Related papers: Multifractal characterisation of length sequences …
We investigate the recovery dynamics of healthy cardiac activity after physical exertion using multimodal biosignals recorded with a polycardiograph. Multifractal features derived from the singularity spectrum capture the scale-invariant…
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)…
This paper considers the problem of matching fragment to organism using its complete genome. Our method is based on the probability measure representation of a genome. We first demonstrate that these probability measures can be modelled as…
We demonstrate analytically and numerically the possibility that the fractal property of a scale-free network cannot be characterized by a unique fractal dimension and the network takes a multifractal structure. It is found that the mass…
We study multifractal properties in time evolution of a single particle subject to repeated measurements. For quantum systems, we consider circuit models consisting of local unitary gates and local projective measurements. For classical…
We introduce a model of DNA sequence evolution which can account for biases in mutation rates that depend on the identity of the neighboring bases. An analytic solution for this class of non-equilibrium models is developed by adopting…
We find that multifractal scaling is a robust property of a large class of continuous stochastic processes, constructed as exponentials of long-memory processes. The long memory is characterized by a power law kernel with tail exponent…
Parts of DNA sequences known as exons and introns play very different role in coding and storage of genetic information. Here we show that their conducting properties are also very different. Taking into account long-range correlations…
The two-dimensional multifractal detrended fluctuation analysis is applied to reveal the multifractal properties of the fracture surfaces of foamed polypropylene/polyethylene blends at different temperatures. Nice power-law scaling…
In this work, we applied the Chaos Game Representation (CGR) to the complete human genomic sequence T2T-CHM13v2.0, analyzing the entire chromosome assembly and each chromosome separately, including mitochondrial DNA. Multifractal spectra…
Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…
We report an algorithm for the partition of a line segment according to a given ratio $\nu$. At each step the length distribution among sets of the partition follows a binomial distribution. We call $k$-set to the set of elements with the…
This methods paper presents computational protocols for the identification of non-coding RNA genes or RNA motifs within genomic sequences. An application to bacterial small RNA is proposed.
Complex systems with tightly coadapted parts frequently appear in living systems and are difficult to account for through Darwinian evolution, that is random variation and natural selection, if the constituent parts are independently coded…
In this paper, I introduce a Sequence-based Multiscale Model (SeqMM) for the biomolecular data analysis. With the combination of spectral graph method, I reveal the essential difference between the global scale models and local scale ones…
Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry,…
In nature the three-dimensional structure of a protein is encoded in the corresponding gene. In this paper we describe a new method for encoding the three-dimensional structure of a protein into a binary sequence. The feature of the method…
We calculate the spectral dimension of a wide class of tree-like fractals by solving the random walk problem through a new analytical technique, based on invariance under generalized cutting-decimation transformations. These fractals are…
Evolution is an extraordinary engine for enzymatic diversity, yet the chemistry it has explored remains a narrow slice of what DNA can encode. Deep generative models can design new proteins that bind ligands, but none have created enzymes…
We first show how the cohomology of some Bernstein-Gelfand-Gelfand (BGG) sequences that are important for the numerical analysis of partial differential equations, can be obtained through the construction of a long exact sequence connecting…