Related papers: Note on half-cube embeddings
Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally…
Partial combinatory algebras are algebraic structures that serve as generalized models of computation. In this paper, we study embeddings of pcas. In particular, we systematize the embeddings between relativizations of Kleene's models, of…
Let $d$ be an integer greater than $1$, and let $t$ be fixed such that $\frac{1}{d} < t < \frac{1}{d-1}$. We prove that for any $n_0$ chosen sufficiently large depending upon $t$, the $d$-dimensional cubes of sidelength $n^{-t}$ for $n \geq…
In this paper we survey with complete proofs some well--known, but hard to find, results about constructing closed embedded minimal surfaces in a closed 3-dimensional manifold via min--max arguments. This includes results of J. Pitts, F.…
Composed of square particles, the tetratic phase is characterised by a four-fold symmetry with quasi-long-range orientational order but no translational order. We construct the elastic free energy for tetratics and find a closed form…
We give a brief proof of a recent result of Avron, Seiler and Simon.
Metric embedding is a powerful tool used extensively in mathematics and computer science. We devise a new method of using metric embeddings recursively, which turns out to be particularly effective in $\ell_p$ spaces, $p>2$, yielding…
Each restriction semigroup is proved to be embeddable in a factorisable restriction monoid, or, equivalently, in an almost factorisable restriction semigroup. It is also established that each restriction semigroup has a proper cover which…
It is proved that for any prescribed orientation of the triples of either a Steiner triple system or a Latin square of odd order, there exists an embedding in an orientable surface with the triples forming triangular faces and one extra…
This is a pedagogical article cited in the foregoing research note, quant-ph/9911050
In this paper, we construct smooth isometric embeddings of multiple warped product manifolds in quadrics of semi-Euclidean spaces. Our main theorem generalizes previous results as given by Blanusa, Rozendorn, Henke and Azov.
We prove that smooth cube manifolds have normal smooth structures.
This paper investigates some univariate and bivariate constrained interpolation problems using rational quartic fractal interpolation functions, which has been submitted long back in a reputed journal and revised as per the journal…
We devise a new embedding technique, which we call measured descent, based on decomposing a metric space locally, at varying speeds, according to the density of some probability measure. This provides a refined and unified framework for the…
Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the…
We prove that under some assumptions on the mean curvature the set of umbilical points of an immersed surface in a $3$-dimensional space form has positive measure. In case of an immersed sphere our result can be seen as a generalization of…
We demonstrate a new approach to the computation of ratios of elliptic integrals. It turns out that almost closed polygons interscribed between two conics retain some of the properties of such closed polygons. We apply these retained…
We prove the existence of multiple closed geodesics on non-compact cylindrica manifolds.
While paragraph embedding models are remarkably effective for downstream classification tasks, what they learn and encode into a single vector remains opaque. In this paper, we investigate a state-of-the-art paragraph embedding method…
This is an appendix to arXiv:1610.04888, "Quantitative null-cobordism", which improves one of the main results of that paper to a near-sharp one. It is not a self-contained paper.