Spread of Infectious Diseases with a Latent Period

Infectious diseases spread through human networks. Susceptible-Infected-Removed (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node represents a population (group) which has many individuals. In this paper, we propose a modified metapopulation SIR model in which a latent period is taken into account. We call it SIIR model. We divide the infection period into two stages: an infected stage, which is the same as the previous model, and a seriously ill stage, in which individuals are infected and cannot move to the other populations. The two infectious stages in our modified metapopulation SIR model produce a discontinuous final size distribution. Individuals in the infected stage spread the disease like individuals in the seriously ill stage and never recover directly, which makes an effective recovery rate smaller than the given recovery rate.Comment: 6 pages, 3 figure

Coordinated optimization of visual cortical maps (I) Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of OP columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about an hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference.Comment: 90 pages, 16 figure

Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Integrating association data and disease dynamics in a social ungulate: bovine tuberculosis in African buffalo in the Kruger National Park

Recognition is a prerequisite for non-random association amongst individuals. We explore how non-random association patterns (i.e. who spends time with whom) affect disease dynamics. We estimated the amount of time individuals spent together per month using radio-tracking data from African buffalo and incorporated these data into a dynamic social network model. The dynamic nature of the network has a strong influence on simulated disease dynamics particularly for diseases with shorter infectious periods. Cluster analyses of the association data demonstrated that buffalo herds were not as well defined as previously thought. Associations were more tightly clustered in 2002 than 2003, perhaps due to drier conditions in 2003. As a result, diseases may spread faster during drought conditions due to increased population mixing. Association data are often collected but this is the first use of empirical data in a network disease model in a wildlife population

The Origin of Minus-end Directionality and Mechanochemistry of Ncd Motors

Adaptation of molecular structure to the ligand chemistry and interaction with the cytoskeletal filament are key to understanding the mechanochemistry of molecular motors. Despite the striking structural similarity with kinesin-1, which moves towards plus-end, Ncd motors exhibit minus-end directionality on microtubules (MTs). Here, by employing a structure-based model of protein folding, we show that a simple repositioning of the neck-helix makes the dynamics of Ncd non-processive and minus-end directed as opposed to kinesin-1. Our computational model shows that Ncd in solution can have both symmetric and asymmetric conformations with disparate ADP binding affinity, also revealing that there is a strong correlation between distortion of motor head and decrease in ADP binding affinity in the asymmetric state. The nucleotide (NT) free-ADP (?-ADP) state bound to MTs favors the symmetric conformation whose coiled-coil stalk points to the plus-end. Upon ATP binding, an enhanced flexibility near the head-neck junction region, which we have identified as the important structural element for directional motility, leads to reorienting the coiled-coil stalk towards the minus-end by stabilizing the asymmetric conformation. The minus-end directionality of the Ncd motor is a remarkable example that demonstrates how motor proteins in the kinesin superfamily diversify their functions by simply rearranging the structural elements peripheral to the catalytic motor head domain

Levels of DNA methylation vary at CpG sites across the BRCA1 promoter, and differ according to triple negative and "BRCA-like" status, in both blood and tumour DNA

Triple negative breast cancer is typically an aggressive and difficult to treat subtype. It is often associated with loss of function of the BRCA1 gene, either through mutation, loss of heterozygosity or methylation. This study aimed to measure methylation of the BRCA1 gene promoter at individual CpG sites in blood, tumour and normal breast tissue, to assess whether levels were correlated between different tissues, and with triple negative receptor status, histopathological scoring for BRCA-like features and BRCA1 protein expression. Blood DNA methylation levels were significantly correlated with tumour methylation at 9 of 11 CpG sites examined (p<0.0007). The levels of tumour DNA methylation were significantly higher in triple negative tumours, and in tumours with high BRCA-like histopathological scores (10 of 11 CpG sites; p<0.01 and p<0.007 respectively). Similar results were observed in blood DNA (6 of 11 CpG sites; p<0.03 and 7 of 11 CpG sites; p<0.02 respectively). This study provides insight into the pattern of CpG methylation across the BRCA1 promoter, and supports previous studies suggesting that tumours with BRCA1 promoter methylation have similar features to those with BRCA1 mutations, and therefore may be suitable for the same targeted therapies

'Collective Making' as knowledge mobilisation: the contribution of participatory design in the co-creation of knowledge in healthcare

The discourse in healthcare Knowledge Mobilisation (KMb) literature has shifted from simple, linear models of research knowledge production and action to more iterative and complex models. These aim to blend multiple stakeholders’ knowledge with research knowledge to address the researchpractice gap. It has been suggested there is no 'magic bullet', but that a promising approach to take is knowledge co-creation in healthcare, particularly if a number of principles are applied. These include systems thinking, positioning research as a creative enterprise with human experience at its core, and paying attention to process within the partnership. This discussion paper builds on this proposition and extends it beyond knowledge co-creation to co-designing evidenced based interventions and implementing them. Within a co-design model, we offer a specific approach to share, mobilise and activate knowledge, that we have termed 'collective making'. We draw on KMb, design, wider literature, and our experiences to describe how this framework supports and extends the principles of co-creation offered by Geenhalgh et al[1] in the context of the state of the art of knowledge mobilisation. We describe how collective making creates the right ‘conditions’ for knowledge to be mobilised particularly addressing issues relating to stakeholder relationships, helps to discover, share and blend different forms of knowledge from different stakeholders, and puts this blended knowledge to practical use allowing stakeholders to learn about the practical implications of knowledge use and to collectively create actionable products. We suggest this collective making has three domains of influence: on the participants; on the knowledge discovered and shared; and on the mobilisation or activation of this knowledge