Probabilistic Representation of Complexity

2001 ◽  
Author(s):  
Nabil I. Al-Najjar ◽  
Ramon Casadesus-Masanell ◽  
Emre Ozdenoren
Keyword(s):  
Probabilistic Representation

Probabilistic representation of harmonic currents in AC traction systems

1984 ◽  
Vol 131 (5) ◽  
pp. 181 ◽  
Author(s):  
R.E. Morrison ◽  
A.D. Clark
Keyword(s):  
Probabilistic Representation ◽  
Harmonic Currents

A Stochastic Model for the Inheritance of the Cancer Proneness Phenotype

1987 ◽  
Vol 26 (03) ◽  
pp. 117-123
Author(s):  
P. Tautu ◽  
G. Wagner
Keyword(s):  
Stochastic Model ◽  
Gaussian Process ◽  
Covariance Function ◽  
Neoplastic Disease ◽  
Disease Phenotype ◽  
Probabilistic Representation ◽  
Temporal Behaviour ◽  
Continuous Trait ◽  
Continuous Parameter ◽  
Level Zero

SummaryA continuous parameter, stationary Gaussian process is introduced as a first approach to the probabilistic representation of the phenotype inheritance process. With some specific assumptions about the components of the covariance function, it may describe the temporal behaviour of the “cancer-proneness phenotype” (CPF) as a quantitative continuous trait. Upcrossing a fixed level (“threshold”) u and reaching level zero are the extremes of the Gaussian process considered; it is assumed that they might be interpreted as the transformation of CPF into a “neoplastic disease phenotype” or as the non-proneness to cancer, respectively.

scholarly journals BSDEs with polynomial growth generators

2000 ◽  
Vol 13 (3) ◽  
pp. 207-238 ◽  
Author(s):  
Philippe Briand ◽  
René Carmona
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Polynomial Growth ◽  
Probabilistic Representation ◽  
Existence And Uniqueness Results ◽  
State Variable ◽  
Cahn Equation ◽  
Uniqueness Results ◽  
Terminal Time

In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

Using Tolerance-Maps to Generate Frequency Distributions of Clearance and Allocate Tolerances for Pin-Hole Assemblies

2007 ◽  
Vol 7 (4) ◽  
pp. 347-359 ◽  
Author(s):  
Gaurav Ameta ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Mathematical Model ◽  
Statistical Method ◽  
Frequency Distribution ◽  
Probabilistic Representation ◽  
Worst Case ◽  
Frequency Distributions ◽  
One Dimensional ◽  
Material Condition ◽  
Geometric Tolerances ◽  
Case Basis

A new mathematical model for representing the geometric variations of lines is extended to include probabilistic representations of one-dimensional (1D) clearance, which arise from positional variations of the axis of a hole, the size of the hole, and a pin-hole assembly. The model is compatible with the ASME/ ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map (T-Map) (Patent No. 69638242), a hypothetical volume of points that models the 3D variations in location and orientation for a segment of a line (the axis), which can arise from tolerances on size, position, orientation, and form. Here, it is extended to model the increases in yield that occur when maximum material condition (MMC) is specified and when tolerances are assigned statistically rather than on a worst-case basis; the statistical method includes the specification of both size and position tolerances on a feature. The frequency distribution of 1D clearance is decomposed into manufacturing bias, i.e., toward certain regions of a Tolerance-Map, and into a geometric bias that can be computed from the geometry of multidimensional T-Maps. Although the probabilistic representation in this paper is built from geometric bias, and it is presumed that manufacturing bias is uniform, the method is robust enough to include manufacturing bias in the future. Geometric bias alone shows a greater likelihood of small clearances than large clearances between an assembled pin and hole. A comparison is made between the effects of choosing the optional material condition MMC and not choosing it with the tolerances that determine the allowable variations in position.

scholarly journals Modelling the N400 brain potential as change in a probabilistic representation of meaning

2018 ◽  
Vol 2 (9) ◽  
pp. 693-705 ◽  
Author(s):  
Milena Rabovsky ◽  
Steven S. Hansen ◽  
James L. McClelland
Keyword(s):  
Probabilistic Representation ◽  
Brain Potential

scholarly journals Time fractional equations and probabilistic representation

2017 ◽  
Vol 102 ◽  
pp. 168-174 ◽  
Author(s):  
Zhen-Qing Chen
Keyword(s):  
Probabilistic Representation ◽  
Fractional Equations

Quantifying Variability in Lumbar L4-L5 Soft Tissue Properties for Use in Finite-Element Analysis

2016 ◽  
Vol 1 (3) ◽  
Author(s):  
Dana J. Coombs ◽  
Paul J. Rullkoetter ◽  
Peter J. Laz
Keyword(s):  
Finite Element ◽  
Soft Tissue ◽  
Experimental Testing ◽  
Intersubject Variability ◽  
Probabilistic Representation ◽  
Posterior Portion ◽  
Annulus Fibrosis ◽  
Interspinous Ligament ◽  
Constitutive Material Model ◽  
The Impact

Soft tissue structures of the L4-L5 level of the human lumbar spine are represented in finite-element (FE) models, which are used to evaluate spine biomechanics and implant performance. These models typically use average properties; however, experimental testing reports variation up to 40% in ligament stiffness and even greater variability for annulus fibrosis (AF) properties. Probabilistic approaches enable consideration of the impact of intersubject variability on model outputs. However, there are challenges in directly applying the variability in measured load–displacement response of structures to a finite-element model. Accordingly, the objectives of this study were to perform a comprehensive review of the properties of the L4-L5 structures and to develop a probabilistic representation to characterize variability in the stiffness of spinal ligaments and parameters of a Holzapfel–Gasser–Ogden constitutive material model of the disk. The probabilistic representation was determined based on direct mechanical test data as found in the literature. Monte Carlo simulations were used to determine the uncertainty of the Holzapfel–Gasser–Ogden constitutive model. A single stiffness parameter was defined to characterize each ligament, with the anterior longitudinal ligament (ALL) being the stiffest, while the posterior longitudinal ligament and interspinous ligament (ISL) had the greatest variation. The posterior portion of the annulus fibrosis had the greatest stiffness and greatest variation up to 300% in circumferential loading. The resulting probabilistic representation can be utilized to include intersubject variability in biomechanics evaluations.

scholarly journals On the probabilistic representation of the wind climate for calibration of structural design standards

2018 ◽  
Vol 70 ◽  
pp. 115-127 ◽  
Author(s):  
Michele Baravalle ◽  
Jochen Köhler
Keyword(s):  
Structural Design ◽  
Probabilistic Representation ◽  
Design Standards ◽  
Wind Climate

scholarly journals On the continuity of the probabilistic representation of a semilinear Neumann–Dirichlet problem

2016 ◽  
Vol 126 (2) ◽  
pp. 572-607 ◽  
Author(s):  
Lucian Maticiuc ◽  
Aurel Răşcanu
Keyword(s):  
Dirichlet Problem ◽  
Probabilistic Representation
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