Search Results (502)

Alzheimer’s Disease and Dementia (ADD) progresses along a continuum of cognitive decline, typically from Subjective Cognitive Impairment (SCI) to Mild Cognitive Impairment (MCI) and eventually to dementia. While many studies have focused on classifying these clinical stages, fewer have examined whether brain connectomes encode this continuum in a low-dimensional, interpretable form. Motivated by the hypothesis that structural brain connectomes undergo complex yet compact changes across cognitive decline, we propose a Graph Neural Network (GNN)-based framework that embeds these connectomes into a two-dimensional manifold to capture the evolving patterns of structural connectivity associated with cognitive deterioration. Using attention-based graph aggregation and Principal Component Analysis (PCA), we find that MCI subjects consistently occupy an intermediate position between SCI and ADD, and that the observed transitions align with known clinical biomarkers of ADD pathology. This hypothesis-driven analysis is further supported by the model’s robust separation performance, with ROC-AUC scores of 0.93 for ADD vs. SCI and 0.81 for ADD vs. MCI. These findings offer an interpretable and neurologically grounded representation of dementia progression, emphasizing structural connectome alterations as potential markers of cognitive decline. Full article

The current work establishes the geometrical bearing for hypersurfaces in a Golden Riemannian manifold with constant golden sectional curvature with respect to k-almost Newton-conformal Ricci solitons. Moreover, we extensively explore the immersed r-almost Newton-conformal Ricci soliton and determine the sufficient conditions for total geodesicity with adequate restrictions on some smooth functions using mathematical operators. Furthermore, we go over some natural conclusions in which the gradient k-almost Newton-conformal Ricci soliton on the hypersurface of the Golden Riemannian manifold becomes compact. Finally, we establish a Schur’s type inequality in terms of k-almost Newton-conformal Ricci solitons immersed in Golden Riemannian manifolds with constant golden sectional curvature. Full article

Investigating brain area functions requires advanced technologies, but meaningful insights depend on correlating neural signals with behavior. Traditional mice behavior annotation methods, including manual and semi-automated approaches, are limited by subjectivity and time constraints. To overcome these limitations, our study employs the YOLO neural network for precise mice tracking and composite RGB frames for behavioral scoring. Our model, trained on over 10,000 frames, accurately classifies sitting, running, and grooming behaviors. Additionally, we provide statistical metrics and data visualization tools. We further combined AI-powered behavior labeling to examine hippocampal neuronal activity using fluorescence microscopy. To analyze neuronal circuit dynamics, we utilized a manifold analysis approach, revealing distinct functional patterns corresponding to transgenic 5xFAD Alzheimer’s model mice. This open-source software enhances the accuracy and efficiency of behavioral and neural data interpretation, advancing neuroscience research. Full article

Point cloud denoising is essential for improving 3D data quality, yet traditional K-means methods relying on Euclidean distance struggle with non-uniform noise. This paper proposes a K-means algorithm leveraging Total Bregman Divergence (TBD) to better model geometric structures on manifolds, enhancing robustness against noise. Specifically, TBDs—Total Logarithm, Exponential, and Inverse Divergences—are defined on symmetric positive-definite matrices, each tailored to capture distinct local geometries. Theoretical analysis demonstrates the bounded sensitivity of TBD-induced means to outliers via influence functions, while anisotropy indices quantify structural variations. Numerical experiments validate the method’s superiority over Euclidean-based approaches, showing effective noise separation and improved stability. This work bridges geometric insights with practical clustering, offering a robust framework for point cloud preprocessing in vision and robotics applications. 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

This study introduces an intrinsic Gaussian Process Regression (iGPR) model for the first time, which incorporates non-Euclidean spatial covariates via a Gaussian process prior to analyzing the relationship between digitalization and carbon emission efficiency. The iGPR model’s hierarchical design embeds a Gaussian process as a flexible spatial random effect with a heat-kernel-based covariance function to capture the manifold geometry of spatial features. To enable tractable inference, we employ a penalized maximum-likelihood estimation (PMLE) approach to jointly estimate regression coefficients and covariance hyperparameters. Using a panel dataset linking a national digitalization (modernization) index to carbon emission efficiency, the empirical analysis demonstrates that digitalization has a significantly positive impact on carbon emission efficiency while accounting for spatial heterogeneity. The iGPR model also exhibits superior predictive accuracy compared to state-of-the-art machine learning methods (including XGBoost, random forest, support vector regression, ElasticNet, and a standard Gaussian process regression), achieving the lowest mean squared error (MSE = 0.0047) and an average prediction error near zero. Robustness checks include instrumental-variable GMM estimation to address potential endogeneity across the efficiency distribution and confirm the stability of the estimated positive effect of digitalization. Full article

Through an examination of his core doctrinal points, I argue that Shinran’s conception of Pure Land Buddhism (Jōdo Shinshū) should not be so readily dismissed as one that is only salvific in an otherworldly sense, with no relevance to contemporary, everyday life, nor should it be reduced to a purely ethnic form of Buddhism without any reference to its universal dimension. Through this analysis, we will find that Shinran’s adoption of a unique and honest evaluation of our inner lives through receiving the wisdom and compassion of Amida Buddha can offer people of today’s world a way to embrace a spirit of self-acceptance so that one can live with confidence, integrity, and a modest joy, despite the manifold shortcomings of the human condition. Through the radical transformation of one’s dissatisfaction and suffering, an uncontrived ethical impulse is able to emerge, accompanied by a keen awareness of deep empathy for others, leading to an existence informed by empathy instead of animosity. Full article

This paper mainly studies the existence of sign-changing solutions for the following $p\left(x\right)$-biharmonic Kirchhoff-type equations: $-\left(a+b{\int }_{{\mathbb{R}}^N}{\displaystyle \frac{1}{p\left(x\right)}}{|\Delta u|}^{p\left(x\right)}\mathrm{d}x\right){\Delta }_{p\left(x\right)}^{2}u+V\left(x\right){|u|}^{p\left(x\right)-2}u$ = $K\left(x\right)f\left(u\right),x\in {\mathbb{R}}^N$, where ${\Delta }_{p\left(x\right)}^{2}u=\Delta \left({|\Delta u|}^{p\left(x\right)-2}\Delta u\right)$ is the $p\left(x\right)$ biharmonic operator, $a,b>0$ are constants, $N\ge 2$, $V\left(x\right),K\left(x\right)$ are positive continuous functions which vanish at infinity, and the nonlinearity f has subcritical growth. Using the Nehari manifold method, deformation lemma, and other techniques of analysis, it is demonstrated that there are precisely two nodal domains in the problem’s least energy sign-changing solution $u_b$. In addition, the convergence property of $u_b$ as $b\to 0$ is also established. Full article

We explore chaos, local dynamics, codimension-one, and codimension-two bifurcations of an asymmetric discrete predator–prey model. More precisely, for all the model’s parameters, it is proved that the model has two boundary fixed points and a trivial fixed point, and also under parametric conditions, it has an interior fixed point. We then constructed the linearized system at these fixed points. We explored the local behavior at equilibria by the linear stability theory. By the series of affine transformations, the center manifold theorem, and bifurcation theory, we investigated the detailed codimensions-one and two bifurcations at equilibria and examined that at boundary fixed points, no flip bifurcation exists. Furthermore, at the interior fixed point, it is proved that the discrete model exhibits codimension-one bifurcations like Neimark–Sacker and flip bifurcations, but fold bifurcation does not exist at this point. Next, for deeper understanding of the complex dynamics of the model, we also studied the codimension-two bifurcation at an interior fixed point and proved that the model exhibits the codimension-two 1:2, 1:3, and 1:4 strong resonances bifurcations. We then investigated the existence of chaos due to the appearance of codimension-one bifurcations like Neimark–Sacker and flip bifurcations by OGY and hybrid control strategies, respectively. The theoretical results are also interpreted biologically. Finally, theoretical findings are confirmed numerically. Full article

Efficient prediction of shallow-water acoustic transmission loss (TL) is crucial for underwater detection, recognition, and communication systems. Traditional physical modeling methods require repeated calculations for each new scenario in practical waveguide environments, leading to low computational efficiency. Deep learning approaches, based on data-driven principles, enable accurate input–output approximation and batch processing of large-scale datasets, significantly reducing computation time and cost. To establish a rapid prediction model mapping sound speed profiles (SSPs) to acoustic TL through controllable generation, this study proposes a hybrid framework that integrates a variational autoencoder (VAE) and a normalizing flow (Flow) through a two-stage training strategy. The VAE network is employed to learn latent representations of TL data on a low-dimensional manifold, while the Flow network is additionally used to establish a bijective mapping between the latent variables and underwater physical parameters, thereby enhancing the controllability of the generation process. Combining the trained normalizing flow with the VAE decoder could establish an end-to-end mapping from SSPs to TL. The results demonstrated that the VAE–Flow network achieved higher computational efficiency, with a computation time of 4 s for generating 1000 acoustic TL samples, versus the over 500 s required by the KRAKEN model, while preserving accuracy, with median structural similarity index measure (SSIM) values over 0.90. Full article

Real-time, high-resolution monitoring of chemically diverse water pollutants remains a critical challenge for smart water management. Here, we report a fully integrated, multi-modal nano-sensor array, combining graphene field-effect transistors, Ag/Au-nanostar surface-enhanced Raman spectroscopy substrates, and CdSe/ZnS quantum dot fluorescence, coupled to an edge-deployable CNN-LSTM architecture that fuses raw electrochemical, vibrational, and photoluminescent signals without manual feature engineering. The 45 mm × 20 mm microfluidic manifold enables continuous flow-through sampling, while 8-bit-quantised inference executes in 31 ms at <12 W. Laboratory calibration over 28,000 samples achieved limits of detection of 12 ppt (Pb²⁺), 17 pM (atrazine) and 87 ng L⁻¹ (nanoplastics), with R² ≥ 0.93 and a mean absolute percentage error <6%. A 24 h deployment in the Cherwell River reproduced natural concentration fluctuations with field R² ≥ 0.92. SHAP and Grad-CAM analyses reveal that the network bases its predictions on Dirac-point shifts, characteristic Raman bands, and early-time fluorescence-quenching kinetics, providing mechanistic interpretability. The platform therefore offers a scalable route to smart water grids, point-of-use drinking water sentinels, and rapid environmental incident response. Future work will address sensor drift through antifouling coatings, enhance cross-site generalisation via federated learning, and create physics-informed digital twins for self-calibrating global monitoring networks. Full article

Syrphid flies (Syrphidae) are among the most significant groups of insect pollinators with approximately 6300 described species worldwide. Within China, more than 15% species have been reported but their diversity and distribution pattern are not well understood. Based on recent collections and published literature records, this study aimed to assess the species diversity, richness, evenness, and distribution pattern of Syrphidae in China. Biodiversity was measured using various indices such as Simpson’s diversity index, the Shannon–Wiener diversity index, Simpson’s reciprocal index, the Shannon equitability index, and the Margalef index. The results indicated that most of the indices showed highest values within Sichuan, Shaanxi, Yunnan, Taiwan, Tibet, and Gansu provinces. However, the lowest values of most of these indices were seen in Tianjin, Chongqing, and Hongkong. The ranges of these values were 0.69–5.55, 0.67–1.00, and 1.44–46.26 for the Shannon–Wiener index, Simpson’s index, and the Margalef index, respectively. Based on UMAP (Uniform Manifold Approximation and Projection) clustering approaches, all provinces of China were divided into two groups where group 1 showed 16 provinces having similar values to each other in a UMAP1 and UMAP2 plot, whereas 17 provinces were categorized into group 2. This clustering was further refined by a hierarchical clustering dendrogram where group 2 was further refined into two subgroups, where three provinces were separated into one small group including Hongkong, Chongqing, and Tianjin because of the lowest values of most of the indices. These results provide significant insights into the species richness and distribution of syrphid flies and inform strategies to help maintain these pollinators to support sustainable agriculture. Full article

The Flamelet Generated Manifold (FGM) method is widely employed in turbulent combustion simulations due to its high accuracy and computational efficiency. However, the model’s ability to capture turbulent combustion interactions is limited by the shape of the presumed probability density function (PDF) of the mixture fraction and progress variable. To construct a conditional $\beta$ PDF with better performance, a systematic PDF modeling and analysis framework coupled with machine learning methods based on the sparse experimental data was proposed. A comparative analysis was conducted for five machine learning methods across two experimental datasets using this framework. The results demonstrate that the random forest algorithm represents the optimal choice when both training complexity and predictive performance are comprehensively considered. To expand the model’s applicable range, a data fusion strategy was applied in different machine learning methods. The effectiveness of data fusion is demonstrated by comparative analysis between single-dataset and fused-dataset models. The analysis of convex hull in low-dimensional space reveals the fundamental mechanism of data fusion in the FGM-PDF method, which is significantly important to construct a data-driven PDF model in sparse-data scenarios with much better performance. Full article

Robust indoor positioning, crucial to modern location-based services, increasingly leverages Channel State Information (CSI) for its superior multipath resolution over the traditional RSSI. However, current CSI-based methods are hampered by three key limitations: susceptibility to skewed, non-Gaussian noise; informational redundancy from multi-AP configurations; and spatial discontinuities arising from Euclidean-based modeling. To address these challenges, we propose a unified framework that synergistically combines three innovations: (1) an adaptive filtering pipeline that uses wavelet decomposition and dynamic Kalman updates to suppress skewed noise; (2) a graph attention network that optimizes AP selection by modeling spatiotemporal correlations; and (3) a hyperbolic covariance model that captures the intrinsic non-Euclidean geometry of signal propagation. Evaluations on experimental data demonstrate that our framework achieves superior positioning accuracy and environmental robustness over state-of-the-art methods. Crucially, the hyperbolic representation enhances resilience to obstructions by preserving the signal manifold’s true structure, thereby advancing the practical deployment of fingerprinting systems. 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