On the construction of probabilistic Newton-type algorithms

It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start assembling probabilistic Newton-type algorithms, applicable in situations where we only have access to noisy observations of the cost function and its derivatives. This is where our interest lies. We make contributions to the use of the non-parametric and probabilistic Gaussian process models in solving these stochastic optimisation problems. Specifically, we present a new algorithm that unites these approximations together with recent probabilistic line search routines to deliver a probabilistic quasi-Newton approach. We also show that the probabilistic optimisation algorithms deliver promising results on challenging nonlinear system identification problems where the very nature of the problem is such that we can only access the cost function and its derivative via noisy observations, since there are no closed-form expressions available

What is the object of the encapsulation of a process?

Several theories have been proposed to describe the transition from process to object in mathematical thinking. Yet, what is the nature of this ''object'' produced by the ''encapsulation'' of a process? Here, we outline the development of some of the theories (including Piaget, Dienes, Davis, Greeno, Dubinsky, Sfard, Gray, and Tall) and consider the nature of the mental objects (apparently) produced through encapsulation and their role in the wider development of mathematical thinking. Does the same developmental route occur in geometry as in arithmetic and algebra? Is the same development used in axiomatic mathematics? What is the role played by imagery

Abyssal fauna of the UK-1 polymetallic nodule exploration area, Clarion-Clipperton Zone, central Pacific Ocean: Mollusca

The file attached is the Published/publisher’s pdf version of the article. This is an OpenAccess article.Copyright Helena Wiklund et al. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Improving techniques for the WaxTag® possum (Trichosurus vulpecula) monitoring index

To manage brushtail possums (Trichosurus vulpecula) accurate estimates of abundance are essential. Direct counts are not feasible for large populations and index techniques are normally employed. A new index technique for estimating possum abundance is the WaxTag®. They are potentially more effective than traps because they are small, easier to use, very lightweight and, therefore, higher numbers can be set out in the field. Whilst a national monitoring protocol for WaxTag®s has been developed, it is important to determine whether improvements can be made. This study investigated firstly whether luminescent-coloured WaxTag®s were more attractive than the WaxTag® with a ‘flour blaze’ and, secondly, whether raising the WaxTag®s 700 mm above the ground reduced detectability. Possums significantly preferred the flour blaze over luminescence and raising WaxTag®s did not significantly reduce detectability. Accordingly, WaxTag®s could be raised up above ground-dwelling non-target species without reducing statistical precision

Inverted appendix mistaken for a polyp during colonoscopy and leading to intussusception

AbstractA spectrum of appendiceal diseases, ranging from simple mucous distension to acute perforated appendicitis, are seen in patients with CF. We report a 6 year old boy with CF and recurrent periumbilical pain. During colonoscopy, a fleshy pedunculated mass at the junction of the ascending colon and caecum was mistaken for a polyp and excised. However, histopathological examination suggested it was a segment of inverted appendix. The remnant of the inverted appendix was subsequently found to be associated with an intussusception