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Non-parametric detrending or noise reduction methods are often employed to separate trends from noisy time series when no satisfactory models exist to fit the data. However, conventional detrending methods depend on subjective choices of…
Training diffusion models is always a computation-intensive task. In this paper, we introduce a novel speed-up method for diffusion model training, called, which is based on a closer look at time steps. Our key findings are: i) Time steps…
As the frontline data for cancer diagnosis, microscopic pathology images are fundamental for providing patients with rapid and accurate treatment. However, despite their practical value, the deep learning community has largely overlooked…
State Space Models (SSMs), particularly Mamba, have shown potential in long-term time series forecasting. However, existing Mamba-based architectures often struggle with datasets characterized by non-stationary patterns. A key observation…
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for…
Detrended fluctuation analysis (DFA) is a simple but very efficient method for investigating the power-law long-term correlations of non-stationary time series, in which a detrending step is necessary to obtain the local fluctuations at…
It is the purpose of the paper to describe the virtues of time-frequency methods for signal processing applications, having astronomical time series in mind. Different methods are considered and their potential usefulness respectively…
Heart rate variability (HRV) series reflects the dynamical variation of heartbeat-to-heartbeat intervals in time and is one of the outputs of the cardiovascular system. Over the years, this system has been recognized for generating…
In recent years, the development of diffusion models has led to significant progress in image and video generation tasks, with pre-trained models like the Stable Diffusion series playing a crucial role. Inspired by model pruning which…
Using pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential…
We study the validity of an averaging principle for a slow-fast system of stochastic reaction diffusion equations. We assume here that the coefficients of the fast equation depend on time, so that the classical formulation of the averaging…
Multiple sequences alignment (MSA) is a traditional and challenging task for time-series analyses. The MSA problem is formulated as a discrete optimization problem and is typically solved by dynamic programming. However, the computational…
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…
An important problem in time series analysis is the discrimination between non-stationarity and longrange dependence. Most of the literature considers the problem of testing specific parametric hypotheses of non-stationarity (such as a…
We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully nonparametric, enjoys effortless tuning and is robust to temporal dependence. One salient and distinct feature of…
The objective of change-point detection is to discover abrupt property changes lying behind time-series data. In this paper, we present a novel statistical change-point detection algorithm based on non-parametric divergence estimation…
We use Diffusing Wave Spectroscopy (DWS) to perform the first direct space- and time-resolved measurement of the dissipation rate~$\epsilon$ at the boundary of a turbulent flow. We have shown in a previous publication that this technique…
We introduce the Statistical Asynchronous Regression (SAR) method: a technique for determining a relationship between two time varying quantities without simultaneous measurements of both quantities. We require that there is a time…
Decomposing complex time series into trend, seasonality, and remainder components is an important task to facilitate time series anomaly detection and forecasting. Although numerous methods have been proposed, there are still many time…
Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral…