Faster Fully-Dynamic Minimum Spanning Forest

We give a new data structure for the fully-dynamic minimum spanning forest problem in simple graphs. Edge updates are supported in $O(\log^4n/\log\log n)$ amortized time per operation, improving the $O(\log^4n)$ amortized bound of Holm et al. (STOC'98, JACM'01). We assume the Word-RAM model with standard instructions.Comment: 13 pages, 2 figure

Methods for Adapting Global Mass Spectrometry Based Metabolomics to the Clinical Enviornment

Metabolomics is a maturing field with successful application to research areas such as biomarker discovery and mechanisms of disease. With the ability to profile hundreds or even thousands of biochemicals simultaneously, many of which are also used in various laboratory diagnostics, the technology has the potential to replace a battery of clinical tests with a single test. However, the current state of global analysis presents several challenges for the clinical environment. This dissertation addresses two of these challenges. First is handling of missing values with respect to comparing an individual sample against a reference population. Second is the semi-quantitative nature of the liquid chromatography mass spectrometry. The first paper explores basic properties of metabolites, specifically the statistical distribution of metabolite concentrations and correlation between them. In human sample sets covering three different sample material appropriate for clinical testing, raw ion counts are shown to be vastly non-normal and consistently having a heavy right skew. Natural log-transformation is effective at removing this skewness and inducing Gaussian behavior, though departures from normality may persist in the tails of the distributions. Correlation between library-matched metabolites after removing artifact related features is also shown to be of only moderate degree in most cases. In the second paper, application of the log transformation is used to account for missing values in estimating population parameters of a reference cohort. Missing values are largely attributed to the true level falling below the detection limit of the instrument. Combining this assumption with the Gaussian model leads to two parametric approaches being introduced for the estimation of population parameters. These methods are shown to outperform standard imputation approaches in the field using a combination of simulations and real metabolomic datasets. The third paper addresses merging multiple global LC-MS metabolomic sets of the same biological sample type together. Typical normalization methods meant to account for sample to sample variation are presented and compared to alternative approaches using technical replicates and within batch scaling. Concentrations from targeted analysis of eight clinical biomarkers are used to show the superiority of these alternative approaches.Doctor of Public Healt

Best Laid Plans of Lions and Men

We answer the following question dating back to J.E. Littlewood (1885-1977): Can two lions catch a man in a bounded area with rectifiable lakes? The lions and the man are all assumed to be points moving with at most unit speed. That the lakes are rectifiable means that their boundaries are finitely long. This requirement is to avoid pathological examples where the man survives forever because any path to the lions is infinitely long. We show that the answer to the question is not always "yes", by giving an example of a region R in the plane where the man has a strategy to survive forever. R is a polygonal region with holes and the exterior and interior boundaries are pairwise disjoint, simple polygons. Our construction is the first truly two-dimensional example where the man can survive. Next, we consider the following game played on the entire plane instead of a bounded area: There is any finite number of unit speed lions and one fast man who can run with speed 1+epsilon for some value epsilon>0. Can the man always survive? We answer the question in the affirmative for any constant epsilon>0

Escaping an Infinitude of Lions

We consider the following game played in the Euclidean plane: There is any countable set of unit speed lions and one fast man who can run with speed $1+\varepsilon$ for some value $\varepsilon>0$. Can the man survive? We answer the question in the affirmative for any $\varepsilon>0$.Comment: Published in American Mathematical Monthly, but references [5] and [10] are new. Note added about this. For a preliminary version, see arXiv:1703.0368

Serum metabolic signatures of primary biliary cirrhosis and primary sclerosing cholangitis

BACKGROUND & AIMS: A greater understanding of cholestatic disease is necessary to advance diagnostic tools and therapeutic options for conditions such as primary biliary cirrhosis (PBC) and primary sclerosing cholangitis (PSC). The purpose of this study was to determine and compare the serum metabolomes of patients with PBC (n = 18) or PSC (n = 21) and healthy controls (n = 10) and to identify metabolites that may differentiate these two cholestatic diseases. METHODS AND RESULTS: Using a mass spectrometry-based, non-targeted biochemical profiling approach, we identified 420 serum metabolites, 101 that differed significantly (P ≤ 0.05) between PBC and control groups, 115 that differed significantly between PSC and control groups, and 56 that differed significantly between PSC and PBC groups. Random forest classification analysis was able to distinguish patients with PBC or PSC with 95% accuracy with selected biochemicals reflective of protein and amino acid metabolism identified as the major contributors. Metabolites related to bile acid metabolism, lipid metabolism, inflammation, and oxidative stress/lipid peroxidation were also identified as differing significantly when comparing the disease groups and controls, with some of these pathways differentially affected in the PBC and PSC groups. CONCLUSION: In this study, we identified novel metabolic changes associated with cholestatic disease that were both consistent and different between PBC and PSC. Validation studies in larger patient cohorts are required to determine the utility of these biochemical markers for diagnosis and therapeutic monitoring of patients with PBC and PSC

Cost-Effectiveness Analysis of Stockholm 3 Testing Compared to PSA as the Primary Blood Test in the Prostate Cancer Diagnostic Pathway:A Decision Tree Approach

OBJECTIVE: This study evaluated the cost effectiveness of using Stockholm 3 (STHLM3) testing compared to the prostate-specific antigen (PSA) test in the diagnostic pathway for prostate cancer. METHODS: We created a decision tree model for PSA (current standard) and STHLM3 (new alternative). Cost effectiveness was evaluated in a hypothetical cohort of male individuals aged 50–69 years. The study applied a Danish hospital perspective with a time frame restricted to the prostate cancer diagnostic pathway, beginning with the initial PSA/STHLM3 test, and ending with biopsy and histopathological diagnosis. Estimated values from the decision-analytical model were used to calculate the incremental cost-effectiveness ratio. Deterministic and probabilistic sensitivity analyses were conducted to test the robustness of the base-case analysis. RESULTS: The model-based analysis revealed that STHLM3 testing was more effective than the PSA, but also more costly, with an incremental cost-effectiveness ratio of €511.7 (95% credible interval, 359.9–674.3) for each additional correctly classified individual. In the deterministic sensitivity analysis, variations in the cost of STHLM3 had the greatest influence on the incremental cost-effectiveness ratio. In the probabilistic sensitivity analysis, all iterations were positioned in the north-east quadrant of the incremental cost-effectiveness scatterplot. At a willingness to pay of €700 for an additional correctly classified individual, STHLM3 had a 100% probability of being cost effective. CONCLUSIONS: Compared to the PSA test as the initial testing modality in the prostate cancer diagnostic workup, STHLM3 testing showed improved incremental effectiveness, however, at additional costs. The results were sensitive to the cost of the STHLM3 test; therefore, a lower cost of the STHLM3 test would improve its cost effectiveness compared with PSA tests. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s40258-022-00741-0

Differential effects of dietary supplements on metabolomic profile of smokers versus non-smokers.

BackgroundCigarette smoking is well-known to associate with accelerated skin aging as well as cardiovascular disease and lung cancer, in large part due to oxidative stress. Because metabolites are downstream of genetic variation, as well as transcriptional changes and post-translational modifications of proteins, they are the most proximal reporters of disease states or reversal of disease states.MethodsIn this study, we explore the potential effects of commonly available oral supplements (containing antioxidants, vitamins and omega-3 fatty acids) on the metabolomes of smokers (n = 11) compared to non-smokers (n = 17). At baseline and after 12 weeks of supplementation, metabolomic analysis was performed on serum by liquid and gas chromatography with mass spectroscopy (LC-MS and GC-MS). Furthermore, clinical parameters of skin aging, including cutometry as assessed by three dermatologist raters blinded to subjects' age and smoking status, were measured.ResultsLong-chain fatty acids, including palmitate and oleate, decreased in smokers by 0.76-fold (P = 0.0045) and 0.72-fold (P = 0.0112), respectively. These changes were not observed in non-smokers. Furthermore, age and smoking status showed increased glow (P = 0.004) and a decrease in fine wrinkling (P = 0.038). Cutometry showed an increase in skin elasticity in smokers (P = 0.049) but not in non-smokers. Complexion analysis software (VISIA) revealed decreases in the number of ultraviolet spots (P = 0.031), and cutometry showed increased elasticity (P = 0.05) in smokers but not non-smokers.ConclusionsAdditional future work may shed light on the specific mechanisms by which long-chain fatty acids can lead to increased glow, improved elasticity measures and decreased fine wrinkling in smokers' skin. Our study provides a novel, medicine-focused application of available metabolomic technology to identify changes in sera of human subjects with oxidative stress, and suggests that oral supplementation (in particular, commonly available antioxidants, vitamins and omega-3 fatty acids) affects these individuals in a way that is unique (compared to non-smokers) on a broad level