Global well-posedness for a coupled modified kdv system

We prove the sharp global well-posedness result for the initial value problem (IVP) associated to the system of the modi ed Korteweg-de Vries (mKdV) equation. For the single mKdV equation such result has been obtained by using Mirura's Transform that takes the KdV equation to the mKdV equation [8]. We do not know the existence of Miura's Transform that takes a KdV system to the system we are considering. To overcome this di culty we developed a new proof of the sharp global well-posedness result for the single mKdV equation without using Miura's Transform. We could successfully apply this technique in the case of the mKdV system to obtain the desired result.Fundação para a Ciência e a Tecnologia (FCT

Variable Yield Responses among Grafted and Nongrafted Late blight–resistant Tomato (Solanum lycopersicum L.) Hybrids in North Carolina

Host resistance is an environmentally and economically sustainable disease management strategy that may be especially beneficial to small-scale and organic growers for whom other management tools such as synthetic pesticides are too costly or not permitted. In western North Carolina, the demand for vine-ripened tomatoes (Solanum lycopersicum L.) from local and organic farms has led to the development of cultivars bred for resistance to geographically relevant diseases, including late blight of tomato, which causes rapid defoliation and lesions on fruit. Grafting tomato plants has the potential to increase plant vigor and yield; however, this effect is known to be dependent on multiple factors, including scion and geographic location. In this study, we evaluated the yield response of one determinate (‘Mountain Gem’) and four indeterminate (‘Mountain Heritage’, ‘Mountain Girl’, ‘Mountain Rouge’, and ‘NC10291’) late blight–resistant tomato cultivars, grafted on tomato rootstock ‘Maxifort’ or nongrafted, on a commercial farm and at two research facilities in western North Carolina. Yield of marketable fruit from grafted plants was greater than that from nongrafted plants at one location (P = 0.008); however, yield response of each cultivar, grafted or not grafted, differed by location. Yield was consistently greater from ‘Mountain Gem’ plants than other cultivars, and grafted ‘Mountain Gem’ plants had greater yields later in the season at two locations than nongrafted plants. Because of the late planting date intended to expose cultivars to the late blight pathogen, the full yield potential of the indeterminate cultivars was not realized at all locations. Disease severity caused by Verticillium wilt (Verticillium dahliae Kleb., Verticillium albo-atrum Reinke & Berthold) was lowest for cultivar Mountain Heritage at two of three locations. Results from this study emphasize the importance of conducting evaluations of grafted tomato plants at multiple locations, including on farm, to optimize the benefits associated with their use

On the supercritical KDV equation with time-oscillating nonlinearity

For the initial value problem (IVP) associated to the generalized Korteweg-de Vries (gKdV) equation with supercritical nonlinearity, \begin{equation*} u_{t}+\partial_x^3u+\partial_x(u^{k+1}) =0,\qquad k\geq 5, \end{equation*} numerical evidence [Bona J.L., Dougalis V.A., Karakashian O.A., McKinney W.R.: Conservative, high-order numerical schemes for the generalized Korteweg–de Vries equation. Philos. Trans. Roy. Soc. London Ser. A 351, 107–164 (1995) ] shows that, there are initial data $\phi\in H^1(\mathbb{R})$ such that the corresponding solution may blow-up in finite time. Also, with the evidence from numerical simulation [Abdullaev F.K., Caputo J.G., Kraenkel R.A., Malomed B.A.: Controlling collapse in Bose–Einstein condensates by temporal modulation of the scattering length. Phys. Rev. A 67, 012605 (2003) and Konotop V.V., Pacciani P.: Collapse of solutions of the nonlinear Schrödinger equation with a time dependent nonlinearity: application to the Bose–Einstein condensates. Phys. Rev. Lett. 94, 240405 (2005) ], it has been claimed that a periodic time dependent coefficient in the nonlinearity would disturb the blow-up solution, either accelerating or delaying it. In this work, we investigate the IVP associated to the gKdV equation \begin{equation*} u_{t}+\partial_x^3u+g(\omega t)\partial_x(u^{k+1}) =0, \end{equation*} where $g$ is a periodic function and $k\geq 5$ is an integer. We prove that, for given initial data $\phi \in H^1(\mathbb{R})$, as $|\omega|\to \infty$, the solution $u_{\omega}$ converges to the solution $U$ of the initial value problem associated to \begin{equation*} U_{t}+\partial_x^3U+m(g)\partial_x(U^{k+1}) =0, \end{equation*} with the same initial data, where $m(g)$ is the average of the periodic function $g$. Moreover, if the solution $U$ is global and satisfies $\|U\|_{L_x^5L_t^{10}}<\infty$, then we prove that the solution $u_{\omega}$ is also global provided $|\omega|$ is sufficiently large.M. P. was partially supported by the Research Center of Mathematics of the University of Minho, Portugal through the FCT Pluriannual Funding Program, and through the project PTDC/MAT/109844/2009, and M. S. was partially supported by FAPESP Brazil

High-Density SNP Genotyping of Tomato (Solanum lycopersicum L.) Reveals Patterns of Genetic Variation Due to Breeding

The effects of selection on genome variation were investigated and visualized in tomato using a high-density single nucleotide polymorphism (SNP) array. 7,720 SNPs were genotyped on a collection of 426 tomato accessions (410 inbreds and 16 hybrids) and over 97% of the markers were polymorphic in the entire collection. Principal component analysis (PCA) and pairwise estimates of F-st supported that the inbred accessions represented seven sub-populations including processing, large-fruited fresh market, large-fruited vintage, cultivated cherry, landrace, wild cherry, and S. pimpinellifolium. Further divisions were found within both the contemporary processing and fresh market sub-populations. These sub-populations showed higher levels of genetic diversity relative to the vintage sub-population. The array provided a large number of polymorphic SNP markers across each sub-population, ranging from 3,159 in the vintage accessions to 6,234 in the cultivated cherry accessions. Visualization of minor allele frequency revealed regions of the genome that distinguished three representative sub-populations of cultivated tomato (processing, fresh market, and vintage), particularly on chromosomes 2, 4, 5, 6, and 11. The PCA loadings and F-st outlier analysis between these three sub-populations identified a large number of candidate loci under positive selection on chromosomes 4, 5, and 11. The extent of linkage disequilibrium (LD) was examined within each chromosome for these sub-populations. LD decay varied between chromosomes and sub-populations, with large differences reflective of breeding history. For example, on chromosome 11, decay occurred over 0.8 cM for processing accessions and over 19.7 cM for fresh market accessions. The observed SNP variation and LD decay suggest that different patterns of genetic variation in cultivated tomato are due to introgression from wild species and selection for market specialization

Transcriptome Profiling of Citrus Fruit Response to Huanglongbing Disease

Huanglongbing (HLB) or “citrus greening” is the most destructive citrus disease worldwide. In this work, we studied host responses of citrus to infection with Candidatus Liberibacter asiaticus (CaLas) using next-generation sequencing technologies. A deep mRNA profile was obtained from peel of healthy and HLB-affected fruit. It was followed by pathway and protein-protein network analysis and quantitative real time PCR analysis of highly regulated genes. We identified differentially regulated pathways and constructed networks that provide a deep insight into the metabolism of affected fruit. Data mining revealed that HLB enhanced transcription of genes involved in the light reactions of photosynthesis and in ATP synthesis. Activation of protein degradation and misfolding processes were observed at the transcriptomic level. Transcripts for heat shock proteins were down-regulated at all disease stages, resulting in further protein misfolding. HLB strongly affected pathways involved in source-sink communication, including sucrose and starch metabolism and hormone synthesis and signaling. Transcription of several genes involved in the synthesis and signal transduction of cytokinins and gibberellins was repressed while that of genes involved in ethylene pathways was induced. CaLas infection triggered a response via both the salicylic acid and jasmonic acid pathways and increased the transcript abundance of several members of the WRKY family of transcription factors. Findings focused on the fruit provide valuable insight to understanding the mechanisms of the HLB-induced fruit disorder and eventually developing methods based on small molecule applications to mitigate its devastating effects on fruit production

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency–Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research