Approximate Set Union Via Approximate Randomization

We develop an randomized approximation algorithm for the size of set union problem \arrowvert A_1\cup A_2\cup...\cup A_m\arrowvert, which given a list of sets $A_1,...,A_m$ with approximate set size $m_i$ for $A_i$ with $m_i\in \left((1-\beta_L)|A_i|, (1+\beta_R)|A_i|\right)$, and biased random generators with Prob(x=\randomElm(A_i))\in \left[{1-\alpha_L\over |A_i|},{1+\alpha_R\over |A_i|}\right] for each input set $A_i$ and element $x\in A_i,$ where $i=1, 2, ..., m$. The approximation ratio for \arrowvert A_1\cup A_2\cup...\cup A_m\arrowvert is in the range $[(1-\epsilon)(1-\alpha_L)(1-\beta_L), (1+\epsilon)(1+\alpha_R)(1+\beta_R)]$ for any $\epsilon\in (0,1)$, where $\alpha_L, \alpha_R, \beta_L,\beta_R\in (0,1)$. The complexity of the algorithm is measured by both time complexity, and round complexity. The algorithm is allowed to make multiple membership queries and get random elements from the input sets in one round. Our algorithm makes adaptive accesses to input sets with multiple rounds. Our algorithm gives an approximation scheme with O(\setCount\cdot(\log \setCount)^{O(1)}) running time and $O(\log m)$ rounds, where $m$ is the number of sets. Our algorithm can handle input sets that can generate random elements with bias, and its approximation ratio depends on the bias. Our algorithm gives a flexible tradeoff with time complexity O\left(\setCount^{1+\xi}\right) and round complexity $O\left({1\over \xi}\right)$ for any $\xi\in(0,1)$

An Urban Accounting for Geographic Concentration of Skills and Welfare Inequality

Using Jones (2014) generalized human capital accounting, we extend the urban accounting model of Desmet and Rossi-Hansberg (2013) to account for the geographic distribution of skills across US metropolitan areas. The methodology allows the productivity of high-skill workers to depend on location advantage and local skill mix; the latter also determines the productivity of low-skill workers. Urban friction, rising with population size, reduces worker consumption relative to their wage income. Amenities for high-skill and low-skill workers in each city are calibrated so that the utility for each skill type is equalized across cities. We examine counterfactual skill-mix distribution across cities and welfare gap between the skill groups by shutting down spatial heterogeneity in location advantage, amenity and excess friction respectively. We show that skill mix becomes more even across cities absent heterogeneity in location advantages or in excess friction but it becomes more dispersed absent amenity heterogeneity. The welfare gap widens when heterogeneity in any of the three factors is eliminated. The generalized urban accounting model can shed light on the causes of increased concentration of skilled workers in large cities in US highlighted by E. Moretti (2008) and Diamond (2012) and the implications for welfare gap between the skill groups

Land Use Rights, Government Land Supply, and the Pattern of Redevelopment in Shanghai

This paper reviews the urban redevelopment activities in Shanghai as the land market reforms were introduced. We focus on the impact of land use institutions on the spatial pattern of these activities. Sites for private real estate redevelopment were supplied by individual districts in the city. But the need for districts to pay for the resettlement of displaced residents contributed to a spatial mismatch between the supply of redevelopment sites and the market demand for commercial real estate space. Resettlement costs are highest at the high demand locations. State owned enterprises and institutions occupying land allocated by the state also engaged in real estate development. Whereas the density of private redevelopment was sensitive to the volume of commercial activities in a district, this does not appear to have been important in determining the location of the significant increase in the stock of commercial space resulting from development by local enterprises and institutions. This growth shows considerable decentralization between 1993 and 1996,indicative of spatially inefficient redevelopment activities by land-rich state enterprises.Institutions, Land Market, Economic Transition, Urban Redevelopment, Shanghai

Quasar Photometric Redshifts and Candidate Selection: A New Algorithm Based on Optical and Mid-Infrared Photometric Data

We present a new algorithm to estimate quasar photometric redshifts (photo-$z$s), by considering the asymmetries in the relative flux distributions of quasars. The relative flux models are built with multivariate Skew-t distributions in the multi-dimensional space of relative fluxes as a function of redshift and magnitude. For 151,392 quasars in the SDSS, we achieve a photo-$z$ accuracy, defined as the fraction of quasars with the difference between the photo-$z$ $z_p$ and the spectroscopic redshift $z_s$, $|\Delta z| = |z_s-z_p|/(1+z_s)$ within 0.1, of 74%. Combining the WISE W1 and W2 infrared data with the SDSS data, the photo-$z$ accuracy is enhanced to 87%. Using the Pan-STARRS1 or DECaLS photometry with WISE W1 and W2 data, the photo-$z$ accuracies are 79% and 72%, respectively. The prior probabilities as a function of magnitude for quasars, stars and galaxies are calculated respectively based on (1) the quasar luminosity function; (2) the Milky Way synthetic simulation with the Besan\c{c}on model; (3) the Bayesian Galaxy Photometric Redshift estimation. The relative fluxes of stars are obtained with the Padova isochrones, and the relative fluxes of galaxies are modeled through galaxy templates. We test our classification method to select quasars using the DECaLS $g$, $r$, $z$, and WISE W1 and W2 photometry. The quasar selection completeness is higher than 70% for a wide redshift range $0.5<z<4.5$, and a wide magnitude range $18<r<21.5$ mag. Our photo-$z$ regression and classification method has the potential to extend to future surveys. The photo-$z$ code will be publicly available.Comment: 22 pages, 17 figure, accepted by AJ. The code is available at https://doi.org/10.5281/zenodo.101440

Pathologically Activated Neuroprotection via Uncompetitive Blockade of \u3cem\u3eN\u3c/em\u3e-Methyl-d-aspartate Receptors with Fast Off-rate by Novel Multifunctional Dimer Bis(propyl)-cognitin

Uncompetitive N-methyl-d-aspartate (NMDA) receptor antagonists with fast off-rate (UFO) may represent promising drug candidates for various neurodegenerative disorders. In this study, we report that bis(propyl)-cognitin, a novel dimeric acetylcholinesterase inhibitor and γ-aminobutyric acid subtype A receptor antagonist, is such an antagonist of NMDA receptors. In cultured rat hippocampal neurons, we demonstrated that bis(propyl)-cognitin voltage-dependently, selectively, and moderately inhibited NMDA-activated currents. The inhibitory effects of bis(propyl)-cognitin increased with the rise in NMDA and glycine concentrations. Kinetics analysis showed that the inhibition was of fast onset and offset with an off-rate time constant of 1.9 s. Molecular docking simulations showed moderate hydrophobic interaction between bis(propyl)-cognitin and the MK-801 binding region in the ion channel pore of the NMDA receptor. Bis(propyl)-cognitin was further found to compete with [3H]MK-801 with a Ki value of 0.27 μm, and the mutation of NR1(N616R) significantly reduced its inhibitory potency. Under glutamate-mediated pathological conditions, bis(propyl)-cognitin, in contrast to bis(heptyl)-cognitin, prevented excitotoxicity with increasing effectiveness against escalating levels of glutamate and much more effectively protected against middle cerebral artery occlusion-induced brain damage than did memantine. More interestingly, under NMDA receptor-mediated physiological conditions, bis(propyl)-cognitin enhanced long-term potentiation in hippocampal slices, whereas MK-801 reduced and memantine did not alter this process. These results suggest that bis(propyl)-cognitin is a UFO antagonist of NMDA receptors with moderate affinity, which may provide a pathologically activated therapy for various neurodegenerative disorders associated with NMDA receptor dysregulation

Discovery of 21 New Changing-look AGNs in Northern Sky

The rare case of changing-look (CL) AGNs, with the appearance or disappearance of broad Balmer emission lines within a few years, challenges our understanding of the AGN unified model. We present a sample of 21 new CL AGNs at $0.08<z<0.58$, which doubles the number of such objects known to date. These new CL AGNs were discovered by several ways, from (1) repeat spectra in the SDSS, (2) repeat spectra in the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) and SDSS, and (3) photometric variability and new spectroscopic observations. We use the photometric data from surveys, including the SDSS imaging survey, the Pan-STARRS1, the DESI Legacy imaging survey, the Wide-field Infrared Survey Explorer (WISE), the Catalina Real-time Transient Survey, and the Palomar Transient Factory. The estimated upper limits of transition timescale of the CL AGNs in this sample spans from 0.9 to 13 years in the rest frame. The continuum flux in the optical and mid-infrared becomes brighter when the CL AGNs turn on, or vice versa. Variations of more than 0.2 mag in $W1$ band were detected in 15 CL AGNs during the transition. The optical and mid-infrared variability is not consistent with the scenario of variable obscuration in 10 CL AGNs at more than $3\sigma$ confidence level. We confirm a bluer-when-brighter trend in the optical. However, the mid-infrared WISE colors $W1-W2$ become redder when the objects become brighter in the $W1$ band, possibly due to a stronger hot dust contribution in the $W2$ band when the AGN activity becomes stronger. The physical mechanism of type transition is important for understanding the evolution of AGNs.Comment: Accepted for publication in Ap

Mating Siegel and Thurston quadratic polynomials

We prove that a quadratic polynomial with a bounded type Siegel disk and a quadratic post-critically finite polynomial are always mateable.Comment: 20 pages, 5 figure