Effective dynamics using conditional expectations

The question of coarse-graining is ubiquitous in molecular dynamics. In this article, we are interested in deriving effective properties for the dynamics of a coarse-grained variable $\xi(x)$, where $x$ describes the configuration of the system in a high-dimensional space $\R^n$, and $\xi$ is a smooth function with value in $\R$ (typically a reaction coordinate). It is well known that, given a Boltzmann-Gibbs distribution on $x \in \R^n$, the equilibrium properties on $\xi(x)$ are completely determined by the free energy. On the other hand, the question of the effective dynamics on $\xi(x)$ is much more difficult to address. Starting from an overdamped Langevin equation on $x \in \R^n$, we propose an effective dynamics for $\xi(x) \in \R$ using conditional expectations. Using entropy methods, we give sufficient conditions for the time marginals of the effective dynamics to be close to the original ones. We check numerically on some toy examples that these sufficient conditions yield an effective dynamics which accurately reproduces the residence times in the potential energy wells. We also discuss the accuracy of the effective dynamics in a pathwise sense, and the relevance of the free energy to build a coarse-grained dynamics

Skull base plasmacytoma in a patient with light chain myeloma

Skull base involvement of plasmacytoma is reported in a patient with light chain myeloma. A 39-year-old man was admitted after experiencing paresthesia on the left side of the face and left arm, intermittent diplopia, and hoarseness for 2 years. Cranial magnetic resonance imaging revealed a large midline mass extending from the middle and posterior skull base into the upper two cervical vertebrae. An extramedullary plasmacytoma associated with light chain multiple myeloma was diagnosed after biopsy of the mass and laboratory investigations. The imaging findings and clinical features associated with this rare site of extramedullary plasmacytoma involvement are reported

Phase II study of loading-dose ibandronate treatment in patients in breast cancer and bone metastases suffering from moderate to severe pain

WOS: 00020885200158

Phase II study of loading-dose ibandronate treatment in patients with breast cancer and bone metastases suffering from moderate to severe pain.

WOS: 00020885200158