Background: Child mortality remains a major public health concern in South Asia, shaping population dynamics and affecting family well-being. Understanding household-level mortality patterns is essential for identifying high-risk groups and developing effective interventions. This study analyzes child mortality data from households in Eastern Uttar Pradesh, India, and Nepal, where deaths are rare but occasionally clustered within families. Methods: Four probabilistic models were applied to the observed number of child deaths per household: the Geometric distribution, the Inflated Geometric distribution to accommodate excess zeros, and the Himanshu compounded distribution. Model parameters were estimated using Maximum Likelihood Estimation (MLE). Model adequacy was evaluated through Chi-square goodness-of-fit tests comparing expected and observed household mortality counts. Results: All models showed strong consistency with the empirical data. Chi-square test results produced high p-values (>0.95), indicating that each model successfully captured the zero-heavy structure and the infrequent higher mortality events present in the datasets from both regions. Conclusions: The findings demonstrate that zero-inflated and compounded probabilistic models provide reliable representations of household-level child mortality in South Asia. These modeling approaches can support better identification of vulnerable households and improve the predictive accuracy of mortality assessments, contributing to more targeted public health strategies aimed at reducing child deaths.

Visual SLAM systems face significant performance degradation under dynamic lighting conditions, where traditional feature extraction methods suffer from reduced keypoint detection and unstable matching. This paper presents LDFE-SLAM, a novel visual SLAM framework that addresses illumination challenges through a Light-Aware Deep Front-End (LDFE) architecture. Our key insight is that low-light degradation in SLAM is fundamentally a geometric feature distribution problem rather than merely a visibility issue. The proposed system integrates three synergistic components: (1) an illumination-adaptive enhancement module based on EnlightenGAN with geometric consistency loss that restores gradient structures for downstream feature extraction, (2) SuperPoint-based deep feature detection that provides illumination-invariant keypoints, and (3) LightGlue attention-based matching that filters enhancement-induced noise while maintaining geometric consistency. Through systematic evaluation of five method configurations (M1–M5), we demonstrate that enhancement, deep features, and learned matching must be co-designed rather than independently optimized. Experiments on EuRoC and TUM sequences under synthetic illumination degradation show that LDFE-SLAM maintains stable localization accuracy (∼1.2 m ATE) across all brightness levels, while baseline methods degrade significantly (up to 3.7 m). Our method operates normally down to severe lighting conditions (30% ambient brightness and 20–50 lux—equivalent to underground parking or night-time streetlight illumination), representing a 4–6× lower illumination threshold compared to ORB-SLAM3 (200–300 lux minimum). Under severe (25% brightness) conditions, our method achieves a 62% tracking success rate, compared to 12% for ORB-SLAM3, with keypoint detection remaining above the critical 100-point threshold, even under extreme degradation.

Abstract High-precision sphere fitting with small spherical central angles remains a formidable challenge in precision measurement. In practical spherical surface measurements, factors such as occlusion often lead to point clouds corresponding to spheres with small spherical central angles, making accurate fitting difficult. To address this, we propose an improved AdaPoinTr model, termed SAdaPoinTr, which facilitates high-precision fitting by leveraging point cloud completion. The improvements integrate two key mechanisms: (1) Standard position encodings (e.g., linear transformations from Cartesian coordinates or simple MLP mappings) in existing models often fail to effectively capture the rotational symmetry inherent in 3D space and the unique geometric distribution of curved surfaces. This limitation is particularly critical for spherical data, which demands precise perception of curvature and directional variations. To overcome this, we introduce a Spherical Position Encoding (SPE) mechanism. SPE explicitly incorporates spherical coordinate information into the encoding process, significantly enhancing the network's ability to represent local spherical geometric structures within point clouds. (2) At the encoder stage, a novel Spherical Attention (SA) mechanism is introduced. This mechanism enhances attention computation by balancing feature similarity and geometric proximity, incorporating spherical geodesic distances between points as geometric constraints, and dynamically adjusting attention weights. Experimental results demonstrate that, even when completing point clouds of spheres with small spherical central angles with over 90% missing data, the proposed SAdaPoinTr method achieves over 50% improvement in fitting accuracy compared to the baseline AdaPoinTr network.

Abstract Life table analyses in entomology are primarily age‐structured, despite many insect species having distinct life stages (e.g., egg, larva, pupa, adult). Stage‐specific parameters are frequently reported in studies using age‐structured models, even though these parameters are not directly incorporated into the analyses A key challenge in stage‐structured modelling is accurately representing stage duration distributions. Simplified assumptions, such as geometric distributions, are often used for convenience but can introduce bias and lead to inaccurate conclusions. This study introduces a method to directly incorporate arbitrary stage duration distributions into stage‐structured models without relying on approximations. The approach is demonstrated with an example and validated through simulations. The method effectively captures population dynamics with non‐standard stage duration distributions. Properly parameterized stage‐structured models enable the identification of critical targets for applications, such as pest management, which is challenging with age‐structured models.

This paper examines a replacement model in which system replacement is carried out either at a random time [Formula: see text] or upon failure, rather than at a fixed time. The lifetime model is formulated for parallel systems with a random number of components, where each component follows a power series distribution. The optimization problem is investigated under a preventive age-replacement policy. The planned replacement time is assumed to be a random variable with a distribution from the proportional hazard rate family, and the lifetimes of system components are modeled using a Weibull distribution. The number of components is assumed to follow geometric, logarithmic, or zero-truncated Poisson distributions. The total expected cost rate function is used as the optimization criterion. Both analytical and numerical results are obtained, and the applicability of the proposed approach is demonstrated using a real data set.

This paper continues the analysis from Parts I and II, which addressed two-dimensional dispersed random composites. This part extends previous analytical studies by incorporating machine learning (ML) methods to quantitatively classify microstructures. The methodology relies on decomposing the expressions for the effective tensors into geometrical and physical parts, represented by structural sums and component-specific physical constants. The study concerns a two-phase composite with non-overlapping circular inclusions embedded in an isotropic elastic matrix. The random distribution of inclusions ensures macroscopic isotropy of the composite. A key outcome is the explicit demonstration of how the effective tensor depends on the geometric probabilistic distributions of inclusions and the computational protocols employed in their realization. These steps constitute the strategy for studying elastic fibrous composites, classifying them by macroscopic properties, and describing an analytical algorithm to derive expressions for computing the effective constants. The decomposition theorem and the construction of feature vectors consisting of structural sums are used as inputs to the ML analysis. As a result, we develop a computationally effective strategy to classify dispersed random composites indistinguishable by simple observations.

Overdispersion is a phenomenon which is quite common in many real-life count data sets and these variability often results due to an excessive number of zeros. To address this issue, zero-inflated distributions provide a flexible modeling approach capable of capturing high levels of dispersion. In this paper we introduce a new count distribution known as the zero-inflated transmuted geometric distribution. We explore its key statistical properties, reliability aspects and actuarial traits. Additionally we employ different estimation strategies and conduct a simulation study to assess the performance of the estimators. We demonstrate the practical utility of the proposed model through the analysis of three empirical data sets. Lastly, we also carry out the likelihood ratio test to justify the use of the proposed zero-inflated distribution.

During relatively low-speed rotation, the receiver captures the signal only when the antenna is turned in the direction of the satellite due to the long signal loss, a process in which the signal may be affected by noncontinuous reception. The conventional numerical preprocessing method for mitigating this is to reject the data with poor convergence as outliers. The conventional approach to this effect is to reject the poorly converged data as outliers, however, in non-continuous reception environments, simple rejection reduces the available satellite data and also affect the satellite geometric distribution, which further deteriorates the positioning results. In this paper, we propose a Global Navigation Satellite System (GNSS) receiver positioning algorithm based on weighting the statistical characteristics of discontinuous signals at lower rotational speeds. The method references the preorder available positioning results and employs a Kalman filtering algorithm designed based on independent model identification of observation weights to fully utilize the observation data of each satellite and improve the positioning accuracy. According to experimental data, the horizontal positioning error is reduced from 37.16 m with the original positioning algorithm to 28.31 m with the proposed method at 1/18 r/s, as an example.

ABSTRACT To address the challenges of low efficiency and poor robustness in point cloud registration under complex conditions – such as noise interference, sparse texture, and large initial pose deviations – we propose Voxel-Guided Normal-Similarity Iterative Closest Point (ViNS-ICP), an improved Iterative Closest Point (ICP) algorithm featuring voxel-guided normal-consistency keypoint extraction and bidirectional Fast Point Feature Histogram (FPFH) feature matching. First, a voxel-based normal-consistency scoring mechanism is introduced to evaluate the directional similarity of normals within each voxel, thereby selecting keypoints that possess both rich geometric detail and uniform spatial distribution. Next, a bidirectional nearest-neighbour strategy is employed for FPFH feature matching, augmented by a spatial distance threshold to eliminate geometrically inconsistent correspondences. Finally, a progressive ICP optimization scheme dynamically tracks the registration error at each iteration, enabling stable and controllable fine registration. Experimental results on the Stanford and 3DMatch point cloud datasets demonstrate that ViNS-ICP achieves high-precision, high-robustness alignment without requiring any initial pose estimate, improves computational efficiency by two orders of magnitude compared to Generalized Iterative Closest Point (GICP), and exhibits superior robustness and accuracy in complex environments.

Abstract The Nalun‐Nalati‐Hongliuhe suture zone, which constitutes the central axis of the Tianshan Orogenic Belt (TSOB), has been reactivated during the late Cenozoic. The Nalati fault, located within the suture zone, facilitates the investigation of the internal structural deformation of the TSOB. However, existing studies focus on the eastern segment of the Nalati fault, its western segment, located in the interior of the Tianshan Orogenic Belt, has received scant attention. Consequently, there remains a substantial gap in understanding the distribution, activity, and paleoseismic events associated with the Nalati fault. This study concentrates on the Tekes segment within the Ili Prefecture, utilizing remote sensing and comprehensive field surveys to delineate its geometric distribution and left‐lateral strike‐slip characteristics. Moreover, Through trench analysis and radiocarbon dating, we have identified four significant paleoseismic events. Utilizing the unmanned aerial vehicle mapping and the LaDiCaoz_v2.1 code, we measured approximately 3.0 m of horizontal displacement from a single seismic event. The application of OxCal age correction has enabled precise dating of these events with 95.4% confidence: Event 1 (1668–2040 years BP), Event 2 (5386–5911 years BP), Event 3 (5897–6651 years BP), and Event 4 (6740–7321 years BP). Our findings imply that the Tekes segment of the Nalati fault remains active during the Holocene, indicating the high seismic hazard of the region. The average left‐lateral slip rate along the Tekes segment is over 1.5 mm/yr during the Holocene. The Nalati fault accommodates approximately 1/3 of the total left‐lateral shear strain within the TSOB.

Abstract Transformer Coupled Plasma (TCP) sources are widely used in etching processes due to their ability to generate low-pressure, highly uniform, and high-density plasma. However, byproducts generated during etching accumulate on chamber walls, degrading plasma reproducibility and increasing both the frequency and duration of cleaning steps, ultimately reducing process throughput. To address this, plasma-based dry cleaning is commonly employed. In conventional dry cleaning processes, however, ion kinetic energies and incidence angles are not actively controlled, which limits further improvement in cleaning performance. In this study, we propose a method to enhance cleaning efficiency in TCP chambers by modulating charged particle dynamics via Lorentz force control through externally applied magnetic fields. Fluid plasma simulations were conducted under various magnetic field configurations to identify efficient field strengths and geometric distributions that enhance ion kinetic energy flux and guide ion incidence angles into the optimal range for wall cleaning. Specifically, the simulations incorporated Maxwell coils installed along the chamber sidewalls to implement realistic magnetic field distributions and verify their effectiveness in controlling ion flux to the chamber walls. Cleaning performance was assessed based on the ion kinetic energy flux and average ion incidence angle on the wall. The results confirm that magnetic field-based control of ion dynamics is an effective strategy for improving the efficiency of plasma-based dry cleaning processes.

This study aims to estimate aggregate loss (total loss) in private passenger car insurance data using the Bayesian approach of the Markov Chain Monte Carlo (MCMC) algorithm Gibbs-Sampling with the help of OpenBUGS software. The approach was carried out by modeling claim frequency data using Geometric and Negative Binomial distributions, and claim severity using Gamma and Lognormal distributions. Next, the prior for each model was determined, along with calculations for the likelihood function, joint distribution, marginal distribution, and posterior distribution. Since the resulting posterior distribution could not be calculated analytically, simulation was performed using OpenBUGS software to calculate it. Simulation was also used in predictive posterior calculations to estimate future aggregate losses. The results show that the Bayesian approach with the Markov Chain Monte Carlo method using the Gibbs-Sampling algorithm and its implementation through OpenBUGS software can be used to estimate aggregate loss. From the simulations used, it was found that the estimation of aggregate loss for private passenger car insurance is influenced by the selection of the frequency and severity of claims models. The Negative-Gamma Binomial model produced the highest posterior predictive estimate of aggregate loss at $75270.0, while the Geometric-Lognormal model provided the lowest estimate at $70500.0. Meanwhile, the model with the smallest standard deviation is the Negative Binomial-Lognormal model, which is $62720.0. This study contributes to insurance risk modeling, particularly in determining reserve funds and setting insurance premiums tailored to the target market of insurance companies.

The Global Positioning System (GPS) delivers precise, continuous, and globally accessible positioning and timing information through satellite-based measurements. Nevertheless, relying on a single satellite constellation imposes limitations related to satellite availability and geometric distribution, which can adversely affect the reliability of positioning, particularly in environments where visibility is reduced or satellite geometry becomes suboptimal. This study examines the performance of static Precise Point Positioning (PPP) as a function of fixing time using the Canadian Spatial Reference System Precise Point Positioning (CSRS-PPP) service under two processing scenarios: GPS-only and GPS+GLONASS. The analysis was conducted under open-sky conditions where multipath effects are negligible. Dual-frequency GNSS data were collected from ten spatially well-distributed stations, each observed continuously for 24 hours. Static PPP solutions were generated for fixing intervals beginning at 1 hour and incrementally increasing to 24 hours. The 24-hour static PPP solution served as the reference for evaluating the accuracy and stability of all other solutions. The results show that utilizing GLONASS observations alongside GPS leads to notable improvements in solution reliability and overall positioning stability throughout the fixing intervals. These benefits are particularly clear during shorter observation durations, especially the first one hour where the absolute errors in N, H, 2D and 3D are reduced by (2.2, 3, 1.8 and 2.22 cm) with GPS+GLONASS, respectively. As for the Easting component, the absolute errors determined from the two constellations are very tiny and rounded about zero. The benefits of adding GLONASS to GPS can also be noted during the first several hours when PPP solutions are most sensitive to satellite geometry and convergence behavior. Although the enhancement in mean absolute positional accuracy becomes marginal for longer observation periods, the multi-constellation configuration significantly reduces the occurrence of outliers and decreases the dispersion of coordinate residuals across the Northing, Height, 2D, and 3D components. The results demonstrate that even under optimal open-sky conditions, where multipath is virtually absent, the integration of GLONASS contributes measurably to improving the robustness and reliability of Static PPP. In summary, although the improvement of integrating GLONASS with GPS in static PPP in the average absolute accuracy is marginal after long fixing time comparing to GPS-alone, the benefits are significant for the first a few hours, specially the first fixing hour where the 3D quality obtained via one-hour static dual-frequency PPP with GPS+GLONASS can be reached after 3 to 4 hours fixing time using GPS-alone.

The development of next-generation sodium (Na)-ion batteries has garnered considerable attention as a sustainable and cost-effective alternative to lithium-ion systems. Among various Na-based battery configurations, anode-free Na batteries (AFSBs) offer notable advantages, including higher energy density and simplified manufacturing processes. Despite these promising features, several critical challenges must be addressed before AFSBs can be commercially realized.The main challenge is the uncontrolled growth of Na dendrites during plating, which can cause internal short circuits and safety risks. During stripping, dendrites often dissolve at their roots and form “dead Na,” leading to an irreversible loss of active sodium. Meanwhile, metallic Na reacts with the organic electrolyte to form a fragile and uneven solid electrolyte interphase (SEI). This heterogeneous SEI promotes nonuniform Na-ion flux and uneven Na deposition, exacerbating dendrite formation. Because it is easily punctured by dendrites, the SEI is repeatedly broken and reformed, consuming both Na and electrolyte. Altogether, these effects result in low Coulombic efficiency, rapid capacity loss, and additional challenges due to limited sodium supply. Therefore, constructing an artificial SEI layer to replace the native SEI has emerged as a key strategy to stabilize AFSBs.Current strategies include electrolyte modification and artificial coatings. Electrolyte modification enhances SEI stability and reduces side reactions with metallic Na. However, the resulting SEI still exhibits geometric and chemical inhomogeneity, causing localized hotspots and dendrite formation. For coatings, inorganic layers have a high Young’s modulus but are brittle, limiting their ability to withstand repeated Na plating/stripping. In contrast, polymeric coatings accommodate volume changes better due to their greater flexibility compared to inorganic materials but lack sufficient mechanical strength to suppress dendrite growth. Moreover, traditional solution-based techniques (spray, dip, spin coating) are hindered by surface tension, making truly conformal coating difficult.Therefore, simultaneously achieving a conformal coating layer with a homogeneous geometric and chemical distribution as well as optimal mechanical properties (high Young’s modulus combined with superior flexibility) remain critical yet unresolved challenges in the construction of artificial SEI layers.To create a well-defined and conformal SEI interphase on the anode of AFSBs, we employ an all-dry polymerization method, initiated chemical vapor deposition (iCVD), to form a homogeneous polymer thin film through free-radical polymerization. We selected an ionic conductive polymer, poly(2,2,3,3,4,4,5,5,6,6,7,7-dodecafluoroheptyl acrylate) (pDFHA), as the coating material due to its highly fluorinated molecular structure. At the interface between plated Na and pDFHA, the difluorocarbene and trifluoromethyl functional groups of pDFHA chemically react with metallic Na, generating inorganic secondary fluorinated species (i.e., NaF). Meanwhile, the polymeric structure remains intact in the upper layer of pDFHA, resulting in a horizontally homogeneous hybrid organic-inorganic artificial SEI interphase. This unique interphase effectively guides evenness Na-ion flux and isolates plated Na from the liquid electrolyte, enabling a uniform Na plating and eliminating the side reactions between plated Na and the electrolyte. More importantly, the inorganic NaF-rich bottom layer mechanically suppresses dendrite growth, while the flexible pDFHA upper layer can accommodate the large volumetric changes of the anode during repetitive plating and stripping cycles in AFSBs, thereby ensuring long-term anode stability. As a result, the cycling lifetime of the Na/aluminum asymmetric cell with the horizontally homogenous organic-inorganic interphase exhibited an extended cycling life by over 1000 h with an average CE of 99.6% compared to the 200 h and 93% of the pristine sample. In an anode-free full-cell configuration with the Na₃V₂(PO₄)₃ cathode, it delivered an enhanced capacity retention of approximately 88% after 100 cycles. This work provides new insights into the anode surface modification to enable stable cycling of anode-free batteries and contributes to their applications in practical devices.This work was supported by the US National Science Foundation, Award numbers CBET-2207302. M. Coclite, R.M. Howden, D.C. Borrelli, C.D. Petruczok, R. Yang, J.L. Yagüe, A. Ugur, N. Chen, S. Lee, W.J. Jo, A. Liu, X. Wang, and K.K. Gleason, Adv. Mater., 25, 5392-5423 (2013). Figure 1

This paper investigates the critical temperature of simply supported I-section steel beams subjected to pure bending under non-uniform heating conditions. A nonlinear numerical model was developed accounting for residual stresses, initial geometric imperfections, length-to-depth ratio, and non-uniform temperature distribution with different fire scenarios. The model is validated against laboratory tests conducted under comparable thermal conditions. Predicted critical temperatures are then benchmarked against the Eurocode 3 formulation. The results of the heat transfer analysis show that the temperature in the top flange is much lower than the temperature in the bottom flange and the web of the steel beam. Eurocode 3 gives unconservative results in most cases when calculating the critical temperature according to the compression flange. Eurocode 3 gives conservative results when calculating the critical temperature according to the compression flange for beams subjected to positive bending moments. The findings motivate further work toward improved assessment procedures for the critical temperature of steel beams in pure bending under spatially varying thermal exposure.

Holographic display has received extensive attention in recent years due to its unique display characteristics. With the discovery of the geometric phase, liquid crystal (LC) devices made by utilizing its excellent property that the phase modulation is independent of the optical path are compact and efficient, providing what we believe to be a new solution for miniaturized holographic devices. In this paper, we demonstrate dynamic holographic devices based on pattern-aligned LC micro-structures, featuring compact sizes and simple electronic driving circuits. The theoretical part of this work is based on the fast Fourier transform and uses self-written code for numerical calculations, which is the calculation and simulation of the two-dimensional light intensity distributions and propagation paths of Fresnel diffraction with arbitrary geometric phase distributions. The geometric phase distribution of the diffractive optical element corresponding to an arbitrary holographic pattern is obtained through the inverse Fourier transform calculation. By using a digital micro-mirror device (DMD), pixelated quasi-continuous modulation from 0 to 2 π of the LC geometric phase can be achieved. Through demonstrating four-frame images generated from two pattern-aligned LC cells, a method of fabricating low-cost and compact dynamic holographic devices based on the LC geometric phase is proposed, which provides a new option for practical applications such as dynamic digital signage and traffic e-signs.

A New Distribution Based on a Mixture of Two Geometric Distributions

We suggest a novel strategy in the theory of elastic plane composites. The macroscopic properties are quantified, and an analytical–numerical algorithm to derive expressions for the effective constants is designed. The effective elastic constants of dispersed random composites are given by new analytical and approximate formulas where the dependence on the location of inclusions is explicitly shown in symbolic form. This essentially extends the results of previous numerical simulations for a fixed set of material constants and fixed locations of inclusions. This paper extends the analysis from Part I, which addressed dispersed random conducting composites, to the two-dimensional elastic composites. Hill’s concept of Representative Volume Element (RVE), traditionally used in elastic composites, is revised. It is rigorously demonstrated that the RVE must be a fundamental domain of the plane torus, for instance, a periodicity parallelogram, since other shapes of RVE may lead to incorrect values of the effective constants. The effective tensors of the elasticity theory are decomposed into geometrical and physical parts, represented by structural sums and material constants of the components. Novel computational methodology based on such decomposition is applied to a two-phase isotropic composite with non-overlapping circular inclusions embedded in an elastic matrix. For the first time, it is demonstrated explicitly how the effective tensors depend on the geometric probabilistic distributions of inclusions and the computational protocols involved. Analytical polynomial formulas for the effective shear modulus for the moderate concentration of inclusions are transformed using the resummation methods into practical expressions valid for all concentrations of inclusions. The critical index for the effective shear modulus is calculated from the polynomials derived for the modulus.

The traditional subjectivity in cinematic photography aesthetic analysis is impeded by a lack of objective and systematic approaches for analysis. The current study mathematically translates and interprets the essence of cinema’s three pillars: composition, narrative structure, and rhythm within the domain of communication sciences. The study uses a combination of theoretical approaches in cinematic aesthetics and quantitative approaches like digital image processing, graph theory, and statistical analysis of shot lengths, and the theoretical foundations of cinematic aesthetics. The results illustrate that mathematical patterns like geometric distributions based on golden ratios in composition, different rhythmic cuts in dramatic scenes, and mathematical network patterns in traditional and contemporary narrative structures directly affect cinematic perception and meaning transfer. The significance and uniqueness of this proposed study are centered on building a connection between the qualitative approaches in film studies and the quantitative approaches in data science to provide a fresh paradigm for visual communications.

Modern manufacturing places increasing demands on assembly accuracy, revealing the limitations of conventional tolerance-based methods and studies that oversimplify multi-surface constraints into single-surface problems. To address this challenge, it is crucial to account for geometric distribution errors on multiple surfaces and constraints from multiple mating surfaces, analyzing their coupling effects in assembly. This paper presents a model that incorporates the effects of machining-induced geometric distribution errors and the constraints arising from multiple mating surfaces. The model determines contact points between two pairs of mating surfaces and calculates the spatial pose of the assembled part to predict assembly accuracy. The model validation was conducted in two stages: initial verification of fundamental principles through a two-dimensional simulation, followed by experimental validation. The experimental study involved mating surfaces with distinct geometric distribution errors manufactured by different machine tools. Assembly tests were performed under two distinct orientations of applied external forces. Results show close agreement between predicted and measured values, with a root mean square error (RMSE) below 2%, confirming the method’s effectiveness. The proposed method offers a solution to the assembly registration problem involving coupled multi-constraints and geometric distribution errors.