A highly concise and effective synthesis of the mannose octasaccharide of the N-linked glycan in the adhesion domain of human CD2 was achieved via TMSOTf-promoted selective 6-glycosylation of a trisaccharide 4,6-diol acceptor with a pentasaccharide donor, followed by deprotection. The pentasaccharide was constructed by selective 3,6-diglycosylation of 1,2-O-ethylidene-beta-D-mannopyranose with ...

The Toxics Release Inventory (TRI) requires facilities with 10 or more full-time employees that process > 25,000 pounds in aggregate or use > 10,000 pounds of any one TRI chemical to report releases annually. However, little is known about releases from non-TRI-reporting facilities, nor has attention been given to the very localized equity impacts associated with air toxics releases. Using geog...

The dependence of the reflectance at the surface on the vertical structure of optical parameters is derived from first principles. It is shown that the depth dependence is a function of the derivative of the round trip attenuation of the downwelling and backscattered light. Previously the depth dependence was usually modeled as being dependent on the round trip attenuation. Using the new relati...

The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime, reconstructing the local data in the bulk from the entanglement on the boundary. W...

We give a derivation of the DeAngelis-Beddington functional response in terms of mechanisms at the individual level, and for the first time involving prey refuges instead of the usual interference between predators.

The time-dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schrödinger equation with a short-scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short-scale correlation structure in the condensate.

Final size relations are known for many epidemic models. The derivations are often tedious and difficult, involving indirect methods to solve a system of integro-differential equations. Often when the details of the disease or population change, the final size relation does not. An alternate approach to deriving final sizes has been suggested. This approach directly considers the underlying sto...

Quaternion measurable processes are introduced and the Dirac equation is derived from the Langevin equation associated with a two-valued process.