Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Models

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of dimensionality for intrinsically high-dimensional data. This limitation is pronounced in graphical models such as Markov random fields, common for image distributions, where the approximation efficiency of score functions remains unestablished. To address this, we observe score functions can often be well-approximated in graphical models through variational inference denoising algorithms. Furthermore, these algorithms are amenable to efficient neural network representation. We demonstrate this in examples of graphical models, including Ising models, conditional Ising models, restricted Boltzmann machines, and sparse encoding models. Combined with off-the-shelf discretization error bounds for diffusion-based sampling, we provide an efficient sample complexity bound for diffusion-based generative modeling when the score function is learned by deep neural networks.Comment: 41 page

House Price Risk in Mortgage Contracts

Research has shown that mortgage default is closely related to house prices. When house prices fall the borrower has an incentive to default. Since default incurs substantial cost to the lender, the borrower and many other market participants, as well as the society, house price is a risk in a mortgage contract. This was clearly demonstrated during the 2007-09 financial crisis. In this thesis I discuss some (potential) measures to manage mortgage default risk arising from low house prices. Chapter 1 is on mortgage insurance. Mortgage insurance is commonly used by lenders to transfer mortgage default risk to an insurer. After a brief introduction of the mortgage and mortgage insurance markets in US and Canada, I specify a simple mortgage insurance contract and a multiple state model for mortgage termination. The contract is then priced under the model. I explore the possibility of hedging house price risk in Chapter 2. If we assume a perfect market where house price risk can be traded exists, and a mortgage contract is a contingent claim on house prices, then the classic delta hedging is useful in hedging house price risk. In chapter 3 I discuss an innovative type of mortgage contract -- property index-linked mortgage. The purpose of this contract design is to reduce the borrower's propensity to default when house price declines. In particular, when house price declines, the mortgage balance and payment are reduced. I analyze this contract from the borrower's perspective and find that such contracts are effective in reducing default incentives and as a result, the lender may also be better off due to lower deadweight default cost. The last chapter focuses on house price basis risk. House price basis risk refers to the situation where the value of an individual property appreciates differently from the index. This may lead to problems such as suboptimal hedging, underpricing and lower efficiency for financial products involving house price index. In this chapter I develop a basis risk model that can be used to simulate reasonable individual house prices for a given index

Vitamin D Signaling through Induction of Paneth Cell Defensins Maintains Gut Microbiota and Improves Metabolic Disorders and Hepatic Steatosis in Animal Models.

Metabolic syndrome (MetS), characterized as obesity, insulin resistance, and non-alcoholic fatty liver diseases (NAFLD), is associated with vitamin D insufficiency/deficiency in epidemiological studies, while the underlying mechanism is poorly addressed. On the other hand, disorder of gut microbiota, namely dysbiosis, is known to cause MetS and NAFLD. It is also known that systemic inflammation blocks insulin signaling pathways, leading to insulin resistance and glucose intolerance, which are the driving force for hepatic steatosis. Vitamin D receptor (VDR) is highly expressed in the ileum of the small intestine, which prompted us to test a hypothesis that vitamin D signaling may determine the enterotype of gut microbiota through regulating the intestinal interface. Here, we demonstrate that high-fat-diet feeding (HFD) is necessary but not sufficient, while additional vitamin D deficiency (VDD) as a second hit is needed, to induce robust insulin resistance and fatty liver. Under the two hits (HFD+VDD), the Paneth cell-specific alpha-defensins including α-defensin 5 (DEFA5), MMP7 which activates the pro-defensins, as well as tight junction genes, and MUC2 are all suppressed in the ileum, resulting in mucosal collapse, increased gut permeability, dysbiosis, endotoxemia, systemic inflammation which underlie insulin resistance and hepatic steatosis. Moreover, under the vitamin D deficient high fat feeding (HFD+VDD), Helicobacter hepaticus, a known murine hepatic-pathogen, is substantially amplified in the ileum, while Akkermansia muciniphila, a beneficial symbiotic, is diminished. Likewise, the VD receptor (VDR) knockout mice exhibit similar phenotypes, showing down regulation of alpha-defensins and MMP7 in the ileum, increased Helicobacter hepaticus and suppressed Akkermansia muciniphila. Remarkably, oral administration of DEFA5 restored eubiosys, showing suppression of Helicobacter hepaticus and increase of Akkermansia muciniphila in association with resolving metabolic disorders and fatty liver in the HFD+VDD mice. An in vitro analysis showed that DEFA5 peptide could directly suppress Helicobacter hepaticus. Thus, the results of this study reveal critical roles of a vitamin D/VDR axis in optimal expression of defensins and tight junction genes in support of intestinal integrity and eubiosis to suppress NAFLD and metabolic disorders

A comparative analysis of morphology, microstructure, and volatile metabolomics of leaves at varied developmental stages in Ainaxiang (Blumea balsamifera (Linn.) DC.)

IntroductionAinaxiang (Blumea balsamifera (Linn.) DC.) is cultivated for the extraction of (-)-borneol and other pharmaceutical raw materials due to its abundant volatile oil. However, there is limited knowledge regarding the structural basis and composition of volatile oil accumulation in fresh B. balsamifera leaves.MethodsTo address this problem, we compare the fresh leaves’ morphology, microstructure, and volatile metabonomic at different development stages, orderly defined from the recently unfolded young stage (S1) to the senescent stage (S4).Results and discussionDistinct differences were observed in the macro-appearance and microstructure at each stage, particularly in the B. balsamifera glandular trichomes (BbGTs) distribution. This specialized structure may be responsible for the accumulation of volatile matter. 213 metabolites were identified through metabolomic analysis, which exhibited spatiotemporal accumulation patterns among different stages. Notably, (-)-borneol was enriched at S1, while 10 key odor metabolites associated with the characteristic balsamic, borneol, fresh, and camphor aromas of B. balsamifera were enriched in S1 and S2. Ultra-microstructural examination revealed the involvement of chloroplasts, mitochondria, endoplasmic reticulum, and vacuoles in the synthesizing, transporting, and storing essential oils. These findings confirm that BbGTs serve as the secretory structures in B. balsamifera, with the population and morphology of BbGTs potentially serving as biomarkers for (-)-borneol accumulation. Overall, young B. balsamifera leaves with dense BbGTs represent a rich (-)-borneol source, while mesophyll cells contribute to volatile oil accumulation. These findings reveal the essential oil accumulation characteristics in B. balsamifera, providing a foundation for further understanding

A C19MC-LIN28A-MYCN Oncogenic Circuit Driven by Hijacked Super-enhancers Is a Distinct Therapeutic Vulnerability in ETMRs: A Lethal Brain Tumor

© 2019 Elsevier Inc. Embryonal tumors with multilayered rosettes (ETMRs) are highly lethal infant brain cancers with characteristic amplification of Chr19q13.41 miRNA cluster (C19MC) and enrichment of pluripotency factor LIN28A. Here we investigated C19MC oncogenic mechanisms and discovered a C19MC-LIN28A-MYCN circuit fueled by multiple complex regulatory loops including an MYCN core transcriptional network and super-enhancers resulting from long-range MYCN DNA interactions and C19MC gene fusions. Our data show that this powerful oncogenic circuit, which entraps an early neural lineage network, is potently abrogated by bromodomain inhibitor JQ1, leading to ETMR cell death. Sin-Chan et al. uncover a C19MC-LIN28A-MYCN super-enhancer-dependent oncogenic circuit in embryonal tumors with multilayered rosettes (ETMRs). The circuit entraps an early neural lineage network to sustain embryonic epigenetic programming and is vulnerable to bromodomain inhibition, which promotes ETMR cell death

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data