Kemeny's constant and enumerating Braess edges in trees

We study the problem of enumerating Braess edges for Kemeny's constant in trees. We obtain bounds and asympotic results for the number of Braess edges in some families of trees

Bounds on Kemeny's constant of a graph and the Nordhaus-Gaddum problem

We study Nordhaus-Gaddum problems for Kemeny's constant $\mathcal{K}(G)$ of a connected graph $G$. We prove bounds on $\min\{\mathcal{K}(G),\mathcal{K}(\overline{G})\}$ and the product $\mathcal{K}(G)\mathcal{K}(\overline{G})$ for various families of graphs. In particular, we show that if the maximum degree of a graph $G$ on $n$ vertices is $n-O(1)$ or $n-\Omega(n)$, then $\min\{\mathcal{K}(G),\mathcal{K}(\overline{G})\}$ is at most $O(n)$

Identification of complex metabolic states in critically injured patients using bioinformatic cluster analysis

IntroductionAdvances in technology have made extensive monitoring of patient physiology the standard of care in intensive care units (ICUs). While many systems exist to compile these data, there has been no systematic multivariate analysis and categorization across patient physiological data. The sheer volume and complexity of these data make pattern recognition or identification of patient state difficult. Hierarchical cluster analysis allows visualization of high dimensional data and enables pattern recognition and identification of physiologic patient states. We hypothesized that processing of multivariate data using hierarchical clustering techniques would allow identification of otherwise hidden patient physiologic patterns that would be predictive of outcome.MethodsMultivariate physiologic and ventilator data were collected continuously using a multimodal bioinformatics system in the surgical ICU at San Francisco General Hospital. These data were incorporated with non-continuous data and stored on a server in the ICU. A hierarchical clustering algorithm grouped each minute of data into 1 of 10 clusters. Clusters were correlated with outcome measures including incidence of infection, multiple organ failure (MOF), and mortality.ResultsWe identified 10 clusters, which we defined as distinct patient states. While patients transitioned between states, they spent significant amounts of time in each. Clusters were enriched for our outcome measures: 2 of the 10 states were enriched for infection, 6 of 10 were enriched for MOF, and 3 of 10 were enriched for death. Further analysis of correlations between pairs of variables within each cluster reveals significant differences in physiology between clusters.ConclusionsHere we show for the first time the feasibility of clustering physiological measurements to identify clinically relevant patient states after trauma. These results demonstrate that hierarchical clustering techniques can be useful for visualizing complex multivariate data and may provide new insights for the care of critically injured patients

Investigation of Gravitational Lens Mass Models

We have previously reported the discovery of strong gravitational lensing by faint elliptical galaxies using the WFPC2 on HST and here we investigate their potential usefulness in putting constraints on lens mass models. We compare various ellipsoidal surface mass distributions, including those with and without a core radius, as well as models in which the mass distributions are assumed to have the same axis ratio and orientation as the galaxy light. We also study models which use a spherical mass distribution having various profiles, both empirical and following those predicted by CDM simulations. These models also include a gravitational shear term. The model parameters and associated errors have been derived by 2-dimensional analysis of the observed HST WFPC2 images. The maximum likelihood procedure iteratively converges simultaneously on the model for the lensing elliptical galaxy and the lensed image components. The motivation for this study was to distinguish between these mass models with this technique. However, we find that, despite using the full image data rather than just locations and integrated magnitudes, the lenses are fit equally well with several of the mass models. Each of the mass models generates a similar configuration but with a different magnification and cross-sectional area within the caustic, and both of these latter quantities govern the discovery probability of lensing in the survey. These differences contribute to considerable cosmic scatter in any estimate of the cosmological constant using gravitational lenses.Comment: 10 pages with 6 embedded figures, tentatively scheduled to be published in the July 2001 issue of The Astronomical Journal. For additional information see http://mds.phys.cmu.edu/lense

The Morphological Butcher-Oemler effect in the SDSS Cut&Enhance Galaxy Cluster Catalog

We investigate the evolution of the fractions of late type cluster galaxies as a function of redshift, using one of the largest, most uniform cluster samples available. The sample consists of 514 clusters of galaxies in the range 0.02<z<0.3 from the Sloan Digital Sky Survey Cut & Enhance galaxy cluster catalog. This catalog was created using a single automated cluster finding algorithm on uniform data from a single telescope, with accurate CCD photometry, thus, minimizing selection biases. We use four independent methods to analyze the evolution of the late type galaxy fraction. Specifically, we select late type galaxies based on: restframe g-r color, u-r color, galaxy profile fitting and concentration index. The first criterion corresponds to the one used in the classical Butcher-Oemler analyses. The last three criteria are more sensitive to the morphological type of the galaxies. In all four cases, we find an increase in the fraction of late type galaxies with increasing redshift, significant at the 99.9% level. The results confirm that cluster galaxies do change colors with redshift (the Butcher-Oemler effect) and, in addition, they change their morphology to later-type toward higher redshift -- indicating a morphological equivalent of the Butcher-Oemler effect. We also find a tendency of richer clusters to have lower fractions of late type galaxies. The trend is consistent with a ram pressure stripping model, where richer clusters have more effective ram pressure due to their higher temperature.Comment: 44 pages, 15 figures, accepted for PAS

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts

Pan-cancer Alterations of the MYC Oncogene and Its Proximal Network across the Cancer Genome Atlas

Although theMYConcogene has been implicated incancer, a systematic assessment of alterations ofMYC, related transcription factors, and co-regulatoryproteins, forming the proximal MYC network (PMN),across human cancers is lacking. Using computa-tional approaches, we define genomic and proteo-mic features associated with MYC and the PMNacross the 33 cancers of The Cancer Genome Atlas.Pan-cancer, 28% of all samples had at least one ofthe MYC paralogs amplified. In contrast, the MYCantagonists MGA and MNT were the most frequentlymutated or deleted members, proposing a roleas tumor suppressors.MYCalterations were mutu-ally exclusive withPIK3CA,PTEN,APC,orBRAFalterations, suggesting that MYC is a distinct onco-genic driver. Expression analysis revealed MYC-associated pathways in tumor subtypes, such asimmune response and growth factor signaling; chro-matin, translation, and DNA replication/repair wereconserved pan-cancer. This analysis reveals insightsinto MYC biology and is a reference for biomarkersand therapeutics for cancers with alterations ofMYC or the PMN

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin

Spatial Organization and Molecular Correlation of Tumor-Infiltrating Lymphocytes Using Deep Learning on Pathology Images

Beyond sample curation and basic pathologic characterization, the digitized H&E-stained images of TCGA samples remain underutilized. To highlight this resource, we present mappings of tumorinfiltrating lymphocytes (TILs) based on H&E images from 13 TCGA tumor types. These TIL maps are derived through computational staining using a convolutional neural network trained to classify patches of images. Affinity propagation revealed local spatial structure in TIL patterns and correlation with overall survival. TIL map structural patterns were grouped using standard histopathological parameters. These patterns are enriched in particular T cell subpopulations derived from molecular measures. TIL densities and spatial structure were differentially enriched among tumor types, immune subtypes, and tumor molecular subtypes, implying that spatial infiltrate state could reflect particular tumor cell aberration states. Obtaining spatial lymphocytic patterns linked to the rich genomic characterization of TCGA samples demonstrates one use for the TCGA image archives with insights into the tumor-immune microenvironment