arXiv research

Paper uses TDA to assess cryptocurrency risk by measuring phase space instability.

Measures time-delay embedding for noisy, sparse data.

Determinants of theta curves and symmetric graphs are studied.

Time-delayed embeddings avoid self-intersections for high enough delay.

Embed spherical quandles into Lie groups smoothly.

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications, including long-term asymptotic patterns. Whereas state-of-the-art data-driven approac…

A smooth counterexample to the Hamiltonian Seifert conjecture for six-dimensional symplectic manifolds is found. In particular, we construct a smooth proper function on the symplectic 2n-dimensional vector space, 2n > 4, such that one of its non-singular level sets carries no periodic orbits of the Hamiltonian flow. Th…

A method models nonlinear dynamics from data using barycentric coordinates and memory.

A neural network learns phase space properties for time series analysis.

DeepEDM forecasts time series by learning dynamics from embeddings.

The definition of quasi-local mass for a bounded space-like region in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary two-surface and should be independent of whichever space-like region it bounds. An impor…

Study embeddings of manifolds via acyclic maps and surgery.

We introduce a natural generalization of marginally outer trapped surfaces, called immersed marginally outer trapped surfaces, and prove that three dimensional asymptotically flat initial data sets either contain such surfaces or are diffeomorphic to R^3. We establish a generalization of the Penrose singularity theorem…

We outline a cohomological treatment for multivalued (classical) action functionals. We point out that an application of Takens' theorem, after Zuckerman, Deligne and Freed, allows to conclude that multivalued functionals yield globally defined variational equations.

We prove the semi-Riemannian bumpy metric theorem using equivariant variational genericity. The theorem states that, on a given compact manifold $M$, the set of semi-Riemannian metrics that admit only nondegenerate closed geodesics is generic relatively to the $C^k$-topology, $k=2,...,\infty$, in the set of metrics of …

A random group contains many subgroups which are isomorphic to the fundamental group of a compact hyperbolic 3-manifold with totally geodesic boundary. These subgroups can be taken to be quasi-isometrically embedded. This is true both in the few relators model, and the density model of random groups (at any density les…

Vogt's theorem, concerning boundary angles of a convex arc with monotonic curvature (spiral arc), is taken as a starting point to establish basic properties of spirals. The theorem is expanded by removing requirements of convexity and curvature continuity; the cases of inflection and multiple windings are considered. P…

New method phenotypes sleep apnea patients using time series analysis.

Stability theorem for concordance embeddings with applications.

Enhanced EEG classification using augmented covariance matrix.

Study finds significant instability in node embeddings due to randomness.

We restrict our discussion to the orientable category. For $g > 1$, let $OE_g$ be the maximum order of a finite group $G$ acting on the closed surface $Σ_g$ of genus $g$ which extends over $(S^3, Σ_g)$, where the maximum is taken over all possible embeddings $Σ_g\hookrightarrow S^3$. We will determine $OE_g$ for each $…

Embeds pre-multisymplectic manifolds into coisotropic ones.

New proof shows no Hölder embeddings into Heisenberg group.

We consider a compact connected CR manifold with a transversal CR locally free $\mathbb R$-action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fourier-Szegő kernel of the CR sections in the high tensor powers admits a full asymptotic expansion and we establish $\mathbb R$-equivariant K…

Alternative proof of coisotropic embedding theorem for pre-symplectic manifolds.

We extend the theorems concerning the equivariant symplectic reduction of the cotangent bundle to contact geometry. The role of the cotangent bundle is taken by the cosphere bundle. We use Albert's method for reduction at zero and Willett's method for non-zero reduction. We provide examples for both cases.

Knowledge graphs are used to represent relational information in terms of triples. To enable learning about domains, embedding models, such as tensor factorization models, can be used to make predictions of new triples. Often there is background taxonomic information (in terms of subclasses and subproperties) that shou…

Survey simplifies embedding theorems for manifolds.

The abstract discusses embedding theorems for pseudo-Kähler manifolds.

Nash's theorem proved with Günther's trick

We generalise theorems of Khodorovskiy and Park-Park-Shin, and give new topological proofs of those theorems, using embedded surfaces in the 4-ball and branched double covers. These theorems exhibit smooth codimension-zero embeddings of certain rational homology balls bounded by lens spaces.

We address the question of when a covering of the boundary of a surface can be extended to a covering of the surface (equivalently: when is there a branched cover with a prescribed monodromy). If such an extension is possible, when can the total space be taken to be connected? When can the extension be taken to be regu…

New guarantees for uniquely identifying transport maps and vector fields from finite measure-valued data.

Extends symplectic reduction and theorem to Lie algebroids.

We give several generalizations of the Kodaira vanishing and embedding theorems for Kähler manifolds to the case where the relevent line bundle has a small region of negative curvature. To prove the vanishing theorems we adapt techniques of Elworthy-Rosenberg for vanishing theorems in Riemannian geometry. For the embed…

This is the second of three papers about the Compression Theorem. We give proofs of Gromov's theorem on directed embeddings [M Gromov, Partial differential relations, Springer--Verlag (1986); 2.4.5 C'] and of the Normal Deformation Theorem [The compression theorem I; 4.7], arxiv:math.GT/9712235.

To a special type of grope embedded in 4-space, that we call an admissible grope, we associate a length function for each real number q at least 1. This gives rise to a family of pseudo-metrics d^q, refining the slice genus metric, on the set of concordance classes of knots, as the infimum of the length function taken …

Condition for embedding metric spaces into curved manifolds.

An complete exposition of Matthias Gunther's elementary proof of Nash's isometric embedding theorem.

The paper proves isometric embeddings for smooth manifolds.

3D Schoenflies theorem for simply-connected 2-complexes.

The Bonnet theorem is proven for statistical manifolds.

Study improves boundary smoothness for area-minimizing currents with complex boundaries.

Theorem proves congruence for compact submanifolds in a sphere.

In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.

Explains Hodge theory and Kodaira embedding theorem for complex manifolds.

Embedding theorem for tractor bundles applied to conformal geometry.