Related papers: Isotopies vis-\`a-vis level-preserving embeddings
Conventional mode tracking operates in the dark: it traces dispersion branches on the non-Hermitian eigenvalue manifold using only local continuity, unaware of the global Riemann-sheet topology. When exceptional points (EPs) lie close to…
A road map can be interpreted as a graph embedded in the plane, in which each vertex corresponds to a road junction and each edge to a particular road section. We consider the cartographic problem to place non-overlapping road labels along…
Doubly periodic tangles, or DP tangles, are embeddings of curves in the thickened plane that are periodically repeated in two directions. They are defined as universal covers of their generating cells, the flat motifs, which represent knots…
Entropic independence is a structural property of measures that underlies modern proofs of functional inequalities, notably (modified) log-Sobolev inequalities, via ``annealing'' or local-to-global schemes. Existing sufficient criteria for…
The embedding theorem of Roelcke and Dierolf for the completions of four standard uniform structures on topological groups and their quotients holds more generally for spaces of uniform measures. The natural mappings between the four spaces…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
If a continuous map f: X->Q is approximable arbitrary closely by embeddings X->Q, can some embedding be taken onto f by a pseudo-isotopy? This question, called Isotopic Realization Problem, was raised by Shchepin and Akhmet'ev. We consider…
Computer simulations show that liquids of molecules with harmonic intramolecular bonds may have "pseudoisomorphic" lines of approximately invariant dynamics in the thermodynamic phase diagram. We demonstrate that these lines can be…
Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…
This paper shows that, modern word embeddings contain information that distinguishes synonyms and antonyms despite small cosine similarities between corresponding vectors. This information is encoded in the geometry of the embeddings and…
The aim of this work is to study a kind of refinement of the entropy conjecture, in the context of partially hyperbolic diffeomorphisms with one dimensional central direction, of d-dimensional torus. We start by establishing a connection…
A precise meaning is given to the notion of continuous iteration of a mapping. Usual discrete iterations are extended into a dynamical flow which is a homotopy of them all. The continuous iterate reveals that a dynamical map is formend by…
This paper presents the notion of a variation entropy. This concept is an entropy framework for the gradient of the solution of a conservation law instead of on the solution itself. It appears that all semi-norms are admissible variation…
We construct a space which is useful in order to study the entropy of meromorphic maps by using projective limits. We deduce a variational principle for meromorphic maps.
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
We discuss a geometrical interpretation of the Z-invariant Ising model in terms of isoradial embeddings of planar lattices. The Z-invariant Ising model can be defined on an arbitrary planar lattice if and only if certain paths on the…
The language and methods of algebraic topology, particularly homotopy theory, have been extensively used in the study of the identification, the classification and the evolution of defects. Topological methods provide the means for the…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
In this paper we introduce the problem of counting embedded spheres in R^3 whose projection to the z-axis yields a level set barcode of a particular type. Two embedded spheres are considered height equivalent if they are related by a…
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…