Finding collective variables to describe some important coarse-grained information on
physical systems, in particular metastable states, remains a key issue in molecular …

We propose a framework of principal manifolds to model high-dimensional data. This
framework is based on Sobolev spaces and designed to model data of any intrinsic …

We consider the problem of finding the``best''approximation of an $ n $-dimensional
probability measure $\rho $ using a measure $\nu $ whose support is parametrized by …

In this paper we discuss nonlinear dimensionality reduction within the framework of principal
curves. We formulate dimensionality reduction as problems of estimating principal …

In this study, an intelligent reflective surface (IRS)-assisted communication system has been
investigated from the perspective of secrecy capacity analysis. Analyses have been …

Résumé En catalyse, les réactions mettent généralement en jeu plusieurs états
intermédiaires méta-stables, les transitions entre chacun d'entre eux étant rares. Ainsi, la …

We propose a model for finding one-dimensional structure in a given measure. Our
approach is based on minimizing an objective functional which combines the average …

Heterogeneity is arguably one of the most important hallmarks of cancer which contributes to
its drug resistance property. Cancer heterogeneity is the consequence of an evolutionary …

In this thesis we investigate the problem of approximating point cloud data, or more
generally, measures, by one-dimensional objects. Our approach is variational, as we will …

Background. Modern single-cell technologies offer a detailed view of the conditions and
states of thousands of cells at the individual level. Often the full spectrum of developmental …