Modelling optical fibre cable

Optical fibre cables are made by placing optical fibres inside a loose tube packed with a water based gel, and then winding these loose tubes on to a central strength member in helically wound sections of alternating twist separated by reversing sections. The length of the loose tubes and their position on the strength member was modelled along with an analysis of where the optical fibres lie in the loose tubes

A note on the 1-prevalence of continuous images with full Hausdorff dimension

We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. It is known that for a prevalent (in the sense of Hunt, Sauer and Yorke) set of functions the Hausdorff dimension of the image is as large as possible, namely 1. We extend this result by showing that `prevalent' can be replaced by `1-prevalent', i.e. it is possible to \emph{witness} this prevalence using a measure supported on a one dimensional subspace. Such one dimensional measures are called \emph{probes} and their existence indicates that the structure and nature of the prevalence is simpler than if a more complicated `infinite dimensional' witnessing measure has to be used.Comment: 8 page

Biological Systems from an Engineer’s Point of View

Mathematical modeling of the processes that pattern embryonic development (often called biological pattern formation) has a long and rich history [1,2]. These models proposed sets of hypothetical interactions, which, upon analysis, were shown to be capable of generating patterns reminiscent of those seen in the biological world, such as stripes, spots, or graded properties. Pattern formation models typically demonstrated the sufficiency of given classes of mechanisms to create patterns that mimicked a particular biological pattern or interaction. In the best cases, the models were able to make testable predictions [3], permitting them to be experimentally challenged, to be revised, and to stimulate yet more experimental tests (see review in [4]). In many other cases, however, the impact of the modeling efforts was mitigated by limitations in computer power and biochemical data. In addition, perhaps the most limiting factor was the mindset of many modelers, using Occam’s razor arguments to make the proposed models as simple as possible, which often generated intriguing patterns, but those patterns lacked the robustness exhibited by the biological system. In hindsight, one could argue that a greater attention to engineering principles would have focused attention on these shortcomings, including potential failure modes, and would have led to more complex, but more robust, models. Thus, despite a few successful cases in which modeling and experimentation worked in concert, modeling fell out of vogue as a means to motivate decisive test experiments. The recent explosion of molecular genetic, genomic, and proteomic data—as well as of quantitative imaging studies of biological tissues—has changed matters dramatically, replacing a previous dearth of molecular details with a wealth of data that are difficult to fully comprehend. This flood of new data has been accompanied by a new influx of physical scientists into biology, including engineers, physicists, and applied mathematicians [5–7]. These individuals bring with them the mindset, methodologies, and mathematical toolboxes common to their own fields, which are proving to be appropriate for analysis of biological systems. However, due to inherent complexity, biological systems seem to be like nothing previously encountered in the physical sciences. Thus, biological systems offer cutting edge problems for most scientific and engineering-related disciplines. It is therefore no wonder that there might seem to be a “bandwagon” of new biology-related research programs in departments that have traditionally focused on nonliving systems. Modeling biological interactions as dynamical systems (i.e., systems of variables changing in time) allows investigation of systems-level topics such as the robustness of patterning mechanisms, the role of feedback, and the self-regulation of size. The use of tools from engineering and applied mathematics, such as sensitivity analysis and control theory, is becoming more commonplace in biology. In addition to giving biologists some new terminology for describing their systems, such analyses are extremely useful in pointing to missing data and in testing the validity of a proposed mechanism. A paper in this issue of PLoS Biology clearly and honestly applies analytical tools to the authors’ research and obtains insights that would have been difficult if not impossible by other means [8]

Now the wars are over: The past, present and future of Scottish battlefields

Battlefield archaeology has provided a new way of appreciating historic battlefields. This paper provides a summary of the long history of warfare and conflict in Scotland which has given rise to a large number of battlefield sites. Recent moves to highlight the archaeological importance of these sites, in the form of Historic Scotland’s Battlefields Inventory are discussed, along with some of the problems associated with the preservation and management of these important cultural sites

Variation in HIV-1 set-point viral load: epidemiological analysis and an evolutionary hypothesis.

The natural course of HIV-1 infection is characterized by a high degree of heterogeneity in viral load, not just within patients over time, but also between patients, especially during the asymptomatic stage of infection. Asymptomatic, or set-point, viral load has been shown to correlate with both decreased time to AIDS and increased infectiousness. The aim of this study is to characterize the epidemiological impact of heterogeneity in set-point viral load. By analyzing two cohorts of untreated patients, we quantify the relationships between both viral load and infectiousness and the duration of the asymptomatic infectious period. We find that, because both the duration of infection and infectiousness determine the opportunities for the virus to be transmitted, this suggests a trade-off between these contributions to the overall transmission potential. Some public health implications of variation in set-point viral load are discussed. We observe that set-point viral loads are clustered around those that maximize the transmission potential, and this leads us to hypothesize that HIV-1 could have evolved to optimize its transmissibility, a form of adaptation to the human host population. We discuss how this evolutionary hypothesis can be tested, review the evidence available to date, and highlight directions for future research

The first definitive Middle Jurassic atoposaurid (Crocodylomorpha, Neosuchia), and a discussion on the genus Theriosuchus

Atoposaurids were a clade of semiaquatic crocodyliforms known from the Late Jurassic to the latest Cretaceous. Tentative remains from Europe, Morocco, and Madagascar may extend their range into the Middle Jurassic. Here we report the first unambiguous Middle Jurassic (late Bajocian–Bathonian) atoposaurid: an anterior dentary from the Isle of Skye, Scotland, UK. A comprehensive review of atoposaurid specimens demonstrates that this dentary can be referred to Theriosuchus based on several derived characters, and differs from the five previously recognized species within this genus. Despite several diagnostic features, we conservatively refer it to Theriosuchus sp., pending the discovery of more complete material. As the oldest known definitively diagnostic atoposaurid, this discovery indicates that the oldest members of this group were small-bodied, had heterodont dentition, and were most likely widespread components of European faunas. Our review of mandibular and dental features in atoposaurids not only allows us to present a revised diagnosis of Theriosuchus, but also reveals a great amount of variability within this genus, and indicates that there are currently five valid species that can be differentiated by unique combinations of dental characteristics. This variability can be included in future broad-scale cladistics analyses of atoposaurids and closely related crocodyliforms, which promise to help untangle the complicated taxonomy and evolutionary history of Atoposauridae