Related papers: Graphs, lattices and deconstruction hierarchies
We study the problem of conjunctive query evaluation relative to a class of queries; this problem is formulated here as the relational homomorphism problem relative to a class of structures A, wherein each instance must be a pair of…
We study the set of all decompositions (clusterings) of a graph through its characterization as a set of lifted multicuts. This leads us to practically relevant insights related to the definition of a class of decompositions by must-join…
The deck of a topological space $X$ is the set $\mathcal{D}(X)=\{[X \setminus \{x\}] \colon x \in X\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever…
We are going to analyze local algorithms over sparse random graphs. These algorithms are based on local information where local regards to a decision made by the exploration of a small neighbourhood of a certain vertex plus a believe of the…
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
We prove that when assuming suitable non-degeneracy conditions equivariant harmonic maps into symmetric spaces of non-compact type depend in a real analytic fashion on the representation they are associated to. The main tool in the proof is…
We prove that the classification problem for graphs and several types of algebraic lattices (distributive, congruence and modular) up to isomorphism contains the classification problem for pairs of matrices up to simultaneous similarity.
Shape recognition and classification is a problem with a wide variety of applications. Several recent works have demonstrated that topological descriptors can be used as summaries of shapes and utilized to compute distances. In this…
In this work, we investigate the relationship between $k$-repre\-sentable graphs and graphs representable by $k$-local words. In particular, we show that every graph representable by a $k$-local word is $(k+1)$-representable. A previous…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
A unified description of the relationship between the Hamiltonian structure of a large class of integrable hierarchies of equations and W-algebras is discussed. The main result is an explicit formula showing that the former can be…
Deep neural networks have achieved remarkable success, yet our understanding of how they learn remains limited. These models can learn high-dimensional tasks, which is generally statistically intractable due to the curse of dimensionality.…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
One of the most basic facts related to the famous Ulam reconstruction conjecture is that the connectedness of a graph can be determined by the deck of its vertex-deleted subgraphs, which are considered up to isomorphism. We strengthen this…
We survey recent advances in the theory of graph and hypergraph decompositions, with a focus on extremal results involving minimum degree conditions. We also collect a number of intriguing open problems, and formulate new ones.
Graphs are widely used for modeling various types of interactions, such as email communications and online discussions. Many of such real-world graphs are temporal, and specifically, they grow over time with new nodes and edges. Counting…
In this paper, we investigate some relations between the invariants (including vertex and edge connectivity and forwarding indices) of a graph and its Laplacian eigenvalues. In addition, we present a sufficient condition for the existence…
The geometric Langlands program is distinguished in assigning spectral decompositions to all representations, not only the irreducible ones. However, it is not even clear what is meant by a spectral decomposition when one works with…
We show how graph theory concepts can provide an insight into the origin of slow dynamics in systems with kinetic constraints. In particular, we observe that slow dynamics is related to the presence of strong hierarchies between nodes on…
Spatial dependency and spatial embedding are basic physical properties of many phenomena modeled by networks. The most indicated computational environment to deal with spatial information is to use Georeferenced Information System (GIS) and…