Density functional versus spin-density functional and the choice of correlated subspace in multi-variable effective action theories of electronic structure

Modern extensions of density functional theory such as the density functional theory plus U and the density functional theory plus dynamical mean-field theory require choices, including selection of variable (charge vs spin density) for the density functional and specification of the correlated subspace. This paper examines these issues in the context of the "plus U" extensions of density functional theory, in which additional correlations on specified correlated orbitals are treated using a Hartree-Fock approximation. Differences between using charge-only or spin-density-dependent exchange-correlation functionals and between Wannier and projector-based definitions of the correlated orbitals are considered on the formal level and in the context of the structural energetics of the rare earth nickelates. It is demonstrated that theories based on spin-dependent exchange-correlation functionals can lead to large and in some cases unphysical effective on-site exchange couplings. Wannier and projector-based definitions of the correlated orbitals lead to similar behavior near ambient pressure, but substantial differences are observed at large pressures. Implications for other beyond density functional methods such as the combination of density functional and dynamical mean field theory are discussed.Comment: 14 pages, 10 figure

Redefining the doctorate.

Many commentators and observers believe that the time is right and the sector is ready for a national debate in the UK on the nature of the doctorate, given the multiple drivers for change, multiple agendas at work, and the multiple stakeholders with an interest in both the debate and the outcome. This discussion paper is designed to help frame and inform such a debate, which will not only bring together the major stakeholder groups in a shared conversation, but also provide opportunities for members of the academic community to contribute to the discussion via a series of national workshops and meetings

Simulating Problem Difficulty in Arithmetic Cognition Through Dynamic Connectionist Models

The present study aims to investigate similarities between how humans and connectionist models experience difficulty in arithmetic problems. Problem difficulty was operationalized by the number of carries involved in solving a given problem. Problem difficulty was measured in humans by response time, and in models by computational steps. The present study found that both humans and connectionist models experience difficulty similarly when solving binary addition and subtraction. Specifically, both agents found difficulty to be strictly increasing with respect to the number of carries. Another notable similarity is that problem difficulty increases more steeply in subtraction than in addition, for both humans and connectionist models. Further investigation on two model hyperparameters --- confidence threshold and hidden dimension --- shows higher confidence thresholds cause the model to take more computational steps to arrive at the correct answer. Likewise, larger hidden dimensions cause the model to take more computational steps to correctly answer arithmetic problems; however, this effect by hidden dimensions is negligible.Comment: 7 pages; 15 figures; 5 tables; Published in the proceedings of the 17th International Conference on Cognitive Modelling (ICCM 2019