Computing algebraic numbers of bounded height

We describe an algorithm for listing all elements of bounded height in a given number field

Quadratic points on dynamical modular curves

Among all the dynamical modular curves associated to quadratic polynomial maps, we determine which curves have infinitely many quadratic points. This yields a classification statement on preperiodic points for quadratic polynomials over quadratic fields, extending previous work of Poonen, Faber, and the authors.Comment: Improvements to the exposition; stronger version of what is now Proposition 4.

Route prediction from trip observations,”

ABSTRACT This paper develops and tests algorithms for predicting the end-to-end route of a vehicle based on GPS observations of the vehicle's past trips. We show that a large portion of a typical driver's trips are repeated. Our algorithms exploit this fact for prediction by matching the first part of a driver's current trip with one of the set of previously observed trips. Rather than predicting upcoming road segments, our focus is on making long term predictions of the route. We evaluate our algorithms using a large corpus of real world GPS driving data acquired from observing over 250 drivers for an average of 15.1 days per subject. Our results show how often and how accurately we can predict a driver's route as a function of the distance already driven

Allele-specific transcriptional elongation regulates monoallelic expression of the IGF2BP1 gene

<p>Abstract</p> <p>Background</p> <p>Random monoallelic expression contributes to phenotypic variation of cells and organisms. However, the epigenetic mechanisms by which individual alleles are randomly selected for expression are not known. Taking cues from chromatin signatures at imprinted gene loci such as the insulin-like growth factor 2 gene 2 (<it>IGF2</it>), we evaluated the contribution of CTCF, a zinc finger protein required for parent-of-origin-specific expression of the <it>IGF2 </it>gene, as well as a role for allele-specific association with DNA methylation, histone modification and RNA polymerase II.</p> <p>Results</p> <p>Using array-based chromatin immunoprecipitation, we identified 293 genomic loci that are associated with both CTCF and histone H3 trimethylated at lysine 9 (H3K9me3). A comparison of their genomic positions with those of previously published monoallelically expressed genes revealed no significant overlap between allele-specifically expressed genes and colocalized CTCF/H3K9me3. To analyze the contributions of CTCF and H3K9me3 to gene regulation in more detail, we focused on the monoallelically expressed <it>IGF2BP1 </it>gene. <it>In vitro </it>binding assays using the CTCF target motif at the <it>IGF2BP1 </it>gene, as well as allele-specific analysis of cytosine methylation and CTCF binding, revealed that CTCF does not regulate mono- or biallelic <it>IGF2BP1 </it>expression. Surprisingly, we found that RNA polymerase II is detected on both the maternal and paternal alleles in B lymphoblasts that express <it>IGF2BP1 </it>primarily from one allele. Thus, allele-specific control of RNA polymerase II elongation regulates the allelic bias of <it>IGF2BP1 </it>gene expression.</p> <p>Conclusions</p> <p>Colocalization of CTCF and H3K9me3 does not represent a reliable chromatin signature indicative of monoallelic expression. Moreover, association of individual alleles with both active (H3K4me3) and silent (H3K27me3) chromatin modifications (allelic bivalent chromatin) or with RNA polymerase II also fails to identify monoallelically expressed gene loci. The selection of individual alleles for expression occurs in part during transcription elongation.</p