skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Area‐Minimizing Currents mod 2 Q : Linear Regularity Theory
Abstract We establish a theory ofQ‐valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently area minimizing currentsmod(p)whenp = 2Q, and to establish a first general partial regularity theorem for everypin any dimension and codimension . © 2020 The Authors.Communications on Pure and Applied Mathematicspublished by Wiley Periodicals LLC.  more » « less
Award ID(s):
1854147
PAR ID:
10470334
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
John Wiley and Sons
Date Published:
Journal Name:
Communications on Pure and Applied Mathematics
Volume:
75
Issue:
1
ISSN:
0010-3640
Page Range / eLocation ID:
83 to 127
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Summary Distyly is an intriguing floral adaptation that increases pollen transfer precision and restricts inbreeding. It has been a model system in evolutionary biology since Darwin. Although theS‐locus determines the long‐ and short‐styled morphs, the genes were unknown inTurnera. We have now identified these genes.We used deletion mapping to identify, and then sequence,BACclones and genome scaffolds to constructS/shaplotypes. We investigated candidate gene expression, hemizygosity, and used mutants, to explore gene function.Thes‐haplotype possessed 21 genes collinear with a region of chromosome 7 of grape. TheS‐haplotype possessed three additional genes and two inversions.TsSPH1was expressed in filaments and anthers,TsYUC6in anthers andTsBAHDin pistils. Long‐homostyle mutants did not possessTsBAHDand a short‐homostyle mutant did not expressTsSPH1.Three hemizygous genes appear to determine S‐morph characteristics inT. subulata. Hemizygosity is common to all distylous species investigated, yet the genes differ. The pistil candidate gene,TsBAHD, differs from that ofPrimula, but both may inactivate brassinosteroids causing short styles.TsYUC6is involved in auxin synthesis and likely determines pollen characteristics.TsSPH1is likely involved in filament elongation. We propose an incompatibility mechanism involvingTsYUC6andTsBAHD. 
    more » « less
  2. PremiseEocene floras of Patagonia document biotic response to the final separation of Gondwana. The conifer genusAraucaria, distributed worldwide during the Mesozoic, has a disjunct extant distribution between South America and Australasia. Fossils assigned to AustralasianAraucariaSect.Eutactausually are represented by isolated organs, making diagnosis difficult.Araucaria pichileufensisE.W. Berry, from the middle Eocene Río Pichileufú (RP) site in Argentine Patagonia, was originally placed in Sect.Eutactaand later reported from the early Eocene Laguna del Hunco (LH) locality. However, the relationship ofA. pichileufensisto Sect.Eutactaand the conspecificity of theAraucariamaterial among these Patagonian floras have not been tested using modern methods. MethodsWe review the type material ofA. pichileufensisalongside large (n= 192) new fossil collections ofAraucariafromLHandRP, including multi‐organ preservation of leafy branches, ovuliferous complexes, and pollen cones. We use a total evidence phylogenetic analysis to analyze relationships of the fossils to Sect.Eutacta. ResultsWe describeAraucaria huncoensissp. nov. fromLHand improve the whole‐plant concept forAraucaria pichileufensisfromRP. The two species respectively resolve in the crown and stem of Sect.Eutacta. ConclusionsOur results confirm the presence and indicate the survival of Sect.Eutactain South America during early Antarctic separation. The exceptionally complete fossils significantly predate several molecular age estimates for crownEutacta. The differentiation of twoAraucariaspecies demonstrates conifer turnover during climate change and initial South American isolation from the early to middle Eocene. 
    more » « less
  3. Abstract ARGONAUTES are the central effector proteins ofRNAsilencing which bind target transcripts in a smallRNA‐guided manner.Arabidopsis thalianahas 10ARGONAUTE(AGO) genes, with specialized roles inRNA‐directedDNAmethylation, post‐transcriptional gene silencing, and antiviral defense. To better understand specialization amongAGOgenes at the level of transcriptional regulation we tested a library of 1497 transcription factors for binding to the promoters ofAGO1,AGO10, andAGO7using yeast 1‐hybrid assays. A ranked list of candidateDNA‐bindingTFs revealed binding of theAGO7promoter by a number of proteins in two families: the miR156‐regulatedSPLfamily and the miR319‐regulatedTCPfamily, both of which have roles in developmental timing and leaf morphology. Possible functions forSPLandTCPbinding are unclear: we showed that these binding sites are not required for the polar expression pattern ofAGO7, nor for the function ofAGO7in leaf shape. NormalAGO7transcription levels and function appear to depend instead on an adjacent 124‐bp region. Progress in understanding the structure of this promoter may aid efforts to understand how the conservedAGO7‐triggeredTAS3pathway functions in timing and polarity. 
    more » « less
  4. ABSTRACT Necrotrophic pathogens cause serious threats to agricultural crops, and understanding the resistance genes and their genetic networks is key to breeding new plant cultivars with better resistance traits. AlthoughAlternaria alternatacauses black spot in important leafy brassica vegetables, and leads to significant loss of yield and food quality, little is known about plant–A. alternatainteractions. In this study, we used a unique and large collection of single, double and triple mutant lines of defence metabolite regulators inArabidopsisto explore how these transcription factors and their epistatic networks may influenceA. alternatainfections. This identified nine novel regulators and 20 pairs of epistatic interactions that modulateArabidopsisplants' defence responses toA. alternatainfection. We further showed that the glucosinolate 4‐methoxy‐indol‐3‐ylmethyl is the only glucosinolate consistently responsive toA. alternatainfection in Col‐0 ecotype. With the further exploration of the regulators and the genetic networks on modulating the accumulation of glucosinolates underA. alternatainfection, an inverted triangle regulatory model was proposed forArabidopsisplants' defence responses at a metabolic level and a phenotypic level. 
    more » « less
  5. Summary Steady‐state photosyntheticCO2responses (A/Cicurves) are used to assess environmental responses of photosynthetic traits and to predict future vegetative carbon uptake through modeling. The recent development of rapidA/Cicurves (RACiRs) permits faster assessment of these traits by continuously changing [CO2] around the leaf, and may reveal additional photosynthetic properties beyond what is practical or possible with steady‐state methods.Gas exchange necessarily incorporates photosynthesis and (photo)respiration. Each process was expected to respond on different timescales due to differences in metabolite compartmentation, biochemistry and diffusive pathways. We hypothesized that metabolic lags in photorespiration relative to photosynthesis/respiration andCO2diffusional limitations can be detected by varying the rate of change in [CO2] duringRACiR assays. We tested these hypotheses through modeling and experiments at ambient and 2% oxygen.Our data show that photorespiratory delays cause offsets in predictedCO2compensation points that are dependent on the rate of change in [CO2]. Diffusional limitations may reduce the rate of change in chloroplastic [CO2], causing a reduction in apparentRACiR slopes under highCO2ramp rates.MultirateRACiRs may prove useful in assessing diffusional limitations to gas exchange and photorespiratory rates. 
    more » « less