Related papers: Classification of Periodic, Chaotic and Random Seq…
We investigate the complexity of short symbolic sequences of chaotic dynamical systems by using lossless compression algorithms. In particular, we study Non-Sequential Recursive Pair Substitution (NSRPS), a lossless compression algorithm…
We argue that Non-sequential Recursive Pair Substitution (NSRPS) as suggested by Jim\'enez-Monta\~no and Ebeling can indeed be used as a basis for an optimal data compression algorithm. In particular, we prove for Markov sequences that…
We present rigorous results on some open questions on NSRPS, non sequential recursive pairs substitution method (see Grassberger in \cite{G}). In particular, starting from the action of NSRPS on finite strings we define a corresponding…
Shannon Entropy has been extensively used for characterizing complexity of time series arising from chaotic dynamical systems and stochastic processes such as Markov chains. However, for short and noisy time series, Shannon entropy performs…
A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the…
There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…
Entropy measures are effective features for time series classification problems. Traditional entropy measures, such as Shannon entropy, use probability distribution function. However, for the effective separation of time series, new entropy…
We investigate how to measure and define the entropy of a simple chaotic system, three hard spheres on a ring. A novel approach is presented, which does not assume the ergodic hypothesis. It consists of transforming the particles collision…
Non-parametric entropy estimation on sequential data is a fundamental tool in signal processing, capturing information flow within or between processes to measure predictability, redundancy, or similarity. Methods based on longest common…
A new run length encoding algorithm for lossless data compression that exploits positional redundancy by representing data in a two-dimensional model of concentric circles is presented. This visual transform enables detection of runs (each…
In this paper, we developed a novel method of nonparametric relative entropy (RlEn) for modelling loss of complexity in intermittent time series. The method consists of two steps. We first fit a nonlinear autoregressive model to each…
Data deduplication saves storage space by identifying and removing repeats in the data stream. Compared with traditional compression methods, data deduplication schemes are more time efficient and are thus widely used in large scale storage…
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…
In the field of biological research, it is essential to comprehend the characteristics and functions of molecular sequences. The classification of molecular sequences has seen widespread use of neural network-based techniques. Despite their…
In-context learning has established itself as an important learning paradigm for Large Language Models (LLMs). In this paper, we demonstrate that LLMs can learn encoding keys in-context and perform analysis directly on encoded…
Our increasingly digital and connected world has led to the generation of unprecedented amounts of data. This data must be efficiently managed, transmitted, and stored to preserve resources and allow scalability. Data compression has…
Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…
This paper presents a novel power spectral density estimation technique for band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and incorporates the advantages of compressed…
We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and real-valued ones and the following four problems: i) estimation of the (limiting)…
High-energy, large-scale particle colliders in nuclear and high-energy physics generate data at extraordinary rates, reaching up to $1$ terabyte and several petabytes per second, respectively. The development of real-time, high-throughput…