364 research outputs found
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
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
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
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
Amoeba Techniques for Shape and Texture Analysis
Morphological amoebas are image-adaptive structuring elements for
morphological and other local image filters introduced by Lerallut et al. Their
construction is based on combining spatial distance with contrast information
into an image-dependent metric. Amoeba filters show interesting parallels to
image filtering methods based on partial differential equations (PDEs), which
can be confirmed by asymptotic equivalence results. In computing amoebas, graph
structures are generated that hold information about local image texture. This
paper reviews and summarises the work of the author and his coauthors on
morphological amoebas, particularly their relations to PDE filters and texture
analysis. It presents some extensions and points out directions for future
investigation on the subject.Comment: 38 pages, 19 figures v2: minor corrections and rephrasing, Section 5
(pre-smoothing) extende
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
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