Echolocation on Manifolds

We consider the question asked by Wyman and Xi [WX23]: ``Can you hear your location on a manifold?” In other words, can you locate a unique point x on a manifold, up to symmetry, if you know the Laplacian eigenvalues and eigenfunctions of the manifold? In [WX23], Wyman and Xi showed that echolocation holds on one- and two-dimensional rectangles with Dirichlet boundary conditions using the pointwise Weyl counting function. They also showed echolocation holds on ellipsoids using Gaussian curvature. In this thesis, we provide full details for Wyman and Xi\u27s proof for one- and two-dimensional rectangles and we show that echolocation also holds on many three-dimensional boxes. We also prove that echolocation holds on rectangles with certain mixed boundary conditions using a similar approach. Secondly, we explore echolocation via Gaussian curvature and we focus on two categories of manifolds, namely surfaces of revolution and minimal surfaces. We provide counterexamples to two conjectures of necessary conditions for echolocation to hold on surfaces of revolution. We also show that Gaussian curvature is not enough for us to echolocate on Enneper\u27s surface and Henneberg\u27s surface by constructing pairs of non-symmetric points that have identical Gaussian curvatures

Study on the Role of Vitamin D in Systemic Lupus Erythematosus

Vitamin D is a hormone precursor with multiple biological effects. It binds to vitamin D receptors on target cells. It is an important participant in the metabolism of calcium and phosphorus in vivo. It is closely related to cell cycle, cell proliferation, differentiation, apoptosis, signal transduction and immune regulation. Its role in the treatment of infection, tumor and even immune diseases has been gradually recognized and studied. Patients with systemic lupus erythematosus generally have decreased levels of active vitamin D, and low levels of vitamin D are associated with disease occurrence, disease activity and complications. In the past ten years, a large number of studies have been carried out on it globally to explore the role of vitamin D in the occurrence and development of systemic lupus erythematosus. This paper summarizes its recent research progress

Learning to Select Cuts for Efficient Mixed-Integer Programming

Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions in the early stage, thus largely reducing the computational burden without hurting the solution accuracy. However, the major cut selection approaches heavily rely on heuristics, which strongly depend on the specific problem at hand and thus limit their generalization capability. In this paper, we propose a data-driven and generalizable cut selection approach, named Cut Ranking, in the settings of multiple instance learning. To measure the quality of the candidate cuts, a scoring function, which takes the instance-specific cut features as inputs, is trained and applied in cut ranking and selection. In order to evaluate our method, we conduct extensive experiments on both synthetic datasets and real-world datasets. Compared with commonly used heuristics for cut selection, the learning-based policy has shown to be more effective, and is capable of generalizing over multiple problems with different properties. Cut Ranking has been deployed in an industrial solver for large-scale MIPs. In the online A/B testing of the product planning problems with more than $10^7$ variables and constraints daily, Cut Ranking has achieved the average speedup ratio of 12.42% over the production solver without any accuracy loss of solution.Comment: Paper accepted at Pattern Recognition journa

Causes of Infection after Earthquake, China, 2008

To determine which organisms most commonly cause infection after natural disasters, we cultured specimens from injured earthquake survivors in Wenchuan, China, 2008. Of 123 cultures, 46 (59%) grew only 1 type of pathogenic bacteria. Smear was more effective than culture for early diagnosis of gas gangrene. Early diagnosis and treatment of wounds are crucial

Hydrodynamic Delivery of Chitosan-Folate-DNA Nanoparticles in Rats with Adjuvant-Induced Arthritis

50 kDa chitosan was conjugated with folate, a specific tissue-targeting ligand. Nanoparticles such as chitosan-DNA and folate-chitosan-DNA were prepared by coacervation process. The hydrodynamic intravenous injection of nanoparticles was performed in the right posterior paw in normal and arthritic rats. Our results demonstrated that the fluorescence intensity of DsRed detected was 5 to 12 times more in the right soleus muscle and in the right gastro muscle than other tissue sections. β-galactosidase gene expression with X-gal substrate and folate-chitosan-plasmid nanoparticles showed best coloration in the soleus muscle. Treated arthritic animals also showed a significant decrease in paw swelling and IL-1β and PGE2 concentration in serum compared to untreated rats. This study demonstrated that a nonviral gene therapeutic approach using hydrodynamic delivery could help transfect more efficiently folate-chitosan-DNA nanoparticles in vitro/in vivo and could decrease inflammation in arthritic rats

Efficient Nonviral Gene Therapy Using Folate-Targeted Chitosan-DNA Nanoparticles In Vitro

Nonviral cationic polymers like chitosan can be combined with DNA to protect it from degradation. The chitosan is a biocompatible, biodegradable, nontoxic, and cheap polycationic polymer with low immunogenicity. The objective of this study was to synthesize and then assess different chitosan-DNA nanoparticles and to select the best ones for selective in vitro transfection in human epidermoid carcinoma (KB) cell lines. It revealed that different combinations of molecular weight, the presence or absence of folic acid ligand, and different plasmid DNA sizes can lead to nanoparticles with various diameters and diverse transfection efficiencies. The intracellular trafficking, nuclear uptake, and localization are also studied by confocal microscopy, which confirmed that DNA was delivered to cell nuclei to be expressed

Presence of Segmented Filamentous Bacteria in Human Children and Its Potential Role in the Modulation of Human Gut Immunity

Segmented filamentous bacteria (SFB) are commensal organisms that grow by anchoring a specialized holdfast structure to the intestinal walls of a variety of animals. Interaction of SFB with Peyer’s patches in mice promotes the post-natal maturation of the immune system. We previously reported that the colonization of SFB in humans mainly occurs by 36 months of age, and is difficult to be detected afterward. In this study, we measured the level of SFB in intestinal fluids of human children. SFB were found via qPCR to represent a small fraction of the whole SFB-positive microbiota (105 SFB in 1011 total bacteria). Bacteria with filamentous segmented morphology were observed in intestinal fluids via fluorescent in situ hybridization, and from gut biopsies via scanning electron microscopy. SFB-specific DNA and peptide fragments were also identified via multiple displacement amplification PCR and mass spectrometry. There was an overall positive correlation between the presence of SFB and the titer of total secretory immunoglobulin A (sIgA), which is more apparent in intestinal fluids of the age group of 8–36 months. Afterward there was a decline of SFB in numbers correlated with a reduction of total sIgA. RT-qPCR analysis of the terminal ileal biopsies revealed that the expression of Th17 pathway genes were induced in SFB-positive samples, while the markers of T and B cell receptor signaling pathways were also upregulated. Collectively, these data suggest that SFB is a rare member of microbiota, and may play an important role in the development of human gut immunity