The Cambridge controversies in the theory of capital: contributions from the complex plane

A controversy in capital theory concerns reswitching. When two production techniques are compared, reswitching occurs when one technique is cheapest at low interest rates, switches to being more expensive at higher rates, and then reswitches to being cheapest at yet higher rates. Some believe this inconsistency undermines neoclassical economics. The time-value-of-money (TVM) equation is at the core of the puzzle. The equation is a polynomial having n roots, implying n interest rates. In most analyses, including reswitching, one interest rate is used and the remaining rates are ignored. This analysis demonstrates that every TVM equation has a ‘dual’ form employing all interest rates. The dual of the reswitching equation explains the puzzle

Rethinking the Patch Test for Phase Measuring Bathymetric Sonars

While conducting hydrographic survey operations in the Florida Keys, NOAA Ship Thomas Jefferson served as a test platform for the initial operational implementation of an L-3 Klein HydroChart 5000 Swath Bathymetry Sonar System1 , a hull-mounted phase measuring bathymetric sonar (PMBS). During the project it became apparent that the traditional patch test typically utilized for multibeam echosounder (MBES) systems was poorly suited to the HydroChart – and perhaps other PMBS systems as well. These systems have several inherent characteristics that make it difficult to isolate and subsequently solve for biases under the traditional patch test paradigm: presence of a nadir gap, wide swaths (typically greater than 6 times water depth), and relatively poor object-detection capability in the outer swath. After “rethinking” the patch test to account for these characteristics, the authors propose a new patch test paradigm that is better suited to the HydroChart and other PMBS systems

Multipliers of embedded discs

We consider a number of examples of multiplier algebras on Hilbert spaces associated to discs embedded into a complex ball in order to examine the isomorphism problem for multiplier algebras on complete Nevanlinna-Pick reproducing kernel Hilbert spaces. In particular, we exhibit uncountably many discs in the ball of $\ell^2$ which are multiplier biholomorphic but have non-isomorphic multiplier algebras. We also show that there are closed discs in the ball of $\ell^2$ which are varieties, and examine their multiplier algebras. In finite balls, we provide a counterpoint to a result of Alpay, Putinar and Vinnikov by providing a proper rational biholomorphism of the disc onto a variety $V$ in $\mathbb B_2$ such that the multiplier algebra is not all of $H^\infty(V)$. We also show that the transversality property, which is one of their hypotheses, is a consequence of the smoothness that they require.Comment: 34 pages; the earlier version relied on a result of Davidson and Pitts that the fibre of the maximal ideal space of the multiplier algebra over a point in the open ball consists only of point evaluation. This result fails for $d = \infty$, and has necessitated some changes; to appear in Complex Analysis and Operator Theor

Automated Hate Speech Detection and the Problem of Offensive Language

A key challenge for automatic hate-speech detection on social media is the separation of hate speech from other instances of offensive language. Lexical detection methods tend to have low precision because they classify all messages containing particular terms as hate speech and previous work using supervised learning has failed to distinguish between the two categories. We used a crowd-sourced hate speech lexicon to collect tweets containing hate speech keywords. We use crowd-sourcing to label a sample of these tweets into three categories: those containing hate speech, only offensive language, and those with neither. We train a multi-class classifier to distinguish between these different categories. Close analysis of the predictions and the errors shows when we can reliably separate hate speech from other offensive language and when this differentiation is more difficult. We find that racist and homophobic tweets are more likely to be classified as hate speech but that sexist tweets are generally classified as offensive. Tweets without explicit hate keywords are also more difficult to classify.Comment: To appear in the Proceedings of ICWSM 2017. Please cite that versio

Properties of developmental gene regulatory networks

The modular components, or subcircuits, of developmental gene regulatory networks (GRNs) execute specific developmental functions, such as the specification of cell identity. We survey examples of such subcircuits and relate their structures to corresponding developmental functions. These relations transcend organisms and genes, as illustrated by the similar structures of the subcircuits controlling the specification of the mesectoderm in the Drosophila embryo and the endomesoderm in the sea urchin, even though the respective subcircuits are composed of nonorthologous regulatory genes

Screw pile design optimisation under tension in sand

Many applications in offshore engineering, such as floating or jacket-founded wind turbines or wave energy converters, require a significant uplift capacity of their foundations to be kept in place. Straight-shafted or suction piles in sands have a limited uplift capacity as they resist by friction only. In contrast, screw piles or screw anchors are a promising solution which provides a similar capacity to plate anchors and does not generate disturbance for marine mammals (e.g. from pile driving operations). The optimisation of the screw pile design does not rely only on the geotechnical assessment of the uplift capacity based on soil strength, but also on operational (installation requirements) and structural (helix bending, core section stress, limiting steel plate thick-ness) constraints. This paper develops a methodology for the design optimisation of screw piles under pure ten-sion in sand, incorporating all of these constraints, based on simplified analytical or semi-analytical approaches. The results show that the uplift capacity provided by an optimised screw pile is able to meet the needs of the offshore industry, across a range of soil densities and different applications (jacket foundation pile or tension leg platform anchor), providing that adequate installation plant could be dev

On the Social Traits of Luminous Blue Variables

In a recent paper, Smith and Tombleson (2015) state that the Luminous Blue Variables (LBVs) in the Milky Way and the Magellanic Clouds are isolated; that they are not spatially associated with young O-type stars. They propose a novel explanation that would overturn the standard view of LBVs. In this paper we test their hypothesis for the LBVs in M31 and M33 as well as the LMC and SMC. In M31 and M33, the LBVs are associated with luminous young stars and supergiants appropriate to their luminosities and positions on the HR Diagram. Moreover, in the Smith and Tombleson scenario most of the LBVs should be runaway stars, but the stars' velocities are consistent with their positions in the respective galaxies. In the Magellanic Clouds, those authors' sample was a mixed population. We reassess their analysis, removing seven stars that have no clear relation to LBVs. When we separate the more massive classical and the less luminous LBVs, the classical LBVs have a distribution similar to the late O-type stars, while the less luminous LBVs have a distribution like the red supergiants. None of the confirmed LBVs have high velocities or are candidate runaway stars. These results support the accepted description of LBVs as evolved massive stars that have shed a lot of mass, and are now close to their Eddington limit.Comment: To appear in the Astrophysical Journal With an expanded discussion of statistical error