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This paper considers the problem of measure estimation under the barycentric coding model (BCM), in which an unknown measure is assumed to belong to the set of Wasserstein-2 barycenters of a finite set of known measures. Estimating a measure under this model is equivalent to estimating the unknown barycentric coordinates. We provide novel geometrical, statistical, and computational insights for measure estimation under the BCM, consisting of three main results. Our first main result leverages the Riemannian geometry of Wasserstein-2 space to provide a procedure for recovering the barycentric coordinates as the solution to a quadratic optimization problem assuming access to the true reference measures. The essential geometric insight is that the parameters of this quadratic problem are determined by inner products between the optimal displacement maps from the given measure to the reference measures defining the BCM. Our second main result then establishes an algorithm for solving for the coordinates in the BCM when all the measures are observed empirically via i.i.d. samples. We prove precise rates of convergence for this algorithm -- determined by the smoothness of the underlying measures and their dimensionality -- thereby guaranteeing its statistical consistency. Finally, we demonstrate the utility of the BCM and associated estimation procedures in three application areas: (i) covariance estimation for Gaussian measures; (ii) image processing; and (iii) natural language processing., Comment: ICML 2022

The framework of optimal transport has been leveraged to extend the notion of rank to the multivariate setting while preserving desirable properties of the resulting goodness-of-fit (GoF) statistics. In particular, the rank energy (RE) and rank maximum mean discrepancy (RMMD) are distribution-free under the null, exhibit high power in statistical testing, and are robust to outliers. In this paper, we point to and alleviate some of the practical shortcomings of these proposed GoF statistics, namely their high computational cost, high statistical sample complexity, and lack of differentiability with respect to the data. We show that all these practically important issues are addressed by considering entropy-regularized optimal transport maps in place of the rank map, which we refer to as the soft rank. We consequently propose two new statistics, the soft rank energy (sRE) and soft rank maximum mean discrepancy (sRMMD), which exhibit several desirable properties. Given $n$ sample data points, we provide non-asymptotic convergence rates for the sample estimate of the entropic transport map to its population version that are essentially of the order $n^{-1/2}$ when the starting measure is subgaussian and the target measure has compact support. This result is novel compared to existing results which achieve a rate of $n^{-1}$ but crucially rely on both measures having compact support. We leverage this result to demonstrate fast convergence of sample sRE and sRMMD to their population version making them useful for high-dimensional GoF testing. Our statistics are differentiable and amenable to popular machine learning frameworks that rely on gradient methods. We leverage these properties towards showcasing the utility of the proposed statistics for generative modeling on two important problems: image generation and generating valid knockoffs for controlled feature selection., Comment: 46 pages, 10 figures. Replacement note: Substantial revision over V2: Title change, first authors contribution change, new improved theoretical results relaxing compactness assumptions

Bacteria respond to environmental changes by inducing transcription of some genes and repressing others. Sialic acids, which coat human cell surfaces, are a nutrient source for pathogenic and commensal bacteria. TheEscherichia coliGntR-type transcriptional repressor, NanR, regulates sialic acid metabolism, but the mechanism is unclear. Here, we demonstrate that three NanR dimers bind a (GGTATA)3-repeat operator cooperatively and with high affinity. Truncation of an N-terminal extension abolishes cooperative binding. The effector,N-acetylneuraminate, binds NanR and attenuates DNA binding. Crystal structure data show thatN-acetylneuraminate binding to NanR causes a domain rearrangement that locks the protein in a conformation that prevents DNA binding. Single-particle cryo-electron microscopy structures of NanR bound to DNA reveal the DNA binding domain is reorganized to engage DNA, while the three dimers assemble in close proximity across the (GGTATA)3-repeat operator allowing protein-protein interactions to formviathe N-terminal extensions. Our data provides a molecular basis for the regulation of bacterial sialic acid metabolism.

This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation. The proposed method is suitable for data generated from mixtures of distributions with densities that are both multimodal and have nonlinear shapes. A crucial aspect of this algorithm is the use of time of a data-adapted diffusion process as a scale parameter that is different from the local spatial scale parameter used in many clustering algorithms. We prove estimates for the behavior of diffusion distances with respect to this time parameter under a flexible nonparametric data model, identifying a range of times in which the mesoscopic equilibria of the underlying process are revealed, corresponding to a gap between within-cluster and between-cluster diffusion distances. These structures can be missed by the top eigenvectors of the graph Laplacian, commonly used in spectral clustering. This analysis is leveraged to prove sufficient conditions guaranteeing the accuracy of the proposed \emph{learning by unsupervised nonlinear diffusion (LUND)} procedure. We implement LUND and confirm its theoretical properties on illustrative datasets, demonstrating the theoretical and empirical advantages over both spectral clustering and density-based clustering techniques., Comment: 40 Pages, 17 Figures

We generalize classical results in spectral graph theory and linear algebra more broadly, from the case where the underlying matrix is Hermitian to the case where it is non-Hermitian. New admissibility conditions are introduced to replace the Hermiticity condition. We prove new variational estimates of the Rayleigh quotient for non-Hermitian matrices. As an application, a new Delsarte-Hoffman-type bound on the size of the largest independent set in a directed graph is developed. Our techniques consist in quantifying the impact of breaking the Hermitian symmetry of a matrix and are broadly applicable.

Supplementary Material: Worked example and information about UKCP09

The future climate change results assessed in this chapter are based on a hierarchy of models, ranging from Atmosphere-Ocean General Circulation Models (AOGCMs) and Earth System Models of Intermediate Complexity (EMICs) to Simple Climate Models (SCMs). These models are forced with concentrations of greenhouse gases and other constituents derived from various emissions scenarios ranging from non- mitigation scenarios to idealised long-term scenarios. In general, we assess non-mitigated projections of future climate change at scales from global to hundreds of kilometres. Further assessments of regional and local climate changes are provided in Chapter 11. Due to an unprecedented, joint effort by many modelling groups worldwide, climate change projections are now based on multi-model means, differences between models can be assessed quantitatively and in some instances, estimates of the probability of change of important climate system parameters complement expert judgement. New results corroborate those given in the Third Assessment Report (TAR). Continued greenhouse gas emissions at or above current rates will cause further warming and induce many changes in the global climate system during the 21st century that would very likely be larger than those observed during the 20th century.

Plasmodium vivax shows a strict host tropism for reticulocytes. We identified transferrin receptor 1 (TfR1) as the receptor for P. vivax reticulocyte-binding protein 2b (PvRBP2b). We determined the structure of the N-terminal domain of PvRBP2b involved in red blood cell binding, elucidating the molecular basis for TfR1 recognition. We validated TfR1 as the biological target of PvRBP2b engagement by means of TfR1 expression knockdown analysis. TfR1 mutant cells deficient in PvRBP2b binding were refractory to invasion of P. vivax but not to invasion of P. falciparum Using Brazilian and Thai clinical isolates, we show that PvRBP2b monoclonal antibodies that inhibit reticulocyte binding also block P. vivax entry into reticulocytes. These data show that TfR1-PvRBP2b invasion pathway is critical for the recognition of reticulocytes during P. vivax invasion.

Mitotic catastrophe (MC) is an important oncosuppressive mechanism that serves to eliminate cells that become polyploid or aneuploidy due to aberrant mitosis. Previous studies have demonstrated that the activation and catalytic function of caspase-2 are key steps in MC to trigger apoptosis and/or cell cycle arrest of mitotically defective cells. However, the molecular mechanisms that regulate caspase-2 activation and its function are unclear. Here we identify six new phosphorylation sites in caspase-2 and show that a key mitotic kinase, Aurora B kinase (AURKB), phosphorylates caspase-2 at the highly conserved residue S384. We demonstrate that phosphorylation at S384 blocks caspase-2 catalytic activity and apoptosis function in response to mitotic insults, without affecting caspase-2 dimerisation. Moreover, molecular modelling suggests that phosphorylation at S384 may affect substrate binding by caspase-2. We propose that caspase-2 S384 phosphorylation by AURKB is a key mechanism that controls caspase-2 activation during mitosis.

Necroptosis is a physiological cell suicide mechanism initiated by receptor-interacting protein kinase-3 (RIPK3) phosphorylation of mixed-lineage kinase domain-like protein (MLKL), which results in disruption of the plasma membrane. Necroptotic cell lysis, and resultant release of proinflammatory mediators, is thought to cause inflammation in necroptotic disease models. However, we previously showed that MLKL signaling can also promote inflammation by activating the nucleotide-binding oligomerization domain (NOD)- like receptor protein 3 (NLRP3) inflammasome to recruit the adaptor protein apoptosis-Associated speck-like protein containing a caspase activation and recruitment domain (ASC) and trigger caspase-1 processing of the proinflammatory cytokine IL-1β. diseases. Here, we provide evidence that MLKL-induced activation of NLRP3 requires (i) the death effector four-helical bundle of MLKL, (ii) oligomerization and association of MLKL with cellular membranes, and (iii) a reduction in intracellular potassium concentration. Although genetic or pharmacological targeting of NLRP3 or caspase-1 prevented MLKLinduced IL-1β secretion, they did not prevent necroptotic cell death. Gasdermin D (GSDMD), the pore-forming caspase-1 substrate required for efficient NLRP3-Triggered pyroptosis and IL-1β release, was not essential for MLKL-dependent death or IL-1β secretion. Imaging of MLKL-dependent ASC speck formation demonstrated that necroptotic stimuli activate NLRP3 cell-intrinsically, indicating that MLKL-induced NLRP3 inflammasome formation and IL-1β cleavage occur before cell lysis. Furthermore, we show that necroptotic activation of NLRP3, but not necroptotic cell death alone, is necessary for the activation of NF-κB in healthy bystander cells. Collectively, these results demonstrate the potential importance of NLRP3 inflammasome activity as a driving force for inflammation in MLKLdependent Refereed/Peer-reviewed

The devil facial tumor disease (DFTD) is caused by clonal transmissible cancers that have led to a catastrophic decline in the wild Tasmanian devil (Sarcophilus harrisii) population. The first transmissible tumor, now termed devil facial tumor 1 (DFT1), was first discovered in 1996 and has been continually transmitted to new hosts for at least 20 years. In 2015, a second transmissible cancer [devil facial tumor 2 (DFT2)] was discovered in wild devils, and the DFT2 is genetically distinct and independent from the DFT1. Despite the estimated 136,559 base pair substitutions and 14,647 insertions/deletions in the DFT1 genome as compared to two normal devil reference genomes, the allograft tumors are not rejected by the host immune system. Additionally, genome sequencing of two sub-strains of DFT1 detected greater than 15,000 single-base substitutions that were found in only one of the DFT1 sub-strains, demonstrating the transmissible tumors are evolving and that generation of neoantigens is likely ongoing. Recent evidence in human clinical trials suggests that blocking PD-1:PD-L1 interactions promotes antitumor immune responses and is most effective in cancers with a high number of mutations. We hypothesized that DFTD cells could exploit the PD-1:PD-L1 inhibitory pathway to evade antitumor immune responses. We developed recombinant proteins and monoclonal antibodies (mAbs) to provide the first demonstration that PD-1 binds to both PD-L1 and PD-L2 in a non-placental mammal and show that PD-L1 is upregulated in DFTD cells in response to IFN-gamma. Immunohistochemistry showed that PD-L1 is rarely expressed in primary tumor masses, but low numbers of PD-L1+ non-tumor cells were detected in the microenvironment of several metastatic tumors. Importantly, in vitro testing suggests that PD-1 binding to PD-L1 and PD-L2 can be blocked by mAbs, which could be critical to understanding how the DFT allografts evade the immune system. Refereed/Peer-reviewed