From the Jordan product to Riemannian geometries on classical and quantum states

The Jordan product on the self-adjoint part of a finite-dimensional $C^{*}$-algebra $\mathscr{A}$ is shown to give rise to Riemannian metric tensors on suitable manifolds of states on $\mathscr{A}$, and the covariant derivative, the geodesics, the Riemann tensor, and the sectional curvature of all these metric tensors are explicitly computed. In particular, it is proved that the Fisher--Rao metric tensor is recovered in the Abelian case, that the Fubini--Study metric tensor is recovered when we consider pure states on the algebra $\mathcal{B}(\mathcal{H})$ of linear operators on a finite-dimensional Hilbert space $\mathcal{H}$, and that the Bures--Helstrom metric tensors is recovered when we consider faithful states on $\mathcal{B}(\mathcal{H})$. Moreover, an alternative derivation of these Riemannian metric tensors in terms of the GNS construction associated to a state is presented. In the case of pure and faithful states on $\mathcal{B}(\mathcal{H})$, this alternative geometrical description clarifies the analogy between the Fubini--Study and the Bures--Helstrom metric tensor.Comment: 32 pages. Minor improvements. References added. Comments are welcome

Differential geometric aspects of parametric estimation theory for states on finite-dimensional C*-algebras

A geometrical formulation of estimation theory for finite-dimensional $C^{\star}$-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer-Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented.Comment: 33 pages. Minor improvements. References added. Comments are welcome

USP9X stabilizes XIAP to regulate mitotic cell death and chemoresistance in aggressive B-cell lymphoma

The mitotic spindle assembly checkpoint (SAC) maintains genome stability and marks an important target for antineoplastic therapies. However, it has remained unclear how cells execute cell fate decisions under conditions of SAC‐induced mitotic arrest. Here, we identify USP9X as the mitotic deubiquitinase of the X‐linked inhibitor of apoptosis protein (XIAP) and demonstrate that deubiquitylation and stabilization of XIAP by USP9X lead to increased resistance toward mitotic spindle poisons. We find that primary human aggressive B‐cell lymphoma samples exhibit high USP9X expression that correlate with XIAP overexpression. We show that high USP9X/XIAP expression is associated with shorter event‐free survival in patients treated with spindle poison‐containing chemotherapy. Accordingly, aggressive B‐cell lymphoma lines with USP9X and associated XIAP overexpression exhibit increased chemoresistance, reversed by specific inhibition of either USP9X or XIAP. Moreover, knockdown of USP9X or XIAP significantly delays lymphoma development and increases sensitivity to spindle poisons in a murine Eμ‐Myc lymphoma model. Together, we specify the USP9X–XIAP axis as a regulator of the mitotic cell fate decision and propose that USP9X and XIAP are potential prognostic biomarkers and therapeutic targets in aggressive B‐cell lymphoma

Genetic drivers of heterogeneity in type 2 diabetes pathophysiology

Type 2 diabetes (T2D) is a heterogeneous disease that develops through diverse pathophysiological processes1,2 and molecular mechanisms that are often specific to cell type3,4. Here, to characterize the genetic contribution to these processes across ancestry groups, we aggregate genome-wide association study data from 2,535,601 individuals (39.7% not of European ancestry), including 428,452 cases of T2D. We identify 1,289 independent association signals at genome-wide significance (P &lt; 5 × 10-8) that map to 611 loci, of which 145 loci are, to our knowledge, previously unreported. We define eight non-overlapping clusters of T2D signals that are characterized by distinct profiles of cardiometabolic trait associations. These clusters are differentially enriched for cell-type-specific regions of open chromatin, including pancreatic islets, adipocytes, endothelial cells and enteroendocrine cells. We build cluster-specific partitioned polygenic scores5 in a further 279,552 individuals of diverse ancestry, including 30,288 cases of T2D, and test their association with T2D-related vascular outcomes. Cluster-specific partitioned polygenic scores are associated with coronary artery disease, peripheral artery disease and end-stage diabetic nephropathy across ancestry groups, highlighting the importance of obesity-related processes in the development of vascular outcomes. Our findings show the value of integrating multi-ancestry genome-wide association study data with single-cell epigenomics to disentangle the aetiological heterogeneity that drives the development and progression of T2D. This might offer a route to optimize global access to genetically informed diabetes care.</p

Pain in the neurodegenerating brain: insights into pharmacotherapy for Alzheimer disease and Parkinson disease

This is the final version. Available on open access from Lippincott, Williams & Wilkins via the DOI in this recordNational Institute for Health Research (NIHR)European Union Horizon 202