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3. Methods for Characterising Oxide Inclusions and Porosity in Powder Ni Alloys for Disk Rotor Applications

Author

Hardy, M. C., Minisandram, R. S., Buckingham, R. C., Broadbent, R. J., Berment-Parr, I. M. D., Mignanelli, P. M., Pickard, A. C., Robb, R. T., Baxter, G. J., Horbury, A., Wright, D. C., Brooks Hardy, R. R., McDevitt, E. T., Mills, D. E., Cormier, Jonathan, editor, Edmonds, Ian, editor, Forsik, Stephane, editor, Kontis, Paraskevas, editor, O’Connell, Corey, editor, Smith, Timothy, editor, Suzuki, Akane, editor, Tin, Sammy, editor, and Zhang, Jian, editor

Published
2024
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4. Weak percolation on multiplex networks with overlapping edges

Author

Baxter, G. J., da Costa, R. A., Dorogovtsev, S. N., and Mendes, J. F. F.

Subjects
Condensed Matter - Disordered Systems and Neural Networks
Abstract

We solve the weak percolation problem for multiplex networks with overlapping edges. In weak percolation, a vertex belongs to a connected component if at least one of its neighbors in each of the layers is in this component. This is a weaker condition than for a mutually connected component in interdependent networks, in which any two vertices must be connected by a path within each of the layers. The effect of the overlaps on weak percolation turns out to be opposite to that on the giant mutually connected component. While for the giant mutually connected component, overlaps do not change the critical phenomena, our theory shows that in two layers any (nonzero) concentration of overlaps drives the weak percolation transition to the ordinary percolation universality class. In three layers, the phase diagram of the problem contains two lines -- of a continuous phase transition and of a discontinuous one -- connected in various ways depending on how the layers overlap. In the case of only doubled overlapped edges, two of the end points of these lines coincide, resulting in a tricritical point like that seen in heterogeneous $k$-core percolation., Comment: 21 pages, 8 figures

Published
2022
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5. Effect of initial infection size on network SIR model

Author

Machado, G. and Baxter, G. J.

Subjects
Physics - Physics and Society
Abstract

We consider the effect of a nonvanishing fraction of initially infected nodes (seeds) on the SIR epidemic model on random networks. This is relevant when, for example, the number of arriving infected individuals is large, but also to the modeling of a large number of infected individuals, but also to more general situations such as the spread of ideas in the presence of publicity campaigns. This model is frequently studied by mapping to a bond percolation problem, in which edges in the network are occupied with the probability, $p$, of eventual infection along an edge connecting an infected individual to a susceptible neighbor. This approach allows one to calculate the total final size of the infection and epidemic threshold in the limit of a vanishingly small seed fraction. We show, however, that when the initial infection occupies a nonvanishing fraction $f$ of the network, this method yields ambiguous results, as the correspondence between edge occupation and contagion transmission no longer holds. We propose instead to measure the giant component of recovered individuals within the original contact network. This has an unambiguous interpretation and correctly captures the dependence of the epidemic size on $f$. We give exact equations for the size of the epidemic and the epidemic threshold in the infinite size limit. We observe a second order phase transition as in the original formulation, however with an epidemic threshold which decreases with increasing $f$. When the seed fraction $f$ tends to zero we recover the standard results., Comment: 10 pages, 6 figures

Published
2022

6. Hidden transition in multiplex networks

Author

da Costa, R. A., Baxter, G. J., Dorogovtsev, S. N., and Mendes, J. F. F.

Subjects
Physics - Physics and Society, Condensed Matter - Disordered Systems and Neural Networks
Abstract

Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem. This anomalous transition occurs in networks of three or more layers without unconnected nodes, $P(0)=0$. Above a critical value of a control parameter, the removal of a tiny fraction $\Delta$ of nodes or edges triggers a failure cascade which ends either with the total collapse of the network, or a return to stability with the system essentially intact. The discontinuity is not accompanied by any singularity of the giant component, in contrast to the discontinuous hybrid transition which usually appears in such problems. The control parameter is the fraction of nodes in each layer with a single connection, $\Pi=P(1)$. We obtain asymptotic expressions for the collapse time and relaxation time, above and below the critical point $\Pi_c$, respectively. In the limit $\Delta\to0$ the total collapse for $\Pi>\Pi_\text{c}$ takes a time $T \propto 1/(\Pi-\Pi_\text{c})$, while there is an exponential relaxation below $\Pi_\text{c}$ with a relaxation time $\tau \propto 1/[\Pi_\text{c}-\Pi]$., Comment: 12 pages, 6 figures

Published
2021
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7. Degree dependent transmission rates in epidemic processes

Author

Baxter, G. J. and Timár, G.

Subjects
Physics - Physics and Society, Condensed Matter - Disordered Systems and Neural Networks
Abstract

The outcome of SIR epidemics with heterogeneous infective lifetimes, or heterogeneous susceptibilities, can be mapped onto a directed percolation process on the underlying contact network. In this paper we study SIR models where heterogeneity is a result of the degree dependence of disease transmission rates. We develop numerical methods to determine the epidemic threshold, the epidemic probability and epidemic size close to the threshold for configuration model contact networks with arbitrary degree distribution and an arbitrary matrix of transmission rates (dependent on transmitting and receiving node degree). For the special case of separable transmission rates we obtain analytical expressions for these quantities. We propose a categorization of spreading processes based on the ratio of the probability of an epidemic and the expected size of an epidemic, and demonstrate that this ratio has a complex dependence on the degree distribution and the degree-dependent transmission rates. For scale-free contact networks and transmission rates that are power functions of transmitting and receiving node degrees, the epidemic threshold may be finite even when the degree distribution powerlaw exponent is below $\gamma < 3$. We give an expression, in terms of the degree distribution and transmission rate exponents, for the limit at which the epidemic threshold vanishes. We find that the expected epidemic size and the probability of an epidemic may grow nonlinearly above the epidemic threshold, with exponents that depend not only on the degree distribution powerlaw exponent, but on the parameters of the transmission rate degree dependence functions, in contrast to ordinary directed percolation and previously studied variations of the SIR model., Comment: 32 pages, 9 figures

Published
2021
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8. Weak Multiplex Percolation

Author

Baxter, G. J., da Costa, R. A., Dorogovtsev, S. N., and Mendes, J. F. F.

Subjects
Condensed Matter - Disordered Systems and Neural Networks
Abstract

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially generalised to multiple layers. We describe a generalisation of percolation to multilayer networks: weak multiplex percolation. A node belongs to a connected component if at least one of its neighbours in each layer is in this component. We fully describe the critical phenomena of this process. In particular, in two layers, with finite second moments of the degree distributions, an unusual continuous transition with quadratic growth above the threshold. When the second moments diverge, the singularity is determined by the asymptotics of the degree distributions, creating a rich set of critical behaviours. In three or more layers we find a discontinuous hybrid transition which persists even in highly heterogeneous degree distributions, becoming continuous only when the powerlaw exponent reaches $1+ 1/(M-1)$ for $M$ layers., Comment: 42 pages, 8 figures

Published
2020

9. Filtering Statistics on Networks

Author

Baxter, G. J., da Costa, R. A., Dorogovtsev, S. N., and Mendes, J. F. F.

Subjects
Nonlinear Sciences - Cellular Automata and Lattice Gases, Condensed Matter - Disordered Systems and Neural Networks
Abstract

We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output, and the statistics of filtering is represented by the distribution of this degeneracy. For a few simple filter patterns on a ring we obtained an exact solution of the problem and described numerically more difficult filter setups. For each of the filter patterns and networks we found a few numbers essentially describing the statistics of filtering and compared them for different networks. Our results for networks with diverse architectures appear to be essentially determined by two factors: whether the graphs structure is deterministic or random, and the vertex degree. We find that filtering in random graphs produces a much richer statistics than in deterministic graphs. This statistical richness is reduced by increasing the graph's degree., Comment: 21 pages, 8 figures, 3 tables

Published
2020
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10. Exotic Critical Behavior of Weak Multiplex Percolation

Author

Baxter, G. J., da Costa, R. A., Dorogovtsev, S. N., and Mendes, J. F. F.

Subjects
Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics, Nonlinear Sciences - Adaptation and Self-Organizing Systems
Abstract

We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is not the case for the more commonly studied generalization of percolation to multiplex networks, the mutually connected clusters, which requires an interconnecting path within each layer between any two vertices in the giant mutually connected component. We study the emergence of a giant connected component of active nodes under the weak percolation rule, finding several non-typical phenomena. In two layers, the giant component emerges with a continuos phase transition, but with quadratic growth above the critical threshold. In three or more layers, a discontinuous hybrid transition occurs, similar to that found in the giant mutually connected component. In networks with asymptotically powerlaw degree distributions, defined by the decay exponent $\gamma$, the discontinuity vanishes but at $\gamma=1.5$ in three layers, more generally at $\gamma = 1+ 1/(M-1)$ in $M$ layers., Comment: 11 pages, 6 figures

Published
2020
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11. Exercise therapy, manual therapy, or both, for osteoarthritis of the hip or knee: a factorial randomised controlled trial protocol

Author

Baxter G David, McKenzie Joanne E, Robertson M Clare, Abbott J Haxby, Theis Jean-Claude, and Campbell A John

Subjects
Medicine (General), R5-920
Abstract

Abstract Background Non-pharmacological, non-surgical interventions are recommended as the first line of treatment for osteoarthritis (OA) of the hip and knee. There is evidence that exercise therapy is effective for reducing pain and improving function in patients with knee OA, some evidence that exercise therapy is effective for hip OA, and early indications that manual therapy may be efficacious for hip and knee OA. There is little evidence as to which approach is more effective, if benefits endure, or if providing these therapies is cost-effective for the management of this disorder. The MOA Trial (Management of OsteoArthritis) aims to test the effectiveness of two physiotherapy interventions for improving disability and pain in adults with hip or knee OA in New Zealand. Specifically, our primary objectives are to investigate whether: 1. Exercise therapy versus no exercise therapy improves disability at 12 months; 2. Manual physiotherapy versus no manual therapy improves disability at 12 months; 3. Providing physiotherapy programmes in addition to usual care is more cost-effective than usual care alone in the management of osteoarthritis at 24 months. Methods This is a 2 × 2 factorial randomised controlled trial. We plan to recruit 224 participants with hip or knee OA. Eligible participants will be randomly allocated to receive either: (a) a supervised multi-modal exercise therapy programme; (b) an individualised manual therapy programme; (c) both exercise therapy and manual therapy; or, (d) no trial physiotherapy. All participants will continue to receive usual medical care. The outcome assessors, orthopaedic surgeons, general medical practitioners, and statistician will be blind to group allocation until the statistical analysis is completed. The trial is funded by Health Research Council of New Zealand Project Grants (Project numbers 07/199, 07/200). Discussion The MOA Trial will be the first to investigate the effectiveness and cost-effectiveness of providing physiotherapy programmes of this kind, for the management of pain and disability in adults with hip or knee OA. Trial registration Australian New Zealand Clinical Trials Registry ref: ACTRN12608000130369.

Published
2009
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12. Complex distributions emerging in filtering and compression

Author

Baxter, G. J., da Costa, R. A., Dorogovtsev, S. N., and Mendes, J. F. F.

Subjects
Condensed Matter - Disordered Systems and Neural Networks, Physics - Data Analysis, Statistics and Probability
Abstract

In filtering, each output is produced by a certain number of different inputs. We explore the statistics of this degeneracy in an explicitly treatable filtering problem in which filtering performs the maximal compression of relevant information contained in inputs (arrays of zeroes and ones). This problem serves as a reference model for the statistics of filtering and related sampling problems. The filter patterns in this problem conveniently allow a microscopic, combinatorial consideration. This allows us to find the statistics of outputs, namely the exact distribution of output degeneracies, for arbitrary input sizes. We observe that the resulting degeneracy distribution of outputs decays as $e^{-c\log^\alpha \!d}$ with degeneracy $d$, where $c$ is a constant and exponent $\alpha>1$, i.e. faster than a power law. Importantly, its form essentially depends on the size of the input data set, appearing to be closer to a power-law dependence for small data set sizes than for large ones. We demonstrate that for sufficiently small input data set sizes typical for empirical studies, this distribution could be easily perceived as a power law. We extend our results to filter patterns of various sizes and demonstrate that the shortest filter pattern provides the maximum informative representations of the inputs., Comment: 17 pages, 8 figures, 1 table, Supplementary Material

Published
2019
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13. Targeted Damage to Interdependent Networks

Author

Baxter, G. J., Timár, G., and Mendes, J. F. F.

Subjects
Physics - Physics and Society, Condensed Matter - Disordered Systems and Neural Networks, Computer Science - Social and Information Networks
Abstract

The giant mutually connected component (GMCC) of an interdependent or multiplex network collapses with a discontinuous hybrid transition under random damage to the network. If the nodes to be damaged are selected in a targeted way, the collapse of the GMCC may occur significantly sooner. Finding the minimal damage set which destroys the largest mutually connected component of a given interdependent network is a computationally prohibitive simultaneous optimization problem. We introduce a simple heuristic strategy -- Effective Multiplex Degree -- for targeted attack on interdependent networks that leverages the indirect damage inherent in multiplex networks to achieve a damage set smaller than that found by any other non computationally intensive algorithm. We show that the intuition from single layer networks that decycling (damage of the $2$-core) is the most effective way to destroy the giant component, does not carry over to interdependent networks, and in fact such approaches are worse than simply removing the highest degree nodes., Comment: 9 pages, 9 figures

Published
2018
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16. A unified approach to percolation processes on multiplex networks

Author

Baxter, G. J., Cellai, D., Dorogovtsev, S. N., Goltsev, A. V., and Mendes, J. F. F.

Subjects
Condensed Matter - Disordered Systems and Neural Networks
Abstract

Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each layer having its own kind of edges, represented by different colours. An important fundamental structural feature of networks is their resilience to damage, the percolation transition. Generalisation of these concepts to multiplex networks requires careful definition of what we mean by connected clusters. We consider two different definitions. One, a rigorous generalisation of the single-layer definition leads to a strong non-local rule, and results in a dramatic change in the response of the system to damage. The giant component collapses discontinuously in a hybrid transition characterised by avalanches of diverging mean size. We also consider another definition, which imposes weaker conditions on percolation and allows local calculation, and also leads to different sized giant components depending on whether we consider an activation or pruning process. This 'weak' process exhibits both continuous and discontinuous transitions., Comment: arXiv admin note: text overlap with arXiv:1312.3814

Published
2016
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18. Critical dynamics of the k-core pruning process

Author

Baxter, G. J., Dorogovtsev, S. N., Lee, K. -E., Mendes, J. F. F., and Goltsev, A. V.

Subjects
Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Other Condensed Matter
Abstract

We present the theory of the k-core pruning process (progressive removal of nodes with degree less than k) in uncorrelated random networks. We derive exact equations describing this process and the evolution of the network structure, and solve them numerically and, in the critical regime of the process, analytically. We show that the pruning process exhibits three different behaviors depending on whether the mean degree of the initial network is above, equal to, or below the threshold _c corresponding to the emergence of the giant k-core. We find that above the threshold the network relaxes exponentially to the k-core. The system manifests the phenomenon known as "critical slowing down", as the relaxation time diverges when tends to _c. At the threshold, the dynamics become critical characterized by a power-law relaxation (1/t^2). Below the threshold, a long-lasting transient process (a "plateau" stage) occurs. This transient process ends with a collapse in which the entire network disappears completely. The duration of the process diverges when tends to _c. We show that the critical dynamics of the pruning are determined by branching processes of spreading damage. Clusters of nodes of degree exactly k are the evolving substrate for these branching processes. Our theory completely describes this branching cascade of damage in uncorrelated networks by providing the time dependent distribution function of branching. These theoretical results are supported by our simulations of the $k$-core pruning in Erdos-Renyi graphs., Comment: 12 pages, 10 figures

Published
2015
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25. Technical Report of the NAEP Mathematics Assessment in Puerto Rico: Focus on Statistical Issues. NCES 2007-462

Author

National Center for Education Statistics (ED), Washington, DC., Baxter, G. P., Ahmed, S., Sikali, E., Waits, T., Sloan, M., and Salvucci, S.

Abstract

In 2003, a trial National Assessment of Educational Progress (NAEP) mathematics assessment was administered in Spanish to public school students at grades 4 and 8 in Puerto Rico. Based on preliminary analyses of the 2003 data, changes were made in administration and translation procedures for the 2005 NAEP administration in Puerto Rico. This report describes the content and administration of the trial NAEP mathematics assessments in Puerto Rico in 2003 and 2005, problems with item misfit in the 2003 data, results of a special validity analysis, and plans to integrate Puerto Rico into the national sample in future administrations. This report is one of a series of three on the administration and results of the 2003 and 2005 trial NAEP mathematics assessments in Puerto Rico: (1) "Mathematics 2003 and 2005 Performance in Puerto Rico: Highlights" [ED495982]; and (2) "Mathematics 2005 Performance in Puerto Rico: Focus on the Content Areas" [ED495981]. This, the third report, focuses on the technical considerations of the trial assessments and plans to include Puerto Rico as part of the national sample in future administrations. (Contains 20 figures and 3 tables.)

Published
2007

27. Fast fixation without fast networks

Author

Baxter, G. J., Blythe, R. A., and McKane, A. J.

Subjects
Condensed Matter - Statistical Mechanics, Physics - Physics and Society, Quantitative Biology - Populations and Evolution
Abstract

We investigate the dynamics of a broad class of stochastic copying processes on a network that includes examples from population genetics (spatially-structured Wright-Fisher models), ecology (Hubbell-type models), linguistics (the utterance selection model) and opinion dynamics (the voter model) as special cases. These models all have absorbing states of fixation where all the nodes are in the same state. Earlier studies of these models showed that the mean time when this occurs can be made to grow as different powers of the network size by varying the the degree distribution of the network. Here we demonstrate that this effect can also arise if one varies the asymmetry of the copying dynamics whilst holding the degree distribution constant. In particular, we show that the mean time to fixation can be accelerated even on homogeneous networks when certain nodes are very much more likely to be copied from than copied to. We further show that there is a complex interplay between degree distribution and asymmetry when they may co-vary; and that the results are robust to correlations in the network or the initial condition., Comment: 11 pages, 5 figures

Published
2012
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28. Avalanche Collapse of Interdependent Network

Author

Baxter, G. J., Dorogovtsev, S. N., Goltsev, A. V., and Mendes, J. F. F.

Subjects
Condensed Matter - Statistical Mechanics, Mathematical Physics, Mathematics - Probability
Abstract

We reveal the nature of the avalanche collapse of the giant viable component in multiplex networks under perturbations such as random damage. Specifically, we identify latent critical clusters associated with the avalanches of random damage. Divergence of their mean size signals the approach to the hybrid phase transition from one side, while there are no critical precursors on the other side. We find that this discontinuous transition occurs in scale-free multiplex networks whenever the mean degree of at least one of the interdependent networks does not diverge., Comment: 4 pages, 5 figures

Published
2012
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29. Voter Model with Time dependent Flip-rates

Author

Baxter, G. J.

Subjects
Condensed Matter - Statistical Mechanics, Mathematical Physics, Mathematics - Probability, Physics - Physics and Society
Abstract

We introduce time variation in the flip-rates of the Voter Model. This type of generalisation is relevant to models of ageing in language change, allowing the representation of changes in speakers' learning rates over their lifetime and may be applied to any other similar model in which interaction rates at the microscopic level change with time. The mean time taken to reach consensus varies in a nontrivial way with the rate of change of the flip-rates, varying between bounds given by the mean consensus times for static homogeneous (the original Voter Model) and static heterogeneous flip-rates. By considering the mean time between interactions for each agent, we derive excellent estimates of the mean consensus times and exit probabilities for any time scale of flip-rate variation. The scaling of consensus times with population size on complex networks is correctly predicted, and is as would be expected for the ordinary voter model. Heterogeneity in the initial distribution of opinions has a strong effect, considerably reducing the mean time to consensus, while increasing the probability of survival of the opinion which initially occupies the most slowly changing agents. The mean times to reach consensus for different states are very different. An opinion originally held by the fastest changing agents has a smaller chance to succeed, and takes much longer to do so than an evenly distributed opinion., Comment: 16 pages, 6 figures

Published
2011
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30. Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks

Author

Baxter, G. J., Dorogovtsev, S. N., Goltsev, A. V., and Mendes, J. F. F.

Subjects
Condensed Matter - Statistical Mechanics, Mathematical Physics, Mathematics - Probability
Abstract

We introduce the heterogeneous-$k$-core, which generalizes the $k$-core, and contrast it with bootstrap percolation. Vertices have a threshold $k_i$ which may be different at each vertex. If a vertex has less than $k_i$ neighbors it is pruned from the network. The heterogeneous-$k$-core is the sub-graph remaining after no further vertices can be pruned. If the thresholds $k_i$ are $1$ with probability $f$ or $k \geq 3$ with probability $(1-f)$, the process forms one branch of an activation-pruning process which demonstrates hysteresis. The other branch is formed by ordinary bootstrap percolation. We show that there are two types of transitions in this heterogeneous-$k$-core process: the giant heterogeneous-$k$-core may appear with a continuous transition and there may be a second, discontinuous, hybrid transition. We compare critical phenomena, critical clusters and avalanches at the heterogeneous-$k$-core and bootstrap percolation transitions. We also show that network structure has a crucial effect on these processes, with the giant heterogeneous-$k$-core appearing immediately at a finite value for any $f > 0$ when the degree distribution tends to a power law $P(q) \sim q^{-\gamma}$ with $\gamma < 3$., Comment: 10 pages, 4 figures

Published
2010
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31. Bootstrap Percolation on Complex Networks

Author

Baxter, G J, Dorogovtsev, S N, Goltsev, A V, and Mendes, J F F

Subjects
Condensed Matter - Statistical Mechanics, Mathematical Physics, Mathematics - Probability, Physics - Physics and Society
Abstract

We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: $f$, the fraction of vertices initially activated, and $p$, the fraction of undamaged vertices in the graph. We observe two transitions: the giant active component appears continuously at a first threshold. There may also be a second, discontinuous, hybrid transition at a higher threshold. Avalanches of activations increase in size as this second critical point is approached, finally diverging at this threshold. We describe the existence of a special critical point at which this second transition first appears. In networks with degree distributions whose second moment diverges (but whose first moment does not), we find a qualitatively different behavior. In this case the giant active component appears for any $f>0$ and $p>0$, and the discontinuous transition is absent. This means that the giant active component is robust to damage, and also is very easily activated. We also formulate a generalized bootstrap process in which each vertex can have an arbitrary threshold., Comment: 9 pages, 3 figures

Published
2010
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32. Long COVID research: an update from the PHOSP-COVID Scientific Summit

Author

Brightling, Christopher E, primary, Evans, Rachael A, additional, Singapuri, Amisha, additional, Smith, Nikki, additional, Wain, Louise V, additional, Brightling, C E, additional, Evans, R A, additional, Wain, L V, additional, Chalmers, J D, additional, Harris, V C, additional, Ho, L P, additional, Horsley, A, additional, Houchen-Wolloff, L, additional, Marks, M, additional, Raman, B, additional, Singapuri, A, additional, Barran, P, additional, Bingham, M, additional, Chilvers, E R, additional, Daynes, E, additional, Efstathiou, C M, additional, Elneima, O, additional, Guillen Guio, B, additional, Harrison, E M, additional, Jenkins, R G, additional, Liew, F, additional, Lone, N I, additional, Lord, J M, additional, McAuley, H J C, additional, McCann, G P, additional, Mitchell, J, additional, Plekhanova, T, additional, Russell, R J, additional, Saunders, R M, additional, Semple, M G, additional, Smith, N, additional, Trivedi, D, additional, Turtle, L, additional, Walker, S, additional, Abel, K, additional, Adamali, H, additional, Adeloye, D, additional, Adeyemi, O, additional, Adrego, R, additional, Aguilar Jimenez, L A, additional, Ahmad, S, additional, Ahmad Haider, N, additional, Ahmed, R, additional, Ahwireng, N, additional, Ainsworth, M, additional, Al-Sheklly, B, additional, Alamoudi, A, additional, Ali, M, additional, Aljaroof, M, additional, Allan, L, additional, Allen, R J, additional, Allerton, L, additional, Allsop, L, additional, Allt, AM, additional, Almeida, P, additional, Altmann, D, additional, Alvarez Corral, M, additional, Amoils, S, additional, Anderson, D, additional, Antoniades, C, additional, Arbane, G, additional, Arias, A, additional, Armour, C, additional, Armstrong, L, additional, Armstrong, N, additional, Arnold, D, additional, Arnold, H, additional, Ashish, A, additional, Ashworth, A, additional, Ashworth, M, additional, Aslani, S, additional, Assefa-Kebede, H, additional, Atkin, P, additional, Atkin, C, additional, Aul, R, additional, Aung, H, additional, Austin, L, additional, Avram, C, additional, Ayoub, A, additional, Babores, M, additional, Baggott, R, additional, Bagshaw, J, additional, Baguley, D, additional, Bailey, L, additional, Baillie, J K, additional, Bain, S, additional, Bakali, M, additional, Bakau, M, additional, Baldry, E, additional, Baldwin, M, additional, Baldwin, D, additional, Ballard, C, additional, Banerjee, A, additional, Bang, D, additional, Barker, R E, additional, Barman, L, additional, Barratt, S, additional, Barrett, F, additional, Basire, D, additional, Basu, N, additional, Bates, M, additional, Bates, A, additional, Batterham, R, additional, Baxendale, H, additional, Baxter, G, additional, Bayes, H, additional, Beadsworth, M, additional, Beckett, P, additional, Beggs, M, additional, Begum, M, additional, Beirne, P, additional, Bell, M, additional, Bell, R, additional, Bennett, K, additional, Beranova, E, additional, Bermperi, A, additional, Berridge, A, additional, Berry, C, additional, Betts, S, additional, Bevan, E, additional, Bhui, K, additional, Birchall, K, additional, Bishop, L, additional, Bisnauthsing, K, additional, Blaikely, J, additional, Bloss, A, additional, Bolger, A, additional, Bolton, C E, additional, Bonnington, J, additional, Botkai, A, additional, Bourne, C, additional, Bourne, M, additional, Bramham, K, additional, Brear, L, additional, Breen, G, additional, Breeze, J, additional, Breeze, K, additional, Briggs, A, additional, Bright, E, additional, Brill, S, additional, Brindle, K, additional, Broad, L, additional, Broadley, A, additional, Brookes, C, additional, Broome, M, additional, Brown, V, additional, Brown, M, additional, Brown, J, additional, Brown, A, additional, Brown, J S, additional, Brugha, T, additional, Brunskill, N, additional, Buch, M, additional, Buckley, P, additional, Bularga, A, additional, Bullmore, E, additional, Bunker, J, additional, Burden, L, additional, Burdett, T, additional, Burn, D, additional, Burns, G, additional, Burns, A, additional, Busby, J, additional, Butcher, R, additional, Butt, A, additional, Byrne, S, additional, Cairns, P, additional, Calder, P C, additional, Calvelo, E, additional, Carborn, H, additional, Card, B, additional, Carr, C, additional, Carr, L, additional, Carson, G, additional, Carter, P, additional, Casey, A, additional, Cassar, M, additional, Cavanagh, J, additional, Chablani, M, additional, Chalder, T, additional, Chambers, R C, additional, Chan, F, additional, Channon, K M, additional, Chapman, K, additional, Charalambou, A, additional, Chaudhuri, N, additional, Checkley, A, additional, Chen, J, additional, Cheng, Y, additional, Chetham, L, additional, Childs, C, additional, Chinoy, H, additional, Chiribiri, A, additional, Chong-James, K, additional, Choudhury, N, additional, Choudhury, G, additional, Chowienczyk, P, additional, Christie, C, additional, Chrystal, M, additional, Clark, C, additional, Clark, D, additional, Clarke, J, additional, Clohisey, S, additional, Coakley, G, additional, Coburn, Z, additional, Coetzee, S, additional, Cole, J, additional, Coleman, C, additional, Conneh, F, additional, Connell, D, additional, Connolly, B, additional, Connor, L, additional, Cook, A, additional, Cooper, S, additional, Cooper, B, additional, Cooper, J, additional, Copeland, D, additional, Cosier, T, additional, Coulding, M, additional, Coupland, C, additional, Cox, E, additional, Craig, T, additional, Crisp, P, additional, Cristiano, D, additional, Crooks, M G, additional, Cross, A, additional, Cruz, I, additional, Cullinan, P, additional, Cuthbertson, D, additional, Daines, L, additional, Dalton, M, additional, Daly, P, additional, Daniels, A, additional, Dark, P, additional, Dasgin, J, additional, David, C, additional, David, A, additional, Davies, F, additional, Davies, E, additional, Davies, K, additional, Davies, G, additional, Davies, G A, additional, Davies, M J, additional, Dawson, J, additional, Dawson, C, additional, De Soyza, A, additional, Deakin, B, additional, Deans, A, additional, Deas, C, additional, Deery, J, additional, Defres, S, additional, Dell, A, additional, Dempsey, K, additional, Denneny, E, additional, Dennis, J, additional, Dewar, A, additional, Dharmagunawardena, R, additional, Diar-Bakerly, N, additional, Dickens, C, additional, Dipper, A, additional, Diver, S, additional, Diwanji, S N, additional, Dixon, M, additional, Djukanovic, R, additional, Dobson, H, additional, Dobson, S L, additional, Docherty, A B, additional, Donaldson, A, additional, Dong, T, additional, Dormand, N, additional, Dougherty, A, additional, Dowling, R, additional, Drain, S, additional, Draxlbauer, K, additional, Drury, K, additional, Dulawan, P, additional, Dunleavy, A, additional, Dunn, S, additional, Dupont, C, additional, Earley, J, additional, Easom, N, additional, Echevarria, C, additional, Edwards, S, additional, Edwardson, C, additional, El-Taweel, H, additional, Elliott, A, additional, Elliott, K, additional, Ellis, Y, additional, Elmer, A, additional, Evans, T, additional, Evans, R I, additional, Evans, D, additional, Evans, R, additional, Evans, H, additional, Evans, J, additional, Evenden, C, additional, Evison, L, additional, Fabbri, L, additional, Fairbairn, S, additional, Fairman, A, additional, Fallon, K, additional, Faluyi, D, additional, Favager, C, additional, Fayzan, T, additional, Featherstone, J, additional, Felton, T, additional, Ferreira, V, additional, Finch, J, additional, Finney, S, additional, Finnigan, J, additional, Finnigan, L, additional, Fisher, H, additional, Fletcher, S, additional, Flockton, R, additional, Flynn, M, additional, Foot, H, additional, Foote, D, additional, Ford, A, additional, Forton, D, additional, Fraile, E, additional, Francis, C, additional, Francis, R, additional, Francis, S, additional, Frankel, A, additional, Fraser, E, additional, Free, R, additional, French, N, additional, Fu, X, additional, Fuld, J, additional, Furniss, J, additional, Garner, L, additional, Gautam, N, additional, Geddes, J R, additional, George, J, additional, George, P, additional, Gibbons, M, additional, Gill, R, additional, Gill, M, additional, Gilmour, L, additional, Gleeson, F, additional, Glossop, J, additional, Glover, S, additional, Goodman, N, additional, Goodwin, C, additional, Gooptu, B, additional, Gordon, H, additional, Gorsuch, T, additional, Greatorex, M, additional, Greenhaff, P L, additional, Greenhalf, W, additional, Greenhalgh, A, additional, Greening, N J, additional, Greenwood, J, additional, Gregory, R, additional, Gregory, H, additional, Grieve, D, additional, Griffin, D, additional, Griffiths, L, additional, Guerdette, A-M, additional, Gummadi, M, additional, Gupta, A, additional, Gurram, S, additional, Guthrie, E, additional, Guy, Z, additional, Hadley, K, additional, Haggar, A, additional, Hainey, K, additional, Hairsine, B, additional, Haldar, P, additional, Hall, L, additional, Hall, I, additional, 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additional, Jastrub, R, additional, Jayaraman, B, additional, Jezzard, P, additional, Jiwa, K, additional, Johnson, C, additional, Johnson, S, additional, Johnston, D, additional, Jolley, C J, additional, Jones, S, additional, Jones, H, additional, Jones, L, additional, Jones, I, additional, Jones, G, additional, Jones, M G, additional, Jones, D, additional, Jose, S, additional, Kabir, T, additional, Kaltsakas, G, additional, Kamwa, V, additional, Kanellakis, N, additional, Kaprowska, S, additional, Kausar, Z, additional, Keenan, N, additional, Kelly, S, additional, Kemp, G, additional, Kerr, S, additional, Kerslake, H, additional, Key, A L, additional, Khan, F, additional, Khunti, K, additional, Kilroy, S, additional, King, B, additional, King, C, additional, Kingham, L, additional, Kirk, J, additional, Kitterick, P, additional, Klenerman, P, additional, Knibbs, L, additional, Knight, S, additional, Knighton, A, additional, Kon, O, additional, Kon, S, additional, Kon, S S, additional, 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additional, Mills, G, additional, Milner, L, additional, Misra, S, additional, Mohamed, A, additional, Mohamed, N, additional, Mohammed, S, additional, Molyneaux, P L, additional, Monteiro, W, additional, Moriera, S, additional, Morley, A, additional, Morrison, L, additional, Morriss, R, additional, Morrow, A, additional, Moss, P, additional, Moss, A J, additional, Motohashi, K, additional, Msimanga, N, additional, Mukaetova-Ladinska, E, additional, Munawar, U, additional, Murira, J, additional, Nanda, U, additional, Nassa, H, additional, Nasseri, M, additional, Nathu, R, additional, Neal, A, additional, Needham, R, additional, Neill, P, additional, Neubauer, S, additional, Newby, D E, additional, Newell, H, additional, Newman, J, additional, Newman, T, additional, Newton-Cox, A, additional, Nichols, T E, additional, Nicholson, T, additional, Nicolaou, C, additional, Nicoll, D, additional, Nikolaidis, A, additional, Nikolaidou, C, additional, Nolan, C M, additional, Noonan, M J, additional, Norman, C, additional, Novotny, P, additional, Nunag, J L, additional, Nwafor, L, additional, Nwanguma, U, additional, Nyaboko, J, additional, O'Brien, C, additional, O'Donnell, K, additional, O'Regan, D P, additional, O'Brien, L, additional, Odell, N, additional, Ogbole, G, additional, Ogg, G, additional, Olaosebikan, O, additional, Oliver, C, additional, Omar, Z, additional, Openshaw, P J M, additional, Orriss-Dib, L, additional, Osborne, L, additional, Osbourne, R, additional, Ostermann, M, additional, Overton, C, additional, Owen, J, additional, Oxton, J, additional, Pack, J, additional, Pacpaco, E, additional, Paddick, S, additional, Painter, S, additional, Pakzad, A, additional, Palmer, S, additional, Papineni, P, additional, Paques, K, additional, Paradowski, K, additional, Pareek, M, additional, Parekh, D, additional, Parfrey, H, additional, Pariante, C, additional, Parker, S, additional, Parkes, M, additional, Parmar, J, additional, Patale, S, additional, Patel, M, 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M, additional, Vere, J, additional, Vickers, C, additional, Vinson, B, additional, Vogiatzis, I, additional, Wade, E, additional, Wade, P, additional, Wainwright, T, additional, Wajero, L O, additional, Walder, S, additional, Wall, E, additional, Wallis, T, additional, Walmsley, S, additional, Walsh, S, additional, Walsh, J A, additional, Warburton, L, additional, Ward, T J C, additional, Warwick, K, additional, Wassall, H, additional, Waterson, S, additional, Watson, L, additional, Watson, E, additional, Watson, J, additional, Webster, M, additional, Weir McCall, J, additional, Welch, H, additional, Welch, C, additional, Welsh, B, additional, Wessely, S, additional, West, S, additional, Weston, H, additional, Wheeler, H, additional, White, S, additional, Whitehead, V, additional, Whitney, J, additional, Whittaker, S, additional, Whittam, B, additional, Whitworth, V, additional, Wight, A, additional, Wild, J M, additional, Wilkins, M, additional, Wilkinson, D, additional, Williams, N, 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Published
2023
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33. Software graphs and programmer awareness

Author

Baxter, G. J. and Frean, M. R.

Subjects
Computer Science - Software Engineering, Computer Science - Programming Languages
Abstract

Dependencies between types in object-oriented software can be viewed as directed graphs, with types as nodes and dependencies as edges. The in-degree and out-degree distributions of such graphs have quite different forms, with the former resembling a power-law distribution and the latter an exponential distribution. This effect appears to be independent of application or type relationship. A simple generative model is proposed to explore the proposition that the difference arises because the programmer is aware of the out-degree of a type but not of its in-degree. The model reproduces the two distributions, and compares reasonably well to those observed in 14 different type relationships across 12 different Java applications., Comment: 9 pages, 8 figures

Published
2008

34. Fixation and consensus times on a network: a unified approach

Author

Baxter, G. J., Blythe, R. A., and McKane, A. J.

Subjects
Condensed Matter - Statistical Mechanics, Physics - Physics and Society, Quantitative Biology - Quantitative Methods
Abstract

We investigate a set of stochastic models of biodiversity, population genetics, language evolution and opinion dynamics on a network within a common framework. Each node has a state, 0 < x_i < 1, with interactions specified by strengths m_{ij}. For any set of m_{ij} we derive an approximate expression for the mean time to reach fixation or consensus (all x_i=0 or 1). Remarkably in a case relevant to language change this time is independent of the network structure., Comment: 4+epsilon pages, two-column, RevTeX4, 3 eps figures; version accepted by Phys. Rev. Lett

Published
2008
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35. Utterance Selection Model of Language Change

Author

Baxter, G. J., Blythe, R. A., Croft, W., and McKane, A. J.

Subjects
Condensed Matter - Statistical Mechanics, Physics - Physics and Society
Abstract

We present a mathematical formulation of a theory of language change. The theory is evolutionary in nature and has close analogies with theories of population genetics. The mathematical structure we construct similarly has correspondences with the Fisher-Wright model of population genetics, but there are significant differences. The continuous time formulation of the model is expressed in terms of a Fokker-Planck equation. This equation is exactly soluble in the case of a single speaker and can be investigated analytically in the case of multiple speakers who communicate equally with all other speakers and give their utterances equal weight. Whilst the stationary properties of this system have much in common with the single-speaker case, time-dependent properties are richer. In the particular case where linguistic forms can become extinct, we find that the presence of many speakers causes a two-stage relaxation, the first being a common marginal distribution that persists for a long time as a consequence of ultimate extinction being due to rare fluctuations., Comment: 21 pages, 17 figures

Published
2005
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36. Exact Solution of the Multi-Allelic Diffusion Model

Author

Baxter, G., Blythe, R. A., and McKane, A. J.

Subjects
Quantitative Biology - Populations and Evolution, Condensed Matter - Statistical Mechanics
Abstract

We give an exact solution to the Kolmogorov equation describing genetic drift for an arbitrary number of alleles at a given locus. This is achieved by finding a change of variable which makes the equation separable, and therefore reduces the problem with an arbitrary number of alleles to the solution of a set of equations that are essentially no more complicated than that found in the two-allele case. The same change of variable also renders the Kolmogorov equation with the effect of mutations added separable, as long as the mutation matrix has equal entries in each row. Thus this case can also be solved exactly for an arbitrary number of alleles. The general solution, which is in the form of a probability distribution, is in agreement with the previously known results--which were for the cases of two and three alleles only. Results are also given for a wide range of other quantities of interest, such as the probabilities of extinction of various numbers of alleles, mean times to these extinctions, and the means and variances of the allele frequencies. To aid dissemination, these results are presented in two stages: first of all they are given without derivations and too much mathematical detail, and then subsequently derivations and a more technical discussion are provided., Comment: 56 pages. 15 figures. Requires Elsevier document class

Published
2005
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48. Avalanches in Multiplex and Interdependent Networks

Author

Baxter, G. J., Dorogovtsev, S. N., Goltsev, A. V., Mendes, J. F. F., Abarbanel, Henry, Series editor, Braha, Dan, Series editor, Érdi, Péter, Series editor, Friston, Karl, Series editor, Haken, Hermann, Series editor, Jirsa, Viktor, Series editor, Kacprzyk, Janusz, Series editor, Kaneko, Kunihiko, Series editor, Kelso, Scott, Series editor, Kirkilionis, Markus, Series editor, Kurths, Jürgen, Series editor, Nowak, Andrzej, Series editor, Reichl, Linda, Series editor, Schuster, Peter, Series editor, Schweitzer, Frank, Series editor, Sornette, Didier, Series editor, Thurner, Stefan, Series editor, D'Agostino, Gregorio, editor, and Scala, Antonio, editor

Published
2014
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