Related papers: Reflexive graph lenses in univalent foundations
Generative self-supervised learning on graphs, particularly graph masked autoencoders, has emerged as a popular learning paradigm and demonstrated its efficacy in handling non-Euclidean data. However, several remaining issues limit the…
We give an invariant nondegeneracy condition for CR--maps between generic submanifolds in different dimensions and use it to prove a reflection principle for these maps.
We introduce (weak) oddomorphisms of graphs which are homomorphisms with additional constraints based on parity. These maps turn out to have interesting properties (e.g., they preserve planarity), particularly in relation to homomorphism…
We introduce Multi-Object Generative Perception (MultiGP), a generative inverse rendering method for stochastic sampling of all radiometric constituents -- reflectance, texture, and illumination -- underlying object appearance from a single…
Unigraphs are graphs uniquely determined by their own degree sequence up to isomorphism. There are many subclasses of unigraphs such as threshold graphs, split matrogenic graphs, matroidal graphs, and matrogenic graphs. Unigraphs and these…
The observables in a strong gravitational lens are usually just the image positions and sometimes the flux ratios. We develop a new and simple algorithm which allows a set of models to be fitted exactly to the observations. Taking our cue…
Some families of graphs, such as the n-cubes and Sierpinski gaskets, are self-similar. In this paper we show how such recursive structure can be used systematically to prove isoperimetric theorems.
The Gruenberg-Kegel graph $\Gamma(G)$ of a finite group $G$ is the graph whose vertex set is the set of prime divisors of $|G|$ and in which two distinct vertices $r$ and $s$ are adjacent if and only if there exists an element of order $rs$…
In a number of recent papers, (k+l)-graphs have been constructed from k-graphs by inserting new edges in the last l dimensions. These constructions have been motivated by C*-algebraic considerations, so they have not been treated…
We unify several seemingly different graph and digraph classes under one umbrella. These classes are all broadly speaking different generalizations of interval graphs, and include, in addition to interval graphs, also adjusted interval…
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered…
We develop a denotational semantics for general reference types in an impredicative version of guarded homotopy type theory, an adaptation of synthetic guarded domain theory to Voevodsky's univalent foundations. We observe for the first…
We prove that an arbitrary compact metrizable group can be realized as the automorphism group of a graphing; this is a continuous analogue to Frucht's theorem recovering arbitrary finite groups are automorphism groups of finite graphs. The…
It is a well-known theorem of homotopy type theory, originally due to Voevodsky, that function extensionality holds inside any univalent universe. We consider a weaker variant of the univalence axiom, asserting that the wild category formed…
Detecting dense landmarks for diverse clothes, as a fundamental technique for clothes analysis, has attracted increasing research attention due to its huge application potential. However, due to the lack of modeling underlying semantic…
Reynolds' original theory of relational parametricity was intended to capture the idea that polymorphically typed System F programs preserve all relations between inputs. But as Reynolds himself later showed, his theory can only be…
Graphs are commonly used to represent objects, such as images and text, for pattern classification. In a dynamic world, an object may continuously evolve over time, and so does the graph extracted from the underlying object. These changes…
We introduce a new class of countably infinite random geometric graphs, whose vertices are points in a metric space, and vertices are adjacent independently with probability p if the metric distance between the vertices is below a given…
We examine spaces of connected tri-/univalent graphs subject to local relations which are motivated by the theory of Vassiliev invariants. It is shown that the behaviour of ladder-like subgraphs is strongly related to the parity of the…
Given a finite, simple, connected graph $G=(V,E)$ with $|V|=n$, we consider the associated graph Laplacian matrix $L = D - A$ with eigenvalues $0 = \lambda_1 < \lambda_2 \leq \dots \leq \lambda_n$. One can also consider the same graph…