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Its conceptual appeal and effectiveness has made latent factor modeling an indispensable tool for multivariate analysis. Despite its popularity across many fields, there are outstanding methodological challenges that have hampered practical…
We discuss the problem for detecting long-range correlations in sequences of values obtained by generators of pseudo-random numbers. The basic idea is that the H{\"o}lder exponent for a sufficiently long sequence of uncorrelated random…
The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
In this work the significance of treating a set of measurements as a time series is being explored. Time Series Analysis (TSA) techniques, part of the Exploratory Data Analysis (EDA) approach, can provide much insight regarding the…
Dynamic statistical process monitoring methods have been widely studied and applied in modern industrial processes. These methods aim to extract the most predictable temporal information and develop the corresponding dynamic monitoring…
The statistical behavior of a nonlinear system described by a mapping with phase rotation is studied. We use the Kolmogorov-Chapman equations for the multi-time probability distribution functions for investigation of dynamics under the…
With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. They are both examples of "functional data", which have become a prevailing…
In this Letter we report new effects of resonance detuning on various dynamical parameters of a generic 3-wave system. Namely, for suitably chosen values of detuning the variation range of amplitudes can be significantly wider than for…
In high-renewable power systems, active-power disturbances are becoming larger and exhibit increasingly diverse time scales, which complicates frequency stability assessment under unanticipated events. This paper presents a response-based…
Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. Sequential detection is an online version in which new data…
Topological Data Analysis (TDA) is increasingly crucial in investigating the shape of complex data structures across scientific fields, particularly in neuroscience and finance. This study delves into persistent homology, a TDA component…
The Duffing oscillator is a paradigm of bistable oscillatory motion in physics, engineering, and biology. Time series of such oscillations are often observed experimentally in a nonlinear system excited by a spontaneously fluctuating force.…
The scaling behaviors of the human electroencephalogram (EEG) time series are studied using detrended fluctuation analysis. Two scaling regions are found in nearly every channel for all subjects examined. The scatter plot of the scaling…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
Motivated by recent experiments and models of biological segmentation, we analyze the exicitation of pattern-forming instabilities of convectively unstable reaction-diffusion-advection (RDA) systems, occuring by means of constant or…
Disentangled representations, where the higher level data generative factors are reflected in disjoint latent dimensions, offer several benefits such as ease of deriving invariant representations, transferability to other tasks,…
Disentanglement is a highly desirable property of representation due to its similarity with human's understanding and reasoning. This improves interpretability, enables the performance of down-stream tasks, and enables controllable…
We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…
Objective: Mixtures of temporally nonstationary signals are very common in biomedical applications. The nonstationarity of the source signals can be used as a discriminative property for signal separation. Herein, a semi-blind source…