## Complex Networks

- MO|20|02: Real-World Networks
- MO|27|02: Visualization and Simulation of Large Real-World Networks
- MO|06|03: Economic and Financial Networks
- MO|13|03: Early-warning Signals in Financial Networks
- MO|20|03: Epidemics on Networks
- MO|27|03: What Makes Network Problems Hard to Solve?

### Challenges and Perspectives

Dr Michael Emmerich, Dr Diego Garlaschelli, Professor Frank den Hollander

Networks are the backbone of modern society. Technological developments have created large networks for the transport of people, goods, information, money and energy. For instance, billions of people in the world are connected via the internet.

In this series we give examples of real-world networks, discuss key questions, describe key models, and explain how networks can be analysed, simulated, controlled and optimised.

Lectures on Monday nights

20 and 27 February

6, 13, 20 and 27 March

7:30 pm to 9:00 pm

Room 011

Lipsius Building

Cleveringaplaats 1

Leiden

### MO|20|02: Real-World Networks

This opening lecture describes examples of large networks in society. Empirical properties of real-world networks show a high degree of universality. Some key questions and key challenges are discussed.

Speaker: Frank den Hollander, Professor of Probability; Analysis and Stochastics, Mathematical Institute, Leiden University

### MO|27|02: Visualization and Simulation of Large Real-World Networks

This lecture discusses how computers can be used to simulate the growth and dynamics of real world networks. Examples from various areas of network simulation will be given, such as biological processes, traffic simulation and dynamics of social networks. Moreover, some ideas about underlying computational techniques, their capabilities and limitations, are discussed.

Speaker: Dr Michael Emmerich, Associate professor; Algorithms and Software Technology, Leiden Institute of Advanced Computer Science, Leiden University

### MO|06|03: Economic and Financial Networks

Investors, traders, banks, firms, and governments form intricately connected networks that determine the functioning and the (in)stability of economies and markets. Often, complete information about these networks is not available. How can these networks be described? Can they be reliably reconstructed from partial information? Can the risk of collapse of a financial network be estimated?

Speaker: Dr Diego Garlaschelli, Associate professor; Econophysics and Network Theory, Leiden Institute of Physics, Leiden University

### MO|13|03: Early-warning Signals in Financial Networks

While financial systems appear to be stable most of the time, big unforeseen events such as the financial crisis in 2008 have shown that major instabilities can develop abruptly. What are the network origins of such instabilities? Is it possible to determine whether a financial network is departing from an equilibrium state? Can early-warning signals of financial collapse be identified in real networks?

Speaker: **Dr Diego Garlaschelli**, Associate professor; Econophysics and Network Theory, Leiden Institute of Physics, Leiden University

### MO|20|03: Epidemics on Networks

What characteristics of a network are crucial in determining how a disease spreads over it? Can a network sustain an epidemic or not? What measures can be taken to avoid an epidemic?

Speaker: **Frank den Hollander**, Professor of Probability; Analysis and Stochastics, Mathematical Institute, Leiden University

### MO|27|03: What Makes Network Problems Hard to Solve?

**Transitions in Computational Complexity
**This lecture is about practically relevant problems on networks and their difficulty, ranging from simple problems to problems that seem to be almost impossible to solve – even on parallel computers. Many of the very difficult problems are related to complex networks: for instance finding optimal round trips, detecting community structures, or finding energy minimal states in crystal structures. Surprisingly, often problems that are at first glance very similar to these problems, such as finding a shortest path or finding energy minimal states on planar lattices, can be solved in short time. Complex network theory has recently offered a partial understanding of what, essentially, makes problems difficult to solve. This research might shed a new light to one of the biggest unsolved problems in computer science and mathematics – the 'NP not equals P' conjecture.

Speaker:

**Dr Michael Emmerich**, Associate professor; Algorithms and Software Technology, Leiden Institute of Advanced Computer Science, Leiden University