Related papers: A complexity measure for symbolic sequences and ap…
It is shown that metric representation of DNA sequences is one-to-one. By using the metric representation method, suppression of nucleotide strings in the DNA sequences is determined. For a DNA sequence, an optimal string length to display…
Topological entropy has been one of the most difficult to implement of all the entropy-theoretic notions. This is primarily due to finite sample effects and high-dimensionality problems. In particular, topological entropy has been…
The paper makes the observation that all orders of information entropy are equal in signals composed of repeating units of distinct symbols where the units can be classified as a member of a symmetry group. This leads to an improved metric…
An accurate assessment of a model's complexity is crucial for topics such as interpretation, generalization, and model selection. However, most existing complexity measures either rely on heuristic assumptions or are computationally…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…
In this paper, we propose a new measure to gauge the complexity of image classification problems. Given an annotated image dataset, our method computes a complexity measure called the cumulative spectral gradient (CSG) which strongly…
In this paper we examine the concept of complexity as it applies to generative and evolutionary art and design. Complexity has many different, discipline specific definitions, such as complexity in physical systems (entropy), algorithmic…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
The coupling complexity index is an information measure introduced within the framework of ordinal symbolic dynamics. This index is used to characterize the complexity of the relationship between dynamical system components. In this work,…
Data samples collected for training machine learning models are typically assumed to be independent and identically distributed (iid). Recent research has demonstrated that this assumption can be problematic as it simplifies the manifold of…
In estimating the complexity of objects, in particular of graphs, it is common practice to rely on graph- and information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these…
Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…
We consider the computation of the mean of sequences in the quantum model of computation. We determine the query complexity in the case of sequences which satisfy a $p$-summability condition for $1\le p<2$. This settles a problem left open…
Sequence classification is the supervised learning task of building models that predict class labels of unseen sequences of symbols. Although accuracy is paramount, in certain scenarios interpretability is a must. Unfortunately, such…
By using the Jensen-Shannon divergence, genomic DNA can be divided into compositionally distinct domains through a standard recursive segmentation procedure. Each domain, while significantly different from its neighbours, may however share…
Computational complexity is a key limitation of genomic analyses. Thus, over the last 30 years, researchers have proposed numerous fast heuristic methods that provide computational relief. Comparing genomic sequences is one of the most…
Given a set of sequences, the distance between pairs of them helps us to find their similarity and derive structural relationship amongst them. For genomic sequences such measures make it possible to construct the evolution tree of…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
Repetitive elements are important in genomic structures, functions and regulations, yet effective methods in precisely identifying repetitive elements in DNA sequences are not fully accessible, and the relationship between repetitive…