Related papers: Modular representation and control of floppy netwo…
We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…
Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to…
The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the…
Understanding conformational change is crucial for programming and controlling the function of many mechanical systems such as allosteric enzymes and tunable metamaterials. Of particular interest is the relationship between the network…
From the complex motions of robots to the oxygen binding of hemoglobin, the function of many mechanical systems depends on large, coordinated movements of their components. Such movements arise from a network of physical interactions in the…
Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…
We study the elasticity of random fiber networks. Starting from a microscopic picture of the non-affine deformation fields we calculate the macroscopic elastic moduli both in a scaling theory and a self-consistent effective medium theory.…
Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. There are many aspects of dynamical networks that require statistical considerations. In this…
We present a framework for simulating signal propagation in geometric networks (i.e. networks that can be mapped to geometric graphs in some space) and for developing algorithms that estimate (i.e. map) the state and functional topology of…
Many real-world networks are directed, sparse and hierarchical, with a mixture of feed-forward and feedback connections with respect to the hierarchy. Moreover, a small number of 'master' nodes are often able to drive the whole system. We…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a…
Floppy modes --- deformations that cost zero energy --- are central to the mechanics of a wide class of systems. For disordered systems, such as random networks and particle packings, it is well-understood how the number of floppy modes is…
The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze from system's robustness to perturbations to coarse graining multilayer…
Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but…
Signatures of glassy dynamics have been identified experimentally for a rich variety of materials in which molecular networks provide rigidity. Here we present a theoretical framework to study the glassy behavior of both passive and active…
Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…
Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…