Constraints on the Star Formation Efficiency of Galaxies During the Epoch of Reionization

Reionization is thought to have occurred in the redshift range of $6 < z < 9$, which is now being probed by both deep galaxy surveys and CMB observations. Using halo abundance matching over the redshift range $5<z<8$ and assuming smooth, continuous gas accretion, we develop a model for the star formation efficiency $f_{\star}$ of dark matter halos at $z>6$ that matches the measured galaxy luminosity functions at these redshifts. We find that $f_{\star}$ peaks at $\sim 30\%$ at halo masses $M \sim 10^{11}$--$10^{12}$~M$_\odot$, in qualitative agreement with its behavior at lower redshifts. We then investigate the cosmic star formation histories and the corresponding models of reionization for a range of extrapolations to small halo masses. We use a variety of observations to further constrain the characteristics of the galaxy populations, including the escape fraction of UV photons. Our approach provides an empirically-calibrated, physically-motivated model for the properties of star-forming galaxies sourcing the epoch of reionization. In the case where star formation in low-mass halos is maximally efficient, an average escape fraction $\sim0.1$ can reproduce the optical depth reported by Planck, whereas inefficient star formation in these halos requires either about twice as many UV photons to escape, or an escape fraction that increases towards higher redshifts. Our models also predict how future observations with JWST can improve our understanding of these galaxy populations.Comment: 19 pages, 12 figures, accepted for publication in MNRAS, minor modification

The Global 21-cm Signal in the Context of the High-z Galaxy Luminosity Function

Motivated by recent progress in studies of the high-$z$ Universe, we build a new model for the global 21-cm signal that is explicitly calibrated to measurements of the galaxy luminosity function (LF) and further tuned to match the Thomson scattering optical depth of the cosmic microwave background, $\tau_e$. Assuming that the $z \lesssim 8$ galaxy population can be smoothly extrapolated to higher redshifts, the recent decline in best-fit values of $\tau_e$ and the inefficient heating induced by X-ray binaries (HMXBs; the presumptive sources of the X-ray background at high-$z$) imply that the entirety of cosmic reionization and reheating occurs at redshifts $z \lesssim 12$. In contrast to past global 21-cm models, whose $z \sim 20$ ($\nu \sim 70$ MHz) absorption features and strong $\sim 25$ mK emission features were driven largely by the assumption of efficient early star-formation and X-ray heating, our new fiducial model peaks in absorption at $\nu \sim 110$ MHz at a depth of $\sim -160$ mK and has a negligible emission component. As a result, a strong emission signal would provide convincing evidence that HMXBs are not the only drivers of cosmic reheating. Shallow absorption troughs should accompany strong heating scenarios, but could also be caused by a low escape fraction of Lyman-Werner photons. Generating signals with troughs at $\nu \lesssim 95$ MHz requires a floor in the star-formation efficiency in halos below $\sim 10^{9} M_{\odot}$, which is equivalent to steepening the faint-end of the galaxy LF. These findings demonstrate that the global 21-cm signal is a powerful complement to current and future galaxy surveys and efforts to better understand the interstellar medium in high-$z$ galaxies.Comment: 17 pages, 9 figures, in pres

An Algebraic-Coding Equivalence to the Maximum Distance Separable Conjecture

We formulate an Algebraic-Coding Equivalence to the Maximum Distance Separable Conjecture. Specifically, we present novel proofs of the following equivalent statements. Let $(q,k)$ be a fixed pair of integers satisfying $q$ is a prime power and $2\leq k \leq q$. We denote by $\mathcal{P}_q$ the vector space of functions from a finite field $\mathbb{F}_q$ to itself, which can be represented as the space $\mathcal{P}_q := \mathbb{F}_q[x]/(x^q-x)$ of polynomial functions. We denote by $\mathcal{O}_n \subset \mathcal{P}_q$ the set of polynomials that are either the zero polynomial, or have at most $n$ distinct roots in $\mathbb{F}_q$. Given two subspaces $Y,Z$ of $\mathcal{P}_q$, we denote by $\langle Y,Z \rangle$ their span. We prove that the following are equivalent. [A] Suppose that either: 1. $q$ is odd 2. $q$ is even and $k \not\in \{3, q-1\}$. Then there do not exist distinct subspaces $Y$ and $Z$ of $\mathcal{P}_q$ such that: 3. $dim(\langle Y, Z \rangle) = k$ 4. $dim(Y) = dim(Z) = k-1$. 5. $\langle Y, Z \rangle \subset \mathcal{O}_{k-1}$ 6. $Y, Z \subset \mathcal{O}_{k-2}$ 7. $Y\cap Z \subset \mathcal{O}_{k-3}$. [B] Suppose $q$ is odd, or, if $q$ is even, $k \not\in \{3, q-1\}$. There is no integer $s$ with $q \geq s > k$ such that the Reed-Solomon code $\mathcal{R}$ over $\mathbb{F}_q$ of dimension $s$ can have $s-k+2$ columns $\mathcal{B} = \{b_1,\ldots,b_{s-k+2}\}$ added to it, such that: 8. Any $s \times s$ submatrix of $\mathcal{R} \cup \mathcal{B}$ containing the first $s-k$ columns of $\mathcal{B}$ is independent. 9. $\mathcal{B} \cup \{[0,0,\ldots,0,1]\}$ is independent. [C] The MDS conjecture is true for the given $(q,k)$.Comment: This is version: 5.6.18. arXiv admin note: substantial text overlap with arXiv:1611.0235

A Simple Alternative House Price Index Method

This paper presents the Sale Price Appraisal Ratio (SPAR) method for constructing house price indexes. The method, which uses ratios of transaction prices and previous appraised values to build up an index, has been applied since the early 1960s to produce semi-annual price indexes for regions and cities in New Zealand. We compare the official New Zealand indexes for three urban areas with repeat sales and hedonic indexes created from the same transactions data, and observe that the SPAR method produces an index very much like those produced by hedonic methods. Given the number of advantages and few disadvantages that we find for the SPAR method relative to the more traditional methods, we maintain that it should be considered by government agencies elsewhere when developing house price indexes.house price indexes

What’s in a View?

The impact of views on property values has not been the specific focus of as much research as has the impact of other externalities on property values. When the impact of views is assessed, it is usually done by adding a single dummy variable to a hedonic regression equation. This paper provides a detailed literature review as well as an empirical analysis of the impact of a view on residential property values using a very rich database of nearly 5,000 sales in Auckland, New Zealand. Several dimensions of a view are analyzed: type of view, scope of view, distance to coast, appearance of immediately surrounding improvements, average quality of landscaping in the neighborhood, and average quality of structures in the neighborhood. It is found that wide views of water add an average of 59% to the value of a waterfront property, but that this effect diminishes quite rapidly as the distance from the coast increases. Attractive buildings in a property’s neighborhood on average add 37% to value relative to properties in neighborhoods with only average quality structures. Particularly attractive improvements in the immediate surroundings of a property add another 27% to value on average. On the other hand, properties in neighborhoods with only poor quality landscaping on average experience a -51% impact on price. Our results lead to the conclusion that aesthetic externalities are multi-dimensional and can have a substantial impact on residential property values.

Prediction of Indoor Climate and Long-Term Air Quality Using the BTA-AQP Model: Part I. BTA Model Development and Evaluation

The objective of this research was to develop a building thermal analysis and air quality predictive (BTA-AQP) model to predict ventilation rate, indoor temperature, and long-term air quality (NH3, H2S, and CO2 concentrations and emissions) for swine deep-pit buildings. This article, part I of II, presents a lumped capacitance model (BTA model) to predict the transient behavior of ventilation rate and indoor air temperature according to the thermo-physical properties of a typical swine building, setpoint temperature scheme, fan staging scheme, transient outside temperature, and the heat fluxes from pigs and supplemental heaters. The obtained ventilation rate and resulting indoor air temperature, combined with animal growth cycle, in-house manure storage level, and typical meteorological year (TMY3) data, were used as inputs to the air quality predictive model (part II) based on the generalized regression neural network (GRNN-AQP model), which was presented in an earlier article. The statistical results indicated that the performance of the BTA model for predicting ventilation rate and indoor air temperature was very good in terms of low mean absolute error, a coefficient of mass residual values equal to 0, an index of agreement value close to 1, and Nash-Sutcliffe model efficiency values higher than 0.65. Graphical presentations of predicted vs. actual ventilation rate and indoor temperature are provided to demonstrate that the BTA model was able to accurately estimate indoor climate and therefore could be used as input for the GRNN-AQP model discussed in part II of this research

Prediction of Indoor Climate and Long-Term Air Quality Using the BTA-AQP Model: Part II. Overall Model Evaluation and Application

The objective of this research was to develop a building thermal analysis and air quality predictive (BTA-AQP) model to predict indoor climate and long-term air quality (NH3, H2S, and CO2 concentrations and emissions) for swine deep-pit buildings. This article presents part II of this research, in which the performance of the BTA-AQP model is evaluated using typical meteorological year (TMY3) data in predicting long-term air quality trends. The good model performance ratings (MAE/SD \u3c 0.5, CRM ˜ 0; IoA ˜ 1; and NSEF \u3e 0.5 for all the predicted parameters) and the graphical presentations reveal that the BTA-AQP model was able to accurately forecast indoor climate and gas concentrations and emissions for swine deep-pit buildings. By comparing the air quality results simulated by the BTA-AQP model using the TMY3 data set with those from a five-year local weather data set, it was found that the TMY3-based predictions followed the long-term mean patterns well, which indicates that the TMY3 data could be used to represent the long-term expectations of source air quality. Future work is needed to improve the accuracy of the BTA-AQP model in terms of four main sources of error: (1) uncertainties in air quality data, (2) prediction errors of the BTA model, (3) prediction errors of the AQP model, and (4) bias errors of the TMY3 and its limited application

Simulation of Impacts of Different Animal Management Practices and Geographic Area on Long-Term Air Quality

Simulated impacts of different animal management practices and geographic areas on long-term air quality have been studied using our proposed BTA-AQP (building thermal analysis-air quality predictive) model and statistical analysis methods with four scenarios: building heat loss factor (BHLF), barn setpoint temperature (SPT), animal production schedule (APS), and geographic area (GA). The purpose was to help animal producers and environmental researchers understand the parameters influencing air quality and find a simple, inexpensive, and effective abatement strategy to alleviate airborne pollution from livestock production facilities instead of numerous high-cost gas/odor control technologies. The predicted results indicated that the BHLF scenario had a negligible effect on the source air quality, and the SPT scenario was capable of reducing indoor gas levels during hot weather conditions while the corresponding gas emissions did not increase substantially. Thus, current barn setpoint temperature strategies provide one method to decrease the risk of relatively high gas concentrations (especially H2S concentration) inside the building and protect the health of workers and animals. The APS scenario had no significant effect on mean annual gas concentrations but could lead to a moderate decrease in mean annual gas emissions. It was also found that the GA factor, for the swine deep-pit barns with similar building characteristics and management practices, might have a large impact on indoor gas concentrations but very little effect on mean annual gas emissions