Related papers: Measure representation and multifractal analysis o…
A representation of frequency of strings of length K in complete genomes of many organisms in a square has led to seemingly self-similar patterns when K increases. These patterns are caused by under-represented strings with a certain…
Background: The trend towards large-scale studies including population imaging poses new challenges in terms of quality control (QC). This is a particular issue when automatic processing tools, e.g. image segmentation methods, are employed…
A stretched DNA molecule which is also under- or overwound, undergoes a buckling transition forming intertwined looped domains called plectonemes. Here we develop a simple theory that extends the two-phase model of stretched supercoiled…
We prove that a positive-definite measure in $\mathbb{R}^n$ with uniformly discrete support and discrete closed spectrum, is representable as a finite linear combination of Dirac combs, translated and modulated. This extends our recent…
In biomedical imaging reliable segmentation of objects (e.g. from small cells up to large organs) is of fundamental importance for automated medical diagnosis. New approaches for multi-scale segmentation can considerably improve performance…
Optical spectrometers are fundamental across numerous disciplines in science and technology. However, miniaturized versions, while essential for in situ measurements, are often restricted to coarse identification of signature peaks and…
We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions subject to projective monitoring of local charge across the measurement-induced phase transition. Our observables are…
In this paper, we aim to give a tutorial for undergraduate students studying statistical methods and/or bioinformatics. The students will learn how data visualization can help in genomic sequence analysis. Students start with a fragment of…
Modern single-cell flow and mass cytometry technologies measure the expression of several proteins of the individual cells within a blood or tissue sample. Each profiled biological sample is thus represented by a set of hundreds of…
We develop the tools necessary to assess the statistical significance of resonant features in the CMB correlation functions, combining power spectrum and bispectrum measurements. This significance is typically addressed by running a large…
A novel approach towards the spectral analysis of stationary random bivariate signals is proposed. Using the Quaternion Fourier Transform, we introduce a quaternion-valued spectral representation of random bivariate signals seen as…
DNA supercoiling, the under or overwinding of DNA, is a key physical mechanism both participating to compaction of bacterial genomes and making genomic sequences adopt various structural forms. DNA supercoiling may lead to the formation of…
Bioinformatics, which is now a well known field of study, originated in the context of biological sequence analysis. Recently graphical representation takes place for the research on DNA sequence. Research in biological sequence is mainly…
It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or…
This paper presents a probabilistic approach for DNA sequence analysis. A DNA sequence consists of an arrangement of the four nucleotides A, C, T and G and different representation schemes are presented according to a probability measure…
A hypercomplex representation of DNA is proposed to facilitate comparison of DNA sequences with fuzzy composition. Using hypercomplex number representation, conventional sequence analysis method, such as, dot matrix analysis, dynamic…
We give a Herglotz-type representation of an arbitrary generalized spectral measure. As an application, a new proof of the classical Naimark's dilation theorem is given. The same approach is used to describe the spectrum of all unitary…
We present a generalization of continuous position measurements that accounts for a spatially inhomogeneous measurement strength. This describes many real measurement scenarios, in which the rate at which information is extracted about…
This work presents the first steps to modelling synthetic rovibrational spectra for all molecules of astrophysical interest using a new approach implemented in the Prometheus code. The goal is to create a new comprehensive source of…
In a multicellular organism different cell types express a gene in different amounts. Samples from which gene expression levels can be measured typically contain a mixture of different cell types, the resulting measurements thus give only…