2,791 research outputs found

    Properties of dense partially random graphs

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    We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small World Graphs (SWGs). But we consider the case where the average degree of each node is of order of the size of the graph (unlike SWGs, which are sparse). This allows us to calculate the mean distance and clustering, that are qualitatively similar (although not in such a dramatic scale range) to the case of SWGs. We also obtain analytically the distribution of eigenvalues of the corresponding adjacency matrices. This distribution is discrete for large eigenvalues and continuous for small eigenvalues. The continuous part of the distribution follows a semicircle law, whose width is proportional to the "disorder" of the graph, whereas the discrete part is simply a rescaling of the spectrum of the substrate. We apply our results to the calculation of the mixing rate and the synchronizability threshold.Comment: 14 pages. To be published in Physical Review

    Chemical Raman Enhancement of Organic Adsorbates on Metal Surfaces

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    Using a combination of first-principles theory and experiments, we provide a quantitative explanation for chemical contributions to surface-enhanced Raman spectroscopy for a well-studied organic molecule, benzene thiol, chemisorbed on planar Au(111) surfaces. With density functional theory calculations of the static Raman tensor, we demonstrate and quantify a strong mode-dependent modification of benzene thiol Raman spectra by Au substrates. Raman active modes with the largest enhancements result from stronger contributions from Au to their electron-vibron coupling, as quantified through a deformation potential, a well-defined property of each vibrational mode. A straightforward and general analysis is introduced that allows extraction of chemical enhancement from experiments for specific vibrational modes; measured values are in excellent agreement with our calculations.Comment: 5 pages, 4 figures and Supplementary material included as ancillary fil

    A study of the gravitational wave form from pulsars II

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    We present analytical and numerical studies of the Fourier transform (FT) of the gravitational wave (GW) signal from a pulsar, taking into account the rotation and orbital motion of the Earth. We also briefly discuss the Zak-Gelfand Integral Transform. The Zak-Gelfand Integral Transform that arises in our analytic approach has also been useful for Schrodinger operators in periodic potentials in condensed matter physics (Bloch wave functions).Comment: 6 pages, Sparkler talk given at the Amaldi Conference on Gravitational waves, July 10th, 2001. Submitted to Classical and Quantum Gravit

    Communities in university mathematics

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    This paper concerns communities of learners and teachers that are formed, develop and interact in university mathematics environments through the theoretical lens of Communities of Practice. From this perspective, learning is described as a process of participation and reification in a community in which individuals belong and form their identity through engagement, imagination and alignment. In addition, when inquiry is considered as a fundamental mode of participation, through critical alignment, the community becomes a Community of Inquiry. We discuss these theoretical underpinnings with examples of their application in research in university mathematics education and, in more detail, in two Research Cases which focus on mathematics students' and teachers' perspectives on proof and on engineering students' conceptual understanding of mathematics. The paper concludes with a critical reflection on the theorising of the role of communities in university level teaching and learning and a consideration of ways forward for future research

    TimeSets: temporal sensemaking in intelligence analysis

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    TimeSets is a temporal data visualization technique designed to reveal insights into event sets, such as all the events linked to one person or organization. In this paper we describe two TimeSets-based visual analytics tools for intelligence analysis. In the first case, TimeSets is integrated with other visual analytics tools to support open-source intelligence analysis with Twitter data, particularly the challenge of finding the right questions to ask. The second case uses TimeSets in a participatory design process with analysts that aims to meet their requirements of uncertainty analysis involving fake news. Lessons learned are potentially beneficial to other application domains

    Representing addition and subtraction : learning the formal conventions

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    The study was designed to test the effects of a structured intervention in teaching children to represent addition and subtraction. In a post-test only control group design, 90 five-year-olds experienced the intervention entitled Bi-directional Translation whilst 90 control subjects experienced typical teaching. Post-intervention testing showed some significant differences between the two groups both in terms of being able to effect the addition and subtraction operations and in being able to determine which operation was appropriate. The results suggest that, contrary to historical practices, children's exploration of real world situations should precede practice in arithmetical symbol manipulation

    The influence of post-2008 legislation on an acquisition that turned hostile: A South African case study

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    Hostile acquisitions have a significant impact on managers and employees. The possibility of an acquisition creates uncertainty and when the acquisition turns hostile it is even more disruptive to the target organisation. Also, negative perceptions are often created in the media about the acquirer that influence employees’ attitudes in the target organisation. Processes to successfully integrate the acquirer and target organisations are impacted by these antagonistic pre-acquisition circumstances.   The Companies Act (no.71 of 2008) created opportunities for shareholders to hold an acquired company’s management accountable for financial performance and the researchers set out to investigate how the intent of the new legislation played out in practice, by studying an acquisition that turned hostile. The single case study research methodology revealed the manoeuvring of both the acquiring and acquired companies which utilised the mechanisms available to them through the new legislative, regulatory and corporate governance landscapes. The researchers provide an extensive review of the relevant mergers and acquisitions’ literature, as well as influence of the international legislative environment on the current local regulations. These regulations in turn, inform corporate governance and ultimately board behaviours. The researchers conducted qualitative interviews with key role players as well as legal and financial experts. The findings of the thematic analysis and triangulation process, informed a conceptual frame of three episodes

    Going SOLO to assess novice programmers

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    This paper explores the programming knowledge of novices using Biggs' SOLO taxonomy. It builds on previous work of Lister et al. (2006) and addresses some of the criticisms of that work. The research was conducted by studying the exam scripts for 120 introductory programming students, in which three specific questions were analyzed using the SOLO taxonomy. The study reports the following four findings: when the instruction to students used by Lister et al. - "In plain English, explain what the following segment of Java code does" - is replaced with a less ambiguous instruction, many students still provide multistructural responses; students are relatively consistent in the SOLO level of their answers; student responses on SOLO reading tasks correlate positively with performance on writing tasks; postgraduates students manifest a higher level of thinking than undergraduates. Copyright 2008 ACM

    Bose-Einstein Condensation on inhomogeneous complex networks

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    The thermodynamic properties of non interacting bosons on a complex network can be strongly affected by topological inhomogeneities. The latter give rise to anomalies in the density of states that can induce Bose-Einstein condensation in low dimensional systems also in absence of external confining potentials. The anomalies consist in energy regions composed of an infinite number of states with vanishing weight in the thermodynamic limit. We present a rigorous result providing the general conditions for the occurrence of Bose-Einstein condensation on complex networks in presence of anomalous spectral regions in the density of states. We present results on spectral properties for a wide class of graphs where the theorem applies. We study in detail an explicit geometrical realization, the comb lattice, which embodies all the relevant features of this effect and which can be experimentally implemented as an array of Josephson Junctions.Comment: 11 pages, 9 figure
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