Actions can be planned in either an intrinsic (body-based) reference frame or an extrinsic (world-based) frame, and understanding how the internal representations associated with these frames contribute to the learning of motor actions is a key issue in motor control. We studied the internal representation of this learning in human subjects by analyzing generalization patterns across an array o...

Over forty years ago, Paneitz, and independently Fradkin Tseytlin, discovered a fourth-order conformally-invariant differential operator, intrinsically defined on conformal manifold, mapping scalars to scalars. This operator is special case of the so-termed extrinsic Paneitz in when manifold itself conformally embedded hypersurface. In particular, this encodes obstruction smoothly solving five-...

Teachers can often readily identify students who demonstrate high or low motivation in a certain task. Motivated students engage in the task with intensity and feeling, whereas unmotivated students procrastinate and indicate in other ways that they would rather do something else. These differences exemplify the quantitative dimension of motivation, ranging from high to low. Teachers can often a...

A central tenet of economics is that individuals respond to incentives. For psychologists and sociologists, in contrast, rewards and punishments are often counterproductive, because they undermine “intrinsic motivation”. We reconcile these two views, showing how performance incentives offered by an informed principal (manager, teacher, parent) can adversely impact an agent’s (worker, child) per...

Extrinsic allergic alveolitis (EAA) or hypersensitivity pneumonitis is an interstitial lung disease associated with repeated exposure to a wide range of inhaled organic dusts and related occupational allergens, especially bird and fungal proteins. We focus on the diagnostic and prognostic findings related to the use of BAL in the management of EAA patients. The presentation of EAA varies from p...

These notes arose from a mini lecture series the author gave at Early Career Researchers Workshop on Geometric Analysis and PDEs, held in January 2020 The Mathematical Research Institute MATRIX. We discussed some classical aspects of expanding curvature flows obtained first applications. In these we will give detailed account what was covered during lectures.