On non-vanishing and sign changes of the Fourier coefficients of Hilbert cusp forms

In this article, we study (simultaneous) non-vanishing, (simultaneous) sign changes of Fourier coefficients of (two) Hilbert cusp forms, respectively

Strongly correlated quantum dynamics of multimode light coupled to a two-level atom in a cavity

We study a composite multimode light-two-level atom system in a cavity. We show that coupling of the two-level atom to multiple modes of the light destroys the Mott phase of the composite system thus making the system less useful platform for developing concepts in quantum information processing

Primordial power spectrum: a complete analysis with the WMAP nine-year data

We have improved further the error sensitive Richardson-Lucy deconvolution algorithm making it applicable directly on the un-binned measured angular power spectrum of Cosmic Microwave Background observations to reconstruct the form of the primordial power spectrum. This improvement makes the application of the method significantly more straight forward by removing some intermediate stages of analysis allowing a reconstruction of the primordial spectrum with higher efficiency and precision and with lower computational expenses. Applying the modified algorithm we fit the WMAP 9 year data using the optimized reconstructed form of the primordial spectrum with more than 300 improvement in \chi^2 with respect to the best fit power-law. This is clearly beyond the reach of other alternative approaches and reflects the efficiency of the proposed method in the reconstruction process and allow us to look for any possible feature in the primordial spectrum projected in the CMB data. Though the proposed method allow us to look at various possibilities for the form of the primordial spectrum, all having good fit to the data, proper error-analysis is needed to test for consistency of theoretical models since, along with possible physical artefacts, most of the features in the reconstructed spectrum might be arising from fitting noises in the CMB data. Reconstructed error-band for the form of the primordial spectrum using many realizations of the data, all bootstrapped and based on WMAP 9 year data, shows proper consistency of power-law form of the primordial spectrum with the WMAP 9 data at all wave numbers. Including WMAP polarization data in to the analysis have not improved much our results due to its low quality but we expect Planck data will allow us to make a full analysis on CMB observations on both temperature and polarization separately and in combination.Comment: 19 pages, 5 figures, discussions extended, results unchanged, matches the final version published in JCAP. Note: JCAP published version contains minor typesetting errors (introduced by JCAP at the proof stage) in the plot label

Primordial power spectrum from Planck

Using modified Richardson-Lucy algorithm we reconstruct the primordial power spectrum (PPS) from Planck Cosmic Microwave Background (CMB) temperature anisotropy data. In our analysis we use different combinations of angular power spectra from Planck to reconstruct the shape of the primordial power spectrum and locate possible features. Performing an extensive error analysis we found the dip near $\ell\sim750-850$ represents the most prominent feature in the data. Feature near $\ell\sim1800-2000$ is detectable with high confidence only in 217 GHz spectrum and is apparently consequence of a small systematic as described in the revised Planck 2013 papers. Fixing the background cosmological parameters and the foreground nuisance parameters to their best fit baseline values, we report that the best fit power law primordial power spectrum is consistent with the reconstructed form of the PPS at 2$\sigma$ C.L. of the estimated errors (apart from the local features mentioned above). As a consistency test, we found the reconstructed primordial power spectrum from Planck temperature data can also substantially improve the fit to WMAP-9 angular power spectrum data (with respect to power-law form of the PPS) allowing an overall amplitude shift of $\sim2.5\%$. In this context low-$\ell$ and 100 GHz spectrum from Planck which have proper overlap in the multipole range with WMAP data found to be completely consistent with WMAP-9 (allowing amplitude shift). As another important result of our analysis we do report the evidence of gravitational lensing through the reconstruction analysis. Finally we present two smooth form of the PPS containing only the important features. These smooth forms of PPS can provide significant improvements in fitting the data (with respect to the power law PPS) and can be helpful to give hints for inflationary model building.Comment: 30 pages, 11 figures, 1 table, matches published version in JCA

Structural Vulnerability Analysis of Electric Power Distribution Grids

Power grid outages cause huge economical and societal costs. Disruptions in the power distribution grid are responsible for a significant fraction of electric power unavailability to customers. The impact of extreme weather conditions, continuously increasing demand, and the over-ageing of assets in the grid, deteriorates the safety of electric power delivery in the near future. It is this dependence on electric power that necessitates further research in the power distribution grid security assessment. Thus measures to analyze the robustness characteristics and to identify vulnerabilities as they exist in the grid are of utmost importance. This research investigates exactly those concepts- the vulnerability and robustness of power distribution grids from a topological point of view, and proposes a metric to quantify them with respect to assets in a distribution grid. Real-world data is used to demonstrate the applicability of the proposed metric as a tool to assess the criticality of assets in a distribution grid