Random walks and random numbers from supercontinuum generation

We report a numerical study showing how the random intensity and phase fluctuations across the bandwidth of a broadband optical supercontinuum can be interpreted in terms of the random processes of random walks and Lévy flights. We also describe how the intensity fluctuations can be applied to physical random number generation. We conclude that the optical supercontinuum provides a highly versatile means of studying and generating a wide class of random processes at optical wavelengths. © 2012 Optical Society of America.

Random walks in local dynamics of network losses

We suggest a model for data losses in a single node (memory buffer) of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that for a finite-capacity buffer at the critical point the loss rate exhibits strong fluctuations and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process.

From Spanish paintings to murder:topic transitions in casual conversations between native and non-native speakers of English

This article explores some of the strategies used by international students of English to manage topic shifts in casual conversations with English-speaking peers. It therefore covers aspects of discourse which have been comparatively under-researched, and where research has also tended to focus on the problems rather than the communicative achievements of non-native speakers. A detailed analysis of the conversations under discussion, which were recorded by the participants themselves, showed that they all flowed smoothly, and this was in large measure due to the ways in which topic shifts were managed. The paper will focus on a very distinct type of topic shift, namely that of topic transitions, which enable a smooth flow from one topic to another, but which do not explicitly signal that a shift is taking place. It will examine how the non-native speakers achieved coherence in the topic transitions which they initiated, which strategies or procedures they employed, and show how their initiations were effective in enabling the proposed topic to be understood, taken up and developed. It therefore adds to our understanding of the interactional achievements of international speakers in informal, social contexts. © 2013 Elsevier B.V.

What do schoolgirls think of engineering? A critique of conversations from a participatory research approach

Whilst statistics vary, putting the percentage of women engineers at between 6%[1] and 9% [2] of the UK Engineering workforce, what cannot be disputed is that there is a need to attract more young women into the profession. Building on previous work which examined why engineering continues to fail to attract high numbers of young women[3,4] and starting with the research question "What do High School girls think of engineering as a future career and study choice?", this paper critiques research conducted utilising a participatory approach[5] in which twenty semi-structured in depth interviews were conducted by two teenage researchers with High School girls from two different schools in the West Midlands area of the UK. In looking at the issues through the eyes of 16 and 17 year old girls, the study provides a unique insight into why girls are not attracted to engineering. © American Society for Engineering Education, 2014.

Self-Avoiding Walks in the Plane

Румен Руменов Данговски, Калина Христова Петрова - Разглеждаме броя на несамопресичащите се разходки с фиксирана дължина върху целочислената решетка. Завършваме анализа върху случая за лента, с дължина едно. Чрез комбинаторни аргументи получаваме точна формула за броя на разходките върху лента, ограничена отляво и отдясно. Формулата я изследваме и асимптотично.

An edge-based matching kernel through discrete-time quantum walks

In this paper, we propose a new edge-based matching kernel for graphs by using discrete-time quantum walks. To this end, we commence by transforming a graph into a directed line graph. The reasons of using the line graph structure are twofold. First, for a graph, its directed line graph is a dual representation and each vertex of the line graph represents a corresponding edge in the original graph. Second, we show that the discrete-time quantum walk can be seen as a walk on the line graph and the state space of the walk is the vertex set of the line graph, i.e., the state space of the walk is the edges of the original graph. As a result, the directed line graph provides an elegant way of developing new edge-based matching kernel based on discrete-time quantum walks. For a pair of graphs, we compute the h-layer depth-based representation for each vertex of their directed line graphs by computing entropic signatures (computed from discrete-time quantum walks on the line graphs) on the family of K-layer expansion subgraphs rooted at the vertex, i.e., we compute the depth-based representations for edges of the original graphs through their directed line graphs. Based on the new representations, we define an edge-based matching method for the pair of graphs by aligning the h-layer depth-based representations computed through the directed line graphs. The new edge-based matching kernel is thus computed by counting the number of matched vertices identified by the matching method on the directed line graphs. Experiments on standard graph datasets demonstrate the effectiveness of our new kernel.

Measuring graph similarity through continuous-time quantum walks and the quantum Jensen-Shannon divergence

In this paper we propose a quantum algorithm to measure the similarity between a pair of unattributed graphs. We design an experiment where the two graphs are merged by establishing a complete set of connections between their nodes and the resulting structure is probed through the evolution of continuous-time quantum walks. In order to analyze the behavior of the walks without causing wave function collapse, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the divergence between the evolution of two suitably initialized quantum walks over this structure is maximum when the original pair of graphs is isomorphic. We also prove that under special conditions the divergence is minimum when the sets of eigenvalues of the Hamiltonians associated with the two original graphs have an empty intersection.

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.