A Spatial Investigation of ƒÐ-Convergence in China

Using techniques of spatial econometrics, this paper investigates ƒÐ-convergence of provincial real per capita gross domestic product (GDP) in China. The empirical evidence concludes that spatial dependence across regions is strong enough to distort the traditional measure of ƒÐ-convergence. This study focuses on the variation of per capita GDP that is dependent on the development processes of neighboring provinces and cities. This refinement of the conditional ƒÐ-convergence model specification allows for analysis of spatial dependence in the mean and variance. The corrected measure of ƒÐ-convergence in China indicates a lower level of dispersion in the economic development process. This implies a smaller divergence in real per capita GDP, although convergence across regions is still a challenging goal to achieve in the 2000s.ƒÐ-Convergence, Moran's index, spatial dependence, spatial lag

Improved Bounds for Sampling Solutions of Random CNF Formulas

Let $\Phi$ be a random $k$-CNF formula on $n$ variables and $m$ clauses, where each clause is a disjunction of $k$ literals chosen independently and uniformly. Our goal is to sample an approximately uniform solution of $\Phi$ (or equivalently, approximate the partition function of $\Phi$). Let $\alpha=m/n$ be the density. The previous best algorithm runs in time $n^{\mathsf{poly}(k,\alpha)}$ for any $\alpha\lesssim2^{k/300}$ [Galanis, Goldberg, Guo, and Yang, SIAM J. Comput.'21]. Our result significantly improves both bounds by providing an almost-linear time sampler for any $\alpha\lesssim2^{k/3}$. The density $\alpha$ captures the \emph{average degree} in the random formula. In the worst-case model with bounded \emph{maximum degree}, current best efficient sampler works up to degree bound $2^{k/5}$ [He, Wang, and Yin, FOCS'22 and SODA'23], which is, for the first time, superseded by its average-case counterpart due to our $2^{k/3}$ bound. Our result is the first progress towards establishing the intuition that the solvability of the average-case model (random $k$-CNF formula with bounded average degree) is better than the worst-case model (standard $k$-CNF formula with bounded maximal degree) in terms of sampling solutions.Comment: 51 pages, all proofs added, and bounds slightly improve

Urban mobility in Urban Design

This design research focus on how to make spaces for food mobility, by improving the quality of public space, making the transportation system more efficient, enhancing the cultural features and providing a good lifestyle in urban city.Architectur

Compressive Holographic Video

Compressed sensing has been discussed separately in spatial and temporal domains. Compressive holography has been introduced as a method that allows 3D tomographic reconstruction at different depths from a single 2D image. Coded exposure is a temporal compressed sensing method for high speed video acquisition. In this work, we combine compressive holography and coded exposure techniques and extend the discussion to 4D reconstruction in space and time from one coded captured image. In our prototype, digital in-line holography was used for imaging macroscopic, fast moving objects. The pixel-wise temporal modulation was implemented by a digital micromirror device. In this paper we demonstrate $10\times$ temporal super resolution with multiple depths recovery from a single image. Two examples are presented for the purpose of recording subtle vibrations and tracking small particles within 5 ms.Comment: 12 pages, 6 figure

Parameter inference for coalescing massive black hole binaries using deep learning

In the 2030s, a new era of gravitational-wave (GW) observations will dawn as multiple space-based GW detectors, such as the Laser Interferometer Space Antenna, Taiji and TianQin, open the millihertz window for GW astronomy. These detectors are poised to detect a multitude of GW signals emitted by different sources. It is a challenging task for GW data analysis to recover the parameters of these sources at a low computational cost. Generally, the matched filtering approach entails exploring an extensive parameter space for all resolvable sources, incurring a substantial cost owing to the generation of GW waveform templates. To alleviate the challenge, we make an attempt to perform parameter inference for coalescing massive black hole binaries (MBHBs) using deep learning. The model trained in this work has the capability to produce 50,000 posterior samples for redshifted total mass, mass ratio, coalescence time and luminosity distance of a MBHB in about twenty seconds. Our model can serve as a potent data pre-processing tool, reducing the volume of parameter space by more than four orders of magnitude for MBHB signals with a signal-to-noise ratio larger than 100. Moreover, the model exhibits robustness when handling input data that contains multiple MBHB signals.Comment: 8 pages, 4 figure

Novel properties and potential applications of functional ligand-modified polyoxotitanate cages.

Functional ligand-modified polyoxotitanate (L-POT) cages of the general type [TixOy(OR)z(L)m] (OR = alkoxide, L = functional ligand) can be regarded as molecular fragments of surface-sensitized solid-state TiO2, and are of value as models for studying the interfacial charge and energy transfer between the bound functional ligands and a bulk semiconductor surface. These L-POTs have also had a marked impact in many other research fields, such as single-source precursors for TiO2 deposition, inorganic-organic hybrid material construction, photocatalysis, photoluminescence, asymmetric catalysis and gas adsorption. Their atomically well-defined structures provide the basis for the understanding of structure/property relationships and ultimately for the rational design of new cages targeting specific uses. This highlight focuses on recent advances in L-POTs research, with emphasis on their novel properties and potential applications.EPSRCThis is the final version of the article. It first appeared from Royal Society of Chemistry via https://doi.org/10.1039/C6CC03788G

2,5-Dimethyl-3,6-bis[(2,6-diisopropylphenylimino)methyl]- and 2,6-Bis[(2,6-diisopropylphenylimino)methyl]pyrazine: Two New Chelating Ligands for Transition Metal Complexes

The reaction of tetramethylpyrazine with SeO2 yields 2,5-dimethylpyrazine-3,6-dicarboxaldehyde (1) from which the 2,5-dimethyl-3,6-bis[(2,6-diisopropylphenylimino)methyl]pyrazine (2) was synthesized by treatment with 2 equivalents of 2,6-diisopropylaniline. 2,6-Dimethylpyrazine reacts with benzaldehyde to give 2,6-distyrylpyrazine (3). Ozonolysis of 3, followed by treatment with Na2SO3 and 2,6-diisopropylaniline resulted in the formation of 2,6-bis[(2,6-diisopropylphenylimino) methyl]pyrazine (5) together with [(2,6-diisopropylphenylimino)methyl]benzene (6)