Related papers: Optimal reinforcing networks for elastic membranes
Plasticity is inherent to many engineering materials such as metals. While it can degrade the load-carrying capacity of structures via material yielding, it can also protect structures through plastic energy dissipation. To fully harness…
Our goal is to develop a design framework for multifunctional mechanical metamaterials that can tune their rigidity while optimizing other desired properties. Towards this goal, we first demonstrate that underconstrained central force…
This paper studies network resilience against structured additive perturbations to its topology. We consider dynamic networks modeled as linear time-invariant systems subject to perturbations of bounded energy satisfying specific sparsity…
Modularity has been widely studied as a mechanism to improve the capabilities of neural networks through various techniques such as hand-crafted modular architectures and automatic approaches. While these methods have sometimes shown…
We consider a periodic lattice structure in $d=2$ or $3$ dimensions with unit cell comprising $Z$ thin elastic members emanating from a similarly situated central node. A general theoretical approach provides an algebraic formula for the…
A biological neural network is constituted by numerous subnetworks and modules with different functionalities. For an artificial neural network, the relationship between a network and its subnetworks is also important and useful for both…
To enhance robustness of complex networked systems, a simple method is introducing reinforced nodes which always function during failure propagation. A random scheme of node reinforcement can be considered as a benchmark for finding an…
Optimal percolation is the problem of finding the minimal set of nodes such that if the members of this set are removed from a network, the network is fragmented into non-extensive disconnected clusters. The solution of the optimal…
While interdependent systems have usually been associated with increased fragility, we show that strengthening the interdependence between dynamical processes on different networks can make them more robust. By coupling the dynamics of…
In this Rapid Communication we investigate spatially constrained networks that realize optimal synchronization properties. After arguing that spatial constraints can be imposed by limiting the amount of `wire' available to connect nodes…
Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random…
We consider shape optimization problems for elasticity systems in architecture. A typical question in this context is to identify a structure of maximal stability close to an initially proposed one. We show the existence of such an…
Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber reinforced materials are also common in technology. An important characteristic of such materials is their…
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…
Artificial neural networks used for reinforcement learning are structurally rigid, meaning that each optimized parameter of the network is tied to its specific placement in the network structure. It also means that a network only works with…
Using numerical simulations, we characterized the behavior of an elastic membrane immersed in an active fluid. Our findings reveal a nontrivial folding and re-expansion of the membrane that is controlled by the interplay of its resistance…
Given a connected network, it can be augmented by applying a growing strategy (e.g. random or scale-free rules) over the previously existing structure. Another approach for augmentation, recently introduced, involves incorporating a direct…
A free boundary problem arising from the optimal reinforcement of a membrane or from the reduction of traffic congestion is considered; it is of the form $$\sup_{\int_D\theta\,dx=m}\ \inf_{u\in H^1_0(D)}\int_D\Big(\frac{1+\theta}{2}|\nabla…
With the rapid growth of online social networks, strengthening their stability has emerged as a key research focus. This study aims to identify influential relationships that significantly impact community stability. In this paper, we…
Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex…