Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSteering complex networks toward desired dynamics
64
0
0.0
(
0
)
Added by
Ricardo Guti\\'errez
Publication date
2020
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We consider networks of dynamical units that evolve in time according to different laws, and are coupled to each other in highly irregular ways. Studying how to steer the dynamics of such systems towards a desired evolution is of great practical interest in many areas of science, as well as providing insight into the interplay between network structure and dynamical behavior. We propose a pinning protocol for imposing specific dynamic evolutions compatible with the equations of motion on a networked system. The method does not impose any restrictions on the local dynamics, which may vary from node to node, nor on the interactions between nodes, which may adopt in principle any nonlinear mathematical form and be represented by weighted, directed or undirected, links. We first explore our method on small synthetic networks of chaotic oscillators, which allows us to unveil a correlation between the ordered sequence of pinned nodes and their topological influence in the network. We then consider a 12-species trophic web network, which is a model of a mammalian food web. By pinning a relatively small number of species, one can make the system abandon its spontaneous evolution from its (typically uncontrolled) initial state towards a target dynamics, or periodically control it so as to make the populations evolve within stipulated bounds. The relevance of these findings for environment management and conservation is discussed.
rate research
Read More
Forecasting the evolution of contagion dynamics is still an open problem to which mechanistic models only offer a partial answer. To remain mathematically or computationally tractable, these models must rely on simplifying assumptions, thereby limiting the quantitative accuracy of their predictions and the complexity of the dynamics they can model. Here, we propose a complementary approach based on deep learning where the effective local mechanisms governing a dynamic on a network are learned from time series data. Our graph neural network architecture makes very few assumptions about the dynamics, and we demonstrate its accuracy using different contagion dynamics of increasing complexity. By allowing simulations on arbitrary network structures, our approach makes it possible to explore the properties of the learned dynamics beyond the training data. Finally, we illustrate the applicability of our approach using real data of the COVID-19 outbreak in Spain. Our results demonstrate how deep learning offers a new and complementary perspective to build effective models of contagion dynamics on networks.
In this work we tackle a kinetic-like model of opinions dynamics in a networked population endued with a quenched plurality and polarization. Additionally, we consider pairwise interactions that are restrictive, which is modeled with a smooth bounded confidence. Our results show the interesting emergence of nonequilibrium hysteresis and heterogeneity-assisted ordering. Such counterintuitive phenomena are robust to different types of network architectures such as random, small-world and scale-free.
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the mathematical tools of statistical physics have proven to be particularly suitable for studying and understanding complex networks. Nevertheless, an important obstacle to this theoretical approach is still represented by the difficulties to draw parallelisms between network science and more traditional aspects of statistical physics. In this paper, we explore the relation between complex networks and a well known topic of statistical physics: renormalization. A general method to analyze renormalization flows of complex networks is introduced. The method can be applied to study any suitable renormalization transformation. Finite-size scaling can be performed on computer-generated networks in order to classify them in universality classes. We also present applications of the method on real networks.
We propose a bare-bones stochastic model that takes into account both the geographical distribution of people within a country and their complex network of connections. The model, which is designed to give rise to a scale-free network of social connections and to visually resemble the geographical spread seen in satellite pictures of the Earth at night, gives rise to a power-law distribution for the ranking of cities by population size (but for the largest cities) and reflects the notion that highly connected individuals tend to live in highly populated areas. It also yields some interesting insights regarding Gibrats law for the rates of city growth (by population size), in partial support of the findings in a recent analysis of real data [Rozenfeld et al., Proc. Natl. Acad. Sci. U.S.A. 105, 18702 (2008)]. The model produces a nontrivial relation between city population and city population density and a superlinear relationship between social connectivity and city population, both of which seem quite in line with real data.
Power grids, road maps, and river streams are examples of infrastructural networks which are highly vulnerable to external perturbations. An abrupt local change of load (voltage, traffic density, or water level) might propagate in a cascading way and affect a significant fraction of the network. Almost discontinuous perturbations can be modeled by shock waves which can eventually interfere constructively and endanger the normal functionality of the infrastructure. We study their dynamics by solving the Burgers equation under random perturbations on several real and artificial directed graphs. Even for graphs with a narrow distribution of node properties (e.g., degree or betweenness), a steady state is reached exhibiting a heterogeneous load distribution, having a difference of one order of magnitude between the highest and average loads. Unexpectedly we find for the European power grid and for finite Watts-Strogatz networks a broad pronounced bimodal distribution for the loads. To identify the most vulnerable nodes, we introduce the concept of node-basin size, a purely topological property which we show to be strongly correlated to the average load of a node.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
