Related papers: $ \mathrm{SE} (3) $ Synchronization by Eigenvector…
The spectral clustering algorithm is often used as a binary clustering method for unclassified data by applying the principal component analysis. To study theoretical properties of the algorithm, the assumption of conditional…
Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of non-identical…
This paper introduces a novel formulation to evaluate the local synchronization of power system devices, namely Synchronization Energy (SE). The formulation is derived based on the complex frequency concept and the Teager Energy Operator…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
Synchronization is central to many complex systems in engineering physics (e.g., the power-grid, Josephson junction circuits, and electro-chemical oscillators) and biology (e.g., neuronal, circadian, and cardiac rhythms). Despite these…
This paper is on the normal approximation of singular subspaces when the noise matrix has i.i.d. entries. Our contributions are three-fold. First, we derive an explicit representation formula of the empirical spectral projectors. The…
Spectral Clustering (SC) is one of the most widely used methods for data clustering. It first finds a low-dimensonal embedding $U$ of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on…
The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear transformation of coordinates and velocities. This is a rather…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
Three-flavor neutrino oscillations in matter can be described by three effective neutrino masses $\widetilde{m}^{}_i$ (for $i = 1, 2, 3$) and the effective mixing matrix $V^{}_{\alpha i}$ (for $\alpha = e, \mu, \tau$ and $i = 1, 2, 3$).…
This work investigates two physics-based models that simulate the non-linear partial differential algebraic equations describing an electric double layer supercapacitor. In one model the linear dependence between electrolyte concentration…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
We address the problem of acoustic source separation in a deep learning framework we call "deep clustering." Rather than directly estimating signals or masking functions, we train a deep network to produce spectrogram embeddings that are…
We present a new simple method for rounding a semidefinite programming relaxation of a constraint satisfaction problem. We apply it to the problem of approximate angular synchronization. Specifically, we are given directed distances on a…
We study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems,…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and…
In speaker diarisation, speaker embedding extraction models often suffer from the mismatch between their training loss functions and the speaker clustering method. In this paper, we propose the method of spectral clustering-aware learning…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
We propose and analyse a general tensor-based framework for incorporating second order features into network measures. This approach allows us to combine traditional pairwise links with information that records whether triples of nodes are…