相关论文: Complexities of Human Promoter Sequences
We study the entropy $S$ of longest increasing subsequences (LIS), i.e., the logarithm of the number of distinct LIS. We consider two ensembles of sequences, namely random permutations of integers and sequences drawn i.i.d.\ from a limited…
A connection is made between the random turns model of vicious walkers and random permutations indexed by their increasing subsequences. Consequently the scaled distribution of the maximum displacements in a particular asymmeteric version…
Human preference evaluations are widely used to compare generative models, yet it remains unclear how many judgments are required to reliably detect small improvements. We show that when preference signal is diffuse across prompts (i.e.,…
Recent studies have shown that in the presence of noise both fronts propagating into a metastable state and so-called pushed fronts propagating into an unstable state, exhibit diffusive wandering about the average position. In this paper we…
The distribution of bases spacing in human genome was investigated. An analysis of the frequency of occurrence in the human genome of different sequence lengths flanked by one type of nucleotide was carried out showing that the distribution…
This article presents the calculation of the entropy of a system with Zipfian distribution and shows that a communication system tends to present an exponent value close to one, but still greater than one, so that it might maximize entropy…
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…
Spread complexity uses the distribution of support of a time-evolving state in the Krylov basis to quantify dispersal across accessible dimensions of a Hilbert space. Here, we describe how variations in initial conditions, the Hamiltonian,…
We study the primary DNA structure of four of the most completely sequenced human chromosomes (including chromosome 19 which is the most dense in coding), using Non-extensive Statistics. We show that the exponents governing the decay of the…
Waves propagate through disordered systems in a variety of regimes. There is a threshold of disorder beyond which waves become localized and transport becomes restricted. The intensity I of the wave transmitted through a system has a…
The problem of random walk is considered in one dimension in the simultaneous presence of a quenched random force field and long-range connections the probability of which decays with the distance algebraically as p_l ~ \beta l^{-s}. The…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
Although there is no doubt that multi-parameter persistent homology is a useful tool to analyse multi-variate data, efficient ways to compute these modules are still lacking in the available topological data analysis toolboxes. Other issues…
The cross section for the diffractive deep-inelastic scattering process ep -> e X p is measured, with the leading final state proton detected in the H1 Forward Proton Spectrometer. The data sample covers the range x_pom<0.1 in fractional…
Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one--directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the…
Multipath propagation of radio waves in indoor/outdoor environments shows a highly irregular behavior as a function of time. Typical modeling of this phenomenon assumes the received signal is a stochastic process composed of the…
The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
Commonly observed patterns typically follow a few distinct families of probability distributions. Over one hundred years ago, Karl Pearson provided a systematic derivation and classification of the common continuous distributions. His…