Random acyclic networks

Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the model's properties, including connection probabilities and component sizes, as well as a fast algorithm for simulating the model on a computer. We compare the predictions of the model to a real-world network of citations between physics papers and find surprisingly good agreement, suggesting that the structure of the real network may be quite well described by the random graph.Comment: 4 pages, 2 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

Evolution equation for a model of surface relaxation in complex networks

In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by the disagreement between the scaling results of the steady state of the fluctuations between the discrete SRM model and the Edward-Wilkinson process found in scale-free networks with degree distribution $P(k) \sim k^{-\lambda}$ for $\lambda <3$ [Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf 76}, 046117 (2007)]. Even though for Euclidean lattices the evolution equation is linear, we find that in complex heterogeneous networks non-linear terms appear due to the heterogeneity and the lack of symmetry of the network; they produce a logarithmic divergency of the saturation roughness with the system size as found by Pastore y Piontti {\it et al.} for $\lambda <3$.Comment: 9 pages, 2 figure

Solution of the 2-star model of a network

The p-star model or exponential random graph is among the oldest and best-known of network models. Here we give an analytic solution for the particular case of the 2-star model, which is one of the most fundamental of exponential random graphs. We derive expressions for a number of quantities of interest in the model and show that the degenerate region of the parameter space observed in computer simulations is a spontaneously symmetry broken phase separated from the normal phase of the model by a conventional continuous phase transition.Comment: 5 pages, 3 figure

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

Effectiveness of a social support intervention on infant feeding practices : randomised controlled trial

Background: To assess whether monthly home visits from trained volunteers could improve infant feeding practices at age 12 months, a randomised controlled trial was carried out in two disadvantaged inner city London boroughs. Methods: Women attending baby clinics with their infants (312) were randomised to receive monthly home visits from trained volunteers over a 9-month period (intervention group) or standard professional care only (control group). The primary outcome was vitamin C intakes from fruit. Secondary outcomes included selected macro and micro-nutrients, infant feeding habits, supine length and weight. Data were collected at baseline when infants were aged approximately 10 weeks, and subsequently when the child was 12 and 18 months old. Results: Two-hundred and twelve women (68%) completed the trial. At both follow-up points no significant differences were found between the groups for vitamin C intakes from fruit or other nutrients. At first follow-up, however, infants in the intervention group were significantly less likely to be given goats’ or soya milks, and were more likely to have three solid meals per day. At the second follow-up, intervention group children were significantly less likely to be still using a bottle. At both follow-up points, intervention group children also consumed significantly more specific fruit and vegetables. Conclusions: Home visits from trained volunteers had no significant effect on nutrient intakes but did promote some other recommended infant feeding practices

Clustering Phase Transitions and Hysteresis: Pitfalls in Constructing Network Ensembles

Ensembles of networks are used as null models in many applications. However, simple null models often show much less clustering than their real-world counterparts. In this paper, we study a model where clustering is enhanced by means of a fugacity term as in the Strauss (or "triangle") model, but where the degree sequence is strictly preserved -- thus maintaining the quenched heterogeneity of nodes found in the original degree sequence. Similar models had been proposed previously in [R. Milo et al., Science 298, 824 (2002)]. We find that our model exhibits phase transitions as the fugacity is changed. For regular graphs (identical degrees for all nodes) with degree k > 2 we find a single first order transition. For all non-regular networks that we studied (including Erdos - Renyi and scale-free networks) we find multiple jumps resembling first order transitions, together with strong hysteresis. The latter transitions are driven by the sudden emergence of "cluster cores": groups of highly interconnected nodes with higher than average degrees. To study these cluster cores visually, we introduce q-clique adjacency plots. We find that these cluster cores constitute distinct communities which emerge spontaneously from the triangle generating process. Finally, we point out that cluster cores produce pitfalls when using the present (and similar) models as null models for strongly clustered networks, due to the very strong hysteresis which effectively leads to broken ergodicity on realistic time scales.Comment: 13 pages, 11 figure

Scale-Free Networks are Ultrasmall

We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) ~ k^-a, i.e. the probability of having k links outgoing from a site. In contrast to the diameter of regular random networks or small world networks which is known to be d ~ lnN, we show, using analytical arguments, that scale free networks with 2<a<3 have a much smaller diameter, behaving as d ~ lnlnN. For a=3, our analysis yields d ~ lnN/lnlnN, as obtained by Bollobas and Riordan, while for a>3, d ~ lnN. We also show that, for any a>2, one can construct a deterministic scale free network with d ~ lnlnN, and this construction yields the lowest possible diameter.Comment: Latex, 4 pages, 2 eps figures, small corrections, added explanation