Stochastic analysis of superresolution microscopy data obtained from receptor trafficking on neurons reveals novel organized molecular assembly generating long range forces. Would that have been possible with single particle tracking? How have we characterized these molecular assemblies?

This paper proposes a biologically inspired ‘molecular assembly line’ — an externally programmable polymeric chain along which molecules are shuttled between chain sites along an arbitrary pathway. Our hope is to construct a scaffold that mimics biological enzymes known as polyketide synthases in their ability to physically hand-off molecules between assembly sites or domains, thereby making al...

We consider a model of self-avoiding walks on the lattice Zd with different weights for steps in each of the 2d lattice directions. We find that the directiondependent mass for the two-point function of this model has three phases: mass positive in all directions; mass identically −∞; and masses of different signs in different directions. The final possibility can only occur if the weights are ...

We have produced extended series for prudent self-avoiding walks on the square lattice. These are subsets of self-avoiding walks. We conjecture the exact growth constant and critical exponent for the walks, and show that the (anisotropic) generating function is almost certainly not differentiably-finite.