Rectifiability of Optimal Transportation Plans

The purpose of this note is to show that the solution to the Kantorovich optimal transportation problem is supported on a Lipschitz manifold, provided the cost is $C^{2}$ with non-singular mixed second derivative. We use this result to provide a simple proof that solutions to Monge's optimal transportation problem satisfy a change of variables equation almost everywhere

S1PR2 variants associated with auditory function in humans and endocochlear potential decline in mouse

Progressive hearing loss is very common in the population but we still know little about the underlying pathology. A new spontaneous mouse mutation (stonedeaf, stdf ) leading to recessive, early-onset progressive hearing loss was detected and exome sequencing revealed a Thr289Arg substitution in Sphingosine-1-Phosphate Receptor-2 (S1pr2). Mutants aged 2 weeks had normal hearing sensitivity, but at 4 weeks most showed variable degrees of hearing impairment, which became severe or profound in all mutants by 14 weeks. Endocochlear potential (EP) was normal at 2 weeks old but was reduced by 4 and 8 weeks old in mutants, and the stria vascularis, which generates the EP, showed degenerative changes. Three independent mouse knockout alleles of S1pr2 have been described previously, but this is the first time that a reduced EP has been reported. Genomic markers close to the human S1PR2 gene were significantly associated with auditory thresholds in the 1958 British Birth Cohort (n = 6099), suggesting involvement of S1P signalling in human hearing loss. The finding of early onset loss of EP gives new mechanistic insight into the disease process and suggests that therapies for humans with hearing loss due to S1P signalling defects need to target strial function

A glimpse into the differential topology and geometry of optimal transport

This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well as the associated linear programming duality. It shows the answers to these questions concern the differential geometry and topology of the chosen transportation cost. It also establishes new connections --- some heuristic and others rigorous --- based on the properties of the cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page

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

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

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

Do quantitative and qualitative shear wave elastography have a role in evaluating musculoskeletal soft tissue masses?

Objectives: To determine if quantitative and qualitative shear wave elastography have roles in evaluating musculoskeletal masses. Methods: 105 consecutive patients, prospectively referred for biopsy within a specialist sarcoma centre, underwent B-mode, quantitative (m/s) and qualitative (colour map) shear wave elastography. Reference was histology from subsequent biopsy or excision where possible. Statistical modelling was performed to test elastography data and/or B-mode imaging in predicting malignancy. Results: Of 105 masses, 39 were malignant and 6 had no histology but benign characteristics at 12 months. Radiologist agreement for B-mode and elastography was moderate to excellent Kw 0.52-0.64; PABAKw 0.85-0.90). B-Mode imaging had 78.8% specificity, 76.9% sensitivity for malignancy. Quantitatively, adjusting for age, B-mode and lesion volume there was no statistically significant association between longitudinal velocity and malignancy (OR [95% CI] 0.40[0.10, 1.60], p=0.193), but some evidence that higher transverse velocity was associated with decreased odds of malignancy (0.28[0.06, 1.28], p=0.101). Qualitatively malignant masses tended to be towards the blue spectrum (lower velocities); 39.5% (17/43) of predominantly blue masses were malignant, compared to 14.3% (1/7) of red lesions. Conclusions: Quantitatively and qualitatively there is no statistically significant association between shear wave velocity and malignancy. There is no clear additional role to B-mode imaging currently. Key Points: • Correlation between shear wave velocity and soft tissue malignancy was statistically insignificant• B-mode ultrasound is 76.9 % sensitive and 78.8 % specific• Statistical models show elastography does not significantly add to lesion assessmen

Protein kinase C and cardiac dysfunction: a review

Heart failure (HF) is a physiological state in which cardiac output is insufficient to meet the needs of the body. It is a clinical syndrome characterized by impaired ability of the left ventricle to either fill or eject blood efficiently. HF is a disease of multiple aetiologies leading to progressive cardiac dysfunction and it is the leading cause of deaths in both developed and developing countries. HF is responsible for about 73,000 deaths in the UK each year. In the USA, HF affects 5.8 million people and 550,000 new cases are diagnosed annually. Cardiac remodelling (CD), which plays an important role in pathogenesis of HF, is viewed as stress response to an index event such as myocardial ischaemia or imposition of mechanical load leading to a series of structural and functional changes in the viable myocardium. Protein kinase C (PKC) isozymes are a family of serine/threonine kinases. PKC is a central enzyme in the regulation of growth, hypertrophy, and mediators of signal transduction pathways. In response to circulating hormones, activation of PKC triggers a multitude of intracellular events influencing multiple physiological processes in the heart, including heart rate, contraction, and relaxation. Recent research implicates PKC activation in the pathophysiology of a number of cardiovascular disease states. Few reports are available that examine PKC in normal and diseased human hearts. This review describes the structure, functions, and distribution of PKCs in the healthy and diseased heart with emphasis on the human heart and, also importantly, their regulation in heart failure