Explicit CM-theory for level 2-structures on abelian surfaces

For a complex abelian variety $A$ with endomorphism ring isomorphic to the maximal order in a quartic CM-field $K$, the Igusa invariants $j_1(A), j_2(A),j_3(A)$ generate an abelian extension of the reflex field of $K$. In this paper we give an explicit description of the Galois action of the class group of this reflex field on $j_1(A),j_2(A),j_3(A)$. We give a geometric description which can be expressed by maps between various Siegel modular varieties. We can explicitly compute this action for ideals of small norm, and this allows us to improve the CRT method for computing Igusa class polynomials. Furthermore, we find cycles in isogeny graphs for abelian surfaces, thereby implying that the `isogeny volcano' algorithm to compute endomorphism rings of ordinary elliptic curves over finite fields does not have a straightforward generalization to computing endomorphism rings of abelian surfaces over finite fields

On the quaternion ℓ\ell-isogeny path problem

Let \cO be a maximal order in a definite quaternion algebra over $\mathbb{Q}$ of prime discriminant $p$, and $\ell$ a small prime. We describe a probabilistic algorithm, which for a given left $O$-ideal, computes a representative in its left ideal class of $\ell$-power norm. In practice the algorithm is efficient, and subject to heuristics on expected distributions of primes, runs in expected polynomial time. This breaks the underlying problem for a quaternion analog of the Charles-Goren-Lauter hash function, and has security implications for the original CGL construction in terms of supersingular elliptic curves.Comment: To appear in the LMS Journal of Computation and Mathematics, as a special issue for ANTS (Algorithmic Number Theory Symposium) conferenc

Comprehensive analysis of gene expression patterns of hedgehog-related genes

BACKGROUND: The Caenorhabditis elegans genome encodes ten proteins that share sequence similarity with the Hedgehog signaling molecule through their C-terminal autoprocessing Hint/Hog domain. These proteins contain novel N-terminal domains, and C. elegans encodes dozens of additional proteins containing only these N-terminal domains. These gene families are called warthog, groundhog, ground-like and quahog, collectively called hedgehog (hh)-related genes. Previously, the expression pattern of seventeen genes was examined, which showed that they are primarily expressed in the ectoderm. RESULTS: With the completion of the C. elegans genome sequence in November 2002, we reexamined and identified 61 hh-related ORFs. Further, we identified 49 hh-related ORFs in C. briggsae. ORF analysis revealed that 30% of the genes still had errors in their predictions and we improved these predictions here. We performed a comprehensive expression analysis using GFP fusions of the putative intergenic regulatory sequence with one or two transgenic lines for most genes. The hh-related genes are expressed in one or a few of the following tissues: hypodermis, seam cells, excretory duct and pore cells, vulval epithelial cells, rectal epithelial cells, pharyngeal muscle or marginal cells, arcade cells, support cells of sensory organs, and neuronal cells. Using time-lapse recordings, we discovered that some hh-related genes are expressed in a cyclical fashion in phase with molting during larval development. We also generated several translational GFP fusions, but they did not show any subcellular localization. In addition, we also studied the expression patterns of two genes with similarity to Drosophila frizzled, T23D8.1 and F27E11.3A, and the ortholog of the Drosophila gene dally-like, gpn-1, which is a heparan sulfate proteoglycan. The two frizzled homologs are expressed in a few neurons in the head, and gpn-1 is expressed in the pharynx. Finally, we compare the efficacy of our GFP expression effort with EST, OST and SAGE data. CONCLUSION: No bona-fide Hh signaling pathway is present in C. elegans. Given that the hh-related gene products have a predicted signal peptide for secretion, it is possible that they constitute components of the extracellular matrix (ECM). They might be associated with the cuticle or be present in soluble form in the body cavity. They might interact with the Patched or the Patched-related proteins in a manner similar to the interaction of Hedgehog with its receptor Patched

Privately Evaluating Decision Trees and Random Forests

Decision trees and random forests are common classifiers with widespread use. In this paper, we develop two protocols for privately evaluating decision trees and random forests. We operate in the standard two-party setting where the server holds a model (either a tree or a forest), and the client holds an input (a feature vector). At the conclusion of the protocol, the client learns only the model\u27s output on its input and a few generic parameters concerning the model; the server learns nothing. The first protocol we develop provides security against semi-honest adversaries. We then give an extension of the semi-honest protocol that is robust against malicious adversaries. We implement both protocols and show that both variants are able to process trees with several hundred decision nodes in just a few seconds and a modest amount of bandwidth. Compared to previous semi-honest protocols for private decision tree evaluation, we demonstrate a tenfold improvement in computation and bandwidth

Orientation of Vortices in a Superconducting Thin-Film: Quantitative Comparison of Spin-Polarized Neutron Reflectivity and Magnetization

We present a quantitative comparison of the magnetization measured by spin-polarized neutron reflectivity (SPNR) and DC magnetometry on a 1370 \AA\ -thick Nb superconducting film. As a function of magnetic field applied in the film plane, SPNR exhibits reversible behavior whereas the DC magnetization shows substantial hysteresis. The difference between these measurements is attributed to a rotation of vortex magnetic field out of the film plane as the applied field is reduced. Since SPNR measures only the magnetization parallel to the film plane whereas DC magnetization is strongly influenced by the perpendicular component of magnetization when there is a slight sample tilt, combining the two techniques allows one to distinguish two components of magnetization in a thin film.Comment: 12 pages, 8 figures, It will be printed in PRB, Oct. 200

Plant responses to photoperiod

Photoperiod controls many developmental responses in animals, plants and even fungi. The response to photoperiod has evolved because daylength is a reliable indicator of the time of year, enabling developmental events to be scheduled to coincide with particular environmental conditions. Much progress has been made towards understanding the molecular mechanisms involved in the response to photoperiod in plants. These mechanisms include the detection of the light signal in the leaves, the entrainment of circadian rhythms, and the production of a mobile signal which is transmitted throughout the plant. Flowering, tuberization and bud set are just a few of the many different responses in plants that are under photoperiodic control. Comparison of what is known of the molecular mechanisms controlling these responses shows that, whilst common components exist, significant differences in the regulatory mechanisms have evolved between these responses

From X-Ray Telescopes to Neutron Focusing

No abstract availabl

The effect of artificial selection on phenotypic plasticity in maize

Remarkable productivity has been achieved in crop species through artificial selection and adaptation to modern agronomic practices. Whether intensive selection has changed the ability of improved cultivars to maintain high productivity across variable environments is unknown. Understanding the genetic control of phenotypic plasticity and genotype by environment (G × E) interaction will enhance crop performance predictions across diverse environments. Here we use data generated from the Genomes to Fields (G2F) Maize G × E project to assess the effect of selection on G × E variation and characterize polymorphisms associated with plasticity. Genomic regions putatively selected during modern temperate maize breeding explain less variability for yield G × E than unselected regions, indicating that improvement by breeding may have reduced G × E of modern temperate cultivars. Trends in genomic position of variants associated with stability reveal fewer genic associations and enrichment of variants 0–5000 base pairs upstream of genes, hypothetically due to control of plasticity by short-range regulatory elements