Abstracts > Wednesday 15

Abstract. We use a percolation approach to estimating the size of SIR or SEIR epidemics in complex networks, using a formulation which allows us to take into account that infection channels are quite often not independent, such as infections through members of any clique. Our approach describes the network of possible infection channels as a bipartite network of Potentially Infected Individuals (PIIs) and Potentially Infectious Places (PIPs). Individuals can catch a virus by attending PIPs that are frequented by PIIs of which some actually are infected.
Both the set of PIIs and the set of PIPs are structured according to the type of connections they make. For PIIs this is to a first approximation correlated with the different age brackets. Depending on age, PIIs may, for instance, attend kindergarten, primary school, secondary school, university or a workplace, or indeed neither of these and instead possibly a care home if they are elderly. The different types of PIPs just mentioned each will have their own statistics concerning total number of individuals typically attending, and in the way attendance is spread across age brackets. We use message passing to evaluate node dependent infection probabilities of PIIs as well as node dependent infectious potential of PIPs in given large instances of structured bi-partite networks, as well as distributions of infection probabilities, both separately for each group of PIIs and across the entire population, as well as node-dependent infectious potential of the various PIPs, once more across the entire set of PIPs but also specifically for the various different types of PIP. This allows us to model and to assess the efficacy of various targeted lockdown and social distancing strategies as well as to assess the risks that go along with their easing. The work is based on earlier work on heterogeneous microstrucutre in percolation and on techniques used to study percolation in gene regulatory networks.

Abstract. Cases in which the number of interacting components is very large are becoming of general interest in disparate fields, such as in ecology and biology, e.g. for bacteria communities, as well as in complex economies where many agents trade and interact simultaneously. As a consequence of the complex interaction network, many of these systems appear often to be poised at the edge of stability, hence displaying enormous responses to external perturbations. In this talk, I will present the problem of ecological complexity by focusing on a reference model in theoretical ecology, the disordered Lotka-Volterra model with random interactions and finite demographic noise. By means of advanced disordered system techniques, I will unveil a very rich - eventually fractal - structure in the organization of the equilibria and relate critical features and slow relaxation dynamics to the appearance of disordered glassy-like phases. Finally, I will discuss the generalization of these results to asymmetric interactions as well as to non-logistic growth functions in the dynamics of the species abundan

Abstract. We present analytical results for the distribution of first return (FR) times of random walks (RWs) on random regular graphs (RRGs) consisting of \(N\) nodes of degree \(c \ge 3\). Starting from a random initial node \(i\) at time \(t=0\), at each time step \(t \ge 1\) an RW hops into a random neighbor of its previous node. We calculate the distribution \(P ( T_{\rm FR} = t )\) of first return times to the initial node \(i\). In the analysis we distinguish between first return trajectories in which the RW retrocedes its own steps backwards all the way to the initial node \(i\) and those in which the RW returns to \(i\) via a path that does not retrocede its own steps. In the retroceding (RETRO) scenario, each edge that belongs to the RW trajectory is crossed the same number of times in the forward and backward directions, while in the non-retroceding (\(\lnot\)RETRO) scenario the subgraph that consists of the nodes visited by the RW and the edges it has crossed between these nodes includes at least one cycle. The first return process is an important landmark in the life-cycle of RWs on networks. The characteristic time scale of this process is of order \(t \sim N\). Another landmark is the first hitting process, which is the first time in which the RW enters a previously visited node, whose characteristic time scale is \(t \sim \min \{c,\sqrt{N} \}\). Yet another event is the cover time, at which the RW completes visiting all the nodes in the network at least once, whose characteristic time scale is \(t \sim N \ln N\).

Abstract. Wealth and income are often used proxies for quantifying social inequalities. Although they are closely related quantities and their probability density function presents a Pareto-type heavy tail, there are also important differences between them. While income distribution is directly estimated from electronic databases, wealth is a more complex quantity that is indirectly measured through quantifiable proxies. Another important difference is that wealth can have also negative values, meaning debts. On the modeling side most of the available econo-physics models target the wealth exchange or wealth growth dynamics and only very few of them focus on income. The presently available models usually treat separately the low/middle class and the wealthier part of the society. A unified analytical probability density function describing all wealth and income ranges is therefore lacking. Here we present a mean-field like master equation approach based on unidirectional growth and reset processes, aimed to offer a unified and realistic description for wealth and income distributions in modern societies. Using the same growth and reset rates with different parameters, income and wealth distribution data are properly modelled for the investigated societies. We give compact analytical forms for the probability density functions for income and wealth distributions that is valid for all classes of the society.

Abstract. Complex networks encountered in biology, ecology, sociology and technology often contract due to node failures, infections or attacks. The ultimate failure, taking place when the network fragments into disconnected components was studied extensively using percolation theory. We show that long before reaching fragmentation, contracting networks lose their distinctive features. In particular, we identify that a very large class of network structures, which experience a broad class of node deletion processes, exhibit a stable flow towards a universal fixed point, representing a maximum-entropy ensemble, namely the Erdös-Rényi ensemble characterized by a Poisson degree distribution. This is in sharp contrast to network expansion processes, which lead to diverse families of complex networks, often scale-free graphs, whose structure is highly sensitive to details of the growth mechanism. These results imply that contracting networks in the late stages of node failure cascades, attacks and epidemics reach a common universal structure, providing a unifying framework for their analysis.

Abstract. One of the outstanding challenges of computer-aided investigation of biological macromolecules, such as proteins and protein complexes, is represented by the intrinsic multi-scale nature of several processes and phenomena; these range from large conformational changes induced by ligand binding to the epigenetic regulation of gene expression and beyond. A unique framework for the in silico study of such phenomena is impossible and inappropriate, as different properties take place at distinct characteristic length- and time-scales; consequently, models and representations at various resolutions have been developed, which address each property specifically. A critical issue, however, is how to integrate these models to account for the interplay of processes occurring at different scales. In this talk I will present methods and techniques that have been recently developed and applied to fill this gap. Particular attention will be posed on those strategies aimed at identifying functionally relevant sites or regions of proteins, based on the amount of information that a reduced representation can preserve from the underlying high-resolution model. Subsequently, I will discuss the general properties of these reduced representations and the issue of integrating models at different levels of detail in the same setup. Finally, I will present multi-disciplinary applications that these methods would allow in fields even very far from molecular biophysics, e.g. neuroscience and quantitative finance.

Abstract. Financial markets are characterized by an enormous network of connections and factors that can influence the structure and dynamics of the system. One of the youngest part of the modern financial markets are cryptocurrencies. Since the Bitcoin invention in 2009, the cryptocurrency market has experienced striking development over the last few years - from being entirely peripheral to being a part of world financial markets.
The Covid-19 pandemic affected essentially all activities in the world and in particular the financial ones. It caused a crash on the stock markets in March 2020 and did not spare the cryptocurrency market valuation either. These strong perturbations have resulted in large price changes, which affected return distributions and also led to a strong increase in the cross- correlations among many assets.
It was long believed that the cryptocurrency market is rather detached from traditional financial markets and can serve as a hedge or ,,safe haven''. However it seems that the pandemic triggered the emergence of correlations between the major cryptocurrencies and the traditional markets. What is the most interesting the positive cross-correlations with risky assets occurred not only during the sharp market fall in March-April 2020, but also during a recovery phase in the second half of 2020, when BTC and S&P500 hit all-time highs. Based on the analysis it can be argued that events related to Covid-19 pandemic changed the paradigm and the most liquid cryptocurrencies cannot be longer considered as hedge for conventional financial assets. Moreover they have become connected part of the global financial markets.

Abstract. Zipf’s law describes the empirical size distribution of the components of many systems in natural and social sciences and humanities. We show, by solving a statistical model, that Zipf’s law co- occurs with the maximization of the diversity of the component sizes. The law ruling the increase of such diversity with the total dimension of the system is derived and its relation with Heaps’ law is discussed. As an example, we show that our analytical results compare very well with linguistics and population datasets.

Abstract. We analyze the effect of temperature on the yielding transition of amorphous solids using different coarsegrained model approaches. On one hand, we use an elastoplastic model, with temperature introduced in the form of an Arrhenius activation law over energy barriers. On the other hand, we implement a Hamiltonian model with a relaxational dynamics, where temperature is introduced in the form of a Langevin stochastic force. In both cases, temperature transforms the sharp transition of the athermal case in a smooth crossover. We show that this thermally smoothed transition follows a simple scaling form that can be fully explained using a one-particle system driven in a potential under the combined action of a mechanical and a thermal noise, namely, the stochastically driven Prandtl-Tomlinson model. Our work harmonizes the results of simple models for amorphous solids with the phenomenological \(T^{2/3}\) law proposed by Johnson and Samwer [Phys. Rev. Lett. 95, 195501 (2005)] in the framework of experimental metallic glasses yield observations, and extend it to a generic case. Conclusively, our results strengthen the interpretation of the yielding transition as an effective mean-field phenomenon.

Abstract. In recent years, there has been intense attention on the constraints posed by quantum mechanics on the dynamics of the correlation at low temperatures, triggered by the postulation and derivation of quantum bounds on the transport coefficients or on the chaos rate. However, the physical meaning and the mechanism enforcing such bounds is still an open question. In this talk, I will discuss the quantum fluctuation-dissipation theorem (the KMS conditions) as the principle underlying bounds on correlation time scales. By restating the problem in a replicated space, I will show that the quantum bound to chaos is a direct consequence of the KMS condition, as applied to a particular pair of two-time correlation and response functions. Encouraged by this, I will describe how quantum fluctuation-dissipation relations act in general as a blurring of the time-dependence of correlations, which can imply bounds on their decay rates. Thinking in terms of fluctuation- dissipation opens a direct connection between bounds and other thermodynamic properties.

Abstract. The Fluctuation-Dissipation Theorem (FDT) is a cardinal tool of Statistical Physics. This relation yields to the Equipartition Principle, thanks to which we can link the fluctuations of an observable with the temperature of the system. In non-equilibrium situations however, such relations between fluctuations and response are not granted, and a higher noise is usually expected with respect to an equilibrium state. In this presentation, we show that the opposite phenomenon can also be experimentally observed: fluctuations smaller than in equilibrium! In our experiment, an atomic force microscope (AFM) µ-cantilever in vacuum is heated at its extremity with a laser. The heat flux sets the system in a Non-Equilibrium Steady State (NESS). We measure the thermal noise driven deflection d and quantify the amplitude of the fluctuations with an effective temperature T eff extending the equipartition principle: \(\frac{1}{2}k_BT_{\rm eff}=\frac{1}{2}k_n\langle d_n^2\rangle\) with \(k_B\) the Boltzmann constant, \(k_n\) the mechanical mode stiffnesses and \(\langle d_n^2\rangle\) the mean square deflections. We observe a strong deficit of thermal noise with respect to the cantilever average temperature.
We will explain how a generalized FDT including the temperature field can account for these observations, when dissipation is not uniform. Further experimental evidence of the validity of this framework, down to cryogenic temperatures, will conclude the presentation. Our approach paves the way for thermal noise engineering: it can be used as a tool to probe the spatial distribution of dissipation, or on the contrary to tune the thermal noise amplitude and spectra by choosing an adequate damping field.
We acknowledge the support of ERC project OutEFLUCOP and ANR project HiResAFM.

Abstract. Active matter systems are non-equilibrium systems in which individual particles, biological or artificial, continually consume internal energy to self-propel, breaking time-reversal symmetry at a local scale and in a sustained way. Their non-equilibrium nature allows a variety of intriguing phenomena to appear, for example, the phase separation in a dense and dilute phase in the complete absence of attractive interactions, called motility induced phase separation (MIPS). We would like to illustrate peculiar features of MIPS in a paradigmatic model of active matter, the Active Brownian Particles (ABPs) in two spatial dimensions. Even though MIPS preserves many aspects of an equilibrium phase separation, the physics at play is more complex, leading to new phenomena. We explain the growth exponent \(z\approx 1/3\) in the law \(L\sim t^z\) , where \(L\) is the typical size of clusters of the dense phase and \(t\) the time, in terms of an aggregation-condensation mechanism, also taking into account the fractal geometry of aggregates and the diffusion properties of single clusters. We found anomalous dependence of the cluster diffusion coefficient, since it decreases as the inverse of the square root of mass, but it is still increasing with the square of the Peclét number as in the case of single particles. Moreover, on top of this ordinary equilibrium-like coarsening, we found evidence of another ordering mechanism, i.e., the micro-phase separation of the dense phase into hexatic domains and vapour bubbles. The growth rate of hexatic domains differs from that of the whole clusters and behaves as \(L_H\approx t^{0.2}\). Steady-state size of bubbles are controlled by the propulsion force and are also quantitatively described. Finally, we show that changing the geometry of active particles from disks to dumbbells has enormous effects on the dynamics of MIPS, both affecting the value of the growth exponent (\(z\approx 3/5\)) and the motion of single clusters that acquire evident ballistic behaviour.

Abstract. It is a very remarkable and yet not understood fact that critical phenomena have conformally invariant statistical properties. Although it is implied by scale invariance for systems with local interactions, there is no reason to expect so when the degrees of freedom are non local, as for instance in percolation phenomena. Nevertheless, it seems that conformal invariance emerges also in these latter cases, and examples of scale but not conformal systems remain extremely rare. Here, we reveal the existence of such symmetry for two-dimensional rigidity percolation that belongs to a different universality class than connectivity percolation, and for which the question of conformal invariance had not been addressed so far. The rigidity transition occurs at higher filling fraction than connectivity percolation, when percolating clusters become able to transmit and ensure mechanical stability to the overall disordered network. We show that i) these clusters are conformally invariant random fractals and ii) we use conformal field theory to predict the form of universal finite size effects. Our findings open a new avenue for the application of conformal field theories in physical and biological systems exhibiting such a mechanical transition.

Abstract. The Kuramoto equation has been solved numerically on the 21.662 node fruit-fly and the 804.113 node human connectomes. While the fly neural connectome resembles to a structureless random graph, the KKI-18 grey matter human connectome exhibits a hierarchical modular organization. The synchronization transition of the fly is mean-field like, but a narrow Griffiths phase cannot be excluded. In contrast, the transition on the KKI-18 is very broad and a frustrated synchronziation phase, with nonuniversal power-laws can be observed, sub-critically.