Related papers: Reduced Connectivity for Local Bilinear Jacobi Set…

We develop a topological lens on relational schema design by encoding functional dependencies (FDs) as simplices of an abstract simplicial complex. This dependency complex exposes multi-attribute interactions and enables homological…

Deep learning methods have achieved impressive performance for multi-class medical image segmentation. However, they are limited in their ability to encode topological interactions among different classes (e.g., containment and exclusion).…

Surgical Scene Graphs abstract the complexity of surgical operating rooms (OR) into a structure of entities and their relations, but existing paradigms suffer from strictly dyadic structural limitations. Frameworks that predominantly rely…

The reduced peripheral system was introduced by Milnor in the fifties for the study of links up to link-homotopy, i.e. up to isotopies and crossing changes within each link component. However, for four or more components, this invariant…

We propose a gradient-based Jacobi algorithm for a class of maximization problems on the unitary group, with a focus on approximate diagonalization of complex matrices and tensors by unitary transformations. We provide weak convergence…

This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition,…

One of the critical steps in improving accurate single neuron reconstruction from three-dimensional (3D) optical microscope images is the neuronal structure segmentation. However, they are always hard to segment due to the lack in quality.…

In this paper we examine a novel addition to the known methods for learning Bayesian networks from data that improves the quality of the learned networks. Our approach explicitly represents and learns the local structure in the conditional…

Random abstract simplicial complex representation provides a mathematical description of wireless networks and their topology. In order to reduce the energy consumption in this type of network, we intend to reduce the number of network…

We consider the problem of identifying a parallel Wiener-Hammerstein structure from Volterra kernels. Methods based on Volterra kernels typically resort to coupled tensor decompositions of the kernels. However, in the case of parallel…

We establish a topological criterion for connection between reducibility to constant rotations and dual localization, for the general family of analytic quasiperiodic Jacobi operators. As a corollary, we obtain the sharp arithmetic phase…

This article describes the application of recently introduced complex networks concepts and methods to the characterization and analysis of cortical bone structure. Three-dimensional reconstructions of the system of channels underlying bone…

Multipoint secant and interpolation methods are effective tools for solving systems of nonlinear equations. They use quasi-Newton updates for approximating the Jacobian matrix. Owing to their ability to more completely utilize the…

Navigating topological transitions in cellular mechanical systems is a significant challenge for existing simulation methods. While abstract models lack predictive capabilities at the cellular level, explicit network representations…

We describe a skeletonization of the spherical harmonic connection problem that reduces the storage and pre-computation to superoptimal complexities at the cost of increasing the execution time by the modest multiplicative factor of…

The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…

We begin by introducing schemes of binoids, invertible $\mathcal{O}_M$-sets and cohomology of sheaves of abelian groups defined on schemes of binoids. We define the so-called punctured combinatorial \v{C}ech-Picard complex, whose first…

Layered neural networks have greatly improved the performance of various applications including image processing, speech recognition, natural language processing, and bioinformatics. However, it is still difficult to discover or interpret…

Researchers in the field of connectomics are working to reconstruct a map of neural connections in the brain in order to understand at a fundamental level how the brain processes information. Constructing this wiring diagram is done by…

Prior works have proposed several strategies to reduce the computational cost of self-attention mechanism. Many of these works consider decomposing the self-attention procedure into regional and local feature extraction procedures that each…