Related papers: Reduced Connectivity for Local Bilinear Jacobi Set…

In this work, we introduce a novel approach based on algebraic topology to enhance graph convolution and attention modules by incorporating local topological properties of the data. To do so, we consider the framework of sheaf neural…

Topological representations are rapidly becoming a popular way to capture and encode higher-order interactions in complex systems. They have found applications in disciplines as different as cancer genomics, brain function, and…

Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…

Complex molecules and mesoscopic structures are naturally described by general networks of elementary building blocks and tight-binding is one of the simplest quantum model suitable for studying the physical properties arising from the…

Within Convolutional Neural Network (CNN), the convolution operations are good at extracting local features but experience difficulty to capture global representations. Within visual transformer, the cascaded self-attention modules can…

In this paper, we develop holomorphic Jacobi structures. Holomorphic Jacobi manifolds are in one-to-one correspondence with certain homogeneous holomorphic Poisson manifolds. Furthermore, holomorphic Poisson manifolds can be looked at as…

This paper provides a method for the simultaneous topology optimization of parts and their corresponding joint locations in an assembly. Therein, the joint locations are not discrete and predefined, but continuously movable. The underlying…

Bilinear models has been shown to achieve impressive performance on a wide range of visual tasks, such as semantic segmentation, fine grained recognition and face recognition. However, bilinear features are high dimensional, typically on…

Existing convolution techniques in artificial neural networks suffer from huge computation complexity, while the biological neural network works in a much more powerful yet efficient way. Inspired by the biological plasticity of dendritic…

Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…

Data analysis often concerns not only the space where data come from, but also various types of maps attached to data. In recent years, several related structures have been used to study maps on data, including Reeb spaces, mappers and…

In this short paper, a neural network that is able to form a low dimensional topological hidden representation is explained. The neural network can be trained as an autoencoder, a classifier or mix of both, and produces different low…

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…

To accurately compute data-based prediction of Hamiltonian systems, especially the long-term evolution of such systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a case that is…

We develop a method of constructing structure-preserving integrators for Hamiltonian systems in Jacobi manifolds. Hamiltonian mechanics, rooted in symplectic and Poisson geometry, has long provided a foundation for modeling conservative…

Accurately segmenting thin tubular structures, such as vessels, nerves, roads or concrete cracks, is a crucial task in computer vision. Standard deep learning-based segmentation loss functions, such as Dice or Cross-Entropy, focus on…

We express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix…

This article presents a new set representation named the hybrid zonotope that is equivalent to the union of $2^N$ constrained zonotopes -- convex polytopes -- through the addition of $N$ binary zonotope factors. The major contribution of…

Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…

In the field of brain-machine interfaces, biohybrids offer an interesting new perspective, as in them, the technological side acts like a closed-loop extension or real counterpart of biological tissue, instead of the usual open loop…