Related papers: Chip-firing on general invertible matrices
Motivated by the notion of chip-firing on the dual graph of a planar graph, we consider `integral flow chip-firing' on an arbitrary graph $G$. The chip-firing rule is governed by ${\mathcal L}^*(G)$, the dual Laplacian of $G$ determined by…
We extend the notion of chip-firing to weighted graphs, and generalize the Greedy Algorithm and Dhar's Burning Algorithm to weighted graphs. For a vertex $q \in V(\Gamma)$, we give an upper bound for the number of linearly equivalent…
We consider chip-firing dynamics defined by arbitrary M-matrices. M-matrices generalize graph Laplacians and were shown by Gabrielov to yield avalanche finite systems. Building on the work of Baker and Shokrieh, we extend the concept of…
Graphical chip-firing is a discrete dynamical system where chips are placed on the vertices of a graph and exchanged via simple firing moves. Recent work has sought to generalize chip-firing on graphs to higher dimensions, wherein graphs…
Statistical generative models for molecular graphs attract attention from many researchers from the fields of bio- and chemo-informatics. Among these models, invertible flow-based approaches are not fully explored yet. In this paper, we…
Chip firing provides a way to study the sandpile group (also known as the Jacobian) of a graph. We use a generalized version of chip firing to bound the number of invariant factors of the critical group of an arithmetical structure on a…
Chip-firing is a combinatorial game played on a graph in which we place and disperse chips on vertices until a stable state is reached. We study a chip-firing variant played on an infinite rooted directed $k$-ary tree, where we place…
Chip-firing is a combinatorial game played on an undirected graph in which we place chips on vertices. We study chip-firing on an infinite binary tree in which we add a self-loop to the root to ensure each vertex has degree 3. A vertex can…
We study chip-firing on a signed graph $G_\phi$, employing a general theory of chip-firing on invertible matrices introduced by Guzm\'an and Klivans. Here a negative edge designates an adversarial relationship, so that firing a vertex…
We introduce a natural variant of the parallel chip-firing game, called the diffusion game. Chips are initially assigned to vertices of a graph. At every step, all vertices simultaneously send one chip to each neighbour with fewer chips. As…
In this article, we provide three formulas allowing to compute the minimum amount of initial chips leading to an infinite Chip-firing game. These formulas hold for strongly connected directed loop-free multigraphs and generalize what was…
In this paper, two efficient iterative algorithms based on the simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the proposed algorithms utilizing the deflated restarting…
We propose a generic framework to describe classical Ising-like models defined on arbitrary graphs. The energy spectrum is shown to be the Hadamard transform of a suitably defined sparse "coding" vector associated with the graph. We expect…
In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…
The report is devoted to the concept of creating block-recursive matrix algorithms for computing on a supercomputer with distributed memory and dynamic decentralized control.
Modeling data sharing in GPU programs is a challenging task because of the massive parallelism and complex data sharing patterns provided by GPU architectures. Better GPU caching efficiency can be achieved through careful task scheduling…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
Graphical flows add further structure to normalizing flows by encoding non-trivial variable dependencies. Previous graphical flow models have focused primarily on a single flow direction: the normalizing direction for density estimation, or…
Chip-firing on a directed graph is a game in which chips, a discrete commodity, are placed on the vertices of the graph and are transferred between vertices. In this paper, we study a chip-firing game on the Hasse diagram of the lattice of…
We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative…