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An emerging way to deal with high-dimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work…
We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…
A time-frequency diagram is a commonly used visualization for observing the time-frequency distribution of radio signals and analyzing their time-varying patterns of communication states in radio monitoring and management. While it excels…
This paper discusses a fast algorithm for analyzing the phases of a multi-tone phase calibration signal. The multi-tone method is superior to its single-tone counterpart. The PCal signal is a wide-band frequency comb derived from an…
In this paper, we propose a novel method for estimating the long-memory parameter in time series. By combining the multi-resolution framework of wavelets with the robustness of the Least Absolute Deviations (LAD) criterion, we introduce a…
A method to upsample insufficiently sampled experimental time series of pseudo-periodic signals is proposed. The result is an estimate of the pseudo-periodic cycle underlying the signal. This hypersampling requires a sufficiently sampled…
Time series analysis is crucial in fields like finance, economics, environmental science, and biomedical engineering, aiding in forecasting, pattern identification, and understanding underlying mechanisms. While traditional time-domain…
Lexical ambiguities naturally arise in languages. We present Lamb, a lexical analyzer that produces a lexical analysis graph describing all the possible sequences of tokens that can be found within the input string. Parsers can process such…
Time-series forecasting in real-world applications such as finance and energy often faces challenges due to limited training data and complex, noisy temporal dynamics. Existing deep forecasting models typically supervise predictions using…
Symbolic regression is a nonlinear regression method which is commonly performed by an evolutionary computation method such as genetic programming. Quantification of uncertainty of regression models is important for the interpretation of…
The method of surrogate data is a tool to test whether data were generated by some class of model. Tests based on the periodogram have been proposed to decide if linear systems driven by Gaussian noise could have generated a sample time…
Time series anomaly detection is critical for supply chain management to take proactive operations, but faces challenges: classical unsupervised anomaly detection based on exploiting data patterns often yields results misaligned with…
From biological systems to cyber-physical systems, monitoring the behavior of such dynamical systems often requires to reason about complex spatio-temporal properties of physical and/or computational entities that are dynamically…
The phenomenon of superoscillation, where band limited signals can oscillate over some time period with a frequency higher than the band limit, is not only very interesting but it also seems to offer many practical applications. The first…
This paper derives practical algorithms, based on Bayesian inference methods, for several data analysis problems common in time series analysis of astronomical and other data. One problem is the determination of the lag between two time…
Cross-spectral analysis is a mathematical tool for extracting the power spectral density of a correlated signal from two time series in the presence of uncorrelated interfering signals. We demonstrate and explain a set of conditions where…
In order for clinicians to manage disease progression and make effective decisions about drug dosage, treatment regimens or scheduling follow up appointments, it is necessary to be able to identify both short and long-term trends in…
In this work, we address the problem of identifying sparse continuous-time dynamical systems when the spacing between successive samples (the sampling period) is not constant over time. The proposed approach combines the…
Label distribution learning (LDL) is an effective method to predict the label description degree (a.k.a. label distribution) of a sample. However, annotating label distribution (LD) for training samples is extremely costly. So recent…
The concept of stochastic Lagrangian and its use in statistical dynamics is illustrated theoretically, and with some examples. Dynamical variables undergoing stochastic differential equations are stochastic processes themselves, and their…