Search Results (658)

Let $\mathcal{G}$ be a homogeneous Lie group of dimension $\varkappa$. In this article, we investigate the mapping properties of the Wolff-type potential ${\mathcal{W}}_{\vartheta ,2}$ on $\mathcal{G}$, associated with a homogeneous quasi-norm, and show that it coincides, up to an explicit dimensional constant, with the Riesz potential of doubled order $2\vartheta$ on $\mathcal{G}$. Using this identity together with Hedberg’s trick and a dyadic decomposition of the convolution kernel, we establish single-weight and two-weight boundedness inequalities for ${\mathcal{W}}_{\vartheta ,2}$ in the global Morrey spaces $M_p^{\mu }\left(\mathcal{G}\right)$. In contrast to the linear Riesz and Bessel–Riesz potentials, the Wolff potential belongs to a broader family of operators associated with quasilinear elliptic equations of p-Laplace type. We believe that these boundedness properties and the associated inequalities play an important role in the further advancement of nonlinear potential theory. Full article

Background: Manual bag-valve ventilation is a fundamental intervention in prehospital and emergency care but remains highly operator-related and frequently associated with inappropriate tidal volume delivery. Excessive or insufficient ventilation may adversely affect hemodynamics and clinical outcomes. Although real-time tidal volume monitoring has the potential to improve ventilation quality, its measurement performance across different airway conditions has not been sufficiently evaluated. Methods: This simulation-based repeated-measures study evaluated the measurement agreement and reliability of a newly developed tidal volume monitoring device during manual ventilation using an adult airway management manikin. Twenty emergency medical technicians performed bag-valve ventilation across three airway scenarios: face mask ventilation, endotracheal tube (ETT) intubation, and supraglottic airway (I-gel) insertion. For each scenario, 10 repeated breaths were recorded. Tidal volumes measured by the test device were compared with simulator-derived reference values. Measurement agreement was assessed using paired t-tests, Pearson correlation coefficients, effect sizes, and Bland–Altman analysis, while measurement reliability was evaluated using intraclass correlation coefficients (ICC). Mixed repeated-measures ANOVA was performed to examine interaction effects between airway scenario and operator characteristics. Results: The test device consistently overestimated tidal volume compared with the simulator reference across all airway scenarios (p < 0.001). Correlation between measurements was weak during mask ventilation (r = 0.174) but strong during ETT (r = 0.854) and I-gel (r = 0.709) ventilation, whereas Bland–Altman analysis demonstrated wider limits of agreement in mask ventilation and narrower limits under intubated conditions. ICC analysis revealed airway-dependent reliability, with minimal agreement in normal BVM ventilation but substantially higher agreement during ET-tube and I-gel intubation. Significant effects of airway scenario and operator characteristics (gender, age group, and clinical experience level) were observed, with notable interaction effects between airway scenario and clinical experience. Conclusions: Despite systematic overestimation, the tidal volume monitoring device demonstrated consistent and repeatable performance, particularly under secured airway conditions. Its primary clinical value may lie in reducing operator-related variability and supporting safer manual ventilation through real-time feedback, rather than replacing gold-standard measurement systems. Further algorithm refinement and clinical validation are warranted. Full article

Background/Objectives: The goal of the study is to examine associations of baseline residential elevation with blood biomarkers and newly reported multisystem chronic diseases among middle-aged and older adults, and to explore whether routine blood indicators may lie on these pathways. Methods: We analyzed 2011, 2015, and 2018 data from the China Health and Retirement Longitudinal Study (CHARLS). Wave 1 provided residential elevation, covariates, and 14 biomarkers; Wave 3 provided intermediate biomarkers; and Wave 4 identified 13 chronic disease outcomes based on participants’ reports of having received a physician diagnosis. High elevation was defined as ≥1500 m. Baseline and longitudinal samples included 11,371 and 9270 participants. Analyses used multivariable linear regression, attrition-weighted Cox models, logistic sensitivity models, restricted cubic splines, and exploratory mediation analysis. Results: High-elevation residence was associated with 9 of 14 biomarkers. Among 182 biomarker–disease Cox models, 35 associations had false-discovery-rate-adjusted q < 0.05, including 32 involving outcomes with at least 50 newly reported cases in the high-elevation group. Direct multiple-imputation inverse-probability-weighted (MI-IPW) Cox models showed that high-elevation residence was associated with higher estimated hazards over the interview interval for newly reported lung disease, kidney disease, arthritis, and hypertension; the first three associations remained significant in weighted logistic models. MI-IPW sensitivity analyses retained 31 of the 32 event-reliable biomarker–disease findings. No indirect effect survived multiple-comparison correction, including after excluding participants who had reported the relevant disease by Wave 3. Among the eight outcomes examined using restricted cubic splines, only kidney disease showed nominal evidence of nonlinearity (p = 0.017). Conclusions: Baseline residential elevation was associated with distinct biomarker patterns and heterogeneous disease risks. Routine blood biomarkers were prospectively associated with later disease reporting but did not provide stable evidence of mediation. These observational findings support cautious, disease-specific interpretation and further prospective and mechanistic research. Full article

We prove the existence and uniqueness of weak solutions to an obstacle problem for a nonlinear elliptic operator in divergence form. The variational inequality under consideration involves an integral over the domain of the Frobenius inner product of the operator $\mathcal{S}(z,\nabla u-\mathcal{O}(u\left)\right)$ with the gradient difference $\nabla (v-u)$, plus the Euclidean inner product of u and $v-u$, which is required to be nonnegative for all admissible functions v. The admissible set consists of functions in the Sobolev space $W^{1,2}(\mathrm{\Omega };{\mathbb{R}}^m)$ with prescribed Dirichlet boundary trace and lying above a given obstacle $\psi$ almost everywhere. The obstacle condition $v\ge \psi$ a.e. models a lower bound constraint (e.g., a membrane or a displacement limit) that the admissible functions must respect, while the boundary value $\delta$ prescribes the Dirichlet data. The principal part contains a solution-dependent shift $\mathcal{O}\left(u\right)$, which is Lipschitz continuous, while $\mathcal{S}$ is assumed to be globally Lipschitz and strongly monotone with respect to equal shifts, with quadratic growth and coercivity. This structural framework can be interpreted in terms of symmetry: the strong monotonicity condition expresses a quantitative symmetry property of $\mathcal{S}$ with respect to equal shifts, and the shift $\mathcal{O}\left(u\right)$ introduces a symmetry-breaking coupling. The smallness condition ensures that this asymmetry remains under control. However, we do not pursue a full group-invariance or Lie-symmetry analysis; the symmetry perspective is used here as a heuristic and interpretative tool. The main difficulty lies in the mismatch of shifts when comparing two admissible functions. This is resolved by a three-term decomposition of the monotonicity estimate, combined with Young’s inequality and Poincaré’s inequality, under the smallness condition that the product of the Lipschitz constant of $\mathcal{S}$, the Lipschitz constant of $\mathcal{O}$, and the Poincaré constant is bounded above by one quarter of the strong monotonicity modulus. Existence follows from the Kinderlehrer–Stampacchia theorem; uniqueness is obtained from the same decomposition. The result unifies and extends previous contributions that treated either the lower-order term or the shift coupling separately, and it does so within a unified quadratic framework that avoids the technical overhead of variable exponents and Young measures. Full article

Historical geographic information systems (HGIS) have evolved from auxiliary tools for digitizing historical materials and displaying maps into infrastructural research environments that connect multidisciplinary forms of historical spatial knowledge production. Yet infrastructure alone does not fully capture the field’s value-oriented epistemic goals. Building on existing research on HGIS and historical spatial data infrastructures (HSDIs), this integrative literature review proposes Historical Geomatics as an agenda-setting heuristic framework organized around the core question of how HGIS can restructure knowledge production in historical geography. It synthesizes the field’s knowledge traditions, workflows, analytical paradigms, and future directions. First, it clarifies that HGIS function across research traditions as a tool, a method, and an environment that can use HSDIs to organize heterogeneous historical materials. Second, it conceptualizes spatialization as a continuous workflow of spatial element recognition, geographic attribute assignment, standardized modeling, and validation and revision. Standardization and explicit uncertainty representation are treated as prerequisites for research quality, while platform-based and public HGISs extend the lifecycle of historical spatial data. Third, the review groups existing scholarship into four analytical paradigms: spatiotemporal reconstruction; urban morphology and spatial structure; networks, mobility, and social space; and place, landscape, and memory. Finally, it examines how geospatial artificial intelligence (GeoAI) is reshaping HGIS knowledge production and argues that Historical Geomatics may serve as an agenda-setting heuristic for the next stage of HGIS. The principal opportunities lie not in accumulating additional cases, but in strengthening HSDIs, improving multimodal automation, representing uncertainty explicitly, and rebalancing space and place, models and narratives, and technical efficiency and historical context. Full article

Let X be a compact Riemann surface of genus $g\ge 2$ equipped with an anti-holomorphic involution $\tau$, and let $\mathcal{M}(G_2)$ denote the moduli space of stable principal $G_2$-bundles over X. We study the fixed-point loci $\mathcal{M}{(G_2)}^{\sigma }$ of the involutions $\sigma ={\theta }^{\ast }\circ {\tau }^{\ast }$ on $\mathcal{M}(G_2)$, where $\theta$ is a Cartan involution of $G_2$ corresponding to one of its two real forms: the compact form $G_2^c$ and the split form $G_2^{2,2}$. We prove that $\mathcal{M}{(G_2)}^{{\sigma }_c}$ is connected with Euler characteristic 1, and that $\mathcal{M}{(G_2)}^{{\sigma }_s}$ has exactly $2^c$ connected components, where c is the number of connected components of the fixed-point set $X^{\tau }$. Each component is shown to be a compact, real-analytic, totally real submanifold of $\mathcal{M}(G_2)$ of real dimension $14(g-1)$. For the split form, we establish that $\chi (\mathcal{M}{(G_2)}^{{\sigma }_s})=3^{g-1}$ when $c=0$, where the factor $3=|W(G_2)|/|W(\mathrm{SO}(4))|$ arises from the Borel–Hirzebruch formula applied to the symmetric space $G_2^{2,2}/\mathrm{SO}(4)$. We further analyse the monodromy element $k_0\in \mathrm{SO}(4)$ associated to the non-trivial topological type over the ovals, proving that its centraliser in $G_2^{2,2}$ is exactly $\mathrm{SO}(4)$ and that its conjugacy class coincides with $G_2^{2,2}/\mathrm{SO}(4)$, with $e(\mathcal{O}(k_0))=3$. This supports a conjecture asserting $\chi \left(C_{(w_1,\dots ,w_c)}\right)=3^{g-1}$ for each component when $c\ge 1$. Finally, exploiting the Langlands self-duality $G_2^{\vee }\cong G_2$, we show that $\mathcal{M}{(G_2)}^{\sigma }$ is a $(B,B,B)$-brane in the hyperkähler manifold $T^{\ast }\mathcal{M}(G_2)$, and that it is self-specular: it is preserved by the derived Fourier–Mukai autoequivalence $\mathrm{\Phi }:D^b\left(\mathrm{Coh}(\mathcal{M}(G_2))\right)\stackrel{\sim }{\to }{D}^b\left(\mathrm{Coh}(\mathcal{M}(G_2))\right)$ induced by the Langlands self-duality, which restricts to a self-equivalence of $D^b\left(\mathrm{Coh}(\mathcal{M}{(G_2)}^{\sigma })\right)$. Full article

Let X be a compact Riemann surface of genus $g\ge 2$, ${\sigma }_X\in Aut\left(X\right)$ (the group of biholomorphic self-maps of X) an involution, and $F_4\left(\mathbb{C}\right)$ (one of the five exceptional complex simple Lie groups) the fixed-point subgroup of the outer involution $\sigma$ of the complex simple Lie group $E_6\left(\mathbb{C}\right)$ of type $E_6$. We study Galois triples $(E,f,\omega )$: a principal $F_4\left(\mathbb{C}\right)$-bundle E with an isomorphism $f:E\stackrel{\sim }{\to }{\sigma }_X^{*}E$ (here ${\sigma }_X^{*}E$ denotes the pull-back bundle, whose fibre over $x\in X$ is the fibre of E over ${\sigma }_X\left(x\right)$) satisfying a cocycle condition, together with a nontrivial finite-order automorphism $\omega$ commuting with f. The automorphism $\omega$ determines a semisimple element $g_e\in F_4\left(\mathbb{C}\right)$ and forces a reduction to the centraliser $Z_{F_4}\left(g_e\right)$, the Levi factor of a proper parabolic subgroup (a proper closed subgroup of $F_4\left(\mathbb{C}\right)$ containing a Borel subgroup, together with its natural reductive quotient, the Levi factor); by Ramanathan’s criterion, E is strictly polystable (built, via such a reduction, from stable bundles of equal slope, and in particular not itself stable). The main theorem proves that $E\left(V_{26}\right)$, the vector bundle associated with E via the representation $V_{26}$ (the smallest nontrivial irreducible representation of $F_4\left(\mathbb{C}\right)$), with fibre $V_{26}$, decomposes into k eigenspace sub-bundles, each fixed by ${\sigma }_X^{*}$, where $2\le k\le 25$ is determined by the eigenvalue pattern of $g_e$ in the 26-dimensional representation $V_{26}$. Structural corollaries show that the decomposition depends only on $\left[g_e\right]$, stratify the set of Galois triples by semisimple conjugacy classes, and give the splitting $\mathrm{Ad}\left({\iota }_{*}\left(E\right)\right)=E\left({\mathfrak{f}}_4\right)\oplus {⨁}_j{\mathcal{E}}_j$ with each summand preserved by ${\sigma }_X^{*}$. Since $Out\left(F_4\left(\mathbb{C}\right)\right)=\left\{1\right\}$ (i.e., every automorphism of $F_4\left(\mathbb{C}\right)$ is inner, meaning it is conjugated by an element of $F_4\left(\mathbb{C}\right)$ itself), there are exactly two conjugacy classes of involutions, with fixed-point subgroups $K_I=(\mathrm{Sp}(6,\mathbb{C})\times \mathrm{SL}(2,\mathbb{C}))/{\mu }_2$ and $K_{II}=\mathrm{Spin}(9,\mathbb{C})$; the general theorem specialises in each case in decompositions reflecting the product structure of $K_I$ and the spinorial geometry of $K_{II}$. Full article

Finite-dimensional closed-system gate synthesis is a geometric optimal-control problem on a compact Lie group, but global solutions require careful treatment of logarithm branches, determinant-one constraints, drift, anisotropic penalties, and amplitude limits. This paper assembles and extends a self-contained family of exactly solved benchmarks under explicit hypotheses. For a positive right-invariant quadratic metric, smooth stationary curves obey the Euler–Arnold equation and possess Lax invariants. Under fully actuated isotropic control on $\mathrm{SU}\left(n\right)$, the fixed-time minimum action is the squared Hilbert–Schmidt distance divided by twice the gate time and is generated by a minimum-norm skew-Hermitian logarithm. A finite eigenphase-unwrapping rule computes that logarithm, while the affine spectral-width cut wall and a branch-gap criterion distinguish stable selection from set-valued behavior. Drift is removed isometrically whenever the metric is invariant under the drift adjoint action. Weighted action and box-constrained time on maximal tori and arbitrary closed commuting subtori reduce to explicit period-lattice problems; the latter gives distinct strict determinant-one and projective period lattices for an ideal fSim sector. Numerical validation uses 1506 Haar-random targets through dimension 128, a complete cost-bounded dynamic-program cross-check for every target, 300 direct Cartesian branch enumerations, 120 random-conjugation tests with analytically prescribed spectra, 240 independently cross-checked random weighted-torus instances, a separate $\mathrm{SU}\left(256\right)$ stress target, large-cluster selector regressions, repeated timing trials, GRAPE–L-BFGS, a first-order sequential Krotov-type update with exact discrete propagation and Fréchet derivatives, randomized and drift-adapted CRAB–Powell bases, and cut-locus tests that exercise the implemented Schur/logarithm solver. When sparse actuation, decoherence, leakage, or uncertainty invalidates the ideal hypotheses, the exact results are positioned as ideal-model reference values, branch-aware seeds, and regression tests rather than as certificates for the enlarged objective. Full article

Current multi-modal pose estimation methods often suffer from severe localization divergence and prohibitive computational overhead when confronted with extreme scenarios such as sudden illumination variations, geometric degeneracy, and wheel slippage. To address these critical challenges, this paper presents a tightly coupled multi-modal pose estimation algorithm for mobile robots utilizing adaptive robust manifold filtering. First, a pre-integration-driven iterated error-state Kalman filter (iESKF) is formulated on the Lie group manifold to eliminate redundant re-integration workloads. Second, the Mahalanobis distance chi-square test and M-estimation are introduced to adaptively isolate non-Gaussian heavy-tailed noise caused by perception degradation. Finally, a perception health quantification system and a smooth degradation state machine are designed to handle concurrent perceptual blindness and wheel slippage. Experimental results demonstrate that the algorithm takes an average of only 12.8 ms per frame on edge computing platforms. Under severely degraded and composite environments, the algorithm limits the typical end-to-end closed-loop drift to 1.37 m (with a statistical average of 1.24 m) over a 100-m trajectory, translating to a relative translation error (RTE) of approximately 1.2% to 1.4%. This demonstrates an exceptional balance between high real-time efficiency and robust survivability. Full article

The study of the so-called $\Pi$-manifolds has been continued. This is a short name for almost paracontact almost paracomplex manifolds with a pair of metrics—Riemannian and pseudo-Riemannian—that are mutually related and compatible with the structure of the manifold. The well-known classification of these manifolds with respect to the Riemannian metric has been used to derive an alternative classification of the same manifolds with respect to the pseudo-Riemannian metric. The interrelations between the two classifications and the corresponding classification tensors are investigated. Finally, a three-dimensional explicit example on a Lie group is given, which illustrates the most interesting case of the transition from one classification to the other. Full article

Some groups of Diphyllobothriid tapeworms can cause foodborne or waterborne taeniasis, yet their systematics and evolution remain poorly understood. Based on mitochondrial genome data, this study reconstructed the phylogenetic trees of 11 cestode orders using maximum likelihood and Bayesian methods, clarified the valid species of Spirometra, traced the evolutionary history of four key ecological traits, and estimated the divergence times of major groups. Phylogenetic analyses supported Diphyllobothriidea and Bothriocephalidea as distinct clades, with Diphyllobothriidea forming a sister group to Haplobothriidea. In addition, three novel types of mitochondrial gene arrangements were identified in tapeworms, and variations in these arrangement types appear to correspond to changes in proglottid morphology. Species validation has shown that the available Spirometra mitogenomes represent only four valid species. Phylogenetic analysis identified two genetic lineages within S. mansoni, and a comparison of their representative sequences showed that the differences mainly lie in 12 PCGs, 7 tRNAs, 2 rRNAs, and 2 mNCRs. Ancestral character reconstruction suggested that tapeworms likely originated from freshwater fish hosts, with gradual adaptation to terrestrial hosts representing the main pathway of diversification, whereas transitions to marine environments were independent evolutionary events occurring in only a few groups. Molecular clock analyses indicated that tapeworm diversification began in the mid-to-late Oligocene, with episodic species radiations in different groups closely linked to host diversification and climatic changes. Notably, most groups within the family Diphyllobothriidae radiated during the Pleistocene, whereas Spirometra radiated during the Pliocene, coinciding with the origin of human-specialized cestodes. This study clarifies the phylogenetic position of diphyllobothriid tapeworms, infers the evolutionary patterns of ancestral traits across different tapeworm groups, and provides a theoretical basis for elucidating the origin and species diversity of tapeworms, as well as for assessing the transmission risk of pathogenic species. Full article

Quantum gate estimation and tomography pipelines routinely combine intrinsically defined likelihoods with priors or regularization terms specified in local Euclidean coordinates. This practice implicitly replaces the Haar reference measure on $SU\left(2\right)$ with Lebesgue measure, specifying a different statistical model rather than a reparametrization of the intended one. We show that omitting the associated chart-volume factor alters the optimization objective itself, modifying its gradient field and stationary-point structure. The gradient discrepancy $\nabla L_G-\nabla L_E=-\nabla \log J_{\exp }$ is nonzero for all $v\ne 0$ so that flat-coordinate surrogate objectives can converge to points that are non-stationary for the corresponding Haar-consistent objective even in regimes where local Gaussian approximations are assumed valid. We prove a formal non-equivalence proposition and validate a leading-order Fisher-information correction analytically and numerically. Large-scale multi-start optimization experiments ($N=\mathrm{11,900}$ runs) demonstrate that the discrepancy is regime dependent and most pronounced under moderate-to-strong regularization or limited data. The fix requires a single-line modification to any gradient-based optimizer. These results identify reference-measure selection as an explicit modeling decision with direct consequences for optimization and inference in gate-set tomography, randomized benchmarking, and Bayesian gate estimation on curved parameter manifolds; quantitative validation is restricted to single-qubit systems, though the mechanism extends to any regularized optimization on a curved parameter manifold. Full article

This paper introduces a graphical framework for smooth Lie group actions based on tangent orbit interactions. In contrast with classical intersection graphs, where vertices usually represent algebraic subobjects and edges record set-theoretic intersections, the present construction uses non-trivial orbits as vertices and creates edges from common nonzero tangent directions inside the fixed ambient embedding. Starting from infinitesimal tangent spaces generated by the action, we construct Lie orbit tangent graphs and analyze their adjacency structure, connectedness, completeness, degrees and diameter estimates. To describe local and global interactions, tangent fibers, local tangent orbit cliques, tangent orbit hypergraphs and incidence structures are introduced. We further develop separating tangent paths and use them to construct neighborhood systems and tangent-separating topologies. The framework gives a unified way to encode orbit-level tangent interactions and may be useful in geometric analysis, symmetry-based dynamical systems, differential topology and mathematical physics, where orbits and infinitesimal directions describe invariant motions, constraints or symmetry-reduced configurations. Several examples are included to illustrate how Lie group actions, graph structures, hypergraphs and tangent geometry interact within the proposed scheme. Full article

The $XY$ model is one of the basic models of statistical mechanics. It is often used for the description of important physical systems like ⁴He films and liquid crystals. In the present work, we consider the Ginzburg–Landau mean-field approximation of the 3D $XY$ model. We study the Lie-point symmetries of the corresponding Ginzburg–Landau Hamiltonian and the associated Euler–Lagrange equations for finite systems with film geometry and establish the variational symmetries among them in the presence of an external ordering field. Then, using the Noether theorem, we find conservation laws that allow us to obtain and present in analytic form, by means of Weierstrass elliptic, zeta, and sigma functions, the general solution of the so-called twisted boundary value problem in the absence of an external ordering field. It should be remarked that exact solutions in the absence of an external ordering field are only known within the so-called $\mathsf{\Psi }$-theory and some other mean-field-like theories. Full article

To address the problem of high-frequency roll disturbances generated during dynamic balancing in non-coaxial two-wheeled robots, this paper proposes a Rotation-Optimized Inertial–Visual SLAM system (ROIV-SLAM) for robust state estimation. The proposed approach adopts a decoupled architecture for translation and rotation estimation. In the front-end, an Extended Kalman Filter (EKF) is employed to fuse LiDAR, an inertial measurement unit (IMU), and wheel odometry to obtain an initial translation estimate. Meanwhile, a physical manifold constraint is constructed using the gravity vector and surface normals extracted from RGB-D point clouds, supporting stable rotation estimation under high-frequency disturbances through Lie-group-based optimization. In the back-end, a factor graph is established, and loop closure robustness is enhanced through vision–LiDAR scan matching. Experimental results indicate that ROIV-SLAM achieves improved trajectory consistency with respect to the optimized reference trajectory and more robust mapping performance compared with the evaluated baseline approaches in the tested scenarios. The results further suggest that introducing task-specific physical dynamic constraints and a decoupled estimation mechanism helps suppress high-frequency motion noise inherent to balancing robots, thereby improving the robustness of state estimation in complex environments. Full article