Information inequalities and Generalized Graph Entropies

In this article, we discuss the problem of establishing relations between information measures assessed for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the R\'{e}nyi entropy have been considered for this study. Our main results involve establishing formal relationship, in the form of implicit inequalities, between these two kinds of measures when defined for graphs. Further, we also state and prove inequalities connecting the classical partition-based graph entropies and the functional-based entropy measures. In addition, several explicit inequalities are derived for special classes of graphs.Comment: A preliminary version. To be submitted to a journa

Experimental Resonance Enhanced Multiphoton Ionization (REMPI) studies of small molecules

Resonance enhanced multiphoton ionization (REMPI) utilizes tunable dye lasers to ionize an atom or molecule by first preparing an excited state by multiphoton absorption and then ionizing that state before it can decay. This process is highly selective with respect to both the initial and resonant intermediate states of the target, and it can be extremely sensitive. In addition, the products of the REMPI process can be detected as needed by analyzing the resulting electrons, ions, fluorescence, or by additional REMPI. This points to a number of exciting opportunities for both basic and applied science. On the applied side, REMPI has great potential as an ultrasensitive, highly selective detector for trace, reactive, or transient species. On the basic side, REMPI affords an unprecedented means of exploring excited state physics and chemistry at the quantum-state-specific level. An overview of current studies of excited molecular states is given to illustrate the principles and prospects of REMPI

Rotationally resolved energy-dispersive photoelectron spectroscopy of H_2O: Photoionization of the C̃(0,0,0) state at 355 nm

Measured and calculated rotationally resolved photoelectron spectra for photoionization of low rotational levels of the C̃^1B_1 Rydberg state of water are reported. This is the first example of rotationally resolved photoionization spectra beyond the special cases of H_2, high-J levels, and threshold spectra. These spectra reveal very nonatomiclike behavior and, surprisingly, the influence of multiple Cooper minima in the photoelectron matrix elements

Global Genetics Research in Prostate Cancer: A Text Mining and Computational Network Theory Approach

Prostate cancer is the most common cancer type in men in Finland and second worldwide. In this paper, we analyze almost 150, 000 published papers about prostate cancer, authored by ten thousands of scientists worldwide, with an integrated text mining and computational network theory approach. We demonstrate how to integrate text mining with network analysis investigating research contributions of countries and collaborations within and between countries. Furthermore, we study the time evolution of individually and collectively studied genes. Finally, we investigate a collaboration network of Finland and compare studied genes with globally studied genes in prostate cancer genetics. Overall, our results provide a global overview of prostate cancer research in genetics. In addition, we present a specific discussion for Finland. Our results shed light on trends within the last 30 years and are useful for translational researchers within the full range from genetics to public health management and health policy

Spectral analysis of Gene co-expression network of Zebrafish

We analyze the gene expression data of Zebrafish under the combined framework of complex networks and random matrix theory. The nearest neighbor spacing distribution of the corresponding matrix spectra follows random matrix predictions of Gaussian orthogonal statistics. Based on the eigenvector analysis we can divide the spectra into two parts, first part for which the eigenvector localization properties match with the random matrix theory predictions, and the second part for which they show deviation from the theory and hence are useful to understand the system dependent properties. Spectra with the localized eigenvectors can be characterized into three groups based on the eigenvalues. We explore the position of localized nodes from these different categories. Using an overlap measure, we find that the top contributing nodes in the different groups carry distinguished structural features. Furthermore, the top contributing nodes of the different localized eigenvectors corresponding to the lower eigenvalue regime form different densely connected structure well separated from each other. Preliminary biological interpretation of the genes, associated with the top contributing nodes in the localized eigenvectors, suggests that the genes corresponding to same vector share common features.Comment: 6 pages, four figures (accepted in EPL

Receptor for advanced glycation endproducts (RAGE) deficiency protects against MPTP toxicity

Copyright © 2011 Elsevier Inc. All rights reserved.Peer reviewedPublisher PD

Persistent topology for natural data analysis - A survey

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classification of cells, lesions, music pieces, gait, oil and gas reservoirs, cyclones, galaxies, bones, brain connections, languages, handwritten and gestured letters are shown

Connections between Classical and Parametric Network Entropies

This paper explores relationships between classical and parametric measures of graph (or network) complexity. Classical measures are based on vertex decompositions induced by equivalence relations. Parametric measures, on the other hand, are constructed by using information functions to assign probabilities to the vertices. The inequalities established in this paper relating classical and parametric measures lay a foundation for systematic classification of entropy-based measures of graph complexity

S 2p photoabsorption of the SF5CF3 molecule: Experiment, theory and comparison with SF6

The S 2p core excitation spectrum of the SF5CF3 molecule has been measured in the total ion yield mode. It resembles a lot the analogous spectrum of SF6, also recorded in this study, displaying intense transitions to the empty molecular orbitals both below and above the S 2p ionization potential (IP) and weak transitions to the Rydberg orbitals. The S 2p photoabsorption spectra of SF6 and SF5CF3 have been calculated using time-dependent density functional theory, whereby the spin–orbit coupling was included for the transitions below the S 2p IP. The agreement between experiment and theory is good for both molecules, which allows us to assign the main S 2p absorption features in SF5CF3