will represent a formidable upheaval for companies. To support this transition, various tools assessing products’ impact have been developed over the past decade. They aim at guiding decision makers, integrating new criteria to assess project success, and promoting the development and industrialization of solutions answering pressing environmental issues. If assessment is a key factor of success, it has become clear that processes and practices also need to evolve for practitioners to properly integrate sustainable requirements from the initial stages of their project. In that context, biomimicry, the approach aimed at taking nature as a model to support the design of more sustainable solutions, has been the center of growing interest. However, no integrated methods exist in the cosmetics sector to assess if a product is properly developed through biomimicry. This missing framework led to difficulties for cosmetic companies to support eco-design through biomimicry. In this article, we present a method called Biomim’Index developed by L’Oréal research and innovation sustainable development team to address three objectives: (i) to characterize cosmetic technologies according to whether they are based on bioinspiration, biomimetics or biomimicry; (ii) to guide the project’s leaders to identify key steps to improve existing cosmetic technologies through biomimicry; and (iii) to support the integration of biomimicry as an operational approach towards the development of new sustainable cosmetic technologies. This method, focusing on the problem-driven biomimetic approach is based on a combination of procedural requirements from the biomimetics TC288 18458:2015 ISO norm and environmental design requirements from L’Oréal for the Future (L4TF) commitments. Results present a proof of concept to outline the method’s efficiency and limits to support innovative eco-designed projects and value cosmetic technologies designed through biomimicry. Full article

Photovoltaic (PV) models are hard to optimize due to their intrinsic complexity and changing operation conditions. Root mean square error (RMSE) is often given precedence in classic single-objective optimization methods, limiting them to address the intricate nature of PV model calibration. To bypass these limitations, this research proposes a novel multi-objective optimization framework balancing accuracy and robustness by considering both maximum error and the L2 norm as significant objective functions. Along with that, we introduce the Random Search Around Bests (RSAB) algorithm, which is a parameterless metaheuristic designed to be effective at exploring the solution space. The primary contributions of this work are as follows: (1) an extensive performance evaluation of the proposed framework; (2) an adaptable function to adjust dynamically the trade-off between robustness and error minimization; and (3) the elimination of manual tuning of the RSAB parameters. Rigorous testing across three PV models demonstrates RSAB’s superiority over 17 state-of-the-art algorithms. By overcoming significant issues such as premature convergence and local minima entrapment, the proposed procedure provides practitioners with a reliable tool to optimize PV systems. Hence, this research supports the overarching goals of sustainable energy technology advancements by offering an organized and flexible solution enhancing the accuracy and efficiency of PV modeling, furthering research in renewable energy. Full article

This study compiles a comprehensive dataset on the occurrence, distribution, and potential impacts of Naturally Occurring Radionuclides (NORMs) near offshore oil and gas platforms. It encompasses data, including activities (Bq/l) and exposure levels (Msv), derived from various environmental matrices. A particular emphasis is placed on petroleum products and waste, such as produced water, scales, and sludges. The dataset contributes to a better understanding of the distribution of NORM wastes in marine environments, informs future radiological safety standards, contributes to the formulation of regulatory policies, and facilitates the design of mitigation strategies. The information—literature and data from five continents over the past 70 years—has been carefully compiled and organized to support intuitive analysis, making it a valuable tool for policymakers and researchers. Full article

We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the coefficients of these projections as functions of the Hurst index and the number of neighboring elements used for the projection. We derive recurrence relations for the coefficients of the two-sided projection. Additionally, we explore the norms of both types of projections. Certain special cases are investigated in greater detail, both theoretically and numerically. Full article