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Royal Society Open Science RSS feed -- recent Mathematics articles2054-5703Royal Society Open Science<![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<![CDATA[Suicides on the Austrian railway network: hotspot analysis and effect of proximity to psychiatric institutions]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/3/160711?rss=1
Railway suicide is a significant public health problem. In addition to the loss of lives, these suicides occur in public space, causing traumatization among train drivers and passengers, and significant public transport delays. Prevention efforts depend upon accurate knowledge of clustering phenomena across the railway network, and spatial risk factors. Factors such as proximity to psychiatric institutions have been discussed to impact on railway suicides, but analytic evaluations are scarce and limited. We identify 15 hotspots on the Austrian railway system while taking case location uncertainties into account. These hotspots represent 0.9% of the total track length (5916 km/3676 miles) that account for up to 17% of all railway suicides (N=1130). We model suicide locations on the network using a smoothed inhomogeneous Poisson process and validate it using randomization tests. We find that the density of psychiatric beds is a significant predictor of railway suicide. Further predictors are population density, multitrack structure and—less consistently—spatial socio-economic factors including total suicide rates. We evaluate the model for the identified hotspots and show that the actual influence of these variables differs across individual hotspots. This analysis provides important information for suicide prevention research and practice. We recommend structural separation of railway tracks from nearby psychiatric institutions to prevent railway suicide.
]]>2017-03-08T00:05:29-08:00info:doi/10.1098/rsos.160711hwp:master-id:royopensci;rsos.1607112017-03-08Mathematics43160711160711<![CDATA[The elastic theory of shells using geometric algebra]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/3/170065?rss=1
We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible.
]]>2017-03-08T00:05:29-08:00info:doi/10.1098/rsos.170065hwp:master-id:royopensci;rsos.1700652017-03-08Mathematics43170065170065<![CDATA[Modelling human perception processes in pedestrian dynamics: a hybrid approach]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/3/160561?rss=1
In this paper, we present a hybrid mathematical model describing crowd dynamics. More specifically, our approach is based on the well-established Helbing-like discrete model, where each pedestrian is individually represented as a dimensionless point and set to move in order to reach a target destination, with deviations deriving from both physical and social forces. In particular, physical forces account for interpersonal collisions, whereas social components include the individual desire to remain sufficiently far from other walkers (the so-called territorial effect). In this respect, the repulsive behaviour of pedestrians is here set to be different from traditional Helbing-like methods, as it is assumed to be largely determined by how they perceive the presence and the position of neighbouring individuals, i.e. either objectively as pointwise/localized entities or subjectively as spatially distributed masses. The resulting modelling environment is then applied to specific scenarios, that first reproduce a real-world experiment, specifically designed to derive our model hypothesis. Sets of numerical realizations are also run to analyse in more details the pedestrian paths resulting from different types of perception of small groups of static individuals. Finally, analytical investigations formalize and validate from a mathematical point of view selected simulation outcomes.
]]>2017-03-01T01:27:27-08:00info:doi/10.1098/rsos.160561hwp:master-id:royopensci;rsos.1605612017-03-01Mathematics43160561160561