Related papers: Measure representation and multifractal analysis o…
A mathematical algorithm to describe DNA or RNA sequences of $N$ nucleotides by a string of $2N$ integers numbers is presented in the framework of the so called crystal basis model of the genetic code. The description allows to define a not…
The statistical properties of wave functions at the critical point of the spin quantum Hall transition are studied. The main emphasis is put onto determination of the spectrum of multifractal exponents $\Delta_q$ governing the scaling of…
Representation learning has driven major advances in natural image analysis by enabling models to acquire high-level semantic features. In microscopy imaging, however, it remains unclear what current representation learning methods actually…
The multifractal structure underlying a self-similar measure stems directly from the weighted self-similar system (or weighted iterated function system) which is used to construct the measure. This follows much in the way that the dimension…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
A time series model of CDS sequences in complete genome is proposed. A map of DNA sequence to integer sequence is given. The correlation dimensions and Hurst exponents of CDS sequences in complete genome of bacteria are calculated. Using…
The nucleotide sequence representation of DNA can be inadequate for resolving protein-DNA binding sites and regulatory substrates, such as those involved in gene expression and horizontal gene transfer. Considering that sequence-like…
The translation action of $\RR^{d}$ on a translation bounded measure $\omega$ leads to an interesting class of dynamical systems, with a rather rich spectral theory. In general, the diffraction spectrum of $\omega$, which is the carrier of…
In special coordinates (codon position--specific nucleotide frequencies) bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial…
Multispectral imaging provides valuable information on tissue composition such as hemoglobin oxygen saturation. However, the real-time application of this technique in interventional medicine can be challenging due to the long acquisition…
This is a review of a set of recent papers with some new data added. After a brief biological introduction a visualization scheme of the string composition of long DNA sequences, in particular, of bacterial complete genomes, will be…
We propose a computational method to measure and visualize interrelationships among any number of DNA sequences allowing, for example, the examination of hundreds or thousands of complete mitochondrial genomes. An "image distance" is…
Recent experimental and theoretical approaches have attempted to quantify the physical organization (compaction and geometry) of the bacterial chromosome with its complement of proteins (the nucleoid). The genomic DNA exists in a complex…
The Complex Scaling Method (CSM) provides scattering wave functions which regularize resonances and suggest a resolution of the identity in terms of such resonances, completed by the bound states and a smoothed continuum. But, in the case…
Periodic patterns play the important regulatory and structural roles in genomic DNA sequences. Commonly, the underlying periodicities should be understood in a broad statistical sense, since the corresponding periodic patterns have been…
My analysis uses methods developed for data mining microarray experiments, adapted for ageing research. Methods bridge knowledge of statistical mechanics with data mining methods developed in statistical mathematics. Analyses can reveal how…
Complex networks, modeled as large graphs, received much attention during these last years. However, data on such networks is only available through intricate measurement procedures. Until recently, most studies assumed that these…
The accurate and reliable description of measurement devices is a central problem in both observing uniquely non-classical behaviors and realizing quantum technologies from powerful computing to precision metrology. To date quantum…
This paper examines two methods for finding whether long-range correlations exist in DNA: a fractal measure and a mutual information technique. We evaluate the performance and implications of these methods in detail. In particular we…
The multifractal characterization of the distribution over disorder of the mean first-passage time in a finite chain is revisited. Both, absorbing-absorbing and reflecting-absorbing boundaries are considered. Two models of dichotomic…