Related papers: Spectral analysis of the zigzag process
The z-transform of a sequence is a classical tool used within signal processing, control theory, computer science, and electrical engineering. It allows for studying sequences from their generating functions, with many operations that can…
We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…
In this paper we present a general procedure that allows for the reduction or expansion of any network (considered as a weighted graph). This procedure maintains the spectrum of the network's adjacency matrix up to a set of eigenvalues…
In this paper we present the Markov variation, a smoothness measure which offers a probabilistic interpretation of graph signal smoothness. This measure is then used to develop an optimization framework for graph signal interpolation. Our…
Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…
With the purpose to devise a novel lasing scheme, we consider a two level system with both a transversal and longitudinal coupling to the electromagnetic field. If the longitudinal coupling is sufficiently strong, multi-photon transitions…
This paper investigates the stability of switched linear systems whose switching signal is modeled as a stochastic process called a regenerative process. We show that the mean stability of such a switched system is characterized by the…
The metabolic process in a cell is modeled with the use of the Fourier transformation. The histograms of the invariant measures of chaotic attractors are constructed. In particular, a scenario of adaptation of the metabolic process under a…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph…
The dynamics of network formation are generally very complex, making the study of distributions over the space of networks often intractable. Under a condition called conservativeness, I show that the stationary distribution of a network…
The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…
Stationary graph process models are commonly used in the analysis and inference of data sets collected on irregular network topologies. While most of the existing methods represent graph signals with a single stationary process model that…
We investigate the normal mode spectrum of a trapped ion chain at the symmetry-breaking linear to zigzag transition and at finite temperatures. For this purpose we modulate the amplitude of the Doppler cooling laser in order to excite and…
We study the persistence probability of a centered stationary Gaussian process on $\mathbb{Z}$ or $\mathbb{R}$, that is, its probability to remain positive for a long time. We describe the delicate interplay between this probability and the…
We define the spectral gap of a Markov chain on a finite state space as the second-smallest singular value of the generator of the chain, generalizing the usual definition of spectral gap for reversible chains. We then define the relaxation…
We study the dynamics of density fluctuations in the steady state of a non-equilibrium system, the Zero-Range Process on a ring lattice. Measuring the time series of the total number of particles in a \emph{segment} of the lattice, we find…
While engineered quantum systems are a general route to the manipulation of multipartite quantum states, access in a physical system to a continuous quantum phase transition under sufficient control offers the possibility of an intrinsic…