Deconvolution Tactics and Normalization in Renal Spatial Transcriptomics

The kidney is composed of heterogeneous groups of epithelial, endothelial, immune, and stromal cells, all in close anatomic proximity. Spatial transcriptomic technologies allow the interrogation of in situ expression signatures in health and disease, overlaid upon a histologic image. However, some spatial gene expression platforms have not yet reached single-cell resolution. As such, deconvolution of spatial transcriptomic spots is important to understand the proportion of cell signature arising from these varied cell types in each spot. This article reviews the various deconvolution strategies discussed in the 2021 Indiana O’Brien Center for Microscopy workshop. The unique features of Seurat transfer score methodology, SPOTlight, Robust Cell Type Decomposition, and BayesSpace are reviewed. The application of normalization and batch effect correction across spatial transcriptomic samples is also discussed.

Changes in Inequality in Utilization of Maternal Health Care: Evidence from Skilled Birth Attendance in Mauritania for the Period 2007-2015

Background: The presence of a skilled health professional at delivery is critical to reduce infant and maternal mortality. Health development plans and strategies, especially in developing countries, consider equity in access to maternal health care services as a priority. This study aimed to measure and analyze the inequality in the use of skilled births attendance services in Mauritania. The study identifies the inequality determinants and to explore its changes over the period 2007–2015. Methods: The concentration curve, concentration index, decomposition of the concentration index and Oaxaca-type decomposition technique were performed to measure socio-economics related inequalities in skilled birth attendance services utilization and identify contribution of different determinants to such inequality as well as the changes in inequality overtime using data from Mauritania Multiple Indicator Cluster Surveys (MICS) 2007, 2011 and 2015. Results: The concentration index for skilled birth attendance services utilization dropped from 0.6324 [P < 0.001] in 2007 to 0.5852 [P < 0.001] in 2015. Prenatal care, household wealth Status and urban-rural location made the biggest contributions to socio-economic related inequalities. Decomposition of the concentration index and Oaxaca-type decomposition revealed changes prenatal care, rural-urban location made positive contributions to decline in inequality. However, alternation in household wealth score, woman’s age, her education level and the number of living children pushed the equality toward deterioration. Conclusion: Clearly, the pro-rich inequality in skilled birth attendance is high in Mauritania despite a slight decrease during the study period. Policy actions on eliminating urban-rural and wealth index disparity should target increase access to skilled birth attendance. Multisectoral Policy actions is needed to improve social determinants of health and to remove health system bottlenecks including socio-economic empowerment of women and girls, enhancing availability and affordability of Reproductive and Maternal Health commodities, improving availability of obstetrical providers in rural area, promoting a better distribution and quality of health infrastructure particularly health posts and health centers, and replacing user fees by an equitable, efficient and sustainable financing scheme under an universal health coverage vision.

Impact of climate change on wintertime European atmospheric blocking

We study the impact of climate change on wintertime atmospheric blocking over Europe focusing on the frequency, duration, and extension of blocking events. These events are identified via the weather type decomposition (WTD) methodology applied on the output of climate models of the Coupled Model Intercomparison Project phase 6 (CMIP6). Historical simulations as well as two future scenarios, SSP2-4.5 and SSP5-8.5, are considered. The models are evaluated against the reanalysis and only a subset of climate models, which better represent the blocking weather regime in the recent-past climate, is considered for the analysis. We find that frequency and duration of blocking events remain relatively stationary over the 21st century. In order to quantify the extension of blocking events, we define a new methodology which relies on the WTD to identify blocking events. We show that the results are in agreement with previous studies that define blocking events with blocking indexes. We find that blocking extension will increase, especially in the worst-case scenario, due to a pressure increase driven by a thermodynamical warming during blocking events rather than atmospheric circulation changes.

Wold decomposition on odometer semigroups

We establish a Wold-type decomposition for isometric and isometric Nica-covariant representations of the odometer semigroup. These generalize the Wold-type decomposition for commuting pairs of isometries due to Popovici and for pairs of doubly commuting isometries due to Słociński.

The Wold-Type Decomposition for m-Isometries

The aim of this paper is to study the Wold-type decomposition in the class of m-isometries. One of our main results establishes an equivalent condition for an analytic m-isometry to admit the Wold-type decomposition for $$m\ge 2$$ m ≥ 2 . In particular, we introduce the k-kernel condition which we use to characterize analytic m-isometric operators which are unitarily equivalent to unilateral operator valued weighted shifts for $$m\ge 2$$ m ≥ 2 . As a result, we also show that m-isometric composition operators on directed graphs with one circuit containing only one element are not unitarily equivalent to unilateral weighted shifts. We also provide a characterization of m-isometric unilateral operator valued weighted shifts with positive and commuting weights.

The role of the algebraic structure in Wold-type decomposition

In recent works [G. A. Bagheri-Bardi, A. Elyaspour and G. H. Esslamzadeh, Wold-type decompositions in Baer ∗ \ast -rings, Linear Algebra Appl. 539 2018, 117–133] and [G. A. Bagheri-Bardi, A. Elyaspour and G. H. Esslamzadeh, The role of algebraic structure in the invariant subspace theory, Linear Algebra Appl. 583 2019, 102–118], the algebraic analogues of the three major decomposition theorems of Wold, Nagy–Foiaş–Langer and Halmos–Wallen were established in the larger category of Baer * {*} -rings. The results have their versions for commuting pairs in von Neumann algebras. In the corresponding proofs, both norm and weak operator topologies are heavily involved. In this work, ignoring topological structures, we give an algebraic approach to obtain them in Baer * {*} -rings.

Moduli of wild Higgs bundles on with -actions

We study a set $\mathcal{M}_{K,N}$ parameterising filtered SL(K)-Higgs bundles over $\mathbb{C}P^1$ with an irregular singularity at $z = \infty$ , such that the eigenvalues of the Higgs field grow like $\vert \lambda \vert \sim \vert z^{N/K} \mathrm{d}z \vert$ , where K and N are coprime. $\mathcal{M}_{K,N}$ carries a $\mathbb{C}^\times$ -action analogous to the famous $\mathbb{C}^\times$ -action introduced by Hitchin on the moduli spaces of Higgs bundles over compact curves. The construction of this $\mathbb{C}^\times$ -action on $\mathcal{M}_{K,N}$ involves the rotation automorphism of the base $\mathbb{C}P^1$ . We classify the fixed points of this $\mathbb{C}^\times$ -action, and exhibit a curious 1-1 correspondence between these fixed points and certain representations of the vertex algebra $\mathcal{W}_K$ ; in particular we have the relation $\mu = {k-1-c_{\mathrm{eff}}}/{12}$ , where $\mu$ is a regulated version of the L 2 norm of the Higgs field, and $c_{\mathrm{eff}}$ is the effective Virasoro central charge of the corresponding W-algebra representation. We also discuss a Białynicki–Birula-type decomposition of $\mathcal{M}_{K,N}$ , where the strata are labeled by isomorphism classes of the underlying filtered vector bundles.