**Date**: Mon 24 Aug - Wed 26 Aug 2015

**Venue**: Room WGB G01, Western Gateway Building, UCC (except where indicated otherwise).

**Schedule** for Theme 3: Complex and Boolean Networks

Plenary talks by other themes are indicated by brackets.

24/08/15 | 25/08/15 | 26/08/15 | 27/08/15 | ||

Time | Monday | Tuesday | Wednesday | Thursday | Time |

08:00–08:30 | On-Site Registration |
08:00–08:30 | |||

08:30–09:00 | 08:30–09:00 | ||||

09:00–09:30 |
WGB 1.07 |
WGB 1.07 |
WGB 1.07 |
09:00–09:30 | |

09:30–10:00 | 09:30–10:00 | ||||

10:00–10:30 | Coffee&Tea | Coffee&Tea | Coffee&Tea | 10:00–10:30 | |

10:30–11:00 | David Arrowsmith | Eckehard Schöll | Charo del Genio | 10:30–11:00 | |

11:00–11:30 | 11:00–11:30 | ||||

11:30–12:00 | Stefano Boccaletti | Johan Dubbeldam | Ingo Fischer | 11:30–12:00 | |

12:00–12:30 | 12:00–12:30 | ||||

12:30–13:00 | Lunch | Lunch | Lunch | 12:30–13:00 | |

13:00–13:30 | Lunch | 13:00–13:30 | |||

13:30–14:00 | 13:30–14:00 | ||||

14:00–14:30 | James Gleeson | Peter Ashwin | Johannes Lohmann |
Room WGB 1.07 |
14:00–14:30 |

14:30–15:00 | Peter Fennel | 14:30–15:00 | |||

15:00–15:30 | James Cruickshank | Rajarshi Roy | Katie Burke | 15:00–15:30 | |

15:30–16:00 | 15:30–16:00 | ||||

16:00–16:30 |
Coffee&Tea |
Coffee&Tea | Coffee&Tea | Coffee&Tea | 16:00–16:30 |

16:30–17:00 |
WGB 1.07 |
WGB 1.07 |
WGB 1.07 |
16:30–17:00 | |

17:00–17:30 | 17:00–17:30 | ||||

... | ... | ||||

19:30-20:00 |
Cornstore Restaurant |
19:30-20:00 | |||

20:00–20:30 |
Public Lecture, Aula Maxima |
20:00–20:30 | |||

20:30–21:00 | 20:30–21:00 |

I will introduce the study of European infrastructure networks and give an overview of a investigation on gas flow disruption. I will also discuss the likely mathematical problems that will arise in modelling a stable transition to a renewables-led energy grid.

In this talk I will review and discuss some work on the mathematics of coupled nonlinear dynamical systems that attempts to understand some of the fundamental aspects of how neural systems store, compute and process information. Focussing on coupled networks of simple dynamical systems such as phase oscillators, firing rate models or bistable units, I explore how attracting heteroclinic and excitable networks in phase space may emerge via the complex interactions between the units and how these may be capable of information storage and processing in the sense of finite state Turing machines.

I will briefly discuss how to engineer a computational unit, so that logical states can be associated to synchronized dynamics. When such a unit is taken as elementary node of a network, different logical gates can be implemented. In particular, I will first show how to realize universal Boolean gates, and how to over-perform Boolean computation by means of specific network's motifs. Second, when each link of the network is associated with a complex value, computations with multi-states can be easily performed.

I will present the results of my master thesis on the synchronization behaviour of small Kuramoto-type networks with time-varying link strengths. Numerical and analytical methods are used to determine the long-time behaviour and stable states of link-configurations.

In geometric rigidity theory one associates a geometric structure, such as a bar joint framework to a network or graph and the basic question is whether the resulting structure is rigid or flexible. Such questions are of obvious interest in structural engineering but also in biochemistry, in particular in the study of allostery. Allostery is concerned with the effect that binding a molecule at one site in a protein can have on the properties of the protein at another possibly remote site. I will discuss an abstracted version of this problem that arises from some recent developments in geometric rigidity.

Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be linked with low-degree nodes. Degree correlations also affect the dynamics of processes supported by a network structure, such as the spread of opinions or epidemics. The proper modelling of these systems, i.e., without uncontrolled biases, requires the sampling of networks with a specified set of constraints. We present a solution to the sampling problem when the constraints imposed are the degree correlations. In particular, we develop an efficient and exact method to construct and sample graphs with a specified joint-degree matrix, which is a matrix providing the number of edges between all the sets of nodes of a given degree, for all degrees, thus completely specifying all pairwise degree correlations, and additionally, the degree sequence itself. Our algorithm always produces independent samples without backtracking. The complexity of the graph construction algorithm is O(NM) where N is the number of nodes and M is the number of edges.

Recent studies of synchronization with highly idealized models found a strong dependence on the network topology. In the future distributed renewable energy sources (DRES) will drastically change the grid topology and induce large and correlated fluctuations in the power generation. In this talk I will discuss the challenges imposed on the future smart power grid. Using the ``swing equations'' the stability of network operation in the presence of large perturbations is investigated. Synchronous operation of the network and the optimal topology to secure stable operation in the future will be discussed.

The spreading of phenomena such as information, sentiment and behavior through social networks is highly complex. The speed and depth of such diffusion can be affected by structural features of the underlying network, such as its connectivity and the level of clustering, as well as the temporally non-uniform manner in which individuals interact. In this talk we examine the complex nature of social diffusion in both an empirical and theoretical manner. We analyze large-scale data sets of social networks, employing hazard rates to quantify the way in which individuals react to information from their peers. We develop theoretical frameworks around these hazard rates, giving a medium to analytically study both the evolution and equilibrium behavior of social diffusion. We present a selection of results, and show the utility of our model when analyzing the factors that affect social diffusion processes.

To learn from the brain how to process information has been a fascinating perspective for several decades. Many advances have been made, and powerful computational schemes have been introduced. Nevertheless, even basic mechanisms and requirements of neural information processing remain unclear.

We choose a minimal design approach (1), allowing for the implementation of neuro-inspired computational concepts on different hardware platforms. By reducing reservoir computing and related concepts to their bare essentials, we find that nonlinear transient responses of a simple dynamical system enable the processing of information with excellent performance and speed (2,3). We particularly demonstrate that reservoir computing can be implemented with a physical system using a single autonomous Boolean logic element with time-delay feedback (4). The reservoir is able to classify short input patterns with performance that decreases over time, illustrating the fading memory properties

Besides the relevance for the understanding of basic mechanisms, this approach opens direct future perspectives.

References:

(1) Appeltant, L., Soriano, M. C., Van der Sande, G., Danckaert, J., Massar, S., Dambre, J., … Fischer, I. (2011). Information processing using a single dynamical node as complex system. Nature Communications 2, 468.

(2) Larger, L., Soriano, M. C., Brunner, D., Appeltant, L., Gutierrez, J. M., Pesquera, L., … Fischer, I. (2012). Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing. Optics Express 20(3), 3241–3249.

(3) Brunner, D., Soriano, M. C., Mirasso, C. R., & Fischer, I. (2013). Parallel photonic information processing at gigabyte per second data rates using transient states. Nature Communications 4, 1364.

(4) Haynes, N. D., Soriano, M. C., Rosin, D. P., Fischer, I., & Gauthier, D. J. (2015). Reservoir computing with a single time-delay autonomous Boolean node. Physical Review E 91, 020801

We consider the spreading of "memes" (distinct pieces of information like ideas, hashtags, URLs, etc.) on a large directed social network, like Twitter. We use a branching-process model to describe how users choose among multiple sources of incoming information, similar to models used in other studies, which rely on intensive computational simulations to fit to data. In contrast, we here develop analytical insights into the respective roles of the network degree distribution, the memory-time distribution of users, and the competition between memes for the limited resource of user attention. The result is a form of self-organised criticality, which we dub "competition-induced criticality". Using this analysis, we fit the model to data on Twitter hashtags, and predict features of the time-dependent data.

Biochemical systems with switch-like interactions, such as gene regulatory networks are well modeled by autonomous Boolean networks (ABNs). Specifically, the topology and logic of gene interactions can be described by systems of continuous piecewise-linear differential equations, enabling analytical predictions of the dynamics of specific networks. However, these models do not account for time delays along links associated with spatial transport, mRNA transcription, and translation.

To begin to address this issue, we have developed an experimental testbed to realize time-delay ABNs with electronic logic gates on field-programmable gate arrays. We use this system to study the dynamics that arise as time delays along the links vary. The nanosecond timescale in the experiments allows me to uncover various oscillatory transient patterns with extremely long lifetime, which emerge in small network motifs due to the delay and are distinct from the eventual stable attractors that the systems approach. In some cases, the transients are so long that it is doubtful some of these stable attractors will ever be approached in a biological system with a finite lifetime.

The problem of random number generation leads us to study the transition from noise to deterministic chaos in the dynamics of a photon counting feedback system. This transition is quantified by computation of entropy generation from experimental measurements. Patterns of synchronization in networks of such dynamical systems are studied using symmetry principles. The formation of synchronized clusters, and desynchronization, is observed is small and large networks.

The eye and brain work together to provide us with perspectives of reality. Signals from the eye to the brain determine what we see and how we interpret images and the dynamical, changing world around us. We will explore simple and complex aspects of "seeing the light" - from the formation of images to their interpretation based on frames of reference that lead us to impressions of the world around us. Visual illusions and demonstrations with simple apparatus will be used to illustrate how eyes and brain work together to help us navigate our way through life with balance and poise.

Chimera states are complex spatiotemporal patterns in nonlocally coupled networks of identical oscillators, characterized by the spatial coexistence of domains with synchronized and desynchronized dynamics.

Here we study autonomous Boolean networks of electronic oscillators that can be described approximately by a Kuramoto-like model. The fast time scale of the oscillators (on the order of 100 ns) allows us to study experimentally the scaling of the extremely long transients, displaying emergence, disapperance, and resurgence of chimera states, in large networks of more than a hundred nodes. We ﬁnd that the average transient time increases exponentially with the network size. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.

This is work in collaboration with David P. Rosin, Damien Rontani, Nicholas D. Haynes, and Daniel J. Gauthier (Duke University, NC, USA), Phys. Rev. E 90, 030902(R) (2014).

GBMS Plenary Talk. Room WGB 1.07

I will present Probabilistic Boolean Networks (PBNs), which are models of genetic regulatory networks that i) incorporate rule-based dependencies between genes; ii) allow the systematic study of global system dynamics; iii) are able to cope with uncertainty; iv) permit the quantification of the relative influence and sensitivity of genes in their interactions with other genes. PBNs share the appealing rule-based properties of Boolean networks, but are robust in the face of uncertainty.

The dynamics of PBNs can be studied in the context of Markov Chains, with standard Boolean networks being special cases. I will also discuss the relationship between PBNs and Bayesian networks – a family of graphical models that explicitly represent probabilistic relationships between the variables. A major objective is the development of computational tools for the identification of potential targets for therapeutic intervention in diseases such as cancer. I will describe several approaches for finding the best genes with which to intervene in order to elicit desirable network behavior.

The dinner for Theme 3 is on Tuesday 25 August, 19:30 at the Cornstore Restaurant 40A Cornmarket Street, Cork.

**For all Speakers of Theme 3**: The dinner is free of charge and you are already booked by default. Please let the Theme organizers know if you cannot come to the dinner so that we can adjust the booking numbers.

**For all delegates of Theme 3, who are not speakers**: you are very welcome to join the dinner on a self-paying basis. Please let the Theme organizers know if you would like to come to the dinner so that we can adjust the booking numbers.

If you enjoy walking to the dinner (about 30 minutes walk), please meet up at 18:50 in the WGB atrium. Weather permitting we will leave WGB at 19:00 sharp and walk to the Cornstore Restaurant. Alternatively you can reach the restaurant by bus number 208 or by taxi.

Group photo for theme 3 is on Monday 24 August, 16:00. Meeting point at coffee station in WGB atrium.

- Andreas Amann (UCC) a.amann@ucc.ie
- Sebastian Wieczorek (UCC)

- David Arrowsmith (Queen Mary University of London)
- Peter Ashwin (University of Exeter)
- Stefano Boccaletti (CNR Italy)
- Katie Burke (UCC)
- James Cruickshank (NUI Galway)
- Charo del Genio (University of Warwick)
- Johan Dubbeldam (Delft University of Technology)
- Peter Fennel (MACSI, University of Limerick)
- Ingo Fischer (IFISC (UIB-CSIC), Palma de Mallorca)
- James Gleeson (University of Limerick)
- Johannes Lohmann (TU Berlin)
- Rajarshi Roy (University of Maryland)
- Eckehard Schöll (TU Berlin)
- Ilya Shmulevich (Institute for Systems Biology, Seattle)

Learn more about the George Boole 200 programme at: www.georgeboole.com

Last updated 22 August, 1pm.