Related papers: Measure representation and multifractal analysis o…
Obtaining effective representations of DNA sequences is crucial for genome analysis. Metagenomic binning, for instance, relies on genome representations to cluster complex mixtures of DNA fragments from biological samples with the aim of…
We study self-similar measures in $\mathbb{R}$ satisfying the weak separation condition along with weak technical assumptions which are satisfied in all known examples. For such a measure $\mu$, we show that there is a finite set of concave…
Involved in mitotic condensation, interaction of transcriptional regulatory elements or isolation of structural domains, understanding loop formation is becoming a paradigm in the deciphering of chromatin architecture and its functional…
As a label-free imaging technique, quantitative phase imaging (QPI) provides optical path length information of transparent specimens for various applications in biology, materials science, and engineering. Multispectral QPI measures…
Based on the numerical representations by T basic vectors of a symbolic sequence consisting of T symbols, first, we prove mathematical that the total Fourier spectrum of the sequence is the square of the length of the sequence. In the…
Biological tissue integrity is actively maintained by cells. It is essential to comprehend how cells accomplish this in order to stage tissue diseases. However, addressing the complexity of a cell's system of interrelated mechanisms poses a…
The estimation of the covariance function of a stochastic process, or signal, is of integral importance for a multitude of signal processing applications. In this work, we derive closed-form expressions for the variance of covariance…
The phase diagram of the metal-insulator transition in a three dimensional quantum percolation problem is investigated numerically based on the multifractal analysis of the eigenstates. The large scale numerical simulation has been…
Multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the so-called spectrum of singularities. In this paper we…
There is an increasing number of potential biomarkers that could allow for early assessment of treatment response or disease progression. However, measurements of quantitative biomarkers are subject to random variability. Hence, differences…
Cavity-enhanced frequency comb spectroscopy for molecule detection in the mid-infrared powerfully combines high resolution, high sensitivity, and broad spectral coverage. However, this technique, and essentially all spectroscopic methods,…
With the increasing amount of experimental data on gene expression and regulation, there is a growing need for quantitative models to describe the data and relate them to the different contexts. The thermodynamic models reviewed in the…
In a recent paper, two multi-representations for the measurable sets in a computable measure space have been introduced, which prove to be topologically complete w.r.t. certain topological properties. In this contribution, we show them…
Learning to disentangle and represent factors of variation in data is an important problem in AI. While many advances have been made to learn these representations, it is still unclear how to quantify disentanglement. While several metrics…
Molecular representation is a critical element in our understanding of the physical world and the foundation for modern molecular machine learning. Previous molecular machine learning models have employed strings, fingerprints, global…
The presence of multifractality in a time series shows different correlations for different time scales as well as intermittent behaviour that cannot be captured by a single scaling exponent. The identification of a multifractal nature…
The simultaneous estimation of multiple unknown parameters is the most general scenario in quantum sensing. Quantum multi-parameter estimation theory provides fundamental bounds on the achievable precision of simultaneous estimation.…
In the present work, some density estimations associated with vector-valued quasi-Ahlfors measures are developed within the mixed multifractal analysis framework. The principle idea based on the fact that being quasi-Ahlfors is sufficient…
The spectral representation is an effecient tool to explore electrical properties of material mixtures. It separates the contributions of geometrical topology and intrinsic properties of the constituents in the system. The aim of this paper…
Based on the measurement of quantum correlation functions, the quantum statistical properties of spectral measurements are studied for broadband radiation fields. The spectral filtering of light before its detection is compared with the…