Related papers: Testing Separability of Functional Time Series

We introduce a novel class of nonlinear tests for serial dependence in functional time series, grounded in the functional quantile autocorrelation framework. Unlike traditional approaches based on the classical autocovariance kernel, the…

Predictive maintenance in complex systems is often complicated by the heterogeneity and redundancy of monitored variables,which can obscure fault-relevant information and reduce model interpretability. This work proposes a semantic feature…

A major goal of dynamical systems theory is the search for simplified descriptions of the dynamics of a large number of interacting states. For overwhelmingly complex dynamical systems, the derivation of a reduced description on the entire…

We present a framework for deciding whether a quantum state is separable or entangled using covariance matrices of locally measurable observables. This leads to the covariance matrix criterion as a general separability criterion. We…

Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new…

Two subsets of a given set are path-disconnected if they lie in different connected components of the larger set. Verification of path-disconnectedness is essential in proving the infeasibility of motion planning and trajectory optimization…

We propose experimentally feasible separability criteria for bipartite systems based on local symmetric measurements. Through detailed examples, we demonstrate that our criteria can detect entanglement more effectively compared to existing…

Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…

Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…

The validity OF a causal model can be tested ONLY IF the model imposes constraints ON the probability distribution that governs the generated data. IN the presence OF unmeasured variables, causal models may impose two types OF constraints :…

The performance of a number of different measures of nonlinearity in a time series is compared numerically. Their power to distinguish noisy chaotic data from linear stochastic surrogates is determined by Monte Carlo simulation for a number…

The distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analogs…

It is shown that separation conditions (separation curves) are fundamental objects of separability theory. They are used for the classification of certain clases of separable systems, for the proof of bi-Hamiltonian property and finally…

Observability is the property that enables to distinguish two different locations in $n$-dimensional state space from a reduced number of measured variables, usually just one. In high-dimensional systems it is therefore important to make…

Separation is a classical problem in mathematics and computer science. It asks whether, given two sets belonging to some class, it is possible to separate them by another set of a smaller class. We present and discuss the separation problem…

Deploying machine learning models in safety-critical domains poses a key challenge: ensuring reliable model performance on downstream user data without access to ground truth labels for direct validation. We propose the suitability filter,…

Structural parameter identifiability is a property of a differential model with parameters that allows for the parameters to be determined from the model equations in the absence of noise. One of the standard approaches to assessing this…

Instruction sequence is a key concept in practice, but it has as yet not come prominently into the picture in theoretical circles. This paper concerns instruction sequences, the behaviours produced by them under execution, the interaction…

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…

Temporal data are increasingly prevalent in modern data science. A fundamental question is whether two time series are related or not. Existing approaches often have limitations, such as relying on parametric assumptions, detecting only…