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Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the…
We show that cloaking of isolated objects is subject to a diameter-bandwidth product limitation: as the size of the object increases, the bandwidth of good (small cross-section) cloaking decreases inversely with the diameter, as a…
We consider the patterns formed by small rod-like objects advected by a random flow in two dimensions. An exact solution indicates that their direction field is non-singular. However, we find from simulations that the direction field of the…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
This work investigates the optimization instability of deep neural networks from a less-explored yet insightful perspective: the emergence and amplification of singularities in the parametric space. Our analysis reveals that parametric…
Segmentation of very large images is a common problem in microscopy, medical imaging or remote sensing. The problem is usually addressed by sliding window inference, which can theoretically lead to seamlessly stitched predictions. However,…
I provide a framework for deriving fast finite-difference algorithms for the numerical modeling of acoustic wave propagation in anisotropic media. I deploy it in the case of transversely isotropic media to implement a kinematically accurate…
We investigate the effect of phase randomness in Ising-type quantum networks. These networks model a large class of physical systems. They describe micro- and nanostructures or arrays of optical elements such as beam splitters…
The robustness of neural networks is challenged by adversarial examples that contain almost imperceptible perturbations to inputs, which mislead a classifier to incorrect outputs in high confidence. Limited by the extreme difficulty in…
Traceroute is widely used: from the diagnosis of network problems to the assemblage of internet maps. Unfortu- nately, there are a number of problems with traceroute methodology, which lead to the inference of erroneous routes. This paper…
The adversarial attack literature contains a myriad of algorithms for crafting perturbations which yield pathological behavior in neural networks. In many cases, multiple algorithms target the same tasks and even enforce the same…
We investigate almost-degenerate perturbation theory of eigenvalue problems, using spectral projectors, also named density matrices. When several eigenvalues are close to each other, the coefficients of the perturbative series become…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
Machine learning models have demonstrated remarkable success across diverse domains but remain vulnerable to adversarial attacks. Empirical defense mechanisms often fail, as new attacks constantly emerge, rendering existing defenses…
A quadratic approximation of neural network loss landscapes has been extensively used to study the optimization process of these networks. Though, it usually holds in a very small neighborhood of the minimum, it cannot explain many…
This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature…
We describe the various types of singularities that can arise for second order rational mappings and we discuss the historical and present-day, practical, role the singularity confinement property plays as an integrability detector. In…
A spatially distributed system contains a large amount of agents with limited sensing, data processing, and communication capabilities. Recent technological advances have opened up possibilities to deploy spatially distributed systems for…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…