Foundations & Physics  (FP) Session 1

Abstract: Empirically, we observe that in concerts, pilgrimages, parades, Black Friday bargain hunters, football matches and other similar social gatherings, the density of people becomes exceptionally high and might give rise to unusual and occasionally tragic collective motions. All these situations are characterised by a high degree of dynamic fluctuations, but little overall motility. While active particle simulations have demonstrated the ability to reproduce most phenomenology of human collective motion, high-density scenarios call for a rethinking of conventional analysis approaches. Here, we take inspiration from jammed granular media and eigenmode analysis to understand the mechanisms underlying human collective motion at extreme densities. Vibrational eigenmodes predict the emergence of long-range correlated motions and unstable areas in simulations of high-density crowds. By introducing agitated individuals to account for behavioural heterogeneity, we find that perturbing the eigenmodes enhances the propagation of long-range correlated motions such as, for example, shock waves. If found in real crowds, these emergent mechanisms would provide a simple explanation of how crowd disasters could arise from purely physical and structural considerations. Our approach could provide powerful tools for predicting the onset of dangerous collective motions with applications in crowd management and in the design of public venues. Close

Abstract: Computational mechanics describes a sophisticated toolset for understanding the structure and complexity of observational phenomena [1]. It captures the idea that we understand nature through cause and effect – the more complex a process, the more causes one must postulate to model its behaviour. This view motivated statistical complexity – the minimal amount of causal information one needs to record about a phenomenon’s past to model its future statistics – as a popular measure of its intrinsic complexity. The standard framework has generally assumed that we understand nature through classical means; processing classical bits. Nature, however, is intrinsically quantum mechanical, allowing quantum bits that exist in superposition of 0 and 1. Can such uniquely quantum behaviour unveil ore refined views of structure and complexity? I this presentation, I review our work in pioneering quantum models that require provably less causal information that any classical counterpart [2] and describe our ongoing experiments in realizing these models within photonic systems [3]. I then outline recent advances in constructing provably optimal quantum models, and how they demonstrate that quantum statistical complexity can exhibits drastically different qualitative behaviour - falling for example, when its classical counterpart rises. Thus many observed phenomena could be significantly simpler than classically possible should quantum effects be involved, and existing notions of structure and complexity may ultimately depend on the type of information theory we use. [1] J.P. Crutchfield and K. Young, Phys. Rev. Lett. 63 105. [2] M. Gu, K. Wiesner, E. Rieper, V. Vedral, Nature communications, 3 762 [3] M. Palsson, M. Gu, J. Ho, Howard M. Wiseman, and Geoff J. Pryde. arXiv:1602.05683 Close

Abstract: From reactions fueling cells in our bodies to internet links binding our society into a small world, networks are at the basis of every structure and random graph theory is the common language widely used to discuss them. Network science is full of empirical data, yet an observer collecting such data is either embedded into the network him/herself, thus viewing it locally, or is his/her distanced far apart and thus observing only the global properties. Indeed, one may study individual servers of the Internet but the question of the global structure is far less trivial. Or a physicist may observe global properties of a complex material not knowing much on how individual molecules are interconnected. This research shows how one, being on one extreme of this dichotomy may transit to the other: converting local information into global, and back. Take a ‘normal’ notion of network and replace all (or a portion of) links with arrows, we obtain a directed network. In such a network every node has a certain probability of having N outgoing arrows and M ingoing arrows – thus a bivariate degree distribution. There are a few generalizations for connected components in this case. Most controversial one is the weak-component -- a set of nodes one may reach if ignoring the direction of the arrows. It is controversial, precisely because it sounds so simple: one may be tempted to say, in this case there is no direction and the task degenerates to a classical problem. But when we posses only a snapshot of local properties – the bivariate degree distribution, we can not ignore the directional data anymore. This work presents correct formulation and the answer to the weak-component problem in directed graphs that are identified by a degree distribution for the first time. Close

Abstract: Multivalency is the phenomenon that describes the interaction between multivalent receptors and multivalent ligands. It is well known to play a pivotal role in biochemistry, particularly in protein-carbohydrate interactions, both in solution (e.g. at pentavalent cholera toxins) and at interfaces (e.g. for the infection of cells by the attachment of viruses or bacteria to cell membranes). In particular in the latter case, multivalency is often poorly understood in a quantitative sense. Supramolecular host-guest chemistry has been well established in solution, but its use at interfaces remains limited to for example sensor development for specific guest compounds. In order to build assemblies at surfaces through supramolecular interactions for nanotechnological applications, other demands have to be met, such as larger thermodynamic and kinetic stabilities of the assemblies. For many supramolecular motifs, this inevitably leads to the use of multivalent interactions. We employ the concept of molecular printboards, which are self-assembled monolayers functionalized with receptor groups suitable for nanofabrication. The design of guest molecules allows precise control over the number of interacting sites and, therefore, over their (un)binding strength and kinetics. A recent focus is on heterotropic multivalency, which is the use of multiple interaction motifs. This has been applied to the controlled, selective, and specific binding of metal-ligand coordination complexes, proteins, antibodies, and even cells. The current paper will focus on less obvious, emerging properties from such assemblies such as supramolecular expression, non-linear amplification, coherent energy transfer, and multivalent surface diffusion. Close

Abstract: Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between non-linear dynamics and network science. In this work we present the sequential visibility graph motifs, smaller substructures of n consecutive nodes that appear with characteristic frequencies inside visibility graphs. We show that the motif frequency profile is a highly informative feature which can be treated analytically for several classes of deterministic and stochastic processes and in general computationally efficient to extract. In particular we have found that this graph feature is surprisingly robust, in the sense that it is still able to distinguish amongst different dynamics even when the signals are polluted with large amounts of observational noise, what enables its use in practical problems such as classification of empirical time series. As an application, we have tackled the problem of disentangling meditative from general relaxation states from the horizontal visibility graph motif profiles of heartbeat time series of different subjects performing different activities. We have been able to provide a positive, unsupervised solution to this question by applying standard clustering algorithms on this simple feature. Our results suggest that visibility graph motifs provide a mathematically sound, computationally efficient and highly informative simple feature which can be extracted from any kind of time series and used to describe complex signals and dynamics from a new viewpoint. In direct analogy with the role played by standard motifs in biological networks, further work should evaluate whether visibility graph motifs can be seen as the building blocks of time series. References: 1) Lacasa L. et al. "From time series to complex networks: The visibility graph." PNAS 105.13 (2008). 2) Iacovacci J. and Lacasa L. "Sequential visibility graph motifs" PRE 93 (2016) Close