The Complexity of Combinations of Qualitative Constraint Satisfaction Problems

The CSP of a first-order theory $T$ is the problem of deciding for a given finite set $S$ of atomic formulas whether $T \cup S$ is satisfiable. Let $T_1$ and $T_2$ be two theories with countably infinite models and disjoint signatures. Nelson and Oppen presented conditions that imply decidability (or polynomial-time decidability) of $\mathrm{CSP}(T_1 \cup T_2)$ under the assumption that $\mathrm{CSP}(T_1)$ and $\mathrm{CSP}(T_2)$ are decidable (or polynomial-time decidable). We show that for a large class of $\omega$-categorical theories $T_1, T_2$ the Nelson-Oppen conditions are not only sufficient, but also necessary for polynomial-time tractability of $\mathrm{CSP}(T_1 \cup T_2)$ (unless P=NP).Comment: Version 2: stronger main result with better presentation of the proof; multiple improvements in other proofs; new section structure; new example

Molecular overview of the glycan “node” analysis procedure.

<p>For glycans from blood plasma and other biofluids, O-linked glycans are released during permethylation, while N-linked glycans and glycolipids are released during acid hydrolysis. The unique pattern of methylation and acetylation in the final partially methylated alditol acetates (PMAAs) corresponds to the unique “glycan node” in the original glycan polymer and provides the molecular basis for separation and quantification by GC-MS. Figure adapted with permission from Borges CR et al. Anal. Chem. 2013, 85(5):2927–2936. Copyright 2013 American Chemical Society.</p

Distributions and ROC curves for the most highly elevated glycan node markers in former & current UCC patients relative to healthy controls when data were normalized to heavy glucose or heavy GlcNAc.

<p>Patient distributions are shown in (a-d). The Kruskal-Wallis test was performed followed by Dunn’s post hoc test. The letters at the top of the data points show statistically significant differences between the patient groups; groups with same letter do not have a significant difference. (e-h) ROC curves for the different sub-cohorts of UCC patients vs. healthy individuals. Areas under the ROC curves are provided in parenthesis next to the stated patient groups. As explained in the Discussion, despite the promising AUCs and shapes of some of these ROC curves, these data do not indicate that plasma/serum glycan nodes will potentially serve as clinically useful diagnostic markers of UCC.</p

Distributions and ROC curves for the most highly elevated glycan node markers in former & current UCC patients relative to healthy controls when data were normalized to sum of endogenous Hexoses or HexNAcs.

<p>Patient distributions are shown in (a-d). The Kruskal-Wallis test was performed followed by Dunn’s post hoc test. The letters at the top of the data points show statistically significant differences between the patient groups; groups with a common letter do not have a significant difference. (e-h) ROC curves for different groups of bladder cancer patients vs. certifiably healthy individuals. Area under the ROC curves are provided in parenthesis next to the stated patient groups. “NS” next to the area under the ROC curves shows that there is no significant difference between the two groups that are being compared. These data do not indicate that plasma/serum glycan nodes will potentially serve as clinically useful diagnostic markers of UCC.</p

Correlation of CRP and glycan nodes.

<p>Log of CRP concentration vs. (a) α2–6 sialylation; r = 0.34 and (b) β1–6 branching; r = 0.38 are plotted. Both correlations are statistically significant (Pearson correlation; <i>p</i> < 0.001).</p

Statistically significant differences between controls and bladder cancer patient sub-cohorts^a.

<p>Statistically significant differences between controls and bladder cancer patient sub-cohorts<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201208#t001fn001" target="_blank">^a</a>.</p

Conceptual overview of the glycan “node” analysis concept.

<p>The procedure consists of applying glycan methylation analysis (i.e., linkage analysis) to whole biofluids. Intact normal and abnormal glycans including O-glycans, N-glycans and glycolipids, are processed and transformed into partially methylated alditol acetates (PMAAs, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201208#pone.0201208.g001" target="_blank">Fig 1</a>), each of which corresponds to a particular monosaccharide-and-linkage-specific glycan “node” in the original polymer. As illustrated, analytically pooling together the glycan nodes from amongst all the aberrant intact glycan structures provides a more direct surrogate measurement of abnormal glycosyltransferase activity than any individual intact glycan, while simultaneously converting unique glycan features such as “core fucosylation”, “α2–6 sialylation”, “bisecting GlcNAc”, and “β1–6 branching” into single analytical signals. Actual extracted ion chromatograms from 9-μL blood plasma samples are shown. Numbers adjacent to monosaccharide residues in glycan structures indicate the position at which the higher residue is linked to the lower residue. Figure adapted with permission from Borges CR et al. Anal. Chem. 2013, 85(5):2927–2936. Copyright 2013 American Chemical Society.</p

Statistically significant differences between controls and bladder cancer patient sub-cohorts with data normalization to the sum of all endogenous hexoses or HexNAcs.

<p>Statistically significant differences between controls and bladder cancer patient sub-cohorts with data normalization to the sum of all endogenous hexoses or HexNAcs.</p

Correlation between age and the most highly elevated glycan node markers in former & current UCC patients relative to healthy controls when data were normalized to heavy glucose or heavy GlcNAc.

<p>Pearson correlation was used to evaluate this correlation. The common age range between all cohorts was 45–67. “NS” next to the r-value indicates that the Pearson correlation was not statistically significant. Distribution of the healthy controls is demonstrated by red dots. Distribution of the different sub-cohorts of UCC patients is demonstrated by black triangles.</p

A Multidisciplinary Biospecimen Bank of Renal Cell Carcinomas Compatible with Discovery Platforms at Mayo Clinic, Scottsdale, Arizona

<div><p>To address the need to study frozen clinical specimens using next-generation RNA, DNA, chromatin immunoprecipitation (ChIP) sequencing and protein analyses, we developed a biobank work flow to prospectively collect biospecimens from patients with renal cell carcinoma (RCC). We describe our standard operating procedures and work flow to annotate pathologic results and clinical outcomes. We report quality control outcomes and nucleic acid yields of our RCC submissions (N=16) to The Cancer Genome Atlas (TCGA) project, as well as newer discovery platforms, by describing mass spectrometry analysis of albumin oxidation in plasma and 6 ChIP sequencing libraries generated from nephrectomy specimens after histone H3 lysine 36 trimethylation (H3K36me3) immunoprecipitation. From June 1, 2010, through January 1, 2013, we enrolled 328 patients with RCC. Our mean (SD) TCGA RNA integrity numbers (RINs) were 8.1 (0.8) for papillary RCC, with a 12.5% overall rate of sample disqualification for RIN <7. Banked plasma had significantly less albumin oxidation (by mass spectrometry analysis) than plasma kept at 25°C (<i>P</i><.001). For ChIP sequencing, the FastQC score for average read quality was at least 30 for 91% to 95% of paired-end reads. In parallel, we analyzed frozen tissue by RNA sequencing; after genome alignment, only 0.2% to 0.4% of total reads failed the default quality check steps of Bowtie2, which was comparable to the disqualification ratio (0.1%) of the 786-O RCC cell line that was prepared under optimal RNA isolation conditions. The overall correlation coefficients for gene expression between Mayo Clinic vs TCGA tissues ranged from 0.75 to 0.82. These data support the generation of high-quality nucleic acids for genomic analyses from banked RCC. Importantly, the protocol does not interfere with routine clinical care. Collections over defined time points during disease treatment further enhance collaborative efforts to integrate genomic information with outcomes.</p></div