Related papers: Dynamic Complexity of Group Problems
Two of the most fundamental distributed symmetry-breaking problems are that of finding a maximal independent set (MIS) and a maximal matching (MM) in a graph. It is a major open question whether these problems can be solved in constant…
In [CG16], Cerf and Gorny constructed a model of self-organized criticality, by introducing an automatic control of the temperature parameter in the generalized Ising Curie-Weiss model. In this article, we build upon this model by replacing…
Designing dynamically feasible trajectories for rigid bodies is a fundamental problem in robotics. Although direct trajectory optimization is widely applied to solve this problem, inappropriate parameterizations of rigid body dynamics often…
We prove that many dynamical properties of group cellular automata (i.e., cellular automata defined on any finite group and with global rule which is an endomorphism), including surjectivity, injectivity, sensitivity to initial conditions,…
The aim of this paper is to study the optimal investment problem by using coherent acceptability indices (CAIs) as a tool to measure the portfolio performance. We call this problem the acceptability maximization. First, we study the…
A general technique is presented for constructing a quantum theory of a finite number of interacting particles satisfying Poincar\'e invariance, cluster separability, and the spectral condition. Irreducible representations and…
The cavity method is one of the cornerstones of the statistical physics of disordered systems such as spin glasses and other complex systems. It is able to analytically and asymptotically exactly describe the equilibrium properties of a…
We begin development of a method for studying dynamical systems using concepts from computational complexity theory. We associate families of decision problems, called telic problems, to dynamical systems of a certain class. These decision…
Multimodal learning integrates complementary information from diverse modalities to enhance the decision-making process. However, the potential of multimodal collaboration remains under-exploited due to disparities in data quality and…
The dynamic cavity method provides the most efficient way to evaluate probabilities of dynamic trajectories in systems of stochastic units with unidirectional sparse interactions. It is closely related to sum-product algorithms widely used…
Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…
In 1992 Drinfeld posed the question of finding the set theoretic solutions of the Yang-Baxter equation. Recently, Gateva-Ivanova and Van den Bergh and Etingof, Schedler and Soloviev have shown a group theoretical interpretation of…
Group-invariant probability distributions appear in many data-generative models in machine learning, such as graphs, point clouds, and images. In practice, one often needs to estimate divergences between such distributions. In this work, we…
The simplicial complexity is an invariant for finitely presentable groups that was recently introduced by Babenko, Balacheff and Bulteau to study systolic area. The simplicial complexity $\kappa(G)$ was proved to be a good approximation of…
Dyck reachability is the standard formulation of a large domain of static analyses, as it achieves the sweet spot between precision and efficiency, and has thus been studied extensively. Interleaved Dyck reachability (denoted $D_k\odot…
The paper describes the coupling of the MercuryDPM discrete element method (DEM) code and the implementation of the kernel-independent fast multipole method (KIFMM). The combined simulation framework allows addressing the large class of…
The earlier proposed Dynamics-Generating Approach (DGA) is reviewed and extended. Starting from an arbitrarily chosen group or semigroup which have structure similar to the structure of Galilei group, DGA allows one to construct…
We investigate numerically the applicability of dynamic facilitation (DF) theory for glass-forming binary hard disk systems where supercompression is controlled by pressure. By using novel efficient algorithms for hard disks, we are able to…
In dynamic complex networks, entities interact and form network communities that evolve over time. Among the many static Community Detection (CD) solutions, the modularity-based Louvain, or Greedy Modularity Algorithm (GMA), is widely…
In this paper, we illustrate a novel method for solving optimization problems when derivatives are not explicitly available. We show that combining implicit filtering (IF), an existing derivative free optimization (DFO) method, with a deep…