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We describe a completely general and fully non-perturbative framework for constructing dynamical reference frames in generally covariant theories, and for understanding the gauge-invariant observables that they yield. Our approach makes use…
The numerical extraction of resonant states of open quantum systems is usually a difficult problem. Regularization techniques, such as the mapping to complex coordinates or the addition of Complex Absorbing Potentials are typically…
The measurement processes that are traditionally described within the realm of non-relativistic quantum mechanics are transcribed into the covariant framework of Cartan's space, the four-valued representation space of the restricted…
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
In this second paper, we develop the full mathematical structure of the algebra of the pseudo-observables, in order to solve the quantum measurement problem. Quantum state vectors are recovered but as auxiliary pseudo-observables storing…
We develop a framework for regularly varying measures on complete separable metric spaces $\mathbb{S}$ with a closed cone $\mathbb{C}$ removed, extending material in Hult & Lindskog (2006), Das, Mitra & Resnick (2013). Our framework…
We demonstrate a novel approach to reservoir computation measurements using random matrices. We do so to motivate how atomic-scale devices could be used for real-world computational applications. Our approach uses random matrices to…
We introduce Stochastic Asymptotical Regularization (SAR) methods for the uncertainty quantification of the stable approximate solution of ill-posed linear-operator equations, which are deterministic models for numerous inverse problems in…
We propose a new space-variant anisotropic regularisation term for variational image restoration, based on the statistical assumption that the gradients of the target image distribute locally according to a bivariate generalised Gaussian…
We consider the problem of simultaneously finding lower-dimensional subspace structures in a given $m$-tuple of possibly corrupted, high-dimensional data sets all of the same size. We refer to this problem as simultaneous robust subspace…
One of the fundamental open questions in computational complexity is whether the class of problems solvable by use of stochasticity under the Random Polynomial time (RP) model is larger than the class of those solvable in deterministic…
This paper concerns the characterisation of second order marginals for random sets in a discrete setting. Under the instance of unit covariances, this problem possesses a combinatorial symmetry, exploited jointly in the companion paper to…
We study an alternative to the prevailing approach to modelling qualitative spatial reasoning (QSR) problems as constraint satisfaction problems. In the standard approach, a relation between objects is a constraint whereas in the…
Quantum statistical models (i.e., families of normalized density matrices) and quantum measurements (i.e., positive operator-valued measures) can be regarded as linear maps: the former, mapping the space of effects to the space of…
The paper addresses the question whether a random functional, a map from a set $E$ into the space of real-valued measurable functions on a probability space, has a measurable version with values in ${\mathbb R}^E$. Similarly, one may ask…
Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. A number of asymptotic results addressing these problems over a fixed…
Analytical approach to SLAM problem was introduced in the recent years. In our work we investigate the method numerically with the motivation of using the algorithm in a real hardware experiments. We perform a robustness test of the…
The Randomized Kaczmarz method (RK) is a stochastic iterative method for solving linear systems that has recently grown in popularity due to its speed and low memory requirement. Selectable Set Randomized Kaczmarz (SSRK) is an variant of RK…
Irregularly sampling a spatially stationary random field does not yield a graph stationary signal in general. Based on this observation, we build a definition of graph stationarity based on intrinsic stationarity, a less restrictive…