79 research outputs found
Properties of periodic solutions near their oscillation threshold for a class of hyperbolic partial differential equations with localized nonlinearity
The periodic solutions of a type of nonlinear hyperbolic partial differential
equations with a localized nonlinearity are investigated. For instance, these
equations are known to describe several acoustical systems with fluid-structure
interaction. It also encompasses particular types of delay differential
equations. These systems undergo a bifurcation with the appearance of a small
amplitude periodic regime. Assuming a certain regularity of the oscillating
solution, several of its properties around the bifurcation are given:
bifurcation point, dependence of both the amplitude and period with respect to
the bifurcation parameter, and law of decrease of the Fourier series
components. All the properties of the standard Hopf bifurcation in the
non-hyperbolic case are retrieved. In addition, this study is based on a
Fourier domain analysis and the harmonic balance method has been extended to
the class of infinite dimensional problems hereby considered. Estimates on the
errors made if the Fourier series is truncated are provided.Comment: 20 page
A survey of uncertainty principles and some signal processing applications
The goal of this paper is to review the main trends in the domain of
uncertainty principles and localization, emphasize their mutual connections and
investigate practical consequences. The discussion is strongly oriented
towards, and motivated by signal processing problems, from which significant
advances have been made recently. Relations with sparse approximation and
coding problems are emphasized
Tracking Time-Vertex Propagation using Dynamic Graph Wavelets
Graph Signal Processing generalizes classical signal processing to signal or
data indexed by the vertices of a weighted graph. So far, the research efforts
have been focused on static graph signals. However numerous applications
involve graph signals evolving in time, such as spreading or propagation of
waves on a network. The analysis of this type of data requires a new set of
methods that fully takes into account the time and graph dimensions. We propose
a novel class of wavelet frames named Dynamic Graph Wavelets, whose time-vertex
evolution follows a dynamic process. We demonstrate that this set of functions
can be combined with sparsity based approaches such as compressive sensing to
reveal information on the dynamic processes occurring on a graph. Experiments
on real seismological data show the efficiency of the technique, allowing to
estimate the epicenter of earthquake events recorded by a seismic network
Principal Patterns on Graphs: Discovering Coherent Structures in Datasets
Graphs are now ubiquitous in almost every field of research. Recently, new
research areas devoted to the analysis of graphs and data associated to their
vertices have emerged. Focusing on dynamical processes, we propose a fast,
robust and scalable framework for retrieving and analyzing recurring patterns
of activity on graphs. Our method relies on a novel type of multilayer graph
that encodes the spreading or propagation of events between successive time
steps. We demonstrate the versatility of our method by applying it on three
different real-world examples. Firstly, we study how rumor spreads on a social
network. Secondly, we reveal congestion patterns of pedestrians in a train
station. Finally, we show how patterns of audio playlists can be used in a
recommender system. In each example, relevant information previously hidden in
the data is extracted in a very efficient manner, emphasizing the scalability
of our method. With a parallel implementation scaling linearly with the size of
the dataset, our framework easily handles millions of nodes on a single
commodity server
On the skeleton method and an application to a quantum scissor
In the spectral analysis of few one dimensional quantum particles interacting
through delta potentials it is well known that one can recast the problem into
the spectral analysis of an integral operator (the skeleton) living on the
submanifold which supports the delta interactions. We shall present several
tools which allow direct insight into the spectral structure of this skeleton.
We shall illustrate the method on a model of a two dimensional quantum particle
interacting with two infinitely long straight wires which cross one another at
a certain angle : the quantum scissor.Comment: Submitte
On critical stability of three quantum charges interacting through delta potentials
We consider three one dimensional quantum, charged and spinless particles
interacting through delta potentials. We derive sufficient conditions which
guarantee the existence of at least one bound state
A Graph-structured Dataset for Wikipedia Research
Wikipedia is a rich and invaluable source of information. Its central place
on the Web makes it a particularly interesting object of study for scientists.
Researchers from different domains used various complex datasets related to
Wikipedia to study language, social behavior, knowledge organization, and
network theory. While being a scientific treasure, the large size of the
dataset hinders pre-processing and may be a challenging obstacle for potential
new studies. This issue is particularly acute in scientific domains where
researchers may not be technically and data processing savvy. On one hand, the
size of Wikipedia dumps is large. It makes the parsing and extraction of
relevant information cumbersome. On the other hand, the API is straightforward
to use but restricted to a relatively small number of requests. The middle
ground is at the mesoscopic scale when researchers need a subset of Wikipedia
ranging from thousands to hundreds of thousands of pages but there exists no
efficient solution at this scale.
In this work, we propose an efficient data structure to make requests and
access subnetworks of Wikipedia pages and categories. We provide convenient
tools for accessing and filtering viewership statistics or "pagecounts" of
Wikipedia web pages. The dataset organization leverages principles of graph
databases that allows rapid and intuitive access to subgraphs of Wikipedia
articles and categories. The dataset and deployment guidelines are available on
the LTS2 website \url{https://lts2.epfl.ch/Datasets/Wikipedia/}
Rigorous perturbation theory versus variational methods in the spectral study of carbon nanotubes
Recent two-photon photo-luminescence experiments give accurate data for the
ground and first excited excitonic energies at different nanotube radii. In
this paper we compare the analytic approximations proved in \cite{CDR}, with a
standard variational approach. We show an excellent agreement at sufficiently
small radii.Comment: Accepted for publication in Contemporary Mathematic
A signal processing method: Detection of LĂ©vy flights in chaotic trajectories
International audienceTransport in low dimensional Hamiltonian chaos can be anomalous due to stickiness and rise of LeÌvy flights. We suggest a signal processing method to detect these flights in signals, in order to characterize the nature of transport (diffusive or anomalous). We use time-frequency techniques such as Fractional Fourier transform and matching pursuit in order to be robust to noise. The method is tested on data obtained from chaotic advection
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