Search Results (210)

Background: Growing disparities in development, governance, and logistics performance across countries pose challenges for global policymaking and Sustainable Development Goal (SDG) monitoring. This study proposes a classification of 137 countries based on multiple structural dimensions. The dataset for 2023 includes six components of the Logistics Performance Index (LPI), six dimensions of the Worldwide Governance Indicators (WGIs), and four proxies of the Human Development Index (HDI). Methods: The Uniform Manifold Approximation and Projection (UMAP) technique was used to reduce dimensionality and allow for meaningful clustering. Based on the reduced space, the K-means algorithm was employed to group countries with similar development characteristics. Results: The classification process allowed the identification of three distinct groups of countries, supported by a Hopkins statistic of 0.984 and an explained variance ratio of 87.3%. These groups exhibit structural differences in the quality of governance, logistics capacity, and social development conditions. Internal consistency checks and multivariate statistical analyses (ANOVA and MANOVA) confirmed the robustness and statistical significance of the clustering. Conclusions: The resulting classification offers a practical analytical tool for policymakers to design differentiated strategies aligned with national contexts. Furthermore, it provides a data-driven approach for comparative monitoring of the SDGs from an integrated and empirical perspective. Full article

In this study, theorems and proofs related to spherical and focal curves are presented in the BCV-Sasakian space. An approximate solution to the differential equation characterizing spherical curves in the BCV-Sasakian manifold ${\mathfrak{M}}^3$ is obtained using the Taylor matrix collocation method. The general equations of canal and tubular surfaces are provided within this geometric framework. Additionally, the curvature properties of the tubular surface constructed around a non-vertex focal curve are computed and analyzed. All of these results are presented for the first time in the literature within the context of the BCV-Sasakian geometry. Thus, this study makes a substantial contribution to the differential geometry of contact metric manifolds by extending classical concepts into a more generalized and complex geometric structure. Full article

Background: Acute myeloid leukemia (AML) is a common and aggressive adults hematological malignancies. This study explored megakaryocyte–erythroid progenitors (MEPs) signature genes and constructed a prognostic model. Methods: Uniform manifold approximation and projection (UMAP) identified distinct cell types, with differential analysis between AML-MEP and normal MEP groups. Univariate and the least absolute shrinkage and selection operator (LASSO) Cox regression selected biomarkers to build a risk model and nomogram for 1-, 3-, and 5-year survival prediction. Results: Ten differentially expressed genes (DEGs) related to overall survival (OS), six (AHSP, MYB, VCL, PIM1, CDK6, as well as SNHG3) were retained post-LASSO. The model exhibited excellent efficiency (the area under the curve values: 0.788, 0.77, and 0.847). Pseudotime analysis of UMAP-defined subpopulations revealed that MYB and CDK6 exert stage-specific regulatory effects during MEP differentiation, with MYB involved in early commitment and CDK6 in terminal maturation. Finally, although VCL, PIM1, CDK6, and SNHG3 showed significant associations with AML survival and prognosis, they failed to exhibit pathological differential expression in quantitative real-time polymerase chain reaction (qRT-PCR) experimental validations. In contrast, the downregulation of AHSP and upregulation of MYB in AML samples were consistently validated by both qRT-PCR and Western blotting, showing the consistency between the transcriptional level changes and protein expression of these two genes (p < 0.05). Conclusions: In summary, the integration of single-cell/transcriptome analysis with targeted expression validation using clinical samples reveals that the combined AHSP-MYB signature effectively identifies high-risk MEP-AML patients, who may benefit from early intensive therapy or targeted interventions. Full article

This study introduces a paradigm shift in permanent magnet synchronous motor (PMSM) control through the development of hybrid dual fractional-order sliding mode control (HDFOSMC) architecture integrated with evolutionary parameter learning (EPL). Conventional PMSM control frameworks face critical limitations in ultra-precision applications due to their inability to reconcile dynamic agility with steady-state precision under time-varying parameters and compound disturbances. The proposed HDFOSMC framework addresses these challenges via two synergistic innovations: (1) a dual fractional-order sliding manifold that fuses the rapid transient response of non-integer-order differentiation with the small steady-state error capability of dual-integral compensation, and (2) an EPL mechanism enabling real-time adaptation to thermal drift, load mutations, and unmodeled nonlinearities. Validation can be obtained through the comparison of the results on PMSM testbenches, which demonstrate superior performance over traditional fractional-order sliding mode control (FOSMC). By integrating fractional-order theory, sliding mode control theory, and parameter self-tuning theory, this study proposes a novel control framework for PMSM. The developed system achieves high-precision performance under extreme operational uncertainties through this innovative theoretical synthesis and comparative results. Full article

This paper is about a problem at the intersection of differential geometry, spectral analysis and the theory of manifolds. The study of finite-type subvarieties was initiated by Chen in the 1970s, with the aim of obtaining improved estimates for the mean total curvature of compact subvarieties in Euclidean space. The concept of a finite-type subvariety naturally extends that of a minimal subvariety or surface, the latter being closely related to variational calculus. In this work, we classify factorable surfaces in the Lorentz–Heisenberg space ${\mathbb{H}}_3$, equipped with a flat metric satisfying ${\Delta }^I{r}_i={\lambda }_i{r}_i$, which satisfies algebraic equations involving coordinate functions and the Laplacian operator with respect to the surface’s first fundamental form. Full article

A 12-membered pyridinophane scaffold containing two pyridine and two tertiary amine residues is examined as a prototype ligand (^tBuN4) for supporting nitrene transfer to olefins. The known [(^tBuN4)M^II(MeCN)₂]²⁺ (M = Mn, Fe, Co, and Ni) and [(^tBuN4)Cu^I(MeCN)]⁺ cations are synthesized with the hexafluorophosphate counteranion. The aziridination of para-substituted styrenes with PhI=NTs (Ts = tosyl) in various solvents proved to be high yielding for the Cu(I) and Cu(II) reagents, in contrast to the modest efficacy of all other metals. For α-substituted styrenes, aziridination is accompanied by products of aziridine ring opening, especially in chlorinated solvents. Bulkier β-substituted styrenes reduce product yields, largely for the Cu(II) reagent. Aromatic olefins are more reactive than aliphatic congeners by a significant margin. Mechanistic studies (Hammett plots, KIE, and stereochemical scrambling) suggest that both copper reagents operate via sequential formation of two N–C bonds during the aziridination of styrene, but with differential mechanistic parameters, pointing towards two distinct catalytic manifolds. Computational studies indicate that the putative copper nitrenes derived from Cu(I) and Cu(II) are each associated with closely spaced dual spin states, featuring high spin densities on the nitrene N atom. The computed electrophilicity of the Cu(I)-derived nitrene reflects the faster operation of the Cu(I) manifold. Full article

In this paper, we investigate the nonlinear dynamic behavior of a cart–double pendulum system with single time delay feedback control. Based on the center manifold theorem and stochastic averaging method, a reduced-order dynamic model of the system is established, with a focus on analyzing the influence of time delay parameters and stochastic excitation on the system’s Hopf bifurcation characteristics. By introducing stochastic differential equation theory, the system is transformed into the form of an Itô equation, revealing bifurcation phenomena in the parameter space. Numerical simulation results demonstrate that decreasing the time delay and increasing the time delay feedback gain can effectively enhance system stability, whereas increasing the time delay and decreasing the time delay feedback gain significantly improves dynamic performance. Additionally, it is observed that Gaussian white noise intensity modulates the bifurcation threshold. This study provides a novel theoretical framework for the stochastic stability analysis of time delay-controlled multibody systems and offers a theoretical basis for subsequent research. Full article

Single-cell RNA sequencing now profiles whole transcriptomes for hundreds of thousands of cells, yet existing trajectory-inference tools rarely pinpoint where and when fate decisions are made. We present single-cell reinforcement learning (scRL), an actor–critic framework that recasts differentiation as a sequential decision process on an interpretable latent manifold derived with Latent Dirichlet Allocation. The critic learns state-value functions that quantify fate intensity for each cell, while the actor traces optimal developmental routes across the manifold. Benchmarks on hematopoiesis, mouse endocrinogenesis, acute myeloid leukemia, and gene-knockout and irradiation datasets show that scRL surpasses fifteen state-of-the-art methods in five independent evaluation dimensions, recovering early decision states that precede overt lineage commitment and revealing regulators such as Dapp1. Beyond fate decisions, the same framework produces competitive measures of lineage-contribution intensity without requiring ground-truth probabilities, providing a unified and extensible approach for decoding developmental logic from single-cell data. Full article

In this paper, we consider six homogeneous manifolds $GL(n,\mathbb{R})/O(n,\mathbb{R})$, $SL(n,\mathbb{R})/SO(n,\mathbb{R})$, $Sp(2n,\mathbb{R})/U\left(n\right),$$(GL(n,\mathbb{R})⋉{\mathbb{R}}^{(m,n)})/O(n,\mathbb{R})$, $(SL(n,\mathbb{R})⋉{\mathbb{R}}^{(m,n)})/SO(n,\mathbb{R}),$$(Sp(2n,\mathbb{R})⋉H_{\mathbb{R}}^{(n,m)})/(U\left(n\right)\times S(m,\mathbb{R})).$ They are homogeneous manifolds which are important geometrically and number theoretically. These first three spaces are well-known symmetric spaces and the other three are not symmetric spaces. It is well known that the algebra of invariant differential operators on a symmetric space is commutative. The algebras of invariant differential operators on these three non-symmetric spaces are not commutative and have complicated generators. We discuss invariant differential operators on these non-symmetric spaces and provide natural but difficult problems about invariant theory. Full article

This paper explores the geometry of 3-dimensional quasi Sasakian manifolds under CL-transformations. We construct both infinitesimal and $CL$-transformation and demonstrate that the former does not necessarily yield projective killing vector fields. A novel invariant tensor, termed the $CL$-curvature tensor, is introduced and shown to remain invariant under $CL$-transformations. Utilizing this tensor, we characterize $CL$-flat, $CL$-symmetric, $CL$-$\phi$ symmetric and $CL$-$\phi$ recurrent structures on such manifolds by mean of differential equations. Furthermore, we investigate conditions under which a Ricci soliton exists on a CL-transformed quasi Sasakian manifold, revealing that under flat curvature, the structure becomes Einstein. These findings contribute to the understanding of curvature dynamics and soliton theory within the context of contact metric geometry. Full article

Full-body movement involving multi-segmental coordination has been essential to our evolution as a species, but its study has been focused mostly on the analysis of one-dimensional data. The field is poised for a change by the availability of high-density recording and data sharing. New ideas are needed to revive classical theoretical questions such as the organization of the highly redundant biomechanical degrees of freedom and the optimal distribution of variability for efficiency and adaptiveness. In movement science, there are popular methods that up-dimensionalize: they start with one or a few recorded dimensions and make inferences about the properties of a higher-dimensional system. The opposite problem, dimensionality reduction, arises when making inferences about the properties of a low-dimensional manifold embedded inside a large number of kinematic degrees of freedom. We present an approach to quantify the smoothness and degree to which the kinematic manifold of full-body movement is distributed among embedding dimensions. The principal components of embedding dimensions are rank-ordered by variance. The power law scaling exponent of this variance spectrum is a function of the smoothness and dimensionality of the embedded manifold. It defines a threshold value below which the manifold becomes non-differentiable. We verified this approach by showing that the Kuramoto model obeys the threshold when approaching global synchronization. Next, we tested whether the scaling exponent was sensitive to participants’ gait impairment in a full-body motion capture dataset containing short gait trials. Variance scaling was highest in healthy individuals, followed by osteoarthritis patients after hip replacement, and lastly, the same patients before surgery. Interestingly, in the same order of groups, the intrinsic dimensionality increased but the fractal dimension decreased, suggesting a more compact but complex manifold in the healthy group. Thinking about manifold dimensionality and smoothness could inform classic problems in movement science and the exploration of the biomechanics of full-body action. Full article

Ionospheric tomography, an effective method for reconstructing 3-D electron density, is traditionally pictured by 3-D IED (ionospheric electron density) slices to express ionospheric disturbances, which may overlook the critical information in 3-D spherical manifold space. Here, we develop a novel visualization framework that integrates tomography reconstruction with a spherical latitude–longitude grid system, enabling the comprehensive characterization of 3-D IED dynamic evolution in 3-D manifold spherical space. Through this method, we visualized two cases: the Hualien earthquake on 2 April 2024 and the geomagnetic storm on 24 April 2023. The results demonstrate the evolution of the electron density during earthquake and geomagnetic storms in the real 3-D space, showing that seismic events induce bottom-up IED negative anomalies localized near epicenters, while geomagnetic storms trigger top-down depletion processes, with IED propagating from higher altitudes in the real 3-D manifold space. Compared to the conventional slice, our visualization model can visualize the characteristics, with the coverage area being observed to increase with the altitude within the same geospatial coordinates. This framework can advance the identification of ionosphere anomalies by enabling the precise differentiation of anomaly sources. This work bridges gaps in geospatial modeling by harmonizing ionospheric tomography with Earth system grids, offering a feasible solution for analyzing multi-scale ionospheric phenomena. Full article

The development of neural networks has made the introduction of multimodal systems inevitable. Computer vision methods are still not widely used in biological research, despite their importance. It is time to recognize the significance of advances in feature extraction and real-time analysis of information from cells. Teacherless learning for the image clustering task is of great interest. In particular, the clustering of single cells is of great interest. This study will evaluate the feasibility of using latent representation and clustering of single cells in various applications in the fields of medicine and biotechnology. Of particular interest are embeddings, which relate to the morphological characterization of cells. Studies of C2C12 cells will reveal more about aspects of muscle differentiation by using neural networks. This work focuses on analyzing the applicability of the latent space to extract morphological features. Like many researchers in this field, we note that obtaining high-quality latent representations for phase-contrast or bright-field images opens new frontiers for creating large visual-language models. Graph structures are the main approaches to non-Euclidean manifolds. Graph-based segmentation has a long history, e.g., the normalized cuts algorithm treated segmentation as a graph partitioning problem—but only recently have such ideas merged with deep learning in an unsupervised manner. Recently, a number of works have shown the advantages of hyperbolic embeddings in vision tasks, including clustering and classification based on the Poincaré ball model. One area worth highlighting is unsupervised segmentation, which we believe is undervalued, particularly in the context of non-Euclidean spaces. In this approach, we aim to mark the beginning of our future work on integrating visual information and biological aspects of individual cells to multimodal space in comparative studies in vitro. Full article

This editorial presents 26 research articles published in the Special Issue entitled Differentiable Manifolds and Geometric Structures of the MDPI Mathematics journal, which covers a wide range of topics particularly from the geometry of (pseudo-)Riemannian manifolds and their submanifolds, providing some of the latest achievements in different areas of differential geometry, among which is counted: the geometry of differentiable manifolds with curvature restrictions such as Golden space forms, Sasakian space forms; diffeological and affine connection spaces; Weingarten and Delaunay surfaces; Chen-type inequalities for submanifolds; statistical submersions; manifolds endowed with different geometric structures (Sasakian, weak nearly Sasakian, weak nearly cosymplectic, LP-Kenmotsu, paraquaternionic); solitons (almost Ricci solitons, almost Ricci–Bourguignon solitons, gradient r-almost Newton–Ricci–Yamabe solitons, statistical solitons, solitons with semi-symmetric connections); vector fields (projective, conformal, Killing, 2-Killing) [...] Full article

This editorial presents 24 research articles published in the Special Issue entitled Geometry of Manifolds and Applications of the MDPI Mathematics journal, which covers a wide range of topics from the geometry of (pseudo-)Riemannian manifolds and their submanifolds, providing some of the latest achievements in many branches of theoretical and applied mathematical studies, among which is counted: the geometry of differentiable manifolds with curvature restrictions such as complex space forms, metallic Riemannian space forms, Hessian manifolds of constant Hessian curvature; optimal inequalities for submanifolds, such as generalized Wintgen inequality, inequalities involving $\delta$-invariants; homogeneous spaces and Poisson–Lie groups; the geometry of biharmonic maps; solitons (Ricci solitons, Yamabe solitons, Einstein solitons) in different geometries such as contact and paracontact geometry, complex and metallic Riemannian geometry, statistical and Weyl geometry; perfect fluid spacetimes [...] Full article