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Prestellar cores are self-gravitating dense and cold structures within molecular clouds where future stars are born. They are expected, at the stage of transitioning to the protostellar phase, to harbor centrally concentrated dense (sub)structures that will seed the formation of a new star or the binary/multiple stellar systems. Characterizing this critical stage of evolution is key to our understanding of star formation. In this work, we report the detection of high density (sub)structures on the thousand-au scale in a sample of dense prestellar cores. Through our recent ALMA observations towards the Orion molecular cloud, we have found five extremely dense prestellar cores, which have centrally concentrated regions ∼ 2000 au in size, and several 10 7 cm −3 in average density. Masses of these centrally dense regions are in the range of 0.30 to 6.89 M . For the first time, our higher resolution observations (0.8 ∼ 320 au) further reveal that one of the cores shows clear signatures of fragmentation; such individual substructures/fragments have sizes of 800 -1700 au, masses of 0.08 to 0.84 M , densities of 2 − 8 × 10 7 cm −3 , and separations of ∼ 1200 au. The substructures are massive enough ( 0.1 M ) to form young stellar objects and are likely examples of the earliest stage of stellar embryos which can lead to widely (∼ 1200 au) separated multiple systems.
Abstract:In this paper, Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks-Climate Data Record (PERSIANN-CDR) is analyzed for the assessment of meteorological drought. The evaluation is conducted over China at 0.5˝spatial resolution against a ground-based gridded China monthly Precipitation Analysis Product (CPAP) from 1983 to 2014 (32 years). The Standardized Precipitation Index (SPI) at various time scales (1 month to 12 months) is calculated for detecting drought events. The results show that PERSIANN-CDR depicts similar drought behavior as the ground-based CPAP in terms of capturing the spatial and temporal patterns of drought events over eastern China, where the intensity of gauge networks and the frequency of droughts are high. 6-month SPI shows the best agreement with CPAP in identifying drought months. However, large differences between PERSIANN-CDR and CPAP in depicting drought patterns and identifying specific drought events are found over northwestern China, particularly in Xinjiang and Qinghai-Tibet Plateau region. Factors behind this may be due to the relatively sparse gauge networks, the complicated terrain and the performance of PERSIANN algorithm.
We consider constructing capacity-achieving linear codes with minimum message size for private information retrieval (PIR) from N non-colluding databases, where each message is coded using maximum distance separable (MDS) codes, such that it can be recovered from accessing the contents of any T databases. It is shown that the minimum message size (sometimes also referred to as the sub-packetization factor) is significantly, in fact exponentially, lower than previously believed. More precisely, when K > T / gcd(N, T ) where K is the total number of messages in the system and gcd(·, ·) means the greatest common divisor, we establish, by providing both novel code constructions and a matching converse, the minimum message size as lcm(N − T, T ), where lcm(·, ·) means the least common multiple. On the other hand, when K is small, we show that it is in fact possible to design codes with a message size even smaller than lcm(N − T, T ). arXiv:1903.08229v2 [cs.IT] 22 Jan 2020 significantly restricts the possible usage scenarios. Moreover, a large message size also usually implies that the encoding and the decoding functions are more complex, which not only requires more engineering efforts to implement but also hinders the efficiency of the system operation. From a theoretical point of view, a code with a smaller message size usually implies a more transparent coding structure, which can be valuable for related problems; see, e.g., [7] for such an example. Thus codes with a smaller message size are highly desirable in both theory and practice.The capacity-achieving code given in [4] requires L = T N K , which can be extremely large for a system with even a moderate number of messages. The problem of reducing the message size of capacity-achieving codes was recently considered by Xu and Zhang [6], and it was shown that under the assumption that all answers are of the same length, the message size must satisfy L ≥ T (N/ gcd(N, T )) K−1 . These existing results may have left the impression that capacityachieving codes would necessitate a message size exponential in the number of messages.In this work, we show that the minimum message size for capacity-achieving PIR codes can in fact be significantly smaller than previously believed, by providing capacity-achieving linear codes with message size L = lcm(N −T, T ). Two linear code constructions, referred to as Construction-A and Construction-B, respectively, are given. The two constructions have the same download cost and message size, however Construction-B has a better upload cost (i.e., a lower communication cost for the user to send the queries), at the expense of being slightly more sophisticated than Construction-A. The key difference between the two proposed constructions and existing codes in the literature is that the proposed codes reduce the reliance on the so-called variety symmetry [8], which should be distinguished from the asymmetry discussed in [9], and the answers may be of different lengths 1 . We further show that this is in fact the minimum message size whe...
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