Searching for generic behaviors has been one of the driving forces leading to a deep understanding and classification diverse phenomena. Usually starting point is development phenomenology based on observations. Such case power law distributions encountered in wealth situations coming from physics, geophysics, biology, lexicography as well social financial networks. This finding however restricted range values outside which finite size corrections are often invoked. Here we uncover universal...

It is well known that many ranked linguistic data can fit with one-parameter models such as Zipf’s law for word frequencies. However, in cases where discrepancies from the model occur (these will come at two extremes of rank), it natural to use one more parameter fitting model. In this paper, we compare several two-parameter models, including Beta function, Yule Weibull function—all be framed a multiple regression logarithmic scale—in their performance data, letter frequencies,...

The amount of non-unique sequence (non-singletons) in a genome directly affects the difficulty read alignment to reference assembly for high throughput-sequencing data. Although greater length increases chance reads being uniquely mapped genome, quantitative analysis influence lengths on mappability has been lacking. To address this question, we evaluate k-mer distribution human genome. frequency is determined k ranging from 20 1000 basepairs. We use proportion non-singleton k-mers...

Abstract The limited range in the abscissa of ranked letter frequency distributions causes multiple functions to fit observed distribution reasonably well. In order critically compare various functions, we apply statistical model selections on ten using texts US and Mexican presidential speeches last few centuries. Despite minor switching ranking certain letters during temporal evolution for both datasets, usage is generally stable. best fitting function, judged by either least-square-error...

Although Zipf's law is widespread in natural and social data, one often encounters situations where or both ends of the ranked data deviate from power-law function. Previously we proposed Beta rank function to improve fitting which does not follow a perfect law. Here show that when two parameters have same value, Lavalette function, probability density can be derived analytically. We also computationally analytically distribution approximately equal, though identical, lognormal distribution....

Hammerhead ribozymes previously were found in satellite RNAs from plant viroids and repetitive DNA certain species of newts schistosomes. To determine if this catalytic RNA motif has a wider distribution, we decided to scrutinize the GenBank database for that contain hammerhead or hammerhead-like motifs. The search shows widespread distribution kind different sequences suggesting they might have more general role biology. frequency is half expected random but fact comes low CpG...

We formulate a susceptible-vaccinated-infected-recovered (SVIR) model by incorporating the vaccination of newborns, vaccine-age, and mortality induced disease into SIR epidemic model. It is assumed that period immunity vaccines varies depending on vaccine-age. Using direct Lyapunov method with Volterra-type function, we show global asymptotic stability infection-free endemic steady states.

Predator-prey relationships are one of the most studied interactions in population ecology. However, little attention has been paid to possibility role exchange between species, despite firm field evidence such phenomena nature. In this paper, we build a mathematical model capable reproducing main phenomenological features reversal classical system and present results for both temporal spatio-temporal cases. We show that, depending on choice parameters, our role-reversal dynamical exhibits...

Human papillomavirus (HPV) has been identified as the main etiological factor in developing of cervical cancer (CC). This finding propitiated development vaccines that help to prevent HPVs 16 and 18 infection. Both genotypes are associated with 70% CC worldwide. In present study, we aimed determine emergence high-risk nonvaccine HPV after actual vaccination scheme estimate impact current vaccines. A SIR-type model was used study dynamics vaccination. According results, our indicates...

Whereas there has been an extended discussion concerning city population distribution, little said about that of administrative divisions. In this work, we investigate the distribution second-level units 150 countries and territories propose discrete generalized beta (DGBD) rank-size function to describe data. After testing balance between goodness fit number parameters compared with a power law, which is most common model for population, DGBD good statistical 96% our datasets preferred over...

Recently, Trifonov's group proposed a 10-mer DNA motif YYYYYRRRRR as solution of the long-standing problem sequence-based nucleosome positioning. To test whether this generic decamer represents biological meaningful signal, we compare distribution in primates and Archaea, which are known to contain nucleosomes, Eubacteria, do not possess nucleosomes. The is analyzed by mutual information function (MIF) with shifted version itself (MIF profile). We found common features patterns on MIF...

The sizes of paralogues—gene families produced by ancestral duplication—are known to follow a power-law distribution. We examine the size distribution gene sets or where genes are grouped similar function share common property. Human Gene Nomenclature Committee (HGNC) deviate from power-law, and can be fitted much better beta rank function. propose simple mechanism break combination splitting merging operations. largest split into two account for subfunctional categories, small proportion...

This study presents multiwall and bamboo-like carbon nanotubes found in samples from the Allende carbonaceous chondrite using high-resolution transmission electron microscopy (HRTEM). A highly disordered lattice observed this material suggests presence of chiral domains it. Our results also show amorphous poorly-graphitized carbon, nanodiamonds, onion-like fullerenes. The have important implications for hypotheses that explain how a probable source asymmetry chondrites might contributed to...

The paper "Critical Truths About Power Laws" (Science, 335, pp665-666) by MPH Stumpf and MA Porter is commented

Human chromosome 21 is the only in human genome that exhibits oscillation of $(\mathrm{G}+\mathrm{C})$ content a cycle length hundreds kilobases (kb) ($500\phantom{\rule{0.3em}{0ex}}\mathrm{kb}$ near right telomere). We aim at establishing existence similar periodicity structure-related sequence features order to relate this $(\mathrm{G}+\mathrm{C})%$ other biological phenomena. The following quantities are shown oscillate with same $500\phantom{\rule{0.3em}{0ex}}\mathrm{kb}$ 21: binding...