Related papers: Statistical mechanics of frustrated assemblies and…

The focus of this thesis is about statistical mechanics on heterogeneous random graphs, i.e. how this heterogeneity affects the cooperative behavior of model systems. It is not intended as a review on it, rather it is showed how this…

The recently introduced structured input-output analysis is a powerful method for capturing nonlinear phenomena associated with incompressible flows, and this paper extends that method to the compressible regime. The proposed method relies…

We start with a simple introduction to topological data analysis where the most popular tool is called a persistent diagram. Briefly, a persistent diagram is a multiset of points in the plane describing the persistence of topological…

Turing patterns, arising from the interplay between competing species of diffusive particles, has long been an important concept for describing non-equilibrium self-organization in nature, and has been extensively investigated in many…

Reduction of flow compressibility with the corresponding ideally invariant helicities, universally for various fluid models of neutral and ionized gases, can be argued statistically and associated with the geometrical scenario in the…

Graph neural networks trained to predict observable dynamics can be used to decompose the temporal activity of complex heterogeneous systems into simple, interpretable representations. Here we apply this framework to simulated neural…

The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing…

We study constraint satisfaction problems on the so-called 'planted' random ensemble. We show that for a certain class of problems, e.g. graph coloring, many of the properties of the usual random ensemble are quantitatively identical in the…

In an increasingly interconnected world, understanding and summarizing the structure of these networks becomes increasingly relevant. However, this task is nontrivial; proposed summary statistics are as diverse as the networks they…

Interconnected networks of rigid struts are critical for application in lightweight, load-bearing structures. However, accurately modeling stress distribution in these strut lattices poses significant computational challenges due to its…

Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…

In order to deal with multidimensional structure representations of real-world networks, as well as with their worst-case irreducible information content analysis, the demand for new graph abstractions increases. This article investigates…

Understanding causal relationships among the variables of a system is paramount to explain and control its behavior. For many real-world systems, however, the true causal graph is not readily available and one must resort to predictions…

One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of…

The theory of pattern formation in reaction-diffusion systems is extended to the case of a directed network. Due to the structure of the network Laplacian of the scrutinised system, the dispersion relation has both real and imaginary parts,…

The aggregation process of fibers suspended in a fluid remains an open question, despite its critical role in numerous natural and industrial processes. This paper presents an experimental setup designed to create fiber aggregates in a…

Network structure is a mechanism for promoting cooperation in social dilemma games. In the present study, we explore graph surgery, i.e., to slightly perturb the given network, towards a network that better fosters cooperation. To this end,…

Geometric frustration lies at the heart of many unconventional quantum phases in strongly interacting electron systems. Here, we analytically determine the ground state magnetization of the half-filled Hubbard model on frustrated geometries…

We investigate collective dynamics in a pulse-coupled adaptive Winfree network under the influence of a frustration (phase-lag) parameter. The coupling strengths coevolve according to a Hebbian adaptation rule and self-organize to support a…

Self-organized complex structures in nature, e.g. viral capsids, hierarchical biopolymers, and bacterial flagella, offer efficiency, adaptability, robustness, and multi-functionality. Can we program the self-assembly of three-dimensional…