scholarly journals Causal Domain Restriction for Eikonal Equations

2014 ◽  
Vol 36 (5) ◽  
pp. A2478-A2505 ◽  
Author(s):  
Z. Clawson ◽  
A. Chacon ◽  
A. Vladimirsky
Keyword(s):  
Domain Restriction ◽  
Eikonal Equations

The Grammar of Prominence

2021 ◽  
pp. 171-186
Author(s):  
Una Stojnić
Keyword(s):  
Context Sensitivity ◽  
Gradable Adjectives ◽  
Domain Restriction ◽  
Context Sensitive ◽  
Future Developments ◽  
Model Context ◽  
The Way

This chapter draws theoretical conclusions and outlines directions for future developments. It summarizes the key theoretical and philosophical upshots of the account developed in the book and discusses further extensions of this framework. It discusses how the account can be applied to model context-sensitivity of situated utterances, in a way that can offer insights into puzzles concerning disagreement in discourse and communication under ignorance, which have plagued standard accounts of context and content. Further, it outlines the way the account is to be extended and applied to various types of context-sensitive items, including relational expressions, gradable adjectives, and domain restriction.

Restrictionism and Expansionism

2019 ◽  
pp. 87-119
Author(s):  
J. P. Studd
Keyword(s):  
Domain Restriction ◽  
Absolute Generality ◽  
The Universe ◽  
Quantifier Domain Restriction ◽  
Universe Of Discourse

If her view is to diffuse charges of mystical censorship, the relativist needs a well-motivated account of what prevents our quantifying over an absolutely comprehensive domain. But relativists may seek to meet this challenge in different ways. One option is to draw on more familiar cases of quantifier domain restriction in order to motivate the thesis that a quantifier’s domain is always subject to restriction. An alternative is to permit unrestricted quantifiers but maintain that even these fail to attain absolute generality on the grounds that the universe of discourse is always open to expansion. This chapter outlines restrictionist and expansionist variants of relativism and argues that the importance of the distinction comes out in two influential objections that have been levelled against relativism.

A fast-marching eikonal solver for tilted transversely isotropic media

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. S385-S393
Author(s):  
Umair bin Waheed
Keyword(s):  
Transversely Isotropic ◽  
Fast Marching Method ◽  
Fast Marching ◽  
P Waves ◽  
Eikonal Equations ◽  
Transversely Isotropic Media ◽  
Fast Sweeping ◽  
Fast Marching Algorithm ◽  
Isotropic Media ◽  
And Migration

Fast and accurate traveltime computation for quasi-P waves in anisotropic media is an essential ingredient of many seismic processing and interpretation applications such as Kirchhoff modeling and migration, microseismic source localization, and traveltime tomography. Fast-sweeping methods are widely used for solving the anisotropic eikonal equation due to their flexibility in solving general equations compared to the fast-marching method. However, it has been observed that fast sweeping can be much less efficient than fast marching for models with curved characteristics and practical grid sizes. By representing a tilted transversely isotropic (TTI) equation as a sequence of elliptically isotropic (EI) eikonal equations, we determine that the fast-marching algorithm can be used to compute fast and accurate traveltimes for TTI media. The tilt angle is absorbed into the description of the effective EI model; therefore, the adopted approach does not compromise on the solution accuracy. Through tests on benchmark synthetic models, we test our fast-marching algorithm and discover considerable improvement in accuracy by using factorization and a second-order finite-difference stencil. The adopted methodology opens the door to the possibility of using the fast-marching algorithm for a wider class of anisotropic eikonal equations.

scholarly journals Poisson superposition processes

2015 ◽  
Vol 52 (04) ◽  
pp. 1013-1027
Author(s):  
Harry Crane ◽  
Peter Mccullagh
Keyword(s):  
Power Series ◽  
Poisson Process ◽  
Explicit Expression ◽  
Negative Binomial ◽  
Poisson Processes ◽  
Domain Restriction ◽  
Point Configuration ◽  
Point Configurations ◽  
Algebraic Properties ◽  
Formal Power

Superposition is a mapping on point configurations that sends the n-tuple into the n-point configuration , counted with multiplicity. It is an additive set operation such that the superposition of a k-point configuration in is a kn-point configuration in . A Poisson superposition process is the superposition in of a Poisson process in the space of finite-length -valued sequences. From properties of Poisson processes as well as some algebraic properties of formal power series, we obtain an explicit expression for the Janossy measure of Poisson superposition processes, and we study their law under domain restriction. Examples of well-known Poisson superposition processes include compound Poisson, negative binomial, and permanental (boson) processes.

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