Search results for "Statistical"
showing 10 items of 4960 documents
Non-Periodic Systems with Continuous Diffraction Measures
2015
The present state of mathematical diffraction theory for systems with continuous spectral components is reviewed and extended. We begin with a discussion of various characteristic examples with singular or absolutely continuous diffraction, and then continue with a more general exposition of a systematic approach via stationary stochastic point processes. Here, the intensity measure of the Palm measure takes the role of the autocorrelation measure in the traditional approach. We furthermore introduce a ‘Palm-type’ measure for general complex-valued random measures that are stationary and ergodic, and relate its intensity measure to the autocorrelation measure.
Analysis of random walks on a hexagonal lattice
2019
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a 2-dimensional Brownian motion is also discussed. Furthermore, we obtain some results on its asymptotic behavior making use of large deviation theory. Finally, we investigate the first-passage-time problem of the random walk through a vertical straight-line. Under suitable symmetry assumptions we are able to determine the first-passage-time probabilities in a closed form, which deserve interest in applied fields.
AKNS and NLS hierarchies, MRW solutions, $P_n$ breathers, and beyond
2018
We describe a unified structure of rogue wave and multiple rogue wave solutions for all equations of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and their mixed and deformed versions. The definition of the AKNS hierarchy and its deformed versions is given in the Sec. II. We also consider the continuous symmetries of the related equations and the related spectral curves. This work continues and summarises some of our previous studies dedicated to the rogue wave-like solutions associated with AKNS, nonlinear Schrodinger, and KP hierarchies. The general scheme is illustrated by the examples of small rank n, n ⩽ 7, rational or quasi-rational solutions. In particular, we consider rank-2 and …
Periodic Classification of Local Anaesthetics (Procaine Analogues)
2006
Algorithms for classification are proposed based on criteria (information entropyand its production). The feasibility of replacing a given anaesthetic by similar ones in thecomposition of a complex drug is studied. Some local anaesthetics currently in use areclassified using characteristic chemical properties of different portions of their molecules.Many classification algorithms are based on information entropy. When applying theseprocedures to sets of moderate size, an excessive number of results appear compatible withdata, and this number suffers a combinatorial explosion. However, after the equipartitionconjecture, one has a selection criterion between different variants resulting fromc…
Contextuality Analysis of the Double Slit Experiment (With a Glimpse Into Three Slits)
2018
The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The experiment is described by a system of contextually labeled binary random variables each of which answers the question: has the particle hit the detector, having passed through a given slit (left or right) in a given state (open or closed)? This system of random variables is a cyclic system of rank 4, formally the same as the system describing the EPR/Bell paradigm with signaling. Unlike the latter, however, the system describing the double-slit experiment is always noncontextual, i.e., the context-dependence in it is entirely explainable in terms of direct influences of…
Quantifying biochemical reaction rates from static population variability within complex networks
2021
Quantifying biochemical reaction rates within complex cellular processes remains a key challenge of systems biology even as high-throughput single-cell data have become available to characterize snapshots of population variability. That is because complex systems with stochastic and non-linear interactions are difficult to analyze when not all components can be observed simultaneously and systems cannot be followed over time. Instead of using descriptive statistical models, we show that incompletely specified mechanistic models can be used to translate qualitative knowledge of interactions into reaction rate functions from covariability data between pairs of components. This promises to tur…
A Lotka-type model for oscillations in surface reactions
1997
In this paper we introduce a reaction model on a lattice which leads to oscillations. The model consists of two monomolecular and one bimolecular reaction step and is related to the Lotka model. Despite the simple evolution rules, the model shows a complex behaviour (i.e. the appearance of oscillations). This offers us the opportunity to test different types of stochastic approximations and compare them with the results of a Monte Carlo simulation. The simulation is performed on a large lattice (L = 1024) in order to take long-range correlations into account. Comparing the results of this simulation with the stochastic approaches shows that only advanced numerical approximations are able to…
A statistical analysis of the three-fold evolution of genomic compression through frame overlaps in prokaryotes
2007
Abstract Background Among microbial genomes, genetic information is frequently compressed, exploiting redundancies in the genetic code in order to store information in overlapping genes. We investigate the length, phase and orientation properties of overlap in 58 prokaryotic species evaluating neutral and selective mechanisms of evolution. Results Using a variety of statistical null models we find patterns of compressive coding that can not be explained purely in terms of the selective processes favoring genome minimization or translational coupling. The distribution of overlap lengths follows a fat-tailed distribution, in which a significant proportion of overlaps are in excess of 100 base…
Genetic variants linked to myopic macular degeneration in persons with high myopia: CREAM Consortium.
2019
Purpose: To evaluate the roles of known myopia-associated genetic variants for development of myopic macular degeneration (MMD) in individuals with high myopia (HM), using case-control studies from the Consortium of Refractive Error and Myopia (CREAM). Methods: A candidate gene approach tested 50 myopia-associated loci for association with HM and MMD, using meta-analyses of case-control studies comprising subjects of European and Asian ancestry aged 30 to 80 years from 10 studies. Fifty loci with the strongest associations with myopia were chosen from a previous published GWAS study. Highly myopic (spherical equivalent [SE] ≤ -5.0 diopters [D]) cases with MMD (N = 348), and two sets of cont…
Bleeding symptoms at disease presentation and prediction of ensuing bleeding in inherited FVII deficiency.
2012
SummaryIndividuals with inherited factor VII (FVII) deficiency display bleeding phenotypes ranging from mild to severe, with 30% of patients having always been asymptomatic (non-bleeding). In 626 FVII-deficient individuals, by analysing data from the International Factor VII (IF7) Registry and the Seven Treatment Evaluation Registry (STER), we determined whether bleeding type at disease presentation and FVII coagulant activity (FVIIc) predict ensuing bleeds. At disease presentation/diagnosis, 272 (43.5%) individuals were non-bleeding, 277 (44.2%) had minor bleeds, and 77 (12.3%) had major bleeds. During a median nine-year index period (IP) observation, 87.9% of non-bleeding individuals at p…