A new realization of rational functions, with applications to linear combination interpolation

We introduce the following linear combination interpolation problem (LCI): Given $N$ distinct numbers $w_1,\ldots w_N$ and $N+1$ complex numbers $a_1,\ldots, a_N$ and $c$, find all functions $f(z)$ analytic in a simply connected set (depending on $f$) containing the points $w_1,\ldots,w_N$ such that $$\sum_{u=1}^Na_uf(w_u)=c.$$ To this end we prove a representation theorem for such functions $f$ in terms of an associated polynomial $p(z)$. We first introduce the following two operations, $(i)$ substitution of $p$, and $(ii)$ multiplication by monomials $z^j, 0\le j < N$. Then let $M$ be the module generated by these two operations, acting on functions analytic near $0$. We prove that every function $f$, analytic in a neighborhood of the roots of $p$, is in $M$. In fact, this representation of $f$ is unique. To solve the above interpolation problem, we employ an adapted systems theoretic realization, as well as an associated representation of the Cuntz relations (from multi-variable operator theory.) We study these operations in reproducing kernel Hilbert space): We give necessary and sufficient condition for existence of realizations of these representation of the Cuntz relations by operators in certain reproducing kernel Hilbert spaces, and offer infinite product factorizations of the corresponding kernels

The Origin and Evolution of the Galaxy Mass-Metallicity Relation

We use high-resolution cosmological zoom-in simulations from the Feedback in Realistic Environment (FIRE) project to study the galaxy mass-metallicity relations (MZR) from z=0-6. These simulations include explicit models of the multi-phase ISM, star formation, and stellar feedback. The simulations cover halo masses Mhalo=10^9-10^13 Msun and stellar mass Mstar=10^4-10^11 Msun at z=0 and have been shown to produce many observed galaxy properties from z=0-6. For the first time, our simulations agree reasonably well with the observed mass-metallicity relations at z=0-3 for a broad range of galaxy masses. We predict the evolution of the MZR from z=0-6 as log(Zgas/Zsun)=12+log(O/H)-9.0=0.35[log(Mstar/Msun)-10]+0.93 exp(-0.43 z)-1.05 and log(Zstar/Zsun)=[Fe/H]-0.2=0.40[log(Mstar/Msun)-10]+0.67 exp(-0.50 z)-1.04, for gas-phase and stellar metallicity, respectively. Our simulations suggest that the evolution of MZR is associated with the evolution of stellar/gas mass fractions at different redshifts, indicating the existence of a universal metallicity relation between stellar mass, gas mass, and metallicities. In our simulations, galaxies above Mstar=10^6 Msun are able to retain a large fraction of their metals inside the halo, because metal-rich winds fail to escape completely and are recycled into the galaxy. This resolves a long-standing discrepancy between "sub-grid" wind models (and semi-analytic models) and observations, where common sub-grid models cannot simultaneously reproduce the MZR and the stellar mass functions.Comment: 17 pages, 14 figures, re-submitted to MNRAS after revisions on referee comment

ALMA Observations of Gas-Rich Galaxies in z~1.6 Galaxy Clusters: Evidence for Higher Gas Fractions in High-Density Environments

We present ALMA CO (2-1) detections in 11 gas-rich cluster galaxies at z~1.6, constituting the largest sample of molecular gas measurements in z>1.5 clusters to date. The observations span three galaxy clusters, derived from the Spitzer Adaptation of the Red-sequence Cluster Survey. We augment the >5sigma detections of the CO (2-1) fluxes with multi-band photometry, yielding stellar masses and infrared-derived star formation rates, to place some of the first constraints on molecular gas properties in z~1.6 cluster environments. We measure sizable gas reservoirs of 0.5-2x10^11 solar masses in these objects, with high gas fractions and long depletion timescales, averaging 62% and 1.4 Gyr, respectively. We compare our cluster galaxies to the scaling relations of the coeval field, in the context of how gas fractions and depletion timescales vary with respect to the star-forming main sequence. We find that our cluster galaxies lie systematically off the field scaling relations at z=1.6 toward enhanced gas fractions, at a level of ~4sigma, but have consistent depletion timescales. Exploiting CO detections in lower-redshift clusters from the literature, we investigate the evolution of the gas fraction in cluster galaxies, finding it to mimic the strong rise with redshift in the field. We emphasize the utility of detecting abundant gas-rich galaxies in high-redshift clusters, deeming them as crucial laboratories for future statistical studies.Comment: 8 pages, 3 figures, published in ApJ Letters; updated to match published versio

A reliability based consistent fuzzy preference relations for risk assessment in oil and gas industry

In decision making, linguistic variables tend to be complex to handle but they make more sense than classical fuzzy numbers. Fuzziness is not sufficient enough to deal with information and degree of reliability of information is critical. Z-numbers is proposed to model the uncertainty produced by human judgment when eliciting information. Therefore, the implementation of z-numbers is taken into consideration, where it has more authority to describe the knowledge of human being and extensively used in the uncertain information development. This issue has motivated the authors to propose fuzzy multi criteria decision making methodology using z-numbers. The proposed methodology is demonstrated the capability to handle knowledge of human being and uncertain information for risk assessment in oil and gas industry. This assessment is due to periodic basis, which will give insights from the operational until the strategic level of decision making process that is capable of dealing with uncertainty in human judgment. The consistent fuzzy preference relations is developed to calculate the preference-weights of the criteria related based on the derived network structure and to resolve conflicts arising from differences in information and opinions provided by the decision makers. The proposed methodology is constructed without losing the generality of the consistent fuzzy preference relations under fuzzy environment

Half-mass radii for ~7,000 galaxies at 1.0 < z < 2.5: most of the evolution in the mass-size relation is due to color gradients

Radial mass-to-light ratio gradients cause the half-mass and half-light radii of galaxies to differ, potentially biasing studies that use half-light radii. Here we present the largest catalog to date of galaxy half-mass radii at z > 1: 7,006 galaxies in the CANDELS fields at 1.0 < z < 2.5. The sample includes both star-forming and quiescent galaxies with stellar masses 9.0 < log(M_* / M_\odot) < 11.5. We test three methods for calculating half-mass radii from multi-band PSF-matched HST imaging: two based on spatially-resolved SED modeling, and one that uses a rest-frame color profile. All three methods agree, with scatter <~0.3 dex. In agreement with previous studies, most galaxies in our sample have negative color gradients (the centers are redder than the outskirts, and r_e,mass < r_e,light). We find that color gradient strength has significant trends with increasing stellar mass, half-light radius, U-V color, and stellar mass surface density. These trends have not been seen before at z>1. Furthermore, color gradients of star-forming and quiescent galaxies show a similar redshift evolution: they are flat at z>~2, then steeply decrease as redshift decreases. This affects the galaxy mass-size relation. The normalizations of the star-forming and quiescent r_mass-M_* relations are 10-40% smaller than the corresponding r_light-M_* relations; the slopes are ~0.1-0.3 dex shallower. Finally, the half-mass radii of star-forming and quiescent galaxies at M_* = 10^{10.5}M_\odot only grow by ~1%$ and ~8% between z~2.25 and z~1.25. This is significantly less than the ~37% and ~47% size increases found when using the half-light radius.Comment: 18 pages, 10 figures. Accepted to Ap

KROSS–SAMI: a direct IFS comparison of the Tully–Fisher relation across 8 Gyr since z ≈ 1

We construct Tully–Fisher relations (TFRs), from large samples of galaxies with spatially resolved H α emission maps from the K-band Multi-Object Spectrograph (KMOS) Redshift One Spectroscopic Survey (KROSS) at z ≈ 1. We compare these to data from the Sydney-Australian-Astronomical-Observatory Multi-object Integral-Field Spectrograph (SAMI) Galaxy Survey at z ≈ 0. We stringently match the data quality of the latter to the former, and apply identical analysis methods and sub-sample selection criteria to both to conduct a direct comparison of the absolute K-band magnitude and stellar mass TFRs at z ≈ 1 and 0. We find that matching the quality of the SAMI data to that of KROSS results in TFRs that differ significantly in slope, zero-point, and (sometimes) scatter in comparison to the corresponding original SAMI relations. These differences are in every case as large as or larger than the differences between the KROSS z ≈ 1 and matched SAMI z ≈ 0 relations. Accounting for these differences, we compare the TFRs at z ≈ 1 and 0. For disc-like, star-forming galaxies we find no significant difference in the TFR zero-points between the two epochs. This suggests the growth of stellar mass and dark matter in these types of galaxies is intimately linked over this ≈8 Gyr period

Compositional Vector Space Models for Knowledge Base Completion

Knowledge base (KB) completion adds new facts to a KB by making inferences from existing facts, for example by inferring with high likelihood nationality(X,Y) from bornIn(X,Y). Most previous methods infer simple one-hop relational synonyms like this, or use as evidence a multi-hop relational path treated as an atomic feature, like bornIn(X,Z) -> containedIn(Z,Y). This paper presents an approach that reasons about conjunctions of multi-hop relations non-atomically, composing the implications of a path using a recursive neural network (RNN) that takes as inputs vector embeddings of the binary relation in the path. Not only does this allow us to generalize to paths unseen at training time, but also, with a single high-capacity RNN, to predict new relation types not seen when the compositional model was trained (zero-shot learning). We assemble a new dataset of over 52M relational triples, and show that our method improves over a traditional classifier by 11%, and a method leveraging pre-trained embeddings by 7%.Comment: The 53rd Annual Meeting of the Association for Computational Linguistics and The 7th International Joint Conference of the Asian Federation of Natural Language Processing, 201

SIGAME simulations of the [CII], [OI] and [OIII] line emission from star forming galaxies at z ~ 6

Of the almost 40 star forming galaxies at z>~5 (not counting QSOs) observed in [CII] to date, nearly half are either very faint in [CII], or not detected at all, and fall well below expectations based on locally derived relations between star formation rate (SFR) and [CII] luminosity. Combining cosmological zoom simulations of galaxies with SIGAME (SImulator of GAlaxy Millimeter/submillimeter Emission) we have modeled the multi-phased interstellar medium (ISM) and its emission in [CII], [OI] and [OIII], from 30 main sequence galaxies at z~6 with star formation rates ~3-23Msun/yr, stellar masses ~(0.7-8)x10^9Msun, and metallicities ~(0.1-0.4)xZsun. The simulations are able to reproduce the aforementioned [CII]-faintness at z>5, match two of the three existing z>~5 detections of [OIII], and are furthermore roughly consistent with the [OI] and [OIII] luminosity relations with SFR observed for local starburst galaxies. We find that the [CII] emission is dominated by the diffuse ionized gas phase and molecular clouds, which on average contribute ~66% and ~27%, respectively. The molecular gas, which constitutes only ~10% of the total gas mass is thus a more efficient emitter of [CII] than the ionized gas making up ~85% of the total gas mass. A principal component analysis shows that the [CII] luminosity correlates with the star formation activity as well as average metallicity. The low metallicities of our simulations together with their low molecular gas mass fractions can account for their [CII]-faintness, and we suggest these factors may also be responsible for the [CII]-faint normal galaxies observed at these early epochs.Comment: 24 pages, 14 figures. Accepted for publication in the Astrophysical Journa

The scaling relations of early--type galaxies in clusters I. Surface photometry in seven nearby clusters

This is the first paper of a series investigating the scaling relations of early-type galaxies in clusters. Here we illustrate the multi-band imagery and the image reduction and calibration procedures relative to the whole sample of 22 clusters at 0.05 < z < 0.25. We also present the detailed surface photometry of 312 early-type galaxies in 7 clusters in the first redshift bin, z~0.025-0.075. We give for each galaxy the complete set of luminosity and geometrical profiles, and and a number of global, photometric and morphological parameters. They have been evaluated taking into account the effects of seeing. Internal consistency checks and comparisons with data in the literature confirm the quality of our analysis. These data, together with the spectroscopic ones presented in the second paper of the series, will provide the local calibration of the scaling relations.Comment: 36 pages, 13 figures, 7 tables, accepted for publication in A&