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In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…
Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…
In this paper, we study the perturbation of the extreme singular values of a matrix in the particular case where it is obtained after appending an arbitrary column vector. Such results have many applications in bifurcation theory, signal…
Modern deep neural networks display striking examples of rich internal computational structure. Uncovering principles governing the development of such structure is a priority for the science of deep learning. In this paper, we explore the…
Understanding how transient dynamics unfold in response to localized inputs is central to predicting and controlling signal propagation in network systems, including neural processing, epidemic intervention, and power-grid resilience.…
We consider the dynamics of bodies with "active" microstructure described by vector-valued phase fields. For waves with time-varying amplitude, the associated evolution equation involves a matrix that can be non-normal, depending on the…
One of the biggest challenges in the field of biomedical imaging is the comprehension and the exploitation of the photon scattering through disordered media. Many studies have pursued the solution to this puzzle, achieving light-focusing…
We present a novel mathematical framework for the specification and analysis of fault-resilient distributed protocols and their implementations, with the following components: 1. Transition systems that allow the specification and analysis…
With the advancements of sensor hardware, traffic infrastructure and deep learning architectures, trajectory prediction of vehicles has established a solid foundation in intelligent transportation systems. However, existing solutions are…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution…
Transient stability assessment is an integral part of dynamic security assessment of power systems. Traditional methods of transient stability assessment, such as time domain simulation approach and direct methods, are appropriate for…
End-to-end autonomous driving has emerged as a dominant paradigm, yet its highly entangled black-box models pose significant challenges in terms of interpretability and safety assurance. To improve model transparency and training…
In this article, we investigate the transient behavior of a sequence of packets/bits traversing a multi-hop wireless network. Our work is motivated by novel applications from the domain of process automation, Machine-Type Communication…
Vehicle platooning, with vehicles traveling in close formation coordinated through Vehicle-to-Everything (V2X) communications, offers significant benefits in fuel efficiency and road utilization. However, it is vulnerable to sophisticated…
We study the transients of linear max-plus dynamical systems. For that, we consider for each irreducible max-plus matrix A, the weighted graph G(A) such that A is the adjacency matrix of G(A). Based on a novel graph-theoretic counterpart to…
This thesis is devoted to the application of random matrix theory to the study of random surfaces, both discrete and continuous; special emphasis is placed on surface boundaries and the associated boundary conditions in this formalism. In…
Matrix perturbation bounds play an essential role in the design and analysis of spectral algorithms. In this paper, we use a "contour bootstrapping" argument to derive several new perturbation bounds. As applications, we discuss new bounds…
Families of regimes for discrete control systems are studied possessing a special quasi-controllability property that is similar to the Kalman controllability property. A new approach is proposed to estimate the amplitudes of transient…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…