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 poorly. Complexity measures which are based on lossless compression algorithms are a good substitute in such scenarios. We evaluate the performance of two s...

A specific topology of Digital Nonlinear Oscillators (DNOs) has been implemented by using commercial off-the-shelf digital components to experimentally verify and demonstrate the capability these circuits support complex dynamics, independently from their implementation technology. In detail, a direct experimental evidence DNO dynamical behavior is presented at analog level with bifurcation dia...

A general class of sequential codes for lossless compression of individual sequences on a finite alphabet is defined, including many types of codes that one would want to implement. The principal requirement for membership in the class is that the encoding and decoding operations be performable on a computer. The OPTA function for the class of codes is then considered, which is the function tha...

The problem of estimating the number of states of a finite-alphabet, finite-state source is investigated. An estimator is developed that asymptotically attains the minimum probability of underestimating the number of states, among all estimators with a prescribed exponential decay rate of overestimation probability. The proposed estimator relies on the Lempel-Ziv data compression algorithm in a...

Investigations of complexity of sequences lead to important applications such as effective data compression, testing of randomness, discriminating between information sources and many others. In this paper we establish formulae describing the distribution functions of random variables representing the complexity of finite sequences introduced by Lempel and Ziv in 1976. It is known that this qua...

We consider a natural generalization of the classical pattern matching problem: given compressed representations of a pattern p[1. . M ] and a text t[1. . N ] of sizes m and n, respectively, does p occur in t? We develop an optimal linear time solution for the case when p and t are compressed using the LZW method. This improves the previously known O((n + m) log(n + m)) time solution of G asien...

Routine clinical practice data often differ from clinical trials. This study describes real-world treatment patterns and effectiveness among patients with metastatic colorectal cancer (mCRC) receiving ziv-aflibercept in non-academic, community oncology practices in the USA. De-identified electronic medical records from Vector Oncology and Altos Solutions databases were analysed. We identified 2...

Recently, several distributed video coding (DVC) solutions based on the distributed source coding (DSC) paradigm have appeared in the literature. Wyner-Ziv (WZ) video coding, a particular case of DVC where side information is made available at the decoder, enable to achieve a flexible distribution of the computational complexity between the encoder and decoder, promising to fulfill novel requir...

This report compares a variety of computable information measures for finite strings. These include Shannon’s n-block entropy, the three best known versions of the Lempel-Ziv production complexity (LZ-76, LZ-77, and LZ-78), and the lesser known T-entropy. We apply these measures to strings of known entropy, each derived from the logistic map. Pesin’s identity allows us to deduce corresponding S...