Counterion distributions and effective electrostatic interactions between spherical macroions in polyelectrolyte solutions are calculated via second-order perturbation (linear response) theory. By modeling the macroions as continuous charge distributions that are permeable to counterions, analytical expressions are obtained for counterion profiles and effective pair interactions in solutions of...

In theories with spontaneous symmetry breaking, the loop expansion of the effective potential is awkward. In such theories, the exact effective potential V (φc, T ) is real and convex (as a function of the classical field φc), but its perturbative series can be complex with a real part that is concave. These flaws limit the utility of the effective potential, particularly in studies of the earl...

We generalize the effective potential to scalar field configurations which are proportional to the Hubble parameter of a homogeneous and isotropic background geometry. This may be useful in situations for which curvature effects are significant. We evaluate the one loop contribution to the Hubble Effective Potential for a massless scalar with arbitrary conformal and quartic couplings, on a back...

The static and dynamic structure of liquid lithium (470 K) in a computer experiment were investigated using a new type of interaction: the pair potential is constructed from an ab initio molecular dynamics method which makes the effective interionic potential self-consistent with the radial distribution functions on the basis of the quantd hypemetted-chain theory. Comparisons of the new calcula...

The encoder-decoder framework for neural machine translation (NMT) has been shown effective in large data scenarios, but is much less effective for low-resource languages. We present a transfer learning method that significantly improves BLEU scores across a range of low-resource languages. Our key idea is to first train a high-resource language pair (the parent model), then transfer some of th...