Related papers: Spectral Control of Mobile Robot Networks
Decentralized control of mobile robotic sensor networks is a fundamental problem in robotics that has attracted intensive research in recent decades. Most of the existing works dealt with two-dimensional spaces. This report is concerned…
We calculate the probability to find exactly $n$ eigenvalues in a spectral interval of a large random $N \times N$ matrix when this interval contains $s \ll N$ eigenvalues on average. The calculations exploit an analogy to the problem of…
We investigate how unitary control can improve parameter estimation by designing the effective spectrum of the imprinting Hamiltonian. We show that, for commuting Hamiltonians, the general problem of spectral manipulation via unitary…
Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define…
This paper proposes a novel monitoring methodology for car-following control of automated vehicles that uses real-time measurements of spacing and velocity obtained through vehicle sensors. This study focuses on monitoring the time gap, a…
This work proposes a fully decentralized strategy for maintaining the formation rigidity of a multi-robot system using only range measurements, while still allowing the graph topology to change freely over time. In this direction, a first…
The main steps of automatic control methodology include the hierarchical representation of management system and the formal definitions of input variables, object and goal of control of each management level. A Petri net model of individual…
The development of robot control programs is a complex task. Many robots are different in their electrical and mechanical structure which is also reflected in the software. Specific robot software environments support the program…
Training of neural networks can be reformulated in spectral space, by allowing eigenvalues and eigenvectors of the network to act as target of the optimization instead of the individual weights. Working in this setting, we show that the…
The study of neuronal interactions is currently at the center of several big collaborative neuroscience projects (including the Human Connectome Project, the Blue Brain Project, the Brainome, etc.) which attempt to obtain a detailed map of…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
This research investigates decentralized control of mobile robots specifically for coverage problems. There are different approaches associated with decentralized control strategy for coverage control problems. We perform a comparative…
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…
Dynamic spectrum management is recognized as a key technique to tackle interference in multi-user multi-carrier communication systems and networks. However existing dynamic spectrum management algorithms may not be suitable when the…
We study the statistical properties of eigenvalues of the Hessian matrix ${\cal H}$ (matrix of second derivatives of the potential energy) for a classical atomic liquid, and compare these properties with predictions for random matrix models…
In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension…
This paper examines the relationship between sparse random network architectures and neural network stability by examining the eigenvalue spectral distribution. Specifically, we generalise classical eigenspectral results to sparse…
Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the network's adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks…
Many real-world complex systems have small-world topology characterized by the high clustering of nodes and short path lengths.It is well-known that higher clustering drives localization while shorter path length supports delocalization of…
This paper develops a closed-form spectral decomposition framework for the Gramian matrices of discrete-time linear dynamical systems. The main results provide explicit decompositions of the discrete-time controllability Gramian and its…