Kinetic and Exchange Energy Densities near the Nucleus

We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals.Comment: 11 pages, 7 figure

Design of a solver for multi-agent epistemic planning

As the interest in Artificial Intelligence continues to grow it is becoming more and more important to investigate formalization and tools that allow us to exploit logic to reason about the world. In particular, given the increasing number of multi-agents systems that could benefit from techniques of automated reasoning, exploring new ways to define not only the world's status but also the agents' information is constantly growing in importance. This type of reasoning, i.e., about agents' perception of the world and also about agents' knowledge of her and others' knowledge, is referred to as epistemic reasoning. In our work we will try to formalize this concept, expressed through epistemic logic, for dynamic domains. In particular we will attempt to define a new action-based language for multi-agent epistemic planning and to implement an epistemic planner based on it. This solver should provide a tool flexible enough to be able to reason on different domains, e.g., economy, security, justice and politics, where reasoning about others' beliefs could lead to winning strategies or help in changing a group of agents' view of the world.Comment: In Proceedings ICLP 2019, arXiv:1909.07646. arXiv admin note: text overlap with arXiv:1511.01960 by other author