Related papers: From axial C-hedra to general P-nets
A Capsule Network (CapsNet) is a relatively new classifier and one of the possible successors of Convolutional Neural Networks (CNNs). CapsNet maintains the spatial hierarchies between the features and outperforms CNNs at classifying images…
We give a combinatorial characterization of generic minimally rigid reflection frameworks. The main new idea is to study a pair of direction networks on the same graph such that one admits faithful realizations and the other has only…
Three themes of general topology: quotient spaces; absolute retracts; and inverse limits - are reapproached here in the setting of metrizable uniform spaces, with an eye to applications in geometric and algebraic topology. The results…
Microstructures are attracting academic and industrial interests with the rapid development of additive manufacturing. The numerical homogenization method has been well studied for analyzing mechanical behaviors of microstructures; however,…
Planar linkages are a rich area of study motivated by practical applications in engineering mechanisms. A central result is Kempe's Universality Theorem, which states that semi-algebraic sets can be realized by planar linkages. Polyhedral…
We introduce an evolving network model in which a new node attaches to a randomly selected target node and also to each of its neighbors with probability $p$. The resulting network is sparse for $p<\frac{1}{2}$ and dense (average degree…
We investigate the computational complexity of testing dominance and consistency in CP-nets. Previously, the complexity of dominance has been determined for restricted classes in which the dependency graph of the CP-net is acyclic. However,…
In the paper we give a complete classification of schemes of abstract perspectives between two tetrahedrons such that intersecting edges corespond under this perspective to intersecting edges.
In this paper, we tackle the task of establishing dense visual correspondences between images containing objects of the same category. This is a challenging task due to large intra-class variations and a lack of dense pixel level…
This paper studies the discrete differential geometry of the checkerboard pattern inscribed in a quadrilateral net by connecting edge midpoints. It turns out to be a versatile tool which allows us to consistently define principal nets,…
We consider linear and nonlinear coherent perfect absorbers (CPAs) in multidimensional geometries and construct explicitly the respective perfectly absorbed solutions. The multidimensional CPAs have a structure of the so-called simple…
A class of nets in constructive (in A.A.Markov's sense) topological space for which the convergence is equivalent to convergence of all subsequences, is described. B.A.Kushner's theorem about coincidence of strong and weak constructive…
We present a new approach to credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. Instead of applying the commonly used notion of strong independence, we replace it by the weaker notion of…
Credal sets are one of the most important models for describing probabilistic uncertainty. They usually arise as convex sets of probabilistic models compatible with judgments provided in terms of coherent lower previsions or more specific…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
The notion of proof-net category defined in this paper is closely related to graphs implicit in proof nets for the multiplicative fragment without constant propositions of linear logic. Analogous graphs occur in Kelly's and Mac Lane's…
Modular meta-learning is a new framework that generalizes to unseen datasets by combining a small set of neural modules in different ways. In this work we propose abstract graph networks: using graphs as abstractions of a system's subparts…
We introduce here a direct method to construct multivariate explicit B-spline bases. B-splines are piecewise polynomials, which are defined on adjacent tetrahedra and which are $C^{r}$ continuous throughout. The $C^{r}$ continuity is…
In this paper, we mainly study subtransversality and two types of strong CHIP (given via Fr\'echet and limiting normal cones) for a collection of finitely many closed sets. We first prove characterizations of Asplund spaces in terms of…
Given a connected graph G with p vertices and q edges, the G-graphicahedron is a vertex-transitive simple abstract polytope of rank q whose edge-graph is isomorphic to a Cayley graph of the symmetric group S_p associated with G. The paper…