Latest Research

Online learning in bifurcating dynamic systems via SINDy and Kalman filtering

contipaolo/ekf-sindy 7 Nov 2024

We propose the use of the Extended Kalman Filter (EKF) for online data assimilation and update of a dynamic model, preliminary identified through the Sparse Identification of Nonlinear Dynamics (SINDy).

Dynamical Systems

40
07 Nov 2024

Manifold Diffusion Geometry: Curvature, Tangent Spaces, and Dimension

Iolo-Jones/ManifoldDiffusionGeometry 6 Nov 2024

We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry.

Differential Geometry Algebraic Topology

23
06 Nov 2024

Fractional Chromatic Numbers from Exact Decision Diagrams

trewes/ddcolors 5 Nov 2024

We prove that the solution to the linear flow relaxation on exact decision diagrams determines the fractional chromatic number of a graph.

Combinatorics Discrete Mathematics 05C15 G.2.2

0
05 Nov 2024

Spectral Transformation for the Dense Symmetric Semidefinite Generalized Eigenvalue Problem

m-a-stewart/DenseSpectralTransformation.jl 5 Nov 2024

Under the same assumptions on the shift, the analysis of the algorithm for the shifted and inverted problem leads to useful error bounds for the original problem, including a bound that shows how a single shift that is of moderate size in a scaled sense can be chosen so that every computed generalized eigenvalue corresponds to a generalized eigenvalue of a pair of matrices close to $A$ and $B$.

Numerical Analysis Numerical Analysis 65F15 (Primary), 15A22, 15A22, 15A23, 15A42 (Secondary)

0
05 Nov 2024

Fast and robust consensus-based optimization via optimal feedback control

AmberYuyangHuang/ControlledCBO 5 Nov 2024

We propose a variant of consensus-based optimization (CBO) algorithms, controlled-CBO, which introduces a feedback control term to improve convergence towards global minimizers of non-convex functions in multiple dimensions.

Optimization and Control 65K10, 35Q93, 90C56

0
05 Nov 2024

Applications of Automatic Differentiation in Image Registration

wdwatson2/ImgRegPytorchProject 5 Nov 2024

We demonstrate that automatic differentiation, which has become commonly available in machine learning frameworks, is an efficient way to explore ideas that lead to algorithmic improvement in multi-scale affine image registration and affine super-resolution problems.

Optimization and Control

0
05 Nov 2024

Novel performant primality test on a Pell's cubic

luckydd99/novel_performant_primality_test 3 Nov 2024

Primality testing is an especially useful topic for public-key cryptography.

Number Theory

0
03 Nov 2024

Computational Bifurcation Analysis

jansieber/ds-handbook24-odebifurcations-resources 1 Nov 2024

Continuation techniques generate continuous families of such solutions in the combined state and parameter space, e. g., curves (branches) of periodic orbits or surfaces of equilibria.

Dynamical Systems

0
01 Nov 2024

FPRev: Revealing the Order of Floating-Point Summation by Numerical Testing

microsoft/repdl 1 Nov 2024

The order of floating-point summation is a key factor in numerical reproducibility.

Numerical Analysis Numerical Analysis Software Engineering

4
01 Nov 2024

Unconditionally stable space-time isogeometric discretization for the wave equation in Hamiltonian formulation

xtiga-waves/xtiga-waves 1 Nov 2024

We consider a family of conforming space-time discretizations for the wave equation based on a first-order-in-time formulation employing maximal regularity splines.

Numerical Analysis Numerical Analysis 65M60, 15A12, 65L60, 15B05

2
01 Nov 2024