156 citations · 366 across the 11 of their papers we have counts for
11 papers
Information Geometry, Jordan Algebras, and a Coadjoint Orbit-Like Construction
Florio M. Ciaglia, Jürgen Jost, Lorenz Schwachhöfer
Jordan algebras arise naturally in (quantum) information geometry, and we want to understand their role and their structure within that framework. Inspired by Kirillov's discussion…
Congruent families and invariant tensors
Lorenz Schwachhöfer, Nihat Ay, Jürgen Jost +1
Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only -tensor field of a statistical model which is invariant under congruent Markov morp…
The Cramér-Rao inequality on singular statistical models I
Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
We introduce the notion of the essential tangent bundle of a parametrized measure model and the notion of reduced Fisher metric on a (possibly singular) 2-integrable measure model.…
Universal moduli spaces of Riemann surfaces
Lizhen Ji, Juergen Jost
We construct a moduli space for Riemann surfaces that is universal in the sense that it represents compact Riemann surfaces of any finite genus. This moduli space is stratifed acco…
On the regular representation of measures
Jürgen Jost, Rostislav Matveev, Jacobus W. Portegies +1
We give sufficient conditions for a parametrised family of probability measures on a Riemannian manifold with boundary to be represented by random maps of class . The conditio…
Forman curvature for complex networks
R. P. Sreejith, Karthikeyan Mohanraj, Jürgen Jost +2
We adapt Forman's discretization of Ricci curvature to the case of undirected networks, both weighted and unweighted, and investigate the measure in a variety of model and real-wor…
Object oriented models vs. data analysis -- is this the right alternative?
Jürgen Jost
We review the role of mathematics from a historical and a conceptual perspective in the light of modern data science.
Parametrized measure models
Nihat Ay, Jürgen Jost, Hông Vân Lê +1
We develope a new and general notion of parametric measure models and statistical models on an arbitrary sample space which does not assume that all measures of the model have…
A spherical Bernstein theorem for minimal submanifolds of higher codimension
J. Jost, Y. L. Xin, Ling Yang
Combining the tools of geometric analysis with properties of Jordan angles and angle space distributions, we derive a spherical and a Euclidean Bernstein theorem for minimal subman…
A notion of nonpositive curvature for general metric spaces
Miroslav Bačák, Bobo Hua, Jürgen Jost +2
We introduce a new definition of nonpositive curvature in metric spaces and study its relationship to the existing notions of nonpositive curvature in comparison geometry. The main…
Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature
Bobo Hua, Jürgen Jost, Shiping Liu
In the present paper, we apply Alexandrov geometry methods to study geometric analysis aspects of infinite semiplanar graphs with nonnegative combinatorial curvature in the sense o…