Search Results (17)

This paper proposes a Distributed Adaptive Regularization Algorithm (DARN) for solving composite non-convex and non-smooth optimization problems in multi-agent systems. The algorithm employs a three-phase iterative framework to achieve efficient collaborative optimization: (1) a local regularized optimization step, which utilizes proximal mappings to enforce strong convexity of weakly convex objectives and ensure subproblem well-posedness; (2) a consensus update based on doubly stochastic matrices, guaranteeing asymptotic convergence of agent states to a global consensus point; and (3) an innovative adaptive regularization mechanism that dynamically adjusts regularization strength using local function value variations to balance stability and convergence speed. Theoretical analysis demonstrates that the algorithm maintains strict monotonic descent under non-convex and non-smooth conditions by constructing a mixed time-scale Lyapunov function, achieving a sublinear convergence rate. Notably, we prove that the projection-based update rule for regularization parameters preserves lower-bound constraints, while spectral decay properties of consensus errors and perturbations from local updates are globally governed by the Lyapunov function. Numerical experiments validate the algorithm’s superiority in sparse principal component analysis and robust matrix completion tasks, showing a 6.6% improvement in convergence speed and a 51.7% reduction in consensus error compared to fixed-regularization methods. This work provides theoretical guarantees and an efficient framework for distributed non-convex optimization in heterogeneous networks. Full article

As an effective computer-aided diagnostic tool, deep learning has been successfully applied to the classification of breast histopathological images. However, the performance of the deep model is data-driven, and it is difficult to obtain satisfied results when the number of histopathological images is small and labelling histopathological images is difficult. Moreover, in traditional deep learning methods, the representation of features is monotonous, which leads to the limitation of the classification performance of the model. This study proposes an auto-encoder reconstructed semi-supervised domain adaptation for a breast histopathological image classification algorithm. First, the model was pre-trained and transferred to extract high-level features of the sample images. Then, the encoding and decoding parts of the auto-encoder were used to reconstruct the feature representation learning and the sample feature reconstruction learning, respectively. This ensured that the useful information for the classification was purified and retained. At the same time, the domain discriminator was used to confuse the source and target domain features to enhance the learning ability of the model. Finally, the distribution difference of features at different depths of the auto-encoder was measured to minimize the discrepancy of feature distribution between domains, so as to complete the classification of histopathological images. Compared to the results of the comparative and ablation algorithms from the BreakHis to SNL datasets, the proposed method achieved the best results in terms of F1 score (93.40%), accuracy (95.24%), sensitivity (94.66%), and specificity (95.56%). The experimental results demonstrate that the proposed method achieves a remarkable classification performance. Full article

Phase-change thermal storage is essential for renewable energy utilization, addressing spatiotemporal energy transfer imbalances. However, enhancing heat transfer in pure phase-change materials (PCMs) has been challenging due to their low thermal conductivity. Rotational actuation, as an active method, improves heat transfer and storage efficiency. This study numerically examined the melting behavior of finned thermal storage units at various rotational speeds. The influence of speed was analyzed via melting time, rate, phase interface, temperature, and flow distribution. Results showed that rotational speed effects were non-monotonic: excessive speeds may hinder complete melting or reduce efficiency. There existed an optimal speed for the fastest melting rate and a limited speed range for complete melting. At the preferred rotation speed of 2.296 rad·s⁻¹, the utilization of PCMs in a finned tube could mitigate the risk of local overheating by 97.2% compared to a static tube, while improving heat storage efficiency by 204.9%. Full article

In order to respond to the greenhouse effect and achieve sustainable development, microbial-induced carbonate precipitation (MICP) technology based on the spraying method was used as a substitute for Portland cement to reinforce calcareous sand. In order to simulate the tide and determine the suitable concentration, the effects of the initial water level and cementing solution (CS) concentration on the reinforcement were analyzed. The results showed that the distributions of penetration resistance and equivalent calcium carbonate content mainly include two patterns: monotonically decreasing, and initially increasing and then decreasing. The fully saturated case only showed a dense, thin layer of calcium carbonate on the surface, and in the completely dry case, middle cementation was produced. When the initial water level was 0.5 m, the largest range of 60 cm of effective cementation appeared, and both the equivalent calcium carbonate content and penetration resistance were the highest because the microorganisms were more likely to migrate to the particle connection. The calcium carbonate generated by the MICP reaction played a role in increasing the water retention capacity of the sand. As the degree of cementation increased, the SWRC gradually moved up and the matrix suction corresponding to the same volume water content increased sequentially. Increasing the spraying times and the concentration of CS generated more calcium carbonate. The penetration resistance of higher CS concentrations was larger with the same calcium carbonate content. There was a linear relationship between the normalized penetration resistance and the normalized shear wave velocity. Full article

In this paper, the authors review and survey some results published since 2020 about (complete) monotonicity, inequalities, and their necessary and sufficient conditions for several newly introduced functions involving polygamma functions and originating from the estimation of the sectional curvature of the Fisher–Rao geometry of the Dirichlet distributions in the two-dimensional case. Full article

Hyperbolic complete monotonicity property ($\mathrm{HCM}$) is a way to check if a distribution is a generalized gamma ($\mathrm{GGC}$), hence is infinitely divisible. In this work, we illustrate to which extent the Mittag-Leffler functions $E_{\alpha },\alpha \in (0,2]$, enjoy the $\mathrm{HCM}$ property, and then intervene deeply in the probabilistic context. We prove that for suitable $\alpha$ and complex numbers z, the real and imaginary part of the functions $x\mapsto E_{\alpha }\left(zx\right)$, are tightly linked to the stable distributions and to the generalized Cauchy kernel. Full article

Hydrogen is receiving growing interest as an energy carrier to facilitate the shift to a green economy. However, hydrogen may cause the significant degradation of mechanical properties of structural materials, premature strain localisation, crack nucleation, and catastrophic fracture. Therefore, mechanical testing in hydrogenating conditions plays a vital role in material integrity assessment. Digital image correlation (DIC) is a versatile optical technique that is ideally suited for studying local deformation distribution under external stimuli. However, during mechanical testing with in situ electrochemical hydrogen charging, gas bubbles inherent to hydrogen recombination are created at the sample surface, causing significant errors in the DIC measurements, and posing significant challenges to researchers and practitioners utilising this technique for testing in harsh environments. A postprocessing technique for the digital removal of gas bubbles is presented and validated for severe charging conditions (−1400 mV vs. Ag/AgCl) under monotonic and cyclic loading conditions. Displacement fields and strain measurements are produced from the filtered images. An example application for measuring the crack tip opening displacement during a slow strain rate tensile test is presented. The limitations of the technique and a comparison to other bubble mitigation techniques are briefly discussed. It was concluded that the proposed filtering technique is highly effective in the digital removal of gas bubbles during in situ electrochemical hydrogen charging, enabling the use of DIC when the sample surface is almost completely obscured by gas bubbles. Full article

Fuzzy arithmetic is of great significance in dealing with vague information, especially the basic arithmetic operations (i.e., ⊕, ⊖, ⊗, ⊙). However, the classical and widely accepted accurate and approximate approaches, the interval arithmetic approach and standard approximation method, cannot output accurate or well-approximated expressions of the membership function, which may prevent decision makers from making the right decisions in real applications. To tackle this problem, this paper first discusses the relationships among the membership function, the credibility distribution, and the inverse credibility distribution and summarizes the relationships as several theorems. Then, by means of the theorems and the newly proposed operational law, this paper proposes an inverse credibility distribution approach that can output the accurate expression of the membership function for continuous and strictly monotone functions of regular $LR$ fuzzy intervals. To better demonstrate the effectiveness of the raised approach, the commonly-used $LR$ fuzzy interval, the symmetric trapezoidal fuzzy number, is employed, and several comparisons with the other two methods are made. The results show that the proposed approach can output an exact or well-approximated expression of the membership function, which the others cannot. In addition, some comparisons of the proposed approach with other methods are also made on a completion time analysis of a construction project to show the effectiveness of the proposed approach in real applications. Full article

In order to guide the optimization design of the nozzle of the aircraft-fixed gas fire extinguishing system, we studied the influence of nozzle geometric parameters including outlet–inlet area ratio, length–diameter aspect ratio, and wall roughness on the distribution of pressure and velocity in the nozzle on the basis of CFD simulations. Although the structure of the nozzle is axisymmetric, the spatial distribution of the pressure and velocity during the flow and release of gas extinguishing agent is not completely symmetric. It was found that both of the outlet–inlet area ratio ($\mathsf{\delta }$) and the length–diameter aspect ratio ($\xi$) had a significant impact on the distribution characteristics of the pressure and axial velocity in the nozzle. With the increase of $\mathsf{\delta }$, the average pressure at the outlet cross-section of the nozzle decreased monotonically, while the average axial velocity at the outlet increased approximately linearly. When $\xi \ge 2$, the uniformity of the pressure and velocity distribution at the nozzle outlet was significantly improved. Moreover, with the increase of $\xi$, the average pressure and the average axial velocity of the outlet both showed a non-monotonic change trend, and the optimal value of $\xi$ should be about 3.0. Compared with $\mathsf{\delta }$ and $\xi$, the influence of the nozzle wall roughness (${\epsilon }_N)$ on the flow and release characteristics of the extinguishing agent was weak. With the increase of ${\epsilon }_N$, the average pressure of the nozzle outlet increased slightly, while the average axial velocity at the nozzle outlet decreased slightly. Full article

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models. Full article

A monotonous relation between strain and measured electric resistance is highly appreciated in stretchable elastomer sensors. In real-life application the voids or technological holes of strained samples often induce non-homogeneous local strain. The present article focused on studying the effect of non-homogeneous local strain on measured direct current (DC) effective electric resistance (EER) on samples of natural rubber (NR), reinforced with 50, 60 and 70 phr of carbon black (CB). Samples were imparted geometrical inhomogeneities to obtain varied local strains. The resulting strain distribution was analyzed using Digital Image Correlation (DIC). EER exhibited a well-detectable influence of locations of inhomogeneities. Expectedly, the EER globally decreased with an increase in CB loading, but showed a steady increase as a function of strain for 50 and 60 phr over the complete testing protocol. Interestingly, for 70 phr of CB, under the same testing conditions, an alternating trend in EER was encountered. This newly observed behavior was explained through a novel hypothesis—“current propagation mode switching phenomenon”. Finally, experimentally measured EERs were compared with the calculated ones, obtained by summing the global current flow through a diversity of strain dependent resistive domains. Full article

Network caching is a technique used to speed-up user access to frequently requested contents in complex data networks. This paper presents a two-layer overlay network caching system for content distribution. It is used to define some caching scenarios with increasing complexity, which refers to real situations, including mobile 5G connectivity. For each scenario our aim is to maximize the hit ratio, which leads to the formulation of NP-complete optimization problems. The heuristic solutions proposed are based on the theory of the maximization of monotone submodular functions under matroid constraints. After the determination of the approximation ratio of the greedy heuristic algorithms proposed, a numerical performance analysis is shown. This analysis includes a comparison with the Least-Frequently Used (LFU) eviction strategy adapted to the analyzed systems. Results show very good performance, under the hypotheses of either known or unknown popularity of contents. Full article

We characterize the complete monotonicity of the Kilbas-Saigo function on the negative half-line. We also provide the exact asymptotics at $-\infty$, and uniform hyperbolic bounds are derived. The same questions are addressed for the classical Le Roy function. The main ingredient for the proof is a probabilistic representation of these functions in terms of the stable subordinator. Full article

We consider the Sparre Andersen risk process with interclaim times that belong to the class of distributions with rational Laplace transform. We construct error bounds for the ruin probability based on the Pollaczek–Khintchine formula, and develop an efficient algorithm to approximate the ruin probability for completely monotone claim size distributions. Our algorithm improves earlier results and can be tailored towards achieving a predetermined accuracy of the approximation. Full article

Rough set theory is an important approach for data mining, and it refers to Shannon’s information measures for uncertainty measurements. The existing local conditional-entropies have both the second-order feature and application limitation. By improvements of hierarchical granulation, this paper establishes double-granule conditional-entropies based on three-level granular structures (i.e., micro-bottom, meso-middle, macro-top ), and then investigates the relevant properties. In terms of the decision table and its decision classification, double-granule conditional-entropies are proposed at micro-bottom by the dual condition-granule system. By virtue of successive granular summation integrations, they hierarchically evolve to meso-middle and macro-top, to respectively have part and complete condition-granulations. Then, the new measures acquire their number distribution, calculation algorithm, three bounds, and granulation non-monotonicity at three corresponding levels. Finally, the hierarchical constructions and achieved properties are effectively verified by decision table examples and data set experiments. Double-granule conditional-entropies carry the second-order characteristic and hierarchical granulation to deepen both the classical entropy system and local conditional-entropies, and thus they become novel uncertainty measures for information processing and knowledge reasoning. Full article