Montgomery's method of polynomial selection for the number field sieve

The number field sieve is the most efficient known algorithm for factoring large integers that are free of small prime factors. For the polynomial selection stage of the algorithm, Montgomery proposed a method of generating polynomials which relies on the construction of small modular geometric progressions. Montgomery's method is analysed in this paper and the existence of suitable geometric progressions is considered

Fast systematic encoding of multiplicity codes

We present quasi-linear time systematic encoding algorithms for multiplicity codes. The algorithms have their origins in the fast multivariate interpolation and evaluation algorithms of van der Hoeven and Schost (2013), which we generalise to address certain Hermite-type interpolation and evaluation problems. By providing fast encoding algorithms for multiplicity codes, we remove an obstruction on the road to the practical application of the private information retrieval protocol of Augot, Levy-dit-Vehel and Shikfa (2014)

Transformées rapides sur les corps finis de caractéristique deux

We describe new fast algorithms for evaluation and interpolation on the "novel" polynomial basis over finite fields of characteristic two introduced by Lin, Chung and Han (FOCS 2014). Fast algorithms are also described for converting between their basis and the monomial basis, as well as for converting to and from the Newton basis associated with the evaluation points of the evaluation and interpolation algorithms. Combining algorithms yields a new truncated additive fast Fourier transform (FFT) and inverse truncated additive FFT which improve upon some previous algorithms when the field possesses an appropriate tower of subfields

Immunological cross-reactivity and neutralisation of European viper venoms with the monospecific Vipera berus antivenom ViperaTAb.

Medically important cases of snakebite in Europe are predominately caused by European vipers of the genus Vipera. The mainstay of snakebite therapy is polyclonal antibody therapy, referred to as antivenom. Here we investigate the capability of the monospecific V. berus antivenom, ViperaTAb®, to cross-react with, and neutralise lethality induced by, a variety of European vipers. Using ELISA and immunoblotting, we find that ViperaTAb® antibodies recognise and bind to the majority of toxic components found in the venoms of the Vipera species tested at comparably high levels to those observed with V. berus. Using in vivo pre-clinical efficacy studies, we demonstrate that ViperaTAb® effectively neutralises lethality induced by V. berus, V. aspis, V. ammodytes and V. latastei venoms and at much higher levels than those outlined by regulatory pharmacopoeial guidelines. Notably, venom neutralisation was found to be superior to (V. berus, V. aspis and V. latastei), or as equally effective as (V. ammodytes), the monospecific V. ammodytes "Zagreb antivenom", which has long been successfully used for treating European snake envenomings. This study suggests that ViperaTAb® may be a valuable therapeutic product for treating snakebite by a variety of European vipers found throughout the continent

On doing hydrology with dragons:Realizing the value of perceptual models and knowledge accumulation

Our ability to fully and reliably observe and simulate the terrestrial hydrologic cycle is limited, and in-depth experimental studies cover only a tiny fraction of our landscape. On medieval maps, unexplored regions were shown as images of dragons—displaying a fear of the unknown. With time, cartographers dared to leave such areas blank, thus inviting explorations of what lay beyond the edge of current knowledge. In hydrology, we are still in a phase where maps of variables more likely contain hydrologic dragons than blank areas, which would acknowledge a lack of knowledge. In which regions is our ability to extrapolate well developed, and where is it poor? Where are available data sets informative, and where are they just poor approximations of likely system properties? How do we best identify and acknowledge these gaps to better understand and reduce the uncertainty in characterizing hydrologic systems? The accumulation of knowledge has been postulated as a fundamental mark of scientific advancement. In hydrology, we lack an effective strategy for knowledge accumulation as a community, and insufficiently focus on highlighting knowledge gaps where they exist. We propose two strategies to rectify these deficiencies. Firstly, the use of open and shared perceptual models to develop, debate, and test hypotheses. Secondly, improved knowledge accumulation in hydrology through a stronger focus on knowledge extraction and integration from available peer-reviewed articles. The latter should include metadata to tag journal articles complemented by a common hydro-meteorological database that would enable searching, organizing and analyzing previous studies in a hydrologically meaningful manner. This article is categorized under: Engineering Water &gt; Planning Water Science of Water &gt; Hydrological Processes Science of Water &gt; Methods.</p

Small mammal responses to long-term large-scale woodland creation: the influence of local and landscape-level attributes

Habitat loss and fragmentation greatly affect biological diversity. Actions to counteract their negative effects include increasing the quality, amount and connectivity of semi-natural habitats at the landscape scale. However, much of the scientific evidence underpinning landscape restoration comes from studies of habitat loss and fragmentation, and it is unclear whether the ecological principles derived from habitat removal investigations are applicable to habitat creation. In addition, the relative importance of local- (e.g. improving habitat quality) vs. landscape-level (e.g. increasing habitat connectivity) actions to restore species is largely unknown, partly because studying species responses over sufficiently large spatial and temporal scales is challenging. We studied small mammal responses to large scale woodland creation spanning 150 years, and assessed the influence of local- and landscape-level characteristics on three small mammal species of varying woodland affinity. Woodland specialists, generalists and grassland specialists were present in woodlands across a range of ages from 10 to 160 years, demonstrating that these species can quickly colonize newly created woodlands. However, we found evidence that woodlands become gradually better over time for some species. The responses of individual species corresponded to their habitat specificity. A grassland specialist (Microtus agrestis) was influenced only by landscape attributes; a woodland generalist (Apodemus sylvaticus) and specialist (Myodes glareolus) were primarily influenced by local habitat attributes, and partially by landscape characteristics. At the local scale, high structural heterogeneity, large amounts of deadwood and a relatively open understory positively influenced woodland species (both generalists and specialists); livestock grazing had strong negative effects on woodland species abundance. Actions to enhance habitat quality at the patch scale focusing on these attributes would benefit these species. Woodland creation in agricultural landscapes is also likely to benefit larger mammals and birds of prey feeding on small mammals and increase ecosystem processes such as seed dispersal