相关论文: Energy Scaling with Control Distance in Complex Ne…

Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…

As neural networks continue to grow in size but datasets might not, it is vital to understand how much performance improvement can be expected: is it more important to scale network size or data volume? Thus, neural network scaling laws,…

Neural scaling laws describe how the performance of deep neural networks scales with key factors such as training data size, model complexity, and training time, often following power-law behaviors over multiple orders of magnitude. Despite…

The dominant dynamics of sensor networks consist of using the energy of the sensor nodes to create the topology of hierarchical clustering using topology control protocols. The topology thus created will always have optimum number of nodes…

Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…

In the study of ad hoc sensor networks, clustering plays an important role in energy conservation therefore analyzing the mechanics of such topology can be helpful to make logistic decisions .Using the theory of complex network the…

When training deep neural networks, a model's generalization error is often observed to follow a power scaling law dependent both on the model size and the data size. Perhaps the best known example of such scaling laws are for…

The study of network structural controllability focuses on the minimum number of driver nodes needed to control a whole network. Despite intensive studies on this topic, most of them consider static networks only. It is well-known, however,…

We address the optimization of the sum rate performance in multicell interference-limited singlehop networks where access points are allowed to cooperate in terms of joint resource allocation. The resource allocation policies considered…

We minimize the dissipation rate of an electrical network under a global constraint on the sum of powers of the conductances. We construct the explicit scaling relation between currents and conductances, and show equivalence to a a previous…

The integration of more renewable energy sources into the power system is presenting system operators with various challenges. At the distribution system level, voltage magnitudes that violate operating limits near large photovoltaic…

In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction…

Recent works have shown that machine learning models improve at a predictable rate with the total amount of training data, leading to scaling laws that describe the relationship between error and dataset size. These scaling laws can help…

Empirical studies on the spatial structures in several real transport networks reveal that the distance distribution in these networks obeys power law. To discuss the influence of the power-law exponent on the network's structure and…

Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and…

Neural scaling laws establish a predictable relationship between model performance and data or compute, offering crucial guidance for resource allocation in new domains and tasks. Yet such laws are most needed precisely where they are…

We formulate a general model for the growth of scale-free networks under filtering information conditions--that is, when the nodes can process information about only a subset of the existing nodes in the network. We find that the…

The spread of perturbative signals in complex networks is governed by the combined effect of the network topology and its intrinsic nonlinear dynamics. Recently, the resulting spreading patterns have been analyzed and predicted, shown to…

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…

Noise-induced escape from a metastable state of a dynamical system is studied close to a saddle-node bifurcation point, but in the region where the system remains underdamped. The activation energy of escape scales as a power of the…