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Nonlinear dynamics has an important role when designing modern synchrotron lattices. In this letter, we introduce a new method of using a square matrix to analyze periodic nonlinear dynamical systems [1, 2]. Applying the method to the…
Clustering short text embeddings is a foundational task in natural language processing, yet remains challenging due to the need to specify the number of clusters in advance. We introduce a scalable spectral method that estimates the number…
Given an undirected measurement graph $\mathcal{H} = ([n], \mathcal{E})$, the classical angular synchronization problem consists of recovering unknown angles $\theta_1^*,\dots,\theta_n^*$ from a collection of noisy pairwise measurements of…
Synchronization is an important dynamical phenomenon in coupled nonlinear systems, which has been studied extensively in recent years. However, analysis focused on individual orbits seems hard to extend to complex systems while a global…
Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…
In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…
A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
Network alignment consists of finding a structure-preserving correspondence between the nodes of two correlated, but not necessarily identical, networks. This problem finds applications in a wide variety of fields, from the alignment of…
We experimentally study the synchronization of two chaotic electronic circuits whose dynamics is relayed by a third parameter-matched circuit, to which they are coupled bidirectionally in a linear chain configuration. In a wide range of…
We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of…
Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known…
We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to…
Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of…
Oscillation synchronization phenomenon is widely observed in natural systems through frequency modulated signals, especially in biological neural networks. Frequency modulation is also one of most widely used technologies in engineering.…
This paper studies the joint community detection and phase synchronization problem on the \textit{stochastic block model with relative phase}, where each node is associated with an unknown phase angle. This problem, with a variety of…
In this article, we introduce a general theoretical framework to analyze non-consistent approximations of the discrete eigenmodes of a self-adjoint operator. We focus in particular on the discrete eigenvalues laying in spectral gaps. We…
We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general…
Synchronization is a widespread phenomenon encountered in many natural and engineered systems with nonlinear classical dynamics. How synchronization concepts and mechanisms transfer to the quantum realm and whether features are universal or…
This paper deals with the approximation of the spectrum of linear and nonautonomous delay differential equations through the reduction of the relevant evolution semigroup from infinite to finite dimension. The focus is placed on classic…