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

Sampling properties of random graphs: the degree distribution

We discuss two sampling schemes for selecting random subnets from a network: Random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling. Here we derive a necessary and sufficient condition that guarantees that the degree distribution of the subnet and the true network belong to the same family of probability distributions. For completely random sampling of nodes we find that this condition is fulfilled by classical random graphs; for the vast majority of networks this condition will, however, not be met. We furthermore discuss the case where the probability of sampling a node depends on the degree of a node and we find that even classical random graphs are no longer closed under this sampling regime. We conclude by relating the results to real {\it E.coli} protein interaction network data.Comment: accepted for publication in Phys.Rev.

Assortative mixing in networks

A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. We define a measure of assortative mixing for networks and use it to show that social networks are often assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortative network, which we study both analytically and numerically. Within the framework of this model we find that assortative networks tend to percolate more easily than their disassortative counterparts and that they are also more robust to vertex removal.Comment: 5 pages, 1 table, 1 figur

The entropy of randomized network ensembles

Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same degree-correlations or the same community structure of any given real network. We characterize these randomized network ensembles by their entropy, i.e. the normalized logarithm of the total number of networks which are part of these ensembles. We estimate the entropy of randomized ensembles starting from a large set of real directed and undirected networks. We propose entropy as an indicator to assess the role of each structural feature in a given real network.We observe that the ensembles with fixed scale-free degree distribution have smaller entropy than the ensembles with homogeneous degree distribution indicating a higher level of order in scale-free networks.Comment: (6 pages,1 figure,2 tables

Portraits of Complex Networks

We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows for rigorous statistical comparison between networks. Dynamic processes such as percolation can be visualized using animations. Applications to graph theory are discussed, as are generalizations to weighted networks, real-world network similarity testing, and applicability to the graph isomorphism problem.Comment: 6 pages, 9 figure

Irreversible Opinion Spreading on Scale-Free Networks

We study the dynamical and critical behavior of a model for irreversible opinion spreading on Barab\'asi-Albert (BA) scale-free networks by performing extensive Monte Carlo simulations. The opinion spreading within an inhomogeneous society is investigated by means of the magnetic Eden model, a nonequilibrium kinetic model for the growth of binary mixtures in contact with a thermal bath. The deposition dynamics, which is studied as a function of the degree of the occupied sites, shows evidence for the leading role played by hubs in the growth process. Systems of finite size grow either ordered or disordered, depending on the temperature. By means of standard finite-size scaling procedures, the effective order-disorder phase transitions are found to persist in the thermodynamic limit. This critical behavior, however, is absent in related equilibrium spin systems such as the Ising model on BA scale-free networks, which in the thermodynamic limit only displays a ferromagnetic phase. The dependence of these results on the degree exponent is also discussed for the case of uncorrelated scale-free networks.Comment: 9 pages, 10 figures; added results and discussion on uncorrelated scale-free networks; added references. To appear in PR

Resilience of the Internet to random breakdowns

A common property of many large networks, including the Internet, is that the connectivity of the various nodes follows a scale-free power-law distribution, P(k)=ck^-a. We study the stability of such networks with respect to crashes, such as random removal of sites. Our approach, based on percolation theory, leads to a general condition for the critical fraction of nodes, p_c, that need to be removed before the network disintegrates. We show that for a<=3 the transition never takes place, unless the network is finite. In the special case of the Internet (a=2.5), we find that it is impressively robust, where p_c is approximately 0.99.Comment: latex, 3 pages, 1 figure (eps), explanations added, Phys. Rev. Lett., in pres

Identifying educator behaviours for high quality verbal feedback in health professions education: literature review and expert refinement

Background Health professions education is characterised by work-based learning and relies on effective verbal feedback. However the literature reports problems in feedback practice, including lack of both learner engagement and explicit strategies for improving performance. It is not clear what constitutes high quality, learner-centred feedback or how educators can promote it. We hoped to enhance feedback in clinical practice by distinguishing the elements of an educator’s role in feedback considered to influence learner outcomes, then develop descriptions of observable educator behaviours that exemplify them. Methods An extensive literature review was conducted to identify i) information substantiating specific components of an educator’s role in feedback asserted to have an important influence on learner outcomes and ii) verbal feedback instruments in health professions education, that may describe important educator activities in effective feedback. This information was used to construct a list of elements thought to be important in effective feedback. Based on these elements, descriptions of observable educator behaviours that represent effective feedback were developed and refined during three rounds of a Delphi process and a face-to-face meeting with experts across the health professions and education. Results The review identified more than 170 relevant articles (involving health professions, education, psychology and business literature) and ten verbal feedback instruments in health professions education (plus modified versions). Eighteen distinct elements of an educator’s role in effective feedback were delineated. Twenty five descriptions of educator behaviours that align with the elements were ratified by the expert panel. Conclusions This research clarifies the distinct elements of an educator’s role in feedback considered to enhance learner outcomes. The corresponding set of observable educator behaviours aim to describe how an educator could engage, motivate and enable a learner to improve. This creates the foundation for developing a method to systematically evaluate the impact of verbal feedback on learner performance

Towards dialogue: audio feedback on politics essays

This paper evaluates the use of audio feedback on assignments through the case study of a politics course, highlighting a number of pedagogical benefits. In particular, and using student testimonies, it argues that audio feedback provides a more personal feel to feedback; criticism, it appears, is easier to accept in the spoken word – as one student suggests, you know the marker is ‘not being harsh’ and is ‘just trying to help you really’. In addition, the paper notes the chief practical benefit of audio feedback: it reduces the overall time spent by lecturers in providing comments. While this paper is positive in favour of audio feedback throughout, it also discusses some potential challenges including anonymous marking – which affects the relationship between marker and student – and the fact that one size does not fit all, with different students preferring different types of feedback. The paper also attempts to provide practical tips to professionals wishing to use this method of feedback

Leadership Training in Graduate Medical Education: Time for a Requirement?

INTRODUCTION: The need for all physicians to function as leaders in their various roles is becoming more widely recognized. There are increasing opportunities for physicians at all levels including Graduate Medical Education (GME) to gain leadership skills, but most of these opportunities are only for those interested. Although not an Accreditation Council for Graduate Medical Education (ACGME) requirement, some US graduate medical education programs have incorporated leadership training into their curricula. Interestingly, the Royal College of Physicians and Surgeons of Canada adopted the Leader role in its 2015 CanMEDS physician training model and requires leadership training. We sought to understand the value of a leadership training program in residency in our institution. MATERIALS AND METHODS: Our 2017 pilot leadership training program for senior military internal medicine residents consisted of four one-hour sessions of mini-lectures, self-assessments, case discussions, and small group activities. The themes were: Introduction to Leadership, Emotional Intelligence, Teambuilding, and Conflict Management. Participants were given an 18-question survey (14 Likert scale multiple-choice questions and 4 open-ended response questions) to provide feedback about the course. The Brooke Army Medical Center Institutional Review Board approved this project as a Quality Improvement effort. RESULTS: The survey response rate was 48.1% (26 of 54). The majority of respondents (84.6%) agreed the leadership training sessions were helpful and relevant. Following the sessions, 80.8% saw a greater role for physicians to function as leaders. Most (88.4%) agreed that these sessions helped them understand the importance of their roles as leaders, with 80.8% feeling more empowered to be leaders in their areas, 76.9% gaining a better understanding of their own strengths and weaknesses as leaders, and 80.8% feeling better prepared to meet challenges in the future. After exposure to leadership training, 73.1% indicated a plan to pursue additional leadership development opportunities. All respondents agreed that internists should be able to lead and manage a clinical team, and every respondent agreed that leadership principles should be taught in residency. CONCLUSIONS: This pilot project supports the premise that leadership training should be integrated into GME. Initial results suggest training can improve leadership skills and inspire trainees to seek additional leadership education. Moreover, much like the published literature, residents believe they should learn about leadership during residency. While more effort is needed to determine the best approach to deliver and evaluate this content, it appears even small interventions can make a difference. Next steps for this program include developing assessment tools for observation of leadership behaviors during routine GME activities, which would allow for reinforcement of the principles being taught. Additionally, our experience has led our institution to make leadership training a requirement in all of our GME programs, and we look forward to reporting future progress. Finally, an ACGME requirement to incorporate leadership training into GME programs nationwide would prove useful, as doing so would reinforce its importance, accelerate implementation, and expand knowledge of best approaches on a national level