Related papers: Coherence for Random Fields
We develop a statistical framework for conducting inference on collections of time-varying covariance operators (covariance flows) over a general, possibly infinite dimensional, Hilbert space. We model the intrinsically non-linear structure…
The quantile-crossing spectrum is the spectrum of quantile-crossing processes created from a time series by the indicator function that shows whether or not the time series lies above or below a given quantile at a given time. This…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but…
We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval.…
Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated…
We propose an alternative framework for quantifying coherence. The framework is based on a natural property of coherence, the additivity of coherence for subspace-independent states, which is described by an operation-independent equality…
In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…
We conduct a study of the aliased spectral densities of Mat\'ern covariance functions on a regular grid of points, providing clarity on the properties of a popular approximation based on stochastic partial differential equations; while…
Most nervous systems encode information about stimuli in the responding activity of large neuronal networks. This activity often manifests itself as dynamically coordinated sequences of action potentials. Since multiple electrode recordings…
When a quantum system is monitored in continuous time, the result of the measurement is a stochastic process. When the output process is stationary, at least in the long run, the spectrum of the process can be introduced and its properties…
The Mat\'ern covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Mat\'ern class is that it is possible to get precise control over the degree of…
Decoherence of a quantum system induced by the interaction with its environment (measuring medium) may be presented phenomenologically as a continuous (or repeated) fuzzy quantum measurement. The dynamics of the system subject to continuous…
Long-term quantum coherence constitutes one of the main challenges when engineering quantum devices. However, easily accessible means to quantify complex decoherence mechanisms are not readily available, nor are sufficiently stable systems.…
A finite phase-coherence time $\tau_{\phi}^{meas}$ emerges from iterative measurement onto a quantum system. For a rapid sequence, the phase-coherence time is found explicitly. For the stationary charge conduction problem, it is bounded. At…
A multi-slit interference experiment, with which-way detectors, in the presence of environment induced decoherence, is theoretically analyzed. The effect of environment is modeled via a coupling to a bath of harmonic oscillators. Through an…
Spatial confounding is a common issue in spatial regression models, occurring when spatially varying covariates correlate with the spatial effect included in the model. This dependence, particularly at high spatial frequencies, can…
This topic review communicates working experiences regarding interaction of a multiplicity of processes. Our experiences come from climate change modelling, materials science, cell physiology and public health, and macroeconomic modelling.…
In many longitudinal settings, time-varying covariates may not be measured at the same time as responses and are often prone to measurement error. Naive last-observation-carried-forward methods incur estimation biases, and existing…