arXiv research

Abstract reviews geometric theories of smooth and F-smooth systems.

We discuss smooth nonlinear control systems with symmetry. For a free and proper action of the symmetry group, the reduction of symmetry gives rise to a reduced smooth nonlinear control system. If the action of the symmetry group is only proper, the reduced nonlinear control system need not be smooth. Using the smooth …

In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering an…

New approach to solving minimal surface system Dirichlet problem on smooth domains.

Estimates multiple linear systems on a graph with smoothness constraints.

Multisections generalize trisections for 4-manifolds, allowing complex operations and explicit diagrams.

Proves local bi-integrability of bi-Hamiltonian systems on real smooth manifolds.

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning,…

Paper develops algorithms for PWA systems with polynomial regret.

Solves Demailly's system for direct sums of ample line bundles on Riemann surfaces.

New theory for nonsmooth systems helps optimize and control complex functions.

Discrete conjugate systems are quadrilateral nets with all planar faces. Discrete orthogonal systems are defined by the additional property of all faces being concircular. Their geometric properties allow one to consider them as proper discretization of conjugate, resp. orthogonal coordinate systems of classical differ…

New nonlinear smoothers improve state estimation in chaotic systems.

We prove a global smooth isometric immersion for negatively curved surfaces with finite total curvature.

Study stabilizes second-order systems to first-order dynamics.

Study proves uniqueness of corrugated negatively curved immersions in differential geometry.

We prove that a topological contact isotopy uniquely defines a topological contact Hamiltonian. Combined with previous results from [MS11], this generalizes the classical one-to-one correspondence between smooth contact isotopies and their generating smooth contact Hamiltonians and conformal factors to the group of top…

Study bandit problem on smooth graph functions for recommender systems.

New solutions found for complex structures on specific manifolds.

Lower bounds for delta invariant of weighted hypersurfaces proved for K-stability.

The paper studies invariant complex manifolds in holomorphic slow-fast systems.

When the Poincaré map associated with a periodic orbit of a hybrid dynamical system has constant-rank iterates, we demonstrate the existence of a constant-dimensional invariant subsystem near the orbit which attracts all nearby trajectories in finite time. This result shows that the long-term behavior of a hybrid model…

Just as an explicit parameterisation of system dynamics by state, i.e., a choice of coordinates, can impede the identification of general structure, so it is too with an explicit parameterisation of system dynamics by control. However, such explicit and fixed parameterisation by control is commonplace in control theory…

Develops theory for data-driven methods in dynamical systems.

The paper proposes a decoupled approach to efficiently estimate CoVaR, a measure of systemic financial risk.

Floer constructs homology from flow lines in generalized dynamical systems and combinatorial vector fields.

We construct new smooth solutions to the Hull-Strominger system, showing that the Fu-Yau solution on torus bundles over K3 surfaces can be generalized to torus bundles over K3 orbifolds. In particular, we prove that, for $13 \leq k \leq 22$ and $14\leq r\leq 22$, the smooth manifolds $S^1\times \sharp_k(S^2\times S^3)$…

We study here systems of symmetries on $|1|$--graded parabolic geometries. We are interested in smooth systems of symmetries and we discuss non--flat homogeneous $|1|$--graded geometries. We show the existence of an invariant admissible affine connection under quite weak condition on the system.

Study shows infinite kernels in topological monodromy for curve families.

Whereas subriemannian geometry usually deals with smooth horizontal distributions, partially hyperbolic dynamical systems provide many examples of subriemannian geometries defined by non-smooth (namely, Hölder continuous) distributions. These distributions are of great significance for the behavior of the parent dynami…

Adaptive NN method improves matrix completion for non-smooth data.

Continuous control imitation learning fails if expert actions are smooth.

FLUID uses flows to unify filtering and smoothing for complex systems.

Smooth flows for physical systems with smooth energies and forces.

In this paper, by the method of moving planes, we establish the monotonicity and symmetry properties of convex solutions for Monge-Ampere systems on bounded smooth planar domains.

Proposes a spectral method for jointly smooth functions on multiple manifolds.

We give a new proof for the local existence of a smooth isometric embedding of a smooth $3$-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into $6$-dimensional Euclidean space. Our proof avoids the sophisticated arguments via microlocal analysis used in earlier proofs. In Part 1, we introduce …

Extends curve theory to non-smooth data with finite curvature and torsion.

We establish a connection between trend filtering and system identification which results in a family of new identification methods for linear, time-varying (LTV) dynamical models based on convex optimization. We demonstrate how the design of the cost function promotes a model with either a continuous change in dynamic…

Consider a Riemannian metric on two-torus. We prove that the question of existence of polynomial first integrals leads naturally to a remarkable system of quasi-linear equations which turns out to be a Rich system of conservation laws. This reduces the question of integrability to the question of existence of smooth (q…

Geometric framework for dynamic feedback linearization of control systems with symmetry.

The paper gives a constructive method, based on greedy algorithms, that provides for the classes of functions with small mixed smoothness the best possible in the sense of order approximation error for the $m$-term approximation with respect to the trigonometric system.

A uniqueness result in the inverse problem for an inhomogeneous hyperbolic system on a real vector bundle over a smooth compact manifold, based on energy measurements for improperly known sources, is established.

Learning optimal resource allocation policies in wireless systems can be effectively achieved by formulating finite dimensional constrained programs which depend on system configuration, as well as the adopted learning parameterization. The interest here is in cases where system models are unavailable, prompting method…

In this paper we construct explicit smooth solutions to the Strominger system on generalized Calabi-Gray manifolds, which are compact non-Kähler Calabi-Yau 3-folds with infinitely many distinct topological types and sets of Hodge numbers.

A (smooth) dynamical system with transformation group $\mathbb{T}^n$ is a triple $(A,\mathbb{T}^n,α)$, consisting of a unital locally convex algebra $A$, the $n$-torus $\mathbb{T}^n$ and a group homomorphism $α:\mathbb{T}^n\rightarrow\Aut(A)$, which induces a (smooth) continuous action of $\mathbb{T}^n$ on $A$. In this…

This paper is being withdrawn by the author due a serious flaw.

We apply Arnold's theory of generic smooth plane curves to Stark-Zeeman systems. This is a class of Hamiltonian dynamical systems that describes the dynamics of an electron in an external electric and magnetic field, and includes many systems from celestial mechanics. Based on Arnold's $J^+$-invariant, we introduce inv…