Related papers: Measure representation and multifractal analysis o…
This article introduces a novel binary representation of the canonical genetic code based on both the structural similarities of the nucleotides, as well as the physicochemical properties of the encoded amino acids. Each of the four mRNA…
Many modern biological assays, including RNA sequencing, yield integer-valued counts that reflect the number of molecules detected. These measurements are often not at the desired resolution: while the unit of interest is typically a single…
The investigation of the static and dynamic structural properties of colloidal systems relies on techniques capable of atomic resolution in real space and femtosecond resolution in time. Recently, the cross-correlation function (CCF)…
The aim of this article is to study the behaviour of the multifractal packing function $B_\mu(q)$ under projections in Euclidean space for $q>1$. We show that $B_\mu(q)$ is preserved under almost every orthogonal projection. As an…
In this paper we present a theoretical foundation for a representation of a data set as a measure in a very large hierarchically parametrized family of positive measures, whose parameters can be computed explicitly (rather than estimated by…
In this work we investigate and characterize linear functionals $L:\mathbb{R}[x_1,\dots,x_n]\to\mathbb{R}$ with absolutely continuous representing measures $\mu$, i.e., $\mathrm{d}\mu(x) = g(x)\,\mathrm{d} x$ for some density $g$. We focus…
Texture characterization is a central element in many image processing applications. Multifractal analysis is a useful signal and image processing tool, yet, the accurate estimation of multifractal parameters for image texture remains a…
The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated…
DNA methylation is an intensely studied epigenetic mark implicated in many biological processes of direct clinical relevance. While sequencing based technologies are increasingly allowing high resolution measurements of DNA methylation,…
We apply multifractal analysis to an experimentally obtained quasi-two-dimensional crystal with fourfold symmetry, in order to characterize the sidebranch structure of a dendritic pattern. In our analysis, the stem of the dendritic pattern…
In systems biology, it is becoming increasingly common to measure biochemical entities at different levels of the same biological system. Hence, data fusion problems are abundant in the life sciences. With the availability of a multitude of…
The continuous quantum measurement within the probability representation of quantum mechanics is discussed. The partial classical propagator of the symplectic tomogram associated to a particular measurement outcome is introduced, for which…
During the last decade, a large number of different numerical methods have been proposed to tackle the automatic identification and quantification in {\gamma}-ray spectrometry. However, the lack of common benchmarks, including datasets,…
A vectorial analysis of magnetic resonance spectrometers, based on traveling wave resonators and including the reference arm and the automatic control of frequency, has been developed. The proposed model, valid also for stationary wave…
We propose a general and formal statistical framework for multiple tests of association between known fixed features of a genome and unknown parameters of the distribution of variable features of this genome in a population of interest. The…
Tools that effectively analyze and compare sequences are of great importance in various areas of applied computational research, especially in the framework of molecular biology. In the present paper, we introduce simple geometric criteria…
Cells receive a wide variety of cellular and environmental signals, which must be processed combinatorially to generate specific and timely genetic responses. We present here a theoretical study on the combinatorial control and integration…
In condensed matter physics, simplified descriptions are obtained by coarse-graining the features of a system at a certain characteristic length, defined as the typical length beyond which some properties are no longer correlated. From a…
Symbolic sequences generated by coupled map lattices (CMLs) can be used to model the chaotic-like structure of genomic sequences. In this study it is shown that diffusively coupled Chebyshev maps of order 4 (corresponding to a shift of 4…
Spectroscopy is a powerful analytical technique for characterizing matter across physical and biological realms1-5. However, its fundamental principle necessitates specialized instrumentation per physical phenomena probed, limiting broad…