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Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have…

In many real-world application, e.g., speech recognition or sleep stage classification, data are captured over the course of time, constituting a Time-Series. Time-Series often contain temporal dependencies that cause two otherwise…

In this paper we introduce an applicative theory which characterizes the polynomial hierarchy of time.

We study the spatio-temporal prediction problem and introduce a novel point-process-based prediction algorithm. Spatio-temporal prediction is extensively studied in Machine Learning literature due to its critical real-life applications such…

We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…

Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…

Time-series stationarity is a property that statistical characteristics such as trend, variance, seasonality remain constant over time. It is considered fundamental to many forecasting and analysis methods. Different tests detect different…

For a class of stationary regularly varying and weakly dependent time series, we prove the so-called complete convergence result for the corresponding space-time point processes. As an application of our main theorem, we give a simple proof…

Explosive growth in spatio-temporal data and its wide range of applications have attracted increasing interests of researchers in the statistical and machine learning fields. The spatio-temporal regression problem is of paramount importance…

In this article we present certain formulas involving arithmetical functions. In the first part we study properties of sums and product formulas for general type of arithmetic functions. In the second part we apply these formulas to the…

Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite, albeit potentially huge, output spaces, in this paper we…

This study introduces a novel forecasting strategy that leverages the power of fractional differencing (FD) to capture both short- and long-term dependencies in time series data. Unlike traditional integer differencing methods, FD preserves…

Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this…

We give some account of investigations for the role of infinite dimensional algebras in time dependent systems.

The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…

Despite the excelling performance of machine learning models, understanding their decisions remains a long-standing goal. Although commonly used attribution methods from explainable AI attempt to address this issue, they typically rely on…

Transformer-based foundation models have emerged as a dominant paradigm in time series analysis, offering unprecedented capabilities in tasks such as forecasting, anomaly detection, classification, trend analysis and many more time series…

We outline the theory of reflections for prederivators, derivators and stable derivators. In order to parallel the classical theory valid for categories, we outline how reflections can be equivalently described as categories of fractions,…

Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null…

Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform (NFT) algorithm, which combines…