Selecting the rank of truncated SVD by Maximum Approximation Capacity

Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled cut-off criterion for the spectrum, we convert the underlying optimization problem into a noisy channel coding problem. The optimal approximation capacity of this channel controls the appropriate strength of regularization to suppress noise. In simulation experiments, this information theoretic method to determine the optimal rank competes with state-of-the art model selection techniques.Comment: 7 pages, 5 figures; Will be presented at the IEEE International Symposium on Information Theory (ISIT) 2011. The conference version has only 5 pages. This version has an extended appendi

The virtual photon approximation for three-body interatomic Coulombic decay

Interatomic Coulombic decay (ICD) is a mechanism which allows microscopic objects to rapidly exchange energy. When the two objects are distant, the energy transfer between the donor and acceptor species takes place via the exchange of a virtual photon. On the contrary, recent ab initio calculations have revealed that the presence of a third passive species can significantly enhance the ICD rate at short distances due to the effects of electronic wave function overlap and charge transfer states [Phys. Rev. Lett. 119, 083403 (2017)]. Here, we develop a virtual photon description of three-body ICD, showing that a mediator atom can have a significant influence at much larger distances. In this regime, this impact is due to the scattering of virtual photons off the mediator, allowing for simple analytical results and being manifest in a distinct geometry-dependence which includes interference effects. As a striking example, we show that in the retarded regime ICD can be substantially enhanced or suppressed depending on the position of the ICD-inactive object, even if the latter is far from both donor and acceptor species

Dispersion forces in macroscopic quantum electrodynamics

The description of dispersion forces within the framework of macroscopic quantum electrodynamics in linear, dispersing, and absorbing media combines the benefits of approaches based on normal-mode techniques of standard quantum electrodynamics and methods based on linear response theory in a natural way. It renders generally valid expressions for both the forces between bodies and the forces on atoms in the presence of bodies, while showing very clearly the intimate relation between the different types of dispersion forces. By considering examples, the influence of various factors like form, size, electric and magnetic properties, or intervening media on the forces is addressed. Since the approach based on macroscopic quantum electrodynamics does not only apply to equilibrium systems, it can be used to investigate dynamical effects such as the temporal evolution of forces on arbitrarily excited atoms.Comment: 112 pages, 7 figures, 4 tables, extended versio

Casimir effect for perfect electromagnetic conductors (PEMCs): A sum rule for attractive/repulsive forces

We discuss the Casimir effect for boundary conditions involving perfect electromagnetic conductors (PEMCs). Based on the corresponding reciprocal Green's tensor we construct the Green's tensor for two perfectly reflecting plates with magnetoelectric coupling (non-reciprocal media) within the framework of macroscopic quantum electrodynamics. We calculate the Casimir force between two PEMC plates in terms of the PEMC parameter M and the duality transformation angle ${\theta}$ resulting in a universal analytic expression that connects the attractive Casimir force with the repulsive Boyer force. We relate the results to the duality symmetry of electromagnetism

Greedy MAXCUT Algorithms and their Information Content

MAXCUT defines a classical NP-hard problem for graph partitioning and it serves as a typical case of the symmetric non-monotone Unconstrained Submodular Maximization (USM) problem. Applications of MAXCUT are abundant in machine learning, computer vision and statistical physics. Greedy algorithms to approximately solve MAXCUT rely on greedy vertex labelling or on an edge contraction strategy. These algorithms have been studied by measuring their approximation ratios in the worst case setting but very little is known to characterize their robustness to noise contaminations of the input data in the average case. Adapting the framework of Approximation Set Coding, we present a method to exactly measure the cardinality of the algorithmic approximation sets of five greedy MAXCUT algorithms. Their information contents are explored for graph instances generated by two different noise models: the edge reversal model and Gaussian edge weights model. The results provide insights into the robustness of different greedy heuristics and techniques for MAXCUT, which can be used for algorithm design of general USM problems.Comment: This is a longer version of the paper published in 2015 IEEE Information Theory Workshop (ITW