Strong convergence rates of an explicit scheme for stochastic Cahn-Hilliard equation with additive noise

In this paper, we propose and analyze an explicit time-stepping scheme for a spatial discretization of stochastic Cahn-Hilliard equation with additive noise. The fully discrete approximation combines a spectral Galerkin method in space with a tamed exponential Euler method in time. In contrast to implicit schemes in the literature, the explicit scheme here is easily implementable and produces significant improvement in the computational efficiency. It is shown that the fully discrete approximation converges strongly to the exact solution, with strong convergence rates identified. To the best of our knowledge, it is the first result concerning an explicit scheme for the stochastic Cahn-Hilliard equation. Numerical experiments are finally performed to confirm the theoretical results.Comment: 24 pages, 3 figure

How are individual-level social capital and poverty associated with health equity? A study from two Chinese cities

<p>Abstract</p> <p>Background</p> <p>A growing body of literature has demonstrated that higher social capital is associated with improved health conditions. However, some research indicated that the association between social capital and health was substantially attenuated after adjustment for material deprivation. Studies exploring the association between poverty, social capital and health still have some serious limitations. In China, health equity studies focusing on urban poor are scarce. The purpose of this study is therefore to examine how poverty and individual-level social capital in urban China are associated with health equity.</p> <p>Methods</p> <p>Our study is based on a household study sample consisting of 1605 participants in two Chinese cities. For all participants, data on personal characteristics, health status, health care utilisation and social capital were collected. Factor analysis was performed to extract social capital factors. Dichotomised social capital factors were used for logistic regression models. A synergy index (if it is above 1, we can know the existence of the co-operative effect) was computed to examine the interaction effect between lack of social capital and poverty.</p> <p>Results</p> <p>Results indicated the poor had an obviously higher probability of belonging to the low individual-level social capital group in all the five dimensions, with the adjusted odds ratios ranging from 1.42 to 2.12. When the other variables were controlled for in the total sample, neighbourhood cohesion (NC), and reciprocity and social support (RSS) were statistically associated with poor self-rated health (NC: OR = 1.40; RSS: OR = 1.34). However, for the non-poor sub-sample, no social capital variable was a statistically significant predictor. The synergy index between low individual-level NC and poverty, and between low individual-level RSS and poverty were 1.22 and 1.28, respectively, indicating an aggravating effect between them.</p> <p>Conclusion</p> <p>In this study, we have shown that the interaction effect between poverty and lack of social capital (NC and RSS) was a good predictor of poor SRH in urban China. Improving NC and RSS may be helpful in reducing health inequity; however, poverty reduction is more important and therefore should be implemented at the same time. Policies that attempt to improve health equity via social capital, but neglect poverty intervention, would be counter-productive.</p

Tumor-targeted RNA-interference: functional non-viral nanovectors

This is the published version, also available here: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3092671/.While small interfering RNA (siRNA) and microRNA (miRNA) have attracted extensive attention and showed significant promise for the study, diagnosis and treatment of human cancers, delivering siRNA or miRNA specifically and efficiently into tumor cells in vivo remains a great challenge. Delivery barriers, which arise mainly from the routes of administration associated with complex physiochemical microenvironments of the human body and the unique properties of RNAs, hinder the development of RNA-interference (RNAi)-based therapeutics in clinical practice. However, in available delivery systems, non-viral nanoparticle-based gene/RNA-delivery vectors, or nanovectors, are showing powerful delivery capacities and huge potential for improvements in functional nanomaterials, including novel fabrication approaches which would greatly enhance delivery performance. In this review, we summarize the currently recognized RNAi delivery barriers and the anti-barrier requirements related to vectors' properties. Recent efforts and achievements in the development of novel nanomaterials, nanovectors fabrication methods, and delivery approaches are discussed. We also review the outstanding needs in the areas of material synthesis and assembly, multifunction combinations, proper delivery and assisting approaches that require more intensive investigation for the comprehensive and effective delivery of RNAi by non-viral nanovectors

Natural Proteasome Inhibitor Celastrol Suppresses Androgen-Independent Prostate Cancer Progression by Modulating Apoptotic Proteins and NF-kappaB

Celastrol is a natural proteasome inhibitor that exhibits promising anti-tumor effects in human malignancies, especially the androgen-independent prostate cancer (AIPC) with constitutive NF-κB activation. Celastrol induces apoptosis by means of proteasome inhibition and suppresses prostate tumor growth. However, the detailed mechanism of action remains elusive. In the current study, we aim to test the hypothesis that celastrol suppresses AIPC progression via inhibiting the constitutive NF-κB activity as well as modulating the Bcl-2 family proteins.We examined the efficacy of celastrol both in vitro and in vivo, and evaluated the role of NF-κB in celastrol-mediated AIPC regression. We found that celastrol inhibited cell proliferation in all three AIPC cell lines (PC-3, DU145 and CL1), with IC₅₀ in the range of 1-2 µM. Celastrol also suppressed cell migration and invasion. Celastrol significantly induced apoptosis as evidenced by increased sub-G1 population, caspase activation and PARP cleavage. Moreover, celastrol promoted cleavage of the anti-apoptotic protein Mcl-1 and activated the pro-apoptotic protein Noxa. In addition, celastrol rapidly blocked cytosolic IκBα degradation and nuclear translocation of RelA. Likewise, celastrol inhibited the expression of multiple NF-κB target genes that are involved in proliferation, invasion and anti-apoptosis. Celastrol suppressed AIPC tumor progression by inhibiting proliferation, increasing apoptosis and decreasing angiogenesis, in PC-3 xenograft model in nude mouse. Furthermore, increased cellular IκBα and inhibited expression of various NF-κB target genes were observed in tumor tissues.Our data suggest that, via targeting the proteasome, celastrol suppresses proliferation, invasion and angiogenesis by inducing the apoptotic machinery and attenuating constitutive NF-κB activity in AIPC both in vitro and in vivo. Celastrol as an active ingredient of traditional herbal medicine could thus be developed as a new therapeutic agent for hormone-refractory prostate cancer

OSIC: A New One-Stage Image Captioner Coined

Mainstream image caption models are usually two-stage captioners, i.e., calculating object features by pre-trained detector, and feeding them into a language model to generate text descriptions. However, such an operation will cause a task-based information gap to decrease the performance, since the object features in detection task are suboptimal representation and cannot provide all necessary information for subsequent text generation. Besides, object features are usually represented by the last layer features that lose the local details of input images. In this paper, we propose a novel One-Stage Image Captioner (OSIC) with dynamic multi-sight learning, which directly transforms input image into descriptive sentences in one stage. As a result, the task-based information gap can be greatly reduced. To obtain rich features, we use the Swin Transformer to calculate multi-level features, and then feed them into a novel dynamic multi-sight embedding module to exploit both global structure and local texture of input images. To enhance the global modeling of encoder for caption, we propose a new dual-dimensional refining module to non-locally model the interaction of the embedded features. Finally, OSIC can obtain rich and useful information to improve the image caption task. Extensive comparisons on benchmark MS-COCO dataset verified the superior performance of our method

DIVA: A Dirichlet Process Based Incremental Deep Clustering Algorithm via Variational Auto-Encoder

Generative model-based deep clustering frameworks excel in classifying complex data, but are limited in handling dynamic and complex features because they require prior knowledge of the number of clusters. In this paper, we propose a nonparametric deep clustering framework that employs an infinite mixture of Gaussians as a prior. Our framework utilizes a memoized online variational inference method that enables the "birth" and "merge" moves of clusters, allowing our framework to cluster data in a "dynamic-adaptive" manner, without requiring prior knowledge of the number of features. We name the framework as DIVA, a Dirichlet Process-based Incremental deep clustering framework via Variational Auto-Encoder. Our framework, which outperforms state-of-the-art baselines, exhibits superior performance in classifying complex data with dynamically changing features, particularly in the case of incremental features. We released our source code implementation at: https://github.com/Ghiara/divaComment: update supplementary material

Application of BSDE in Standard Inventory Financing Loan

This paper examines the issue of loans obtained by the small and medium-sized enterprises (SMEs) from banks through the mortgage inventory of goods. And the loan-to-value (LTV) ratio which affects the loan business is a very critical factor. In this paper, we provide a general framework to determine a bank’s optimal loan-to-value (LTV) ratio when we consider the collateral value in the financial market with Knightian uncertainty. We assume that the short-term prices of the collateral follow a geometric Brownian motion. We use a set of equivalent martingale measures to build the models about a bank’s maximum and minimum levels of risk tolerance in an environment with Knightian uncertainty. The models about the LTV ratios are established with the bank’s maximum and minimum risk preferences. Applying backward stochastic differential equations (BSDEs), we get the explicit solutions of the models. Applying the explicit solutions, we can obtain an interval solution for the optimal LTV ratio. Our numerical analysis shows that the LTV ratio in the Knightian uncertainty-neutral environment belongs to the interval solutions derived from the models