Related papers: The Depth of a Hypersubstitution
An arbitrary-depth reduction theorem for the `convolution' multiple L-values of Euler-Zagier type is proven by an analytic method. To this end, generalized polylogarithms associated to Dirichlet characters are defined. The proof uses the…
Generating a description of an image is called image captioning. Image captioning requires to recognize the important objects, their attributes and their relationships in an image. It also needs to generate syntactically and semantically…
Depth measures quantify central tendency in the analysis of statistical and geometric data. Selecting a depth measure that is simple and efficiently computable is often important, e.g., when calculating depth for multiple query points or…
We study here a sequence of secondary measures, so called because the set of secondary polynomials on a given term become orthogonal for the next measure. The main result is a formula making explicit the density of any term of the sequence,…
We give an alternative definition of relative hyperbolicity based on properties of closest-point projections on peripheral subgroups. We also derive a distance formula for relatively hyperbolic groups, similar to the one for mapping class…
There is presented an algorithm for computing the topological degree for a large class of polynomial mappings. As an application there is given an effective algebraic formula for the intersection number of a polynomial immersion M --> R^2m,…
Color encoding of depth is shown to occur naturally in holograms that are reconstructed under white light illumination. It can be registered in a common color photograph, allowing a simple method of visual decoding by means of ordinary…
For some images, descriptions written by multiple people are consistent with each other. But for other images, descriptions across people vary considerably. In other words, some images are specific $-$ they elicit consistent descriptions…
The set of matrix tuples with invariant subspaces whose dimensions sum up to the dimension of the space, but which do not span the whole space form an algebraic hypersurface. We found the equation of this hypersurface. This generalizes…
We obtain sharp estimates involving the mean curvatures of higher order of a complete bounded hypersurface immersed in a complete Riemannian manifold. Similar results are also given for complete spacelike hypersurfaces in Lorentzian ambient…
Necessary and sufficient conditions are given for the existence of extended Schmidt decompositions, with more than two subspaces.
We present a novel method to train machine learning algorithms to estimate scene depths from a single image, by using the information provided by a camera's aperture as supervision. Prior works use a depth sensor's outputs or images of the…
In this paper, we present a formula describing the formation and decay of shock wave type solutions in some special cases.
We define and study a higher-dimensional version of model theoretic internality, and relate it to higher-dimensional definable groupoids in the base theory.
We present a generalization of a formula of higher order derivatives and give a short proof.
An expression for the first variation of the area functional of the second fundamental form is given for a hypersurface in a semi-Riemannian space. The concept of the "mean curvature of the second fundamental form" is then introduced. Some…
Depth map estimation from images is an important task in robotic systems. Existing methods can be categorized into two groups including multi-view stereo and monocular depth estimation. The former requires cameras to have large overlapping…
We are interested in the impact of entropies on the geometry of a hypersurface of a Riemannian manifold. In fact, we will be able to compare the volume entropy of a hypersurface with that of the ambient manifold, provided some geometric…
For finite reflection groups of types A and B, we determine the diameter of the graph whose vertices are reduced words for the longest element and whose edges are braid relations. This is deduced from a more general theorem that applies to…
We present a simple and effective image super-resolution algorithm that imposes an image formation constraint on the deep neural networks via pixel substitution. The proposed algorithm first uses a deep neural network to estimate…