Uniformizing the Stacks of Abelian Sheaves

Elliptic sheaves (which are related to Drinfeld modules) were introduced by Drinfeld and further studied by Laumon--Rapoport--Stuhler and others. They can be viewed as function field analogues of elliptic curves and hence are objects "of dimension 1". Their higher dimensional generalisations are called abelian sheaves. In the analogy between function fields and number fields, abelian sheaves are counterparts of abelian varieties. In this article we study the moduli spaces of abelian sheaves and prove that they are algebraic stacks. We further transfer results of Cerednik--Drinfeld and Rapoport--Zink on the uniformization of Shimura varieties to the setting of abelian sheaves. Actually the analogy of the Cerednik--Drinfeld uniformization is nothing but the uniformization of the moduli schemes of Drinfeld modules by the Drinfeld upper half space. Our results generalise this uniformization. The proof closely follows the ideas of Rapoport--Zink. In particular, analogies of $p$-divisible groups play an important role. As a crucial intermediate step we prove that in a family of abelian sheaves with good reduction at infinity, the set of points where the abelian sheaf is uniformizable in the sense of Anderson, is formally closed.Comment: Final version, appears in "Number Fields and Function Fields - Two Parallel Worlds", Papers from the 4th Conference held on Texel Island, April 2004, edited by G. van der Geer, B. Moonen, R. Schoo

The encoding of individual identity in dolphin signature whistles : how much information is needed?

Bottlenose dolphins (Tursiops truncatus) produce many vocalisations, including whistles that are unique to the individual producing them. Such “signature whistles” play a role in individual recognition and maintaining group integrity. Previous work has shown that humans can successfully group the spectrographic representations of signature whistles according to the individual dolphins that produced them. However, attempts at using mathematical algorithms to perform a similar task have been less successful. A greater understanding of the encoding of identity information in signature whistles is important for assessing similarity of whistles and thus social influences on the development of these learned calls. We re-examined 400 signature whistles from 20 individual dolphins used in a previous study, and tested the performance of new mathematical algorithms. We compared the measure used in the original study (correlation matrix of evenly sampled frequency measurements) to one used in several previous studies (similarity matrix of time-warped whistles), and to a new algorithm based on the Parsons code, used in music retrieval databases. The Parsons code records the direction of frequency change at each time step, and is effective at capturing human perception of music. We analysed similarity matrices from each of these three techniques, as well as a random control, by unsupervised clustering using three separate techniques: k-means clustering, hierarchical clustering, and an adaptive resonance theory neural network. For each of the three clustering techniques, a seven-level Parsons algorithm provided better clustering than the correlation and dynamic time warping algorithms, and was closer to the near-perfect visual categorisations of human judges. Thus, the Parsons code captures much of the individual identity information present in signature whistles, and may prove useful in studies requiring quantification of whistle similarity.Publisher PDFPeer reviewe

Preparation and characterization of poly(D,L-lactide-co-glycolide) microspheres for controlled release of human growth hormone

The purpose of this research was to assess the physicochemical properties of a controlled release formulation of recombinant human growth hormone (rHGH) encapsulated in poly(D,L-lactide-co-glycolide) (PLGA) composite microspheres. rHGH was loaded in poly(acryloyl hydroxyethyl) starch (acHES) microparticles, and then the protein-containing microparticles were encapsulated in the PLGA matrix by a solvent extraction/evaporation method. rHGH-loaded PLGA microspheres were also prepared using mannitol without the starch hydrogel microparticle microspheres for comparison. The detection of secondary structure changes in protein was investigated by using a Fourier Transfer Infrared (FTIR) technique. The composite microspheres were spherical in shape (44.6±2.47 μm), and the PLGA-mannitol microspheres were 39.7±2.50 μm. Drug-loading efficiency varied from 93.2% to 104%. The composite microspheres showed higher overall drug release than the PLGA/mannitol microspheres. FTIR analyses indicated good stability and structural integrity of HGH localized in the microspheres. The PLGA-acHES composite microsphere system could be useful for the controlled delivery of protein drugs