Unfolding spectral analysis of the Fermi-LAT data

The Large Area Telescope (LAT) onboard the Fermi satellite is observing the gamma-ray sky in the high energy region, above 20 MeV. We have developed a method to reconstruct the energy spectra of the gamma-rays detected by the Fermi LAT instrument based on a Bayesian unfolding approach, that takes into account the energy dispersion introduced by the instrument response. The method has been successfully applied to reconstruct the energy spectra of both steady and pulsating point sources. The analysis technique will be illustrated and the results obtained in some significant test cases will be discussed.Comment: 6 pages, 9 figure

Comprehensive Spectral Analysis of Cyg X-1 using RXTE Data

We analyse a large number ($> 500$) pointed RXTE observations of Cyg X-1 and model the spectrum of each one. A subset of the observations for which there is simultaneous reliable measure of the hardness ratio by the All Sky Monitor, shows that the sample covers nearly all the spectral shapes of Cyg X-1. The relative strength, width of the Iron line and the reflection parameter are in general correlated with the high energy photon spectral index $\Gamma$. This is broadly consistent with a geometry where for the hard state (low $\Gamma \sim 1.7$) there is a hot inner Comptonizing region surrounded by a truncated cold disk. The inner edge of the disk moves inwards as the source becomes softer till finally in the soft state (high $\Gamma > 2.2$) the disk fills the inner region and active regions above the disk produce the Comptonized component. However, the reflection parameter shows non-monotonic behaviour near the transition region ($\Gamma \sim 2$), suggestive of a more complex geometry or physical state of the reflector. Additionally, the inner disk temperature, during the hard state, is on the average higher than in the soft one, albeit with large scatter. These inconsistencies could be due to limitations in the data and the empirical model used to fit them. The flux of each spectral component is well correlated with $\Gamma$ which shows that unlike some other black hole systems, Cyg X-1 does not show any hysteresis behaviour. In the soft state, the flux of the Comptonized component is always similar to the disk one, which confirms that the ultra-soft state (seen in other brighter black hole systems) is not exhibited by Cyg X-1. The rapid variation of the Compton Amplification factor with $\Gamma$, naturally explains the absence of spectra with $\Gamma < 1.6$, despite a large number having $\Gamma \sim 1.65$.Comment: 12 pages, 8 figures, accepted for publication in Research in Astronomy and Astrophysics (RAA

Midinfrared spectral investigations of carbonates: Analysis of remotely sensed data

Recent airborne thermal infrared observations of Mars from the Kuiper Airborne Observatory (KAO) have provided evidence for the presence of carbonates, sulfates, and hydrates. Using the optical properties of calcite and anhydrite, it was estimated that CO3's and SO4's constituted about 1 to 3 and 10 to 15 wt. percent, repectively of the materials composing the atmospheric dust. Using the derived value as an estimate of total CO3 abundance, and making an assumption that the CO3's were uniformly distributed within the Martian regolith, it was estimated that such a CO3 reservoir could contain roughly 2 to 5 bars of CO2. While the results indicate that several volatile-bearing materials are present on Mars, the observations from the KAO are inherently limited in their ability to determine the spatial distributions of these materials. However, previous spacecraft observations of Mars provide both the spectral coverage necessary to identify these materials, as well as the potential for investigating their spatial variability. This has prompted us to pursue a reinvestigation of the Mariner 6 and 7 infrared spectrometer and Mariner 9 infrared interferometer spectrometer observations. The former data have been recently made available in digital format and calibration of wavelengths and intensities are almost complete. Additionally, we are pursuing the derivation of optical constants of more appropriate carbonates and sulfates

Making Laplacians commute

In this paper, we construct multimodal spectral geometry by finding a pair of closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are jointly diagonalizable and hence have the same eigenbasis. Our construction naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of applications in dimensionality reduction, shape analysis, and clustering, demonstrating that our method better captures the inherent structure of multi-modal data

The spectral analysis of nonstationary categorical time series using local spectral envelope

Most classical methods for the spectral analysis are based on the assumption that the time series is stationary. However, many time series in practical problems shows nonstationary behaviors. The data from some fields are huge and have variance and spectrum which changes over time. Sometimes,we are interested in the cyclic behavior of the categorical-valued time series such as EEG sleep state data or DNA sequence, the general method is to scale the data, that is, assign numerical values to the categories and then use the periodogram to find the cyclic behavior. But there exists numerous possible scaling. If we arbitrarily assign the numerical values to the categories and proceed with a spectral analysis, then the results will depend on the particular assignment. We would like to find the all possible scaling that bring out all of the interesting features in the data. To overcome these problems, there have been many approaches in the spectral analysis. Our goal is to develop a statistical methodology for analyzing nonstationary categorical time series in the frequency domain. In this dissertation, the spectral envelope methodology is introduced for spectral analysis of categorical time series. This provides the general framework for the spectral analysis of the categorical time series and summarizes information from the spectrum matrix. To apply this method to nonstationary process, I used the TBAS(Tree-Based Adaptive Segmentation) and local spectral envelope based on the piecewise stationary process. In this dissertation,the TBAS(Tree-Based Adpative Segmentation) using distance function based on the Kullback-Leibler divergence was proposed to find the best segmentation