Supercongruences and Complex Multiplication

We study congruences involving truncated hypergeometric series of the form_rF_{r-1}(1/2,...,1/2;1,...,1;\lambda)_{(mp^s-1)/2} = \sum_{k=0}^{(mp^s-1)/2} ((1/2)_k/k!)^r \lambda^k where p is a prime and m, s, r are positive integers. These truncated hypergeometric series are related to the arithmetic of a family of algebraic varieties and exhibit Atkin and Swinnerton-Dyer type congruences. In particular, when r=3, they are related to K3 surfaces. For special values of \lambda, with s=1 and r=3, our congruences are stronger than what can be predicted by the theory of formal groups because of the presence of elliptic curves with complex multiplications. They generalize a conjecture made by Rodriguez-Villegas for the \lambda=1 case and confirm some other supercongruence conjectures at special values of \lambda.Comment: 19 page

Efficient multistep methods for tempered fractional calculus: Algorithms and Simulations

In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative operators in the sense that the tempered fractional derivative operator is interpreted in terms of the Hadamard finite-part integral. We develop two fast methods, Fast Method I and Fast Method II, with linear complexity to calculate the discrete convolution for the approximation of the (tempered) fractional operator. Fast Method I is based on a local approximation for the contour integral that represents the convolution weight. Fast Method II is based on a globally uniform approximation of the trapezoidal rule for the integral on the real line. Both methods are efficient, but numerical experimentation reveals that Fast Method II outperforms Fast Method I in terms of accuracy, efficiency, and coding simplicity. The memory requirement and computational cost of Fast Method II are $O(Q)$ and $O(Qn_T)$, respectively, where $n_T$ is the number of the final time steps and $Q$ is the number of quadrature points used in the trapezoidal rule. The effectiveness of the fast methods is verified through a series of numerical examples for long-time integration, including a numerical study of a fractional reaction-diffusion model

How prudent are rural households in developing transition economies:

Rural households in developing economies frequently use precautionary saving to cope with income risk. Such prudent behavior can be strengthened in transition economies where more risks are typically faced by households during and after reforms. This paper uses a rich panel of rural households in Zhejiang, China, to examine the correlation between income uncertainty and the target ratio of wealth to permanent income as suggested by the buffer-stock model. The empirical results suggest that Chinese rural households hold a significant level of wealth to mitigate the adverse impacts of income risk. Simulation results show that an increase in income risk leads to a sharp increase in household wealth and precautionary saving could drop substantially if income risk is eliminated. The high level of prudence of rural households under economic transition can help us better understand the developments in China, which will have policy implications for both developing and transition countries.buffer-stock model, Income risk, precautionary saving,

Revised Annotations, Sex-Biased Expression, and Lineage-Specific Genes in the Drosophila melanogaster group

Here, we provide revised gene models for D. ananassae, D. yakuba, and D. simulans, which include UTRs and empirically verified intron-exon boundaries, as well as ortholog groups identified using a fuzzy reciprocal-best-hit blast comparison. Using these revised annotations, we perform differential expression testing using the cufflinks suite to provide a broad overview of differential expression between reproductive tissues and the carcass. We identify thousands of genes that are differentially expressed across tissues in D. yakuba and D. simulans, with roughly 60% agreement in expression patterns of orthologs in D. yakuba and D. simulans. We identify several cases of putative polycistronic transcripts, pointing to a combination of transcriptional read-through in the genome as well as putative gene fusion and fission events across taxa. We furthermore identify hundreds of lineage specific genes in each species with no blast hits among transcripts of any other Drosophila species, which are candidates for neofunctionalized proteins and a potential source of genetic novelty.Comment: Revised manuscript, also available online preprint at G3: Genes, Genomes, Genetics. Gene models, ortholog calls, and tissue specific expression results are available at http://github.com/ThorntonLab/GFF or the UCSC browser on the Thornton Lab public track hub at http://genome.ucsc.ed

Structural Basis of Error-prone Replication and Stalling at a Thymine Base by Human DNA Polymerase iota

Human DNA polymerase iota (pol iota) is a unique member of Y-family polymerases, which preferentially misincorporates nucleotides opposite thymines (T) and halts replication at T bases. The structural basis of the high error rates remains elusive. We present three crystal structures of pol complexed with DNA containing a thymine base, paired with correct or incorrect incoming nucleotides. A narrowed active site supports a pyrimidine to pyrimidine mismatch and excludes Watson-Crick base pairing by pol. The template thymine remains in an anti conformation irrespective of incoming nucleotides. Incoming ddATP adopts a syn conformation with reduced base stacking, whereas incorrect dGTP and dTTP maintain anti conformations with normal base stacking. Further stabilization of dGTP by H-bonding with Gln59 of the finger domain explains the preferential T to G mismatch. A template \u27U-turn\u27 is stabilized by pol and the methyl group of the thymine template, revealing the structural basis of T stalling. Our structural and domain-swapping experiments indicate that the finger domain is responsible for pol\u27s high error rates on pyrimidines and determines the incorporation specificity

Landscape of standing variation for tandem duplications in Drosophila yakuba and Drosophila simulans

We have used whole genome paired-end Illumina sequence data to identify tandem duplications in 20 isofemale lines of D. yakuba, and 20 isofemale lines of D. simulans and performed genome wide validation with PacBio long molecule sequencing. We identify 1,415 tandem duplications that are segregating in D. yakuba as well as 975 duplications in D. simulans, indicating greater variation in D. yakuba. Additionally, we observe high rates of secondary deletions at duplicated sites, with 8% of duplicated sites in D. simulans and 17% of sites in D. yakuba modified with deletions. These secondary deletions are consistent with the action of the large loop mismatch repair system acting to remove polymorphic tandem duplication, resulting in rapid dynamics of gain and loss in duplicated alleles and a richer substrate of genetic novelty than has been previously reported. Most duplications are present in only single strains, suggesting deleterious impacts are common. D. simulans shows larger numbers of whole gene duplications in comparison to larger proportions of gene fragments in D. yakuba. D. simulans displays an excess of high frequency variants on the X chromosome, consistent with adaptive evolution through duplications on the D. simulans X or demographic forces driving duplicates to high frequency. We identify 78 chimeric genes in D. yakuba and 38 chimeric genes in D. simulans, as well as 143 cases of recruited non-coding sequence in D. yakuba and 96 in D. simulans, in agreement with rates of chimeric gene origination in D. melanogaster. Together, these results suggest that tandem duplications often result in complex variation beyond whole gene duplications that offers a rich substrate of standing variation that is likely to contribute both to detrimental phenotypes and disease, as well as to adaptive evolutionary change.Comment: Revised Version- Accepted at Molecular Biology and Evolutio

Precision Landing of a Quadrotor UAV on a Moving Target Using Low-Cost Sensors

With the use of unmanned aerial vehicles (UAVs) becoming more widespread, a need for precise autonomous landings has arisen. In the maritime setting, precise autonomous landings will help to provide a safe way to recover UAVs deployed from a ship. On land, numerous applications have been proposed for UAV and unmanned ground vehicle (UGV) teams where autonomous docking is required so that the UGVs can either recover or service a UAV in the field. Current state of the art approaches to solving the problem rely on expensive inertial measurement sensors and RTK or differential GPS systems. However, such a solution is not practical for many UAV systems. A framework to perform precision landings on a moving target using low-cost sensors is proposed in this thesis. Vision from a downward facing camera is used to track a target on the landing platform and generate high quality relative pose estimates. The landing procedure consists of three stages. First, a rendezvous stage commands the quadrotor on a path to intercept the target. A target acquisition stage then ensures that the quadrotor is tracking the landing target. Finally, visual measurements of the relative pose to the landing target are used in the target tracking stage where control and estimation are performed in a body-planar frame, without the use of GPS or magnetometer measurements. A comprehensive overview of the control and estimation required to realize the three stage landing approach is presented. Critical parts of the landing framework were implemented on an AscTec Pelican testbed. The AprilTag visual fiducial system is chosen for use as the landing target. Implementation details to improve the AprilTag detection pipeline are presented. Simulated and experimen- tal results validate key portions of the landing framework. The novel relative estimation scheme is evaluated in an indoor positioning system. Tracking and landing on a moving target is demonstrated in an indoor environment. Outdoor tests also validate the target tracking performance in the presence of wind

Implementation of an Automated Grading System with an Adaptive Learning Component to Affect Student Feedback and Response Time

This research focuses on the development and implementation of an adaptive learning and grading system with a goal to increase the effectiveness and quality of feedback to students. By utilizing various concepts from established learning theories, the goal of this research is to improve the quantity, quality, and speed of feedback as it pertains specifically to the grading of computer skills with a focus on personal productivity software. Feedback has been identified as a key component of successful learning among students. This research builds upon the previous knowledge from the cognitive, behavioral, and resourcebased views of learning as well as upon the establishment of grading rubrics. An automated grading system was developed that allows instructors to quickly grade multiple complex computer literacy assignments. Key to the success of the system is the ability of the system to “learn” the correct and incorrect responses and store them for future use. To understand the impact of the system on feedback, three hypotheses were created and experiments were developed to test them. The system was shown to positively affect the quantity of feedback and reduce the time required for grading assignments. No effect on the quality of the feedback comments was shown and may be a subject of further study