Sufficient Dimension Reduction

In regression analysis, it is difficult to uncover the dependence relationship between a response variable and a covariate vector when the dimension of the covariate vector is high. To reduce the dimension of the covariate vector, one approach is sufficient dimension reduction. Sufficient dimension reduction is based on the assumption that the response variable relates to only a few linear combinations of the covariate vector. Thus, by replacing the covariate vector with these linear combinations, sufficient dimension reduction achieves dimension reduction. The goal of sufficient dimension reduction is to estimate the space spanned by these linear combinations of the covariate vector. We denote this space by S. In this thesis, we give an introductory review on three important sufficient dimension reduction methods. They are Sliced Inverse Regression (SIR), Sliced Average Variance Estimate (SAVE) and Principle Hessian Directions (pHd). Li proposed SIR in 1991. SIR is a method that exploits the simplicity of the inverse regression. Given the univariate response variable and the high dimensional covariate, it is much easier to regress the covariate against the response variable than the other way around. Motivated by a theorem that connects forward regression and inverse regression, SIR estimates S using inverse regression lines. Since SIR uses first moments only, it fails when there exists symmetry dependence between the response variable and the covariate. To make up for this defect, Cook proposed SAVE in a comment on SIR in 1991. SAVE follows the general lines of SIR but uses second moments as well as first moments to estimate S. pHd is also a second moment method. Li developed pHd in 1992 based on the observation that the eigenvectors for the Hessian matrices of the regression function are closely related to the basis vectors of S. Therefore pHd provides an estimate of S by using these eigenvectors. To compare these methods, a simulation study is presented at the end. From the simulation results, SIR is the most efficient method and SAVE is the most time consuming method. Since SIR fails when symmetry dependence exists, we recommend pHd when symmetry dependence presents and SIR in other cases

Branch and Bound for Piecewise Linear Neural Network Verification

The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. In this context, verification involves proving or disproving that an NN model satisfies certain input-output properties. Despite the reputation of learned NN models as black boxes, and the theoretical hardness of proving useful properties about them, researchers have been successful in verifying some classes of models by exploiting their piecewise linear structure and taking insights from formal methods such as Satisifiability Modulo Theory. However, these methods are still far from scaling to realistic neural networks. To facilitate progress on this crucial area, we exploit the Mixed Integer Linear Programming (MIP) formulation of verification to propose a family of algorithms based on Branch-and-Bound (BaB). We show that our family contains previous verification methods as special cases. With the help of the BaB framework, we make three key contributions. Firstly, we identify new methods that combine the strengths of multiple existing approaches, accomplishing significant performance improvements over previous state of the art. Secondly, we introduce an effective branching strategy on ReLU non-linearities. This branching strategy allows us to efficiently and successfully deal with high input dimensional problems with convolutional network architecture, on which previous methods fail frequently. Finally, we propose comprehensive test data sets and benchmarks which includes a collection of previously released testcases. We use the data sets to conduct a thorough experimental comparison of existing and new algorithms and to provide an inclusive analysis of the factors impacting the hardness of verification problems

Catechol-chitosan/polyacrylamide hydrogel wound dressing for regulating local inflammation

Chronic wounds and the accompanying inflammation are ongoing challenges in clinical treatment. They are usually accompanied by low pH and high oxidative stress environments, limiting cell growth and proliferation. Ordinary medical gauze has limited therapeutic effects on chronic wounds, and there is active research to develop new wound dressings. The chitosan hydrogel could be widely used in biomedical science with great biocompatibility, but the low mechanical properties limit its development. This work uses polyacrylamide to prepare double-network (DN) hydrogels based on bioadhesive catechol-chitosan hydrogels. Cystamine and N, N′-Bis(acryloyl)cystamine, which can be cross-linking agents with disulfide bonds to prepare redox-responsive DN hydrogels and pH-responsive nanoparticles (NPs) prepared by acetalized cyclodextrin (ACD) are used to intelligently release drugs against chronic inflammation microenvironments. The addition of catechol groups and ACD-NPs loaded with the Resolvin E1 (RvE1), promotes cell adhesion and regulates the inflammatory response at the wound site. The preparation of the DN hydrogel in this study can be used to treat and regulate the inflammatory microenvironment of chronic wounds accurately. It provides new ideas for using inflammation resolving factor loaded in DN hydrogel of good biocompatibility with enhanced mechanical properties to intelligent regulate the wound inflammation and promote the wound repaired

Metagenomic analysis reveals gut plasmids as diagnosis markers for colorectal cancer

BackgroundColorectal cancer (CRC) is linked to distinct gut microbiome patterns. The efficacy of gut bacteria as diagnostic biomarkers for CRC has been confirmed. Despite the potential to influence microbiome physiology and evolution, the set of plasmids in the gut microbiome remains understudied.MethodsWe investigated the essential features of gut plasmid using metagenomic data of 1,242 samples from eight distinct geographic cohorts. We identified 198 plasmid-related sequences that differed in abundance between CRC patients and controls and screened 21 markers for the CRC diagnosis model. We utilize these plasmid markers combined with bacteria to construct a random forest classifier model to diagnose CRC.ResultsThe plasmid markers were able to distinguish between the CRC patients and controls [mean area under the receiver operating characteristic curve (AUC = 0.70)] and maintained accuracy in two independent cohorts. In comparison to the bacteria-only model, the performance of the composite panel created by combining plasmid and bacteria features was significantly improved in all training cohorts (mean AUCcomposite = 0.804 and mean AUCbacteria = 0.787) and maintained high accuracy in all independent cohorts (mean AUCcomposite = 0.839 and mean AUCbacteria = 0.821). In comparison to controls, we found that the bacteria-plasmid correlation strength was weaker in CRC patients. Additionally, the KEGG orthology (KO) genes in plasmids that are independent of bacteria or plasmids significantly correlated with CRC.ConclusionWe identified plasmid features associated with CRC and showed how plasmid and bacterial markers could be combined to further enhance CRC diagnosis accuracy

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

What Matters Most for Community Social Capital among Older Adults Living in Urban China: The Role of Health and Family Social Capital

The present study investigated individual-level determinants of community social capital among older adults in urban China, with a particular emphasis on health and family social capital. A quota sampling method was used to select 456 adults aged 60 or older from 16 local communities in the city of Suzhou in 2015. Multiple indicators and multiple courses in structural equation modeling were used to examine the proposed model. Latent constructs of community social capital (i.e., cognitive social capital and structural social capital) were established. The results showed that family social capital and instrumental activities of daily living were the most influential determinants of cognitive social capital, whereas activities of daily living and socioeconomic status were the most important determinants of structural social capital. We demonstrate the application of social capital theory in an urban Chinese context. Future policy development and social work interventions should use a more comprehensive social capital latent constructs and health indicators as screening instruments. The promotion of family social capital could play an important role in enhancing cognitive social capital among older adults

Forward-looking Multi-channel SAR Adaptive Identification to Suppress Deception Jamming

Forward-looking multi-channel SAR imaging suffers from ambiguity regarding left and right echoes. To deblur the imaging process, spatial resources must be used, which make the imaging process more complex than the general side-looking SAR. In complex electromagnetic environments, it is very difficult to obtain forward-looking SAR images without interference or ambiguity. In this paper, we present an adaptive discriminant suppression algorithm that addresses deception jamming based on Azimuth ADaptive Beam Forming (AADBF). First, we use the AADBF technique to cancel the multi-channel received echo signal and retain the deception jamming samples. Then, we use the threshold detection method to identify the pixel location of the deception jamming on high-resolution SAR images. Finally, we apply adaptive spatial filtering to pixels with interference to achieve anti-deception jamming. Simulation results show that this method can effectively identify and suppress deception jamming, while realizing forward-looking SAR non-interference focusing imaging