Functional Equations Involving Laurent Polynomials and Meromorphic Functions, with Applications to Dynamics and Diophantine Equations.

In this thesis, our main theorem gives the classification of all Laurent polynomials $f(X)$ such that the numerator of $frac{f(X)-f(Y)}{X-Y}$ has an irreducible factor whose normalization has genus zero or one. The work in this thesis uses various tools from algebraic geometry, and heavily relies on Galois theory and the classification of finite simple groups. As an application of our main theorem, we prove a theorem which gives all the solutions to the functional equation $fcirc P=fcirc Q$, where $f$ is a complex Laurent polynomial and $P, Q$ are distinct complex meromorphic functions. This theorem gives many classes of negative examples to an open question of Lyubich and Minsky. Moreover, this theorem has consequences for many important problems in complex dynamics and the distribution of values of meromorphic functions, since these problems can be reduced to solving the functional equation. As another application of the main theorem, we prove a theorem which gives all Laurent polynomials, such that there are infinitely many $c$ in a number field for which $f(X)=c$ has at least two solutions in the number field. The polynomial case analogue was recently proved by Carney, Hortsch and Zieve, and they used the analogue to prove the following unexpected result: for any polynomial $f(X)inmathbb{Q}[X]$, the function $f: mathbb{Q}rightarrowmathbb{Q}$ defined by $xmapsto f(x)$ is at most $6$-to-$1$ for all but finitely many values. A Laurent polynomial analogue of their result can be expected using the theorem in this thesis. It will provide evidence in support of an analogous conjecture about rational functions which would be a far-reaching generalization of the results of Mazur and Merel about rational torsion points on elliptic curves.PHDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108867/1/siliu_1.pd

Next Generation Sequencing Technologies for Insect Virus Discovery

Insects are commonly infected with multiple viruses including those that cause sublethal, asymptomatic, and latent infections. Traditional methods for virus isolation typically lack the sensitivity required for detection of such viruses that are present at low abundance. In this respect, next generation sequencing technologies have revolutionized methods for the discovery and identification of new viruses from insects. Here we review both traditional and modern methods for virus discovery, and outline analysis of transcriptome and small RNA data for identification of viral sequences. We will introduce methods for de novo assembly of viral sequences, identification of potential viral sequences from BLAST data, and bioinformatics for generating full-length or near full-length viral genome sequences. We will also discuss implications of the ubiquity of viruses in insects and in insect cell lines. All of the methods described in this article can also apply to the discovery of viruses in other organisms

Tissue-specific transcription of proteases and nucleases across the accessory salivary gland, principal salivary gland and gut of Nezara viridula

The phytophagous stink bug, Nezara viridula (L.) infests multiple plant species and impacts agricultural production worldwide. We analyzed the transcriptomes of N. viridula accessory salivary gland (ASG), principal salivary gland (PSG) and gut, with a focus on putative digestive proteases and nucleases that present a primary obstacle for the stability of protein- or nucleic acid- based stink bug control approaches. We performed high throughput Illumina sequencing followed by de novo transcriptome assemblies. We identified the sequences of 141 unique proteases and 134 nucleases from the N. viridula transcriptomes. Analysis of relative transcript abundance in conjunction with previously reported proteome data (Lomate and Bonning, 2016) supports high levels of serine protease expression in the salivary glands and high cysteine protease expression in the gut. Specifically, trypsin and chymotrypsin transcripts were abundant in the PSG, and cathepsin L-like cysteine protease transcripts were abundant in the gut. Nuclease transcript levels were generally lower than those of the proteases, the exception being abundant transcripts of ribonuclease-C20 in the PSG. The abundance of chymotrypsin, trypsin, and some carboxypeptidase transcripts suggests a significant role for the PSG in production of digestive enzymes. This result is at odds with the premise that the ASG produces watery saliva, which is high in enzymatic activity, while the PSG produces only sheath saliva. We have generated a comprehensive transcriptome sequence dataset from the digestive organs of N. viridula, identified major protease and nuclease genes and confirmed expression of the most abundant enzymes thereby providing greater insight into the digestive physiology of N. viridula

Deep Sequencing of the Transcriptomes of Soybean Aphid and Associated Endosymbionts

Background The soybean aphid has significantly impacted soybean production in the U.S. Transcriptomic analyses were conducted for further insight into leads for potential novel management strategies. Methodology/Principal Findings Transcriptomic data were generated from whole aphids and from 2,000 aphid guts using an Illumina GAII sequencer. The sequence data were assembled de novo using the Velvet assembler. In addition to providing a general overview, we demonstrate (i) the use of the Multiple-k/Multiple-C method for de novo assembly of short read sequences, followed by BLAST annotation of contigs for increased transcript identification: From 400,000 contigs analyzed, 16,257 non-redundant BLAST hits were identified; (ii) analysis of species distributions of top non-redundant hits: 80% of BLAST hits (minimum e-value of 1.0-E3) were to the pea aphid or other aphid species, representing about half of the pea aphid genes; (iii) comparison of relative depth of sequence coverage to relative transcript abundance for genes with high (membrane alanyl aminopeptidase N) or low transcript abundance; (iv) analysis of theBuchnera transcriptome: Transcripts from 57.6% of the genes from Buchnera aphidicola were identified; (v) identification of Arsenophonus and Wolbachia as potential secondary endosymbionts; (vi) alignment of full length sequences from RNA-seq data for the putative salivary gland protein C002, the silencing of which has potential for aphid management, and the putative Bacillus thuringiensis Cry toxin receptors, aminopeptidase N and alkaline phosphatase. Conclusions/Significance This study provides the most comprehensive data set to date for soybean aphid gene expression: This work also illustrates the utility of short-read transcriptome sequencing and the Multiple-k/Multiple-C method followed by BLAST annotation for rapid identification of target genes for organisms for which reference genome sequences are not available, and extends the utility to include the transcriptomes of endosymbionts

Genome Sequence of a Novel Positive-Sense, Single-Stranded RNA Virus Isolated from Western Corn Rootworm, Diabrotica virgifera virgifera LeConte

The genome sequence of a novel small RNA virus was assembled from the transcriptome of the western corn rootworm, Diabrotica virgifera virgifera. The assembled genome has 13,182 nucleotides with a 3′ polyadenylated tail. Two open reading frames are predicted to encode polyproteins of 2,838 and 1,073 amino acids

Genome Sequence of Diabrotica virgifera virgifera virus 2, a Novel Small RNA Virus of the Western Corn Rootworm, Diabrotica virgifera virgifera LeConte

The genome of a novel small RNA virus, tentatively named Diabrotica virgifera virgifera virus 2 (DvvV2), was identified in the western corn rootworm, Diabrotica virgifera virgifera LeConte, through transcriptome sequencing and confirmed by reverse transcription-PCR. Here, we report the near-complete nucleotide sequence and the genome organization of DvvV2

Genome Sequence of the First Coleopteran Iflavirus Isolated from Western Corn Rootworm, Diabrotica virgifera virgifera LeConte

The genome sequence of a novel iflavirus was identified from the transcriptome of the western corn rootworm, Diabrotica virgifera virgifera. The RNA sequence consists of 9,823 nucleotides (nt) with a 3′ polyadenylated tail, containing a single open reading frame that encodes a 3,028-amino-acid polyprotein

Optimisation and Management of Energy Generated by a Multifunctional MFC-Integrated Composite Chassis for Rail Vehicles

With the advancing trend towards lighter and faster rail transport, there is an increasing interest in integrating composite and advanced multifunctional materials in order to infuse smart sensing and monitoring, energy harvesting and wireless capabilities within the otherwise purely mechanical rail structures and the infrastructure. This paper presents a holistic multiphysics numerical study, across both mechanical and electrical domains, that describes an innovative technique of harvesting energy from a piezoelectric micro fiber composites (MFC) built-in composite rail chassis structure. Representative environmental vibration data measured from a rail cabin have been critically leveraged here to help predict the actual vibratory and power output behaviour under service. Time domain mean stress distribution data from the Finite Element simulation were used to predict the raw AC voltage output of the MFCs. Conditioned power output was then calculated using circuit simulation of several state-of-the-art power conditioning circuits. A peak instantaneous rectified power of 181.9 mW was obtained when eight-stage Synchronised Switch Harvesting Capacitors (SSHC) from eight embedded MFCs were located. The results showed that the harvested energy could be sufficient to sustain a self-powered structural health monitoring system with wireless communication capabilities. This study serves as a theoretical foundation of scavenging for vibrational power from the ambient state in a rail environment as well as to pointing to design principles to develop regenerative and power neutral smart vehicles

Genome Sequence of a Small RNA Virus of the Southern Corn Rootworm, Diabrotica undecimpunctata howardi Barber (Coleoptera: Chrysomelidae)

The genome sequence of a novel small RNA virus, tentatively named Diabrotica undecimpunctata virus 1 (DuV1), was discovered from the transcriptome of the southern corn rootworm, Diabrotica undecimpunctata howardi Barber. DuV1 has a positive-sense, single-stranded RNA genome that encodes a single polyprotein of 3,401 amino acids with limited similarity to other viruses

Diabrotica undecimpunctata virus 2, a Novel Small RNA Virus Discovered from Southern Corn Rootworm, Diabrotica undecimpunctata howardi Barber (Coleoptera: Chrysomelidae)

The genome of Diabrotica undecimpunctata virus 2 (DuV2), a positive-sense, single-stranded RNA virus identified from the southern corn root- worm transcriptome, comprises 5,313 nucleotides, including a short poly(A) tail. The two open reading frames encode a nonstructural polyprotein (p156) and a putative capsid protein (p25)