SIGNET: Exploring the Interface between Signal Processing and Network Science
EPSRC Early Career Fellowship
A combinatorial framework for peak/pit asymmetry in complex dynamics
The qualitative step forward that Complexity Science has experienced in the last years is directly related to an increase of computation capacity, enabling the possibility of running large scale simulations and handling large amounts of (empirical) data: the so called Big Data paradigm. It is fundamental to come along with new methods and insights to deal, store and extract information from large amounts of data.
These datasets naturally come in two different types. First, from the time evolution of some financial indicator or the irregular motion of turbulent fluids to the waveform signal of speech, complex systems produce incredibly complicated univariate/multivariate time series, whose hidden structure should be processed and analysed using fast and novel approaches. Second, the intertwined architecture of the interaction patterns of complex systems is naturally represented and modeled in terms of graphs -a paradigmatic of this approach being the brain, modeled by single units (neurons) connected by edges that model synaptic connections. These distributed processing systems usually lay at the edge between order and randomness (the so-called complex network paradigm) and come in different flavours (undirected/directed, static/temporal, monolayer/multilayer). Each of these two families of datasets have its own mathematical corpus that deals with the description and characterisation of these data, namely signal processing and network science.
The working hypothesis of this project is that information encoded or hidden in a data set can be retrieved by mapping such data set into an alternative mathematical representation, where the extraction of information may be eventually simpler. As such, we aim to explore what new information can be extracted by mapping time series into graphs and therefore using network science to characterise signals and their underlying dynamics: in short, to make graph-theoretical time series analysis. We are also interested in the dual problem, namely extracting time series from graphs and therefore using the tools of time series analysis and signal processing to describe, compare and classify networks of many kinds: a signal processing of graphs.
We will consider specific methods (visibility algorithms, Markov chain theory, fluctuation analysis) and will be able to define and validate new graph-theoretical measures to describe signals and new signal-theoretic measures to describe graphs, as well as to build a mathematically sound and solid theory to relate these two approaches.
Ultimately, the results of our research will be implemented in a software whose input is a time series/complex network and whose output is a set of key features which describe the object under study from several angles (both the signal processing and graph theoretic angle). These features will then feed automatic classifiers for pattern recognition and data analytics.
Uri Hasson, Jacopo Iacovacci, Ben Davis, Ryan Flanagan, Enzo Tagliazucchi, Helmut Laufs, Lucas Lacasa
Submitted for publication
Visibility graphs and symbolic dynamics
Lucas Lacasa, Wolfram Just
Submitted for publication
Visibility graphs of random scalar fields and spatial data
Lucas Lacasa, Jacopo Iacovacci
Physical Review E 96, 012318 (2017)
Visibility graphs for fMRI data: multiplex temporal graphs and their modulations across resting state networks
Speranza Sannino, Sebastiano Stramaglia, Lucas Lacasa, Daniele Marinazzo
Network Neuroscience (in press 2017)
Identifying the hidden multiplex architecture of complex systems
Lucas Lacasa, Ines Perez-Marino, Joaquin Miguez, Vincenzo Nicosia and Jesus Gomez-Gardenes
Submitted for publication
Emergence of linguistic laws in human voice
Ivan Gonzalez Torre, Bartolo Luque, Lucas Lacasa, Jordi Luque and Antoni Hernandez-Fernandez
Nature Scientific Reports 7, 43862 (2017)
Other activities related to this fellowship
Research stay at UCLA: I am visiting Prof. Mason Porter at the Maths Department, UCLA in July-August 2017.
I now am an Associate Member of the EPSRC Review College.
I have been invited to deliver a talk at the 2017 British Applied Mathematics Colloquium (Surrey, UK, April 2017)
I have participated in EPSRC's Complexity Science Review Scoping Workshop (April 2017), a kick-off meeting to discuss long-term strategy on EPSRC's funding of the Complexity Science research area.
I will deliver a talk in the conference Crossroads in Complex Systems (Palma, Spain, June 2017).
I am part of the Technical Program Commitee of the Complex Networks Conference 2017, which takes place in November in Lyon (France).
On 31st July 2017 I am delivering a seminar on visibility graph theory in the Department of Mathematics, UCLA
I am part of the Technical Program Commitee of Complenet'18, which takes place in 2018 in Boston (US).
Our recent paper on the emergence of linguistic laws in audio signals has been featured in the research news portal of the Technical University of Madrid (Spain), link Featured in here
From September I am developing a researvh stay at Technical University of Madrid.
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