175,442 research outputs found
Development of a Translator from LLVM to ACL2
In our current work a library of formally verified software components is to
be created, and assembled, using the Low-Level Virtual Machine (LLVM)
intermediate form, into subsystems whose top-level assurance relies on the
assurance of the individual components. We have thus undertaken a project to
build a translator from LLVM to the applicative subset of Common Lisp accepted
by the ACL2 theorem prover. Our translator produces executable ACL2 formal
models, allowing us to both prove theorems about the translated models as well
as validate those models by testing. The resulting models can be translated and
certified without user intervention, even for code with loops, thanks to the
use of the def::ung macro which allows us to defer the question of termination.
Initial measurements of concrete execution for translated LLVM functions
indicate that performance is nearly 2.4 million LLVM instructions per second on
a typical laptop computer. In this paper we overview the translation process
and illustrate the translator's capabilities by way of a concrete example,
including both a functional correctness theorem as well as a validation test
for that example.Comment: In Proceedings ACL2 2014, arXiv:1406.123
Evolution PDEs and augmented eigenfunctions. I finite interval
The so-called unified method expresses the solution of an initial-boundary value problem for an evolution PDE in the finite interval in terms of an integral in the complex Fourier (spectral) plane. Simple initial-boundary value problems, which will be referred to as problems of type~I, can be solved via a classical transform pair. For example, the Dirichlet problem of the heat equation can be solved in terms of the transform pair associated with the Fourier sine series. Such transform pairs can be constructed via the spectral analysis of the associated spatial operator. For more complicated initial-boundary value problems, which will be referred to as problems of type~II, there does \emph{not} exist a classical transform pair and the solution \emph{cannot} be expressed in terms of an infinite series. Here we pose and answer two related questions: first, does there exist a (non-classical) transform pair capable of solving a type~II problem, and second, can this transform pair be constructed via spectral analysis? The answer to both of these questions is positive and this motivates the introduction of a novel class of spectral entities. We call these spectral entities augmented eigenfunctions, to distinguish them from the generalised eigenfunctions introduced in the sixties by Gel'fand and his co-authors
Molecular dynamics study of nanoparticle stability at liquid interfaces : effect of nanoparticle-solvent interaction and capillary waves
While the interaction of colloidal particles (sizes in excess of 100 nm) with liquid interfaces may be understood in terms of continuum models, which are grounded in macroscopic properties such as surface and line tensions, the behaviour of nanoparticles at liquid interfaces may be more complex. Recent simulations [D. L. Cheung and S. A. F. Bon, Phys. Rev. Lett. 102, 066103 (2009)] of nanoparticles at an idealised liquid-liquid interface showed that the nanoparticle-interface interaction range was larger than expected due, in part, to the action of thermal capillary waves. In this paper, molecular dynamics simulations of a Lennard-Jones nanoparticle in a binary Lennard-Jones mixture are used to confirm that these previous results hold for more realistic models. Furthermore by including attractive interactions between the nanoparticle and the solvent, it is found that the detachment energy decreases as the nanoparticle-solvent attraction increases. Comparison between the simulation results and recent theoretical predictions [H. Lehle and M. Oettel, J. Phys. Condens. Matter 20, 404224 (2008)] shows that for small particles the incorporation of capillary waves into the predicted effective nanoparticle-interface interaction improves agreement between simulation and theory
Oxygen isotopic paleotemperatures across the Runangan-Whaingaroan (Eocene-Oligocene) boundary in a New Zealand shelf sequence
Oxygen isotopic compositions of the tests of mainly benthic foraminifera, from sections of conformable Late Eocene (Runangan) to Early Oligocene (Whaingaroan) shelf mudstones, at both Cape Foulwind and Port Elizabeth, western South Island, indicate that shelf sea paleotemperatures followed the global open-ocean trend towards a Paleogene minimum near the Eocene-Oligocene boundary. Throughout the latest Eocene, temperatures declined steadily by 3°C, showed a temporary minor warming at the Eocenc-Oligocene boundary, dropped sharply by 2°C in the Early Oligocene, and ameliorated significantly later in the Early Oligocene. The qualitative temperature trends for New Zealand shelf waters at this time are similar to those inferred from earlier paleontologic syntheses and limited oxygen isotopic work, but involve a range of temperatures within the warm and cool temperate climatic zones and an absolute temperature depression across the Eocene-Oligocene boundary of only 5°C from about 17 to 12°C. Results are consistent with isotopic paleotemperatures determined from deep-sea sediment cores south of New Zealand where the cooling is inferred to mark the onset of production of Antarctic bottom waters at near-freezing temperatures
ecp: An R Package for Nonparametric Multiple Change Point Analysis of Multivariate Data
There are many different ways in which change point analysis can be
performed, from purely parametric methods to those that are distribution free.
The ecp package is designed to perform multiple change point analysis while
making as few assumptions as possible. While many other change point methods
are applicable only for univariate data, this R package is suitable for both
univariate and multivariate observations. Estimation can be based upon either a
hierarchical divisive or agglomerative algorithm. Divisive estimation
sequentially identifies change points via a bisection algorithm. The
agglomerative algorithm estimates change point locations by determining an
optimal segmentation. Both approaches are able to detect any type of
distributional change within the data. This provides an advantage over many
existing change point algorithms which are only able to detect changes within
the marginal distributions
- …