Counting approximately-shortest paths in directed acyclic graphs

Given a directed acyclic graph with positive edge-weights, two vertices s and t, and a threshold-weight L, we present a fully-polynomial time approximation-scheme for the problem of counting the s-t paths of length at most L. We extend the algorithm for the case of two (or more) instances of the same problem. That is, given two graphs that have the same vertices and edges and differ only in edge-weights, and given two threshold-weights L_1 and L_2, we show how to approximately count the s-t paths that have length at most L_1 in the first graph and length at most L_2 in the second graph. We believe that our algorithms should find application in counting approximate solutions of related optimization problems, where finding an (optimum) solution can be reduced to the computation of a shortest path in a purpose-built auxiliary graph

Weakly supervised semantic segmentation with a multi-image model

We propose a novel method for weakly supervised semantic segmentation. Training images are labeled only by the classes they contain, not by their location in the image. On test images instead, the method predicts a class label for every pixel. Our main innovation is a multi-image model (MIM)- a graphical model for recovering the pixel labels of the training images. The model connects superpixels from all training images in a data-driven fashion, based on their appearance similarity. For generalizing to new test images we integrate them into MIM using a learned multiple kernel metric, instead of learning conventional classifiers on the recovered pixel labels. We also introduce an “objectness” potential, that helps separating objects (e.g. car, dog, human) from background classes (e.g. grass, sky, road). In experiments on the MSRC 21 dataset and the LabelMe subset of [18], our technique outperforms previous weakly supervised methods and achieves accuracy comparable with fully supervised methods. 1

Casimir Friction Force and Energy Dissipation for Moving Harmonic Oscillators

The Casimir friction problem for a pair of dielectric particles in relative motion is analyzed, utilizing a microscopic model in which we start from statistical mechanics for harmonically oscillating particles at finite temperature moving nonrelativistically with constant velocity. The use of statistical mechanics in this context has in our opinion some definite advantages, in comparison with the more conventional quantum electrodynamic description of media that involves the use of a refractive index. The statistical-mechanical description is physical and direct, and the oscillator model, in spite of its simplicity, is nevertheless able to elucidate the essentials of the Casimir friction. As is known, there are diverging opinions about this kind of friction in the literature. Our treatment elaborates upon, and extends, an earlier theory presented by us back in 1992. There we found a finite friction force at any finite temperature, whereas at zero temperature the model led to a zero force. As an additional development in the present paper we evaluate the energy dissipation making use of an exponential cutoff truncating the relative motion of the oscillators. For the dissipation we also establish a general expression that is not limited to the simple oscillator model.Comment: 12 pages, no figures. Discussion extended, references added. To appear in Europhysics Letter

Population redistribution in optically trapped polar molecules

We investigate the rovibrational population redistribution of polar molecules in the electronic ground state induced by spontaneous emission and blackbody radiation. As a model system we use optically trapped LiCs molecules formed by photoassociation in an ultracold two-species gas. The population dynamics of vibrational and rotational states is modeled using an ab-initio electric dipole moment function and experimental potential energy curves. Comparison with the evolution of the v"=3 electronic ground state yields good qualitative agreement. The analysis provides important input to assess applications of ultracold LiCs molecules in quantum simulation and ultracold chemistry.Comment: 6 pages, 5 figures, EPJD Topical issue on Cold Quantum Matter - Achievements and Prospect

Electromagnetic-field quantization and spontaneous decay in left-handed media

We present a quantization scheme for the electromagnetic field interacting with atomic systems in the presence of dispersing and absorbing magnetodielectric media, including left-handed material having negative real part of the refractive index. The theory is applied to the spontaneous decay of a two-level atom at the center of a spherical free-space cavity surrounded by magnetodielectric matter of overlapping band-gap zones. Results for both big and small cavities are presented, and the problem of local-field corrections within the real-cavity model is addressed.Comment: 15 pages, 5 figures, RevTe