Optimal geometry of transportation networks.

Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network G of given length L that is optimal in a certain sense. In the general model, the optimality criterion is to minimize the average (over pairs of points chosen independently from the distribution) time to travel between the points, where a travel path consists of any line segments in the plane traversed at slow speed and any route within the subway network traversed at a faster speed. Of major interest is how the shape of the optimal network changes as L increases.

True scale-invariant random spatial networks.

Some aspects of real-world road networks seem to have an approximate scale invariance property, motivating study of mathematical models of random networks whose distributions are exactly invariant under Euclidean scaling. This requires working in the continuum plane, so making a precise definition is not trivial. We introduce an axiomatization of a class of processes we call scale-invariant random spatial networks, whose primitives are routes between each pair of points in the plane.

Dimerization of β-tryptase inhibitors, does it work for both basic and neutral P1 groups?

The tetrameric folding of β-tryptase and the pair-wise distribution of its substrate binding sites offer a unique opportunity for development of inhibitors that span two adjacent binding sites. A series of dimeric inhibitors with two basic P1 moieties was discovered using this design strategy and exhibited tight-binder characteristics. Using the same strategy, an attempt was made to design and synthesize dimeric inhibitors with two neutral-P1 groups in hope to exploit the dimeric binding mode to achieve a starting point for further optimization.

Metal-organic frameworks for the storage and delivery of biologically active hydrogen sulfide.

Hydrogen sulfide is an extremely toxic gas that is also of great interest for biological applications when delivered in the correct amount and at the desired rate. Here we show that the highly porous metal-organic frameworks with the CPO-27 structure can bind the hydrogen sulfide relatively strongly, allowing the storage of the gas for at least several months. Delivered gas is biologically active in preliminary vasodilation studies of porcine arteries, and the structure of the hydrogen sulfide molecules inside the framework has been elucidated using a combination of powder X-ray diffraction and pair distribution function analysis.

An ionothermally prepared S = 1/2 vanadium oxyfluoride kagome lattice.

Frustrated magnetic lattices offer the possibility of many exotic ground states that are of great fundamental importance. Of particular significance is the hunt for frustrated spin-1/2 networks as candidates for quantum spin liquids, which would have exciting and unusual magnetic properties at low temperatures. The few reported candidate materials have all been based on d(9) ions.