Related papers: Measure representation and multifractal analysis o…
We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical…
Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal…
2D display is a fast and economical way of visualizing polymorphism and comparing genomes, which is based on the separation of DNA fragments in two steps, according first to their size and then to their sequence composition. In this paper,…
We study statistical properties of DNA chains of thirteen microbial complete genomes. We find that the power spectrum of several of the sequences studied flattens off in the low frequency limit. This implies that the correlation length in…
Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…
For a Borel measure and a sequence of partitions on the unit interval, we define a multifractal spectrum based on coarse Holder regularity. Specifically, the coarse Holder regularity values attained by a given measure and with respect to a…
Spectrogram-based representations have grown to dominate the feature space for deep learning audio analysis systems, and are often adopted for speech analysis also. Initially, the primary motivator for spectrogram-based representations was…
We extend a formal framework that previously derived time from the multifractal structure of biological lineages (Hudnall \& D'Souza, 2025). That work showed that time itself is multifractal -- not a universal background dimension, but an…
Earlier formulations of the DNA assembly problem were all in the context of perfect assembly; i.e., given a set of reads from a long genome sequence, is it possible to perfectly reconstruct the original sequence? In practice, however, it is…
A gene expression compendium is a heterogeneous collection of gene expression experiments assembled from data collected for diverse purposes. The widely varied experimental conditions and genetic backgrounds across samples creates a…
In this paper, we review the literature on statistical long-range correlation in DNA sequences. We examine the current evidence for these correlations, and conclude that a mixture of many length scales (including some relatively long ones)…
In this paper we treat some fractal and statistical features of the DNA sequences. First, a fractal record model of DNA sequence is proposed by mapping DNA sequences to integer sequences, followed by R/S analysis of the model and…
The concept of k-spectrum for genomes is here investigated as a basic tool to analyze genomes. Related spectral notions based on k-mers are introduced with some related mathematical properties which are relevant for informational analysis…
Microscopy images contain rich information about how cells respond to perturbations, making them essential to applications like drug screening. To quantify images, researchers often use representation extraction methods, and recent years…
Spectrograms visualize the frequency components of a given signal which may be an audio signal or even a time-series signal. Audio signals have higher sampling rate and high variability of frequency with time. Spectrograms can capture such…
We study the time evolution of wavepackets of non-interacting electrons in a two-dimensional disordered system in strong magnetic field. For wavepackets built from states near the metal-insulator transition in the center of the lowest…
This commentary discusses a recently proposed measure of heterogeneity of DNA sequences and compares with the measures of complexity.
There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has…
The mean length and the variability of coding sequences for 48 genomes of bacteria and archaea were analyzed. It was found that the plotted data can be described by an angular area. This suggests the followings: a) The variability of a…
Metagenome, a mixture of different genomes (as a rule, bacterial), represents a pattern, and the analysis of its composition is, currently, one of the challenging problems of bioinformatics. In the present study, the possibility of…