Search Results (133)

Objective: Postpartum maternal readmission is a significant burden for patients as well as the health system. Postpartum readmission rate is a known factor in evaluating quality of care and in guiding potential beneficial interventions. Use of the Robson Group (RG) classification, initially used for analysis of cesarean section (CS) rates, has been recently expanded to evaluate other obstetrical outcomes. We aimed to describe the rates of postpartum maternal readmission across RG classification and to identify risk factors among the different maternity groups. Study Design: We carried out a retrospective register-based cohort study of all women who delivered >24 weeks gestation at a tertiary medical center over an 18-year period, with classification into the 10 RGs. Rates of postpartum readmission within 42 days of delivery were calculated for each group, as well as indications for readmission. The risk for maternal readmission was analyzed by univariate binary logistic regressions with comparison of results among RC groups, as well as by multivariate analysis models. Results: During the study period, 296,768 deliveries were classified according to Robson Group (RG) classification. The overall readmission rate for the study population was 0.5%. The following groups had a significant risk of readmission: RG 9 (transverse lie), 1.9%; RG 8 (multifetal pregnancies), 1.90=3%; RG 7 (multiparous breech pregnancies) 1.2% and RG2 (nulliparous pregnancies > 37 w, labor induction or prelabor cesarean), 1.2%. The most common indication for readmission among all RGs was fever (61.4%). Conclusions: Postpartum readmission rates varied among the RGs. The highest-risk groups were those with a higher risk of operative delivery, prolonged labor, or malpresentations. Interventions aimed to reduce the number of women in these groups; these included use of external cephalic version, vaginal delivery of breech, and multifetal pregnancies, all of which may be beneficial. Full article

This paper advances a Lie-group approach to measurement by identifying symmetry conditions that determine when effect sizes from different instruments can be meaningfully compared. Measurement transformations are modeled as elements of a two-parameter affine Lie group, and the associated Lie algebra describes the infinitesimal flow linking true scores and measurement-error variability across instruments. Within this framework, it is shown that the population standardized mean difference (SMD) is invariant across measures if and only if the transformation between them consists of a uniform affine transformation of true scores together with a uniform scaling of measurement-error standard deviations by the same factor. These symmetry conditions arise directly from the Lie algebra and ensure that the SMD remains constant along the exponential transformation flow; even slight departures from this symmetry produce a non-zero derivative of the SMD, marking a precise breakdown of invariance. A simulation study demonstrates how small nonlinear perturbations of the affine symmetry generate systematic distortions in the population true-score SMD. The results provide a mathematically grounded characterization of effect-size comparability and illustrate how continuous symmetries, Lie algebras, and transformation flows can clarify fundamental issues in measurement equivalence, meta-analysis, and longitudinal or cross-cultural research. Full article

Reaction–diffusion equations provide a fundamental framework for modelling spatial population dynamics and invasion processes in mathematical biology. Among these, Fisher’s equation combines diffusion with logistic growth to describe the spread of an advantageous gene and the formation of travelling population fronts. In this work, we investigate the one-dimensional Fisher’s equation using Lie symmetry analysis to obtain a deeper analytical understanding of its wave propagation behaviour. The Lie point symmetries of the partial differential equation are derived and used to construct similarity variables that reduce Fisher’s equation to ordinary differential equations. These reduced equations are then solved by a combination of direct integration and the tanh method, yielding explicit invariant and travelling-wave solutions. Symbolic computations in MAPLE are employed to compute the symmetries, verify the reductions, and generate illustrative plots of the resulting wave profiles. The computed solutions capture sigmoidal fronts connecting stable and unstable steady states, providing clear information about wave speed and shape. Overall, this study demonstrates that Lie group methods, combined with hyperbolic-function techniques, offer a powerful and systematic approach for analysing Fisher-type reaction–diffusion models and interpreting their biologically relevant invasion dynamics. Full article

Operational inefficiencies hinder progress in the architecture, engineering, and construction (AEC) industry. Platform-based approaches systematically utilize standardized and variable components and workflows to support customization and reuse across projects, making them viable solutions. This study addresses two research questions: (1) What are the current trends and challenges facing platform-based approaches in the AEC industry? (2) What research opportunities and future directions exist for platform-based approaches in the AEC industry? It conducted a bibliometric review and trend analysis using data collected from Engineering Village, Google Scholar, ScienceDirect, Scopus, SpringerLink, and Web of Science. Research interest increased from 16 publications between 2001 and 2014 to 18 publications in 2024. The UK dominates the field with 193 publications; however, collaboration across author groups remains weak. The trend analysis revealed an imbalanced research distribution, with 70% of publications focusing on product platforms and technological innovation, while governance, knowledge sharing, and stakeholders remain underexplored. Insights from the automotive and consumer goods industries highlight transferable strategies. The novelty and timeliness of this research lie in the multi-layer analyses, which integrated artificial intelligence-assisted bibliometric analysis with qualitative thematic and cross-industry analysis to generate insights on trends and challenges, translating them into a roadmap addressing AEC industry challenges. Full article

The problem of unsteady heat transfer between the gaseous and solid phases in two-phase flows with solid nanoparticles is considered. Based on a symmetry analysis, a solution to the unsteady heat conduction equation in spherical coordinates is obtained. Dependencies for the temperature profile and the Nusselt number are derived. The time-dependent change in the Nusselt number during the interaction between the solid particle and the surrounding medium is demonstrated. Full article

We consider the nonlinear reaction–diffusion equation on the unit sphere $u_t={\mathrm{\Delta }}_{{\mathbb{S}}^2}u+f\left(u\right)$, $f_{uu}\ne 0$, and carry out a complete Lie point symmetry analysis. Solving the associated determining system yields a rigidity theorem: for every genuinely nonlinear $f\left(u\right)$, the admitted symmetry algebra is $\mathfrak{so}\left(3\right)\oplus ⟨{\partial }_t⟩$, generated by the rotational Killing fields and time translation. We further show through a group classification that the source families that enlarge symmetries in Euclidean space do not produce any additional point symmetries on ${\mathbb{S}}^2$. From an optimal system of subalgebras, we derive curvature-adapted reductions in which the Laplace–Beltrami operator becomes a Legendre-type operator in intrinsic invariants. For the specific nonlinear source $f\left(u\right)=-e^u-2$, specific reduced ODEs admit a hidden one-parameter symmetry, yielding a first integral and explicit steady states on ${\mathbb{S}}^2$. Full article

The past decade has seen growing applications of the information flow-based causality analysis, particularly with the concise formula of its maximum likelihood estimator. At present, the algorithm for its estimation is based on differential dynamical systems, which, however, may raise an issue for coarsely sampled time series. Here, we show that, for linear systems, this is suitable at least qualitatively, but, for highly nonlinear systems, the bias increases significantly as the sampling frequency is reduced. This study provides a partial solution to this problem, showing how causality analysis can be made faithful with coarsely sampled series, provided that the statistics are sufficient. The key point here is that, instead of working with a Lie algebra, we turn to work with its corresponding Lie group. An explicit and concise formula is obtained, with only sample covariances involved. It is successfully applied to a system comprising a pair of coupled Rössler oscillators. Particularly remarkable is the success when the two oscillators are nearly synchronized. As more often than not observations may be scarce, this solution, albeit partial, is very timely. Full article

Surface crack detection and temporal evolution analysis are fundamental tasks in remote sensing and photogrammetry, providing critical information for slope stability assessment, infrastructure safety inspection, and long-term geohazard monitoring. However, current unmanned aerial vehicle (UAV)-based crack detection pipelines typically treat spatial detection and temporal change analysis as separate processes, leading to weak geometric consistency across time and limiting the interpretability of crack evolution patterns. To overcome these limitations, we propose the Longitudinal Crack Fitting Network (LCFNet), a unified and physically interpretable framework that achieves, for the first time, integrated time-series crack detection and evolution analysis from UAV remote sensing imagery. At its core, the Longitudinal Crack Fitting Convolution (LCFConv) integrates Fourier-series decomposition with affine Lie group convolution, enabling anisotropic feature representation that preserves equivariance to translation, rotation, and scale. This design effectively captures the elongated and oscillatory morphology of surface cracks while suppressing background interference under complex aerial viewpoints. Beyond detection, a Lie-group-based Temporal Crack Change Detection (LTCCD) module is introduced to perform geometrically consistent matching between bi-temporal UAV images, guided by a partial differential equation (PDE) formulation that models the continuous propagation of surface fractures, providing a bridge between discrete perception and physical dynamics. Extensive experiments on the constructed UAV-Filiform Crack Dataset (10,588 remote sensing images) demonstrate that LCFNet surpasses advanced detection frameworks such as You only look once v12 (YOLOv12), RT-DETR, and RS-Mamba, achieving superior performance (mAP_50:95 = 75.3%, F1 = 85.5%, and CDR = 85.6%) while maintaining real-time inference speed (88.9 FPS). Field deployment on a UAV–IoT monitoring platform further confirms the robustness of LCFNet in multi-temporal remote sensing applications, accurately identifying newly formed and extended cracks under varying illumination and terrain conditions. This work establishes the first end-to-end paradigm that unifies spatial crack detection and temporal evolution modeling in UAV remote sensing, bridging discrete deep learning inference with continuous physical dynamics. The proposed LCFNet provides both algorithmic robustness and physical interpretability, offering a new foundation for intelligent remote sensing-based structural health assessment and high-precision photogrammetric monitoring. Full article

We study the controllability of right-invariant bilinear systems on the complex and quaternionic special linear groups $\mathrm{Sl}(n,\mathbb{C})$ and $\mathrm{Sl}(n,\mathbb{H})$. The analysis relies on the Lie saturate$\mathrm{LS}(\Gamma )$, which characterizes controllability through convexity and closure properties of attainable sets, avoiding explicit Lie algebra computations. For $\mathrm{Sl}(n,\mathbb{C})$ with a strongly regular diagonal control matrix, we show that controllability is equivalent to the irreducibility of the drift matrix A, a property verified by the strong connectivity of its associated directed graph. For $\mathrm{Sl}(n,\mathbb{H})$, we derive controllability criteria based on quaternionic entries and the convexity of ${\mathbb{T}}^2$-orbits, which provide efficient sufficient conditions for general n and exact ones in the $2\times 2$ case. These results link algebraic and geometric viewpoints within a unified framework and connect to recent graph-theoretic controllability analyses for bilinear systems on Lie groups. The proposed approach yields constructive and scalable controllability tests for complex and quaternionic systems. Full article

This paper tackles the ill-posed inversion of initial conditions and diffusion coefficient for Burgers’ equation with a source term. Using optimal control theory combined with a finite difference discretization scheme and a dual-functional descent method (DFDM), it sets the unknown boundary function $g\left(\tau \right)$ and diffusion coefficient u as control variables to build a multi-objective functional, proving the existence of the optimal solution via the variational method. Symmetry analysis reveals the intrinsic connection between the equation’s Lie group invariances and conservation laws through Noether’s theorem, providing a natural regularization framework for the inverse problem. Uniqueness and stability are demonstrated by the adjoint equation under cost function convexity. An energy-consistent discrete scheme is created to verify the energy conservation law while preserving the underlying symmetry structure. A comprehensive error analysis reveals dual error sources in inverse problems. A multi-scale adaptive inversion algorithm incorporating symmetry considerations achieves high-precision recovery under noise: boundary error $<1\%$, energy conservation error $\approx 0.13\%$. The symmetry-aware approach enhances algorithmic robustness and maintains physical consistency, with the solution showing linear robustness to noise perturbations. Full article

This paper studies a mixed PDE containing the second time derivative and a quadratic nonlinearity of the Monge–Ampère type in two spatial variables, which is encountered in geophysical fluid dynamics. The Lie group symmetry analysis of this highly nonlinear PDE is performed for the first time. An invariant point transformation is found that depends on fourteen arbitrary constants and preserves the form of the equation under consideration. One-dimensional symmetry reductions leading to self-similar and some other invariant solutions that described by single ODEs are considered. Using the methods of generalized and functional separation of variables, as well as the principle of structural analogy of solutions, a large number of new non-invariant closed-form solutions are obtained. In general, the extensive list of all exact solutions found includes more than thirty solutions that are expressed in terms of elementary functions. Most of the obtained solutions contain a number of arbitrary constants, and several solutions additionally include two arbitrary functions. Two-dimensional reductions are considered that reduce the original PDE in three independent variables to a single simpler PDE in two independent variables (including linear wave equations, the Laplace equation, the Tricomi equation, and the Guderley equation) or to a system of such PDEs. A number of specific examples demonstrate that the type of the mixed, highly nonlinear PDE under consideration, depending on the choice of its specific solutions, can be either hyperbolic or elliptic. To analyze the equation and construct exact solutions and reductions, in addition to Cartesian coordinates, polar, generalized polar, and special Lorentz coordinates are also used. In conclusion, possible promising directions for further research of the highly nonlinear PDE under consideration and related PDEs are formulated. It should be noted that the described symmetries, transformations, reductions, and solutions can be utilized to determine the error and estimate the limits of applicability of numerical and approximate analytical methods for solving complex problems of mathematical physics with highly nonlinear PDEs. Full article

This review article explores the theory of control sets for linear control systems defined on two-dimensional Lie groups, with a focus on the plane ${\mathbb{R}}^2$ and the affine group $Af{f}_{+}\left(2\right)$. We systematically summarize recent advances, emphasizing how the geometric and algebraic structures inherent in low-dimensional Lie groups influence the formation, shape, and properties of control sets—maximal regions where controllability is maintained. Control sets with non-empty interiors are of particular interest as they characterize regions where the system can be steered between states via bounded inputs. The review highlights key results concerning the existence, uniqueness, and boundedness of these sets, including criteria based on the Ad-rank condition and orbit analysis. We also underscore the central role of the symmetry properties of Lie groups, which facilitate the systematic classification and description of control sets, linking the abstract mathematical framework to concrete, physically motivated applications. To illustrate the practical relevance of the theory, we present examples from mechanics, motion planning, and neuroscience, demonstrating how control sets naturally emerge in diverse domains. Overall, this work aims to deepen the understanding of controllability regions in low-dimensional Lie group systems and to foster future research that bridges geometric control theory with applied problems. Full article

This work investigates the stability analysis of linear control systems defined on Lie groups, with a particular focus on low-dimensional cases. Unlike their Euclidean counterparts, such systems evolve on manifolds with non-Euclidean geometry, where trajectories respect the group’s intrinsic symmetries. Stability notions, such as inner asymptotic, inner, and input–output (BIBO) stability, are studied. The qualitative behavior of solutions is shown to depend critically on the spectral decomposition of derivations associated with the drift, and on the algebraic structure of the underlying Lie algebra. We study two classes of examples in detail: Abelian and solvable two-dimensional Lie groups, and the three-dimensional nilpotent Heisenberg group. These settings, while mathematically tractable, retain essential features of non-commutativity, geometric non-linearity, and sub-Riemannian geometry, making them canonical models in control theory. The results highlight the interplay between algebraic properties, invariant submanifolds, and trajectory behavior, offering insights applicable to robotic motion planning, quantum control, and signal processing. Full article

This study explores the nonlinear dynamics and interdependencies among major commodity markets—Gold, Oil, Natural Gas, and Silver—by employing advanced chaos theory and information-theoretic tools. Using daily data from 2020 to 2024, we estimate key complexity measures including Lyapunov exponents, correlation dimension, Shannon and Rényi entropy, and mutual information. We also apply the stochastic SO(2) Lie group method to model dynamic correlations, and wavelet coherence analysis to detect time-frequency co-movements. Our findings reveal evidence of low-dimensional deterministic chaos and time-varying nonlinear relationships, especially among pairs like Gold–Silver and Oil–Gas. These results highlight the importance of using nontraditional approaches to uncover hidden structure and co-movement dynamics in commodity markets, providing useful insights for portfolio diversification and systemic risk assessment. Full article

In this paper, we present Lie symmetry analysis of a generalized (1+1)-dimensional porous medium equation characterized by parameters m and d. Through group classification, we examine how these parameters influence the Lie symmetry structure of the equation. Our analysis establishes conditions under which the equation admits either a three-dimensional or a five-dimensional Lie algebra. Using the obtained symmetry algebras, we construct optimal systems of one-dimensional subalgebras. Subsequently, we derive invariant solutions corresponding to each subalgebra, providing explicit formulas in relevant parameter regimes. These solutions deepen our understanding of the nonlinear diffusion processes modeled by porous medium equations and offer valuable benchmarks for analytical and numerical studies. Full article