Related papers: Reduced Connectivity for Local Bilinear Jacobi Set…

Lichnerowicz-Jacobi cohomology and homology of Jacobi manifolds are reviewed. We present both in a unified approach using the representation of the Lie algebra of functions on itself by means of the hamiltonian vector fields. The use of the…

We propose a new method for the reconstruction of simplicial complexes (combining points, edges and triangles) from 3D point clouds from Mobile Laser Scanning (MLS). Our main goal is to produce a reconstruction of a scene that is adapted to…

Segmenting curvilinear structures in medical images is essential for analyzing morphological patterns in clinical applications. Integrating topological properties, such as connectivity, improves segmentation accuracy and consistency.…

Understanding brain connectivity has become one of the most important issues in neuroscience. But connectivity data can reflect either the functional relationships of the brain activities or the anatomical properties between brain areas.…

This paper focuses on improving the performance of current convolutional neural networks in visual recognition without changing the network architecture. A hierarchical matcher is proposed that builds chains of local binary neural networks…

Bipartite networks are a well known strategy to study a variety of phenomena. The commonly used method to deal with this type of network is to project the bipartite data into a unipartite weighted graph and then using a backboning technique…

For a nonautonomous linear system with nonuniform contraction, we construct a topological equivalence between this system and an unbounded nonlinear perturbation. This topological equivalence is constructed as a composition of…

In this research, we propose a deep learning based approach for speeding up the topology optimization methods. The problem we seek to solve is the layout problem. The main novelty of this work is to state the problem as an image…

Although traditionally binary visual representations are mainly designed to reduce computational and storage costs in the image retrieval research, this paper argues that binary visual representations can be applied to large scale…

Here we propose a new method to compare the modular structure of a pair of node-aligned networks. The majority of current methods, such as normalized mutual information, compare two node partitions derived from a community detection…

This publication serves as an overview of clique topology -- a novel matrix analysis technique used to extract structural features from neural activity data that contains hidden nonlinearities. We highlight work done by Gusti et al. which…

Each complex hyperplane arrangement gives rise to a Milnor fibration of its complement. Although the Betti numbers of the Milnor fiber $F$ can be expressed in terms of the jump loci for rank 1 local systems on the complement, explicit…

Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine…

In this paper, we propose a method using the fusion of CNN and transformer structure to improve image classification performance. In the case of CNN, information about a local area on an image can be extracted well, but there is a limit to…

We present a unified framework to systematically embed complex knotted and linked structures, beyond the torus family, into diverse topological phases, including Hopf insulators, classical spin liquids, topological semimetals, and…

The classic method for computing the spectral decomposition of a real symmetric matrix, the Jacobi algorithm, can be accelerated by using mixed precision arithmetic. The Jacobi algorithm is aiming to reduce the off-diagonal entries…

Sparse autoencoders have become a standard tool for uncovering interpretable latent representations in neural networks. Yet salient concepts often span manifolds that current linear methods cannot capture without post hoc analysis. This…

We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…

In this paper we propose and analyze a fractional Jacobi-collocation spectral method for the second kind Volterra integral equations (VIEs) with weakly singular kernel $(x-s)^{-\mu},0<\mu<1$. First we develop a family of fractional Jacobi…

We study the homology groups of the complement of a complexified real line arrangement with coefficients in complex rank-one local systems. Using Borel--Moore homology, we establish an algorithm computing their dimensions via the real…