129 research outputs found
From the Jordan product to Riemannian geometries on classical and quantum states
The Jordan product on the self-adjoint part of a finite-dimensional
-algebra is shown to give rise to Riemannian metric
tensors on suitable manifolds of states on , 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 of linear operators on a finite-dimensional
Hilbert space , and that the Bures--Helstrom metric tensors is
recovered when we consider faithful states on .
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 , 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
-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
A coadjoint orbit-like construction for Jordan superalgebras
We investigate the canonical pseudo-Riemannian metrics associated with
Jordan-analogues of the coadjoint orbits for pseudo-Euclidean Jordan
superalgebras.Comment: 20 pages, 1 figur
Parametric models and information geometry on W*-algebras
We introduce the notion of smooth parametric model of normal positive linear
functionals on possibly infinite-dimensional W*-algebras generalizing the
notions of parametric models used in classical and quantum information
geometry. We then use the Jordan product naturally available in this context in
order to define a Riemannian metric tensor on parametric models satsfying
suitable regularity conditions. This Riemannian metric tensor reduces to the
Fisher-Rao metric tensor, or to the Fubini-Study metric tensor, or to the
Bures-Helstrom metric tensor when suitable choices for the W*-algebra and the
models are made.Comment: 24 pages. Comments are welcome
Information geometry and sufficient statistics
Information geometry provides a geometric approach to families of statistical
models. The key geometric structures are the Fisher quadratic form and the
Amari-Chentsov tensor. In statistics, the notion of sufficient statistic
expresses the criterion for passing from one model to another without loss of
information. This leads to the question how the geometric structures behave
under such sufficient statistics. While this is well studied in the finite
sample size case, in the infinite case, we encounter technical problems
concerning the appropriate topologies. Here, we introduce notions of
parametrized measure models and tensor fields on them that exhibit the right
behavior under statistical transformations. Within this framework, we can then
handle the topological issues and show that the Fisher metric and the
Amari-Chentsov tensor on statistical models in the class of symmetric 2-tensor
fields and 3-tensor fields can be uniquely (up to a constant) characterized by
their invariance under sufficient statistics, thereby achieving a full
generalization of the original result of Chentsov to infinite sample sizes.
More generally, we decompose Markov morphisms between statistical models in
terms of statistics. In particular, a monotonicity result for the Fisher
information naturally follows.Comment: 37 p, final version, minor corrections, improved presentatio
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 \u3c 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
- …