Group law computations on Jacobians of hyperelliptic Curves

We derive an explicit method of computing the composition step in Cantor’s algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the geometric description of the group law and applies to hyperelliptic curves of arbitrary genus. While Cantor’s general composition involves arithmetic in the polynomial ring F_q[x], the algorithm we propose solves a linear system over the base field which can be written down directly from the Mumford coordinates of the group elements. We apply this method to give more efficient formulas for group operations in both affine and projective coordinates for cryptographic systems based on Jacobians of genus 2 hyperelliptic curves in general form.

Fast formulas for computing cryptographic pairings

The most powerful known primitive in public-key cryptography is undoubtedly elliptic curve pairings. Upon their introduction just over ten years ago the computation of pairings was far too slow for them to be considered a practical option. This resulted in a vast amount of research from many mathematicians and computer scientists around the globe aiming to improve this computation speed. From the use of modern results in algebraic and arithmetic geometry to the application of foundational number theory that dates back to the days of Gauss and Euler, cryptographic pairings have since experienced a great deal of improvement. As a result, what was an extremely expensive computation that took several minutes is now a high-speed operation that takes less than a millisecond. This thesis presents a range of optimisations to the state-of-the-art in cryptographic pairing computation. Both through extending prior techniques, and introducing several novel ideas of our own, our work has contributed to recordbreaking pairing implementations.

The dynamics of cellular automata on 2-manifolds is affected by topology

In this paper, we demonstrate that the distribution of Wolfram classes within a cellular automata rule space in the triangular tessellation is not consistent across different topological general. Using a statistical mechanics approach, cellular automata dynamical classes were approximated for cellular automata defined on genus-0, genus-1 and genus-2 2-manifolds. A distribution-free equality test for empirical distributions was applied to identify cases in which Wolfram classes were distributed differently across topologies. This result implies that global structure and local dynamics contribute to the long term evolution of cellular automata.

Elements of arithmetic /

pt. 1. Primary arithmetic. --pt. 2. Grammar-school arithmetic. --pt. 3. Arithmetic practically applied.

On the effect of topology on cellular automata rule spaces

This thesis presents an empirical study of the effects of topology on cellular automata rule spaces. The classical definition of a cellular automaton is restricted to that of a regular lattice, often with periodic boundary conditions. This definition is extended to allow for arbitrary topologies. The dynamics of cellular automata within the triangular tessellation were analysed when transformed to 2-manifolds of topological genus 0, genus 1 and genus 2. Cellular automata dynamics were analysed from a statistical mechanics perspective. The sample sizes required to obtain accurate entropy calculations were determined by an entropy error analysis which observed the error in the computed entropy against increasing sample sizes. Each cellular automata rule space was sampled repeatedly and the selected cellular automata were simulated over many thousands of trials for each topology. This resulted in an entropy distribution for each rule space. The computed entropy distributions are indicative of the cellular automata dynamical class distribution. Through the comparison of these dynamical class distributions using the E-statistic, it was identified that such topological changes cause these distributions to alter. This is a significant result which implies that both global structure and local dynamics play a important role in defining long term behaviour of cellular automata.

RIGIDITY OF HOLOMORPHIC MAPS BETWEEN FIBER SPACES

In the study of holomorphic maps, the term ``rigidity'' refers to certain types of results that give us very specific information about a general class of holomorphic maps owing to the geometry of their domains or target spaces. Under this theme, we begin by studying when, given two compact connected complex manifolds X and Y, a degree-one holomorphic map f :Y -> X is a biholomorphism. Given that the real manifolds underlying X and Y are diffeomorphic, we provide a condition under which f is a biholomorphism. Using this result, we deduce a rigidity result for holomorphic self-maps of the total space of a holomorphic fiber space. Lastly, we consider products X = X-1 x X-2 and Y = Y-1 x Y-2 of compact connected complex manifolds. When X-1 is a Riemann surface of genus >= 2, we show that any non-constant holomorphic map F:Y -> X is of a special form.

计算流体力学

Queen-worker conflict over male production and sex ratio in a facultatively polyandrous bumble bee, Bombus hypnorum: the consequences of nest usurpation.

Evolutionary conflicts among social hymenopteran nestmates are theoretically likely to arise over the production of males and the sex ratio. Analysis of these conflicts has become an important focus of research into the role of kin selection in shaping social traits of hymenopteran colonies. We employ microsatellite analysis of nestmates of one social hymenopteran, the primitively eusocial and monogynous bumblebee Bombus hypnorum, to evaluate these conflicts. In our 14 study colonies, B. hypnorum queens mated between one and six times (arithmetic mean 2.5). One male generally predominated, fathering most of the offspring, thus the effective number of matings was substantially lower (1–3.13; harmonic mean 1.26). In addition, microsatellite analysis allowed the detection of alien workers, those who could not have been the offspring of the queen, in approximately half the colonies. Alien workers within the same colony were probably sisters. Polyandry and alien workers resulted in high variation among colonies in their sociogenetic organization. Genetic data were consistent with the view that all males (n = 233 examined) were produced by a colony’s queen. Male parentage was therefore independent of the sociogenetic organization of the colony, suggesting that the queen, and not the workers, was in control of the laying of male-destined eggs. The population-wide sex ratio (fresh weight investment ratio) was weakly female biased. No evidence for colony-level adaptive sex ratio biasing could be detected.

Revisão da seção setacea do gênero Batrachospermum (Rhodophyta, Batrachospermales)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Two New Species of Prosorhynchinae (Trematoda : Gasterostomata) from the Fiji Islands

The following trematodes are part of a collection made by the author at Suva, Fiji in 1951. 1. Prosorhynchus squamatus Odhner, 1905 is believed to be distinct from P. crucibulus and most other species in the genus on the basis of its oval-shaped rhynchus. It thus remains, as originally, the type species of the genus. 2. Prosorhynchus thapari n. sp. is described from Plectropoma maculatum (Bloch) from Suva, Fiji. The "P. facilis (Ozaki, 1924)" of Nagaty (1937) is considered to be a synonym. 3. Neidhartia polydactyli n. sp. is described from Polydactylus plebius (Bonnaterre) from Suva, Fiji.

Hardware processors for pairing-based cryptography

Bilinear pairings can be used to construct cryptographic systems with very desirable properties. A pairing performs a mapping on members of groups on elliptic and genus 2 hyperelliptic curves to an extension of the finite field on which the curves are defined. The finite fields must, however, be large to ensure adequate security. The complicated group structure of the curves and the expensive field operations result in time consuming computations that are an impediment to the practicality of pairing-based systems. The Tate pairing can be computed efficiently using the ɳT method. Hardware architectures can be used to accelerate the required operations by exploiting the parallelism inherent to the algorithmic and finite field calculations. The Tate pairing can be performed on elliptic curves of characteristic 2 and 3 and on genus 2 hyperelliptic curves of characteristic 2. Curve selection is dependent on several factors including desired computational speed, the area constraints of the target device and the required security level. In this thesis, custom hardware processors for the acceleration of the Tate pairing are presented and implemented on an FPGA. The underlying hardware architectures are designed with care to exploit available parallelism while ensuring resource efficiency. The characteristic 2 elliptic curve processor contains novel units that return a pairing result in a very low number of clock cycles. Despite the more complicated computational algorithm, the speed of the genus 2 processor is comparable. Pairing computation on each of these curves can be appealing in applications with various attributes. A flexible processor that can perform pairing computation on elliptic curves of characteristic 2 and 3 has also been designed. An integrated hardware/software design and verification environment has been developed. This system automates the procedures required for robust processor creation and enables the rapid provision of solutions for a wide range of cryptographic applications.

PHYLOGENETIC STUDIES OF SOME SPECIES OF THE GENUS COFFEA .2. NUMERICAL-ANALYSIS OF ISOENZYMATIC DATA

Thirteen species of Coffea were studied for five enzymes systems, including alpha and beta esterase, alkaline phosphatase, acid phosphatase, malate dehydrogenase and acid dehydrogenase. Three coefficients of similarity: Simple Matching, Jaccard and Ochiai and three different clustering methods: Single Linkage, Complete Linkage and Unweighted Pair Group, using Arithmetic Averages (UPGMA) were used to analyse the data.The phylogenetic relationships among the twelve diploid species and between them and the tetraploid species C. arabica showed that similarity among species of the same subsection is not always greater than among species of different subsections. In addition, although there are several similarity groups in common, established by isoenzymatic polymorphism, morphological characteristics, chemical data, crossability and geographic distribution, there is no common trend among the phylogenetic relationships as indicated by all these different evaluating procedures.

Phylogeny of Oedogoniales (Chlorophyceae, Chlorophyta) inferred from 18S rDNA sequences with emphasis on the relationships in the genus Oedogonium based on ITS-2 sequences

The phylogeny of Oedogoniales was investigated by using nuclear 18S rDNA sequences. Results showed that the genus Oedocladium, as a separated clade, was clustered within the clade of Oedogonium; whereas the genus Bulbochaete was in a comparatively divergent position to the other two genera. The relationship among the species of Oedogonium was discussed, focusing on ITS-2 phylogeny analyzed combining with some morphological characteristics. Our results showed that all the dioecious nannandrous taxa involved in this study were resolved into one clade, while all the monocious taxa were clustered into another clade as a sister group to the former. The report also suggests that the dioecious macrandrous taxa form a paraphyly and could be more basally situated than the dioecious nannandrous and the monoecious taxa by means of molecular phylogeny and morphotype investigations.

Sequence of genome segments 1, 2, and 3 of the grass carp reovirus (Genus Aquareovirus, family Reoviridae)

The genome segments 1, 2, and 3 of the grass carp reovirus (GCRV), a tentative species assigned to genus Aquareouirus, family Reouiridae, were sequenced. The respective segments 1, 2, and 3 were 3949, 3877, and 3702 nucleotides long. Conserved moths 5' (GUUAUUU) and 3' (UUCAUC) were found at the ends of each segment. Each segment contains a single ORF and the negative strand does not permit identification of consistent ORFs. Sequence analysis revealed that VP2 is the viral polymerase, while VPI might represent the viral guanyly/methyl transferase (involved in the capping process of RNA transcripts) and VP3 the NTPase/helicase (involved in the transcription and capping of viral RNAs), The highest amino acid identities (26-41%) were found with orthoreovirus proteins. Further genomic characterization should provide insight about the genetic relationships between GCRV, aquareoviruses, and orthoreoviruses, It should also permit to precise the taxonomic status of these different viruses. (C) 2000 Academic Press.