Royal Society Open Science Mathematics
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Royal Society Open Science RSS feed -- recent Mathematics articles2054-5703Royal Society Open Science<![CDATA[Integrating sentiment and social structure to determine preference alignments: the Irish Marriage Referendum]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/7/170154?rss=1
We examine the relationship between social structure and sentiment through the analysis of a large collection of tweets about the Irish Marriage Referendum of 2015. We obtain the sentiment of every tweet with the hashtags #marref and #marriageref that was posted in the days leading to the referendum, and construct networks to aggregate sentiment and use it to study the interactions among users. Our analysis shows that the sentiment of outgoing mention tweets is correlated with the sentiment of incoming mentions, and there are significantly more connections between users with similar sentiment scores than among users with opposite scores in the mention and follower networks. We combine the community structure of the follower and mention networks with the activity level of the users and sentiment scores to find groups that support voting ‘yes’ or ‘no’ in the referendum. There were numerous conversations between users on opposing sides of the debate in the absence of follower connections, which suggests that there were efforts by some users to establish dialogue and debate across ideological divisions. Our analysis shows that social structure can be integrated successfully with sentiment to analyse and understand the disposition of social media users around controversial or polarizing issues. These results have potential applications in the integration of data and metadata to study opinion dynamics, public opinion modelling and polling.
]]>2017-07-12T00:08:29-07:00info:doi/10.1098/rsos.170154hwp:master-id:royopensci;rsos.1701542017-07-12Mathematics47170154170154<![CDATA[Population patterns in Worlds administrative units]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/7/170281?rss=1
Whereas there has been an extended discussion concerning city population distribution, little has been said about that of administrative divisions. In this work, we investigate the population distribution of second-level administrative units of 150 countries and territories and propose the discrete generalized beta distribution (DGBD) rank-size function to describe the data. After testing the balance between the goodness of fit and number of parameters of this function compared with a power law, which is the most common model for city population, the DGBD is a good statistical model for 96% of our datasets and preferred over a power law in almost every case. Moreover, the DGBD is preferred over a power law for fitting country population data, which can be seen as the zeroth-level administrative unit. We present a computational toy model to simulate the formation of administrative divisions in one dimension and give numerical evidence that the DGBD arises from a particular case of this model. This model, along with the fitting of the DGBD, proves adequate in reproducing and describing local unit evolution and its effect on the population distribution.
]]>2017-07-05T00:08:13-07:00info:doi/10.1098/rsos.170281hwp:master-id:royopensci;rsos.1702812017-07-05Mathematics47170281170281<![CDATA[A quantum Samaritans dilemma cellular automaton]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/6/160669?rss=1
The dynamics of a spatial quantum formulation of the iterated Samaritan’s dilemma game with variable entangling is studied in this work. The game is played in the cellular automata manner, i.e. with local and synchronous interaction. The game is assessed in fair and unfair contests, in noiseless scenarios and with disrupting quantum noise.
]]>2017-06-14T00:39:50-07:00info:doi/10.1098/rsos.160669hwp:master-id:royopensci;rsos.1606692017-06-14Mathematics46160669160669<![CDATA[Drug delivery in a tumour cord model: a computational simulation]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/5/170014?rss=1
The tumour vasculature and microenvironment is complex and heterogeneous, contributing to reduced delivery of cancer drugs to the tumour. We have developed an in silico model of drug transport in a tumour cord to explore the effect of different drug regimes over a 72 h period and how changes in pharmacokinetic parameters affect tumour exposure to the cytotoxic drug doxorubicin. We used the model to describe the radial and axial distribution of drug in the tumour cord as a function of changes in the transport rate across the cell membrane, blood vessel and intercellular permeability, flow rate, and the binding and unbinding ratio of drug within the cancer cells. We explored how changes in these parameters may affect cellular exposure to drug. The model demonstrates the extent to which distance from the supplying vessel influences drug levels and the effect of dosing schedule in relation to saturation of drug-binding sites. It also shows the likely impact on drug distribution of the aberrant vasculature seen within tumours. The model can be adapted for other drugs and extended to include other parameters. The analysis confirms that computational models can play a role in understanding novel cancer therapies to optimize drug administration and delivery.
]]>2017-05-24T00:08:06-07:00info:doi/10.1098/rsos.170014hwp:master-id:royopensci;rsos.1700142017-05-24Mathematics45170014170014<![CDATA[The contact process on scale-free networks evolving by vertex updating]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/5/170081?rss=1
We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all infection rates the infection survives for a long time, at least exponential in the network size, and a phase where for sufficiently small infection rates extinction occurs quickly, at most polynomially in the network size. The phase transition occurs when the power-law exponent crosses the value four. This behaviour is in contrast with that of the contact process on the corresponding static model, where there is no phase transition, as well as that of a classical mean-field approximation, which has a phase transition at power-law exponent three. The new observation behind our result is that temporal variability of networks can simultaneously increase the rate at which the infection spreads in the network, and decrease the time at which the infection spends in metastable states.
]]>2017-05-24T00:08:00-07:00info:doi/10.1098/rsos.170081hwp:master-id:royopensci;rsos.1700812017-05-24Mathematics45170081170081<![CDATA[Classification of self-assembling protein nanoparticle architectures for applications in vaccine design]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/4/161092?rss=1
We introduce here a mathematical procedure for the structural classification of a specific class of self-assembling protein nanoparticles (SAPNs) that are used as a platform for repetitive antigen display systems. These SAPNs have distinctive geometries as a consequence of the fact that their peptide building blocks are formed from two linked coiled coils that are designed to assemble into trimeric and pentameric clusters. This allows a mathematical description of particle architectures in terms of bipartite (3,5)-regular graphs. Exploiting the relation with fullerene graphs, we provide a complete atlas of SAPN morphologies. The classification enables a detailed understanding of the spectrum of possible particle geometries that can arise in the self-assembly process. Moreover, it provides a toolkit for a systematic exploitation of SAPNs in bioengineering in the context of vaccine design, predicting the density of B-cell epitopes on the SAPN surface, which is critical for a strong humoral immune response.
]]>2017-04-26T00:53:58-07:00info:doi/10.1098/rsos.161092hwp:master-id:royopensci;rsos.1610922017-04-26Mathematics44161092161092<![CDATA[Optimal strategies for throwing accurately]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/4/170136?rss=1
The accuracy of throwing in games and sports is governed by how errors in planning and initial conditions are propagated by the dynamics of the projectile. In the simplest setting, the projectile path is typically described by a deterministic parabolic trajectory which has the potential to amplify noisy launch conditions. By analysing how parabolic trajectories propagate errors, we show how to devise optimal strategies for a throwing task demanding accuracy. Our calculations explain observed speed–accuracy trade-offs, preferred throwing style of overarm versus underarm, and strategies for games such as dart throwing, despite having left out most biological complexities. As our criteria for optimal performance depend on the target location, shape and the level of uncertainty in planning, they also naturally suggest an iterative scheme to learn throwing strategies by trial and error.
]]>2017-04-26T00:05:43-07:00info:doi/10.1098/rsos.170136hwp:master-id:royopensci;rsos.1701362017-04-26Mathematics44170136170136<![CDATA[On strongly connected networks with excitable-refractory dynamics and delayed coupling]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/4/160912?rss=1
We consider a directed graph model for the human brain’s neural architecture that is based on small scale, directed, strongly connected sub-graphs (SCGs) of neurons, that are connected together by a sparser mesoscopic network. We assume transmission delays within neuron-to-neuron stimulation, and that individual neurons have an excitable-refractory dynamic, with single firing ‘spikes’ occurring on a much faster time scale than that of the transmission delays. We demonstrate numerically that the SCGs typically have attractors that are equivalent to continual winding maps over relatively low-dimensional tori, thus representing a limit on the range of distinct behaviour. For a discrete formulation, we conduct a large-scale survey of SCGs of varying size, but with the same local structure. We demonstrate that there may be benefits (increased processing capacity and efficiency) in brains having evolved to have a larger number of small irreducible sub-graphs, rather than few, large irreducible sub-graphs. The network of SCGs could be thought of as an architecture that has evolved to create decisions in the light of partial or early incoming information. Hence the applicability of the proposed paradigm to underpinning human cognition.
]]>2017-04-05T00:05:32-07:00info:doi/10.1098/rsos.160912hwp:master-id:royopensci;rsos.1609122017-04-05Mathematics44160912160912