相关论文: Effective medium theory of random regular networks

Turbulence is ubiquitous in nature yet even for the case of ordinary Newtonian fluids like water our understanding of this phenomenon is limited. Many liquids of practical importance however are more complicated (e.g. blood, polymer melts…

Transformer-based Diffusion Probabilistic Models (DPMs) have shown more potential than CNN-based DPMs, yet their extensive computational requirements hinder widespread practical applications. To reduce the computation budget of…

Human social interactions tend to vary in intensity over time, whether they are in person or online. Variable rates of interaction in structured populations can be described by networks with the time-varying activity of links and nodes. One…

By performing extensive simulations with unprecedentedly large system sizes, we unveil how rigidity influences the fracture of disordered materials. We observe the largest damage in networks with connectivity close to the isostatic point…

We present a scattering theory for the efficient transmission of an excitation across a finite network with designed disorder. We show that the presence of randomly positioned networks sites allows to significantly accelerate the excitation…

Understanding the intricate operations of Recurrent Neural Networks (RNNs) mechanistically is pivotal for advancing their capabilities and applications. In this pursuit, we propose the Episodic Memory Theory (EMT), illustrating that RNNs…

Social network interference induces complex dependencies where a unit's outcome is influenced not only by its own exposure and mediator but also by those of connected neighbors. In such settings, a significant challenge lies in…

Understanding how information, diseases, or influence spread across networks is a fundamental challenge in complex systems. While network diameter has been extensively studied in static networks, its definition and behavior in temporal…

Whether deep neural networks can exhibit emergent behaviour is not only relevant for understanding how deep learning works, it is also pivotal for estimating potential security risks of increasingly capable artificial intelligence systems.…

Prestrained elastic networks arise in a number of biological and technological systems ranging from the cytoskeleton of cells to tensegrity structures. To understand the response of such a network as a function of the prestrain, we consider…

Recent theoretical work suggests that systematic pruning of disordered networks consisting of nodes connected by springs can lead to materials that exhibit a host of unusual mechanical properties. In particular, global properties such as…

Turbulence Models represent the workhorse for simulations used in engineering design and analysis. Despite their low computational cost and robustness, these models suffer from substantial predictive uncertainty, most of which is epistemic.…

We study the dynamical rheology of spring networks with a percolation model constructed by bond dilution in a two-dimensional triangular lattice. Hydrodynamic interactions are implemented by a Stokesian viscous coupling between the network…

Real-world complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in…

The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the…

Disordered elastic networks provide a framework for describing a wide variety of physical systems, ranging from amorphous solids, through polymeric fibrous materials to confluent cell tissues. In many cases, such networks feature two widely…

Recent studies have shown that high disparities in effective learning rates (ELRs) across layers in deep neural networks can negatively affect trainability. We formalize how these disparities evolve over time by modeling weight dynamics…

Disordered athermal biopolymer materials, such as collagen networks that constitute a major component in extracellular matrices and various connective tissues, are initially soft and compliant but stiffen dramatically under strain. Such…

We present an effective medium theory that includes bending as well as stretching forces, and we use it to calculate mechanical response of a diluted filamentous triangular lattice. In this lattice, bonds are central-force springs, and…

The monotonic dependence of the outputs of a neural network on some of its inputs is a crucial inductive bias in many scenarios where domain knowledge dictates such behavior. This is especially important for interpretability and fairness…