This result is a direct method for inverting nonuniform discrete transforms with a complexity that is nearly linear with respect to the degrees of freedom in the problem.
Numerical Analysis Numerical Analysis 65T50, 65F55, 65F20
This paper presents a new boundary-value problem formulation for quantifying uncertainty induced by the presence of small Brownian noise near transversally stable periodic orbits (limit cycles) and quasiperiodic invariant tori of the deterministic dynamical systems obtained in the absence of noise.
Dynamical Systems Numerical Analysis Numerical Analysis Probability Chaotic Dynamics
This work presents a new algorithm to compute the matrix exponential within a given tolerance.
Numerical Analysis Numerical Analysis 15A16 G.1.3; G.1.7
Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian inference.
Numerical Analysis Numerical Analysis
We present an exposition of the *Chain Bounding Lemma*, which is a common generalization of both Zorn's Lemma and the Bourbaki-Witt fixed point theorem.
Logic History and Overview 06A06, 03E25, 68V20, 03-01 F.4.1; I.2.3
Furthermore, for a finite discrete set of points in the Euclidean space, we provide the construction of persistent interaction Vietoris-Rips complexes and compute their interaction homology and interaction Laplacians.
Algebraic Topology
The zonotope containment problem, i. e., whether one zonotope is contained in another, is a central problem in control theory to compute invariant sets, obtain fixed points of reachable sets, detect faults, and robustify controllers.
Optimization and Control
The technique of inducing spectral gaps for cohomological Laplacians in degree zero was used by Kaluba, Kielak and Nowak to prove property (T) for $\operatorname{SAut}(F_n)$ and $\operatorname{SL}_n(\mathbb{Z})$.
Group Theory
Furthermore, by partitioning the time-dependent domain into macroelements, a more efficient stabilization procedure for the cut finite element method in time-dependent domains is presented.
Numerical Analysis Numerical Analysis 65N30, 65N22, 65N85, 65N99
We discuss formulas for the asymptotic growth rate of the number of summands in tensor powers in certain (finite or infinite) monoidal categories.
Category Theory Combinatorics Representation Theory Primary: 11N45, 18M05, Secondary: 05C81, 15A18, 20C20
