Related papers: An intrinsic homotopy for intersecting algebraic v…
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…
Interactions in complex systems are widely observed across various fields, drawing increased attention from researchers. In mathematics, efforts are made to develop various theories and methods for studying the interactions between spaces.…
Motivated by the need to develop a general framework for performing statistical inference for discretely observed random rough differential equations, our aim is to construct a geometric $p$-rough path ${\bf X}$ whose response $Y$, when…
In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This…
We combine tools from homotopy continuation solvers with the methods of analytic combinatorics in several variables to give the first practical algorithm and implementation for the asymptotics of multivariate rational generating functions…
A numerical irreducible decomposition for a polynomial system provides representations for the irreducible factors of all positive dimensional solution sets of the system, separated from its isolated solutions. Homotopy continuation methods…
This paper investigates the upper bound of the number of integer (natural) solutions of inhomogeneous algebraic Diophantine diagonal equations with integer coefficients without a free member via the circle method of Hardy and Littlewood.…
We propose an automatic algorithm for 3D inverse electromagnetic scattering based on the combination of topological derivatives and regularized Gauss-Newton iterations. The algorithm is adapted to decoding digital holograms. A hologram is a…
In this paper, we obtain an asymptotic formula for the number of integral solutions to a system of diagonal equations. We obtain an asymptotic formula for the number of solutions with variables restricted to smooth numbers as well. We…
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…
In this paper we propose a primal-dual homotopy method for $\ell_1$-minimization problems with infinity norm constraints in the context of sparse reconstruction. The natural homotopy parameter is the value of the bound for the constraints…
This paper introduces the induced matching distance, a novel topological metric designed to compare discrete structures represented by a symmetric non-negative function. We apply this notion to analyze agent trajectories over time. We use…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can…
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to…
For digital images, there is an established homotopy equivalence relation which parallels that of classical topology. Many classical homotopy equivalence invariants, such as the Euler characteristic and the homology groups, do not remain…
How can Transformers model and learn enumerative geometry? What is a robust procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work, we introduce a Transformer-based…
Twisted Lie algebroid cohomologies, i.e. with values in representations, are shown to be Lie algebroid homotopy-invariant. Several important classes of examples are discussed. As an application, a generalized version of the Poincar\'e lemma…
We consider the problem of inferring the topology of a network using the measurements available at the end nodes, without cooperation from the internal nodes. To this end, we provide a simple method to obtain path interference which…