What does a vector field know about volume?

What Does a Lie Algebra Know about a Lie Group?

We define Lie groups and Lie algebras and show how invariant vector fields on a Lie group form a Lie algebra. We prove that this correspondence respects natural maps and discuss conditions under which it is a bijection. Finally, we introduce the exponential map and use it to write the Lie group operation as a function on its Lie algebra.

What every pediatrician should know about liver transplantation

Liver transplantation is the treatment of choice for children with end-stage liver disease.  Improvement in outcomes (allograft and patient survival) has led to widespread use of pediatric LT worldwide. This success is due to improvement in patient selection, transplant surgery, anesthesia/postoperative care and immunosuppression management. This review will focus on different aspects of LT whi...

What Does the Right Hemisphere Know about Phoneme Categories?

Innate auditory sensitivities and familiarity with the sounds of language give rise to clear influences of phonemic categories on adult perception of speech. With few exceptions, current models endorse highly left-hemisphere-lateralized mechanisms responsible for the influence of phonemic category on speech perception, based primarily on results from functional imaging and brain-lesion studies....

What Does the Retina Know about Natural Scenes?

By examining the experimental data on the statistical properties of natural scenes together with (retinal) contrast sensitivity data, we arrive at a first principles, theoretical hypothesis for the purpose of retinal processing and its relationship to an animal's environment. We argue that the retinal' goal is to transform the visual input as much as possible into a statistically independent ba...

What does the brain know about blood pressure?