A Reciprocity Theorem for Monomer-Dimer Coverings

The problem of counting monomer-dimer coverings of a lattice is a longstanding problem in statistical mechanics. It has only been exactly solved for the special case of dimer coverings in two dimensions. In earlier work, Stanley proved a reciprocity principle governing the number $N(m,n)$ of dimer coverings of an $m$ by $n$ rectangular grid (also known as perfect matchings), where $m$ is fixed and $n$ is allowed to vary. As reinterpreted by Propp, Stanley's result concerns the unique way of extending $N(m,n)$ to $n < 0$ so that the resulting bi-infinite sequence, $N(m,n)$ for $n \in {Z}$, satisfies a linear recurrence relation with constant coefficients. In particular, Stanley shows that $N(m,n)$ is always an integer satisfying the relation $N(m,-2-n) = \epsilon_{m,n}N(m,n)$ where $\epsilon_{m,n} = 1$ unless $m\equiv$ 2(mod 4) and $n$ is odd, in which case $\epsilon_{m,n} = -1$. Furthermore, Propp's method is applicable to higher-dimensional cases. This paper discusses similar investigations of the numbers $M(m,n)$, of monomer-dimer coverings, or equivalently (not necessarily perfect) matchings of an $m$ by $n$ rectangular grid. We show that for each fixed $m$ there is a unique way of extending $M(m,n)$ to $n < 0$ so that the resulting bi-infinite sequence, $M(m,n)$ for $n \in {Z}$, satisfies a linear recurrence relation with constant coefficients. We show that $M(m,n)$, a priori a rational number, is always an integer, using a generalization of the combinatorial model offered by Propp. Lastly, we give a new statement of reciprocity in terms of multivariate generating functions from which Stanley's result follows.Comment: 13 pages, 12 figures, to appear in the proceedings of the Discrete Models for Complex Systems (DMCS) 2003 conference. (v2 - some minor changes

Identification and profiling of miRNAs during herbivory reveals jasmonate-dependent and -independent patterns of accumulation in Nicotiana attenuata

Background Plant microRNAs (miRNAs) play key roles in the transcriptional responses to environmental stresses. However, the role of miRNAs in responses to insect herbivory has not been thoroughly explored. To identify herbivory-responsive miRNAs, we identified conserved miRNAs in the ecological model plant Nicotiana attenuata whose interactions with herbivores have been well-characterized in both laboratory and field studies. Results We identified 59 miRNAs from 36 families, and two endogenous trans-acting small interfering RNAs (tasiRNA) targeted by miRNAs. We characterized the response of the precursor and mature miRNAs to simulated attack from the specialist herbivore Manduca sexta by quantitative PCR analysis and used ir-aoc RNAi transformants, deficient in jasmonate biosynthesis, to identify jasmonate-dependent and -independent miRNA regulation. Expression analysis revealed that groups of miRNAs and tasiRNAs were specifically regulated by either mechanical wounding or wounding plus oral secretions from M. sexta larvae, and these small RNAs were accumulated in jasmonate-dependent or -independent manners. Moreover, cDNA microarray analysis indicated that the expression patterns of the corresponding target genes were correlated with the accumulation of miRNAs and tasiRNAs. Conclusions We show that a group of miRNAs and tasiRNAs orchestrates the expression of target genes involved in N. attenuata’s responses to herbivore attack

Ferromagnetic resonance force microscopy on a thin permalloy film

Ferromagnetic Resonance Force Microscopy (FMRFM) offers a means of performing local ferromagnetic resonance. We have studied the evolution of the FMRFM force spectra in a continuous 50 nm thick permalloy film as a function of probe-film distance and performed numerical simulations of the intensity of the FMRFM probe-film interaction force, accounting for the presence of the localized strongly nonuniform magnetic field of the FMRFM probe magnet. Excellent agreement between the experimental data and the simulation results provides insight into the mechanism of FMR mode excitation in an FMRFM experiment.Comment: 9 pages, 2 figure

An unbiased approach elucidates variation in (S)-(+)-linalool, a context-specific mediator of a tri-trophic interaction in wild tobacco

Plant volatile organic compounds (VOCs) mediate many interactions, and the function of common VOCs is especially likely to depend on ecological context. We used a genetic mapping population of wild tobacco, Nicotiana attenuata, originating from a cross of 2 natural accessions from Arizona and Utah, separated by the Grand Canyon, to dissect genetic variation controlling VOCs. Herbivory-induced leaf terpenoid emissions varied substantially, while green leaf volatile emissions were similar. In a field experiment, only emissions of linalool, a common VOC, correlated significantly with predation of the herbivore Manduca sexta by native predators. Using quantitative trait locus mapping and genome mining,we identified an (S)-(+)-linalool synthase (NaLIS). Genome resequencing, gene cloning, and activity assays revealed that the presence/absence of a 766-bp sequence in NaLIS underlies the variation of linalool emissions in 26 natural accessions. We manipulated linalool emissions and composition by ectopically expressing linalool synthases for both enantiomers, (S)-(+)- and (R)-(−)-linalool, reported to oppositely affect M. sexta oviposition, in the Arizona and Utah accessions.We used these lines to test ovipositingmoths in increasingly complex environments. The enantiomers had opposite effects on oviposition preference, but themagnitude of the effect depended strongly both on plant genetic background, and complexity of the bioassay environment. Our study reveals that the emission of linalool, a common VOC, differs by orders-of-magnitude among geographically interspersed conspecific plants due to allelic variation in a linalool synthase, and that the response of a specialist herbivore to linalool depends on enantiomer, plant genotype, and environmental complexity

Phaseless VLBI mapping of compact extragalactic radio sources

The problem of phaseless aperture synthesis is of current interest in phase-unstable VLBI with a small number of elements when either the use of closure phases is not possible (a two-element interferometer) or their quality and number are not enough for acceptable image reconstruction by standard adaptive calibration methods. Therefore, we discuss the problem of unique image reconstruction only from the spectrum magnitude of a source. We suggest an efficient method for phaseless VLBI mapping of compact extragalactic radio sources. This method is based on the reconstruction of the spectrum magnitude for a source on the entire UV plane from the measured visibility magnitude on a limited set of points and the reconstruction of the sought-for image of the source by Fienup's method from the spectrum magnitude reconstructed at the first stage. We present the results of our mapping of the extragalactic radio source 2200 +420 using astrometric and geodetic observations on a global VLBI array. Particular attention is given to studying the capabilities of a two-element interferometer in connection with the putting into operation of a Russian-made radio interferometer based on Quasar RT-32 radio telescopes.Comment: 21 pages, 6 figure

Quantum Hall line junction with impurities as a multi-slit Luttinger liquid interferometer

We report on quantum interference between a pair of counterpropagating quantum Hall edge states that are separated by a high quality tunnel barrier. Observed Aharonov-Bohm oscillations are analyzed in terms of resonant tunneling between coupled Luttinger liquids that creates bound electronic states between pairs of tunnel centers that act like interference slits. We place a lower bound in the range of 20-40 $\mu$m for the phase coherence length and directly confirm the extended phase coherence of quantum Hall edge states.Comment: 4 pages, 3 figures, 1 tabl

Sex ratio of mirid populations shifts in response to hostplant co-infestation or altered cytokinin signaling

Herbivore species sharing a host plant often compete. In this study, we show that host plant-mediated interaction between two insect herbivores – a generalist and a specialist – results in a sex ratio shift of the specialist's offspring. We studied demographic parameters of the specialist Tupiocoris notatus (Hemiptera: Miridae) when co-infesting the host plant Nicotiana attenuata (Solanaceae) with the generalist leafhopper Empoasca sp. (Hemiptera: Cicadellidae). We show that the usually female-biased sex ratio of T. notatus shifts toward a higher male proportion in the offspring on plants co-infested by Empoasca sp. This sex ratio change did not occur after oviposition, nor is it due differential mortality of female and male nymphs. Based on pyrosequencing and PCR of bacterial 16S rRNA amplicons, we concluded that sex ratio shifts were unlikely to be due to infection with Wolbachia or other known sex ratio- distorting endosymbionts. Finally, we used transgenic lines of N. attenuata to evaluate if the sex ratio shift could be mediated by changes in general or specialized host plant metabolites. We found that the sex ratio shift occurred on plants deficient in two cytokinin receptors (irCHK2/3). Thus, cytokinin-regulated traits can alter the offspring sex ratio of the specialist T. notatus

The Trans-Pacific Partnership Agreement: Looking Ahead to the Next Steps

Pressure has been building for the conclusion of the 12-country Trans-Pacific Partnership (TPP) negotiations. Getting the deal done is important, but the TPP is not just another free trade agreement (FTA). It represents the chance to set a trade agenda for the future across a wide range of topics for countries throughout the Asia-Pacific region. This means that the agreement should not be settled in haste. More importantly, it also means that key decisions need to be reached about broader issues related to the institutional structure of the TPP. These decisions must be made now, before the deal is closed, on issues such as how to create the TPP as a living agreement, the formation of a TPP Secretariat, and the clarification of entry conditions for future members such as the People’s Republic of China (PRC). These choices must be made deliberately and carefully even while officials are struggling with reaching closure on the most highly sensitive issues still remaining in the agreement. It will not be easy, but wise decisions are necessary now to ensure the long-term success of the TPP

Variability of Optical Counterparts in the Chandra Galactic Bulge Survey

We present optical lightcurves of variable stars consistent with the positions of X-ray sources identified with the Chandra X-ray Observatory for the Chandra Galactic Bulge Survey. Using data from the Mosaic-II instrument on the Blanco 4m Telescope at CTIO, we gathered time-resolved photometric data on timescales from $\sim2$ hr to 8 days over the $\frac{3}{4}$ of the X-ray survey containing sources from the initial GBS catalog. Among the lightcurve morphologies we identify are flickering in interacting binaries, eclipsing sources, dwarf nova outbursts, ellipsoidal variations, long period variables, spotted stars, and flare stars. $87\%$ of X-ray sources have at least one potential optical counterpart. $24\%$ of these candidate counterparts are detectably variable; a much greater fraction than expected for randomly selected field stars, which suggests that most of these variables are real counterparts. We discuss individual sources of interest, provide variability information on candidate counterparts, and discuss the characteristics of the variable population.Comment: Accepted for publication in the Astrophysical Journal Supplement

Evolution of a novel and adaptive floral scent in wild tobacco

Many plants emit diverse floral scents that mediate plant-environment interactions and attain reproductive success. However, how plants evolve novel adaptive floral volatiles remains unclear. Here, we show that in the wild tobacco, Nicotiana attenuata, a dominant species-specific floral volatile (benzyl acetone, BA) that attracts pollinators and deters florivore is synthesized by phenylalanine ammonia-lyase 4 (NaPAL4), isoflavone reductase 3 (NaIFR3), and chalcone synthase 3 (NaCHAL3). Transient expression of NaFIR3 alone in N. attenuata leaves is sufficient and necessary for ectopic foliar BA emissions, and the BA emission level is increased by co-expressing NaIFR3 with NaPAL4 and NaCHAL3. Independent changes in transcription in all three genes contributed to intraspecific variations of floral BA emission. However, among species, the gain-of-expression in NaIFR3 resulted in the biosynthesis of BA that was only found in N. attenuata. This study suggests that novel metabolic pathways associated with adaptation can arise via re-configurations of gene expression