Search Results (264)

To investigate the underlying mechanisms of talent mobility in higher-education institutions influenced by factors such as the development environment, macroeconomic policies, and evaluation mechanisms, this paper proposes a nonlinear stochastic differential equation (SDE) dynamical model that incorporates time delays and multiplicative noise. We analyze the dynamic processes of talent mobility under varying conditions regarding the number of nodes, policy implementation cycles, and noise intensity. First, we employ central manifold theory and stochastic averaging methods to reduce the system to a one-dimensional averaged $It\widehat{o}$ equation. Subsequently, with $\tau$ as a parameter, we conduct an in-depth study of the system’s stochastic bifurcation behavior using the corresponding Fok–Planck–Kolmogorov equations. Finally, we validate the theoretical conclusions through numerical simulations. The results indicate that the number of nodes, policy delay, and noise intensity all have significant effects on system stability; an increasing delay induces random P-bifurcation in the system, and when $N\le 3$ and $N>3$, the system exhibits distinctly different steady-state behaviors. We also found that excessively high noise intensity disrupts system stability, whereas moderate noise intensity has a positive effect on stability. This study not only provides theoretical insights into the dynamic evolution mechanisms of talent mobility in regional universities but also offers valuable guidance for universities in formulating talent recruitment and evaluation policies. The methodology employed in this study opens up a promising avenue for analyzing complex dynamic problems in the field of sociology. Full article

This article presents results on four-dimensional CR submanifolds of the homogeneous nearly Kähler product manifold ${\mathbb{S}}^3\times {\mathbb{S}}^3$. In the research of CR submanifolds of ${\mathbb{S}}^3\times {\mathbb{S}}^3$, the most important role in the classification is played by the action of the almost product structure P. Here, the investigation of the action of the almost product structure on the tangent bundle of four-dimensional CR submanifolds of ${\mathbb{S}}^3\times {\mathbb{S}}^3$ is extended. Classifications are obtained for certain types of submanifolds whose almost complex distribution is almost product invariant, such as the class characterized by a special type of angle functions, as well as those whose tangent bundle is almost product invariant. The previously mentioned classes of four-dimensional CR submanifolds lead to the classification of those submanifolds that are locally usual product manifolds of Lagrangian submanifolds of ${\mathbb{S}}^3\times {\mathbb{S}}^3$ and curves. Full article

We develop an information-geometric framework for describing quantum state-update processes associated with measurement and statistical distinguishability. The approach is based on the quantum relative entropy and the quantum Fisher information metric, which together induce a natural Riemannian geometry on the manifold of quantum states. Using the second-order expansion of relative entropy, we show how the Fisher metric governs the local structure of distinguishability between nearby states and defines a corresponding thermodynamic length. This geometric structure provides an effective description of finite quantum state transitions in terms of fluctuation geometry and information-space distance. The formalism is applied to thermal two-level systems and harmonic oscillator states, illustrating how the Fisher metric encodes susceptibilities, fluctuations, and geometric transition costs. We also discuss the relation between thermodynamic length, dissipation bounds, and optimal paths in state space. Within this framework, wave function collapse is interpreted not as a microscopic dynamical mechanism, but as an effective state-update process that admits a geometric characterization in the manifold of density operators. The resulting perspective unifies concepts from quantum information theory, thermodynamics, and differential geometry within a common operational framework based on statistical distinguishability. Possible connections with quantum speed limits, entanglement geometry, and holographic relations between relative entropy and gravitational dynamics are briefly discussed. Full article

In this paper, we discuss extensions of the canonical quantization procedure in quantum field theories. We focus specifically on S-matrix representation as a T-exponent. This extension involves flat bundles on certain infinite dimensional functional manifolds of local time. The motivating problem is first principles treatment of bound states in quantum chromodynamics as well as precision physics of the hydrogen atom and the muonium. Our main results include systematic treatment of flat bundles in an infinite dimensional setting, generalization of Hamiltonian evolution and functional renormalization group evolution equations in quantum field theories. We discuss several results from finite dimensional theory that have analogies in the functional setting. This includes construction of moduli space of flat connections and isomonodromic deformations. One of the outcomes of our analysis is a construction of a rich family of functional flat bundles with rational connections. This class of connections exhibits a rich set of mathematical properties. In particular, we construct examples of the fundamental groups of spaces which have a definable continuum of generators. Physical states correspond to points in the moduli space of bundles on these spaces. On the physics side of things, we conclude that spacetime notions, such as spaces of particle configurations, emerge effectively as spectral sets of functional differential operators. Full article

This article investigates the geometric and structural properties of almost pure metric pseudo-F-manifolds, with a focus on Walker 4-manifolds. We analyze integrability conditions and characterize pure metric pseudo-F-Kählerian Walker manifolds, identifying criteria under which the Riemann curvature tensor vanishes. The study also examines the existence of Killing vector fields and Ricci soliton structures. In particular, we show that integrability conditions for almost pure metric pseudo-F-structures are governed by partial differential equations and highlight the role of constant functions in defining pure metric pseudo-F-Kählerian properties. Additionally, we investigate special connections with torsion that preserve certain tensor structures, exploring their relationship to Codazzi pairs and the conditions necessary for torsion-freeness. Full article

Software effort estimation (SEE) serves as a cornerstone of effective software project management, and case-based reasoning (CBR) stands out as one of the most extensively adopted approaches within this domain. Nevertheless, CBR-based SEE models are still plagued by two critical challenges: conventional case retrieval mechanisms lack the ability to differentiate the relative importance of various features, and data scarcity remains a persistent bottleneck. Both issues significantly compromise the estimation accuracy and interpretability of the models. To address these limitations, we propose a SHAP–Mixup synergistic framework that enhances both feature-aware similarity learning and data distribution modeling. Specifically, we introduce (1) a stability-aware SHAP-weighted similarity metric that integrates both the magnitude and variance of feature contributions to improve retrieval robustness, and (2) a density-aware Mixup augmentation strategy that generates synthetic samples guided by local data manifold structure rather than random interpolation. Experimental results on seven benchmark datasets demonstrate that the proposed method reduces MAE and MSE by up to 20.2% on average compared to baseline CBR models, while consistently improving Pred(0.25). Furthermore, by enhancing model interpretability, the proposed method equips project managers with actionable insights into the key drivers of software effort, thereby facilitating more informed and efficient resource allocation. Building on these findings, this study provides a novel and effective pathway for developing SEE models that are more accurate, robust, and transparent. Full article

This paper investigates a discrete-time fractional-order predator–prey model incorporating a double Allee effect in the prey population, derived from a fractional differential system via the piecewise constant argument method to capture both memory effects and density-dependent constraints. We establish the existence and local stability of all biologically meaningful equilibria and show that the interaction between fractional memory and the double Allee threshold significantly influences the stability of the coexistence state. Through the integration of linear stability analysis and center manifold reduction, we are able to obtain explicit conditions for Neimark–Sacker and period-doubling bifurcations. The system exhibits rich dynamics, including periodic oscillations, quasi-periodicity, and chaos. The double Allee effect plays a key role in shaping system stability. To suppress instability and chaotic behavior, feedback and hybrid control strategies are applied and shown to be effective. Numerical simulations are given to confirm the results obtained by the theoretical analysis and to show the transitions among different dynamical states, in which the fractional-order memory and multiple Allee effects play important roles. Full article

Let $\beta$ be a contact form on a compact smooth manifold X and $v_{\beta }$ its Reeb vector field. This study applies the general results of different authors regarding Hodge structures that are transversal to a given foliation to the special case of 1-dimensional foliation generated by the Reeb flow $v_{\beta }$. The de Rham differential complex ${\Omega }_{\mathtt{basic}}^{*}(X,v_{\beta })$ of so-called basic forms relative to $v_{\beta }$-flow differential forms is the focus of this investigation. By definition, basic forms vanish when being contracted with $v_{\beta }$, and so do their differentials. We prove that under the change of $\beta ⇝{\beta }_1=\beta +df$, where a function $f:X\to \mathbb{R}$ such that $df\left(v_{\beta }\right)>-1$, the differential complexes ${\Omega }_{\mathtt{basic}}^{*}(X,v_{{\beta }_1})$ and ${\Omega }_{\mathtt{basic}}^{*}(X,v_{\beta })$ are canonically isomorphic. We investigate when the 2-form $d\beta$ and its powers deliver nontrivial elements in the basic de Rham cohomology $H_{\mathtt{basic}d\mathcal{R}}^{*}(X,v_{\beta })$ of the differential complex ${\Omega }_{\mathtt{basic}}^{*}(X,v_{\beta })$. Answers to these questions contrast sharply in the cases of a closed X and an X with boundary. Building on the work of Raźny, we show that on a closed manifold X equipped with a transversal to the Reeb flow Hodge structure that satisfies the Basic Hard Lefschetz Property, the basic de Rham cohomology $H_{\mathtt{basic}d\mathcal{R}}^{*}(X,v_{\beta })$ is a topological invariant of X. Full article

As a rigorous and comprehensive foundation for electromagnetic information theory (EIT), we develop a general theory that elucidates the universal stochastic structure of radiated electromagnetic (EM) fields and induced currents in generic EM information transmission systems. The framework encompasses arbitrary random scatterers, input information fields, and EM mutual coupling. The system is modeled as a multiply connected, arbitrary Riemannian manifold within the language of differential geometry. Our approach exploits exact Green’s functions (GFs) on manifolds to construct a novel electromagnetic random field theory (EM-RFT). Interpreted as response functions localized on the surfaces of transceivers and scatterers, the GFs allow us to treat the internal physical details of the EM system as a black box, redirecting analytical attention toward external input–output relations in line with signal processing and communication theory. This integration of random fields (RFs), electromagnetics, and GFs yields a unified framework for deriving and characterizing the stochastic structure of arbitrary EM information transmission systems. We rigorously establish that EM random fields satisfying Maxwell’s equations can always be constructed using system GFs driven by external information fields. The theory further decouples stochastic input RFs from random fluctuations associated with the communication medium (e.g., scatterers), and introduces general correlation propagators valid for arbitrary EM links. Using the Karhunen–Loève expansion, all EM random fields are represented as sums of random variables, providing both a simulation framework for arbitrary EM RFs and a basis for evaluating mutual information between input and output spatial domains at arbitrary locations in the system. Full article

Background: High-grade serous ovarian carcinoma (HGSOC) is the most common and lethal subtype of epithelial ovarian cancer and is frequently diagnosed at advanced stages. Because currently available blood-based biomarkers have limited performance in early-stage disease, there is a need to identify circulating biomarker candidates associated with early-stage HGSOC. In this retrospective multi-institutional case–control study, we evaluated whether serum extracellular vesicle (EV)-associated protein signatures distinguish early-stage HGSOC from healthy controls. Methods: Serum samples (n = 252) were obtained retrospectively from multiple institutions and included healthy controls and patients with early- and advanced-stage HGSOC. EV-associated proteins were profiled using liquid chromatography–tandem mass spectrometry (LC–MS/MS) and proximity extension assay (PEA) to identify candidate proteins enriched in early-stage HGSOC. Selected candidates were evaluated by enzyme-linked immunosorbent assay (ELISA), and tissue-level expression was examined in early-stage HGSOC specimens. A multimarker combination model was generated using a smoothed empirical estimate of hyper-volume under the manifold (SHUM) approach and internally assessed by leave-one-out cross-validation. Results: Ten EV-associated serum proteins were prioritized on the basis of differential expression and fold change and were confirmed to be expressed in early-stage HGSOC tissues. In ELISA-based analyses, the combined 10-protein EV panel distinguished early-stage HGSOC from healthy controls with an area under the curve (AUC) of 0.99 in the study dataset, whereas MUC16 (CA-125) showed substantially lower performance in this comparison. The SHUM-based model yielded a true-positive rate of 0.971, a false-positive rate of 0.057, and a Matthews correlation coefficient of 0.915 in the analyzed cohort. Several candidate proteins were differentially enriched in EV fractions but not in matched whole serum. Conclusions: Serum EV-associated proteins are altered in early-stage HGSOC and define a multi-protein signature associated with this disease state in a retrospective case–control setting. These findings support further evaluation of EV-based biomarker candidates in clinically representative and prospectively collected cohorts that include benign gynecologic conditions, symptomatic patients, and pre-diagnostic samples. Full article

Recent advancements in satellite optical reconnaissance have elevated the sun angle to a critical factor in orbital pursuit-evasion games. The stringent imaging constraints imposed by sun angle and relative distance induce non-smoothness in the terminal region of such differential games, significantly complicating equilibrium-solution derivation. To address this challenge, we formulated a novel differential game model where the pursuer minimizes the time-to-entry into the evader’s effective imaging region. We first constructed a sequence of low-dimensional manifolds that collectively cover the terminal region, solving the differential game with this sequence to yield the Nash equilibrium. Subsequently, we approximated the terminal region using a smooth manifold of identical dimensions, enabling a computationally efficient approximate solution. Both methodologies demonstrate broad applicability to orbital differential games featuring non-smooth terminal regions. Simulation results confirm that the approximation error becomes pronounced only under extreme initial sun angles, though this error remains acceptable for practical space reconnaissance applications. Full article

This paper synthesizes classical results in Hodge theory, curvature positivity, and vanishing theorems to give a concise curvature–cohomology criterion for the projectivity of compact Kähler manifolds. While each analytic component—Yau’s solution of the Calabi conjecture, the Bochner–Kodaira–Nakano identity, and Kodaira’s embedding theorem—is well-known, their combination yields a transparent geometric criterion: if the first Chern class $c_1\left(M\right)$ admits a semi-positive real $(1,1)$ representative that is strictly positive at some point (or equivalently has a maximal rank n somewhere), then M is projective. Beyond the maximal rank case, we refine Girbau’s classical vanishing theorem to obtain an optimal rank-sensitive bound: if $2\pi c_1\left(M\right)$ has a semi-positive representative whose pointwise rank is k somewhere, then $H^{p,0}\left(M\right)=0$ for all $p>n-k$. This sharpens the classical Girbau–Griffiths–Harris vanishing theorem and quantifies how partial positivity of a Ricci representative constrains Hodge cohomology. We situate these criteria alongside classical tests (Kodaira integrality and Moishezon) and numerical descriptions of the Kähler cone (Demailly–Paun), discuss deformation-invariance properties, and relate them to RC positivity and Campana–Peternell-type statements. Examples illustrate the sharpness of the hypotheses, and we survey the effective bounds—ranging from rigorous uniform high ampleness results to conjectural optimal constants—with clear distinction between proven theorems, refinements of classical results, and open problems. The contribution of this work lies not in new analytic techniques but in (1) isolating a sharp curvature condition at the level of $c_1\left(M\right)$; (2) organizing classical tools into a direct projectivity criterion; and (3) clarifying the rank-dependent vanishing behavior that follows from partial positivity. Full article

The framework of the research whose part of results are published in this work is the category of real vector bundles over finite dimensional differentiable manifolds. The objects of studies are gauge structures on these vector bundles. We are interested in the dynamical properties of the holonomy groups of Koszul connections as well as on their topological properties, i.e., properties that are of homological nature. For the most part the context is the subcategory of Lie algebroids. In addition to other investigations, three open problems are studied in detail. (P1-Affine Geometry): When is a Koszul connection an affine connection? (P2-Riemannian Geometry): When is a Koszul connection a metric connection? (P3-Fedosov Geometry): When is a Koszul connection a symplectic connection? In the category of tangent Lie algebroids our homological approach leads to deep relations of our homological ingredients with the open problem of how to produce labeled foliations the most studied of which are Riemannian foliations. On a Lie algebroid we define two families of differential equations, the family of differential Hessian equations and the family of differential gauge equations. The solutions of these differential equations are implemented to construct homological ingredients which are key tools for our studies of open problems we are concerned with. We introduce Koszul Homological Series. This notion is a machine for converting obstructions whose nature is vector space into obstructions whose nature is homological class. We define the property of Degeneracy and the property Nondegeneracy of Koszul homological Series. The property of Degeneracy is implemented to solve problems (P1), (P2), and (P3). In the abundant literature on Riemannian foliations, we have only cited references directly related to the open problems which are studied using the tools which are introduced in this work. Thus, the property of nondegeneracy is implemented to give a complete solution of the problem posed by E. Ghys, (P4-Differential Topology): How does one produce Riemannian foliations? See our Theorems 12 and 13, which are fruits of a happy conjunction between gauge geometry and differential topology. Full article

Non-parametric information geometry has long faced an “intractability barrier”: in the infinite-dimensional setting, the Fisher–Rao metric is a weak Riemannian metric functional that lacks a bounded inverse, rendering classical optimization and estimation techniques computationally inaccessible. This paper resolves this barrier by building the statistical manifold on the Orlicz space $L_0^{\mathsf{\Phi }}\left(P_f\right)$ (the Pistone–Sempi manifold), which provides the necessary exponential integrability for score functions and a rigorous Fréchet differentiability for the Kullback–Leibler divergence. We introduce a novel Structural Decomposition of the Tangent Space ($T_{f}M=S\oplus S^{\perp }$), where the infinite-dimensional space is split into a finite-dimensional covariate subspace (S)—representing the observable system—and its orthogonal complement ($S^{\perp }$). Through this decomposition, we derive the Covariate Fisher Information Matrix (cFIM), denoted as $G_f$, which acts as the computable “Hilbertian slice” of the otherwise intractable metric functional. Key theoretical contributions include proving the Trace Theorem ($H_G\left(f\right)=\mathrm{Tr}\left(G_f\right)$) to identify G-entropy as a fundamental geometric invariant; demonstrating the Geometric Invariance of the Covariate Fisher Information Matrix (cFIM) as a covariant $(0,2)$-tensor under reparameterization; establishing the cFIM as the local Hessian of the KL-divergence; and characterizing the Efficiency Standard through a generalized Cramer–Rao Lower Bound for semi-parametric inference within the Orlicz manifold. Furthermore, we demonstrate that this framework provides a formal mathematical justification for the Manifold Hypothesis, as the structural decomposition naturally identifies the low-dimensional subspace where information is concentrated. By shifting the focus from the intractable global manifold to the tractable covariate geometry, this framework proves that statistical information is not a property of data alone, but an active geometric interaction between the environment (data), the system (covariate subspace), and the mechanism (Fisher–Rao connection). Full article

Improving absolute accuracy in industrial manipulators remains difficult because rigid-body kinematic calibration cannot fully represent configuration-dependent non-geometric effects. Drawing inspiration from biological brain–body co-adaptation, this study presents an Evolutionary Neuro-Physical Hybrid (Evo-NPH) framework in which rigid geometric parameters and neural compensator weights are treated as a single co-evolving decision vector. In the offline phase, a Dual-Strategy Adaptive Differential Evolution (DS-ADE) optimizer performs global joint identification using complementary exploration–exploitation behaviors and success-history inheritance, analogous to morphology-control co-evolution in biological systems. In the online phase, a Neuro-Physical Hybrid Jacobian (NPHJ) solver augments the analytical Jacobian with gradients from a Graph Kolmogorov–Arnold Network (GKAN), enabling sensorimotor-like real-time compensation on the learned physical manifold. Experiments on an ABB IRB 120 manipulator with 600 configurations (500 training, 100 testing) report a testing distance-residual RMSE of 0.62 mm, STD of 0.59 mm, and MAX of 0.83 mm. Relative to the uncalibrated baseline, RMSE is reduced by 86.75%; compared with the strongest published baseline, RMSE improves by 23.46%. Ablation results show that joint DS-ADE optimization outperforms a sequential pipeline by 32.6%, and the graph-structured KAN outperforms a parameter-matched MLP by 26.2%. Wilcoxon signed-rank tests ($p<0.001$) confirm statistical significance. Full article