The Topological Theory of the Milnor Invariant μˉ(1,2,3)\bar{\mu}(1,2,3)

We study a topological Abelian gauge theory that generalizes the Abelian Chern-Simons one, and that leads in a natural way to the Milnor's link invariant $\bar{\mu}(1,2,3)$ when the classical action on-shell is calculated.Comment: 4 pages; corrected equatio

Excited State Specific Multi-Slater Jastrow Wave Functions

We combine recent advances in excited state variational principles, fast multi-Slater Jastrow methods, and selective configuration interaction to create multi-Slater Jastrow wave function approximations that are optimized for individual excited states. In addition to the Jastrow variables and linear expansion coefficients, this optimization includes state-specific orbital relaxations in order to avoid the compromises necessary in state-averaged approaches. We demonstrate that, when combined with variance matching to help balance the quality of the approximation across different states, this approach delivers accurate excitation energies even when using very modest multi-Slater expansions. Intriguingly, this accuracy is maintained even when studying a difficult chlorine-anion-to-$\pi^{*}$ charge transfer in which traditional state-averaged multi-reference methods must contend with different states that require drastically different orbital relaxations.Comment: 16 pages, 6 figures, 2 table

[C II] emission from galactic nuclei in the presence of X-rays

The luminosity of [C II] is used to probe the star formation rate in galaxies, but the correlation breaks down in some active galactic nuclei (AGNs). Models of the [C II] emission from galactic nuclei do not include the influence of X-rays on the carbon ionization balance, which may be a factor in reducing the [C II] luminosity. We calculate the [C II] luminosity in galactic nuclei under the influence of bright sources of X-rays. We solve the balance equation of the ionization states of carbon as a function of X-ray flux, electron, atomic hydrogen, and molecular hydrogen density. These are input to models of [CII] emission from the interstellar medium (ISM) in galactic nuclei. We also solve the distribution of the ionization states of oxygen and nitrogen in highly ionized regions. We find that the dense warm ionized medium (WIM) and dense photon dominated regions (PDRs) dominate the [C II] emission when no X-rays are present. The X-rays in galactic nuclei can affect strongly the C$^+$ abundance in the WIM converting some fraction to C$^{2+}$ and higher ionization states and thus reducing its [C II] luminosity. For an X-ray luminosity > 10$^{43}$ erg/s the [C II] luminosity can be suppressed by a factor of a few, and for very strong sources, >10$^{44}$ erg/s, such as found for many AGNs by an order of magnitude. Comparison of the model with extragalactic sources shows that the [C II] to far-infrared ratio declines for an X-ray luminosity >10$^{43}$ erg/s, in reasonable agreement with our model.Comment: 16 pages and 14 figures, accepted for publication in A&

EM Algorithms for Weighted-Data Clustering with Application to Audio-Visual Scene Analysis

Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical properties and to the existence of maximum-likelihood estimators based on expectation-maximization (EM). In this paper we propose a new mixture model that associates a weight with each observed point. We introduce the weighted-data Gaussian mixture and we derive two EM algorithms. The first one considers a fixed weight for each observation. The second one treats each weight as a random variable following a gamma distribution. We propose a model selection method based on a minimum message length criterion, provide a weight initialization strategy, and validate the proposed algorithms by comparing them with several state of the art parametric and non-parametric clustering techniques. We also demonstrate the effectiveness and robustness of the proposed clustering technique in the presence of heterogeneous data, namely audio-visual scene analysis.Comment: 14 pages, 4 figures, 4 table