Related papers: Higher-Order Group Synchronization
We study the computational phase transition in a multi-frequency group synchronization problem, where pairwise relative measurements of group elements are observed across multiple frequency channels and corrupted by Gaussian noise. Using…
Recent developments in complex systems have witnessed that many real-world scenarios, successfully represented as networks are not always restricted to binary interactions but often include higher-order interactions among the nodes. These…
Criticality and symmetry, studied by the renormalization groups, lie at the heart of modern physics theories of matters and complex systems. However, surveying these properties with massive experimental data is bottlenecked by the…
Transformation Synchronization is the problem of recovering absolute transformations from a given set of pairwise relative motions. Despite its usefulness, the problem remains challenging due to the influences from noisy and outlier…
In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…
This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…
Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional…
Complex systems, such as economic, social, biological, and ecological systems, usually feature interactions not only between pairwise entities but also among three or more entities. These multi-entity interactions are known as higher-order…
Group synchronization aims to recover the group elements from their noisy pairwise measurements. It has found many applications in community detection, clock synchronization, and joint alignment problem. This paper focuses on the orthogonal…
Synchronous Counting is the task of reaching agreement on a common round counter in a synchronous system of $n$ nodes with up to $t$ Byzantine faults in a self-stabilizing manner. That is, after transient faults may have arbitrarily…
Chaotic oscillators have gained significant attention in the research community because of their ability to reproduce and investigate the complex dynamics of real-world phenomena. Recent advances in the design of chaotic oscillator…
We tackle the quantification of synchrony in globally coupled populations. Furthermore, we treat the problem of incomplete observations when the population mean field is unavailable, but only a small subset of units is observed. We…
Hypergraphs provide a natural way of representing group relations, whose complexity motivates an extensive array of prior work to adopt some form of abstraction and simplification of higher-order interactions. However, the following…
Synchronization has received a lot of attention from the scientific community for systems evolving on static networks or higher-order structures, such as hypergraphs and simplicial complexes. In many relevant real world applications, the…
Partial orders and directed acyclic graphs are commonly recurring data structures that arise naturally in numerous domains and applications and are used to represent ordered relations between entities in the domains. Examples are task…
Synchronization is of central importance in power distribution, telecommunication, neuronal, and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
In synchronization problems, the goal is to estimate elements of a group from noisy measurements of their ratios. A popular estimation method for synchronization is the spectral method. It extracts the group elements from eigenvectors of a…
The estimation of correspondences between two images resp. point sets is a core problem in computer vision. One way to formulate the problem is graph matching leading to the quadratic assignment problem which is NP-hard. Several so called…
Group-testing refers to the problem of identifying (with high probability) a (small) subset of $D$ defectives from a (large) set of $N$ items via a "small" number of "pooled" tests. For ease of presentation in this work we focus on the…