23,405 research outputs found
Transient Response Dynamic Module Modifications to Include Static and Kinetic Friction Effects
A methodology that supports forced transient response dynamic solutions when both static and kinetic friction effects are included in a structural system model is described. Modifications that support this type of nonlinear transient response solution are summarized for the transient response dynamics (TRD) NASTRAN module. An overview of specific modifications for the NASTRAN processing subroutines, INITL, TRD1C, and TRD1D, are described with further details regarding inspection of nonlinear input definitions to define the type of nonlinear solution required, along with additional initialization requirements and specific calculation subroutines to successfully solve the transient response problem. The extension of the basic NASTRAN nonlinear methodology is presented through several stages of development to the point where constraint equations and residual flexibility effects are introduced into the finite difference Newmark-Beta recurrsion formulas. Particular emphasis is placed on cost effective solutions for large finite element models such as the Space Shuttle with friction degrees of freedom between the orbiter and payloads mounted in the cargo bay. An alteration to the dynamic finite difference equations of motion is discussed, which allows one to include friction effects at reasonable cost for large structural systems such as the Space Shuttle. Data are presented to indicate the possible impact of transient friction loads to the payload designer for the Space Shuttle. Transient response solution data are also included, which compare solutions without friction forces and those with friction forces for payloads mounted in the Space Shuttle cargo bay. These data indicate that payload components can be sensitive to friction induced loads
To Teach Modal Logic: An Opinionated Survey
I aim to promote an alternative agenda for teaching modal logic chiefly
inspired by the relationships between modal logic and philosophy. The guiding
idea for this proposal is a reappraisal of the interest of modal logic in
philosophy, which do not stem mainly from mathematical issues, but which is
motivated by central problems of philosophy and language. I will point out some
themes to start elaborating a guide for a more comprehensive approach to teach
modal logic, and consider the contributions of dual-process theories in
cognitive science, in order to explore a pedagogical framework for the proposed
point of view.Comment: Proceedings of the Fourth International Conference on Tools for
Teaching Logic (TTL2015), Rennes, France, June 9-12, 2015. Editors: M.
Antonia Huertas, Jo\~ao Marcos, Mar\'ia Manzano, Sophie Pinchinat,
Fran\c{c}ois Schwarzentrube
The hardness of the iconic must: Can Peirceâs existential graphs assist modal epistemology?
The current of development in 20th century logic bypassed Peirceâs existential graphs, but recently much good work has been done by formal logicians excavating the graphs from Peirceâs manuscripts, regularizing them and demonstrating the soundness and completeness of the alpha and beta systems (e.g. Roberts 1973, Hammer 1998, Shin 2002). However, given that Peirce himself considered the graphs to be his âchef dâoeuvreâ in logic, and explored the distinction between icons, indices and symbols in detail within the context of a much larger theory of signs, much about the graphs arguably remains to be thought through from the perspective of philosophical logic. For instance, are the graphs always merely of heuristic value or can they convey an âessential iconâ (analogous to the now standardly accepted âessential indexicalâ)? This paper claims they can and do, and suggests important consequences follow from this for the epistemology of modality. It is boldly suggested that structural articulation, which is characteristic of icons alone, is the source of all necessity. In other words, recognizing a statement as necessarily true consists only in an unavoidable recognition that a structure has the particular structure that it in fact has. (What else could it consist in?
The hardness of the iconic must: Can Peirceâs existential graphs assist modal epistemology?
Charles Peirceâs diagrammatic logic - the Existential Graphs - is presented as a tool for illuminating how we know necessity, in answer to Benacerrafâs famous challenge that most âsemantics for mathematicsâ do not âfit an acceptable epistemologyâ. It is suggested that necessary reasoning is in essence a recognition that a certain structure has the structure that it has. This means that, contra Hume and his contemporary heirs, necessity is observable. One just needs to pay attention, not just to individual things but to how those things are related in larger structures, certain aspects of which force certain others to be a particular way
Bayesian model search and multilevel inference for SNP association studies
Technological advances in genotyping have given rise to hypothesis-based
association studies of increasing scope. As a result, the scientific hypotheses
addressed by these studies have become more complex and more difficult to
address using existing analytic methodologies. Obstacles to analysis include
inference in the face of multiple comparisons, complications arising from
correlations among the SNPs (single nucleotide polymorphisms), choice of their
genetic parametrization and missing data. In this paper we present an efficient
Bayesian model search strategy that searches over the space of genetic markers
and their genetic parametrization. The resulting method for Multilevel
Inference of SNP Associations, MISA, allows computation of multilevel posterior
probabilities and Bayes factors at the global, gene and SNP level, with the
prior distribution on SNP inclusion in the model providing an intrinsic
multiplicity correction. We use simulated data sets to characterize MISA's
statistical power, and show that MISA has higher power to detect association
than standard procedures. Using data from the North Carolina Ovarian Cancer
Study (NCOCS), MISA identifies variants that were not identified by standard
methods and have been externally ``validated'' in independent studies. We
examine sensitivity of the NCOCS results to prior choice and method for
imputing missing data. MISA is available in an R package on CRAN.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS322 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Fixed-point elimination in the intuitionistic propositional calculus
It is a consequence of existing literature that least and greatest
fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic
models of the Intuitionistic Propositional Calculus-always exist, even when
these algebras are not complete as lattices. The reason is that these extremal
fixed-points are definable by formulas of the IPC. Consequently, the
-calculus based on intuitionistic logic is trivial, every -formula
being equivalent to a fixed-point free formula. We give in this paper an
axiomatization of least and greatest fixed-points of formulas, and an algorithm
to compute a fixed-point free formula equivalent to a given -formula. The
axiomatization of the greatest fixed-point is simple. The axiomatization of the
least fixed-point is more complex, in particular every monotone formula
converges to its least fixed-point by Kleene's iteration in a finite number of
steps, but there is no uniform upper bound on the number of iterations. We
extract, out of the algorithm, upper bounds for such n, depending on the size
of the formula. For some formulas, we show that these upper bounds are
polynomial and optimal
- âŠ