Multiplicity of solutions for polyharmonic Dirichlet problems with exponential nonlinearities and broken symmetry

We prove the existence of infinitely many solutions to a class of non-symmetric Dirichlet problems with exponential nonlinearities. Here the domain $\Omega \subset\subset \mathbb{R}^{2l}$ where $2l$ is the order of the equation. Considered are the problem with no symmetry requirements on the domain, the radial problem on an annulus, and the radial problem on a ball with a Hardy potential term

Evolutionary relationships in Panicoid grasses based on plastome phylogenomics (Panicoideae; Poaceae)

Background: Panicoideae are the second largest subfamily in Poaceae (grass family), with 212 genera and approximately 3316 species. Previous studies have begun to reveal relationships within the subfamily, but largely lack resolution and/or robust support for certain tribal and subtribal groups. This study aims to resolve these relationships, as well as characterize a putative mitochondrial insert in one linage. Results: 35 newly sequenced Panicoideae plastomes were combined in a phylogenomic study with 37 other species: 15 Panicoideae and 22 from outgroups. A robust Panicoideae topology largely congruent with previous studies was obtained, but with some incongruences with previously reported subtribal relationships. A mitochondrial DNA (mtDNA) to plastid DNA (ptDNA) transfer was discovered in the Paspalum lineage. Conclusions: The phylogenomic analysis returned a topology that largely supports previous studies. Five previously recognized subtribes appear on the topology to be non-monophyletic. Additionally, evidence for mtDNA to ptDNA transfer was identified in both Paspalum fimbriatum and P. dilatatum, and suggests a single rare event that took place in a common progenitor. Finally, the framework from this study can guide larger whole plastome sampling to discern the relationships in Cyperochloeae, Steyermarkochloeae, Gynerieae, and other incertae sedis taxa that are weakly supported or unresolved.Fil: Burke, Sean V.. Northern Illinois University; Estados UnidosFil: Wysocki, William P.. Northern Illinois University; Estados UnidosFil: Zuloaga, Fernando Omar. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Botánica Darwinion. Academia Nacional de Ciencias Exactas, Físicas y Naturales. Instituto de Botánica Darwinion; ArgentinaFil: Craine, Joseph M.. Jonah Ventures; Estados UnidosFil: Pires, J. Chris. University of Missouri; Estados UnidosFil: Edger, Patrick P.. Michigan State University; Estados UnidosFil: Mayfield Jones, Dustin. Donald Danforth Plant Science Center; Estados UnidosFil: Clark, Lynn G.. Iowa State University; Estados UnidosFil: Kelchner, Scot A.. University of Idaho; Estados UnidosFil: Duvall, Melvin R.. Northern Illinois University; Estados Unido

Resolving deep relationships of PACMAD grasses: a phylogenomic approach

Background Plastome sequences for 18 species of the PACMAD grasses (subfamilies Panicoideae, Aristidoideae, Chloridoideae, Micrairoideae, Arundinoideae, Danthonioideae) were analyzed phylogenomically. Next generation sequencing methods were used to provide complete plastome sequences for 12 species. Sanger sequencing was performed to determine the plastome of one species, Hakonechloa macra, to provide a reference for annotation. These analyses were conducted to resolve deep subfamilial relationships within the clade. Divergence estimates were assessed to determine potential factors that led to the rapid radiation of this lineage and its dominance of warmer open habitats. Results New plastomes were completely sequenced and characterized for 13 PACMAD species. An autapomorphic ~1140 bp deletion was found in Hakonechloa macra putatively pseudogenizing rpl14 and eliminating rpl16 from this plastome. Phylogenomic analyses support Panicoideae as the sister group to the ACMAD clade. Complete plastome sequences provide greater support at deep nodes within the PACMAD clade. The initial diversification of PACMAD subfamilies was estimated to occur at 32.4 mya. Conclusions Phylogenomic analyses of complete plastomes provides resolution for deep relationships of PACMAD grasses. The divergence estimate of 32.4 mya at the crown node of the PACMAD clade coincides with the Eocene-Oligocene Transition (EOT). The Eocene was a period of global cooling and drying, which led to forest fragmentation and the expansion of open habitats now dominated by these grasses. Understanding how these grasses are related and determining a cause for their rapid radiation allows for future predictions of grassland distribution in the face of a changing global climate.This work was supported in part by the Plant Molecular Biology Center, the Department of Biological Sciences at Northern Illinois University and the National Science Foundation under Grant Numbers DEB-1120750 to LGC, DEB-1120856 to SAK and DEB-1120761 to MRD.This article is made openly accessible in part by an award from the Northern Illinois University Libraries’ Open Access Publishing Fund

The Lived Experiences of Evangelical Christian Men Who Self-Identify as Sexual Addicts

Issues of sexual addiction have swept the evangelical movement, and ongoing concerns in the evangelical community are evidenced by its self-help literature, men\u27s movements, and sex manuals. The purpose of this investigation was to examine the lived experiences of evangelical Christian men who self-identify as sexual addicts. This qualitative method was existential-phenomenological and focused on the lived experiences of this population. Individual interviews and follow-up individual interviews of six self-identified evangelical male sexual addicts were analyzed. The results of the study indicated that the male evangelical self-identified sexual addict lives through compartmentalized worlds: the religious or spiritual world, the committed relationship or marital world, and the sexual world. Only through the forced convergence of these spaces due to exposure along with the risk of extreme consequences do self-identified evangelical men surrender to change. After surrendering to change, subjects willingly grasp on to the concept of sexual addiction as they identify with others in the Christian recovering community and with Christian literature. Sexual addiction becomes an identity that gives them a sense of relief, and a growing dependence on a recovery program emerges along with a necessary and renewed reliance, appreciation, and understanding of God. The findings of this investigation illuminate the need for counselors to recognize the inextricable link between evangelicals and their relationship with God as they counsel the evangelical Christian male who struggles with sexual behaviors

Origin and evolution of the octoploid strawberry genome.

Cultivated strawberry emerged from the hybridization of two wild octoploid species, both descendants from the merger of four diploid progenitor species into a single nucleus more than 1 million years ago. Here we report a near-complete chromosome-scale assembly for cultivated octoploid strawberry (Fragaria × ananassa) and uncovered the origin and evolutionary processes that shaped this complex allopolyploid. We identified the extant relatives of each diploid progenitor species and provide support for the North American origin of octoploid strawberry. We examined the dynamics among the four subgenomes in octoploid strawberry and uncovered the presence of a single dominant subgenome with significantly greater gene content, gene expression abundance, and biased exchanges between homoeologous chromosomes, as compared with the other subgenomes. Pathway analysis showed that certain metabolomic and disease-resistance traits are largely controlled by the dominant subgenome. These findings and the reference genome should serve as a powerful platform for future evolutionary studies and enable molecular breeding in strawberry

Single-molecule sequencing and optical mapping yields an improved genome of woodland strawberry (Fragaria vesca) with chromosome-scale contiguity

Background: Although draft genomes are available for most agronomically important plant species, the majority are incomplete, highly fragmented, and often riddled with assembly and scaffolding errors. These assembly issues hinder advances in tool development for functional genomics and systems biology. Findings: Here we utilized a robust, cost-effective approach to produce high-quality reference genomes. We report a near-complete genome of diploid woodland strawberry (Fragaria vesca) using single-molecule real-time sequencing from Pacific Biosciences (PacBio). This assembly has a contig N50 length of similar to 7.9 million base pairs (Mb), representing a similar to 300-fold improvement of the previous version. The vast majority (>99.8%) of the assembly was anchored to 7 pseudomolecules using 2 sets of optical maps from Bionano Genomics. We obtained similar to 24.96 Mb of sequence not present in the previous version of the F. vesca genome and produced an improved annotation that includes 1496 new genes. Comparative syntenic analyses uncovered numerous, large-scale scaffolding errors present in each chromosome in the previously published version of the F. vesca genome. Conclusions: Our results highlight the need to improve existing short-read based reference genomes. Furthermore, we demonstrate how genome quality impacts commonly used analyses for addressing both fundamental and applied biological questions.Peer reviewe

Infinitely Many Solutions to Asymmetric, Polyharmonic Dirichlet Problems

In this dissertation we prove new results on the existence of infinitely many solutions to nonlinear partial differential equations that are perturbed from symmetry. Our main theorems focus on polyharmonic Dirichlet problems with exponential nonlinearities, and are now published in Topol. Methods Nonlinear Anal. Vol. 50, No.1, (2017), 27-63. In chapter 1 we give an introduction to the problem, its history, and the perturbation argument itself. In chapter 2 we prove the variational principle of Bolle on the behavior of critical values under perturbation, and the variational principle of Tanaka on the existence of critical points of large augmented Morse index. In chapter 3 we use the framework created by Birman and Solomyak for deriving eigenvalue estimates to find alternatives of the CLR inequality specifically designed for our particular nonlinear PDE applications. Chapters 2 and 3 comprise the tools of the perturbation argument. In chapter 4 we bring everything together and prove our main results. We also include new results on non-homogeneous boundary values, and unbounded domains