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 $\xi\in(0,1)$

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

Mating Siegel and parabolic quadratic polynomials

Let $f_\theta(z)=e^{2\pi i\theta}z+z^2$ be the quadratic polynomial having an indifferent fixed point at the origin. For any bounded type irrational number $\theta\in\mathbb{R}\setminus\mathbb{Q}$ and any rational number $\nu\in\mathbb{Q}$, we prove that $f_\theta$ and $f_\nu$ are conformally mateable, and that the mating is unique up to conjugacy by a M\"{o}bius map. This gives an affirmative (partial) answer to a question raised by Milnor in 2004. A crucial ingredient in the proof relies on an expansive property when iterating certain rational maps near Siegel disk boundaries. Combining this with the expanding property in repelling petals of parabolic points, we also prove that the Julia sets of a class of Siegel rational maps with parabolic points are locally connected.Comment: 40 pages, 9 figure

Do objects in working memory compete with objects in perception?

It is generally assumed that "perceptual object" is the basic unit for processing visual information and that only a small number of objects can be either perceptually selected or encoded in working memory (WM) at one time. This raises the question whether the same resource is used when objects are selected and tracked as when they are held in WM. In two experiments, we measured dual-task interference between a memory task and a Multiple Object Tracking task. The WM tasks involve explicit, implicit, or no spatial processing. Our results suggest there is no resource competition between working memory and perceptual selection except when the WM task requires encoding spatial properties

Railway service quality in northern Italy: A multilevel synthetic assessment:

In order to reasonably assess the railway service quality, a multilevel extensible assessment model is proposed based on the matter element theory and the extension theory. The proposed model is applied to a real case study of some railway lines. The matter element to assess the railway service quality is established on the basis of the characteristics of passenger transit which included 7 primary assessment indices and 26 senior assessment indices. The index weights are determined by the passengers who were interviewed on board during their journey. Railway service quality is assessed by the values of the correlation degree of the matter element with all the assessment grades. The multilevel extensible assessment method can fully reflect the distance between the overall railway service quality or one kind of service attribute and the assessment grades and then it can realize the continuous assessment. The method can provide not only the passengers' overall satisfaction degree on the railway service quality but also the passengers' satisfaction degree on one assessment index

Modeling coral bleaching mitigation potential of water vertical translocation – an analogue to geoengineered artificial upwelling

Artificial upwelling (AU) is a novel geoengineering technology that brings seawater from the deep ocean to the surface. Within the context of global warming, AU techniques are proposed to reduce sea surface temperature at times of thermal stress around coral reefs. A computationally fast but coarse 3D Earth System model (3.6° longitude × 1.8° latitude) was used to investigate the environmental impacts of hypothetically implemented AU strategies in the Great Barrier Reef, South China Sea, and Hawaiian regions. While omitting the discussion on sub-grid hydrology, we simulated in our model a water translocation from either 130 or 550 m depth to sea surface at rates of 1 or 50 m3 s−1 as analogues to AU implementation. Under the Representative Concentration Pathway 8.5 emissions scenario from year 2020 on, the model predicted a prevention of coral bleaching until the year 2099 when AU was implemented, except under the least intense AU scenario (water from 130 m depth at 1 m3 s−1). Yet, intense AU implementation (water from 550 m depth at 50 m3 s-1) will likely have adverse effects on coral reefs by overcooling the surface water, altering salinity, decreasing calcium carbonate saturation, and considerably increasing nutrient levels. Our result suggests that if we utilize AU for mitigating coral bleaching during heat stress, AU implementation needs to be carefully designed with respect to AU’s location, depth, intensity and duration so that undesirable environmental effects are minimized. Following a proper installation and management procedure, however, AU has the potential to decelerate destructive bleaching events and buy corals more time to adjust to climate change