• KICK-OFF MEETING OF THE DYNASNET ERC SYNERGY PROJECT
  (due to space limitation participation is only by invitation)

Program
 

The time for the talks (50 or 20 mins) includes discussions. Speakers should encourage the audience to interrupt their talks by questions. The entire workshop should be as interactive as possible.

Monday Sept 23, 2019: Day 1

    9:00 Miklos Abert: Graph limit theory for beginners
   10:00 Janos Kertesz: Statistical physics for beginners 

   11:00 COFFEE BREAK 

   11.20 Laszlo Lovasz: Dynamical networks: mathematical models 

   12:30 LUNCH 

   14:00 István Kovács: Link prediction, brain and graph embeddings 
   15:00 Balazs Szegedy: Convergence for graphs of intermediate density 

   16:00 COFFEE BREAK 

   16:20 Dani Barabasi: Bicliques in the brain: Genetically driven wiring of connectivity  
   16:40 Endre Csoka: Local algorithms and statistical physics on random graphs and graph limits 
   17:00 Gerardo Iniguez Gonzales: Cumulative effects of triadic closure and homophily in social networks

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Tuesday Sept 24, 2019 : Day 2 

    9:00 Patrice Ossona de Mendez: Sparsity and graph limits 
   10:00 Baruch Barzel: Network dynamics - stability, resilience and signals propagation

   11:00 COFFEE BREAK 

   11.20 Laszlo Barabasi: From Network Control to Physical Networks

   12:30 LUNCH 

   14:00 Balázs Ráth: Time evolution of dense multigraph limits under edge-conservative preferential attachment dynamics 
   15:00 Marton Karsai: Higher-order representations of temporal networks
   15:20 Tiago Peixoto: Reconstructing networks from indirect and noisy measurements
   15:40 Agnes Backhausz: On the almost eigenvectors of random d-regular graphs  

   16:00 COFFEE BREAK BRAINSTORM SMALL GROUPS  

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Wednesday Sept 25, 2019: Day 3 

    9:00 Balazs Hangya: Statical and dynamical analysis of functional brain networks 
   10:00 Balazs Szegedy: AI and networks

   11:00 COFFEE BREAK

   11.20 Jarik Nesetril: Sparse and dense, discrete and continuous 

   12:30 LUNCH 

   14:00 Peter Simon: The effect of graph properties on the dynamics of epidemic spread on networks 
   15:00 Federico Battiston: Random walks, diffusion and reaction from a physics perspective 

    COFFEE BREAK (shorter) 

   16:10 Marton Posfai: Controllability and complex networks 
   17:10 Laszlo Acsady: Variability of neuronal networks

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Venue:

Central European University

1051 Budapest, Nádor u. 15.

Room 101 (Quantum Room)

Capacity: 48

The venue is open to the public.

There is a cloakroom on the ground floor near the entrance (free of charge).

Map of the venue (You will need the N15 Ground Floor and First Floor maps, blue color, left-hand side)

Default equipment/features of the room:

The room has 2 large touchscreens, one of which doubles as a digital board (or ‘smartboard’, see below).

The ‘presenter’ is the remote control to be used for presentation slides.

A Mac adapter will also be provided.

Additional rooms for the small group discussions

on Sep 24, 4:00pm-6:00pm

N15 102 Nimetz Room (same floor as the Quantum Room, no card needed for access)

N13 G10 (visitor’s card needed for access)

N13 310 (visitor’s card needed for access)

Equipment in the rooms:

N15 102 Nimetz Room (digital board)

N13 G10 (whiteboard)

Markers will be provided for the whiteboard.

N13 310 (flipchart)

Plus a flipchart and markers will be provided.

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PREVIOUS EVENTS:

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• On the mathematics of forgetting

Balázs Szegedy
May 20, 2019  2:15pm (at the Rényi Institute) 

The notion of a factor is arguably one of the most powerful concepts in algebra. Factoring something is essentially forgetting information in a "smart" way. Here "smart" means that it is consistent with certain prescribed operations. A similar notion (also called factor) arises in the theory of dynamical systems and it is a key component in Furstenberg's program. Quite surprisingly Szemeredi's famousregularity lemma can also be viewed as finding an approximate factor of a graph and this idea can be given a precise meaning using non-standard analysis. Similar approximate factors appear in higher order Fourier analysis, a topic started by W.T. Gowers. We show that there is a rich connection between all the above subjects. Motivated by this, we turn to deep learning (the most dominant branch of artificial intelligence) where "smart forgetting" also called "abstraction" is a key ingredient. It usually comes in the form of a dimension reduction.
We discuss how abstraction in deep learning is related to the above subjects.

The talk can be viewed at the following link: https://video.renyi.hu/hu/video/osszintezeti-szeminarium-1-123

• Kinetics of social contagion

János Kertész
May 17, 2019  12:15 pm

Diffusion of information, behavioral patterns or innovations follows diverse pathways depending on a number of conditions, including the structure of the underlying social network, the sensitivity of individuals to peer pressure and the influence of media. We introduce a general model (the generalization of the Watts threshold model) that incorporates threshold mechanism capturing sensitivity to peer pressure, the effect of ‘immune’ nodes who never adopt, as well as a perpetual flow of external information and study it by analytical methods and simulations. While any constant, non-zero rate of dynamically-introduced spontaneous adopters leads to global spreading, the kinetics by which the asymptotic state is approached shows rich behavior. In particular we find that, as a function of the immune node density, there is a transition from fast to slow spreading and the kinetics in these regimes are governed by entirely different mechanisms. This transition happens below the percolation threshold of network fragmentation, and has its origin in the competition between cascading behavior induced by adopters and blocking due to immune nodes. This change is accompanied by a percolation transition of the induced clusters. We calibrate and validate the model using Big Data. In collaboration with Zhongyuan Ruan, Gerardo Iniguez and Marton Karsai.

The talk can be viewed at the following link: https://old.renyi.hu/videos/dynasnet/2019-05-17.mp4

• Brain networks

László Acsády and Balázs Hangya
May 3, 2019  12:15 pm

Our brains are composed of large networks of neurons. But how can one apply general laws of network science on these brain networks? Is the mathematics of the brain the same as mathematics of networks? What can graph theory tell us about graphs of neurons? We study brain networks and thus cannot answer these questions on our own. We consider our talk as a discussion starter, providing food for thought by showcasing a diverse set of examples on how we think the brain operates.

The talk can be viewed at the following link: https://old.renyi.hu/videos/dynasnet/2019.05.03.mp4

• ​Distributed graph analysis with LynxKite

András Németh
April 12, 2019  12:15 pm

Lynx Analytics is a Singapore based (but founded by Hungarians) data analytics consultancy focusing on leveraging network data to create positive business impact for our clients, most typically large telcos. While doing this, Lynx faced very early on that there were no good ways available to carry out graph algorithms on really large graphs.  Existing tools/libraries only worked as long as the graph fit in the memory of a single computer. So the decision was made to create an R&D team here in Budapest with the mission to create such a tool, and LynxKite was born.

 Today, LynxKite is extensively used internally and now Lynx Analytics is actively considering to release it publicly in some way. We have just started a free evaluation program and open sourcing is a high probability mid-term outcome.  Regardless of the opensourcing decision, we are happy to make it available for research purposes.

 This talk is going to be a deep dive into LynxKite. A detailed look on how it works, what are the kinds of things that can be done with it. But I will also talk a little bit about some of the technology behind the software and ways it could be extended.

The talk can be viewed at the following link: https://old.renyi.hu/videos/dynasnet/2019.04.12-LynxKyte.mp4

• About graphings

László Lovász
April 5, 2019   12:15 pm

Graphings are certain graphs on infinite spaces, typically on the [0,1] interval. A major property of them is that they allow "double counting" of subgraphs, which is trivial in the finite case but not possible for infinite graphs in general.  They can represent limits of graph sequences, in a sense that is stronger than local (Benjamini-Schramm) limits. We describe basic properties of graphings, and state some open problems.

The talk can be viewed at the following link: https://old.renyi.hu/videos/dynasnet/2019-04-05_Laszlo_Lovasz.mp4

• Concentration and convergence of the matching ratio of random graphs

Dorottya Beringer
March 29, 2019   12:15 pm

As mentioned by Albert-László Barabási last weak, there is an important parameter in control theory which is closely related to the directed matching ratio of the network. In this talk, I will speak about the concentration and convergence of the matching ratio of random graphs.  I will introduce three important families of random graphs investigated in our research: the random configuration model, Erd#s-Rényi graphs and preferential attachment graphs. The concentration of the matching ratio fit into other results that show that many important parameters of the random graphs are basically the same for most of the realizations of the above random graphs.  The convergence of the matching ratio demonstrates how techniques from the limit theory of random graphs can be used to justify results in network science. This is joint work with Ádám Timár.

The talk can be viewed at the following link: https://old.renyi.hu/videos/dynasnet/2019_03_29.mp4

• Taming Complexity: Controlling Networks

Albert-László Barabási
Center of Complex Networks Research, Northeastern University and Division of Network Medicine, Harvard University.
March 22, 2019 12:15 pm

The ultimate proof of our understanding of biological or technological systems is reflected in our ability to control them. While control theory offers mathematical tools to steer engineered and natural systems towards a desired state, we lack a framework to control complex self-organized systems. Here I will explore the controllability of an arbitrary complex network, identifying the set of driver nodes whose time-dependent control can guide the systemâs entire dynamics. Virtually all technological and biological networks must be able to control their internal processes. Given that, issues related to control deeply shape the topology and the vulnerability of real systems. Consequently, unveiling the control principles of real networks, the goal of our research, forces us to address series of fundamental questions pertaining to our understanding of complex systems. Finally, I will discuss how control principles inform our ability to predict neurons involved in specific processes in the brain, offering an avenue to experimentally falsify and test the predictions of network control.

The talk can be viewed at the following link: https://old.renyi.hu/videos/dynasnet/2019-03-22.mp4

• Embedding things

Dániel Varga
March 8, 2019  12:15 pm

The talk gives an overview of the emerging fields of deep representation learning and neural message passing.

The goal of deep representation learning algorithms is to embed objects into a vector space so that many of their complex relationships become simple linear relationships in the embedding space. This idea works for a surprisingly diverse set of domains, from images through written text to music and more. It forms the basis of the current deep learning revolution in natural language understanding, image processing, and many other fields.

For neural message passing algorithms, the objects to be embedded are vertices of some graph, and this goal is to be achieved by a local algorithm (a constant-time distributed algorithm where communication between vertices only happens along the edges). PageRank is an important simple classic example that we will discuss, but more general message passing algorithms can solve a diverse set of engineering tasks, from product recommendation to computational chemistry.

These are engineering-focused subjects, but several of the appearing concepts will be familiar to the participants, like low rank matrix approximations, the Laplacian, and local algorithms. The goal of the talk is to start an open-ended conversation between graph theorists and deep learning researchers.

The talk can be viewed at the following link: https://old.renyi.hu/videos/dynasnet/2019-03-08.mp4

• Basic notions in graph convergence

Miklós Abért and Balázs Szegedy
March 1, 2019   12:15 pm

Abstract: In this talk we define some basic notions and results of both dense and sparse graph convergence and discuss some applications to the theory. This particular occasion is an introductory talk aimed at college and PhD students, so people familiar with the topic may not want to attend.

The talk can be viewed at the following link: https://old.renyi.hu/videos/dynasnet/2019-02-28.mp4

• Dynamics and Structure of Networks

Miklós Abért and Balázs Szegedy
February 22, 2019   12:15 pm

This is a kickoff seminar for the DYNASET Synergy Program supported by the European Research Council, led by László Lovász, Albert-László Barabási and Jaroslav Nesetril. The main aim is to create a synergy between graph theory and network science. The planned activities range from theoretical mathematics, including dynamical systems and graph limits, to real life applications, like brain research.

In this talk, the speakers will define some of the basic objects of investigations and provide an insight to the project.

The talk can be viewed at the following link: https://old.renyi.hu/videos/dynasnet/2019-02-22.mp4