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One of the challenges in epidemiology is to account for the complex morphological structure of hosts such as plant roots, crop fields, farms, cells, animal habitats and social networks, when the transmission of infection occurs between contiguous hosts. Morphological complexity brings an inherent heterogeneity in populations and affects the dynamics of pathogen spread in such systems. We have analysed the influence of realistically complex host morphology on the threshold for invasion and epidemic outbreak in an SIR (susceptible–infected–recovered) epidemiological model. We show that disorder expressed in the host morphology and anisotropy reduces the probability of epidemic outbreak and thus makes the system more resistant to epidemic outbreaks. We obtain general analytical estimates for minimally safe bounds for an invasion threshold and then illustrate their validity by considering an example of host data for branching hosts (salamander retinal ganglion cells). Several spatial arrangements of hosts with different degrees of heterogeneity have been considered in order to separately analyse the role of shape complexity and anisotropy in the host population. The estimates for invasion threshold are linked to morphological characteristics of the hosts that can be used for determining the threshold for invasion in practical applications.
1. Introduction
One of the main questions in epidemiology regards the outbreak of epidemics, i.e. whether an infectious disease can spread throughout a given ensemble of hosts or not. Many systems display a threshold for epidemics which divides the parameter space into regions where an outbreak may occur from regions where the disease cannot spread (Marro & Dickman 1999; Murray 2002). Identification of the factors that determine such a threshold is of great importance in devising robust strategies to control the spread of disease through a population of susceptible hosts. Successful control deflects the system into the non-invasive region of parameter space so that a pathogen fails to invade. This simple concept can be applied to the spread of infection and disease, at a range of scales from the cellular, in which the host comprises a single cell, through populations of plants and animals in which a host equates with an individual organism, up to larger-scale systems, in which the unit of interest may be an individual field or farm for crop and livestock disease, a school, a village or other natural clustering for human disease. The challenge at each scale lies in dealing in a quantitative manner with factors such as stochasticity and heterogeneity, so that thresholds used to identify strategies for control are robust to these uncertainties. Stochasticity in disease spread is linked to the fact that susceptible hosts become infected only with a certain probability when challenged by inoculum from infected hosts under otherwise identical circumstances. Heterogeneity, on the other hand, is associated with a range of factors that may differ among hosts. These include disorder in characteristics such as pathogen infectivity and host susceptibility, and the spatial arrangement of hosts. For certain types of hosts, heterogeneity also includes the inherent morphological complexity (i.e. irregularity in shape) of the host. Morphological complexity is especially important in epidemiological spread where it affects the contact rate between contiguous hosts. Examples of morphologically complex hosts include dendritic cells and plants, crop fields and farms, and individual clusters in social networks (Boender et al. 2007; Davis et al. 2008; Eisinger & Thulke 2008; González et al. 2008; Soriano et al. 2008).
While the problem of disease invasion has been extensively studied, both experimentally and theoretically, most attention has been focused first on deterministic systems and increasingly on stochastic models (Murray 2002; Truscott & Gilligan 2003; Gibson et al. 2004). Heterogeneity has traditionally received less attention although there are some remarkable exceptions (e.g. Levin & Durrett 1996; Newman 2002; Sander et al. 2002, 2003; Cook et al. 2007; Boender et al. 2007; Kenah & Robins 2007; Miller 2007; Eisinger & Thulke 2008; Volz 2008). However, none of the previous work has established a link between heterogeneity and morphological features of the system leading to such a heterogeneity. In particular, the heterogeneity associated with the host morphology and the effects it may have on the features of the epidemics remain to be understood.
In systems where the pathogen is transmitted between hosts owing to their proximity, one can identify three main factors that determine the invasion threshold (see figure 1): (i) spatial arrangement of the hosts in the population, (ii) morphology, i.e. the shape of the hosts, and (iii) the infection efficiency resulting from the net effect of the interplay between the pathogen infectivity and the host susceptibility upon contact.
Several models have been proposed for the dynamics of epidemics spreading by contacts between hosts (Liggett 1985; Marro & Dickman 1999; Hinrichsen 2000; Murray 2002; Ódor 2004). In such models, the hosts can be in different states, e.g. susceptible (S), infected (I) and recovered (or removed) (R) in the prototype SIR epidemiological model. The state of each host may change according to certain model-dependent rules. For instance, the SIR model assumes that infected hosts can infect others that are susceptible and then become recovered and fully immune to further pathogen attacks. In such models, the stochasticity and heterogeneity for the spreading process are treated in a simplistic way by using phenomenological probability densities for relevant parameters and thus not linking the host morphology and invasion threshold.
In this paper, we establish a quantitative link between host morphology and the invasion threshold in an ensemble of hosts with realistically complex morphology. By analysing the conditions for epidemic outbreak in several systems with different degrees of configurational heterogeneity, we conclude that the invasion threshold is mainly determined by (i) the average overlap between neighbouring hosts, (ii) the morphological complexity of hosts, and (iii) the host shape anisotropy. In particular, we demonstrate analytically and numerically that the resilience of the system to invasion increases with morphological complexity and anisotropy of hosts. This result is valid under very general conditions and is therefore applicable to a wide range of host ensembles. We show that irrespective of the degree of the host anisotropy, the spreading process can be described in terms of a mean-field system, so that analytical estimates for the invasion threshold can be obtained. In addition, we complete our analysis by identifying several morphological characteristics that can be used for determining the threshold for invasion resulting in an epidemic outbreak.
2. Methods
We consider a set of N morphologically different branching structures, , placed on all nodes of an regular lattice with spacing a and nearest-neighbour links only (see table 1 for a summary of the notation used in the text). In particular, we deal with a triangular lattice (see figure 1) because this arrangement corresponds to the organization of hosts with the highest risk of epidemic spread, in the sense that any other two-dimensional regular lattices with the same lattice spacing is more resistant to epidemic invasion (Isichenko 1992; Stauffer & Aharony 1994). An additional advantage of the triangular lattice is that the next-nearest-neighbour links (ignored in our approach) are less likely in such a lattice as compared with other two-dimensional lattices. A certain spatial configuration of generally anisotropic branching structures is fully defined in terms of the set of hosts placed on the lattice nodes, (where is the host number placed on node i), and their orientations, . The system of hosts can be either homogeneous, if morphologically identical hosts, , of the same orientation, , are placed on the lattice, or heterogeneous if the hosts and/or their orientations are chosen, e.g. at random. Specifically, we consider three types of arrangements with different degrees of heterogeneity which allow the various factors contributing to the invasion threshold to be analysed separately.
— Arrangements 1. Both and are distributed according to uniform distributions so that all possible hosts and orientations are equally probable. These are highly disordered configurations.
— Arrangements 2. The same host is placed on all the nodes with the same orientation (i.e. and for all the nodes i). Such ordered arrangements highlight the role of the host anisotropy leading to different overlaps along different lattice directions.
— Arrangements 3. The same host is placed on all the nodes and its orientation is drawn from a uniform distribution of width and mean value . Such arrangements allow both the morphological complexity and anisotropy of hosts to be analysed in a comparative manner and they contain arrangements of type 2 as particular cases with and .
In order to investigate the spread of epidemics in such systems, we apply the dynamical rules of the SIR formalism. Infection and hence disease can be transmitted between infected and susceptible hosts with transmission rate β, and infected hosts recover after a fixed time τ. We assume that the value of τ is time independent, identical for all the hosts, and thus can be chosen as the time scale of the problem, . Such homogeneity in τ provides a minimally safe bound for the invasion threshold (Kuulasmaa 1982; Cox & Durrett 1988; see brief explanation in the electronic supplementary material).
The transmission of infection from an infected host, at node i, to a susceptible nearest neighbour, at node j, separated by a unit-cell vector a, is a Poisson process with a transmission rate . The value of is assumed to be proportional to the overlap between hosts i and j, i.e. , where k is the infection efficiency which accounts for the effectiveness of the overlap for transmission of infection. We shall set k to be identical for all the pairs of nearest neighbours. Possible variability in k can be easily incorporated into the model but it does not change the main results qualitatively.
The overlap between hosts is defined as 2.1 in terms of the host density, 2.2 where the position vector p scans all the points in the host structure .
One of the main quantities involved in the SIR process is the transmissibility defined as the probability that the pathogen is transmitted from an infected host at node i to infect a susceptible host located at node j during the lifetime, , of the infected node. For a Poisson process, the transmissibility is given by the following expression (Grassberger 1983): 2.3 Therefore, the value of depends on the lattice spacing, a, which determines the overlap, , and the infection efficiency, k.
In a finite-size population, the SIR process lasts for finite time and after its termination two types of hosts, R and S, can be found in the system. The region of the recovered hosts can be mapped onto one of the clusters in the bond-percolation problem by mapping the transmissibilities to the bond probabilities (Grassberger 1983). According to this mapping, the probability of invasion of disease starting from a single host, , is identified with the probability that this first infected host belongs to the infinite cluster of connected sites in the bond-percolation problem. The invasion threshold is formally defined as the boundary between the invasive and the non-invasive regimes characterized by and , respectively. This condition introduces a separatrix in the parameter space which can be given in terms of several (control) parameters of the system, such as, for example, the infection efficiency and lattice spacing. In terms of the infection efficiency, the invasion threshold is the value such that relatively small values of correspond to the non-invasive regime (i.e. ), while larger values, , describe the invasive domain (i.e. ). Similarly, the critical lattice spacing, , splits the range of lattice spacings into two regions: and corresponding to invasive and non-invasive regimes, respectively. The host morphology affects implicitly (through the overlaps between hosts ) both and . The morphological variability of the hosts together with the heterogeneity in their arrangement makes the set disperse in general. The overlap can then be regarded as a random variable 𝒥 taking the values . We will describe 𝒥 in terms of its average, 〈𝒥〉, and deviations from 〈𝒥〉 originated by its dispersion. Consequently, it is convenient to split the expression for invasion threshold into two contributions 2.4 where kc0 and Δk are associated with the average and the dispersion of 𝒥, respectively. For the spatial arrangements of branching hosts considered below, the source of dispersion in the overlaps is twofold: (i) V1, which is due to variability arising from complexity in the shapes of different hosts for arrangements of type 1 and (ii) V2, which is due to variability in shape anisotropy for arrangements of type 2. Correspondingly, the value of Δk can be split into two components, i.e. , where and . Both complexity and anisotropy contribute to dispersion of the overlaps for arrangements of type 3.
For numerical illustration and concreteness, in this paper we use a set of N () neurons (figure 1) corresponding to salamander retinal ganglion cells (Ascoli 2006), which are mostly planar, as typical representatives of complex branching structures. In this case, the vector p introduced in equation (2.2) scans all the pixels defining the digital image of each neuron. Technically, the δ-functions in equation (2.2) are replaced by Gaussians of width comparable with the pixel size. This broadening mimics the (diffusive) spreading of the pathogen around the host. While we are not aware of documented examples of pathogen transmission in these structures, they are representative of a broad class of structures that are known to transmit virus infections (e.g. Lavail et al. 1997; Ehrengruber et al. 2002; Chen et al. 2007; Samuel et al. 2007). The importance here is to use the published data on complex morphology to test the general methods introduced below.
3. Results
In this section, we analyse the invasion threshold resulting in each of the spatial arrangements listed above and propose morphological characteristics for description of the invasion threshold.
3.1. Arrangements 1. ni and ϕi random
The invasion probability in host arrangements of type 1 is presented in figure 2. In particular, the inset shows the dependence of the probability of invasion on the infection efficiency. The value of is zero at small values of k and becomes positive above the threshold, . As expected, increases with the distance between hosts (cf. the curves marked by different symbols in the inset), a, as the infection mechanism between neighbouring hosts should be more efficient in order to invade the system with larger lattice spacing. However, the curves for at different a collapse onto a single master curve (figure 2), if plotted as a function of an alternative control parameter, the average transmissibility, 〈𝒯 〉, which plays the same role as bond probability in the percolation problem (Sander et al. 2002, 2003). This statement was first demonstrated heuristically by Sander et al. (2002) for SIR processes with heterogeneous transmissibility. Indeed, it is easy to go beyond heuristic arguments and prove that the statement is valid if the transmissibilities are independent and self-averaging quantities (see demonstration in the electronic supplementary material, and Kuulasmaa 1982; Kenah & Robins 2007; Miller 2007, for cases in which the transmissibilities are not independent and such description is not appropriate). The collapse in figure 2 suggests that transmissibilities in arrangements of type 1 satisfy these conditions. In fact, the master curve defined by the collapse coincides with that obtained for the effective homogeneous 'mean-field' system with transmissibility 〈𝒯〉 between all the nearest neighbours (see the dashed curve in figure 2 which is identical for all lattice spacings). This means that the heterogeneous system is equivalent to a homogeneous mean-field one for which the invasion threshold can be determined in an efficient manner by solving the following equation: 3.1 where is the bond-percolation threshold in an infinite (i.e. ) triangular lattice (Isichenko 1992; Stauffer & Aharony 1994). The value of provides the minimally safe bound for invasion threshold in other two-dimensional lattices (Isichenko 1992; Stauffer & Aharony 1994). As the average 〈𝒯〉 converges very fast with L to its limiting value for , the value of estimated from equation (3.1) is representative for macroscopic systems. The dependence of infection efficiency on lattice spacing defines the phase boundary in the (k,a) plane (see solid circles in figure 3a) between the invasive and non-invasive regimes. The threshold provides the same separatrix.
The influence of the host morphology on the invasion threshold can be better understood by analysing the dependence of on the overlaps 𝒥. The first term in equation (2.4) can be found by solving equation (3.1) for the homogeneous system in which all the overlaps are replaced by its mean value, 〈𝒥〉, i.e. 3.2 It can be rigorously shown that the value of underestimates the threshold, i.e. (cf. circles and dashed line in figure 3b). To prove this inequality, we write the expression (3.1) in terms of the overlap as . Applying then the general inequality to the above relation, we obtain which reduces to after using the expression (3.2) for . This inequality implies that the contribution Δk to associated with the dispersion of the overlaps makes systems more resilient to epidemic invasion. An approximate solution of equation (3.1) obtained by keeping the first correction to gives the low-bound estimate of Δk, i.e. 3.3 which is proportional to the variance of the overlaps, , with other central moments of higher order being dropped (see the derivation of equation (3.3) in the electronic supplementary material). The upper inset in figure 3 shows that the value of V1 is non-zero, as expected from the comparison of and plotted in the main figure.
The low-bound estimate of Δk given by equation (3.3) provides a safe threshold, , for the actual system. We expect this to be the case for a wide class of morphologically complex hosts so that describing 𝒥 in terms of its average and standard deviation provides a minimally safe bound to the invasion threshold in heterogeneous arrangements.
3.2. Arrangements 2. Identical ni and ϕi at all the nodes
In ordered arrangements of type 2, all the hosts are identical branching structures with the same orientation. The host overlaps along the main lattice directions, (figure 4a), depend on the lattice spacing a, the host used as a motif, n, and its orientation, ϕ. For a given n, the set of all possible overlaps obtained by varying a and ϕ within their respective domains define the host overlap locus. Figure 4b shows the overlap locus corresponding to a typical branching host displayed in figure 4a. Each configuration with given a and ϕ is represented by a point belonging to the overlap locus. The inherent anisotropy of the host is reflected in the dispersion of the overlaps, , and gives rise to a significant deviation of the overlap locus (surface in blue) from the straight line (in black) corresponding to the locus for isotropic host ().
Similarly to arrangements of type 1, the spread of disease in ordered arrangements can be mapped onto the bond-percolation problem but now with anisotropic bond probabilities corresponding to the values of transmissibilities, , along the main lattice directions defined as for . From this mapping, the invasion threshold is defined by the following condition (Sykes & Essam 1964): 3.4 This condition can be recast in terms of the infection efficiency and overlaps, as , where 3.5 For given value of k, the condition defines a critical surface (in red in figure 4b) in the overlap space. Therefore, the intersection of the critical surface with the overlap locus (in blue) defines the invasion threshold, . On the other hand, for a given value of a and ϕ, the critical infection efficiency is given by the value of k which generates a critical surface containing the point .
In practice, it is useful to consider the minimally resilient thresholds or which ensure that the system is safe for any orientation if or , respectively. The invasion thresholds are host-dependent and define different separatrices in the (a, k) plane for each host. Figure 3a shows the average thresholds and over all the branching hosts {n}. The phase boundary, , gives the safest estimate for the invasion threshold, which is a consequence of the multi-valued nature of in contrast to single-valued function (see the electronic supplementary material for more detail).
The effects of the host anisotropy on the invasion threshold can be analysed in a similar way as for configurations of type 1 by investigating the dependence of on the overlaps. Similarly, the critical infection efficiency is given by equation (2.4) with the mean-field value evaluated for the system with mean overlap . The dispersion in the overlaps results in the following approximate expression for Δk (see detailed derivation in the electronic supplementary material): 3.6 where the quantity V2 = (1/3(1 + pc))∑α=13(Jα − 〈𝒥〉)2 accounts for the anisotropy of the overlaps. The value of is non-negative meaning that , i.e. the anisotropy in host shape makes the system more resilient as compared with the system of isotropic hosts with the same mean overlap.
As an example, figure 3b shows that in the system of branching hosts, in agreement with the predicted behaviour (cf. diamonds and the dashed line). The inset shows the corresponding dispersion V2. Given that the deviation of from is small in the system of branching hosts considered, the correction is in fact a good approximation to the actual deviation Δk. This is the expected behaviour for systems of hosts with moderate anisotropy.
3.3. Arrangements 3. Identical ni and random ϕi
In the two previous sections, it has been shown that both the disorder and anisotropy of the hosts make systems of branching hosts more resilient against epidemics. The arrangements of types 1 and 2 are extreme cases in the sense that the first type highlights the morphological complexity ( and ) whereas the second type highlights the effects of the anisotropy of the hosts ( and ). In generic arrangements, such as those of type 3 defined above, the two effects are present. By assuming that the transmissibilities between different pairs of hosts are independent, it is possible to show that the behaviour of the actual heterogeneous system is equivalent to that of a mean-field homogeneous system with anisotropic transmissibilities , where is the average of the transmissibility along the direction α in the lattice. A proof for this statement, which represents a generalization to systems with anisotropic transmissibilities of the mean-field description suggested in Sander et al. (2002, 2003), is given in the electronic supplementary material. The equation for the invasion threshold in this case is 3.7 which generalizes the formulae (3.1) and (3.4) in such a way that equation (3.1) corresponds to the particular case of equation (3.7) when is the same along all the directions and equation (3.4) emerges when there is no disorder in the anisotropic transmissibilities.
As for the previous arrangements, the critical infection efficiency obeys equation (2.4) with both heterogeneity and anisotropy contributing to Δk. The lowest-order approximation to the lower bound for Δk is given by the relation (see details in the electronic supplementary material) where and are defined in equations (3.3) and (3.6), respectively, with the dispersions terms generalized to 3.8 and 3.9
Figure 3b shows that the increase in orientational variability brings additional heterogeneity in the system and thus results in a decrease of V2 but this does not necessarily induce a decrease in the value of critical infection efficiency as the contribution V1 may increase. This illustrates the interplay between the role of disorder and host anisotropy.
3.4. Description of the invasion threshold in terms of morphological characteristics
In the previous sections, we have established a link between the invasion threshold and host overlaps 𝒥 characterized by the first moment, , and the deviations from the mean, V1 and V2. The missing link between the host morphology and invasion threshold can be recovered by studying how the morphology affects overlaps. Here, we show that both and the anisotropy of 𝒥 (i.e. V2) can be well described in terms of a reduced number of morphological characteristics. In contrast, a proper description of the disorder-induced contribution from in terms of a reasonably small set of morphological characteristics is hardly possible and requires instead knowledge of the spatial host density, (see equation (2.2)). However, we can ignore the disorder-induced contributions from in order to obtain a safe lower bound for critical infection efficiency and thus connect this quantity with morphological characteristics of hosts.
We start the analysis by considering arrangements of type 1. The overlaps 𝒥 are statistically isotropic (i.e. , figure 3b) so that the invasion threshold can be described in terms of a mean-field system with homogeneous and isotropic overlaps, , and corresponding transmissibilities 〈𝒯 〉. The mean-field system consists of effective circular hosts of radius with overlap . These effective circles are fully described by the radius, , and density, , which is positive for and is zero otherwise. The functional form of is the same as of real branching hosts in [0, rmf], i.e. where stands for the fractal dimension (see the electronic supplementary material for more detail). The radius of the effective circles is defined as to ensure that the average radius of the effective circles coincides with the average radius of the actual hosts, (see the electronic supplementary material). Under these assumptions, the expression for the overlap between neighbouring effective circles is given by 3.10 valid for small overlaps when . The parameter M is a normalization constant (see the electronic supplementary material). The substitution of this expression for into equation (3.2) gives the required link between the invasion threshold and the effective radius, . In fact, for the particular system of branching hosts studied here, this is a very good estimate for the value of the critical infection efficiency, , as demonstrated in figure 3 (the solid circled line falls inside the shaded grey area representing the set of possible values for within statistical errors). This means that for the arrangements of type 1, the mean-field homogeneous system of effective circles can be reliably used for estimating the phase boundaries.
In the case of ordered (type 2) and partially ordered (type 3) arrangements, the overlaps along distinct lattice directions can be significantly different and thus crucial for evaluation of the invasion threshold in contrast to the mean overlap which is important for disordered (mean-field-like) arrangements of type 1. Therefore, instead of a single characteristic such as mean radius of the effective circles for disordered arrangements, we introduce an ordered set of linear sizes of branching hosts along the lattice directions, i.e. the set of lattice-adapted diameters (LADs), (; see illustration in figure 5). The second lattice-adapted diameter (SLAD), , plays the most important role for finding the critical value of, for example, lattice spacing, and thus estimating the invasion threshold. This is due to the fact that equations (3.4) and (3.7) have a solution for the critical threshold only if the overlaps at least along two directions are finite. The overlaps become greater than zero if the LADs are comparable or greater than the lattice spacing and thus solution of equations (3.4) and (3.7) exists if . This qualitative analysis suggests the existence of strong correlations between the SLAD and . Indeed, we have observed such correlations, i.e. , for ordered arrangements of type 2 (figure 5). The description of in terms of SLAD gets worse for small values of k (see the black circles in figure 5) when the strong overlaps between hosts should be achieved at criticality and thus the interior density of the hosts, rather than the diameter only, becomes important.
4. Discussion and conclusions
Using the framework of an SIR epidemiological model, we have investigated the transmission of infection and spread of disease in systems of hosts with realistically complex morphology. Our main finding is that the greater the irregularity in the host morphology, the more resilient is the population to epidemic invasion under otherwise identical conditions (for instance, identical spatial arrangement of hosts). We derive a safe lower bound for the invasion threshold, which has been obtained for branching hosts with independent transmission rates placed on a triangular lattice. We have shown mathematically that this bound holds for all other two-dimensional topological arrangements of hosts with nearest-neighbour transmission and even in the case when the transmission rates between different hosts are correlated with each other. In particular, irregularity in the host positions, i.e. small random displacements of hosts from lattice nodes, brings correlations in transmissibilities and thus makes the system more resilient. Of course, for some real systems, the assumption about nearest-neighbour transmission may be violated by the presence of short-cuts between remote nodes owing, for example, to wind or animal motion. In this case, it is known that the system becomes less resilient to epidemic invasion (Sander et al. 2002) and the bounds given above are no longer valid.
We have used a set of planar neurons to illustrate the effects of complex branching hosts on the spread of infection. We have identified two sources of heterogeneity in the systems considered: (i) morphological complexity of hosts and (ii) the host shape anisotropy. Both contribute to the resilience of the system against epidemic invasion and can be described by means of two morphological characteristics of hosts, i.e. by the mean effective radius and the SLAD. Such characterization is not exact in general but it provides a safe bound to the invasion threshold. The main conclusions are generic and remain valid for any type of morphologically complex hosts. In particular, the methodology introduced here and the bounds for resilience to invasion apply to the transmission of infection in other two-dimensional systems with analogous disorder expressed in the host morphology and anisotropy. Examples include the spread of plant disease through contacts between adjacent plants in a field, orchard or forest in which the host plants frequently occur on a two-dimensional lattice. Here, the contact structures between nearest neighbours are determined by overlap of shoots (for aerial pathogens) or roots (for soil-borne pathogens; Gilligan 2008) in which the three-dimensional structure of the plant can be collapsed onto a two-dimensional framework when considering transmission of infection between nearest neighbours. In principle, a similar analysis could be performed for ensembles of morphologically complex three-dimensional hosts arranged on a two-dimensional lattice that takes explicit account of the three-dimensional host structure. Expressions for the invasion threshold are not known analytically in this case, and the precise definition of quantities directly linked to host morphologies such as fractal dimensions or average radius is system-dependent that requires further study. Other potential applications of the methods include analysis of the transmission of infection via the 'morphology' of contacts between clusters of susceptible hosts in social networks, in which the clusters can be approximated by a two-dimensional lattice (cf. recent work on percolation models for the spread of plague through gerbil populations in lattices of interconnecting burrows; Davis et al. 2008).
The present work opens several possible directions of further research for practical applications in considering disease control strategies and for basic understanding of epidemic spread involving heterogeneous transmission of infection. For instance, our analysis suggests new ways for control of epidemics in real systems where host morphology is inherently complex. For example, in a system where an epidemic is active, a treatment enhancing the anisotropy in the transmission rates would be more efficient as compared with reduction of transmission rates in all directions, i.e. isotropically. Such might arise with the deployment of biological control agents to restrict the spread of infection of soil-borne pathogens in plant populations (Gibson et al. 1999). Biological control agents often exhibit marked variability in performance (Gibson et al. 1999), failing to provide isotropic control of infection on targeted hosts, for example, owing to uneven colonization of roots by microbial antagonists deployed as biological control agents. Our results suggest that increasing the degree of anisotropy owing to these organisms may yet contribute to success in controlling invasion. Anisotropy may also be fostered in social or animal systems by preferential treatment of some, rather than all, connections between clusters. The findings in the current paper are also important for better understanding virus tracing of neurons (e.g. Loewy 1998), which is a biological staining method where virus propagation from neuron to neuron is used as a means to histologically mark the interconnections, so that they become visible to the microscope. More specifically, our results imply that virus tracing might be not so effective in the case of anisotropic or not so complex neuronal cells, which could therefore be overlooked by this type of marking. Analogue effects can also be important in transneuronal spreading of virus in order to deliver gene therapy (Oztas 2003).
Finally, the approach presented here is relevant to epidemics for which an SIR model is suitable and a mapping to ordinary percolation exists. While many diseases can be described by the SIR framework, others cannot. It would be interesting to analyse the effect of host morphology within the framework of a different family of epidemiological models with final state not immune to the disease (such as the susceptible–infected–susceptible model). Such an extension is challenging as the mapping to ordinary percolation is no longer possible requiring tools such as directed percolation (Marro & Dickman 1999; Hinrichsen 2000) from non-equilibrium physics.
F.J.P.R., S.N.T., F.M.N. and C.A.G. thank BBSRC for funding (grant no. RG46853). C.A.G. also acknowledges support of a BBSRC professorial fellowship. The authors are grateful to Prof. David Schubert (Salk Institute) for comments on disease spreading among neurons. L.D.F.C. thanks CNPq (308231/03-1) and FAPESP (05/00587-5) for sponsorship. Part of this work was performed during a Visiting Scholarship of L.D.F.C. to St Catharine's College, University of Cambridge.
- Received October 28, 2009.
- Accepted December 21, 2009.
- © 2010 The Royal Society


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Sunday, November 1, 2009
Wendy Bevan
I am in love with Wendy Bevan's photographs. She reminds me of what would happen if Cindy Sherman only used a Polaroid and shot exclusively for Vogue. Find more of her work here.
Posted by Thrush Vintage at 6:32 AM
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Gorgeous images!!ReplyDelete
(...and I love your blog header...)
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I love these pictures. They have a nostalgic touch...ReplyDelete
I love Wendy Bevan too! so informal yet so perfect. Very Sarah Moon-esque. Thanks for commenting on my blog, as I'm just starting and all. I've checked out your etsy and I must admit I'm eyeing one of those gorgeous knit bows...ReplyDelete
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Oh goodness, these are some of the most stunning polaroids I've ever seen.ReplyDelete
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Building the personality is also known as another reason to make money online. Practically every venture in the web can take relentless endeavors.


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Database Migration From Excel To Mysql mySQL SQL vs. Oracle SQL. Expert Oracle Database Tips by Donald BurlesonDecember 27, 2015 White Paper Gallery for SQL Server – TechNet Articles. – Database Backup Encryption: To manage the security of data which has been backed up to the file system in form of database backup files by using SQL Server 2014. MySQL to
Jan 8, 2009. I've been using South, but Migratory looks promising as well.
Feb 8, 2017. Use database migration tools to test compatibility prior to database. Use the latest version of SQL Server Management Studio to remain.
Welcome to Flask-Migrate's documentation! — Flask-Migrate. – Flask-Migrate is an extension that handles SQLAlchemy database migrations. python manage.py db init $ python manage.py db migrate $ python manage.py.
If you want to migrate an existing SAP system (running on anyDB) to a SAP HANA database, required steps may be a dual-stack split, a unicode conversion, a database.
Migrations are a convenient way for you to alter your database in a structured and. The Phalcon Developer Tools provides scripts to manage migrations.
A database is an organized collection of data. A relational database, on the other hand, is a collection of schemas, tables, queries, reports, views, and other elements.
Oct 23, 2016. At the end, we will present an example of managing a MySQL database using a Maven Flyway plugin. Flyway updates a database from one.
For assessment and migration, choose Azure Database Migration Service for moving on-premises SQL Server and Oracle databases to the cloud.
I was tasked with migration an OperationsManager database off to another SQL server on an SQL Instance other than the default "SQLSERVER" instance.


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1930s Venues
These camp venues are named in Garry Wotherspoon's Gay Sydney: A History (2016) (GW) and slotted into the decades he allocates them. References are also made to his book, Being Different (1986).
Restaurants, coffee shops
Cahill's Coffee Shop
GW notes the Market Street, Sydney branch opposite David Jones was as a discreet meeting place (GW interviews with Ian D September 1977 and John C March 1980). The telephone directory had no Cahills in Market Street.
Latin Cafe
Run by Madam Helen Pura, it attracted a wide spectrum of society, including a large homosexual clientele. (GW source: Interview with Madam Pura 1979). Listed in the phone directory from 1927 – 1956 at No.1, 2nd Floor Royal Arcade, between Market and Park Streets.
Mockbell's Restaurant
GW notes it was a venue frequented by (male) artists and bohemians. (GW source: J. Lindsay The Roaring Twenties Penguin 1980). The phone directory lists "Mockbell Kabell, Mecca Coffee Houses" from 1925. In 1949 a Mockbells Restaurant was at 53 Castlereagh Street until 1954.
Rainard's Restaurant
Located in the basement of 180 King Street, Sydney a favourite for Sydney's homosexuals. It is listed in the 1930 telephone directory and was still operating into the 1950s.
Repin's Coffee Shop
GW says this was patronised by workers and actors from the nearby Theatre Royal pre-war. The 1955 telephone directory lists two Repins, one at 130 and another at 138 Market Street, Sydney.
Shalimar Restaurant
A middle class restaurant, with musicians playing light music. Downstairs in the old T & G Insurance Building cnr Elizabeth and Park Streets. (GW source: Interview with Ian D, September 1977). Listed in the 1950 phone directory and was still operating in the 1960s.
Adam's (Tattersall's) Hotel (Marble Bar)
In Garry Wotherspoon's Being Different John O'Donnell remembers the toilets always being busy pre-war. The address in the 1930 telephone directory is 259 Pitt Street, Sydney.
Belfields Hotel
A working class hotel on the corner of King and George Streets, Sydney. (GW source: B Warren "The Good Old Days of Kamp" Campaign 53 May 1980) Not listed in listed in telephone directory. Site developed as shops in 1955 (City Council records)
Carlton Hotel/Carlton Rex (Dugout Bar)
At 56 Castlereagh Street, Sydney the Carlton was close by other hotels popular with homosexuals in the City in the 1930s. The telephone directory lists this hotel in 1950 and for Adrian Dixon in Being Different it was among the "gayest bars mid-week". It was renamed the Carlton Rex Hotel in 1958. The Boomerangs Social Group was formed in the Dugout Bar in 1967.
Hotel Australia, the Long bar/Sportsman's Bar
One of the gayest bars mid-week, with a discreet entrance in Rowe Street, attracting professionals, white collar and country visitors. (Source: G Wotherspoon, "History" Campaign 53) It was located at 45 Castlereagh Street, between Martin Place and King Street. Closed in 1971.
Pfahlerts Hotel
Described by Ken Johnson (PHG interview 051126 KJ) as "pimms, cocktails, leisurely, bit more screamy, possibly a queen's bar". Listed in 1930 – 1955 telephone directories at 50 Margaret Street, Sydney. (GW source: Ian D September 1977, Brian B March 1980 and R Connell "The Way it Was" OWN 25, 20 October 1983)
Ushers Metropolitan Hotel
In Garry Wotherspoon's Being Different John O'Donnell remembers this hotel as the "main one" pre-war and Adrian Dixon says that it was among the "gayest bars mid-week" in the 1950s. The 1955 telephone directory lists the address as 64-68 Castlereagh Street, Sydney.
Dance venues
Black Ada's Academy School of Dancing
This was a major Saturday night venue for homosexuals, in a dimly lit large studio with a dance floor lined with tables. Admittance only if Ada knew you. Wentworth Avenue. GW source: B Warren, "The Good Old Days of Kamp", Campaign 53, May 1980). Not listed in phone directory.
Revised and updated: John Witte 22 August 2016


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Tuesday, October 2, 2012
Thursday, September 13, 2012
Wednesday, September 5, 2012
James E. Bruce Convention Center Bridal Expo
Tuesday, August 7, 2012
Family Canvas Decor
- Paint the sides of the canvas
- Sand your letters if needed
- Paint your letters
- Paint a second coat on the canvas and letters
- Cut the scrapbook paper to size
- Use Mod Podge to adhere the paper to the canvas
- Put a layer of Mod Podge over the paper and on the sides
- Mod Podge over the letters for a complete look
- Cut various lengths of ribbon
- Use a hot glue gun to attach the ribbon to the back of the canvas
- Use glue to attach the letter the the canvas
- Put the finished products on the curtain rod
- Hang and enjoy!
Friday, July 13, 2012
How to Make a Fabric Rosette {TUTORIAL}
- ~3″ x 22″ strip of fabric {this will make a 2″ diameter rosette} {I just cut up an old t-shirt}
- ~approx 2″ circle of scrap fabric or felt
- ~hot glue gun
- ~scissors
Monday, July 9, 2012
Create Fest 2012
Thursday, July 5, 2012
New Ribbon!
New ribbon option for your customized hanger!
Monday, July 2, 2012
DIY Weekend Project
I was going thru my stuff and was planning on having a garage sale, but there was no way I was going to sit out in this heat.
I had an old picture frame that was my future husbands, but it just didn't fit in our house together.
I finally decided to just make something with it. So, I took the frame apart and painted it a dark brown. Then after it dried, I used Mod Podge to give it a glossy look. I took the back of the frame and spray painted it with chalkboard paint so we could write messages to each other. Unfortunately, we didn't have any chalk and I wanted to surprise him when he got home from work. So, I just decided to write a permanent message using puffy paint that I had. I had seen on another blog how to make a rosette out of fabric. I put my own little twist to it. After all was put together this, this is how it turned out. I think its pretty good for a almost free craft and new wall decor. Now, my future husband has something to look at while going to the bathroom.
Lots of love,
Future Mrs. K
Thursday, May 31, 2012
How to order your own!
Custom Wire Wedding Hangers!
Orders yours TODAY! Email: email@example.com !!


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Bad blogger!
I've been in the new house for THREE WEEKS and haven't posted pictures yet!
Crazy, eh? It's like I've been busy or something!
At least that's what my poor body keeps telling me! I swear it thinks that my alarm-clock is out to kill me, too.
But that's another story for another time.
Right now it's picture time.
So sit back and enjoy!
|The house itself! The garage is SO full of boxes that we have to park out front for right now!
|The entry from the front door. Ignore the lighting. I had to go sans flash in order to avoid a weird reflection from the mirror.
|The Master Bedroom. (The door leads to the master bathroom).
|The Master Bathroom has dual vanities.
|And dual closets on either side of the shower.
|The living room Featuring one cute little boy playing on the Wii.
|There's normally one cute little boy and one cute big boy playing the Wii, but the big boy was busy preparing food for company. He's well on his way to being a good husband. ;)
|From the living room looking over into the kitchen/dining area.
|The kitchen.
|Ty's bathroom.
|The vanity in Ty's bathroom.
|Ty's bedroom with his new bed and freshly painted chest of drawers....which was a MAJOR headache that is going to require psychological counseling at some point in time before I'll even be able to consider blogging about it.
|The other end of Ty's room. The other guest room is comparable, though slightly wider and not quite as long. Both rooms have the closets with the dual-doors.
|And lastly...the view from the back yard of the mountains. Though I'm waiting for the perfect sunset to capture what is truly one of God's finest works of art. The sunsets are AMAZINGLY beautiful up here!
Hope all is well with each of you!


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Previous Commentaries
October 2017
The Sustainability of a Global Upswing
Martin Investment Management, LLC believes that the S&P 500 Index continued to move higher in the third quarter of 2017, increasing 4.48% on a total return basis, because domestic and global growth are reaccelerating. Profits from corporate earnings and GDP growth are intertwined, and the U.S. economic output grew at a 3.1% annual rate in the second quarter of 2017, the best quarterly rate of growth in two years. The U.S. economy remains stable with steady job growth, a rising stock market, and little inflation. According to survey data from the Purchasing Managers' Index (PMI), which provides a useful indication of GDP's direction, growth in the third quarter should also be strong. Based on market exchange rates, the global GDP growth rate for the third quarter of 2017 is estimated by J.P. Morgan to have been around 3.8%, which might be higher than the U.S. third quarter GDP estimates. This is the highest growth rate recorded since mid-2010.1 The MSCI World Index (USD Net) increased 4.84% and the MSCI EAFE Index (USD Net) increased 5.4% for the third quarter of 2017.
Core inflation has been undershooting the Phillips Curve, which assumes the inverse relationship between inflation and unemployment, giving the Federal Reserve some hesitancy in raising interest rates by 0.25% in December of 2017. The U.S. Federal Reserve policy acknowledges some downside risks to its goal of price stability and may be undershooting inflation. Although the Federal Reserve has raised rates four times since 2015, the consensus opinion is that more tightening is warranted as bond yields appear too complacent about growth. The Federal Reserve will also start to reduce its balance sheet this October, a quantitative easing (QE) in reverse. While the process will begin slowly, once begun it will accelerate on autopilot between 2022 and 2023. The Federal Reserve has detailed a pace of mortgage backed securities (MBS) runoff of $4 billion a month rising to $20 billion a month by the end of next year and $6 billion a month of Treasuries (TSY), rising to $30 billion by next year. The Federal Reserve is taking great precautions to send a smooth message to investors. To put the Federal Reserve policy in perspective, the $6 billion per month of initial unwinding is approximately one fifth of the average monthly maturities over the next year.2
In Europe, growth has not been hampered by the euro's strength. Unemployment across the Eurozone is at eight-year lows, while manufacturing leading indicators are at six-year highs. There is now widespread acceptance that real activity growth in the Eurozone and Japan has been much firmer than originally expected this year. Traditionally, when inflation does tick up in Europe, earnings start coming back at a faster rate than in other parts of the world due to the large proportion of financials and commodity companies in the region. The European Central Bank (ECB) is beginning to discuss tapering for 2018 while the Bank of England (BOE) is considering an interest rate hike. Presently, the U.K. is suffering from stagflation, a weak currency and increased inflation. According to BOE Governor Mark Carney, Brexit could lead to persistently higher U.K. inflation. European corporate earnings are in the early stages of recovery. Japan's recovery continues as the weak yen has helped exports. China appears stable although the yuan strength softens Chinese demand for foreign currency, including U.S. Treasuries.3
The G7 economies are finally reaccelerating from a 1.8% average annual growth rate over the 2010-2017 post crisis-period, even when the combined central banks afforded the markets about $6.2 trillion of excess liquidity with their accommodative policy bias. The strategy that helped the crisis in 2008 has not worked for a cyclical rebound in the real economy. The current equity price/earnings multiple of 21.3x is remarkably close to the average of the last quarter century, approximately a price/earnings multiple of 20x, even though easy monetary policy was believed to prop up equity prices. Most equity valuations are not extreme at this time. The central banks' policies will begin to remove monetary accommodations of zero bound interest and asset purchases, but their policies are well advertised and still quite accommodative. Long-term interest rates and volatility risk may increase as the cost of capital increases, but the risks are to the bond market and weak companies only supported by the low cost of money.4
Given the robust corporate earnings, fiscal policy changes (tax cuts), deregulation of the financial and energy sectors, the cash excess of large corporations, and infrastructure spending, Strategas expects that U.S. monetary policy will be somewhat overshadowed going forward. The most recent phase of the equity bull market has fundamental support, as consumer confidence continues to support earnings gains. There is still pent-up capex demand in the economy, particularly in defense and infrastructure. Manufacturing has expanded at a torrid pace in the third quarter of 2017. Corporate earnings are projected to grow by roughly 4% and 9% in 2017 and 2018 respectively. The rally continues despite no major legislative accomplishments. Equity markets remain solid investment choices given these assumptions. The U.S. economy has never had a recession with corporate profits rising.5
"Inflation will not move higher without wage increases, which remain stable. The present inflation backdrop is significant as it will likely sustain the corporate sector's pricing power gains, suggesting that the market has a long way to rise. BCA Research's analysis shows that 75% of their covered industries are able to increase selling prices, and 45% are doing so at a faster pace than the overall inflation. Only twelve industries are experiencing a downtrend in selling price inflation, a decrease of seven since late June of 2017, of which nine industries are deep cyclical/commodity related industries. Their analysis suggests that corporate sector pricing power is recovering and is positively influencing sales growth, operating leverage, profit margins, and earnings per share (EPS) growth as well as modest wage inflation for the second half of 2017.6
The interest rates on the U.S. 10-Year Treasury have not risen significantly since bottoming during the 2008-2009 recession and financial crisis. The last stretch of rising rates was just after June 2016 Brexit vote, when the yield of the 10-Year Treasury Note hit an all-time low of 1.37%. It subsequently hit a two-year high after the November 2016 presidential election of 2.60% and has ranged between 2.2% and 2.5% throughout most of 2017. The current 10-Year Treasury rate is 2.3%. In the 1990s, a 10-Year Treasury note returned close to 6.7% per year versus a 2.3% yield now, about a 440 basis points drop in income for 10-Year Treasury holders. Bond investors now face two challenges. The first is relying on bonds for cash flow presents challenges to generating a robust income. Secondly, if rates rise, the prices of existing bonds will fall. While the risk of rising interest rates is important, the risk of rates remaining low for an extended period of time is more significant.7
Since the 1980s, many public corporations have increasingly used share buybacks instead of dividends to reward shareholders. Across the U.S. stock market, buybacks have surpassed dividends in eight of the last ten years. The impact of buybacks on stock return has been overlooked or misinterpreted by investors according to Philip U. Straehl and Roger G. Ibbotson. Buy-and-hold investors, who exercise their right to hold on to their shares during a buyback offer, wind up owning a larger proportion of a company, given that the total shares in issue are reduced after the buyback. The authors' models show that long-term equity returns are almost completely driven by total payouts–dividends and buybacks. The total payout model is found to more accurately attribute long-term returns than models based on dividends only. Total payouts per share grow in tandem with economic productivity, implying that total payouts contribute to the long-term growth of the economy. Between 1980 and 2014, approximately 32% of the economic growth measured is attributable to buybacks, not to the growth of the underlying cash flows of the business. Buybacks have a fundamentally different impact on the return generation process than dividends do. According to this study, although payouts via dividends increase the income return, buybacks increase the price return per share because a buy-and-hold investor's share in a company is increased.8
In the Grant Interest Rate Observer of 2016, Steve Bregman suggests that many strategies are reliant on a moderate Federal Reserve. He believes that weakness in some passive strategies might be exposed as investors assess the challenge of the potential volatility created by a quantitative easing exit. He believes that the growth of exchange-traded funds (ETFs) is the world's biggest potential bubble. "It has distorted clearing prices in every sort of financial asset in every corner of the globe."9 The real push to index funds began in 2013. Inflows to U.S. Equity ETFs have reached record levels in 2017, over $300 billion. Stocks added to indices may experience an anomaly of exceptional short-lived gains with increased demand for shares, unrelated to specific company news. As the fees of ETFs have decreased, product differentiation has increased. There has been a proliferation of subsets of the market, for which a higher fee could be charged: country funds, industry sector funds, style funds, etc. Many specialized index trackers can be expensive and do not have long track records established for return, volatility, or correlation. Devising subsets of the index accentuates a structural flaw of the market-capitalization weighting system: the top heaviness problem. Over time an index of stocks tends to get concentrated in a few names, which may increase systemic market risk or specific risk in certain securities. Since investors in ETFs do not buy shares individually they cannot sell them individually with price discovery. Passive investors cannot be dismissed for underperformance but carry unrecognized concentration and liquidity risk if the market declines.10
Martin Investment Management, LLC believes that the analyses of the two mentioned studies reinforce our view on investing in large, financially sound companies traded on recognized exchanges with strong liquidity. These companies have been able to participate in buybacks, increasing shareholder ownership over time. They also have the ability to pay a dividend. These companies have growing revenues and earnings, positive free cash flow, a low level of debt to equity, a current price close to or less than fair value, and very importantly, trading liquidity.
Wishing you a wonderful summer!
1. "Gavyn Davies' Blog, "Global Growth Still at Record Rates for This Expansion," Financial Times, September 3, 2017.
2. "Yellen Firm on Rates; Inflation a 'Mystery'," Wall Street Journal, September 27, 2017.
3. "Team of Alliance Bernstein, "Are Risks to Global Economic Growth Still Skewed to the Upside," September 26, 2017.
4. "Roach, Stephen S., "The Courage to Normalize Monetary Policy," September 16, 2017.
5. "Strategas Research Partners, "Growth vs. Value: More of the Same or Inflection Point?" September 29, 2017.
6. "BCA Research, September 25, 2017.
7. "Fall, Brian Nick, "Fixed-Income for Low and Rising Rates," Nuveen, 2017.
8. "Straehl, Philip U. and Roger G. Ibbotson, "The Long-Run Drivers of Stock Returns: Total Payouts and the Real Economy," Financial Analysts Journal, Volume 73, Number 3.
9. "Bregman, Steven, "On the ETF Divide," Grant's Interest Rate Observer, October 14, 2016.
10. "Bregman, Steven, "On the ETF Divide," Grant's Interest Rate Observer, October 14, 2016.


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Shizuo & Izaya - Durarara
I discovered Durarara through these two. I knew that they can never be together, and of course I don't believe they love each other, But the love-heat (except for the fact that they don't love each other) is what drawed me in. I found that this pairing was great and just quite enjoyable to ship. I vote for it because of the many reasons as to why I love shizaya.
First off, I believe that the other wouldn't be the other without the other person there. Besides, if one died what would the other do? Izaya would be extremely bored, and Shizuo would probably felt a bit empty inside, perhaps missing those fights he had with Izaya. But one thing that stood out to me was that the anime points out the pairing, mostly through Erika. Now, before people nag at me about how 'Thia pairing can never happen' I would like to say that this is simply my opinion. If you respect mine I will respect yours. Thank you.
I LOVE these two! They're amazing characters as it is separately! I mean who can't love the short tempered man who hates violence? Or the sly 'flea' who you're supposed to hate, but that just makes you love him more? I love these two separately, but together they're AMAZING! Watching these two fight is exciting, and thinking of the depths of their feelings is even more grand! No one else can send the monster Shizuo Heiwajima's blood racing like Izaya, and there's no more fun time to Izaya Orihara then his famous chases with Shizuo. I just love how complex these two are because they claim to hate each other, but they can't keep away from each other! No matter how you look at it there's just no one else in the world that they can me this emotional to. There's so much tension between these two, but they only claim it to be hate. But how can hate drive two people together so much?! They're always drawn to one another (whether it be Izaya searching for Shizuo for a chase, or Shizuo hunting ...more
There's just so much tension between them, and they're totally obsessed with each other! I mean, come ON! If you really hate someone, that's a perfect reason to avoid that other person, but no. Izaya goes out of his way ALL the way from Shinjuku to Ikebukuro just to see Shizuo. And Shizuo? The guy knows Izaya's SCENT. If that's not obsession, of which can often lead to or sprout from love, I don't know WHAT IS.
Shizuo and Izaya have the best chemistry of any two characters I have ever come across in fiction. Their passion for each other is borderline obsessive, no, scratch that, it is obsessive. There is literally no Shizuo without Izaya. I can't even begin to count the number of times Izaya mentions Shizuo.
They fit together perfectly, seamlessly. They are two sides of the same coin. I doubted their capability as a couple when I started the fandom, but as I got to the light novels, their intense feelings of mutual contempt won me over.
No one in the series has a stronger relationship than those two have for each other. Even if you're not looking at it in a romantic light
Izaya and Shizuo have a love/hate kind of relationship. Both of them are not (in my opinion) really good people but they are realistic and interesting characters, especially Izaya (by the way, it's a pity that we don't know why he turned into twisted and manipulative bastard, like we can see him in the show). In my opinion both of them are a little lonely but in a different ways. Shizuo has friends but most of people are scared of him and his strenght. Izaya... like I said, he is a MANIPULATIVE BASTARD, arrogant, annoying and, like sometimes seems, sociopath. But in a book we can see a little more human, little lonely (in the end of the volume 4 it's written that he felt a little lonely).I feel sorry for him because of hatered that his sisters feels towards him. I would like to know HIS STORY. Why he is like that? And I think he didn't deserve what happend to him in the end of the story. A weird thing about the story is that AUTHOR CREATED SHIZUO BECAUSE OF IZAYA! They are both not ...more
Love-hate relationships are the best! Especially with these two. THIS IS MY OPT AND NO ONE CAN TAKE IT FROM ME! A sly man and a short-tempered guy works really well together. I had always liked how Shizuo would yell Izaya's name at the top of his lungs then in a matter of 1 nano-second (which would be an underestimate) would try to kill Izaya! There is a VERY thin line between love and hate... My opinion is that since they first saw each other it is 'hate at first sight' but I'm pretty sure that they mixed up love and hate. However this relationship continued on until adulthood where the two became one of the most crazy/dangerous/etc people in Ikebukuro. I enjoyed how Izaya seemed to love all humans except Shizuo, who he considered an animal or even a monster. What makes it even more interesting that he would often go out of his way to get Shizuo in trouble, often ending up being chased by a angered rampaging man. To conclude, Shizaya/Izuo should be canon.
These two are really something special. I could literally write a 10 page essay on how beautiful and complex the ship is, but for the sake of time and space I will just focus on one point about why I love this ship so much. It's that you can find fan art of them in really any scenerio, and my favorite are the ones of them as a real couple. Like when they are cuddling in bed or just holding hands. It says so much and I truly believe that they have feelings for eachother though it may not be too obvious to themselves. I'm 100% convinced that Izaya really does have feelings for Shizuo, but makes the excuse that Shizuo is a monster and creates his own hate so that he won't get further hurt and have to deal with the feelings. Then, from reading a couple of different headcannons I have come to the conclusion myself that when Shizuo first met Izaya, he felt the feeling of love, but didn't know what to make of it so just associated it with dislike. Of course Izaya was hurt and slashed at him ...more
When I first herd about this pairing I thought "No way and how is that even possible" but then after reading and watching the series I went MAD over them I mean you get hints and clues all over the anime and the novel look very closely but look at it without your fan-girl instinct and you can still notice it. " even the creator supports it"
I think these two are made for each other. the reaction of shizuo from the sight of izaya is unique, he never showed that kind of reaction to anyone. and izaya shows interests in shizuo in many ways. I feel it's kind of unbearable but inseparable relationship for them. They both feel hatred for each other but at the same time I see love under their hatred. their relationship is like lemon. It is sour and by smashing it is more bitter. but with water, tea leaves and sugar it becomes a fine cup of tea. I seriously think they need some catalysts to power up their relationship.
NO DOUBT ABOUT IT THERE IS NO ONE ELSE WHO WILL EVER LOVE SHIZUO AS MUCH AS IZAYA! They are by far the best couple nobody could ever deal with either of them except each other obviously they are meant to be no if ands or buts
These two are just amazing. No matter how much I try not to ship them, they're like magnetic! It's basically canon. Shizuo has this sixth sense to Izaya while Izaya loves to play hard to get. Sure they claim to hate each other, but that just makes it more exciting. I love seeing the episodes how they interact, how the fight, how close they get... Anyhow, these two are perfect for each other, no matter how much they'll deny. But like said, "denial is the first step in love."
Which Izaya always in Shizuo's mind as much as Shizuo's place in Izaya's mind.
Izaya made Shizuo keep catching him means that their relationship will never been broken.
Shizuo had fallen in love with Izaya since the day they've met! He just mistaken what loves it means. And he even more love Izaya when Izaya said "I'm not afraid of you"
In this couple opposites attract completely, these two were so meant to be! Izaya totally fell in love with shizuo, and shizuo still has yet to realize it! Beautiful beautiful pairing, the most awesome ever in the history of the universe!
Admittedly, before I became obsessed with yaoi I was quite the hater after accidentally exposed to some pretty hardcore stuff while under the impression that it was romance. When I watched Durarara, my world turned upside down and this pairing is the sole reason I got into the fandom. While it seems improbable, this is definitely the best yaoi pairing I've ever seen!
I saw a few videos about those two and totally fell in love with this pairing. So I started watch the anime and was surprised to see that they're actually hating each other. But now I think.. It isn't hate. It's love.
I absolutely love this pairing. It is a love/ hate relationship that seems to Strangely go together so well its like they are like peanut butter and chocolate, or jelly it all depends
That love/hate thing is why everyone ships them actually. They got me so addicted and I cannot take the passion and chemistry between their hate...even Shizuo was created because of Izaya! And the author even wrote a one-shot story or them (based in Erika's thoughts actually). Unfortuantely Durarara's genre doesn't focus on that and I doubt that they'll ever become cannon...And I don't really expect them to be cannon, But I swear I'd cry if they ended up with someone else...
You know they have a past and Izaya bleeped it up. So is this his way of making up? Well Shizuo is having none of that and I can't blame him. Therefore, they have an intense hate/love relationship. It's fun to imagine what happens behind the scenes.
At first I didn't understand why they should be together, but then, I started seeing them together myself. I mean, every time Izaya says "Shizu-chan" it's like he's calling for attention, and then Shizuo answers Izaya's love call by chasing him all over the town. This is what is called "The chase of love". (I made that up)
At the beginning I could never see them together as they always show their hate for one another, but as I continued watching the anime I realised that they could actually have an intense love-hate relationship. I'll go down with this ship. These two are amazing!
I love love/hate relationships, and they defiantly have the hate, the love part is suggested especially by Erika!
I love how she ships them in the show!
Yes yes yes this is the cutest couple ever! They belong together! :) I really unlike this ship because even if it's a hate relationship both characters pay attention to the other very carefully and love and hate isn't that far apart!
They're amazing! I love this love/hate relationship. And what's more, scenes, when they're together are so great: all those Izaya's coments about Shizuo and Shizuo's anger. They just match to each other.
I love shizuo and izaya together they make the perfect couple! You can tell they really care for each other even if they are always fighting
Just-- I can't. It's interesting as hell for me to observe how both Izaya and Shizuo feel nothing special for anyone but each other (even though this special feeling is hatred). It's just so canon,.


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Maitre Parfumeur & Gantier - Santal Noble (90 ml)
Quantity in Basket:noneCode: MAI-021
Santal Noble "Noble Sandalwood" (90 ml)France
It is all the delicate feel of the wood which on the skin takes the body odor of each one. Linked to amber, it is the perfume of seduction.
Description: Sandalwood, Vetiver, Precious woods.
Family: Woods. Unisex Fragrance


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Thank you for taking the time to visit my website. I specialize in assisting buyers and sellers, whether you are a first-time buyer, a seasoned buyer, or a seller looking to upsize or downsize. I specialize in Aurora, Centennial, Denver, Englewood, Highlands Ranch, Littleton, Parker, Castle Rock, and other surrounding areas. I work with resales as well as new construction.
On my website you can search for homes and land, income properties, and foreclosures. The information offers current, up-to-date listings, so there's no need to look anywhere else. Property information contains photos, maps, descriptions, and other information you will find helpful. Feel free to explore all areas of my website. Don't forget to look for additional pages and links.


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A Q&A with Kyle KupeckyEdit
Hometown: King of Prussia, PA
Nickname(s): Ky, Kyle 2.0, Kupretty (I remain firm in my distaste for the last nickname - I'm talking to you Alan, haha!)
Describe yourself in 5 words or less: Cheerful, Passionate, Kind, Creative, Sincere
Favorite Bible verse/passage: 2 Corinthians 12:9-10 But he said to me, "My grace is sufficient for you, for my power is made perfect in weakness." Therefore I will boast all the more gladly about my weaknesses, so that Christ's power may rest on me. That is why, for Christ's sake, I delight in weaknesses, insults, in hardships, in persecutions, in difficulties. For when I am weak, then I am strong.
This passage just wrecks me. It goes against all human logic because we try so hard to be the greatest and the strongest, but what God wants is for us to hand him our weakness. It is through our weaknesses that God's power shines through. His grace picks us up, gives us hope, and restores our hearts. He knows we can't be perfect, and His love and grace are made all the more powerful because of our imperfection. Delighting in weaknesses, in persecutions, and in difficulties has got to be one of the hardest things imaginable. It will probably be something that will take me a lifetime to learn. But doing these things will keep me humble and keep my heart focused on the One who is strong.
Childhood hero? My dad. He's part Jack Bauer from 24 (the strong, loyal side) and part Michael Scott from The Office (the corny, funny side). I feel extremely blessed to have a father like him. My parents' guidance and support has shaped my life.
Best advice from Mom or Dad that still is with you today? Love God, love people. Simple as that. It's something my parents would say before I headed off to middle school in the mornings and something they would text me when I was away at college. That daily reminder always kept me focused.
What do you know now that you wish you knew 5 years ago? That God is always faithful. I knew that in my head, but my heart had not fully experienced that yet.
Who do you consider to be your greatest musical influences? The people who have shaped pop music. The bigness of the sound - the beats, the vocals, the melodies - has always been something that grabbed my attention. Michael Jackson, Beyonce, and Justin Timberlake are huge influences.
Who did you imitate singing when you were a kid? Steven Curtis Chapman, Backstreet Boys, Christina Aguilera
What artist(s) would you love to collaborate with someday? Justin Timberlake, tobyMac, Timbaland, Group 1 Crew, Rihanna, Jordin Sparks
What is the most embarrassing song or album on your iPod? Any Britney Spears tracks
What's the first album you remember buying? Backstreet Boys' 1st album
What is one of your favorite all-time TV shows and why? Lost. That show had me going nuts. I'd be on the blogs after an episode aired trying to decipher hidden clues - it was a little crazy. The show Alias comes in a close second to Lost.
Favorite movies? The Dark Knight, Up, The Lord of the Rings Trilogy
Favorite sports teams? Philadelphia Eagles
Beverage of choice? Coke Zero
Favorite breakfast cereal(s)? Basic 4 (yeah it sounds healthy, but it tastes so good)
Favorite late-night snack(s)? Ice cream. It's my favorite food.
Who do you recommend people follow on Twitter: Jimmy Fallon (http://twitter.com/jimmyfallon)
If you weren't in Anthem Lights, what might you be doing? Still singing, recording, and writing, but probably singing, recording, and writing in a ghetto basement.
Biggest strength besides singing or unusual talent? Does being awesome at using TiVo count as an unusual talent...?
What's a little-known or fun fact about someone else in Anthem Lights that people should know? Caleb has been the best man at 3 weddings within the same year. He's really good at the whole friend thing.


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Northern Lights Exteriors Outshines Other Roofing Contractors in the Westminster, CO, Area
While many roofing contractors serve homeowners in Westminster, Colorado, and the surrounding communities, not all of them share an equal commitment to quality and customer care. At Northern Lights Exteriors, we are committed to both, providing our customers with durable, long-lasting roofs and exceptional customer service throughout the process.
We start each reroof with a thorough consultation, during which one of our knowledgeable project managers will inspect your current roof and help you decide which material will be best to invest in for your home. Unlike many other roofing contractors in Westminster, CO, and the surrounding areas, Northern Lights Exteriors offers and is experienced with a variety of different roofing materials, so you can trust us for an honest recommendation – not to sell you a particular kind of roof because that's all we have.
Some of the different roofing materials that we work with here at Northern Lights Exteriors include:
- Asphalt shingles and shake
- Stone-coated steel
- Clay and concrete tile
- Polymer slate and shake tile
- Metal roofing
- TPO and EPDM (otherwise known as "flat" roofing)
In addition to our commitment to customer service and experience with a variety of materials, Northern Lights Exteriors distinguishes itself from other roofing contractors by our dedication to provide Westminster-area homeowners with the most durable roofing in the industry. That's why we source our materials only from respected manufacturers, such as Owens Corning, Malarkey Roofing Products, GAF, TAMKO, CertainTeed, DECRA, Boral, DaVinci Roofscapes, and Metal Sales.
If you're looking for roofing contractors in the Westminster, CO, area that you can trust for long-lasting materials and exceptional customer care, contact Northern Lights Exteriors today.


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|To find the lowest Urelle prices, click below on the strength of interest.
|Choose Strength for: Urelle - Brand Version
The lowest prices for Urelle from online pharmacies and prescription discount cards! Before you buy Urelle, compare the best prices on Urelle from licensed, top-rated pharmacies in the U.S., Canada, and internationally. Find the lowest cost Urelle from the best pharmacy.


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Do you enjoy running on uneven terrain? The Sertig T-Shirt Men is made from a lightweight, comfortable and stretchable material that will provide functionality to support your challenges. Active moisture-wicking transports sweat away from your body to prevent chilling. At the same time, an antimicrobial treatment with FreshTech reduces unpleasant odors. The specially designed flatlock seams offer extra elasticity and prevent chafing on the skin. The Sertig T-Shirt Men will impress you in your training sessions with its high functionality and comfort.
Hiking is an extremely diverse activity, but the Trovat T-Shirt Men will be an ideal companion any place and any time. The T-shirt is made from the exclusive pleasantly soft and quick-drying drirelease® fabric. A benefit you will quickly appreciate if your climb has brought you out in a sweat. UV protection of 50+ also protects you from aggressive sunshine. A real all-rounder in the mountains!


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ANGRY homeowners have branded a council's decision to increase council taxes by more than 12 per cent as "diabolical".
Oldham council leader Richard Knowles said the rise was a "huge disappointment", but insisted most of it was out of the council's direct control.
He said 9.8 per cent was the result of increases in funding for county services including the police, fire and ambulance services, passenger transport and waste disposal.
Also there were rises in employers' national insurance contributions and pay rises above government guidelines.
But residents are furious they are once again being asked to stump up more cash.
Roy Houghton, chairman of the Egerton Street tenants and residents' association, said: "It's diabolical, but it's no surprise.
"And no matter what we say or do, we are still going to have to accept the increase and pay the difference."
Sandra Percy, chairman of the Abbeyhills area tenants and residents' association, said: "It's a major increase and there are going to be a lot of people unhappy with the announcement.
"Nobody knows just exactly what we get for our council tax anyway."
The rises - which come into force in April - will be recommended to the council's budget-setting meeting next week and will also result in cuts of over é2m.
The 12.3 per cent rise will mean band D property holders now face a total annual council tax bill of é1,218.75 - up é133.52.
A band A property will be é812.50 (up é89.01), band B é947.92 (up é103.85), band C é1,083.33 (up é118.68), band E é1,489.58 (up é163.19), band F é1,760.42 (up é192.87), and band G é2,031.25 (up é222.33).
Fury over council tax hike
ANGRY homeowners have branded a council's decision to increase council taxes by more than 12 per cent as "diabolical".


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Our stories: Doing GCSES and A Levels in prison
So far this year, PET has funded over 200 people to take GCSE, AS Levels and A Levels in prison, a handful of whom managed to take their exams inside. As they await, lament or celebrate their results along with students up and down the country, we asked them why they chose to study these subjects, what effect it has had, and what they hope to do next.
'Andrew' - AS Level Philosophy
"It is not just something to do, it is something to devote myself to."
I had done A Levels upon leaving school, but failed miserably. I was, at the time, more interested in drugs. I've chosen to start studying because I cannot face the idea of spending my life doing nothing, going nowhere. I am doing a long sentence (deservedly so) but I see no reason why being in prison should mean I just stop. In studying I gain a sense of purpose, of development, of change, of movement; of autonomy, of agency, of responsibility. All things that, for many prisoners, are missing.
I chose Philosophy because I have an almost compulsive need to understand reality, myself, society etc. Thinking philosophically and reading philosophers has been a really important part of my coming to understand what I have done, why I did it, and how best to move forward. I hope to complete more A-levels before going on to study Philosophy Politics & Economics at degree level. It is not just something to do, it is something to devote myself to. That sounds quite serious - but I really do love philosophy!
Taking the exam was actually really fun. I was pleasantly surprised to understand the questions! I was getting A's in some assignments, so hopefully I've got an A, but I've been doubting my answers ever since I finished the exam!
I think my family are happy that I am doing something constructive, so that perhaps in spite of what I have done, it is something they can be proud I am doing. It certainly makes me feel more human.
'Kosta' - GCSE English Language
"[P]ersonally I've been changed and am looking for hope."
IGCSE English Language was the first exam I've ever done. The motive was simply that it could better make me understand English, so I can go to study for A Levels. I am planning to study computer science. When I told that to my relatives, they were very happy and surprised, at the same time.
I was a bit nervous when I took the exam, but it was not as hard as I was expected it would be. I hope my grade will be above my expectations.
Because of the circumstances we are in, as prisoners, it is much better to study instead of just thinking about your sentence. Despite the challenges I face, I believe I've been rewarded just by getting funding for my course. After this, the higher the grade, the better.
Prisoners' Education Trust can make a difference in a prisoner's life, and personally I've been changed and am looking for hope.
'Jon' - A Level History
"You can say, 'yes I can do it' and then tell your family."
Some think I have chosen a strange subject in British and German history. But I chose it because it was a subject I found that you could easily form your opinion on from the sources given and [decide] what could have been done differently in hindsight. Instead of plunging straight in, I was advised to do the GCSE first to see if I had a feel for it. I enjoyed it so much I decided to apply for an A Level.
Every prison I have been in, I cannot fault the education department. They bend over backwards to assist, but they can only go so far. There are many challenges at studying at this level in prison - there is a lack of additional material; and if something major has occurred you are locked in the cell and not the classroom. On the other hand, this can work to your advantage as once you are locked in, you can study without interruptions.
One of the main rewards is achievement. You can say, 'yes I can do it' and then tell your family. It is also something to keep my mind active, to use up the time I have without just watching TV. It is too easy to go bonkers in here and by feeding my brain I wish to avoid that.
'Shaun' - AS Level Government and Politics
"I got through it, like everyone does."
I left school at 14 years old, no exams taken, never much liked school except football and P.E. I came to prison at 54 years old. The careers lady got me placed on a Level 2 course, then did a few GCSEs. I've now got eight and today I started another two. I took A Level Sociology last year and then started an AS in Government and Politics. I felt a bit nervous taking the exams, but I got through it, like everyone does. Dad would have been proud; alas he died during my Sociology course, but Mum seems pleased for me.
'Tom' - GCSE Business
"Doing a life sentence made me realise I need positivity, hope and a purpose to change."
The biggest benefits have come out of being dedicated to something purposeful and learning something. I wouldn't say it's too difficult to study in here and there's a lot of support from the tutors, staff and peers - it's more about dedication.
It was nerve racking to take the exam, especially the build-up to it. But I got my head stuck in. Now I want to go on do a few more A level Business-related courses or onto a degree.
All names have been changed for the purpose of anonymity


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Just Your Average Gay DivorceREAD NEXT STORY
Looking hotter than hell, literally, in Valentino Couture, Chrysta Bell enlightens us about a little something she calls "Friday night fly in the city." From what we can tell it seems to be a romantic mystical dark world, but whatever it may be, we definitely want to be a part of it.
David Lynch produced and cowrote Bell's newest album, This Train. We couldn't have picked a more perfect protégé and muse for the master of dark seduction.
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|Proposed site highlighted in red
Working alongside local chartered surveyors, Fisher German, the developers have announced they will be looking to build up to 85 homes on the site with 20% being 'affordable' dwellings.
The developers have confirmed that it will be their intention to retain existing hedgerows and trees as well as adding additional planting, landscaping and public open space.
If approved the developers will seek to access the site directly off Loughborough Road which will mean some rearrangement of existing traffic calming measures.
As part of the next steps Fisher German will be holding a public exhibition of their current intentions and asking for local resident views on Thursday 27 February between 4pm and 7pm at Thringstone Community Centre, The Green.
District Councillor for Thringstone, Leon Spence, said "I would urge all local residents to attend the exhibition and let the developers know their views.
"Developers really do listen at these type of events and will usually finalise their planning applications informed by them."


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UNC Blanks BC to Advance to ACC Title Game
Nov. 12, 2010
Courtesy of UNC Athletics
CARY, N.C. - Enzo Martinez put away his own rebound in the 55th minute to provide the game winning goal in Carolina's (16-2-1) 1-0 win over Boston College (10-4-5) Friday night in the ACC Tournament semifinals. The win extends Carolina's unbeaten streak to an even dozen as Carolina will look for number 13 on Sunday when the Tar Heels take on No. 3 Maryland at 1 p.m. at the WakeMed Soccer Park in Cary, N.C.
The Tar Heels and Eagles battled for possession throughout the opening half as neither team was able to connect many passes in a row. Boston College a trio of shots in the opening 15 minutes as Kyle Bekker had a shot blocked and Amit Aburmad drove a pair of shots that never found the frame.
The Tar Heels had chances of their own as Alex Dixon and Martin Murphy both sent shots wide in the opening half. Elmar Bolowich brought on three new faces in the closing minutes of the first half to make an offensive push but Kirk Urso's shot at 40:37 that sailed wide was the lone shot in the final 30 minutes of the opening half.
Carolina came out of the locker room and immediately put pressure on the Eagle defense and goalkeeper Justin Luthy. Michael Farfan forced Luthy into a save in the 51st minute with a challenging shot. Less than two minutes later Enzo Martinez had an opportunity when he received a pass outside the box and fired a quick shot that rose too quickly over the crossbar.
Midfielder Kirk Urso was challenging Luthy throughout the night from distance but the breakthrough came in the 54th minute.
Urso took a shot from 40 yards out forcing Luthy to the ground to save the blast but he was unable to corral the rebound and Enzo Martinez was johnny on the spot waiting for the ball.
Martinez chipped the ball with his right foot, the ball then hit the left post and bounced right back to the sophomore midfielder. The Rock Hill, S.C., native followed with a quick shot that found the back of the net to give Carolina the one goal lead.
"As soon as I saw Kirk (Urso) wind up, I just took my chance. The keeper dropped it and luckily I was there to take a shot," Martinez said.
Josh Rice nearly made it 2-0 in the 70th minute when he was fed a perfect ball from Michael Farfan just inside the box. Rice ran onto the ball and struck a shot that Luthy was able to deflect out of play for a Tar Heel corner.
Carolina would wind down the clock the rest of the way controlling possession and making occasional runs looking to extend its lead.
"Things started to happen more in front of the ball," head coach Elmar Bolowich said. "I think that made a difference in the game because after Kirk (Urso) took that shot Enzo (Martinez) was right there to finish off the play. Our games are where you just need that one break, where you just need that one opportunistic play to finish it off and break the ice."
The shutout win was Carolina's 10th of the season and third straight shutout for a defense allowing just 0.63 goals against per game.
Carolina snapped a four-game unbeaten streak to Boston College with the win after drawing with the Eagles in Newton, Mass. earlier in the year.
The Tar Heels will make their fifth appearance in the ACC Tournament Final on Sunday when they take on Maryland and will be looking for their third ACC Tournament Title in school history. The Terrapins are riding a 12-game winning streak of their own having won every game since a 2-1 loss at the hands of the Tar Heels Sept. 24 in Chapel Hill.
"It's not only playing Maryland, but it's also playing for a championship. This is something that is big and something that you will always remember if you come out on top," Bolowich said.
The title game can be seen on Fox Sports Carolinas with a kick off scheduled for 1 p.m.


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Magic Broomstick Tours has been teaching people to ride the fabulous Segway Personal Transporter and taking guided tours around Auckland's Historic Village of Devonport (New Zealand) the Volcanic Cones and historic Military Forts since 2008. Therefore we know what it takes to teach people how to safely ride this "State of the Art" Machine, to have FUN and explore all the best places that make Devonport Village unique and exciting.
One of The Best Things to do in Auckland
My late husband started the business after a holiday in Paris where he took a guided tour and fell in love with the sensational Segway Personal Transporter. He was determined to make them one of the top Auckland Attractions, bringing them specifically to Devonport, which then had been our home of 20 years. You'll understand why he named the business "Magic Broomstick Tours" when you experience 'gliding' effortlessly to the top of Devonport's Volcanic Cones, a favourite tourist attraction in Auckland.
I've been running the business since mid 2009, learning the ropes and being the Tour Guide. As the business has grown I now employ other Segway Tour Guides especially in the Summer Season.
Activities in Auckland That Are Fun
It's human nature to be a little apprehensive when learning something totally new therefore your tour guide will take the time to individually help you through the process of learning to ride a Segway (it really is easy) and give you plenty of time to practice before you embark on your Sightseeing Tour. Your guide will be an experienced Segway Rider who is able to handle all conditions while keeping a watchful eye on you as you ride your Segway Personal Transporter. Magic Broomstick Tours is committed to delivering a high quality of service and to giving you value for your money. Our aim is to keep you safe, to give you the most unique experience and to have lots of FUN as you explore the historic village of Devonport.
When your tour comes to an end, you'll know why it's one of the best things to do in Auckland because you will want one of your own and you'll have the "Segway Smile" – a Smile from ear to ear that you cannot wipe off.
See you on a Segway
Call us on +64 (0) 9 4454 035 or +64 (0) 27 3393 155
Best regards