Search results for "probability"
showing 10 items of 3417 documents
Macroscopic capillarity without a constitutive capillary pressure function
2006
This paper challenges the foundations of the macroscopic capillary pressure concept. The capillary pressure function, as it is traditionally assumed in the constitutive theory of two-phase immiscible displacement in porous media, relates the pressure difference between nonwetting and wetting fluid to the saturation of the wetting fluid. The traditional capillary pressure function neglects the fundamental difference between percolating and nonpercolating fluid regions as first emphasized in R. Hilfer [Macroscopic equations of motion for two phase flow in porous media, Phys. Rev. E 58 (1998) 2090]. The theoretical approach proposed here starts from residual saturations as the volume fractions…
TiFoSi: an efficient tool for mechanobiology simulations of epithelia
2020
[Motivation]: Emerging phenomena in developmental biology and tissue engineering are the result of feedbacks between gene expression and cell biomechanics. In that context, in silico experiments are a powerful tool to understand fundamental mechanisms and to formulate and test hypotheses.
Morphology changes induced by intercellular gap junction blocking: A reaction-diffusion mechanism.
2021
Complex anatomical form is regulated in part by endogenous physiological communication between cells; however, the dynamics by which gap junctional (GJ) states across tissues regulate morphology are still poorly understood. We employed a biophysical modeling approach combining different signaling molecules (morphogens) to qualitatively describe the anteroposterior and lateral morphology changes in model multicellular systems due to intercellular GJ blockade. The model is based on two assumptions for blocking-induced patterning: (i) the local concentrations of two small antagonistic morphogens diffusing through the GJs along the axial direction, together with that of an independent, uncouple…
Response models for mixed binary and quantitative variables
1992
SUMMARY A number of special representations are considered for the joint distribution of qualitative, mostly binary, and quantitative variables. In addition to the conditional Gaussian models and to conditional Gaussian regression chain models some emphasis is placed on models derived from an underlying multivariate normal distribution and on models in which discrete probabilities are specified linearly in terms of unknown parameters. The possibilities for choosing between the models empirically are examined, as well as the testing of independence and conditional independence and the estimation of parameters. Often the testing of independence is exactly or nearly the same for a number of di…
Hölder Continuity up to the Boundary of Minimizers for Some Integral Functionals with Degenerate Integrands
2007
We study qualitative properties of minimizers for a class of integral functionals, defined in a weighted space. In particular we obtain Hölder regularity up to the boundary for the minimizers of an integral functional of high order by using an interior local regularity result and a modified Moser method with special test function.
Consensus among preference rankings: a new weighted correlation coefficient for linear and weak orderings
2021
AbstractPreference data are a particular type of ranking data where some subjects (voters, judges,...) express their preferences over a set of alternatives (items). In most real life cases, some items receive the same preference by a judge, thus giving rise to a ranking with ties. An important issue involving rankings concerns the aggregation of the preferences into a “consensus”. The purpose of this paper is to investigate the consensus between rankings with ties, taking into account the importance of swapping elements belonging to the top (or to the bottom) of the ordering (position weights). By combining the structure of $$\tau _x$$ τ x proposed by Emond and Mason (J Multi-Criteria Decis…
Flow of Homeomorphisms and Stochastic Transport Equations
2007
Abstract We consider Stratonovich stochastic differential equations with drift coefficient A 0 satisfying only the condition of continuity where r is a positive C 1 function defined on a neighborhood ]0, c 0] of 0 such that (Osgood condition), and s → r(s) is decreasing while s → sr(s 2) is increasing. We prove that the equation defines a flow of homeomorphisms if the diffusion coefficients A 1,…, A N are in . If , we prove limit theorems for Wong–Zakai approximation as well as for regularizing the drift A 0. As an application, we solve a class of stochastic transport equations.
Power of the Wilcoxon–Mann–Whitney test for non‐inferiority in the presence of death‐censored observations
2017
In clinical trials with patients in a critical state, death may preclude measurement of a quantitative endpoint of interest, and even early measurements, for example for intention-to-treat analysis, may not be available. For example, a non-negligible proportion of patients with acute pulmonary embolism will die before 30 day measurements on the efficacy of thrombolysis can be obtained. As excluding such patients may introduce bias, alternative analyses, and corresponding means for sample size calculation are needed. We specifically consider power analysis in a randomized clinical trial setting in which the goal is to demonstrate noninferiority of a new treatment as compared to a reference t…
Opportunities and challenges of combined effect measures based on prioritized outcomes
2013
Many authors have proposed different approaches to combine multiple endpoints in a univariate outcome measure in the literature. In case of binary or time-to-event variables, composite endpoints, which combine several event types within a single event or time-to-first-event analysis are often used to assess the overall treatment effect. A main drawback of this approach is that the interpretation of the composite effect can be difficult as a negative effect in one component can be masked by a positive effect in another. Recently, some authors proposed more general approaches based on a priority ranking of outcomes, which moreover allow to combine outcome variables of different scale levels. …
Sample size planning for survival prediction with focus on high-dimensional data
2011
Sample size planning should reflect the primary objective of a trial. If the primary objective is prediction, the sample size determination should focus on prediction accuracy instead of power. We present formulas for the determination of training set sample size for survival prediction. Sample size is chosen to control the difference between optimal and expected prediction error. Prediction is carried out by Cox proportional hazards models. The general approach considers censoring as well as low-dimensional and high-dimensional explanatory variables. For dimension reduction in the high-dimensional setting, a variable selection step is inserted. If not all informative variables are included…