相关论文: Energy Scaling with Control Distance in Complex Ne…
We demonstrate the emergence of scaling laws in the benchmark top versus QCD jet classification problem in collider physics. Six distinct physically-motivated classifiers exhibit power-law scaling of the binary cross-entropy test loss as a…
The smart power grid aims at harnessing information and communication technologies to enhance reliability and enforce sensible use of energy. Its realization is geared by the fundamental goal of effective management of demand load. In this…
The control of complex networks has generated a lot of interest in a variety of fields from traffic management to neural systems. A commonly used metric to compare two particular control strategies that accomplish the same task is the…
We study the energy delivered through a small-resistance series ``victim'' load during electrostatic discharge events in air. For gap lengths over 1~mm, the fraction of the stored energy delivered is mostly gap-length independent, with a…
This paper studies optimum power control and sum-rate scaling laws for the distributed cognitive uplink. It is first shown that the optimum distributed power control policy is in the form of a threshold based water-filling power control.…
The population loss of trained deep neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains the origins of…
We present a simple, unified approach to determining the growth law for the characteristic length scale, $L(t)$, in the phase ordering kinetics of a system quenched from a disordered phase to within an ordered phase. This approach, based on…
A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its $i$-th predecessor of degree $k_i$ with a directed link of length $\ell$ using a probability…
Power management is an expensive and important issue for large computational infrastructures such as datacenters, large clusters, and computational grids. However, measuring energy consumption of scalable systems may be impractical due to…
Predicting how the brain can be driven to specific states by means of internal or external control requires a fundamental understanding of the relationship between neural connectivity and activity. Network control theory is a powerful tool…
The problem of controllability of the dynamical state of a network is central in network theory and has wide applications ranging from network medicine to financial markets. The driver nodes of the network are the nodes that can bring the…
We show that there are two classes of finite size effects for dynamic models taking place on a scale-free topology. Some models in finite networks show a behavior that depends only on the system size N. Others present an additional distinct…
Metcalfe's Law captures the relationship between the value of a network and its scale, asserting that a network's value is directly proportional to the square of its size. Over the past four decades, various researchers have proposed…
The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources. Yet, while empirically validated, its theoretical underpinnings remain poorly…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
n source and destination pairs randomly located in an area want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power loss of r^{-alpha}, as well as a random phase. We…
When data is plentiful, the loss achieved by well-trained neural networks scales as a power-law $L \propto N^{-\alpha}$ in the number of network parameters $N$. This empirical scaling law holds for a wide variety of data modalities, and may…
Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e. models that generate uncorrelated scale-free networks. Most models to date however show structural negative…
The widespread deployment of power electronic technologies is transforming modern power systems into fast, nonlinear, and heterogeneous networks. Conventional modeling and control approaches, rooted in quasi-static analysis and centralized…
In this research we consider linear time-invariant plants and assume that the regressor finite excitation requirement is met. In such case, a new law to adjust the controller parameters, which ensures the exponential stability of the…