Related papers: The Block Neighborhood
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
This is an introductory survey on cluster algebras and their (additive) categorification using derived categories of Ginzburg algebras. After a gentle introduction to cluster combinatorics, we review important examples of coordinate rings…
One of the roadmap plans for quantum computers is an integration within HPC ecosystems assigning them a role of accelerators for a variety of computationally hard tasks. However, in the near term, quantum hardware will be in a constant…
The character of an irreducible admissible representation of a $p$-adic reductive group is known to be a constant function in some neighborhood of any regular semisimple element $\gamma$ in the group. Under certain mild restrictions on…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials. We present explicit and self-contained proof for all of them,…
This article describes an approach to designing a distributed and modular neural classifier. This approach introduces a new hierarchical clustering that enables one to determine reliable regions in the representation space by exploiting…
Inspired by connections to two dimensional quantum theory, we define several models of computation based on permuting distinguishable particles (which we call balls), and characterize their computational complexity. In the quantum setting,…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
We explore the combinatorial properties of the branching areas of execution paths in higher dimensional automata. Mathematically, this means that we investigate the combinatorics of the negative corner (or branching) homology of a globular…
Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…
Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder…
Community detection is the problem of identifying community structure in graphs. Often the graph is modeled as a sample from the Stochastic Block Model, in which each vertex belongs to a community. The probability that two vertices are…
Let G be a finite group, let N be a normal subgroup of G, and let theta in Irr(N) be a G-invariant character. We fix a prime p, and we introduce a canonical partition of Irr(G|theta) relative to p. We call each member B_theta of this…
Consider a one-parameter family of algebraic varieties degenerating to a reducible one. Our main result is a formula for the fundamental cycle of the limit subscheme of any family of effective Cartier divisors. The formula expresses this…
In this work we present a new methodology to study the structure of the configuration spaces of hard combinatorial problems. It consists in building the network that has as nodes the locally optimal configurations and as edges the weighted…
The problem of community detection in networks is usually formulated as finding a single partition of the network into some "correct" number of communities. We argue that it is more interpretable and in some regimes more accurate to…
We formulate a notion of "geometric reductivity" in an abstract categorical setting which we refer to as adequacy. The main theorem states that the adequacy condition implies that the ring of invariants is finitely generated. This result…
Attributed network embedding has attracted plenty of interest in recent years. It aims to learn task-independent, low-dimensional, and continuous vectors for nodes preserving both topology and attribute information. Most of the existing…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…