Related papers: Lossless Compression and Complexity of Chaotic Seq…
An L-system (for lossless compression) is a CPD0L-system extended with two parameters $d$ and $n$, which determines unambiguously a string $w = \tau(\varphi^d(s))[1:n]$, where $\varphi$ is the morphism of the system, $s$ is its axiom, and…
Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…
Symbolic regression (SR) searches for parametric models that accurately fit a dataset, prioritizing simplicity and interpretability. Despite this secondary objective, studies point out that the models are often overly complex due to…
Deep learning has significantly improved the accuracy of crop classification using multispectral temporal data. However, these models have complex structures with numerous parameters, requiring large amounts of data and costly training. In…
We explore an extension to straight-line programs (SLPs) that outperforms, for some text families, the measure $\delta$ based on substring complexity, a lower bound for most measures and compressors exploiting repetitiveness (which are…
In this paper we present a new algorithm for compressive sensing that makes use of binary measurement matrices and achieves exact recovery of ultra sparse vectors, in a single pass and without any iterations. Due to its noniterative nature,…
We present an algorithm for searching regular expression matches in compressed text. The algorithm reports the number of matching lines in the uncompressed text in time linear in the size of its compressed version. We define efficient data…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
Recent work in Deep Learning has re-imagined the representation of data as functions mapping from a coordinate space to an underlying continuous signal. When such functions are approximated by neural networks this introduces a compelling…
In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing…
Approximation of entropies of various types using machine learning (ML) regression methods are shown for the first time. The ML models presented in this study define the complexity of the short time series by approximating dissimilar…
Time series play a crucial role in many fields, including finance, healthcare, industry, and environmental monitoring. The storage and retrieval of time series can be challenging due to their unstoppable growth. In fact, these applications…
We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in…
This study is focused on the qualitative and quantitative characterization of chaotic systems with the use of symbolic description. We consider two famous systems: Lorenz and R\"ossler models with their iconic attractors, and demonstrate…
Sparse signal representations based on linear combinations of learned atoms have been used to obtain state-of-the-art results in several practical signal processing applications. Approximation methods are needed to process high-dimensional…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming of paramount importance. In this article we propose a new lossless…
Estimating the spectral characteristics of a nonstationary random process is an important but challenging task, which can be facilitated by exploiting structural properties of the process. In certain applications, the observed processes are…
Motivated by computing duplication patterns in sequences, a new fundamental problem called the longest subsequence-repeated subsequence (LSRS) is proposed. Given a sequence $S$ of length $n$, a letter-repeated subsequence is a subsequence…
We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in…