Improved quasiparticle wave functions and mean field for G(0)W(0) calculations: Initialization with the COHSEX operator

The GW approximation to the electron self-energy has become a standard method for ab initio calculation of excited-state properties of condensed-matter systems. In many calculations, the G W self-energy operator, E, is taken to be diagonal in the density functional theory (DFT) Kohn-Sham basis within the G0 W0 scheme. However, there are known situations in which this diagonal Go Wo approximation starting from DFT is inadequate. We present two schemes to resolve such problems. The first, which we called sc-COHSEX-PG W, involves construction of an improved mean field using the static limit of GW, known as COHSEX (Coulomb hole and screened exchange), which is significantly simpler to treat than GW W. In this scheme, frequency-dependent self energy E(N), is constructed and taken to be diagonal in the COHSEX orbitals after the system is solved self-consistently within this formalism. The second method is called off diagonal-COHSEX G W (od-COHSEX-PG W). In this method, one does not self-consistently change the mean-field starting point but diagonalizes the COHSEX Hamiltonian within the Kohn-Sham basis to obtain quasiparticle wave functions and uses the resulting orbitals to construct the G W E in the diagonal form. We apply both methods to a molecular system, silane, and to two bulk systems, Si and Ge under pressure. For silane, both methods give good quasiparticle wave functions and energies. Both methods give good band gaps for bulk silicon and maintain good agreement with experiment. Further, the sc-COHSEX-PGW method solves the qualitatively incorrect DFT mean-field starting point (having a band overlap) in bulk Ge under pressure.

A mean-reverting stochastic model for the political business cycle

In this article, we look at the political business cycle problem through the lens of uncertainty. The feedback control used by us is the famous NKPC with stochasticity and wage rigidities. We extend the New Keynesian Phillips Curve model to the continuous time stochastic set up with an Ornstein-Uhlenbeck process. We minimize relevant expected quadratic cost by solving the corresponding Hamilton-Jacobi-Bellman equation. The basic intuition of the classical model is qualitatively carried forward in our set up but uncertainty also plays an important role in determining the optimal trajectory of the voter support function. The internal variability of the system acts as a base shifter for the support function in the risk neutral case. The role of uncertainty is even more prominent in the risk averse case where all the shape parameters are directly dependent on variability. Thus, in this case variability controls both the rates of change as well as the base shift parameters. To gain more insight we have also studied the model when the coefficients are time invariant and studied numerical solutions. The close relationship between the unemployment rate and the support function for the incumbent party is highlighted. The role of uncertainty in creating sampling fluctuation in this set up, possibly towards apparently anomalous results, is also explored.

Influence of recombination on acquisition and reversion of immune escape and compensatory mutations in HIV-1

Following transmission, HIV-1 adapts in the new host by acquiring mutations that allow it to escape from the host immune response at multiple epitopes. It also reverts mutations associated with epitopes targeted in the transmitting host but not in the new host. Moreover, escape mutations are often associated with additional compensatory mutations that partially recover fitness costs. It is unclear whether recombination expedites this process of multi-locus adaptation. To elucidate the role of recombination, we constructed a detailed population dynamics model that integrates viral dynamics, host immune response at multiple epitopes through cytotoxic T lymphocytes, and viral evolution driven by mutation, recombination, and selection. Using this model, we compute the expected waiting time until the emergence of the strain that has gained escape and compensatory mutations against the new host's immune response, and reverted these mutations at epitopes no longer targeted. We find that depending on the underlying fitness landscape, shaped by both costs and benefits of mutations, adaptation proceeds via distinct dominant pathways with different effects of recombination, in particular distinguishing escape and reversion. When adaptation at a single epitope is involved, recombination can substantially accelerate immune escape but minimally affects reversion. When multiple epitopes are involved, recombination can accelerate or inhibit adaptation depending on the fitness landscape. Specifically, recombination tends to delay adaptation when a purely uphill fitness landscape is accessible at each epitope, and accelerate it when a fitness valley is associated with each epitope. Our study points to the importance of recombination in shaping the adaptation of HIV-1 following its transmission to new hosts, a process central to T cell-based vaccine strategies. (C) 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license.