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A sound theory for analysing the complex behaviour of dynamic networks

The aim of the EU-funded DYNASNET project is to engage leading experts in network science and graph theory to build a mathematically sound theory of dynamic networks.

## News

### First-hand Experience from the Summer Schools

2022-06-17
During the past few weeks, I participated in two summer schools at the Alfréd Rényi Institute of Mathematics, as part of the Erdős Center semester on Large Networks and their Limits. Aranka Hrušková and I helped to keep things running smoothly for both schools, and we organized some social events for the second summer school.

### Minicourses Available for Summer School: Graphs, Groups, Stochastic Processes

2022-03-22
The School focuses on discrete structures and their limits. This is an active area of research that connects discrete mathematics with ergodic theory, stochastic processes, spectral theory, measured group theory and various branches of analysis and topology.

### Spectral Collective - Mathematical Animation with Manim

2022-03-17

You can check out a new lecture recording on Spectral Collective YouTube channel,

Mathematical Animation with Manim

Lecture by Vilas Winstein at the Alfréd Rényi Institute of Mathematics on 2022/02/16.

## Latest Publications

### Longer-term seeding effects on epidemic processes: a network approach

2022-03-26
In this paper we touch upon three phenomena observed in real life as well as in simulations; in one case, we state mathematical results about the appearance of the phenomenon on arbitrary graphs (networks) under rather general conditions. We discuss a phenomenon of critical fluctuations, demonstrating that an epidemic can behave very differently even if it runs on the same network, with the same transmission probabilities and started from the same initial seeds.

### Twin-width and generalized coloring numbers

2021-11-28
In Twin-width and generalized coloring numbers paper, we prove that a graph $$G$$ with no $$K\, s,s\,$$-subgraph and twin-width $$d$$ has $$r$$-admissibility and $$r$$-coloring numbers bounded from above by an exponential function of $$r$$ and that we can construct graphs achieving such a dependency in $$r$$.

### Towards solving the 7-in-a-row game

2021-11-17

Our paper explores the game theoretic value of the 7-in-a-row game. We reduce the problem to solving a finite board game, which we target using Proof Number Search. We present a number of heuristic improvements to Proof Number Search and examine their effect within the context of this particular game. Although our paper does not solve the 7-in-a-row game, our experiments indicate that we have made significant progress towards it.

## Events

2022.06.06. - 2022.06.10.
Erdős Center, Rényi Institute

The School focuses on discrete structures and their limits. This is an active area of research that connects discrete mathematics with ergodic theory, stochastic processes, spectral theory, measured group theory and various branches of analysis and topology. There will be six minicourses given by distinguished researchers of the field.

Lecturers:

2022.05.30. - 2022.06.03.
Erdős Center, Rényi Institute
The Mathematics of Large Networks summer school aims to bring together mathematicians and network scientists to foster the exchange of ideas between these two fields. During the school four minicourses will be given by distinguished researchers in graph theory and network science for students from both fields, who are interested in multidisciplinary approaches to networks.
2022.05.09. - 2022.05.13.
Erdős Center, Rényi Institute
The idea of the Mathematics of Large Networks Workshop is to bring together mathematicians and network scientists with the aim of fostering the exchange of ideas. The speakers and the audience will also consist of researchers coming from these two communities. The main themes of the Workshop include geometry of networks, dynamics of/on networks, higher order structures, network inference and applications.