Mathematics Institute, University of Warwick,
July 3 - 5 2019
Summary
This 3-day school will provide a postgraduate level introduction to network science, dynamical processes on networks and applications of control theory to networked systems.
Lecturers:
Registration:
Please register here (you need to scroll down a bit to select this event)
Draft programme
All lectures are in Room D1.07 in the Zeeman (Mathematics) building - follow signs for the Centre for Complexity Science.
Lunches, breaks etc are in the Complexity Science common room adjacent to D1.07.
Wednesday July 03
10:15 - 10:45 Registration
10:45 - 11:00 Welcome from the organisers
12:30 - 13:30 lunch
15:00 - 15:30 break
17:00 - Poster session with refreshments
Thursday July 04
09:00 - 10:30 Weisi Guo (lecture 1) [
slides]
10:30 - 11:00 - break
12:30 - 13:30 lunch
13:30 - 15:00 Sam Johnson (lecture 1)
15:00 - 15:30 break
15:30 - 17:00 Francisco Rodrigues (lecture 3)
17:00 - Dinner
Friday July 05
09:00 - 10:30 Claudio De Persis (lecture 1) [
slides]
10:30 - 11:00 - break
11:00 - 12:30 Sam Johnson (lecture 2)
12:30 - 13:30 lunch
13:30 - 15:00 Claudio De Persis (lecture 2) [
slides]
15:00 - 15:30 break / close
Summary of topics
Claudio De Persis
Designing controllers for unknown systems using data
Control is the science of modifying the behaviour of physical systems by applying input signals. It requires accurate mathematical models of the physical systems and devises algorithms that are also mathematically described.
The increasing complexity of modern engineering systems, however, is making harder to derive precise models from first principles and even when these models are available, they might be so complex that they are useless for control design purposes. In recent years a very active research area is aiming at understanding how to design controllers when the system's dynamics is unknown, complementing the limited knowledge about the system's model with data that are collected during experiments.
In these lectures, after recalling what a control system is and introducing two basic yet quintessential control problems, namely stabilisation and linear quadratic (LQ) regulation, I introduce a new technique for designing control algorithms starting from input-output data collected in an "one-shot" experiment performed on the system to control. For simplicity, we confine ourselves to the case of linear control systems. We show that designing a stabiliser or an LQ regulator for a completely unknown linear system boils down to the solution of a data-dependent semi-definite program, that is, a linear program with linear matrix inequalities as constraints, which can be solved very efficiently.
Konstantinos Efstathiou
Dynamics and synchronization of globally coupled oscillators
The topic of these lectures is the dynamics of oscillators coupled in a network. Such models have been used to study the synchronization in systems as disparate as fireflies, neurons, heart cells, lasers, and microwave oscillators. We will start with the most accessible such model, the Kuramoto model, and we will first discuss how to predict synchronization through the self-consistent method. Then, we will consider a reduction of the dynamics, to one dimension through the Ott-Antonsen ansatz. The next step will be to consider second-order oscillator networks where the oscillator dynamics is affected by an inertia term giving rise to phenomena such as explosive synchronization. We will focus on the self-consistent method for second-order oscillators. If there is sufficient time we will discuss the Winfree model, which historically precedes the Kuramoto model, and which exhibits much richer dynamics.
Weisi Guo
Resilience and Data Science for Networked Complex Systems
We live in a time of increased uncertainty and there is a need to monitor our infrastructures and ecosystems to build greater resilience. Many of our critical infrastructures and ecosystems have a networked dimension. Whilst the resilience and data sampling process is well understood for single dynamical entities or stationary graphs, it is not understood for large-scale networked dynamical systems. This is particularly the case when the size of the network is large (e.g. millions of nodes at the national scale). This talk will present recent advances in understanding the resilience of dynamical networks and optimal sampling theory for data collection on them. This will inform the UK in establishing both a complexity twin and a digital twin for its critical systems.
Sam Johnson
Lecture 1: Neural networks
The brain is often called ‘the most complex system in the known universe’. Despite the puzzling recursivity of that description, the organ with which we appear to think, feel, remember and decide what to do is certainly a paradigm of complexity. It provides an ideal case study into how networks have been used, in combination with various dynamical system models, to tackle some of the most challenging problems we face. Our current understanding of cognition and our most powerful artificial intelligence are both underpinned by neural networks. I will describe some of the research that has led us to where we are now, and consider the main difficulties in progressing further.
Lecture 2: Directed networks
In many, if not most, complex systems the interactions between elements are not necessarily symmetric, so they are best described by directed networks (in which edges can be represented with arrows rather than lines). But when it comes to studying such networks mathematically, it is usually assumed that they are essentially like undirected networks, with directionality being just another property which might be thought of as a random binary number associated with each edge. In fact, the directions of edges in a network can exhibit a degree of global order somewhat analogous to ferromagnetism in spin systems. In some networks edge directions are indeed statistically independent of each other; but in others they can be aligned to a greater of lesser degree with a global direction, and this can be crucial for many topological and dynamical properties. I will describe recent research into aspects of directed networks – such as trophic coherence, non-normality and the prevalence of feedback loops – and its relevance for the study of complex systems.
Francisco A. Rodrigues
Introduction to Complex Networks: structure and dynamics
In this course, we will introduce the basic concepts and methods to study the structure and dynamics of complex networks. Measures to characterize the network structure and find patterns of connections will be presented. We will also consider some concepts related to the simulation of dynamical processes in networks, like epidemic and rumour spreading. The course will contain practical examples in Python.