Paramagnetic metal ions generate pseudocontact shifts (PCSs) in nuclear magnetic resonance spectra that are manifested as easily measurable changes in chemical shifts. Metals can be incorporated into proteins through metal binding tags, and PCS data constitute powerful long-range restraints on the positions of nuclear spins relative to the coordinate system of the magnetic susceptibility anisot...

We introduce the notions of measurable and strong measurable sensitivity, which are measure-theoretic versions of the conditions of sensitive dependence on initial conditions and strong sensitive dependence on initial conditions, respectively. Strong measurable sensitivity is a consequence of light mixing, implies that a transformation has only finitely many eigenvalues, and does not exist in t...

We develop the theory of categories of measurable fields of Hilbert spaces and bounded fields of operators. We examine classes of functors and natural transformations with good measure theoretic properties, providing in the end a rigorous construction for the bicategory used in [4] and [3] as the basis for a representation theory of (Lie) 2-groups. Two important technical results are establishe...

We give an example of a measurable set E ⊆ R such that the set E ′ = {(x, y) : x + y ∈ E} is not in the σ-algebra generated by the rectangles with measurable sides. We also prove a stronger result that there exists an analytic (Σ11) set E such that E ′ is not in the σ-algebra generated by rectangles whose horizontal side is measurable and vertical side is arbitrary. The same results are true wh...

In this letter, we present an excavation controller for a full-sized hydraulic excavator that can adapt online to different soil characteristics. Soil properties are hard predict and vary even within one scoop, which requires the encountered conditions. The objective is fill bucket with material while respecting machine limitations prevent stalling or lifting of machine. To end, train control p...