Related papers: Separation properties of codimension-1 maps betwee…
The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…
Recent work in unsupervised multi-object segmentation shows impressive results by predicting motion from a single image despite the inherent ambiguity in predicting motion without the next image. On the other hand, the set of possible…
Most previous works of outdoor instance segmentation for images only use color information. We explore a novel direction of sensor fusion to exploit stereo cameras. Geometric information from disparities helps separate overlapping objects…
Cobordism groups of cooriented fold maps of codimension 1 are computed completely. Namely their odd torsion part coincides with that of the stable homotopy group of spheres in the same dimension, while the 2-primary part is the kernel of…
In this paper we give some coupled fixed point results for mappings satisfying different contractive conditions on complete partial metric spaces.
Given $n$ distinct points $\mathbf{x}_1, \ldots, \mathbf{x}_n$ in $\mathbb{R}^d$, let $K$ denote their convex hull, which we assume to be $d$-dimensional, and $B = \partial K $ its $(d-1)$-dimensional boundary. We construct an explicit…
We present a complete set of criteria for determining A-types of plane-to-plane map-germs of corank one with A-codimension <7, which provides a new insight into the A-classification theory from the viewpoint of recognition problem. As an…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
Object co-segmentation has drawn significant attention in recent years, thanks to its clarity on the expected foreground, the shared object in a group of images. Saliency fusion has been one of the promising ways to carry it out. However,…
Extension dimension is characterized in terms of $\omega$-maps. We apply this result to prove that extension dimension is preserved by refinable maps between metrizable spaces. It is also shown that refinable maps preserve some…
For every strong coarse homology theory we construct a coarse assembly map as a natural transformation between coarse homology theories. We provide various conditions implying that this assembly map is an equivalence. These results…
A new kind of Convolutional Codes generalizing Goppa Codes is proposed. This provides a systematic method for constructing convolutional codes with prefixed properties. In particular, examples of Maximum-Distance Separable (MDS)…
Special generic maps are generalizations of Morse functions with exactly two singular points on spheres and canonical projections of unit spheres. They restrict the manifolds of the domains strongly in considerable cases and are important…
We review recent results that lead to a very precise understanding of the dynamics of typical unimodal maps from the statistical point of view. We also describe the (generalized) renormalization approach to the study of the statistical…
We characterize maps between $n$-dimensional N\"obeling manifolds that can be approximated by homeomorphisms.
We present a constructive approach for approximating the conformal map (uniformization) of a polyhedral surface to a canonical domain in the plane. The main tool is a characterization of convex spaces of quasiconformal simplicial maps and…
This paper studies first the differential inequalities that make it possible to build a global theory of pseudo-holomorphic functions in the case of one or several complex variables. In the case of one complex dimension, we prove that the…
In this short note, we establish a quantitative description of the genericity of transversality of $C^1$-submanifolds in $\mathbb{R}^n$: Let $\Sigma \subset \mathbb{R}^n$ be a $d$-dimensional $C^1$-embedded submanifold where $n \geq d+1$.…
We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some…