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 study of the radiation emitted by 180-GeV/c electrons and positrons volume-reflected in a bent crystal

The radiation emitted by 180-GeV/c volume-reflected electrons and positrons impinging on a bent crystal has been measured by the H8RD22 Collaboration on the H8 beamline at the CERN SPS. A dedicated spectrometer has been developed to measure high-energy photon spectra (up to similar to 100 GeV) under volume reflection: photon and charged particle beams have been separated by a bending magnet and leptons were detected and tagged by microstrip silicon detectors and a Pb-scintillator sampling calorimeter. A comparison between the experimental and analytical data for the amorphous and volume-reflection cases is presented and the differences are discussed

Experimental study of the radiation emitted by 180-GeV/c electrons and positrons volume-reflected in a bent crystal

The radiation emitted by 180-GeV/c volume-reflected electrons and positrons impinging on a bent crystal has been measured by the H8RD22 Collaboration on the H8 beamline at the CERN SPS. A dedicated spectrometer has been developed to measure high-energy photon spectra (up to similar to 100 GeV) under volume reflection: photon and charged particle beams have been separated by a bending magnet and leptons were detected and tagged by microstrip silicon detectors and a Pb-scintillator sampling calorimeter. A comparison between the experimental and analytical data for the amorphous and volume-reflection cases is presented and the differences are discussed

Information Indices with High Discriminative Power for Graphs

In this paper, we evaluate the uniqueness of several information-theoretic measures for graphs based on so-called information functionals and compare the results with other information indices and non-information-theoretic measures such as the well-known Balaban index. We show that, by employing an information functional based on degree-degree associations, the resulting information index outperforms the Balaban index tremendously. These results have been obtained by using nearly 12 million exhaustively generated, non-isomorphic and unweighted graphs. Also, we obtain deeper insights on these and other topological descriptors when exploring their uniqueness by using exhaustively generated sets of alkane trees representing connected and acyclic graphs in which the degree of a vertex is at most four

High-efficiency deflection of high energy protons due to channeling along the (110) axis of a bent silicon crystal

A deflection efficiency of about 61% was observed for 400 GeV/c protons due to channeling, most strongly along the 〈110〉 axis of a bent silicon crystal. It is comparable with the deflection efficiency in planar channeling and considerably larger than in the case of the 〈111〉 axis. The measured probability of inelastic nuclear interactions of protons in channeling along the 〈110〉 axis is only about 10% of its amorphous level whereas in channeling along the (110) planes it is about 25%. High efficiency deflection and small beam losses make this axial orientation of a silicon crystal a useful tool for the beam steering of high energy charged particles

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

Integrative Network Biology: Graph Prototyping for Co-Expression Cancer Networks

Network-based analysis has been proven useful in biologically-oriented areas, e.g., to explore the dynamics and complexity of biological networks. Investigating a set of networks allows deriving general knowledge about the underlying topological and functional properties. The integrative analysis of networks typically combines networks from different studies that investigate the same or similar research questions. In order to perform an integrative analysis it is often necessary to compare the properties of matching edges across the data set. This identification of common edges is often burdensome and computational intensive. Here, we present an approach that is different from inferring a new network based on common features. Instead, we select one network as a graph prototype, which then represents a set of comparable network objects, as it has the least average distance to all other networks in the same set. We demonstrate the usefulness of the graph prototyping approach on a set of prostate cancer networks and a set of corresponding benign networks. We further show that the distances within the cancer group and the benign group are statistically different depending on the utilized distance measure

Exploring Statistical and Population Aspects of Network Complexity

The characterization and the definition of the complexity of objects is an important but very difficult problem that attracted much interest in many different fields. In this paper we introduce a new measure, called network diversity score (NDS), which allows us to quantify structural properties of networks. We demonstrate numerically that our diversity score is capable of distinguishing ordered, random and complex networks from each other and, hence, allowing us to categorize networks with respect to their structural complexity. We study 16 additional network complexity measures and find that none of these measures has similar good categorization capabilities. In contrast to many other measures suggested so far aiming for a characterization of the structural complexity of networks, our score is different for a variety of reasons. First, our score is multiplicatively composed of four individual scores, each assessing different structural properties of a network. That means our composite score reflects the structural diversity of a network. Second, our score is defined for a population of networks instead of individual networks. We will show that this removes an unwanted ambiguity, inherently present in measures that are based on single networks. In order to apply our measure practically, we provide a statistical estimator for the diversity score, which is based on a finite number of samples

Crystal undulator experiment at IHEP

Accelerator-based sources of hard-photon radiation are a rapidly developing field. Coherent radiation of a particle beam in an undulator is a popular choice. The crystalline undulators with periodically deformed crystallographic planes offer electromagnetic fields of the order of 1000 T and could provide a period L in the sub-millimeter range. In this way, a hundred-fold gain in the energy of emitted photons would be reached, as compared to a usual undulator. The first real construction of a crystal channeling undulator was recently proposed and realised by the present collaboration. After the sine-like deformation of crystal was proven in X-ray tests, four undulators were tested for channeling in a beam of 70-GeV protons. It was observed in the experiment that the crystal cross-section is efficiently channeling high energy particles, similarly to usual crystal deflectors. The experimentally established transparence for channeling of high energy particles allows one to start a direct experiment on photon production from a positron beam in the crystalline undulator. Details of commissioning of the experimental setup in the first run with 3 GeV positron beam are presented