Self-avoiding walks on scale-free networks

Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAWs) are expected to be more suitable than unrestricted random walks to explore various kinds of real-life networks. Here we study long-range properties of random SAWs on scale-free networks, characterized by a degree distribution $P(k) \sim k^{-\gamma}$. In the limit of large networks (system size $N \to \infty$), the average number $s_n$ of SAWs starting from a generic site increases as $\mu^n$, with $\mu = / - 1$. For finite $N$, $s_n$ is reduced due to the presence of loops in the network, which causes the emergence of attrition of the paths. For kinetic growth walks, the average maximum length, $$, increases as a power of the system size: $\sim N^{\alpha}$, with an exponent $\alpha$ increasing as the parameter $\gamma$ is raised. We discuss the dependence of $\alpha$ on the minimum allowed degree in the network. A similar power-law dependence is found for the mean self-intersection length of non-reversal random walks. Simulation results support our approximate analytical calculations.Comment: 9 pages, 7 figure

How technology shapes assessment design: findings from a study of university teachers

A wide range of technologies has been developed to enhance assessment, but adoption has been inconsistent. This is despite assessment being critical to student learning and certification. To understand why this is the case and how it can be addressed, we need to explore the perspectives of academics responsible for designing and implementing technology-supported assessment strategies. This paper reports on the experience of designing technology-supported assessment based on interviews with 33 Australian university teachers. The findings reveal the desire to achieve greater efficiencies and to be contemporary and innovative as key drivers of technology adoption for assessment. Participants sought to shape student behaviors through their designs and made adaptations in response to positive feedback and undesirable outcomes. Many designs required modification because of a lack of appropriate support, leading to compromise and, in some cases, abandonment. These findings highlight the challenges to effective technology-supported assessment design and demonstrate the difficulties university teachers face when attempting to negotiate mixed messages within institutions and the demands of design work. We use these findings to suggest opportunities to improve support by offering pedagogical guidance and technical help at critical stages of the design process and encouraging an iterative approach to design

Emergence of Clusters in Growing Networks with Aging

We study numerically a model of nonequilibrium networks where nodes and links are added at each time step with aging of nodes and connectivity- and age-dependent attachment of links. By varying the effects of age in the attachment probability we find, with numerical simulations and scaling arguments, that a giant cluster emerges at a first-order critical point and that the problem is in the universality class of one dimensional percolation. This transition is followed by a change in the giant cluster's topology from tree-like to quasi-linear, as inferred from measurements of the average shortest-path length, which scales logarithmically with system size in one phase and linearly in the other.Comment: 8 pages, 6 figures, accepted for publication in JSTA

Reframing assessment research: through a practice perspective

Assessment as a field of investigation has been influenced by a limited number of perspectives. These have focused assessment research in particular ways that have emphasised measurement, or student learning or institutional policies. The aim of this paper is to view the phenomenon of assessment from a practice perspective drawing upon ideas from practice theory. Such a view places assessment practices as central. This perspective is illustrated using data from an empirical study of assessment decision-making and uses as an exemplar the identified practice of ‘bringing a new assessment task into being’. It is suggested that a practice perspective can position assessment as integral to curriculum practices and end separations of assessment from teaching and learning. It enables research on assessment to de-centre measurement and take account of the wider range of people, phenomena and things that constitute it

What makes for effective feedback: staff and student perspectives

Since the early 2010s the literature has shifted to view feedback as a process that students do where they make sense of information about work they have done, and use it to improve the quality of their subsequent work. In this view, effective feedback needs to demonstrate effects. However, it is unclear if educators and students share this understanding of feedback. This paper reports a qualitative investigation of what educators and students think the purpose of feedback is, and what they think makes feedback effective. We administered a survey on feedback that was completed by 406 staff and 4514 students from two Australian universities. Inductive thematic analysis was conducted on data from a sample of 323 staff with assessment responsibilities and 400 students. Staff and students largely thought the purpose of feedback was improvement. With respect to what makes feedback effective, staff mostly discussed feedback design matters like timing, modalities and connected tasks. In contrast, students mostly wrote that high-quality feedback comments make feedback effective – especially comments that are usable, detailed, considerate of affect and personalised to the student’s own work. This study may assist researchers, educators and academic developers in refocusing their efforts in improving feedbac

The usefulness of feedback

Feedback can occur before and after assessment submission, but needs to be useful in order for students to improve their subsequent performance. Arguably, undergraduate students, and particularly international, online and new students, are especially in need of feedback to effectively engage in academic and disciplinary expectations. Therefore, this article draws on survey data from students, disaggregated by mode of study, citizenship of enrolment and year of study, to explore their experiences of feedback usefulness both before and after assessment submission. Overall, undergraduate students were positive; however, this perception decreased according to their year level. Comparisons between online and international students also revealed key differences. A conclusion is that undergraduate students cannot be treated homogeneously, and educators need to attend to the feedback experiences of different student groups as they progress through their programme

Random Networks with Tunable Degree Distribution and Clustering

We present an algorithm for generating random networks with arbitrary degree distribution and Clustering (frequency of triadic closure). We use this algorithm to generate networks with exponential, power law, and poisson degree distributions with variable levels of clustering. Such networks may be used as models of social networks and as a testable null hypothesis about network structure. Finally, we explore the effects of clustering on the point of the phase transition where a giant component forms in a random network, and on the size of the giant component. Some analysis of these effects is presented.Comment: 9 pages, 13 figures corrected typos, added two references, reorganized reference

Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks

In this work we investigate the spectra of Laplacian matrices that determine many dynamic properties of scale-free networks below and at the percolation threshold. We use a replica formalism to develop analytically, based on an integral equation, a systematic way to determine the ensemble averaged eigenvalue spectrum for a general type of tree-like networks. Close to the percolation threshold we find characteristic scaling functions for the density of states rho(lambda) of scale-free networks. rho(lambda) shows characteristic power laws rho(lambda) ~ lambda^alpha_1 or rho(lambda) ~ lambda^alpha_2 for small lambda, where alpha_1 holds below and alpha_2 at the percolation threshold. In the range where the spectra are accessible from a numerical diagonalization procedure the two methods lead to very similar results.Comment: 9 pages, 6 figure

Spin Glass Phase Transition on Scale-Free Networks

We study the Ising spin glass model on scale-free networks generated by the static model using the replica method. Based on the replica-symmetric solution, we derive the phase diagram consisting of the paramagnetic (P), ferromagnetic (F), and spin glass (SG) phases as well as the Almeida-Thouless line as functions of the degree exponent $\lambda$, the mean degree $K$, and the fraction of ferromagnetic interactions $r$. To reflect the inhomogeneity of vertices, we modify the magnetization $m$ and the spin glass order parameter $q$ with vertex-weights. The transition temperature $T_c$ ($T_g$) between the P-F (P-SG) phases and the critical behaviors of the order parameters are found analytically. When $2 < \lambda < 3$, $T_c$ and $T_g$ are infinite, and the system is in the F phase or the mixed phase for $r > 1/2$, while it is in the SG phase at $r=1/2$. $m$ and $q$ decay as power-laws with increasing temperature with different $\lambda$-dependent exponents. When $\lambda > 3$, the $T_c$ and $T_g$ are finite and related to the percolation threshold. The critical exponents associated with $m$ and $q$ depend on $\lambda$ for $3 < \lambda < 5$ ($3 < \lambda < 4$) at the P-F (P-SG) boundary.Comment: Phys. Rev. E in pres

Exact Solution for the Time Evolution of Network Rewiring Models

We consider the rewiring of a bipartite graph using a mixture of random and preferential attachment. The full mean field equations for the degree distribution and its generating function are given. The exact solution of these equations for all finite parameter values at any time is found in terms of standard functions. It is demonstrated that these solutions are an excellent fit to numerical simulations of the model. We discuss the relationship between our model and several others in the literature including examples of Urn, Backgammon, and Balls-in-Boxes models, the Watts and Strogatz rewiring problem and some models of zero range processes. Our model is also equivalent to those used in various applications including cultural transmission, family name and gene frequencies, glasses, and wealth distributions. Finally some Voter models and an example of a Minority game also show features described by our model.Comment: This version contains a few footnotes not in published Phys.Rev.E versio