Related papers: Spectral Simplicity of Apparent Complexity, Part I…
Phase unwrapping is a key problem in many coherent imaging systems, such as synthetic aperture radar (SAR) interferometry. A general formulation for redundant integration of finite differences for phase unwrapping (Costantini et al., 2010)…
In this survey paper we review classical results and recent progress about a certain topic in the spectral theory of two-dimensional canonical systems. Namely, we consider the questions whether the spectrum $\sigma$ is discrete, and if it…
We report on calculations of smoothed spectral correlations in the two-dimensional Anderson model for weak disorder. As pointed out in (M. Wilkinson, J. Phys. A: Math. Gen. 21, 1173 (1988)), an analysis of the smoothing dependence of the…
Two-dimensional electronic spectroscopy (2DES) provides a detailed picture of electronically nonadiabatic dynamics that can be interpreted with the aid of simulations. Here, we develop and contrast trajectory-based nonadiabatic dynamics…
The self consistent version of the density functional theory is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems. An exact functional equation for the effective interaction, from…
In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as…
The spectral representation is an effecient tool to explore electrical properties of material mixtures. It separates the contributions of geometrical topology and intrinsic properties of the constituents in the system. The aim of this paper…
We introduce derangetropy, a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation…
We consider the universal part of entanglement entropy across a plane in flat space for a QFT, giving a non-perturbative expression in terms of a spectral function. We study the change in entanglement entropy under a deformation by a…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
Variational models with coupling terms are becoming increasingly popular in image analysis. They involve auxiliary variables, such that their energy minimisation splits into multiple fractional steps that can be solved easier and more…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
Graph spectra have been successfully used to classify network types, compute the similarity between graphs, and determine the number of communities in a network. For large graphs, where an eigen-decomposition is infeasible, iterative moment…
We review the ageing phenomenon in the context of simplest trap model, Bouchaud's REM-like trap model from a spectral theoretic point of view. We show that the generator of the dynamics of this model can be diagonalised exactly. Using this…
In this paper we present an unconventional image segmentation approach which is devised to meet the requirements of image understanding and pattern recognition tasks. Generally image understanding assumes interplay of two sub-processes:…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
We forge connections between the theory of fractal sets obtained as attractors of iterated function systems and process calculi. To this end, we reinterpret Milner's expressions for processes as contraction operators on a complete metric…
We develop a generalization of correlated trend-cycle decompositions that avoids prior assumptions about the long-run dynamic characteristics by modelling the permanent component as a fractionally integrated process and incorporating a…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition…