Hilbert space renormalization for the many-electron problem

Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction ansatz, namely the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the 'physical indices' or the coupling rules in the HS-MPS. Alternatively, simply truncating the 'virtual dimension' of the HS-MPS leads to a family of size-extensive wave function ansaetze that can be used efficiently in variational calculations. We make formal and numerical comparisons between the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI approximations. The analysis and results shed light on fundamental aspects of the efficient representation of many-electron wavefunctions through the renormalization of many-body states.Comment: 23 pages, 14 figures, The following article has been submitted to The Journal of Chemical Physic

Towards a Layered Architectural View for Security Analysis in SCADA Systems

Supervisory Control and Data Acquisition (SCADA) systems support and control the operation of many critical infrastructures that our society depend on, such as power grids. Since SCADA systems become a target for cyber attacks and the potential impact of a successful attack could lead to disastrous consequences in the physical world, ensuring the security of these systems is of vital importance. A fundamental prerequisite to securing a SCADA system is a clear understanding and a consistent view of its architecture. However, because of the complexity and scale of SCADA systems, this is challenging to acquire. In this paper, we propose a layered architectural view for SCADA systems, which aims at building a common ground among stakeholders and supporting the implementation of security analysis. In order to manage the complexity and scale, we define four interrelated architectural layers, and uses the concept of viewpoints to focus on a subset of the system. We indicate the applicability of our approach in the context of SCADA system security analysis.Comment: 7 pages, 4 figure