Related papers: Gadget construction and structural convergence
We prove a theorem computing the number of solutions to a system of equations which is generic subject to the sparsity conditions embodied in a graph. We apply this theorem to games obeying graphical models and to extensive-form games. We…
We develop a categorical framework for reasoning about abstract properties of differentiation, based on the theory of fibrations. Our work encompasses the first-order fragments of several existing categorical structures for differentiation,…
We consider first order expressible properties of random perfect graphs. That is, we pick a graph $G_n$ uniformly at random from all (labelled) perfect graphs on $n$ vertices and consider the probability that it satisfies some graph…
Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…
We study the scenario of graph-based clustering algorithms such as spectral clustering. Given a set of data points, one first has to construct a graph on the data points and then apply a graph clustering algorithm to find a suitable…
The Union Closed Sets Conjecture is one of the most renowned problems in combinatorics. Its appeal lies in the simplicity of its statement contrasted with the potential complexity of its resolution. The conjecture posits that, in any union…
In this work we develop a numerical method for solving a type of convex graph-structured tensor optimization problems. This type of problems, which can be seen as a generalization of multi-marginal optimal transport problems with…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
The processes of constructing some graphs from others using binary operations of union with intersection (gluing) are studied. For graph classes closed with respect to gluing operations the elemental and operational bases are introduced.…
Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…
In this work we explore the fundamental structure-adaptiveness of state of the art randomized first order algorithms on regularized empirical risk minimization tasks, where the solution has intrinsic low-dimensional structure (such as…
We present novel graph kernels for graphs with node and edge labels that have ordered neighborhoods, i.e. when neighbor nodes follow an order. Graphs with ordered neighborhoods are a natural data representation for evolving graphs where…
In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…
A class of structures is monadically dependent if one cannot interpret all graphs in colored expansions from the class using a fixed first-order formula. A tree-ordered $\sigma$-structure is the expansion of a $\sigma$-structure with a…
\begin{abstract} Greedy permutations, also known as Gonzalez Orderings or Farthest Point Traversals are a standard way to approximate $k$-center clustering and have many applications in sampling and approximating metric spaces. A greedy…
Graphs are a fundamental abstraction in computer science and discrete mathematics, where information is encoded in their combinatorial structure. Graph-reduction techniques aim at simplifying graphs while preserving selected structural…
(First-order) transductions are a basic notion capturing graph modifications that can be described in first-order logic. In this work, we propose an efficient algorithmic method to approximately reverse the application of a transduction,…
We present a form convergence theorem for sequences of sectorial forms and their associated semigroups in a complex Hilbert space. Roughly speaking, the approximating forms $a_n$ are all `bounded below' by the limiting form $a$, but in…
A foundational theory of compositional categorical rewriting theory is presented, based on a collection of fibration-like properties that collectively induce and intrinsically structure the large collection of lemmata used in the proofs of…
We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…