Inversion of sparse matrices using Monte Carlo methods

A frequent need in many scientific applications is the flexibility to compute some suitable elements of the inverse of well-conditioned, large, sparse, and positive definite matrices. In this research, we have explored some aspects of the inversion of such matrices. For this class of matrices, it has been shown that desired elements of their inverse may be evaluated with desired accuracy via a statistical approach. In this approach, each element of the inverse matrix is decomposed as the sum of two components: a fixed quantity and an expectation of a well defined random variable. This approach works directly with the original matrix W. Thus, it is devoid of the good ordering, fill-ins and choice of critical parameter problems. This approach will always yield positive estimates for variances. In addition, this approach has four attractive advantages. Firstly, it is flexible, that is, a desired entry of the inverse matrix can be evaluated, without computing any other entry. Secondly, it takes advantage of the sparsity of the matrix. Thirdly, it computes the exact value for some entries. And finally, it is easily parallelizable, which provides gains inefficiency and computing time;The expectation in the above decomposition may be computed using either the ordinary Importance Sampling technique or the Adaptive Importance Sampling;For moderate dimension of the matrix the ordinary importance sampling yields reasonable results when the importance sampler is the MVt3 with a diagonal covariance matrix;The A.I.S. may be started with three different covariance matrices. In general, A.I.S. provides \u27better\u27 results than the ordinary importance sampling and requires fewer iterations;Using an efficient sparse storage scheme, we have explored the implementation of this approach under a distributed system with PVM as a message passing protocol and under a shared memory environment using a 4 processor share memory machine. The method yields reasonable results under both environment

Metabolic system alterations in pancreatic cancer patient serum: potential for early detection

BACKGROUND: The prognosis of pancreatic cancer (PC) is one of the poorest among all cancers, due largely to the lack of methods for screening and early detection. New biomarkers for identifying high-risk or early-stage subjects could significantly impact PC mortality. The goal of this study was to find metabolic biomarkers associated with PC by using a comprehensive metabolomics technology to compare serum profiles of PC patients to healthy control subjects. METHODS: A non-targeted metabolomics approach based on high-resolution, flow-injection Fourier transform ion cyclotron resonance mass spectrometry (FI-FTICR-MS) was used to generate comprehensive metabolomic profiles containing 2478 accurate mass measurements from the serum of Japanese PC patients (n=40) and disease-free subjects (n=50). Targeted flow-injection tandem mass spectrometry (FI-MS/MS) assays for specific metabolic systems were developed and used to validate the FI-FTICR-MS results. A FI-MS/MS assay for the most discriminating metabolite discovered by FI-FTICR-MS (PC-594) was further validated in two USA Caucasian populations; one comprised 14 PCs, six intraductal papillary mucinous neoplasims (IPMN) and 40 controls, and a second comprised 1000 reference subjects aged 30 to 80, which was used to create a distribution of PC-594 levels among the general population. RESULTS: FI-FTICR-MS metabolomic analysis showed significant reductions in the serum levels of metabolites belonging to five systems in PC patients compared to controls (all p<0.000025). The metabolic systems included 36-carbon ultra long-chain fatty acids, multiple choline-related systems including phosphatidylcholines, lysophosphatidylcholines and sphingomyelins, as well as vinyl ether-containing plasmalogen ethanolamines. ROC-AUCs based on FI-MS/MS of selected markers from each system ranged between 0.93 ±0.03 and 0.97 ±0.02. No significant correlations between any of the systems and disease-stage, gender, or treatment were observed. Biomarker PC-594 (an ultra long-chain fatty acid), was further validated using an independently-collected US Caucasian population (blinded analysis, n=60, p=9.9E-14, AUC=0.97 ±0.02). PC-594 levels across 1000 reference subjects showed an inverse correlation with age, resulting in a drop in the AUC from 0.99 ±0.01 to 0.90 ±0.02 for subjects aged 30 to 80, respectively. A PC-594 test positivity rate of 5.0% in low-risk reference subjects resulted in a PC sensitivity of 87% and a significant improvement in net clinical benefit based on decision curve analysis. CONCLUSIONS: The serum metabolome of PC patients is significantly altered. The utility of serum metabolite biomarkers, particularly PC-594, for identifying subjects with elevated risk of PC should be further investigated

Inversion of sparse matrices using Monte Carlo methods

A frequent need in many scientific applications is the flexibility to compute some suitable elements of the inverse of well-conditioned, large, sparse, and positive definite matrices. In this research, we have explored some aspects of the inversion of such matrices. For this class of matrices, it has been shown that desired elements of their inverse may be evaluated with desired accuracy via a statistical approach. In this approach, each element of the inverse matrix is decomposed as the sum of two components: a fixed quantity and an expectation of a well defined random variable. This approach works directly with the original matrix W. Thus, it is devoid of the good ordering, fill-ins and choice of critical parameter problems. This approach will always yield positive estimates for variances. In addition, this approach has four attractive advantages. Firstly, it is flexible, that is, a desired entry of the inverse matrix can be evaluated, without computing any other entry. Secondly, it takes advantage of the sparsity of the matrix. Thirdly, it computes the exact value for some entries. And finally, it is easily parallelizable, which provides gains inefficiency and computing time;The expectation in the above decomposition may be computed using either the ordinary Importance Sampling technique or the Adaptive Importance Sampling;For moderate dimension of the matrix the ordinary importance sampling yields reasonable results when the importance sampler is the MVt3 with a diagonal covariance matrix;The A.I.S. may be started with three different covariance matrices. In general, A.I.S. provides 'better' results than the ordinary importance sampling and requires fewer iterations;Using an efficient sparse storage scheme, we have explored the implementation of this approach under a distributed system with PVM as a message passing protocol and under a shared memory environment using a 4 processor share memory machine. The method yields reasonable results under both environment.</p

High HIV prevalence and associated risk factors among female sex workers in Rwanda

Human immunodeficiency virus (HIV) prevalence is often high among female sex workers (FSWs) in sub-Saharan Africa. Understanding the dynamics of HIV infection in this key population is critical to developing appropriate prevention strategies. We aimed to describe the prevalence and associated risk factors among a sample of FSWs in Rwanda from a survey conducted in 2010. A cross-sectional biological and behavioral survey was conducted among FSWs in Rwanda. Time-location sampling was used for participant recruitment from 4 to 18 February 2010. HIV testing was done using HIV rapid diagnostic tests (RDT) as per Rwandan national guidelines at the time of the survey. Elisa tests were simultaneously done on all samples tested HIV-positive on RDT. Proportions were used for sample description; multivariable logistic regression model was performed to analyze factors associated with HIV infection. Of 1338 women included in the study, 1112 consented to HIV testing, and the overall HIV prevalence was 51.0%. Sixty percent had been engaged in sex work for less than five years and 80% were street based. In multivariable logistic regression, HIV prevalence was higher in FSWs 25 years or older (adjusted odds ratio [aOR] = 1.83, 95% [confidence interval (CI): 1.42-2.37]), FSWs with consistent condom use in the last 30 days (aOR = 1.39, [95% CI: 1.05-1.82]), and FSWs experiencing at least one STI symptom in the last 12 months (aOR = 1.74 [95% CI: 1.34-2.26]). There was an inverse relationship between HIV prevalence and comprehensive HIV knowledge (aOR = 0.65, [95% CI: 0.48-0.88]). HIV prevalence was high among a sample of FSWs in Rwanda, and successful prevention strategies should focus on HIV education, treatment of sexually transmitted infections, and proper and consistent condom use using an outreach approach

Associations between latent TB infection, as identified by TST results, and presumptive risk factors for health facility workers from Kigali, Rwanda.

<p>¹Odds ratios for age/years represent the effects of each additional year of exposure. For example, an AOR of 1.02 implies a 2% increase in odds per year.</p><p>Associations between latent TB infection, as identified by TST results, and presumptive risk factors for health facility workers from Kigali, Rwanda.</p