Discrete logarithms in curves over finite fields

A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields

The complexity of class polynomial computation via floating point approximations

We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart of the algorithm is the evaluation of modular functions in several arguments. The fastest one of the presented approaches uses a technique devised by Dupont to evaluate modular functions by Newton iterations on an expression involving the arithmetic-geometric mean. It runs in time $O (|D| \log^5 |D| \log \log |D|) = O (|D|^{1 + \epsilon}) = O (h^{2 + \epsilon})$ for any $\epsilon > 0$, where $D$ is the CM discriminant and $h$ is the degree of the class polynomial. Another fast algorithm uses multipoint evaluation techniques known from symbolic computation; its asymptotic complexity is worse by a factor of $\log |D|$. Up to logarithmic factors, this running time matches the size of the constructed polynomials. The estimate also relies on a new result concerning the complexity of enumerating the class group of an imaginary-quadratic order and on a rigorously proven upper bound for the height of class polynomials

Digital analysis of wind tunnel imagery to measure fluid thickness

Documented here are the procedure and results obtained from the application of digital image processing techniques to the problem of measuring the thickness of a deicing fluid on a model airfoil during simulated takeoffs. The fluid contained a fluorescent dye and the images were recorded under flash illumination on photographic film. The films were digitized and analyzed on a personal computer to obtain maps of the fluid thickness

Heavy ion measurement on LDEF

A stack of CR-39 and Kodak CN track detectors was exposed on the NASA satellite LDEF and recovered after almost six years in space. The quick look analysis yielded heavy ion tracks on a background of low energy secondaries from proton interaction. The detected heavy ions show a steep energy spectrum which indicates a radiation belt origin

Generalised Weber Functions

A generalised Weber function is given by \w_N(z) = \eta(z/N)/\eta(z), where $\eta(z)$ is the Dedekind function and $N$ is any integer; the original function corresponds to $N=2$. We classify the cases where some power \w_N^e evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a general formula for the degree of the modular equation relating \w_N(z) and $j(z)$. Our ultimate goal is the use of these invariants in constructing reductions of elliptic curves over finite fields suitable for cryptographic use

Measurement of low energy cosmic rays aboard Spacelab-1

In December 1983 the first Spacelab mission was launched for a duration of 10 days. Aboard was the Kiel experiment Isotopic Stack designed for measurement of heavy cosmic ray nuclei with nuclear charge equal to or greater than 3 and energies up to some 100MeV/nuc. One part of the stack was rotated in well defined steps registered by an angle encoder to receive information on impact times of the nuclei. Using this time resolving system geomagnetically forbidden particles can be detected. The chemical composition and energy spectra of mainly CNO particles are examined using a rotated 300 microns m thick CR-39 foil beneath a fixed 100 microns m thick Kodak-Cellulose Nitrate foil. About 600 sq cm have been scanned yielding nearly 100 nuclear tracks within an energy range of approximately 8 to 30 MeV/nuc. The calibration is done by means of a postflight irradiation with 410 MeV/nuc Fe-56 at Berkeley Laboratory, California, USA. Relative abundances and energy spectra are presented

Renormalization in periodically driven quantum dots

We report on strong renormalization encountered in periodically driven interacting quantum dots in the non-adiabatic regime. Correlations between lead and dot electrons enhance or suppress the amplitude of driving depending on the sign of the interaction. Employing a newly developed flexible renormalization group based approach for periodic driving to an interacting resonant level we show analytically that the magnitude of this effect follows a power law. Our setup can act as a non-Markovian, single-parameter quantum pump.Comment: 6 pages, 3 figure

Seaweed Invasions and Novel Chemical Defences

Biological invasions pose a risk to the biodiversity and the functioning of ecosystems in invaded areas. The reasons why some introduced species become dominant and widespread in their new environments is still largely an unsettled question. It has commonly been predicted that introduced plants will invade when they are less affected by herbivores, since this will provide the introduced species with a competitive advantage over native plants. Furthermore, it has been suggested that introduced species with chemical defences that are novel to native herbivores in the new range are most likely to become successful invaders. The scope of this thesis was to investigate ecological processes that underlie the successful invasion of plant/seaweed species and how chemical compounds mediate these processes, using the filamentous red alga Bonnemaisonia hamifera as a model organism. Having its origin in the Northwest Pacific, this alga has invaded large parts of the North Atlantic rocky shores and became dominant in many seaweed communities. Feeding preference experiments showed that native generalist herbivores explicitly preferred native seaweeds to the invader (paper I). Using a bioassay-guided fractionation, B. hamifera was found to be chemically defended against native herbivores by producing 1,1,3,3-tetrabromo-2-heptanone as the main feeding deterrent compound (paper I). The production of this compound was demonstrated to be costly, but also to increase the fitness of the invader by reducing the impact of pathogenic bacteria (paper IV) in addition to the shown reduced herbivory. Resource allocation to a chemical defence may also explain the relatively poor performance (in terms of growth) of B. hamifera in direct interactions with native seaweeds when herbivores were absent in experimental algal communities (paper II, III). In the presence of herbivores, however, the abundance of B. hamifera increased in the community as a result of both consumption of neighbouring algal competitors and an enhanced performance of the invader (paper III). In return, the invasive species was found to provide a superior refuge to herbivores from fish predation compared to native seaweeds, which may explain the previously observed rich species diversity and abundance of invertebrates associated with the alga. Overall, these results suggest that the invasion of B. hamifera has been facilitated by refuge-mediated apparent competition (paper III). In conclusion, B. hamifera provides a remarkable example of how a novel chemical defence can drive different ecological processes in the new community and how this jointly contributes to the invasiveness of the introduced species. The further development of the invaded community is difficult to predict and depends on the ability of the native species to adapt to the chemical defence of the invader, as well as on the potential of the invader to respond to the novel selection regimes in the invaded area. Sufficient genetic variation is generally considered essential for the potential of adaptations. In Swedish waters, B. hamifera mainly propagates asexually by fragmentation, which suggests that the alga should be highly clonal with low genetic diversity within these introduced populations. Preliminary results from 83 amplified fragment length polymorphism markers analysed for 44 individuals indicated reduced genetic diversity in Swedish populations compared to populations from the native range in Korea. No clones were found in the Swedish population, although the low degree of differentiation and high similarity between the Swedish individuals suggests that the individuals belong to a single clonal lineage, that is well intermixed by fragment dispersal (paper V)