Related papers: A complexity measure for symbolic sequences and ap…
We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite…
The symmetries of the DNA double helix require a new term in its linear response to stress: the coupling between twist and stretch. Recent experiments with torsionally-constrained single molecules give the first direct measurement of this…
Understanding the evolution of complexity is an important topic in a wide variety of academic fields. Implications of better understanding complexity include increased knowledge of major evolutionary transitions and the properties of living…
The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is…
Calculating the Shannon entropy for symbolic sequences has been widely considered in many fields. For descriptive statistical problems such as estimating the N-gram entropy of English language text, a common approach is to use as much data…
We describe general approach to classification of character sequences (texts, DNA) using relative entropy estimated by off-the-shelf compression and Markov Chains and find them precise enough. We also notice that the method for estimating…
Domain knowledge can often be encoded in the structure of a network, such as convolutional layers for vision, which has been shown to increase generalization and decrease sample complexity, or the number of samples required for successful…
Frequency tagging is a powerful approach to investigate the neural processing of sensory features, and is recently adapted to study the neural correlates of superordinate structures, i.e., chunks, in complex sequences such as speech and…
This paper presents a novel method to segment/decode DNA sequences based on n-grams statistical language model. Firstly, we find the length of most DNA 'words' is 12 to 15 bps by analyzing the genomes of 12 model species. Then we design an…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
Deep convolutional neural networks (CNNs) have been shown to be able to fit a random labeling over data while still being able to generalize well for normal labels. Describing CNN capacity through a posteriori measures of complexity has…
We review several statistical complexity measures proposed over the last decade and a half as general indicators of structure or correlation. Recently, Lopez-Ruiz, Mancini, and Calbet [Phys. Lett. A 209 (1995) 321] introduced another…
The set of indices that correspond to the positive entries of a sequence of numbers is called its positivity set. In this paper, we study the density of the positivity set of a given linear recurrence sequence, that is the question of how…
At the core of high throughput DNA sequencing platforms lies a bio-physical surface process that results in a random geometry of clusters of homogenous short DNA fragments typically hundreds of base pairs long - bridge amplification. The…
Much of the on-going statistical analysis of DNA sequences is focused on the estimation of characteristics of coding and non-coding regions that would possibly allow discrimination of these regions. In the current approach, we concentrate…
Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…
A powerful tool is developed for the characterization of chaotic signals. The approach is based on the symbolic encoding of time series (according to their ordinal patterns) combined with the ensuing characterization of the corresponding…
Nonlinear complexity, as an important measure for assessing the randomness of sequences, is defined as the length of the shortest feedback shift registers that can generate a given sequence. In this paper, the structure of n-periodic binary…