Search Results (23)

Individual differences and long calibration time present significant challenges to the practical implementation of brain–computer interfaces (BCIs). Domain adaptation technology can help mitigate these challenges by leveraging knowledge from existing subjects. Although domain adaptation methods have achieved progress in BCIs, there remains a need for further exploration in class structure and cross-domain dispersion. In this paper, we propose a novel framework, multi-constrained transfer learning with selective pseudo-label update (MCTLP). First, Euclidean alignment is applied to reduce inter-subject variability at the data level. Then, multi-constrained feature alignment (MCFA) is introduced, which iteratively constructs a kernel mapping space and then determines an optimized subspace to align both marginal and conditional distributions at the feature level under class structure and dispersion constraints. Moreover, in this iterative process of feature alignment, a selective pseudo-label update method is proposed to update the pseudo-labels of only the target samples with high classification confidence to realize more reliable conditional distribution alignment. Two benchmark datasets were used to verify the presented MCTLP. The results showed that MCTLP outperformed other existing methods, demonstrating its strong ability for cross-subject transfer. Full article

The symmetry between different representation spaces plays a crucial role in effectively modeling complex multimodal data. To address the challenge of equipment knowledge graphs containing hierarchical relationships that cannot be fully represented in a single space, this study proposes UMEAD, an unsupervised multimodal entity alignment method based on dual-space embeddings. The method simultaneously learns graph embeddings in both Euclidean and hyperbolic spaces, forming a structural symmetry where the Euclidean space captures local regularities and the hyperbolic space models global hierarchies. Their complementarity achieves a balanced and symmetric representation of multimodal knowledge. An adaptive feature fusion strategy is further employed to dynamically weight semantic and visual modalities, enhancing the symmetry and complementarity between different modalities. To reduce reliance on scarce pre-aligned data, pseudo seed instances are generated from multimodal features, and an iterative constraint mechanism progressively enlarges the training set, enabling unsupervised alignment. Experiments on public datasets, including EMMEAD, FB15K-DB15K, and FB15K-YAGO15K, demonstrate that the combination of dual-space embeddings, adaptive fusion, and iterative constraints significantly improves alignment accuracy. In summary, the proposed method reduces dependence on pre-aligned data, strengthens multimodal and structural alignment, and its symmetric embedding and fusion design offers a promising approach for the construction and application of multimodal knowledge graphs in the equipment domain. Full article

In this paper, we introduce Kluitenberg’s formulation of non-equilibrium thermodynamics with internal variables in the context of a Riemannian space, as required by Einstein’s general relativity. Using the formulation of the second law of thermodynamics in general coordinates with a pseudo-Euclidean metric, we derive a Levi-Civita-like energy tensor and propose a generalization of the second law within a Riemannian space, in agreement with Tolman’s approach. In addition, we determine the expression for the entropy density in a general Riemannian space and identify the new variables upon which it depends. This allows us to deduce, within this framework, the equilibrium inelastic and viscous stress tensors as well as the entropy production. These expressions are consistent with the principle of general covariance and Einstein’s equivalence principle. Full article

Imaginary coquaternions cℍ can be represented by matrices of negative feedback $N^{-}$, positive feedback $P^{+}$, and reciprocal links $R^{\pm }$. An added environmental element $E^{\pm }$ endows biologic systems with the structure of cℍ module. Although cℍ representation links base patterns with the geometric structure of the pseudo-Euclidean ${\mathbb{R}}_2^4$ space, unknown physiologic aspects of relationships between base elements may add new functional features to the structure of a functional module. Another question is whether achieving and remaining in the equilibrium state provides stability for a biologic system. Considering the property of a biologic system to return deviated conditions to the equilibrium, the system of ordinary differential equations describing the behavior of a mechanical pendulum was modified and used as a basic tool to find the answers. The results obtained show that in evolving systems, the regulatory patterns are organized in a sequence $NPRN$ of base elements, allowing the system to perform a high amount of energy-consuming functions. In order to keep dissipating energy at the same level, the system bifurcates and finalizes its regulatory cycle in $R^{\pm }$ by splitting $P^{+}$ after which the next cycle may begin. Obtained flows are continuous pathways that do not interfere with equilibrium states, thus providing a homeostasis mechanism with nonequilibrium dynamics. Functional transformations reflect changes in the geometry and metric index of the coquaternion. Related coquaternion dynamics show the transformation of a hyperbolic hyperboloid into the closed surface, which is the fusion of the portions of the hyperbolic hyperboloid and two spheres. Full article

The present article explores the possibilities of using artificial neural networks to solve problems related to reconstructing complex geometric surfaces in Euclidean and pseudo-Euclidean spaces, examining various approaches and techniques for training the networks. The main focus is on the possibility of training a set of neural networks with information about the available surface points, which can then be used to predict and complete missing parts. A method is proposed for using separate neural networks that reconstruct surfaces in different spatial directions, employing various types of architectures, such as multilayer perceptrons, recursive networks, and feedforward networks. Experimental results show that artificial neural networks can successfully approximate both smooth surfaces and those containing singular points. The article presents the results with the smallest error, showcasing networks of different types, along with a technique for reconstructing geographic relief. A comparison is made between the results achieved by neural networks and those obtained using traditional surface approximation methods such as Bézier curves, k-nearest neighbors, principal component analysis, Markov random fields, conditional random fields, and convolutional neural networks. Full article

Within the geophysical exploration utilising seismic methods, it is well known that if the explored distances are much greater than the wavelength of the seismic waves with which the exploration is carried out, the ray approach of the wave theory can be used. In this way, when the rays travel through an inhomogeneous medium, they follow curved trajectories, which is imperative to determine the geological features that produce reflection and refraction phenomena. In this paper, a simple algorithm for the calculation of the trajectory of a seismic beam through an inhomogeneous stratum is presented. For this, the construction of a pseudo-Riemannian metric is required from the function of P-wave velocities of the geological stratum. Thus, the problem is inverted because instead of finding the curved trajectory of the seismic beam in a background with a Euclidean metric, it is proposed that the beam follows a geodesic of a curved space-time specific to each stratum, becoming a simple and automatic process using the differential geometry apparatus. For the reader to gain insight into this tool, different geological setups from idealised ones up to a salt dome are presented. Full article

Let ${\mathbb{S}}^m\left(c\right)$ denote a sphere with a positive constant curvature c and $M^n(n\ge 3)$ be an n-dimensional compact pseudo-umbilical submanifold in a Riemannian product space ${\mathbb{S}}^m\left(c\right)\times \mathbb{R}$ with a nonzero parallel mean curvature vector (PMC), where $\mathbb{R}$ is a Euclidean line. In this paper, we prove a sequence of pinching theorems with respect to the Ricci, sectional and scalar curvatures of $M^n$, which allow us to generalize some classical curvature pinching results in spheres. Full article

In supervised deep learning object detection, the quantity of object information and annotation quality in a dataset affect model performance. To augment object detection datasets while maintaining contextual information between objects and backgrounds, we proposed a Background Instance-Based Copy-Paste (BIB-Copy-Paste) data augmentation model. We devised a method to generate background pseudo-labels for all object classes by calculating the similarity between object background features and image region features in Euclidean space. The background classifier, trained with these pseudo-labels, can guide copy-pasting to ensure contextual relevance. Several supervised object detectors were evaluated on the PASCAL VOC 2012 dataset, achieving a 1.1% average improvement in mean average precision. Ablation experiments with the BlitzNet object detector on the PASCAL VOC 2012 dataset showed an improvement of mAP by 1.19% using the proposed method, compared to a 0.18% improvement with random copy-paste. Images from the MS COCO dataset containing objects of the same classes as in PASCAL VOC 2012 were also selected for object pasting experiments. The contextual relevance of pasted objects demonstrated our model’s effectiveness and transferability between datasets with same class of objects. Full article

We present a family of hypersurfaces of revolution distinguished by four parameters in the five-dimensional pseudo-Euclidean space ${\mathbb{E}}_2^5$. The matrices corresponding to the fundamental form, Gauss map, and shape operator of this family are computed. By utilizing the Cayley–Hamilton theorem, we determine the curvatures of the specific family. Furthermore, we establish the criteria for maximality within this framework. Additionally, we reveal the relationship between the Laplace–Beltrami operator of the family and a $5\times 5$ matrix. Full article

In this paper, the concept of ultrametric structure is intertwined with the SLAM procedure. A set of pre-existing transformations has been used to create a new simultaneous localization and mapping (SLAM) algorithm. We have developed two new parallel algorithms that implement the time-consuming Boolean transformations of the space dissimilarity matrix. The resulting matrix is an important input to the vector quantization (VQ) step in SLAM processes. These algorithms, written in Compute Unified Device Architecture (CUDA) and Open Multi-Processing (OpenMP) pseudo-codes, make the Boolean transformation computationally feasible on a real-world-size dataset. We expect our newly introduced SLAM algorithm, ultrametric Fast Appearance Based Mapping (FABMAP), to outperform regular FABMAP2 since ultrametric spaces are more clusterable than regular Euclidean spaces. Another scope of the presented research is the development of a novel measure of ultrametricity, along with creation of Ultrametric-PAM clustering algorithm. Since current measures have computational time complexity order, $O\left(n^3\right)$ a new measure with lower time complexity, $O\left(n^2\right)$, has a potential significance. Full article

The six-dimensional pseudo-Euclidean space ${\mathbb{E}}_{3,3}$ with signature $(3,3)$ is proposed as a model of real physical space at the subparticle scale. The conserved quantum characteristics of elementary particles, such as spin, isospin, electric and baryon charges, and hypercharge, are expressed through the symmetries of this space. The symmetries are brought out by the various representation of the metric in ${\mathbb{E}}_{3,3}$ with the aid of spinors and hyperbolic complex numbers. The properties of the metric allow predicting the number of quarks equal to 18. The violation of strong conservation laws in weak interactions is treated through compactifying the three-dimensional temporal subspace at the subparticle scale into single-dimensional time at bigger scales, which reduces symmetry from the spherical to axial type. Full article

In this paper, we find some new information on Legendrian dualities and extend them to the case of Legendrian dualities for continuous families of pseudo-spheres in general semi-Euclidean space. In particular, we construct all contact diffeomorphic mappings between the contact manifolds and display them in a table that contains all information about Legendrian dualities. Full article

This is a review paper on the generalization of Euclidean as well as pseudo-Euclidean groups of interest in quantum mechanics. The Weyl–Heisenberg groups, $H_n$, together with the Euclidean, $E_n$, and pseudo-Euclidean $E_{p,q}$, groups are two families of groups with a particular interest due to their applications in quantum physics. In the present manuscript, we show that, together, they give rise to a more general family of groups, $K_{p,q}$, that contain $H_{p,q}$ and $E_{p,q}$ as subgroups. It is noteworthy that properties such as self-similarity and invariance with respect to the orientation of the axes are properly included in the structure of $K_{p,q}$. We construct generalized Hermite functions on multidimensional spaces, which serve as orthogonal bases of Hilbert spaces supporting unitary irreducible representations of groups of the type $K_{p,q}$. By extending these Hilbert spaces, we obtain representations of $K_{p,q}$ on rigged Hilbert spaces (Gelfand triplets). We study the transformation laws of these generalized Hermite functions under Fourier transform. Full article

The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action, which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the electromagnetic field in multi-dimensional pseudo-Euclidean (flat) spaces has also been developed and investigated. Based on the two arising first-class constraints, we have generalized to multi-dimensional spaces a number of different gauges known for the three-dimensional electromagnetic field. For multi-dimensional spaces of non-zero curvature the governing equations for the multi-dimensional electromagnetic field are written in a manifestly covariant form. Multi-dimensional Einstein’s equations of metric gravity in the presence of an electromagnetic field have been re-written in the true tensor form. Methods of scalar electrodynamics are applied to analyze Maxwell equations in the two and one-dimensional spaces. Full article

We consider Lorentz surfaces in ${\mathbb{R}}_1^3$ satisfying the condition $H^2-K\ne 0$, where K and H are the Gaussian curvature and the mean curvature, respectively, and call them Lorentz surfaces of general type. For this class of surfaces, we introduce special isotropic coordinates, which we call canonical, and show that the coefficient F of the first fundamental form and the mean curvature H, expressed in terms of the canonical coordinates, satisfy a special integro-differential equation which we call a natural equation of the Lorentz surfaces of a general type. Using this natural equation, we prove a fundamental theorem of Bonnet type for Lorentz surfaces of a general type. We consider the special cases of Lorentz surfaces of constant non-zero mean curvature and minimal Lorentz surfaces. Finally, we give examples of Lorentz surfaces illustrating the developed theory. Full article