Related papers: Universal power law behaviors in genomic sequences…
Spatial fluctuations of guanine and cytosine base content (GC%) are studied by spectral analysis for the complete set of human genomic DNA sequences. We find that (i) the 1/f^alpha decay is universally observed in the power spectra of all…
We investigate the distributions of epsilon-drawdowns and epsilon-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion of runs…
The mechanisms underlying lifespan evolution in organisms have long been mysterious. However, recent studies have demonstrated that organisms evolutionarily gain noncoding RNAs (ncRNAs) that carry endogenous profound functions in higher…
Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…
Membrane tension is an acknowledged regulator of a wide array of cell functions; however, whether it acts locally or globally in different contexts remains debated. Recent experiments that locally perturb tension and measure the response…
We consider a population with non-overlapping generations, whose size goes to infinity. It is described by a discrete genealogy which may be time non-homogeneous and we pay special attention to branching trees in varying environments. A…
Transcriptional pulsing has been observed in both prokaryotes and eukaryotes and plays a crucial role in cell to cell variability of protein and mRNA numbers. The issue is how the time constants associated with episodes of transcriptional…
Data on the number of Open Reading Frames (ORFs) coded by genomes from the 3 domains of Life show some notable general features including essential differences between the Prokaryotes and Eukaryotes, with the number of ORFs growing linearly…
Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…
One of the first steps to understand and forecast economic downturns is identifying their frequency distribution, but it remains uncertain. This problem is common in phenomena displaying power-law-like distributions. Power laws play a…
The frequency distributions of DNA k-mers are shaped by fundamental biological processes and offer a window into genome structure and evolution. Inspired by analogies to natural language, prior studies have attempted to model genomic k-mer…
In this paper, we consider the outer channel for DNA-based data storage. When transmitting over the outer channel, each DNA string is treated as a unit/symbol that would be either correctly received, or erased, or corrupted by uniformly…
Emerging evidence suggests that the introns and intergenic sequences of the genomes of higher eukaryotes (the ``junk'' DNA) codes for a vast, RNA-based, genetic regulatory network. It is believed that this network is responsible for the…
While the emergence of a power law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the betweenness centrality displays a power-law distribution with an exponent \eta which is…
Large scale molecular dynamics (MD) simulations are performed to study and to model the ejecta production from the dynamic fragmentation of shock-loaded metals under melt conditions. A generic 3D crystal in contact with vacuum containing…
A general theoretical framework is put forth to organize and understand various observed phenomena and mathematical relationships in the field of molecular biology. By modeling each cell in eukaryotic organisms as a processor having a…
We study the extragalactic protons with universal spectrum, which is independent of mode of propagation, when distance between sources is less than the propagation lengths, such as energy attenuation length or diffusion length (for…
Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the…
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…