Related papers: Statistics for Differential Topological Properties…

In this paper, we develop topological data analysis methods for classification tasks on univariate time series. As an application, we perform binary and ternary classification tasks on two public datasets that consist of physiological…

Reservoir computing is a form of machine learning that utilizes nonlinear dynamical systems to perform complex tasks in a cost-effective manner when compared to typical neural networks. Many recent advancements in reservoir computing, in…

The reservoir computing based on the thin film embedded with magnetic impurities in the presence of the long-range (the dipole-dipole) interaction is numerically investigated. We simulated the magnetization dynamics by taking into account…

Interpreting partial information collected from systems subject to noise is a key problem across scientific disciplines. Theoretical frameworks often focus on the dynamics of variables that result from coarse-graining the internal states of…

We develop in this paper a theoretical framework for the topological study of time series data. Broadly speaking, we describe geometrical and topological properties of sliding window (or time-delay) embeddings, as seen through the lens of…

Classification of multivariate time series (MTS) has been tackled with a large variety of methodologies and applied to a wide range of scenarios. Reservoir Computing (RC) provides efficient tools to generate a vectorial, fixed-size…

Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large…

We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, i.e., the dimension of the…

There has been active investigation into deep learning approaches for time series analysis, including foundation models. However, most studies do not address significant scientific applications. This paper aims to identify key features in…

Structural identifiability is an important property of parametric ODE models. When conducting an experiment and inferring the parameter value from the time-series data, we want to know if the value is globally, locally, or non-identifiable.…

We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and…

The raster model is widely used in Geographic Information Systems to represent data that vary continuously in space, such as temperatures, precipitations, elevation, among other spatial attributes. In applications like weather forecast…

Reservoir computing (RC), first applied to temporal signal processing, is a recurrent neural network in which neurons are randomly connected. Once initialized, the connection strengths remain unchanged. Such a simple structure turns RC into…

Delay-based reservoir computing has gained a lot of attention due to the relative simplicity with which this concept can be implemented in hardware. However,there is still an misconception about the relationship between the delay-time and…

Reservoir computing is a best-in-class machine learning algorithm for processing information generated by dynamical systems using observed time-series data. Importantly, it requires very small training data sets, uses linear optimization,…

We numerically investigate a time-delayed reservoir computer architecture based on a single mode laser diode with optical injection and optical feedback. Through a high-resolution parametric analysis, we reveal unforeseen regions of high…

Recurrent networks are a special class of artificial neural systems that use their internal states to perform computing tasks for machine learning. One of its state-of-the-art developments, i.e. reservoir computing (RC), uses the internal…

A minimal model for reservoir computing is studied. We demonstrate that a reservoir computer exists that emulates given coupled maps by constructing a modularized network. We describe a possible mechanism for collapses of the emulation in…

Understanding the fundamental relationships between physics and its information-processing capability has been an active research topic for many years. Physical reservoir computing is a recently introduced framework that allows one to…

Reservoir computing - information processing based on untrained recurrent neural networks with random connections - is expected to depend on the nonlinear properties of the neurons and the resulting oscillatory, chaotic, or fixpoint…