Related papers: Random Tight Frames
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
Equiangular tight frames (ETFs) may be used to construct examples of feasible points for semidefinite programs arising in sum-of-squares (SOS) optimization. We show how generalizing the calculations in a recent work of the authors' that…
Probabilistic computing excels in approximating combinatorial problems and modelling uncertainty. However, using conventional deterministic hardware for probabilistic models is challenging: (pseudo) random number generation introduces…
This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…
Fundamental Measure Theory (FMT) is a successful and versatile approach for describing the properties of the hard-sphere fluid and hard-sphere mixtures within the framework of classical density functional theory (DFT). Lutsko [Phys. Rev. E…
A probabilistic framework is proposed for the optimization of efficient switched control strategies for physical systems dominated by stochastic excitation. In this framework, the equation for the state trajectory is replaced with an…
Optical turbulence modelling and simulation are crucial for developing astronomical ground-based instruments, laser communication, laser metrology, or any application where light propagates through a turbulent medium. In the context of…
We introduce the notion of a random relaxed asymptotic contraction in the setting of random normed modules. The contraction condition employs two quasi-metrics that are built directly from the random operator: a lower quasi-metric which…
Probabilistic Latent Tensor Factorization (PLTF) is a recently proposed probabilistic framework for modelling multi-way data. Not only the common tensor factorization models but also any arbitrary tensor factorization structure can be…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
We introduce the notion of a telescope of groups. Very roughly a telescope is a directed system of groups that contains various commuting images of some fixed group $B$. Telescopes are inspired from the theory of groups acting on rooted…
We study how to implement and transform frame perspectives for quantum processes in the process-matrix formalism. We argue that, for pure processes, the causal reference frames (CRF)and time-delocalized subsystems (TDS) formalisms should be…
Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…
We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…
Finite frame theory has a number of real-world applications. In applications like sparse signal processing, data transmission with robustness to erasures, and reconstruction without phase, there is a pressing need for deterministic…