Search results for "Permutation"
showing 10 items of 132 documents
Substitution systems and nonextensive statistics
2015
Abstract Substitution systems evolve in time by generating sequences of symbols from a finite alphabet: At a certain iteration step, the existing symbols are systematically replaced by blocks of N k symbols also within the alphabet (with N k , a natural number, being the length of the k th block of the substitution). The dynamics of these systems leads naturally to fractals and self-similarity. By using B -calculus (Garcia-Morales, 2012) universal maps for deterministic substitution systems both of constant and non-constant length, are formulated in 1D. It is then shown how these systems can be put in direct correspondence with Tsallis entropy. A ‘Second Law of Thermodynamics’ is also prove…
On the empirical spectral distribution for certain models related to sample covariance matrices with different correlations
2021
Given [Formula: see text], we study two classes of large random matrices of the form [Formula: see text] where for every [Formula: see text], [Formula: see text] are iid copies of a random variable [Formula: see text], [Formula: see text], [Formula: see text] are two (not necessarily independent) sets of independent random vectors having different covariance matrices and generating well concentrated bilinear forms. We consider two main asymptotic regimes as [Formula: see text]: a standard one, where [Formula: see text], and a slightly modified one, where [Formula: see text] and [Formula: see text] while [Formula: see text] for some [Formula: see text]. Assuming that vectors [Formula: see t…
Dynamical block analysis in a non-equilibrium system
1991
Abstract We present molecular dynamics simulation results of quenches into the unstable region of a two-dimensional Lennard-Jones system. The evolution of the system from the non-equilibrium state into equilibrium was analyzed with a dynamical block analysis. This can lead to a new approach in the study of non-equilibrium phenomena. We show that with such an analysis one can obtain results on the dynamic evolution as the system evolves, consistent with those obtained from and analysis of the pair-distribution function, structure factor and excess energy. The simulations were carried out on the parallel computer of the condensed matter theory group at the University of Mainz.
Block–Savits Characterization and Star Ordering of Exponential Mixtures
2008
Block and Savits (1980) established a characterization of life distributions using the Laplace transform. In this article, we remark that one of the necessary conditions to be IFRA distribution is equivalent to the star ordering of exponential mixtures. It leads to the definition of two new classes of life distributions, called LIFR and LIFRA, and their dual classes: LDFR and LDFRA. It occurs that these classes have many useful aging properties and preserve known reliability operations. Properties of the classes are studied and relations with known classes are established.
On the Analysis of a Random Interleaving Walk–Jump Process with Applications to Testing
2011
Abstract Although random walks (RWs) with single-step transitions have been extensively studied for almost a century as seen in Feller (1968), problems involving the analysis of RWs that contain interleaving random steps and random “jumps” are intrinsically hard. In this article, we consider the analysis of one such fascinating RW, where every step is paired with its counterpart random jump. In addition to this RW being conceptually interesting, it has applications in testing of entities (components or personnel), where the entity is never allowed to make more than a prespecified number of consecutive failures. The article contains the analysis of the chain, some fascinating limiting proper…
Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials
2019
We investigate signatures of convergence for a sequence of diffusion processes on a line, in conservative force fields stemming from superharmonic potentials $U(x)\sim x^m$, $m=2n \geq 2$. This is paralleled by a transformation of each $m$-th diffusion generator $L = D\Delta + b(x)\nabla $, and likewise the related Fokker-Planck operator $L^*= D\Delta - \nabla [b(x)\, \cdot]$, into the affiliated Schr\"{o}dinger one $\hat{H}= - D\Delta + {\cal{V}}(x)$. Upon a proper adjustment of operator domains, the dynamics is set by semigroups $\exp(tL)$, $\exp(tL_*)$ and $\exp(-t\hat{H})$, with $t \geq 0$. The Feynman-Kac integral kernel of $\exp(-t\hat{H})$ is the major building block of the relaxatio…
Comparing fMRI inter-subject correlations between groups using permutation tests
2018
AbstractInter-subject correlation (ISC) based analysis is a conceptually simple approach to analyze functional magnetic resonance imaging (fMRI) data acquired under naturalistic stimuli such as a movie. We describe and validate the statistical approaches for comparing ISCs between two groups of subjects implemented in the ISC toolbox, which is an open source software package for ISC-based analysis of fMRI data. The approaches are based on permutation tests. We validated the approaches using five different data sets from the ICBM functional reference battery tasks. First, we created five null datasets (one for each task) by dividing the subjects into two matched groups and assumed that no gr…
A rapid method for the differentiation of yeast cells grown under carbon and nitrogen-limited conditions by means of partial least squares discrimina…
2012
This paper shows the ease of application and usefulness of mid-IR measurements for the investigation of orthogonal cell states on the example of the analysis of Pichia pastoris cells. A rapid method for the discrimination of entire yeast cells grown under carbon and nitrogen-limited conditions based on the direct acquisition of mid-IR spectra and partial least squares discriminant analysis (PLS-DA) is described. The obtained PLS-DA model was extensively validated employing two different validation strategies: (i) statistical validation employing a method based on permutation testing and (ii) external validation splitting the available data into two independent sub-sets. The Variable Importa…
Algebraic (2, 2)-transformation groups
2009
This paper contains the more significant part of the article with the same title that will appear in the Volume 12 of Journal of Group Theory (2009). In this paper we determine all algebraic transformation groups $G$, defined over an algebraically closed field $\sf k$, which operate transitively, but not primitively, on a variety $\Omega$, provided the following conditions are fulfilled. We ask that the (non-effective) action of $G$ on the variety of blocks is sharply 2-transitive, as well as the action on a block $\Delta$ of the normalizer $G_\Delta$. Also we require sharp transitivity on pairs $(X,Y)$ of independent points of $\Omega$, i.e. points contained in different blocks.
The pure descent statistic on permutations
2017
International audience; We introduce a new statistic based on permutation descents which has a distribution given by the Stirling numbers of the first kind, i.e., with the same distribution as for the number of cycles in permutations. We study this statistic on the sets of permutations avoiding one pattern of length three by giving bivariate generating functions. As a consequence, new classes of permutations enumerated by the Motzkin numbers are obtained. Finally, we deduce results about the popularity of the pure descents in all these restricted sets. (C) 2017 Elsevier B.V. All rights reserved.