Convergent finite difference methods for one-dimensional fully nonlinear second order partial differential equations

This paper develops a new framework for designing and analyzing convergent finite difference methods for approximating both classical and viscosity solutions of second order fully nonlinear partial differential equations (PDEs) in 1-D. The goal of the paper is to extend the successful framework of monotone, consistent, and stable finite difference methods for first order fully nonlinear Hamilton-Jacobi equations to second order fully nonlinear PDEs such as Monge-Amp\`ere and Bellman type equations. New concepts of consistency, generalized monotonicity, and stability are introduced; among them, the generalized monotonicity and consistency, which are easier to verify in practice, are natural extensions of the corresponding notions of finite difference methods for first order fully nonlinear Hamilton-Jacobi equations. The main component of the proposed framework is the concept of "numerical operator", and the main idea used to design consistent, monotone and stable finite difference methods is the concept of "numerical moment". These two new concepts play the same roles as the "numerical Hamiltonian" and the "numerical viscosity" play in the finite difference framework for first order fully nonlinear Hamilton-Jacobi equations. In the paper, two classes of consistent and monotone finite difference methods are proposed for second order fully nonlinear PDEs. The first class contains Lax-Friedrichs-like methods which also are proved to be stable and the second class contains Godunov-like methods. Numerical results are also presented to gauge the performance of the proposed finite difference methods and to validate the theoretical results of the paper.Comment: 23 pages, 8 figues, 11 table

A comparison in association and linkage genome-wide scans for alcoholism susceptibility genes using single-nucleotide polymorphisms

We conducted genome-wide linkage scans using both microsatellite and single-nucleotide polymorphism (SNP) markers. Regions showing the strongest evidence of linkage to alcoholism susceptibility genes were identified. Haplotype analyses using a sliding-window approach for SNPs in these regions were performed. In addition, we performed a genome-wide association scan using SNP data. SNPs in these regions with evidence of association (P ≦ 0.0001) were identified. We found that the general patterns for nonparametric linkage (NPL) scores from SNP and microsatellite genome scans are fairly consistent; however, the peaks of the NPL scores are mostly higher in the SNP-based scan than those using microsatellite markers, which might be located at different regions. Furthermore, SNPs identified from linkage screens were not so strongly associated with alcoholism (the most significant SNP had a p-value of 0.030) as those identified from association genomic screening (the most significant SNP had a p-value of 2.0 × 10(-8))

Incorporation of covariates in simultaneous localization of two linked loci using affected relative pairs

<p>Abstract</p> <p>Background</p> <p>Many dichotomous traits for complex diseases are often involved more than one locus and/or associated with quantitative biomarkers or environmental factors. Incorporating these quantitative variables into linkage analysis as well as localizing two linked disease loci simultaneously could therefore improve the efficiency in mapping genes. We extended the robust multipoint Identity-by-Descent (IBD) approach with incorporation of covariates developed previously to simultaneously estimate two linked loci using different types of affected relative pairs (ARPs).</p> <p>Results</p> <p>We showed that the efficiency was enhanced by incorporating a quantitative covariate parametrically or non-parametrically while localizing two disease loci using ARPs. In addition to its help in identifying factors associated with the disease and in improving the efficiency in estimating disease loci, this extension also allows investigators to account for heterogeneity in risk-ratios for different ARPs. Data released from the collaborative study on the genetics of alcoholism (COGA) for Genetic Analysis Workshop 14 (GAW 14) were used to illustrate the application of this extended method.</p> <p>Conclusions</p> <p>The simulation studies and example illustrated that the efficiency in estimating disease loci was demonstratively enhanced by incorporating a quantitative covariate and by using all relative pairs while mapping two linked loci simultaneously.</p

Assessment of gene-covariate interactions by incorporating covariates into association mapping

The HLA region is considered to be the main genetic risk factor for rheumatoid arthritis. Previous research demonstrated that HLA-DRB1 alleles encoding the shared epitope are specific for disease that is characterized by antibodies to cyclic citrullinated peptides (anti-CCP). In the present study, we incorporated the shared epitope and either anti-CCP antibodies or rheumatoid factor into linkage disequilibrium mapping, to assess the association between the shared epitope or antibodies with the disease gene identified. Incorporating the covariates into the association mapping provides a mechanism 1) to evaluate gene-gene and gene-environment interactions and 2) to dissect the pathways underlying disease induction/progress in quantitative antibodies

Bronchiolitis Obliterans Organizing Pneumonia in Swine Associated with Porcine Circovirus Type 2 Infection

Bronchiolitis obliterans organizing pneumonia (BOOP) is a chronic respiratory disease. Although the pathogenesis of BOOP is still incompletely understood, BOOP is responsive to steroids and has a good prognosis. In our five pigs with chronic postweaning multisystemic wasting syndrome (PMWS), typical BOOP lesions were revealed. All five porcine lungs showed typical intraluminal plugs, and porcine circovirus type 2 (PCV2) was identified. They also exhibited similar pathologic findings such as proliferation of type II pneumocytes and myofibroblasts (MFBs), extracellular collagen matrix (ECM) deposition, and fragmentation of elastic fibers. MFBs migration correlative molecules, for instance, gelatinase A, B and osteopontin, appeared strongly in the progressing marginal area of polypoid intraluminal plugs of fibrotic lesion. These molecules colocalized with the active MFBs. Both gelatinase activity and intercellular level of active MFBs were significantly increased (P < .05). Porcine chronic bronchopneumonia leads to BOOP and it is associated with PCV2 persistent infection. Swine BOOP demonstrates similar cellular constituents with human BOOP. Perhaps their molecular mechanisms of pathogenesis operate in a similar way. Thus we infer that the swine BOOP can be considered as a potential animal model for human BOOP associated with natural viral infection. Moreover, it is more convenient to obtain samples

Effects of mycophenolate mofetil on cutaneous lupus erythematosus in (NZB × NZW) F1 mice

AbstractBackgroundFew studies have evaluated the effects and precise molecular mechanism of mycophenolate mofetil (MMF) in the treatment of human cutaneous lupus erythematosus (CLE). Our findings shed light on the therapeutic effects of MMF in a UVB-induced NZB × NZW (NZBW) F1 CLE mouse model.MethodsContinuous MMF treatment (60 mg/kg/day) was administered up to Day 50 from the beginning of UVB induction (Day 0; 20 weeks old), as the pathologic features of CLE are present after 50 days. The therapeutic effects of MMF treatment in NZBW lupus mice were examined by comparing histopathological changes, lupus band test (deposition of immune complexes at the dermal–epidermal junction) and colocalization of autoantibodies with a dermal autoantigen Dsg3, and by evaluating the associations of local matrix metalloprotease activities.ResultsMMF improved survival in the NZBW lupus mice from 35.7% to 81.8%. The proteinuria, blood urea nitrogen, and interleukin 6 levels were significantly reduced after MMF treatment. The dermal lymphocytic infiltration, deposition of immune complexes at the dermal–epidermal junction, colocalized autoantibodies with Dsg3, and epidermal matrix metalloprotease activity were also attenuated in MMF-treated NZBW F1 mice.ConclusionThe results confirmed that MMF could substantially attenuate skin damage due to CLE in the NZBW F1 mouse model

Necrotizing fasciitis in liver cirrhosis

SummaryBackgroundNecrotizing fasciitis (NF) is associated with a high mortality rate. Hepatitis is endemic in Taiwan, and liver cirrhosis is associated with the development of NF. The characteristics of these patients, however, have not been well documented or the predictors of mortality clearly identified. The purpose of this study is to identify predictors of mortality in patients with liver cirrhosis and necrotizing fasciitis.MethodsThis study was conducted at the Chi-Mei Medical Center in southern Taiwan. Demographic data, clinical characteristics, and the microorganisms responsible for NF in patients with liver cirrhosis were recorded. To identify independent predictors associated with mortality, univariate analysis followed by multivariate logistic regression modeling was performed.ResultsDuring the period 2003–2011, a total of 55 patients with liver cirrhosis and NF were treated at the Chi-Mei Medical Center. Most patients had infections by monomicrobial Gram-negative bacilli. Univariate analysis revealed that severity of liver cirrhosis, shock, band polymorphonuclear neutrophil (>10%), international normalized ratio (>1.5), serum creatinine (>2.0 mg/dL), serum albumin (<2.5 g/dL), and activated partial thromboplastin time (>60 seconds) were significantly associated with mortality. However, multivariate logistic regression analysis revealed that serum albumin of <2.5 g/dL was the only independent predictor of mortality in patients with liver cirrhosis and NF.ConclusionNF in the vast majority of cirrhotic patients was caused by Gram-negative bacilli. Hypoalbuminemia (serum albumin <2.5 g/dL) was associated with mortality in patients with liver cirrhosis and NF. Further studies are needed to assess whether resuscitation with albumin-containing solutions lowers the mortality rate in such patients