A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Node centrality for continuous-time quantum walks

The study of complex networks has recently attracted increasing interest because of the large variety of systems that can be modeled using graphs. A fundamental operation in the analysis of complex networks is that of measuring the centrality of a vertex. In this paper, we propose to measure vertex centrality using a continuous-time quantum walk. More specifically, we relate the importance of a vertex to the influence that its initial phase has on the interference patterns that emerge during the quantum walk evolution. To this end, we make use of the quantum Jensen-Shannon divergence between two suitably defined quantum states. We investigate how the importance varies as we change the initial state of the walk and the Hamiltonian of the system. We find that, for a suitable combination of the two, the importance of a vertex is almost linearly correlated with its degree. Finally, we evaluate the proposed measure on two commonly used networks. © 2014 Springer-Verlag Berlin Heidelberg.

Approximate axial symmetries from continuous time quantum walks

The analysis of complex networks is usually based on key properties such as small-worldness and vertex degree distribution. The presence of symmetric motifs on the other hand has been related to redundancy and thus robustness of the networks. In this paper we propose a method for detecting approximate axial symmetries in networks. For each pair of nodes, we define a continuous-time quantum walk which is evolved through time. By measuring the probability that the quantum walker to visits each node of the network in this time frame, we are able to determine whether the two vertices are symmetrical with respect to any axis of the graph. Moreover, we show that we are able to successfully detect approximate axial symmetries too. We show the efficacy of our approach by analysing both synthetic and real-world data. © 2012 Springer-Verlag Berlin Heidelberg.

Efficient computation of decoherent quantum walks through eigenvalue perturbation

A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly,it has been shown that algorithmic properties of quantum walks with decoherence such as the spreading rate are sometimes better than their purely quantum counterparts. Not only quantum walks with decoherence provide a generalization of quantum walks that naturally encompasses both the quantum and classical case, but they also give rise to new and different probability distribution. The application of quantum walks with decoherence to large graphs is limited by the necessity of evolving state vector whose sizes quadratic in the number of nodes of the graph, as opposed to the linear state vector of the purely quantum (or classical) case. In this technical report,we show how to use perturbation theory to reduce the computational complexity of evolving a continuous-time quantum walk subject to decoherence. More specifically, given a graph over n nodes, we show how to approximate the eigendecomposition of the n2×n2 Lindblad super-operator from the eigendecomposition of the n×n graph Hamiltonian.

Policewoman walks past demonstrating policemen's wives who are against policewomen riding in radio cars with policemen

General note: Title and date provided by Bettye Lane.

Musically Consonant, Socially Dissonant: Orange Walks and Catholic Interpretation in West-Central Scotland

This article examines the music used by the Orange Order, in its public parades, more commonly referred to as “Orange Walks.” The Orange Order is an exclusively Protestant fraternal organization, which traces its roots to 1690 and the victory of the Protestant Prince William of Orange over the Catholic King James. Yet, as in Northern Ireland, many consider the group to be sectarian and view its public celebrations as a display of ethno-religious triumphalism. This article explores the extra-musical factors associated with Orangeism’s most iconic song, “The Sash My Father Wore,” how other groups have misappropriated the song, and how this has distorted its meaning and subsequent interpretation.

Recent statistics have shown that Glasgow hosts more Orange parades each year than in Belfast and Derry/Londonderry combined, yet while there have been many anthropological and ethnomusicological studies of Northern Ireland’s Orange parades, very little research has focused on similar traditions in Scotland. This article seeks to address that gap in the literature and is intended as a preparatory study, laying the groundwork for further analysis.

Decoherence models for discrete-time quantum walks and their application to neutral atom experiments

We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk experiments realized with neutral atoms walking in an optical lattice. From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic-instead of diffusive-expansion in position space is not a good indicator of the range of coherent delocalization. We provide further physical insight by distinguishing the effects of short- and long-time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences. For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.

The Cat Who Walks Through Years: Chris Claremont's X-Men as Kitty Pryde's bildungsroman

This dissertation examines the fictional character Kitty Pryde from the X-Men comic book series during the tenure of writer Chris Claremont. Claremont's work on the character primarily involves the years 1980-1990, though a return to writing the character in the 2000s is also discussed when relevant. The thesis question revolves around the definition of the bildungsroman genre and whether Claremont's narrative arc for Kitty Pryde's character fulfills that definition. Jerome Hamilton Buckley's 1974 book Season of Youth: The Bildungsroman from Dickens to Golding is used as the primary authority for the bildungsroman genre, and more specifically a list of nine criteria that Buckley deems particularly key to the definition of the genre. Each of the nine criteria is looked at in depth, demonstrating where and how they can be found in the narrative, if at all. However, because Buckley's perspective and criteria come from a time of less diversity, examination from a feminist and minority perspective is also added with ideas from Rita Felski and Stella Bolaki. Combining Buckley's initial list of nine criteria with more modern criticism, these ideas are then used to analyze Kitty Pryde's narrative arc and to determine whether it can be seen as a bildungsroman. The findings support reading Claremont's narrative arc of the Kitty Pryde character as a bildungsroman. Three of Buckley's nine key themes are identified as particularly prevalent in the narrative: the search for a vocation, ordeal by love, and the conflict of generations. Three more key themes are found to be less prevalent but still clearly present: the search for a working philosophy, the larger society, and alienation. Because Buckley's definition for the bildungsroman genre requires the presence of six of his nine key themes, the presence of the aforementioned six thus validate the reading of the narrative as a bildungsroman. The text also provides some suggestions for finding the three least applicable key themes within the narrative, but because their presence is not necessary to fulfill the definition of the bildungsroman, they are not rigorously examined. In addition to fulfilling Buckley's key themes, the paper also discusses the more modern minority-oriented views. It is shown how the narrative can be read in terms of a journey to diverge from norms, as per Felski's ideas of the unique qualities of the specifically female bildungsroman. As Kitty Pryde's narrative can be shown to conform to the bildungsroman ideas of both Buckley and Felski, the thesis question is thus answered positively: Chris Claremont's X-Men can indeed be read as Kitty Pryde's bildungsroman.

Quantum kernels for unattributed graphs using discrete-time quantum walks

In this paper, we develop a new family of graph kernels where the graph structure is probed by means of a discrete-time quantum walk. Given a pair of graphs, we let a quantum walk evolve on each graph and compute a density matrix with each walk. With the density matrices for the pair of graphs to hand, the kernel between the graphs is defined as the negative exponential of the quantum Jensen–Shannon divergence between their density matrices. In order to cope with large graph structures, we propose to construct a sparser version of the original graphs using the simplification method introduced in Qiu and Hancock (2007). To this end, we compute the minimum spanning tree over the commute time matrix of a graph. This spanning tree representation minimizes the number of edges of the original graph while preserving most of its structural information. The kernel between two graphs is then computed on their respective minimum spanning trees. We evaluate the performance of the proposed kernels on several standard graph datasets and we demonstrate their effectiveness and efficiency.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

A comparison of registered and unregistered organ donors’ perceptions about transplant recipients

Background: We examined whether registered and unregistered donors’ perceptions about transplant recipients’ previous behavior (e.g., substance use) and responsibility for illness differed based on their deceased organ donor registration decisions. ----- ----- ----- Methods: Students and community members from Queensland, Australia were surveyed about their perceptions of transplant recipients.----- ----- ----- Results: Respondents (N = 465) were grouped based on their organ donor registration status to determine if their perceptions about transplant recipients differed. Compared to registered respondents, a higher proportion of unregistered respondents held more negative and less favorable perceptions of recipients. Multivariate analysis of variance confirmed statistically that unregistered respondents evaluated recipients more negatively than registered respondents, F(6,449) = 5.33, p <.001. Unregistered respondents were more likely to view recipients as a smoker, substance user, or alcohol dependent and as undeserving of a transplant, blameworthy, and responsible for their illness. ----- ----- ----- Conclusion: Potential donors’ perceptions of transplant recipients’ behavior and responsibility for illness differ according to their registration status. Future interventions should challenge negative perceptions about recipients’ deservingness and responsibility and promote the perspective that people from all walks of life need transplants in the aim of ultimately encouraging an increase in donor registration.

Experiences of a walking intervention in a University community : Qualitative perspectives

Background: This study explored the experiences of university employees that participated in a walking intervention that encouraged individuals to walk more throughout their workday. The 10-week program was comprised of 5 phases (i.e. baseline, anticipating barriers, short planned walks, longer planned walks and maintenance) and utilized a pedometer diary and an online website for logging steps. The pedometer diary included “action plans” for addressing barriers and planning walking and the online dashboard provided graphical outputs that allowed participants to visualize whether they were reaching or exceeding their step targets. Methods: A subsample of 12 academic and administrative employees from the study completed open ended questionnaires at the end of the study. The questions focused on capturing the major themes of benefits/mediators and problems/moderators of the program and were assessed using phenomenological approaches. Results: Participants found a raised consciousness of physical inactivity throughout the work day. They also found it useful to have a graphical display of physical activity patterns, but found time constraints and lack of managerial support to be the primary barriers/moderators of the program. Those most likely to withdraw from the program experienced technical difficulties with objective monitors and the online website. Conclusions: Findings highlight the value in being involved in a group forum and provide insights into the challenges of supporting such programs within the workplace.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Design overview of USDL

Enabling web-based service networks and ecosystems requires a way of describing services by a "commercial envelope" as discussed in Chapter 1. A uniform conception of services across all walks of life (including technical services) is required capturing business, operational and technical aspects. Therefore, our proposed Unified Service Description Language (USDL) particularly draws from and generalizes the best-of-breed approaches presented in Part I. The following chapter presents the design rationale of USDL where the different aspects are put in a framework of descriptions requirements. This is followed by the subsequent chapters of this part that provide details on specific aspects such as pricing or legal issues.

Surviving an avalanche of data

Open the sports or business section of your daily newspaper, and you are immediately bombarded with an array of graphs, tables, diagrams, and statistical reports that require interpretation. Across all walks of life, the need to understand statistics is fundamental. Given that our youngsters’ future world will be increasingly data laden, scaffolding their statistical understanding and reasoning is imperative, from the early grades on. The National Council of Teachers of Mathematics (NCTM) continues to emphasize the importance of early statistical learning; data analysis and probability was the Council’s professional development “Focus of the Year” for 2007–2008. We need such a focus, especially given the results of the statistics items from the 2003 NAEP. As Shaughnessy (2007) noted, students’ performance was weak on more complex items involving interpretation or application of items of information in graphs and tables. Furthermore, little or no gains were made between the 2000 NAEP and the 2003 NAEP studies. One approach I have taken to promote young children’s statistical reasoning is through data modeling. Having implemented in grades 3 –9 a number of model-eliciting activities involving working with data (e.g., English 2010), I observed how competently children could create their own mathematical ideas and representations—before being instructed how to do so. I thus wished to introduce data-modeling activities to younger children, confi dent that they would likewise generate their own mathematics. I recently implemented data-modeling activities in a cohort of three first-grade classrooms of six year- olds. I report on some of the children’s responses and discuss the components of data modeling the children engaged in.