Related papers: Scaling in Local Optimal Paths Cracks
In close analogy to diffusion limited aggregation (DLA) and inspired by a work of Roux, a random walker algorithm is constructed to solve the problem of crack growth in an elastic medium. In contrast to conventional lattice approaches, the…
We study avalanches in a model for a planar crack propagating in a disordered medium. Due to long-range interactions, avalanches are formed by a set of spatially disconnected local clusters, the sizes of which are distributed according to a…
To lower the complexity of network codes over packet line networks with arbitrary schedules, chunked codes (CC) and overlapped chunked codes (OCC) were proposed in earlier works. These codes have been previously analyzed for relatively…
On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…
We propose a model for path-planning based on a single performance metric that accurately accounts for the the potential (spatially inhomogeneous) cost of breakdowns and repairs. These random breakdowns (or system faults) happen at a known,…
The dynamical processes taking place on a network depend on its topology. Influencing the growth process of a network therefore has important implications on such dynamical processes. We formulate the problem of influencing the growth of a…
The rapid urbanization and increasing traffic have serious social, economic, and environmental impact on metropolitan areas worldwide. It is of a great importance to understand the complex interplay of road networks and traffic conditions.…
Recently the scaling laws describing the roughness development of fracture surfaces was proposed to be related to the macroscopic elastic energy released during crack propagation [Mor00]. On this basis, an energy-based asymptotic analysis…
A new, fully-localised, energy growth optimal is found over large times and in long pipe domains at a given mass flow rate. This optimal emerges at a threshold disturbance energy below which a nonlinear version of the known…
We consider the optimal paths in a $d$-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random potential.…
Probabilistic message-passing algorithms are developed for routing transmissions in multi-wavelength optical communication networks, under node and edge-disjoint routing constraints and for various objective functions. Global routing…
Cracks, the major vehicle for material failure, tend to accelerate to high velocities in brittle materials. In three-dimensions, cracks generically undergo a micro-branching instability at about 40% of their sonic limiting velocity. Recent…
We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…
Electrical networks contain thousands of interconnected nodes and edges, which leads to computational challenges in some power system studies. To address these challenges, we contend that network reductions can serve as a framework to…
We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative…
Restoring operation of critical infrastructure systems after catastrophic events is an important issue, inspiring work in multiple fields, including network science, civil engineering, and operations research. We consider the problem of…
Finding shortest paths in a given network (e.g., a computer network or a road network) is a well-studied task with many applications. We consider this task under the presence of an adversary, who can manipulate the network by perturbing its…
This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree $\Delta$, and each node has up to $L$ units of load. The task is to distribute the load more evenly so that the loads of…
We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned…
Traffic networks have been proved to be fractal systems. However, previous studies mainly focused on monofractal networks, while complex systems are of multifractal structure. This paper is devoted to exploring the general regularities of…