Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the pp-Adics-Quantum Group Connection

We establish a previously conjectured connection between $p$-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which ``interpolate'' between the zonal spherical functions of related real and $p$\--adic symmetric spaces. The elliptic quantum algebras underlie the $Z_n$\--Baxter models. We show that in the n \air \infty limit, the Jost function for the scattering of {\em first} level excitations in the $Z_n$\--Baxter model coincides with the Harish\--Chandra\--like $c$\--function constructed from the Macdonald polynomials associated to the root system $A_1$. The partition function of the $Z_2$\--Baxter model itself is also expressed in terms of this Macdonald\--Harish\--Chandra\ $c$\--function, albeit in a less simple way. We relate the two parameters $q$ and $t$ of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular the $p$\--adic ``regimes'' in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of ``$q$\--deforming'' Euler products.Comment: 25 page

Quantum Dynamical Algebra SU(1,1) in One-Dimensional Exactly Solvable Potentials

We mainly explore the linear algebraic structure like SU(2) or SU(1,1) of the shift operators for some one-dimensional exactly solvable potentials in this paper. During such process, a set of method based on original diagonalizing technique is presented to construct those suitable operator elements, J0, J_\pm that satisfy SU(2) or SU(1,1) algebra. At last, the similarity between radial problem and one-dimensional potentials encourages us to deal with the radial problem in the same way.Comment: No figures, 9 Pages accepted by International Journal of Theoretical Physic

The construction of a Solanum habrochaites LYC4 introgression line population and the identification of QTLs for resistance to Botrytis cinerea

Tomato (Solanum lycopersicum) is susceptible to grey mold (Botrytis cinerea). Partial resistance to this fungus has been identified in accessions of wild relatives of tomato such as Solanum habrochaites LYC4. In a previous F2 mapping study, three QTLs conferring resistance to B. cinerea (Rbcq1, Rbcq2 and Rbcq4a) were identified. As it was probable that this study had not identified all QTLs involved in resistance we developed an introgression line (IL) population (n = 30), each containing a S. habrochaites introgression in the S. lycopersicum cv. Moneymaker genetic background. On average each IL contained 5.2% of the S. habrochaites genome and together the lines provide an estimated coverage of 95%. The level of susceptibility to B. cinerea for each of the ILs was assessed in a greenhouse trial and compared to the susceptible parent S. lycopersicum cv. Moneymaker. The effect of the three previously identified loci could be confirmed and seven additional loci were detected. Some ILs contains multiple QTLs and the increased resistance to B. cinerea in these ILs is in line with a completely additive model. We conclude that this set of QTLs offers good perspectives for breeding of B. cinerea resistant cultivars and that screening an IL population is more sensitive for detection of QTLs conferring resistance to B. cinerea than the analysis in an F2 population

A Model for the Detection of Moving Targets in Visual Clutter Inspired by Insect Physiology

We present a computational model for target discrimination based on intracellular recordings from neurons in the fly visual system. Determining how insects detect and track small moving features, often against cluttered moving backgrounds, is an intriguing challenge, both from a physiological and a computational perspective. Previous research has characterized higher-order neurons within the fly brain, known as ‘small target motion detectors’ (STMD), that respond robustly to moving features, even when the velocity of the target is matched to the background (i.e. with no relative motion cues). We recorded from intermediate-order neurons in the fly visual system that are well suited as a component along the target detection pathway. This full-wave rectifying, transient cell (RTC) reveals independent adaptation to luminance changes of opposite signs (suggesting separate ON and OFF channels) and fast adaptive temporal mechanisms, similar to other cell types previously described. From this physiological data we have created a numerical model for target discrimination. This model includes nonlinear filtering based on the fly optics, the photoreceptors, the 1st order interneurons (Large Monopolar Cells), and the newly derived parameters for the RTC. We show that our RTC-based target detection model is well matched to properties described for the STMDs, such as contrast sensitivity, height tuning and velocity tuning. The model output shows that the spatiotemporal profile of small targets is sufficiently rare within natural scene imagery to allow our highly nonlinear ‘matched filter’ to successfully detect most targets from the background. Importantly, this model can explain this type of feature discrimination without the need for relative motion cues

Y-Like Retinal Ganglion Cells Innervate the Dorsal Raphe Nucleus in the Mongolian Gerbil (Meriones unguiculatus)

Background: The dorsal raphe nucleus (DRN) of the mesencephalon is a complex multi-functional and multi-transmitter nucleus involved in a wide range of behavioral and physiological processes. The DRN receives a direct input from the retina. However little is known regarding the type of retinal ganglion cell (RGC) that innervates the DRN. We examined morphological characteristics and physiological properties of these DRN projecting ganglion cells. Methodology/Principal Findings: The Mongolian gerbils are highly visual rodents with a diurnal/crepuscular activity rhythm. It has been widely used as experimental animals of various studies including seasonal affective disorders and depression. Young adult gerbils were used in the present study. DRN-projecting RGCs were identified following retrograde tracer injection into the DRN, characterized physiologically by extracellular recording and morphologically after intracellular filling. The result shows that DRN-projecting RGCs exhibit morphological characteristics typical of alpha RGCs and physiological response properties of Y-cells. Melanopsin was not detected in these RGCs and they show no evidence of intrinsic photosensitivity. Conclusions/Significance: These findings suggest that RGCs with alpha-like morphology and Y-like physiology appear to perform a non-imaging forming function and thus may participate in the modulation of DRN activity which includes regulation of sleep and mood

The GALAH Survey : Non-LTE departure coefficients for large spectroscopic surveys

19 pages, 25 figures, 2 tables, arXiv abstract abridged; accepted for publication in A&AMassive sets of stellar spectroscopic observations are rapidly becoming available and these can be used to determine the chemical composition and evolution of the Galaxy with unprecedented precision. One of the major challenges in this endeavour involves constructing realistic models of stellar spectra with which to reliably determine stellar abundances. At present, large stellar surveys commonly use simplified models that assume that the stellar atmospheres are approximately in local thermodynamic equilibrium (LTE). To test and ultimately relax this assumption, we have performed non-LTE calculations for $13$ different elements (H, Li, C, N, O, Na, Mg, Al, Si, K, Ca, Mn, and Ba), using recent model atoms that have physically-motivated descriptions for the inelastic collisions with neutral hydrogen, across a grid of $3756$ 1D MARCS model atmospheres that spans $3000\leq T_{\mathrm{eff}}/\mathrm{K}\leq8000$, $-0.5\leq\log{g/\mathrm{cm\,s^{-2}}}\leq5.5$, and $-5\leq\mathrm{[Fe/H]}\leq1$. We present the grids of departure coefficients that have been implemented into the GALAH DR3 analysis pipeline in order to complement the extant non-LTE grid for iron. We also present a detailed line-by-line re-analysis of $50126$ stars from GALAH DR3. We found that relaxing LTE can change the abundances by between $-0.7\,\mathrm{dex}$ and $+0.2\,\mathrm{dex}$ for different lines and stars. Taking departures from LTE into account can reduce the dispersion in the $\mathrm{[A/Fe]}$ versus $\mathrm{[Fe/H]}$ plane by up to $0.1\,\mathrm{dex}$, and it can remove spurious differences between the dwarfs and giants by up to $0.2\,\mathrm{dex}$. The resulting abundance slopes can thus be qualitatively different in non-LTE, possibly with important implications for the chemical evolution of our Galaxy.Peer reviewe