Inverse Density as an Inverse Problem: The Fredholm Equation Approach

In this paper we address the problem of estimating the ratio $\frac{q}{p}$ where $p$ is a density function and $q$ is another density, or, more generally an arbitrary function. Knowing or approximating this ratio is needed in various problems of inference and integration, in particular, when one needs to average a function with respect to one probability distribution, given a sample from another. It is often referred as {\it importance sampling} in statistical inference and is also closely related to the problem of {\it covariate shift} in transfer learning as well as to various MCMC methods. It may also be useful for separating the underlying geometry of a space, say a manifold, from the density function defined on it. Our approach is based on reformulating the problem of estimating $\frac{q}{p}$ as an inverse problem in terms of an integral operator corresponding to a kernel, and thus reducing it to an integral equation, known as the Fredholm problem of the first kind. This formulation, combined with the techniques of regularization and kernel methods, leads to a principled kernel-based framework for constructing algorithms and for analyzing them theoretically. The resulting family of algorithms (FIRE, for Fredholm Inverse Regularized Estimator) is flexible, simple and easy to implement. We provide detailed theoretical analysis including concentration bounds and convergence rates for the Gaussian kernel in the case of densities defined on $\R^d$, compact domains in $\R^d$ and smooth $d$-dimensional sub-manifolds of the Euclidean space. We also show experimental results including applications to classification and semi-supervised learning within the covariate shift framework and demonstrate some encouraging experimental comparisons. We also show how the parameters of our algorithms can be chosen in a completely unsupervised manner.Comment: Fixing a few typos in last versio

Revisiting Kernelized Locality-Sensitive Hashing for Improved Large-Scale Image Retrieval

We present a simple but powerful reinterpretation of kernelized locality-sensitive hashing (KLSH), a general and popular method developed in the vision community for performing approximate nearest-neighbor searches in an arbitrary reproducing kernel Hilbert space (RKHS). Our new perspective is based on viewing the steps of the KLSH algorithm in an appropriately projected space, and has several key theoretical and practical benefits. First, it eliminates the problematic conceptual difficulties that are present in the existing motivation of KLSH. Second, it yields the first formal retrieval performance bounds for KLSH. Third, our analysis reveals two techniques for boosting the empirical performance of KLSH. We evaluate these extensions on several large-scale benchmark image retrieval data sets, and show that our analysis leads to improved recall performance of at least 12%, and sometimes much higher, over the standard KLSH method.Comment: 15 page

Analysis of Hong Kong to be an offshore financial center of RMB

In this article we aim to discuss the possibility and feasibility as well as the disadvantages and barriers for Hong Kong to be an offshore financial center of RMB. As the most biggest financial center in China, Hong Kong need to develop the RMB business for strengthening its position in the international competition. And we think that to become an RMB offshore financial center is not only an opportunity but also a responsibility for Hong Kong. We also give some suggestions on this issue

Health Care Reform in China

Since the founding of the People's Republic of China, the goal of health programs has been to provide care to every member of the population and to make maximum use of limited health-care personnel, equipment, and financial resources. The emphasis has been on preventive rather than curative medicine. The health of the people has been dramatically improved as reflected by the remarkable increase in average life expectancy from about thirty-two years in 1950 to sixty-nine years in 1985

Solid-state graft copolymer electrolytes for lithium battery applications

Battery safety has been a very important research area over the past decade. Commercially available lithium ion batteries employ low flash point ( < 80 °C), flammable, and volatile organic electrolytes. These organic based electrolyte systems are viable at ambient temperatures, but require a cooling system to ensure that temperatures do not exceed 80 °C. These cooling systems tend to increase battery costs and can malfunction which can lead to battery malfunction and explosions, thus endangering human life. Increases in petroleum prices lead to a huge demand for safe, electric hybrid vehicles that are more economically viable to operate as oil prices continue to rise. Existing organic based electrolytes used in lithium ion batteries are not applicable to high temperature automotive applications. A safer alternative to organic electrolytes is solid polymer electrolytes. This work will highlight the synthesis for a graft copolymer electrolyte (GCE) poly(oxyethylene) methacrylate (POEM) to a block with a lower glass transition temperature (Tg) poly(oxyethylene) acrylate (POEA). The conduction mechanism has been discussed and it has been demonstrated the relationship between polymer segmental motion and ionic conductivity indeed has a Vogel-Tammann-Fulcher (VTF) dependence. Batteries containing commercially available LP30 organic (LiPF6 in ethylene carbonate (EC):dimethyl carbonate (DMC) at a 1:1 ratio) and GCE were cycled at ambient temperature. It was found that at ambient temperature, the batteries containing GCE showed a greater overpotential when compared to LP30 electrolyte. However at temperatures greater than 60 °C, the GCE cell exhibited much lower overpotential due to fast polymer electrolyte conductivity and nearly the full theoretical specific capacity of 170 mAh/g was accessed

METAGENOMIC INSIGHTS INTO MICROBIAL COMMUNITY RESPONSES TO LONG-TERM ELEVATED CO2

Understanding how belowground microbial communities respond to increasing atmospheric CO2 is of crucial importance for global change biology, microbial ecology and predictive biology. However, our understanding of CO2 effects on microbial communities is still limited, especially due to the immense diversity and as yet-uncultivable nature of most soil microorganisms. By implementing next generation sequencing (NGS) technologies, we comprehensively surveyed the responses of microbial communities to elevated CO2 (eCO2) in the BioCON experimental site, a grassland ecosystem, which had been exposed to eCO2 for 12 years. In the beginning of this study, it was noticed that computational approaches to identify microbial strains/species from shotgum metagenomes are very limited, thus we have developed a computational algorithm, termed GSMer that identifies genome-specific markers (GSMs) from currently sequenced microbial genomes for strain/species identification in metagenomes. Although GSMer was not very successfully applied in our soil metagenomes due to the extremely low coverage and high diversity of soil microbial communities as well as short sequencing reads from early Illumina GAII performs, it was successfully used to analyze microbial communities with a good coverage of reference genomes, such as human microbiomes. Sensitivity evaluation against synthetic metagenomes with different levels of coverage suggested that 50 GSMs per strain were sufficient to identify most microbial strains with ≥ 0.25x coverage, and 10% of selected GSMs in a database should be detected for confident positive callings. Application of GSMs respectively identified 45 and 74 microbial strains/species significantly associated with type-2-diabetes (T2D) patients and obese/lean individuals from corresponding gastrointestinal tract metagenomes. Our results agreed well with previous studies, but provided strain-level information. In the following, we analyzed the biodiversity, composition, structure and functional potential of soil microbial communities in response to eCO2 at multiple (e.g., phylogenetic, taxonomic, genetic, functional) dimensions using next generation sequencing approaches. For each dimension of microbial biodiversity, all components of diversity, including alpha-, beta- and gamma-diversity were analyzed. Our results suggested that long-term eCO2 decreased the overall microbial biodiversity. Beta-diversity analysis suggested eCO2 decreased functional beta-diversity, but increased taxonomic and phylogenetic diversity, suggesting long-term eCO2 selected for microbial function rather than taxonomy. Further meta-analysis suggested that such decreased biodiversity was significantly negatively correlated with increased soil ammonification rate. Moreover, the abundance of gene families involved in ammonium producing pathways increased significantly as well, indicating a functional convergence process as a result of higher demand for biologically available nitrogen (N) by stimulated plant growth as a result of eCO2. Our findings present evidence that plant-microbe interactions for NH4+ as result of progressive nitrogen limitation were an important driving factor, responsible for decreased microbial biodiversity under eCO2. We also analyzed the response of fungal communities to long-term eCO2 by sequencing of 28S rRNA gene amplicons. Long-term eCO2 did not significantly alter the overall fungal community structure and species richness, but significantly increased community evenness and diversity. Relative abundances of 119 OTUs (~ 27% of the total captured sequences) were changed significantly. More interestingly, significantly changed OTUs under eCO2 were associated with increased overall relative abundance of Ascomycota, but decreased relative abundance of Basidiomycota. Co-occurrence ecological network analysis indicated that eCO2 increased fungal community interactions, as evidenced by higher intermodular and intramodular connectivity and shorter geodesic distance. In contrast, decreased connections for dominant fungal species were observed in the eCO2 network. Community reassembly of unrelated fungal species into highly connected dense modules was observed. Such changes in the network structure were significantly associated with altered soil and plant properties under eCO2, especially with increased plant biomass and NH4+ availability. This study provides novel insights into our understanding of how eCO2 shapes soil fungal communities in grassland ecosystems. Since it was noticed that changes of both belowground microbial biodiversity and fungal communities were significantly correlated with soil ammonification rate, and our previous studies showed that the abundance of nifH significantly increased at eCO2, we hypothesized that N2-fixing microorganisms would play important roles in response to eCO2. Therefore, we analyzed N2-fixing communities by sequencing of nifH gene amplicons as well as extraction of nifH fragments from shotgun metagenomes. Surprisingly, long-term eCO2 significantly increased the abundance of nifH genes, but did not change the overall nifH diversity and diazotrophic community structure. Taxonomic and phylogenetic analysis of amplified nifH sequences suggested a high diversity of nifH genes in the soil ecosystem, with the majority belonging to cluster I and II nifH genes. We then constructed a microbial ecological network using 16S rRNA gene and nifH gene profiles. Co-occurrence ecological network analysis suggested a clear preference of co-occurrence patterns between diazotrophs and other microbial species with different patterns observed for different subgroups of diazotrophs, such as Azospirillum/Actinobacteria, Mesorhizobium/Conexibacter, and Bradyrhizobium/Acidobacteria. This indicated a potential attraction of these non-N2-fixers by diazotrophs in the soil ecosystem. Interestingly, more complex co-occurrence patterns were found for free-living diazotrophs than commonly known symbiotic diazotrophs, consistent with the physical isolation nature of symbiotic diazotrophs from the environment by root nodules. The study provides novel insights of our understanding microbial ecology of soil diazotrophs in natural ecosystems. All studies included in this work provided novel insights into the long-term eCO2 effects on belowground microbial communities, which are of merit for next generation sequencing analysis for microbial ecologists, global change biologists and bioinformaticians