University of California, Santa Cruz

About: University of California, Santa Cruz is a education organization based out in Santa Cruz, California, United States. It is known for research contribution in the topics: Galaxy & Population. The organization has 15541 authors who have published 44120 publications receiving 2759983 citations. The organization is also known as: UCSC & UC, Santa Cruz.

The statistical inevitability of stability-diversity relationships in community ecology.

Abstract: In this article, we explain an often overlooked process has revitalized interest in stability-diversity relationships that may significantly contribute to positive correlations between and the ecological mechanisms that cause them. How- measures of species diversity and community stability. Empirical studies showing positive stability-diversity relationships have, for ever, while this and previous studies have supplied im- the most part, used a single class of stability (or, more accurately, portant documentation of stability-diversity correlations, instability) measures: the temporal variation in aggregate commu- the range of processes creating these relationships still re- nity properties such as biomass or productivity. We show that for mains unclear. In particular, from its beginnings until the these measures, stability will essentially always rise with species di- present, the ecological literature on stability-diversity versity because of the statistical averaging of the fluctuations in patterns has overlooked the possibility that random fluc- species' abundances. This simple probabilistic process will operate tuations in the abundances of individual species may be in the absence of any strong species interactions, although its strength is driven by the relative abundances of species, as well as as or more important than species interactions in creat- by the existence of positive or negative correlations in the fluctua- ing stability-diversity relationships. However, as we show tions of species. To explore the possible importance of this effect here, some stability-diversity correlations, including all in real communities, we fit a simple simulation model to Tilman's those clearly documented in the field, are at least partially grassland community. Our results indicate that statistical averaging explainable as the outcomes of probabilistic processes in- might play a substantial role in explaining stability-diversity corre- volving fluctuations in species abundances and would lations for this and other systems. Models of statistical averaging arise to greater or lesser extents even in the complete ab- can serve as a useful baseline for predictions of community stabil- ity, to which the influences of both negative and positive species sence of ecological interactions. An understanding of this interactions may then be added and tested. statistical averaging process is useful because it both makes the very general prediction that stability-diversity

Introduction to Random Matrices

Abstract: Here I = S j (a2j 1,a2j) andI(y) is the characteristic function of the set I. In the Gaussian Unitary Ensemble (GUE) the probability that no eigenvalues lie in I is equal to �(a). Also �(a) is a tau-function and we present a new simplified derivation of the system of nonlinear completely integrable equations (the aj's are the independent variables) that were first derived by Jimbo, Miwa, Mori, and Sato in 1980. In the case of a single interval these equations are reducible to a Painleve V equation. For large s we give an asymptotic formula for E2(n;s), which is the probability in the GUE that exactly n eigenvalues lie in an interval of length s. These notes provide an introduction to that aspect of the theory of random matrices dealing with the distribution of eigenvalues. To first orient the reader, we present in Sec. II some numerical experiments that illustrate some of the basic aspects of the subject. In Sec. III we introduce the invariant measures for the three "circular ensembles" involving unitary matrices. We also define the level spacing distributions and express these distributions in terms of a particular Fredholm determinant. In Sec. IV we explain how these measures are modified for the orthogonal polynomial ensembles. In Sec. V we discuss the universality of these level spacing distribution functions in a particular scaling limit. The discussion up to this point (with the possible exception of Sec. V) follows the well-known path pioneered by Hua, Wigner, Dyson, Mehta and others who first developed this theory (see, e.g., the reprint volume of Porter (34) and Hua (17)). This, and much more, is discussed in Mehta's book (25)—the classic reference in the subject. An important development in random matrices was the discovery by Jimbo, Miwa, Mori, and Sato (21) (hereafter referred to as JMMS) that the basic Fredholm determinant mentioned above is a �-function in the sense of the Kyoto School. Though it has been some twelve years since (21) was published, these results are not widely appreciated by the practitioners of random matrices. This is due no doubt to the complexity of their paper. The methods of JMMS are methods of discovery; but now that we know the result, simpler proofs can be constructed. In Sec. VI we give such a proof of the JMMS equations. Our proof is a simplification and generalization of Mehta's (27) simplified proof of the single interval case. Also our methods build on the earlier work of Its, Izergin, Korepin, and Slavnov (18) and Dyson (12). We include in this section a discussion of the connection between the JMMS equations and the integrable Hamiltonian systems that appear in the geometry of quadrics and spectral theory as developed by Moser (31). This section concludes with a discussion of the case of a single interval (viz., probability that exactly n eigenvalues lie in a given interval). In this case the JMMS equations can be reduced to a single ordinary differential equation—the Painleve V equation. Finally, in Sec. VII we discuss the asymptotics in the case of a large single interval of the various level spacing distribution functions (4,38,28). In this analysis both the Painleve representation and new results in Toeplitz/Wiener- Hopf theory are needed to produce these asymptotics. We also give an approach based on the asymptotics of the eigenvalues of the basic linear integral operator (14,25,35). These results are then compared with the continuum model calculations of Dyson (12).

A new nonparametric approach to galaxy morphological classification

Abstract: We present two new nonparametric methods for quantifying galaxy morphology: the relative distribution of the galaxy pixel flux values (the Gini coefficient or G) and the second-order moment of the brightest 20% of the galaxy's flux (M20). We test the robustness of G and M20 to decreasing signal-to-noise ratio (S/N) and spatial resolution and find that both measures are reliable to within 10% for images with average S/N per pixel greater than 2 and resolutions better than 1000 and 500 pc, respectively. We have measured G and M20, as well as concentration (C), asymmetry (A), and clumpiness (S) in the rest-frame near-ultraviolet/optical wavelengths for 148 bright local normal Hubble-type galaxies (E–Sd) galaxies, 22 dwarf irregulars, and 73 0.05 < z < 0.25 ultraluminous infrared galaxies (ULIRGs). We find that most local galaxies follow a tight sequence in G-M20-C, where early types have high G and C and low M20 and late-type spirals have lower G and C and higher M20. The majority of ULIRGs lie above the normal galaxy G-M20 sequence because of their high G and M20 values. Their high Gini coefficients arise from very bright nuclei, while the high second-order moments are produced by multiple nuclei and bright tidal tails. All of these features are signatures of recent and on-going mergers and interactions. We also find that in combination with A and S, G is more effective than C at distinguishing ULIRGs from the normal Hubble types. Finally, we measure the morphologies of 491.7 < z < 3.8 galaxies from HST NICMOS observations of the Hubble Deep Field North. We find that many of the z ~ 2 galaxies possess G and A higher than expected from degraded images of local elliptical and spiral galaxies and have morphologies more like low-redshift ULIRGs.

A New Non-Parametric Approach to Galaxy Morphological Classification

Abstract: We present two new non-parametric methods for quantifying galaxy morphology: the relative distribution of the galaxy pixel flux values (the Gini coefficient or G) and the second-order moment of the brightest 20% of the galaxy's flux (M20). We test the robustness of G and M20 to decreasing signal-to-noise and spatial resolution, and find that both measures are reliable to within 10% at average signal-to-noise per pixel greater than 3 and resolutions better than 1000 pc and 500 pc, respectively. We have measured G and M20, as well as concentration (C), asymmetry (A), and clumpiness (S) in the rest-frame near-ultraviolet/optical wavelengths for 150 bright local "normal" Hubble type galaxies (E-Sd) galaxies and 104 0.05 < z < 0.25 ultra-luminous infrared galaxies (ULIRGs).We find that most local galaxies follow a tight sequence in G-M20-C, where early-types have high G and C and low M20 and late-type spirals have lower G and C and higher M20. The majority of ULIRGs lie above the normal galaxy G-M20 sequence, due to their high G and M20 values. Their high Gini coefficients arise from very bright nuclei, while the high second-order moments are produced by multiple nuclei and bright tidal tails. All of these features are signatures of recent and on-going mergers and interactions. We also find that in combination with A and S, G is more effective than C at distinguishing ULIRGs from the "normal" Hubble-types. Finally, we measure the morphologies of 45 1.7 < z < 3.8 galaxies from HST NICMOS observations of the Hubble Deep Field North. We find that many of the z $\sim$ 2 galaxies possess G and A higher than expected from degraded images of local elliptical and spiral galaxies, and have morphologies more like low-redshift single nucleus ULIRGs.

Flavonoids Act as Negative Regulators of Auxin Transport in Vivo in Arabidopsis

Abstract: Polar transport of the plant hormone auxin controls many aspects of plant growth and development. A number of synthetic compounds have been shown to block the process of auxin transport by inhibition of the auxin efflux carrier complex. These synthetic auxin transport inhibitors may act by mimicking endogenous molecules. Flavonoids, a class of secondary plant metabolic compounds, have been suggested to be auxin transport inhibitors based on their in vitro activity. The hypothesis that flavonoids regulate auxin transport in vivo was tested in Arabidopsis by comparing wild-type (WT) and transparent testa (tt4) plants with a mutation in the gene encoding the first enzyme in flavonoid biosynthesis, chalcone synthase. In a comparison between tt4 and WT plants, phenotypic differences were observed, including three times as many secondary inflorescence stems, reduced plant height, decreased stem diameter, and increased secondary root development. Growth of WT Arabidopsis plants on naringenin, a biosynthetic precursor to those flavonoids with auxin transport inhibitor activity in vitro, leads to a reduction in root growth and gravitropism, similar to the effects of synthetic auxin transport inhibitors. Analyses of auxin transport in the inflorescence and hypocotyl of independent tt4 alleles indicate that auxin transport is elevated in plants with a tt4 mutation. In hypocotyls of tt4, this elevated transport is reversed when flavonoids are synthesized by growth of plants on the flavonoid precursor, naringenin. These results are consistent with a role for flavonoids as endogenous regulators of auxin transport.