In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes. We present...
Digital holograms are a prime example for signals, which are best understood in phase space—the joint space of spatial coordinates and spatial frequencies. Many characteristics, as well as optical operations can be visualized therein with so ca...
The continuous nature of space and time is a fundamental tenet of many scientific endeavors. That digital representation imposes granularity is well recognized, but whether it is possible to address space completely remains unanswered. This paper arg...
This paper explores the structural representation and Fourier analysis of elements in Horváth distribution spaces Sk′, for k<−n. We prove that any element in Sk′ can be expressed as a finite sum of derivatives of continuou...
Monocular vision-based pose estimation for known uncooperative space targets plays an increasingly important role in on-orbit operations. The existing state-of-the-art methods of space target pose estimation build the 2D-3D correspondences to recover...
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Paraplegia following spinal cord injury (SCI) affects the mental representation and peripersonal space of the paralysed body parts (i.e., lower limbs). Physical rehabilitation programs can improve these aspects, but the benefits are mostly partial an...
Hysteresis is a fundamental characteristic of magnetic materials. The Jiles–Atherton (J-A) hysteresis model, which is known for its few parameters and clear physical interpretations, has been widely employed in simulating hysteresis characteris...
The L-space and P-space are two essential representations for studying complex networks that contain different clusters. Existing network models can successfully generate networks in L-space, but generating networks in P-space poses significant chall...
Recently, source code mining has received increasing attention due to the rapid increase of open-sourced code repositories and the tremendous values implied in this large dataset, which can help us understand the organization of functions or classes...
In this work, we focus on sparse representation of two-dimensional (2-D) radar signatures for man-made targets. Based on the damped exponential (DE) model, a 2-D augmented state–space approach (ASSA) is proposed to estimate the parameters of sc...
This paper presents a novel method to extract local features, which instead of calculating local extrema computes global maxima in a discretized scale-space representation. To avoid interpolating scales on few data points and to achieve perfect rotat...
Relations in knowledge graphs have rich relational structures and various binary relational patterns. Various relation modelling strategies are proposed for embedding knowledge graphs, but they fail to fully capture both features of relations, rich r...
Accurate extraction of weak fault information from non-stationary vibration signals collected by vibration sensors is challenging due to severe noise and interference. While variational mode decomposition (VMD) has been effective in fault diagnosis,...
Network data analysis is a crucial method for mining complicated object interactions. In recent years, random walk and neural-language-model-based network representation learning (NRL) approaches have been widely used for network data analysis. Howev...
Semi-supervised non-negative matrix factorization (NMF) has achieved successful results due to the significant ability of image recognition by a small quantity of labeled information. However, there still exist problems to be solved such as the inter...
Hyperbolic space has received extensive attention because it can accurately and concisely represent hierarchical data. Currently, for knowledge graph completion tasks, the introduction of exogenous information of entities can enrich the knowledge rep...
Despite the success of deep learning models, it remains challenging for the over-parameterized model to learn good representation under small-sample-size settings. In this paper, motivated by previous work on out-of-distribution (OoD) generalization,...
This review is devoted to the universal algebraic and geometric properties of the non-relativistic quantum current algebra symmetry and to their representations subject to applications in describing geometrical and analytical properties of quantum an...
For this paper, we proposed the fractional category representation vector (FV) based on fractional calculus (FC), of which one-hot label is only the special case when the derivative order is 0. FV can be considered as a distributional representation...
Traditionally, the standards of spatial modeling are oriented to represent the quantitative information of space. However, in recent years an increasingly common challenge is appearing: flexibly and appropriately integrating quantitative information...
We revisit the fundamental notion of continuity in representation theory, with special attention to the study of quantum physics. After studying the main theorem in the context of representation theory, we draw attention to the significant aspect of...
In recent years, the collaborative representation-based classification (CRC) method has achieved great success in visual recognition by directly utilizing training images as dictionary bases. However, it describes a test sample with all training samp...
Chipman contended, in stark contrast to the conventional view, that, utility is not a real number but a vector, and that it is inherently lexicographic in nature. On the other hand, in recent years continuous multi-utility representations of a preord...
We study densely defined unbounded operators acting between different Hilbert spaces. For these, we introduce a notion of symmetric (closable) pairs of operators. The purpose of our paper is to give applications to selected themes at the cross road o...
Color texture classification aims to recognize patterns by the analysis of their colors and their textures. This process requires using descriptors to represent and discriminate the different texture classes. In most traditional approaches, these des...
Cancer, with its complexity and numerous origins, continues to provide a huge challenge in medical research. Anticancer peptides are a potential treatment option, but identifying and synthesizing them on a large scale requires accurate prediction alg...
Finitely-additive measures invariant to the action of some groups on a separable infinitedimensional real Hilbert space are constructed. The invariantness of a measure is studied with respect to the group of shifts on a vector of Hilbert space, the o...
In this paper, we propose using quiver representations as a tool for understanding artificial neural network algorithms. Specifically, we construct these algorithms by utilizing the group algebra of a finite cyclic group as vertices and convolution t...
Quivers are oriented graphs that have profound connections to various areas of mathematics, including representation theory and geometry. Quiver representations correspond to a vast generalization of classical linear algebra problems. The geometry of...
The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical quantization. The previously established relationship bet...
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 i...
Wigner’s little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take different mathe...
We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special functions se...
We define a Euler characteristic χ(X,G) for a finite cell complex X with a finite group G acting cellularly on it. Then, each Ki(X) (a complex vector space with basis the i-cells of X) is a representation of G, and we define χ(X,G) to be the...
Graph-embedding algorithms map a graph into a vector space with the aim of preserving its structure and its intrinsic properties. Unfortunately, many of them are not able to encode the neighborhood information of the nodes well, especially from a top...
Estimating and predicting space weather is important to the space industry and space missions. The driver of space weather, especially near the Earth, is solar activity, the study of which is an important task. In particular, there is a direction of...
We present some lifting theorems for continuous order-preserving functions on locally and σ-compact Hausdorff preordered topological spaces. In particular, we show that a preorder on a locally and σ-compact Hausdorff topological space has...
We consider spaces of smooth functions obtained by relaxing Gevrey-type regularity and decay conditions. It is shown that these classes can be introduced by using the general framework of the weighted matrices approach to ultradifferentiable function...
Fine-grained change detection in sensor data is very challenging for artificial intelligence though it is critically important in practice. It is the process of identifying differences in the state of an object or phenomenon where the differences are...
We introduce a multi-parameter family of bases in the Hilbert space L2(R) that are associated to a set of Hermite functions, which also serve as a basis for L2(R). The Hermite functions are eigenfunctions of the Fourier transform, a property that is,...
The performance of quantitative structure–activity relationship (QSAR) models largely depends on the relevance of the selected molecular representation used as input data matrices. This work presents a thorough comparative analysis of two main...
The present paper elaborates on the development of a theory of discrete-time dynamical systems on finite-dimensional structured state spaces. Dynamical systems on structured state spaces possess well-known applications to solving differential equatio...
This article seeks to investigate the design and creation of several models and dioramas of Holocaust death camps as spatial and historical representations of Holocaust memory. It broadly discusses their use as pedagogical tools, forms of art, testim...
Based on the G. Goldin’s quantum current algebra symmetry representation theory, have succeeded in explaining a hidden relationship between the quantum many-particle Hamiltonian operators, defined in the Fock space, their factorized structure a...
Accurately modeling the effects of illumination and shadows during head rotation is critical in computer vision for enhancing image realism and reducing artifacts. This study delves into the latent space of denoising diffusion models to identify comp...
Representing visual experiences is an essential part of architectural design education for creativity. The representation of creative ideas relates to the ability to communicate spatial design concepts. This study examined whether filmic spaces could...
As the field of deep learning experiences a meteoric rise, the urgency to decipher the complex geometric properties of feature spaces, which underlie the effectiveness of diverse learning algorithms and optimization techniques, has become paramount....
Space-time adaptive processing (STAP) plays an essential role in clutter suppression and moving target detection in airborne radar systems. The main difficulty is that independent and identically distributed (i.i.d) training samples may not be suffic...
We study a separable Hilbert space of smooth curves taking values in the Segal–Bergmann space of analytic functions in the complex plane, and two of its subspaces that are the domains of unbounded non self-adjoint linear partial differential op...
This paper proposes the transformation S→C→, where S is a digital gray-level image and C→ is a vector expressed through the textural space. The proposed transformation is denominated Vectorial Image Representation on the...
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