Optimal transport distances for directed, weighted graphs: a case study with cell-cell communication networks

Comparing graphs by means of optimal transport has recently gained significant attention, as the distances induced by optimal transport provide both a principled metric between graphs as well as an interpretable description of the associated changes between graphs in terms of a transport plan. As the lack of symmetry introduces challenges in the typically considered formulations, optimal transport distances for graphs have mostly been developed for undirected graphs. Here, we propose two distance measures to compare directed graphs based on variants of optimal transport: (i) an earth movers distance (Wasserstein) and (ii) a Gromov-Wasserstein (GW) distance. We evaluate these two distances and discuss their relative performance for both simulated graph data and real-world directed cell-cell communication graphs, inferred from single-cell RNA-seq data.Comment: 5 pages, 1 figur

The Shape of Galaxy Cluster Dark Matter Haloes: Systematics of Its Imprint on Cluster Gas, and Comparison to Observations

(Abridged) We study predictions for galaxy cluster observables that can test the statistics of dark matter halo shapes expected in a flat LCDM universe. We present a simple analytical model for the prediction of cluster-scale X-ray observations, approximating clusters as isothermal systems in hydrostatic equilibrium, and dark matter haloes as ellipsoids with uniform axial ratios. We test the model against high-resolution, hydrodynamic cluster simulations to gauge its reliability. We find that this simple prescription does a good job of predicting the distribution of cluster X-ray ellipticities compared to the simulations as long as one focuses on cluster regions that are less sensitive to recent mergers. Based on this simple model, the distribution of cluster-size halo shapes expected in the concordance LCDM cosmology implies an X-ray ellipticity distribution with a mean of 0.32 +- 0.01 and a scatter of 0.14 +- 0.01 for the mass range (1-4)x10^{14} Msun/h. We find it important to include the mass dependence of halo shape to make comparisons to observational samples that contain many, very massive clusters. We analyse the systematics of four observational samples of cluster ellipticities and find that our results are statistically compatible with observations. In particular, we find remarkably good agreement between two recent ROSAT samples and LCDM predictions that DO NOT include gas cooling. We also test how well our analytical model can predict Sunyaev-Zel'dovich decrement maps and find that it is less successful although still useful; the model does not perform as well as a function of flux level in this case because of the changing triaxiality of dark matter haloes as a function of radial distance. Both this effect and the changing alignment of isodensity shells of dark matter haloes leave an imprint on cluster gas...Comment: 16 pages, 9 figures; corrected typo (no result affected) submitted to MNRA

Constraining the Scatter in the Mass-Richness Relation of maxBCG Clusters With Weak Lensing and X-ray Data

We measure the logarithmic scatter in mass at fixed richness for clusters in the maxBCG cluster catalog, an optically selected cluster sample drawn from SDSS imaging data. Our measurement is achieved by demanding consistency between available weak lensing and X-ray measurements of the maxBCG clusters, and the X-ray luminosity--mass relation inferred from the 400d X-ray cluster survey, a flux limited X-ray cluster survey. We find \sigma_{\ln M|N_{200}}=0.45^{+0.20}_{-0.18} (95% CL) at N_{200} ~ 40, where N_{200} is the number of red sequence galaxies in a cluster. As a byproduct of our analysis, we also obtain a constraint on the correlation coefficient between \ln Lx and \ln M at fixed richness, which is best expressed as a lower limit, r_{L,M|N} >= 0.85 (95% CL). This is the first observational constraint placed on a correlation coefficient involving two different cluster mass tracers. We use our results to produce a state of the art estimate of the halo mass function at z=0.23 -- the median redshift of the maxBCG cluster sample -- and find that it is consistent with the WMAP5 cosmology. Both the mass function data and its covariance matrix are presented.Comment: 14 pages, 6 figures, submitted to Ap

Anisotropy of magnetothermal conductivity in Sr2RuO4

The dependence of in-plane and interplane thermal conductivities of Sr2RuO4 on temperature, as well as magnetic field strength and orientation, is reported. We found no notable anisotropy in the thermal conductivity for the magnetic field rotation parallel to the conducting plane in the whole range of experimental temperatures and fields, except in the vicinity of the upper critical field Hc2, where the anisotropy of the Hc2 itself plays a dominant role. This finding imposes strong constraints on the possible models of superconductivity in Sr2RuO4 and supports the existence of a superconducting gap with a line of nodes running orthogonal to the Fermi surface cylinder.Comment: published in Phys. Rev. Lett. 4pages, 4 eps figures, LaTe

Detection of PatIent-Level distances from single cell genomics and pathomics data with Optimal Transport (PILOT)

Although clinical applications represent the next challenge in single-cell genomics and digital pathology, we still lack computational methods to analyze single-cell or pathomics data to find sample-level trajectories or clusters associated with diseases. This remains challenging as single-cell/pathomics data are multi-scale, i.e., a sample is represented by clusters of cells/structures, and samples cannot be easily compared with each other. Here we propose PatIent Level analysis with Optimal Transport (PILOT). PILOT uses optimal transport to compute the Wasserstein distance between two individual single-cell samples. This allows us to perform unsupervised analysis at the sample level and uncover trajectories or cellular clusters associated with disease progression. We evaluate PILOT and competing approaches in single-cell genomics or pathomics studies involving various human diseases with up to 600 samples/patients and millions of cells or tissue structures. Our results demonstrate that PILOT detects disease-associated samples from large and complex single-cell or pathomics data. Moreover, PILOT provides a statistical approach to find changes in cell populations, gene expression, and tissue structures related to the trajectories or clusters supporting interpretation of predictions.</p

Basement membrane and vascular remodelling in smokers and chronic obstructive pulmonary disease: a cross-sectional study

<p>Abstract</p> <p>Background</p> <p>Little is known about airway remodelling in bronchial biopsies (BB) in smokers and chronic obstructive pulmonary disease (COPD). We conducted an initial pilot study comparing BB from COPD patients with nonsmoking controls. This pilot study suggested the presence of reticular basement membrane (Rbm) fragmentation and altered vessel distribution in COPD.</p> <p>Methods</p> <p>To determine whether Rbm fragmentation and altered vessel distribution in BB were specific for COPD we designed a cross-sectional study and stained BB from 19 current smokers and 14 ex-smokers with mild to moderate COPD and compared these to 15 current smokers with normal lung function and 17 healthy and nonsmoking subjects.</p> <p>Results</p> <p>Thickness of the Rbm was not significantly different between groups; although in COPD this parameter was quite variable. The Rbm showed fragmentation and splitting in both current smoking groups and ex-smoker COPD compared with healthy nonsmokers (p < 0.02); smoking and COPD seemed to have additive effects. Rbm fragmentation correlated with smoking history in COPD but not with age. There were more vessels in the Rbm and fewer vessels in the lamina propria in current smokers compared to healthy nonsmokers (p < 0.05). The number of vessels staining for vascular endothelial growth factor (VEGF) in the Rbm was higher in both current smoker groups and ex-smoker COPD compared to healthy nonsmokers (p < 0.004). In current smoker COPD VEGF vessel staining correlated with FEV1% predicted (r = 0.61, p < 0.02).</p> <p>Conclusions</p> <p>Airway remodelling in smokers and mild to moderate COPD is associated with fragmentation of the Rbm and altered distribution of vessels in the airway wall. Rbm fragmentation was also present to as great an extent in ex-smokers with COPD. These characteristics may have potential physiological consequences.</p

PIP5KIβ Selectively Modulates Apical Endocytosis in Polarized Renal Epithelial Cells

Localized synthesis of phosphatidylinositol 4,5-bisphosphate [PtdIns(4,5)P2] at clathrin coated pits (CCPs) is crucial for the recruitment of adaptors and other components of the internalization machinery, as well as for regulating actin dynamics during endocytosis. PtdIns(4,5)P2 is synthesized from phosphatidylinositol 4-phosphate by any of three phosphatidylinositol 5-kinase type I (PIP5KI) isoforms (α, β or γ). PIP5KIβ localizes almost exclusively to the apical surface in polarized mouse cortical collecting duct cells, whereas the other isoforms have a less polarized membrane distribution. We therefore investigated the role of PIP5KI isoforms in endocytosis at the apical and basolateral domains. Endocytosis at the apical surface is known to occur more slowly than at the basolateral surface. Apical endocytosis was selectively stimulated by overexpression of PIP5KIβ whereas the other isoforms had no effect on either apical or basolateral internalization. We found no difference in the affinity for PtdIns(4,5)P2-containing liposomes of the PtdIns(4,5)P2 binding domains of epsin and Dab2, consistent with a generic effect of elevated PtdIns(4,5)P2 on apical endocytosis. Additionally, using apical total internal reflection fluorescence imaging and electron microscopy we found that cells overexpressing PIP5KIβ have fewer apical CCPs but more internalized coated structures than control cells, consistent with enhanced maturation of apical CCPs. Together, our results suggest that synthesis of PtdIns(4,5)P2 mediated by PIP5KIβ is rate limiting for apical but not basolateral endocytosis in polarized kidney cells. PtdIns(4,5)P2 may be required to overcome specific structural constraints that limit the efficiency of apical endocytosis. © 2013 Szalinski et al

Bose-Einstein Correlations of Three Charged Pions in Hadronic Z^0 Decays

Bose-Einstein Correlations (BEC) of three identical charged pions were studied in 4 x 10^6 hadronic Z^0 decays recorded with the OPAL detector at LEP. The genuine three-pion correlations, corrected for the Coulomb effect, were separated from the known two-pion correlations by a new subtraction procedure. A significant genuine three-pion BEC enhancement near threshold was observed having an emitter source radius of r_3 = 0.580 +/- 0.004 (stat.) +/- 0.029 (syst.) fm and a strength of \lambda_3 = 0.504 +/- 0.010 (stat.) +/- 0.041 (syst.). The Coulomb correction was found to increase the \lambda_3 value by \~9% and to reduce r_3 by ~6%. The measured \lambda_3 corresponds to a value of 0.707 +/- 0.014 (stat.) +/- 0.078 (syst.) when one takes into account the three-pion sample purity. A relation between the two-pion and the three-pion source parameters is discussed.Comment: 19 pages, LaTeX, 5 eps figures included, accepted by Eur. Phys. J.

Search for the Higgs boson in events with missing transverse energy and b quark jets produced in proton-antiproton collisions at s**(1/2)=1.96 TeV

We search for the standard model Higgs boson produced in association with an electroweak vector boson in events with no identified charged leptons, large imbalance in transverse momentum, and two jets where at least one contains a secondary vertex consistent with the decay of b hadrons. We use ~1 fb-1 integrated luminosity of proton-antiproton collisions at s**(1/2)=1.96 TeV recorded by the CDF II experiment at the Tevatron. We find 268 (16) single (double) b-tagged candidate events, where 248 +/- 43 (14.4 +/- 2.7) are expected from standard model background processes. We place 95% confidence level upper limits on the Higgs boson production cross section for several Higgs boson masses ranging from 110 GeV/c2 to 140 GeV/c2. For a mass of 115 GeV/c2 the observed (expected) limit is 20.4 (14.2) times the standard model prediction.Comment: 8 pages, 2 figures, submitted to Phys. Rev. Let