Search Results (23)

Complex fractal dimensions, defined as poles of appropriate fractal zeta functions, describe the geometric oscillations in fractal sets. In this work, we show that the same possible complex dimensions in the geometric setting also govern the asymptotics of the heat content on self-similar fractals. We consider the Dirichlet problem for the heat equation on bounded open regions whose boundaries are self-similar fractals. The class of self-similar domains we consider allows for non-disjoint overlap of the self-similar copies, provided some control over the separation. The possible complex dimensions, determined strictly by the similitudes that define the self-similar domain, control the scaling exponents of the asymptotic expansion for the heat content. We illustrate our method in the case of generalized von Koch snowflakes and, in particular, extend known results for these fractals with arithmetic scaling ratios to the generic (in the topological sense), non-arithmetic setting. Full article

Constructing an effective importance sampling density is crucial for structural reliability analysis via importance sampling (IS), particularly when dealing with performance functions that have multiple design points or disjoint failure domains. This study introduces an adaptive importance sampling technique leveraging an improved Markov chain Monte Carlo (IMCMC) approach. The method begins by efficiently gathering distributed samples across all failure regions using IMCMC. Subsequently, based on the obtained samples, it constructs the importance sampling density adaptively through a kernel density estimation (KDE) technique that integrates local bandwidth factors. Case studies confirm that the proposed approach successfully constructs an importance sampling density that closely mirrors the theoretical optimum, thereby boosting both the accuracy and efficiency of failure probability estimations. Full article

We present a novel method for localizing inequality within probability distributions by applying a recursive Hahn decomposition to the degree of uniformity—a measure derived from the exponential of Shannon entropy. This approach partitions the probability space into disjoint regions exhibiting progressively sharper deviations from uniformity, enabling structural insights into how and where inequality is concentrated. To demonstrate its broad applicability, we apply the method to both standard and contextualized systems: the discrete binomial and continuous exponential distributions serve as canonical cases, while two hypothetical examples illustrate domain-specific applications. In the first, we analyze localized risk concentrations in disease contraction data, revealing targeted zones of epidemiological disparity. In the second, we uncover stress localization in a non-uniformly loaded beam, demonstrating the method’s relevance to physical systems with spatial heterogeneity. This decomposition reveals aspects of structural disparity that are often obscured by scalar summaries. The resulting recursive tree offers a multi-scale representation of informational non-uniformity, capturing the emergence and localization of inequality across the distribution. The framework may have implications for understanding entropy localization, transitions in informational structure, and the dynamics of heterogeneous systems. Full article

Gender recognition from pedestrian imagery is acknowledged by many as a quasi-solved problem, yet most existing approaches evaluate performance in a within-domain setting, i.e., when the test and training data, though disjoint, closely resemble each other. This work provides the first exhaustive cross-domain assessment of six architectures considered to represent the state of the art: ALM, VAC, Rethinking, LML, YinYang-Net, and MAMBA, across three widely known benchmarks: PA-100K, PETA, and RAP. All train/test combinations between datasets were evaluated, yielding 54 comparable experiments. The results revealed a performance split: median in-domain F1 approached 90% in most models, while the average drop under domain shift was up to 16.4 percentage points, with the most recent approaches degrading the most. The adaptive-masking ALM achieved an F1 above 80% in most transfer scenarios, particularly those involving high-resolution or pose-stable domains, highlighting the importance of strong inductive biases over architectural novelty alone. Further, to characterize robustness quantitatively, we introduced the Unified Robustness Metric (URM), which integrates the average cross-domain degradation performance into a single score. A qualitative saliency analysis also corroborated the numerical findings by exposing over-confidence and contextual bias in misclassifications. Overall, this study suggests that challenges in gender recognition are much more evident in cross-domain settings than under the commonly reported within-domain context. Finally, we formalize an open evaluation protocol that can serve as a baseline for future works of this kind. Full article

The growing complexity of cybersecurity threats demands a robust framework that integrates various security domains, addressing the issue of disjointed security practices that fail to comply with evolving regulations. This paper introduces a novel information security management and compliance framework that integrates operational, technical, human, and physical security domains. The aim of this framework is to enable organizations to identify the requisite information security controls and legislative compliance needs effectively. Unlike traditional approaches, this framework systematically aligns with both current and emerging security legislation, including GDPR, NIS2 Directive, and the Artificial Intelligence Act, offering a unified approach to comprehensive security management. The experimental methodology involves evaluating the framework against five distinct risk scenarios to test its effectiveness and adaptability. Each scenario assesses the framework’s capability to manage and ensure compliance with specific security controls and regulations. The results demonstrate that the proposed framework not only meets compliance requirements across multiple security domains but also provides a scalable solution for adapting to new threats and regulations efficiently. These findings represent a significant step forward in holistic security management, indicating that organizations can enhance their security posture and legislative compliance simultaneously through this integrated framework. Full article

Although the effects of the environment on human health are well-established, the literature on the relationship between the quality of the environment and expenditures on healthcare is relatively sparse and disjointed. In this study, the Environmental Quality Index developed by the Environmental Protection Agency and heatwave days were compared against per capita Medicare spending at the county level. A general additive model with a Markov Random Field smoothing term was used for the analysis to ensure that spatial dependence did not undermine model results. The Environmental Quality Index was found to hold a statistically significant (p < 0.05), multifaceted nonlinear association with spending, as was the average seasonal maximum heat index. The same was not true of heatwave days, however. In a secondary analysis on the individual domains of the index, the social and built environment components were significantly related to spending, but the air, water, and land domains were not. These results provide initial support for the simultaneous benefits of healthcare financing systems to mitigate some dimensions of poor environmental quality and consistently high air temperatures. Full article

In this paper, we introduce an invariant by image viewpoint changes by applying an important theorem in conformal geometry stating that every surface of the Minkowski space ${\mathbb{R}}^{3,1}$ leads to an invariant by conformal transformations. For this, we identify the domain of an image to the disjoint union of horospheres ${\coprod }_{\alpha }{H}_{\alpha }$ of ${\mathbb{R}}^{3,1}$ by means of the powerful tools of the conformal Clifford algebras. We explain that every viewpoint change is given by a planar similarity and a perspective distortion encoded by the latitude angle of the camera. We model the perspective distortion by the point at infinity of the conformal model of the Euclidean plane described by D. Hestenesand we clarify the spinor representations of the similarities of the Euclidean plane. This leads us to represent the viewpoint changes by conformal transformations of ${\coprod }_{\alpha }{H}_{\alpha }$ for the Minkowski metric of the ambient space. Full article

A body may have a structural, thermal, electromagnetic or optical role. In wave propagation, many models are described for transmission problems, whose solutions are defined in two or more domains. In this paper, we consider an inverse source hyperbolic problem on disconnected intervals, using solution point constraints. Applying a transform method, we reduce the inverse problems to direct ones, which are studied for well-posedness in special weighted Sobolev spaces. This means that the inverse problem is said to be well posed in the sense of Tikhonov (or conditionally well posed). The main aim of this study is to develop a finite difference method for solution of the transformed hyperbolic problems with a non-local differential operator and initial conditions. Numerical test examples are also analyzed. Full article

In this paper, two-dimensional (2D) heat equations on disjoint rectangles are considered. The solutions are connected by interface Robin’s-type internal conditions. The problem has external Dirichlet boundary conditions that, in the forward (direct) formulation, are given functions. In the inverse problem formulation, the Dirichlet conditions are unknown functions, and the aim is to be reconstructed upon integral observations. Well-posedness both for direct and inverse problems is established. Using the given 2D integrals of the unknown solution on each of the domains and the specific interface boundary conditions, we reduce the 2D inverse problem to a forward heat 1D one. The resulting 1D problem is solved using the explicit Saul’yev finite difference method. Numerical test examples are discussed to illustrate the efficiency of the approach. Full article

This study delves into the intricate realm of recognizing handwritten Arabic characters, specifically targeting children’s script. Given the inherent complexities of the Arabic script, encompassing semi-cursive styles, distinct character forms based on position, and the inclusion of diacritical marks, the domain demands specialized attention. While prior research has largely concentrated on adult handwriting, the spotlight here is on children’s handwritten Arabic characters, an area marked by its distinct challenges, such as variations in writing quality and increased distortions. To this end, we introduce a novel dataset, “Dhad”, refined for enhanced quality and quantity. Our investigation employs a tri-fold experimental approach, encompassing the exploration of pre-trained deep learning models (i.e., MobileNet, ResNet50, and DenseNet121), custom-designed Convolutional Neural Network (CNN) architecture, and traditional classifiers (i.e., Support Vector Machine (SVM), Random Forest (RF), and Multilayer Perceptron (MLP)), leveraging deep visual features. The results illuminate the efficacy of fine-tuned pre-existing models, the potential of custom CNN designs, and the intricacies associated with disjointed classification paradigms. The pre-trained model MobileNet achieved the best test accuracy of 93.59% on the Dhad dataset. Additionally, as a conceptual proposal, we introduce the idea of a computer application designed specifically for children aged 7–12, aimed at improving Arabic handwriting skills. Our concluding reflections emphasize the need for nuanced dataset curation, advanced model architectures, and cohesive training strategies to navigate the multifaceted challenges of Arabic character recognition. Full article

Twenty-first century rural development (RD) demands a new paradigm of sustainability capable of addressing the difficulties and leveraging on the possibilities, such as climate change, demographic shift, international competitiveness, and rapid technological progress. Amidst these challenges, it is necessary to have a guiding framework from a long-term perspective that aids the integration of current RD policies while allowing space for location and community-specific innovations for implementing sustainable and resilient development strategies. India has witnessed several schemes and programmes for RD with exclusive objectives, varied focus areas, and separate domains, resulting in compartmentalisation in policy frameworks and disjointed implementation. Such initiatives were also often ideated from an urban perspective when it came to peri-urban rural areas or offered a generalist rural perspective (when referring to other rural regions, including those nested in ecological zones, thereby disregarding their local relevance). Accordingly, this study proposes a synchronised SMART village framework to tailor existing RD approaches for sustainable transformations aligned with the sustainable development goals and with a possibility of scaling its applicability in the local context. We initially conducted a bibliometric analysis to gain a comprehensive understanding of the emerging transformative approaches to RD, such as smart village (SV). Though in its nascent stage, the SV initiatives in India primarily envision information and communication technology enabled transformations in rural areas, often forcing villages to establish the relevance of such interventions. The study recognises key challenges to RD in India by using the problem tree analysis and further defines a SMART village framework that can be catalytic in transforming rural areas towards a sustainable and resilient state. Full article

We consider fractional mathematical models of fluid-porous interfaces in channel geometry. This provokes us to deal with numerical identification of the external boundary conditions for 1D and 2D time fractional parabolic problems on disjoint domains. First, we discuss the time discretization, then we decouple the full inverse problem into two Dirichlet problems at each time level. On this base, we develop decomposition techniques to obtain exact formulas for the unknown boundary conditions at point measurements. A discrete version of the analytical approach is realized on time adaptive mesh for different fractional order of the equations in each of the disjoint domains. A variety of numerical examples are discussed. Full article

It is a great challenge to solve nonhomogeneous elliptic interface problems, because the interface divides the computational domain into two disjoint parts, and the solution may change dramatically across the interface. A soft constraint physics-informed neural network with dual neural networks is proposed, which is composed of two separate neural networks for each subdomain, which are coupled by the connecting conditions on the interface. It is beneficial to capture the singularity of the solution across the interface. We formulate the PDEs, boundary conditions, and jump conditions on the interface into the loss function by means of the physics-informed neural network (PINN), and the different terms in the loss function are balanced by optimized penalty weights. To enhance computing efficiency for increasingly difficult issues, adaptive activation functions and the adaptive sampled method are used, which may be improved to produce the optimal network performance, as the topology of the loss function involved in the optimization process changes dynamically. Lastly, we present many numerical experiments, in both 2D and 3D, to demonstrate the proposed method’s flexibility, efficacy, and accuracy in tackling nonhomogeneous interface issues. Full article

In computer programming languages, partial additive semantics are used. Since partial functions under disjoint-domain sums and functional composition do not constitute a field, linear algebra cannot be applied. A partial ring can be viewed as an algebraic structure that can process natural partial orderings, infinite partial additions, and binary multiplications. In this paper, we introduce the notions of a one-prime partial bi-ideal, a two-prime partial bi-ideal, and a three-prime partial bi-ideal, as well as their extensions to partial rings, in addition to some characteristics of various prime partial bi-ideals. In this paper, we demonstrate that two-prime partial bi-ideal is a generalization of a one-prime partial bi-ideal, and three-prime partial bi-ideal is a generalization of a two-prime partial bi-ideal and a one-prime partial bi-ideal. A discussion of the $m_{pb1},(m_{pb2},m_{pb3})$ systems is presented. In general, the $m_{pb2}$ system is a generalization of the $m_{pb1}$ system, while the $m_{pb3}$ system is a generalization of both $m_{pb2}$ and $m_{pb1}$ systems. If $\mathrm{\Phi }$ is a prime bi-ideal of ℧, then $\mathrm{\Phi }$ is a one-prime partial bi-ideal (two-prime partial bi-ideal, three-prime partial bi-ideal) if and only if $\mho \backslash \mathrm{\Phi }$ is a $m_{pb1}$ system ($m_{pb2}$ system, $m_{pb3}$ system) of ℧. If $\mathrm{\Theta }$ is a prime bi-ideal in the complete partial ring ℧ and $\mathrm{\Delta }$ is an $m_{pb3}$ system of ℧ with $\mathrm{\Theta }\cap \mathrm{\Delta }=\varphi$, then there exists a three-prime partial bi-ideal $\mathrm{\Phi }$ of ℧, such that $\mathrm{\Theta }\subseteq \mathrm{\Phi }$ with $\mathrm{\Phi }\cap \mathrm{\Delta }=\varphi$. These are necessary and sufficient conditions for partial bi-ideal $\mathrm{\Theta }$ to be a three-prime partial bi-ideal of ℧. It is shown that partial bi-ideal $\mathrm{\Theta }$ is a three-prime partial bi-ideal of ℧ if and only if $H_{\mathrm{\Theta }}$ is a prime partial ideal of ℧. If $\mathrm{\Theta }$ is a one-prime partial bi-ideal (two-prime partial bi-ideal) in ℧, then $H_{\mathrm{\Theta }}$ is a prime partial ideal of ℧. It is guaranteed that a three-prime partial bi-ideal $\mathrm{\Phi }$ with a prime bi-ideal $\mathrm{\Theta }$ does not meet the $m_{pb3}$ system. In order to strengthen our results, examples are provided. Full article

Determining the optimal feature set is a challenging problem, especially in an unsupervised domain. To mitigate the same, this paper presents a new unsupervised feature selection method, termed as densest feature graph augmentation with disjoint feature clusters. The proposed method works in two phases. The first phase focuses on finding the maximally non-redundant feature subset and disjoint features are added to the feature set in the second phase. To experimentally validate, the efficiency of the proposed method has been compared against five existing unsupervised feature selection methods on five UCI datasets in terms of three performance criteria, namely clustering accuracy, normalized mutual information, and classification accuracy. The experimental analyses have shown that the proposed method outperforms the considered methods. Full article