Aedes aegypti in the tropical and sub-tropical countries in the world. Understanding these dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. For this reason, a new model has been proposed to investigate the population dynamics of mosquitoes in a city.The global incidences of dengue virus have increased the interest in studying and understanding the mosquito population dynamics. It is predominantly spread by Ae. aegypti mosquitoes in an urban neighborhood of a city using the finite volume method. The model describes how populations spread through the city assisted by the wind. This model allows incorporating external factors  and topography data . The proposed model has been successfully tested in examples involving two Brazilian cities .The present paper discusses the numerical modeling of population dynamics of Ae. aegypti mosquitoes have been observed in each of the simulations. It was observed that, inside the blocks, the growth of the population for both winged and aquatic phase causes an infestation of Ae. aegypti in a short time. Within the blocks the mosquito population was concentrated and diffused slowly. In the streets, there was a long-distance spread, which was influenced by wind and diffusion with a low concentration of mosquito population. The model was also tested taking into account chemical insecticides spread in two different configurations. It has been observed that the insecticides have a significant effect on the mosquito population for both winged and aquatic phases when the chemical insecticides spread more uniformly along all the streets in a neighborhood of a city.Invasion phenomena of The presented methodology can be employed to evaluate and to understand the epidemic risks in a specific region of the city. Moreover the model allows an increase in efficiency of the existing mosquito population control techniques and to theoretically test new methods before involving the human population.The online version of this article (10.1186/s13071-018-2829-1) contains supplementary material, which is available to authorized users. Ae. aegypti mosquito populations . The. TheAe. m in Eq. . The foum in Eq.  represenquations  and 4)  Ae. aegy∂xM = 0 at the left and right sides and ∂yM = 0 on the top and bottom sides. This type of boundary is used in Examples 1, 2 and 3 in the In order to solve the system of PDEs, we need to specify the boundary conditions of the domain. The case of known net influx of mosquitoes to the city along one side of the domain is referred to mathematically as Neumann boundary conditions. For example, this is the case when considering an isolated part of the city with zero net influx of mosquitoes along each side of the domain. We consider The case, when the amount of mosquitoes is known at one of the sides of the domain, is called Dirichlet boundary conditions. For example, when modeling sea coastal areas, the mosquito population was assumed to be zero along the side which faces the sea. This case is studied in Example 4 in the Ae. aegypti have been discretized using standard FVM, see  × . The system (1)-(2) can be written as a scalar transport equation:U = [M A]T, ϕ is the source term and the others terms are the same as in Eq.  can xi, yj). For the temporal derivative, it results in:U = Uni,j. The integral for the source term isTo obtain the discretization, we integrate the Eq.  in the cX direction. The integral of flow term is:For the convective and diffusion terms in Eq.  considerv = , D = . To find the values of Y direction, see [ion, see .The System (1)-(4) was solved using an in-house finite volume code developed using MATLAB. The forward Euler method was used for time integration. For all time steps the Courant-Friedrichs-Lewy (CFL) condition has been tested guaranteeing the numerical stability.Ae. aegypti mosquitoes in the city of Juiz de Fora with and without the use of chemical insecticides. In the fourth example, we present the numerical results for Copacabana Beach in the city of Rio de Janeiro. The model parameters summarized in Table In this section we present the numerical results obtained by solving System 1)-(4). The simulations were carried out for four different scenarios. The first example corresponds to a city quarter. In the second and third examples, we investigate the population dynamics of -(4). TheY direction is assumed to be larger than the component in the X direction.Let us consider an arbitrary urban square neighborhood composed of building blocks (red) and streets (blue) as plotted in Fig. t = 0), Fig. t = 21 days) and Fig. t = 42 days). Notice that the population for both phases slowly penetrates, by diffusion, from the street into blocks as shown in Fig. Y direction explained by the presence of larger component of wind velocity along the Y direction. As time progresses, we observe that the population of mosquitoes increases inside the blocks  are shown for different times in Fig. cks Fig. , b. The ψ, which represents the coefficient for mosquito area support. In both map and model blocks are separated by streets as shown in Fig. X direction is assumed to be larger in both streets and park as compared to the wind velocity in the Y direction.In order to simulate the population dynamics of mosquitoes in Juiz de Fora, a simplified domain is considered as shown in Fig. ψ) was chosen (Table t = 21 days) and Fig. t = 42 days). One observes that the population in both phases slowly diffuses from the park into the streets and blocks as shown in Fig. X direction due to the larger component of wind velocity along the X direction. As time progresses, the population of mosquitoes increase inside the blocks as expected . Note that for both simulations we used the same amount of insecticides.In this section, the population dynamics of h1 is given in Table As shown in Fig. t = 21 days) and Fig. t = 42 days). Initially, the population of mosquitoes was concentrated in the park. It was observed that the population for both phases slowly diffused from the park into the streets. Notice that, after the use of insecticides along a street, the mosquito concentration near the street was reduced  is shown in Fig. ced Fig. .Fig. 12Eh1) was used to control the mosquito population for the winged phase. However, the reduction in the winged phase has a direct impact on the reduction of the aquatic phase due to the dependence on the source term in Eqs.  and A.The reduction in population for the winged phase is bigger when compared to the one for the aquatic phase. This happens because the killing term h was used in Eqs.  on both h1 is given in the Table The effect of insecticides on the mosquito population was studied along all the streets of the city center in Juiz de Fora Fig. . The valt = 21 days) and Fig. t = 42 days). Notice that, in this example when insecticides have been used in all streets, the mosquito concentration near the streets has been reduced significantly  is shown in Fig. tly Fig. , b.Fig. ΩψM dΩ and ∫ΩψAdΩ for winged and aquatic phases, respectively. From the simulation, we observed that when insecticides were used uniformly along all the streets, the total population of mosquitoes for both phases was reduced significantly , we observed that the population of mosquitoes increased inside the blocks , climate conditions  and human action (insecticides). The modeling was based on the idea that the mosquitoes’ erratic movement depends significantly on the environment and needs to be taken into account when planning public health policies. The model depends on several parameters that can be measured or obtained through history matching. Despite other improvements, the presented model introduces the concept of mosquito area support, which allows the modeling of the non-uniformity of the mosquito population in a different environment.In the present work, the model addressing the proliferation of Ae. aegypti mosquitoes for both the winged and aquatic phase at an urban scale.In order to illustrate the model, four examples were presented for the population dynamics of The first example simulated the generic building blocks neighborhood. The mosquito population grew and dispersed rapidly due to the wind influence. In the second, the example city center of Juiz de Fora was simulated, showing the population growth spread from the park area into the building blocks. The third example used the same data as the previous one with the use of chemical insecticides attacking winged phase in two different configurations maintaining the same total amount of the insecticide. Furthermore, we observed that if the chemical insecticides spread more uniformly along all the streets in a neighborhood of a city, the insecticides have a significant effect on the mosquito population for both winged and aquatic phases. This observation gives a new insight regarding the optimal use of insecticides in a city. The fourth example describes Copacabana Beach area in Rio de Janeiro city taking into account strong and direction-changing winds.The presented methodology is a tool that can be employed to evaluate and to understand not only general epidemic risks but point city regions that are more susceptible to vector transmitted diseases. Moreover, as shown in the Example 3, the model can be used to increase efficiency of the existing mosquito population control techniques and test new methods theoretically, before involving the human population. Furthermore, this model can be coupled with SIR type models to investigate the disease dynamics in a city and include financial costs to assist in public health decisions.Additional file 1:Figure S1. An enlarged view of the center of Juiz de Fora and its surroundings. The figure shows the surroundings of the city of Juiz de Fora (Source: Google Maps). The area marked on the map (red) is shown in Fig. Additional file 2:Figure S2. An enlarged view of Copacabana in Rio de Janeiro and its surroundings. The figure shows the surroundings of the Copacabana Beach, Rio de Janeiro (Source: Google Maps). The area marked on the map (red) is shown in Fig.


XEN glaucoma implant  is a new minimally invasive device approved for the treatment of glaucoma.A 45 year old female was being followed and treated for primary open angle glaucoma in our tertiary referral center. Due to failure of medical treatment in controlling the glaucoma, surgery was offered to the patient. The XEN 45 μ-fistula implant was successfully placed in both eyes and adequate intraocular pressure control was achieved for 4 months. The left eye pressure then increased and the XEN implant was found in the anterior chamber. Topical intraocular pressure lowering therapy had to be re-initiated to achieve adequate pressure control.We describe a new potential complication of the XEN glaucoma implant. Subconjunctival drainage of aqueous humor with bleb formation has been the most widely used surgical option for the treatment of glaucoma. Microinvasive glaucoma surgery (MIGS) has gained considerable interest during the last years and is expected to play an important role in the management of glaucoma patients in the future –3.The XEN implant is one of the new commercially available MIGS devices that can be offered to glaucoma patients. It has recently been approved by the FDA for the treatment of glaucoma. The XEN Gel stent is a 6 mm hydrophilic tube with a 45-μm lumen size composed of a porcine collagen-derived gelatin crosslinked with glutaraldehyde. It has been designed to be non-degrading, cause no foreign body sensation, and bend and conform to tissue reducing risk of erosion. It comes preloaded and it can be injected ab interno creating a drainage pathway between the anterior chamber and the subconjunctival space. Subconjunctival injection of 0.2 mg/ml of mitomycin-C can be also used to improve the long-term outcomes. XEN implantation can be offered as a standalone procedure or in combination with cataract surgery and close postoperative follow up is recommended , 4.Early reports about XEN implantation of different lumen tubes suggest favorable outcomes regarding the intraocular pressure control and number of pressure lowering medications , 6. HoweIn our report we present a case of dislocation of the XEN implant into the anterior chamber. Consent for the publication of this case report and any additional related information was taken from the patient involved in the study. A 45 year old female was being followed and treated for primary open angle glaucoma in our clinic. Pretreatment intraocular pressure was 31 mmHg in the right eye and 26 mmHg in the left eye and central corneal thickness was 496 μm and 494 μm respectively. The patient was asthmatic  and was on immunosuppressive treatment (including short term courses of systemic steroids) because of severe eczema. She also presented with multiple allergies to pharmacological and non-pharmacological agents. Patient showed intolerance to topical preservatives so preservative free treatment had to be initiated. Despite maximum tolerated topical treatment with two IOP lowering medications (tafluprost 15 μm/ml once in the evening and dorzolamide 20 mg/ml preservative free twice per day) intraocular pressure was not well controlled in either of the eyes, being as high as 26 mmHg in both eyes. As the glaucoma was progressing and the pressure was not controlled, XEN implantation was offered to the patient for both eyes. After risks and benefits of surgery were discussed, patient consented to the treatment offered. XEN implantation was performed as a standalone procedure first in the left eye and then in the right eye on different dates. Since its introduction, XEN implant has gained its position in our unit in the management of open angle glaucoma and we have performed over 40 cases during the first year.The routine surgical steps for XEN implantation in our unit followed in both eyes included: 0.2 mg/ml of Mitomycin C injected subconjunctivally at the area of planned XEN implantation, marking the conjunctiva 3 mm from the limbus superonasally, 7–0 silk as traction suture at the superior cornea, temporal clear cornea incision, filling of the anterior chamber with Healon GV  and use of the preloaded 27 gauge needle to insert the XEN implant at the superonasal part of the anterior chamber angle under gonioscopic view. Following that a 10–0 nylon suture was placed at the corneal incision and Healon GV was irrigated out of the anterior chamber. Following this technique only the tip of the stent projects in the anterior chamber and can be viewed during gonioscopy. The implant was successfully implanted in both eyes and patient received frequent topical steroids slowly tapering over the next 3 months and topical antibiotics for 1 week.Surgery was successful in both eyes, with an un-eventful postoperative period and no adjunctive procedures (e.g. needling) were needed in either of the eyes. Slit lamp biomicroscopy and anterior segment OCT confirmed proper positioning of the XEN implant Fig. . IOP wasSix months after XEN implantation the patient presented to the Accidents and Emergency Department of our Eye Hospital complaining of a painful left eye for 1 week. Intraocular pressure was 15 mmHg in the left eye at that point and the anterior chamber was deep and quiet. Episcleral injection was noticed during the slit lamp biomicroscopy and the patient was diagnosed with diffuse unilateral episcleritis in the left eye and started with a 2 weeks tapering treatment of loteprednol etabonate (5 mg/ml). The patient was reviewed at the outpatients 1 month later. Episcleritis had resolved at that point but intraocular pressure was 35 mmHg and the whole XEN implant was noted to lie inferiorly in the anterior chamber angle (Fig. Our report suggests that dislocation of the XEN implant into the anterior chamber can happen after successful placement. The implant has been designed to become soft and swell up slightly within 1 or 2 min after implantation. This flexibility and tissue conforming of XEN has been suggested to reduce the risk of implant migration. More specifically the implant has been shown to form an “S” curve going through the scleral channel and this characteristic is supposed to mitigate potential migration. [In conclusion, our report suggests a new potential complication of the placement of the XEN implant: dislocation to the anterior chamber. It is unclear if the episcleritis was a triggering factor and patients should be advised to avoid rubbing the eye after XEN placement. The implant was well tolerated in the anterior chamber and no anterior chamber inflammation was observed during the period of follow-up.Financial Disclosure: Kestrel, who were marketing the product mentioned in the case study, paid for Miss Lewis to go on a training course to learn how to use the product. No disclosure for the rest of the authors


The dynamic behavior of a nematic liquid crystal with added carbon nanotubes (CNTs) in an electric field was analyzed. A theoretical model based on elastic continuum theory was developed and the relaxation times of nematic liquid crystals with CNTs were evaluated. Experiments made with single-walled carbon nanotubes dispersed in nematic 4-cyano-4’-pentylbiphenyl (5CB) indicated a significant difference of the relaxation time when compared to pure liquid crystal. We also noticed that the relaxation time when the field is switched off depends on how long the field was applied. It is shorter when the field is switched off immediately after application and longer when the field was applied for at least one hour. The increased interest for nanomaterials in different domains such as chemistry, medicine or engineering, makes their characterization quite necessary. This might be the reason why there are so many research papers presenting new materials and new experiments regarding their behavior in different external electric, magnetic or laser fields –8. In ma6When nanoparticles are inserted in liquid crystals, nematic molecules are attached to the particle surface due to anchoring forces. Experimental studies revealed that carbon nanotubes have a strong interaction with liquid crystal molecules and align themselves parallel with the long axis of the nematic –14. UndeWhen a liquid crystal with positive dielectric anisotropy is exposed to an external electric field higher than the critical Fréedericksz transition threshold, its molecules have a tendency to orient their director parallel to the applied field, deviating by an angle θ from their initial direction .m) after a time period called the relaxation time. Consequently, the refractive index of the cell is also changing:This deviation reaches its maximum value /λ. For a planar aligned cell in which small values of θ are considered, this phase difference becomes:The intensity of the beam traversing through the sample placed between two cross polarizers is:m). For the analysis of this angle we must take into account all the interactions of the nematic molecules with the surrounding molecules, with the carbon nanotube surfaces, with the glass support and with the applied field. By applying the elastic continuum theory we can write the free energy of a system consisting of a liquid crystal and SWCNTs in electric field as:The time dependency of the emergent beam intensity is given by the maximum deviation angle , the molecular orientation is characterized by the distortion angle θ between the director and the x-axis  and low concentration (0.1% volumetric fraction) we assumed that the carbon nanotubes will not change their orientation as fast as the liquid crystal molecules. The case of strong anchoring of nematic molecules to the nanotubes surface and a homogeneous alignment of the cell was considered. Thus, in the absence of any external fields, the nematic director and carbon nanotubes axis are parallel to the  support . If the  support . If the  support . In thisWhen reaching the threshold value, θ increases by a small amount. Consequently, we consider only small values of θ to evaluate the free energy:andUsing Equations As the first two terms in Using the Euler–Lagrange equation:d/2) = θ(d/2) = 0, we obtain the threshold voltage for the Fréedericksz transition:and considering the boundary conditions for a strong anchoring on the cell support, θ is the maximum value of the deviation angle when the electric field is applied for a very long period of time, x0 is a constant parameter and τon is the relaxation time when the field is switched on. Following a similar procedure as in [where θre as in –24, we gx-axis. In this case the relaxation time will be smaller than that of a pure nematic because the interaction forces between nematic molecules and carbon nanotubes pull the molecules back to a planar alignment. The free energy density results from U = 0:We consider two different cases for switching the field off: First, when the field is switched off immediately, the nanotubes are still aligned along the The time variation of the maximum deviation angle is: is the initial value of the maximum deviation angle, ζ is a parameter depending on the carbon nanotube concentration, the interaction energy and the physical properties of nanotubes and liquid crystal. The relaxation time when the field is switched off immediately after its application to the SWCNT containing sample is:where while for the pure liquid crystal it is:It can be seen the relaxation time for LC + SWCNTs is shorter than that of the pure nematic. The second case we consider is the application of the field for a period of time that is long enough to allow the carbon nanotubes to align themselves in parallel to the field. In this case the free energy density is:and the relaxation time is:As shown in We used SWCNTs provided by Aldrich having a diameter of 1.2–1.5 nm and a length of 2 up to 5 μm. A 0.1% volumetric fraction of nanotubes was mixed with 5CB and sonicated for several hours at 40 °C. The mixture in the isotoropic phase was used to fill a planar aligned cell with a thickness of 15 μm from Insteck also warmed at 40 °C. Then the samples were slowly cooled down to 29 °C in a holder placed inside a Mettler Toledo stage. The terminals of the holder were connected to a HIOKI RLC power source from which a 10 kHz ac voltage was applied. A 632.8 He–Ne laser sent a beam through the sample placed between two crossed polarizers . A Thor By slowly increasing the electric field applied, the Fréedericksz transition was determined both for LC and LC + SWCNTs .Since the theoretical evaluation considered only small deviation angles, the first intensity maxima from off)I is the relaxation time when the field is switched off immediately and (τoff)L is the relaxation time when the is switched off after one hour.The calculated relaxation times when the field is switched on or off provided from the fitting parameters are similar to the times obtained from experimental data. When the field is switched on, the molecules begin to align with the field but the interaction forces with the nanotube surfaces pull them back. This might explain why the Fréedericksz transition threshold and the relaxation times of the SWCNT-containing samples are higher than those of the pure nematic. When the field is switched off immediately, the anchoring forces act in the same direction as the elastic molecular forces making the molecules move faster to their original position. Other dynamic measurements performed on similar systems –26 confiWe present a simplified theoretical model to explain the behavior of nematic liquid crystals with added carbon nanotubes in an external electric field. This model is in good agreement with our experimental results but also with other published studies. Thus, a proper characterization of these nanomaterial compounds can be made and a deeper understanding of the anchoring forces influence on the physical properties of the mixture is provided.


Inference of gene regulatory network structures from RNA-Seq data is challenging due to the nature of the data, as measurements take the form of counts of reads mapped to a given gene. Here we present a model for RNA-Seq time series data that applies a negative binomial distribution for the observations, and uses sparse regression with a horseshoe prior to learn a dynamic Bayesian network of interactions between genes. We use a variational inference scheme to learn approximate posterior distributions for the model parameters.The methodology is benchmarked on synthetic data designed to replicate the distribution of real world RNA-Seq data. We compare our method to other sparse regression approaches and find improved performance in learning directed networks. We demonstrate an application of our method to a publicly available human neuronal stem cell differentiation RNA-Seq time series data set to infer the underlying network structure.Our method is able to improve performance on synthetic data by explicitly modelling the statistical distribution of the data when learning networks from RNA-Seq time series. Applying approximate inference techniques we can learn network structures quickly with only moderate computing resources. Methods for the inference of gene regulatory networks from RNA-Seq data are currently not as mature as those developed for microarray datasets. Normalised microarray data posses the desirable property of being approximately normally distributed so that they are readily amenable to various forms of inference, and in the literature many graphical modelling schemes have been explored that exploit the normality of the data –9.The data generated by RNA-Seq studies on the other hand present a more challenging inference problem, as the data are no longer approximately normally distributed, and before normalisation take the form of non-negative integers. In the detection of differential expression in RNA-Seq data, negative binomial distributions have been applied –13, provOne specific case of interest in the analysis of RNA-Seq data is the study of time series in a manner that takes into account the temporal relationships between data points. Previous work in the literature has developed sophisticated models for the inference of networks from microarray time series data , 5, but Here we present a method for the inference of networks from RNA-Seq time series data through the application of a Dynamic Bayesian Network (DBN) approach, that models the RNA-Seq count data as being negative binomially distributed conditional on the expression levels of a set of predictors. Whilst there has been work applying negative binomial regularised regression approaches in the literature , here wet is dependent only on the values of a set of parent variables at time t−1. This is illustrated in Fig. In a DBN framework , considei) is the set of parents of variable i in the network. In our case we wish to model the expression level of a gene conditional on a set of parent genes that have some influence on it. To learn the set of parent variables of a given gene, it is possible to perform variable selection in a Markov Chain Monte Carlo framework, proposing to add or remove genes to the parent set in a Metropolis-Hastings sampler. Another option is to consider all possible sets of parent genes as suggested in [where Pa whose coefficients are significantly larger than zero as parents. To simplify the presentation, below we consider the regression of the counts for a single gene i, y=DL,i2:, conditional on the counts of the remaining W=M−1 genes X=DL−1),−i1:t and dispersion ω, where β is a vector of regression coefficients βw and a constant term βc. The model for a gene i is then The counts st is a scaling factor for each sample to account for sequencing depth. The st can be estimated from the data by considering the sum of counts for each sample, or by the more robust approach of [βc and to enforce sparsity of the βw we apply a horseshoe prior [where we have applied the NB2 formulation of the negative binomial distribution, and roach of  where thoe prior , 24, assτ that allows the degree of shrinkage to be learnt from the data Then as in  we set aβw can be seen in figure 8 in Appendix 2. Finally we place a gamma prior on the dispersion parameter ω. This gives a joint probability (subsuming the model parameters into θ) of An example of the sparsity induced in the p(θ|x) with a distrubtion q(θ). To do so we attempt to minimise the Kullback-Leibler (KL) divergence between the two, defined as We now apply a variational inference –30 schemAs the KL divergence is bounded below by zero, it follows from and so we can define a lower bound on the logarithm of the model evidence as q(θi) on some partition of the parameters, To make the problem of minimising the KL divergence tractable we can consider a mean field approximation where the posterior is approximated by a series of independent distributions p(θ|x) and q(θ), or equivalently to maximise the model evidence lower bound (or ELBO) q(θi) is Under the mean field assumption it can be shown that to minimise the KL divergence between q(θj≠i). In many cases this formalism is sufficient to derive a coordiante ascent algorithm to maximise the ELBO where the variational parameters of the where the expectation is over the remaining βw does not have a tractable solution. However following [Unfortunately in our model the optimal distribution ollowing  we can sollowing , and we θi by considering the neighbours of θi. Then we can rewrite Eq. Considering our model as a graphical model as in Fig. i denotes the children of node i in the graphical model. Considering each term on the right hand side of Eq. where Chly as in . In the ly as in , derivedly as in .Saccharomyces cerevisiae gene regulatory network, and then simulating the dynamics of the networks under our DBN model. Subnetworks of 25 and 50 nodes were generated and used to simulate 20 time points with 3 replicates.We apply our method to the task of inferring directed networks from simulated gene expression time series. The time series were generated by utilising the GeneNetWeaver  softwareβ sampled from a mixture of equally weighted ERP003613) consisting of 171 samples from 25 tissues in humans [Synthetic count data were generated by constructing a negative binomial DBN model as in Eq. database   true positives than true negatives, a situation in which the AUC-ROC does not distinguish performance as well as AUC-PR [For networks of 25 nodes in Fig. s AUC-PR , 40.As can be seen in Fig. SRP041159. The data consist of RNA-Seq counts from neuronal stem cells for 3 replicates over 7 time points after the induction of neuronal differentiation [To illustrate an application of our model to a real world RNA-Seq data set, we consider a publicly available RNA-Seq time course data set available from the recount2 database , accessintiation , and selApplying our method and selecting edges with a posterior probability > 0.95 produced the network shown in Fig. For each node we also calculate the betweenness centrality, which is the fraction of the total number of shortest paths between nodes in the network that pass through a given node. This gives a measure of the importance of a node in the network, as nodes with a larger betweeness centrality will disrupt more paths within the network if deleted, and act as bottlenecks that connect modules within the network. Looking at the betweenness centrality of each node it appears that PARP12 and CDON, and to a lesser extent COL17A1, are important carriers of information within the network. Of these genes playing a central role in the network, CDON has been shown to be promote neuronal differentiation through the activation of p38MAPK pathway , 43 and We have developed a fast and robust methodology for the inference of gene regulatory networks from RNA-Seq data that specifically models the observed count data as being negative binomially distributed. Our approach outperforms other sparse regression based methods in learning directed networks from time series data.Another approach to network inference from RNA-Seq data could be to further develop mutual information based methodologies with this specific problem in mind. Mutual information based methods have the benefit of being independent of any specific model of the distribution of the data, and so could help sidestep issues in parametric modelling of RNA-Seq data. However this comes at the cost of abandoning the simplifying assumptions that are made by applying a parametric model that provides a reasonable fit to the data, and presents challenges of its own in the reliable estimation of the mutual information between random variables.From the results in  the modeβ represented using a mixture of inverse gamma distributions, and the horseshoe prior on The mean field approximation of the posterior is then λt can be derived as The variational updates for and due to the properties of the log-normal distribution Σ is the covariance matrix of β under where β is As derived in , applyinω we apply numerical integration as described in [and for the dispersion ribed in .β, the variational updates are Then for the horseshoe prior on


Although glaucoma is the lead cause of irreversible blindness globally, the condition shows no signs or symptoms until later stages. Knowledge about the disease is known to influence utilization of eye screening services. This study aimed at understanding knowledge and perception of risk for glaucoma, as well as eye screening behaviour among residents of Abokobi, a peri-urban community.This was a cross-sectional study that employed quantitative data collection methods, with the use of a questionnaire. Descriptive statistics were used to describe the socio-demographic characteristics, knowledge about glaucoma and eye screening behaviour. Also, associations between socio-demographic factors and awareness as well as perception of risk were analysed using Chi-square test or Univariate Fisher’s exact test.p <0.0001) were statistically significant with glaucoma awareness. Approximately, 20.7 % of the respondents have had their eye screened with just a few (4.3 %) screening for glaucoma.Out of a total of 300 respondents, 60.3 % were females and 39.3 % were aware of glaucoma. Majority (99.1 %) of respondents aware of glaucoma also agreed the disease can result in blindness with only (28 %) affirming that blindness from glaucoma is irreversible. Nearly half (49.7 %) of the respondents perceived themselves to be at risk of developing glaucoma. The results showed that age and education  contains supplementary material, which is available to authorized users. Glaucoma is defined as a neuropathy with structural (optic disc damage) and functional loss  , 2. GlauGlaucoma is a global public health problem, because it is the highest cause of irreversible blindness and the second leading cause of blindness after cataract , 4, 6. YHigh glaucoma morbidity among some African communities may be attributed to low awareness, under-utilization of eye care services as well as the limited availability of treatment procedures , 19–21. In Ghana the healthcare system does not currently provide enough incentive for people to seek regular ophthalmologic care . Rather,Use of alternative healthcare services is driven by how glaucoma is often perceived , 33. WheThis is a cross-sectional survey conducted in Abokobi, the district capital of the Ga East Municipality. Ga East is one of the districts in Greater Accra region with a population of about 33,500 people. Eligibility criteria for the study population was based on age and residence of the individual. The study population is adults, 18 years and above who are residents of Abokobi.Simple random sampling was done to select study population. The sample size of 300 was determined using Cochran’s formula (1963–1975). The principal investigator together with the research assistants drove through the community and counted the residential structures in it. Approximately 2700 structures were counted and this was divided by the sample size of 300 to get an interval of nine. In the community, the principal investigator and research assistants tossed a bottle to determine a random direction. The first structure in the determined direction was used as the starting point and an interval of nine structures was counted to determine the next structure to be sampled until the sample size of 300 was obtained. Eligible respondents found at home or workplace were asked to ballot and either pick a yes or no after which the respondent who picked the yes was asked willingness to participate and consent taken. One respondent was taken from each structure.. Ethical approval for the study was obtained from the Ghana Health Service. Permission was also obtained from the Health Directorate of the Ga East District.Interviewer administered structured questionnaires was used to obtain data from the respondents. Data was collected by the principal investigator and two research assistants who were trained on research ethics, seeking informed consent and the research questionnaire  of the respondents being between 40 and 49 years old (Table n = 118) of all the respondents indicated they had heard about the eye condition glaucoma. Out of the respondents who had heard about glaucoma, 56.8 % of them were females . Likewise religious affiliation was also not statistically significant  irrespective of the fact that a greater percentage of Christians (36.3 %) affirmed to glaucoma awareness as opposed to 3.0 % of Muslims. However, there was a significant relationship between glaucoma awareness and age  with most (42) of the respondents between the ages of 40 and 49 years being aware of the disease. Likewise, most of the Junior High School graduates were aware of glaucoma and this was also statistically significant .Thirty nine percent  of the respondents agreed that glaucoma results in blindness. About 77.1 % of the respondents also agreed that glaucoma causes reduction of visual acuity. Approximately 64.4 % of them also affirmed it was possible to have glaucoma without knowing with 28.8 % of the respondents agreeing that blindness from glaucoma is irreversible and the least (4.2 %) number of respondents agreeing that Africans stand a higher risk of developing the disease than whites Table .Table 3RGenerally all respondents were asked if they perceived themselves to be at risk of developing glaucoma of which 149 out of the 300 respondents perceived themselves to be at risk of developing the disease. Respondents were further asked if they perceived their sex, age, religion, occupation, educational or marital status made them susceptible to developing glaucoma. The perception of risk of glaucoma in relation to sex, age and religion was not statistically significant (Table N = 62) had ever gone for an eye screening. Respondents reported screening for eye conditions such as glaucoma, refractive error, pain in eyes and even driver’s license  of awareness aand basic knowledge of glaucoma as well as low perception of risk among respondents. The low awareness of the disease is not surprising as a study conducted by Ntim-Amponsah et al. in Ghana showed that about 94 % of people diagnosed with glaucoma were unaware that they had the disease prior to being diagnosed. Furthermore, the Low awareness levels and knowledge of glaucoma in this study population could be due to the little or non-existent publicity about glaucoma in the community or the country as a whole. Moreover, access to ophthalmic care in Abokobi may have contributed to the low levels of glaucoma awareness since Abokobi’s ophthalmic needs are attended to by one ophthalmic nurse who visits the Abokobi Health Centre once a week. Adequate access to ophthalmic services and proper utilisation of eye care services can create greater awareness and publicity to information about various eye diseases including glaucoma  Unfortun.3 % of aAge was statistically significant with glaucoma awareness in this study, respondents between the ages of 40 and 49 years were significantly more aware of glaucoma than the other age brackets. The low level of glaucoma awareness (2.7 %) in the younger generation could be because younger people perceive eye diseases to be a problem of the older generation. They therefore do not pay much attention to eye diseases, much more a disease like glaucoma which is asymptomatic. A study in the United Kingdom among African Caribbean’s on glaucoma awareness and perception of risk discovered that they perceived themselves to be at risk of glaucoma in their old age . HoweverThe translation of some English words to the local dialects Ga and Twi may have resulted in some missing emphasis or misrepresentation on the translated words.The findings of this study on glaucoma awareness and knowledge bring to light the need to intensify efforts to create awareness and reduce morbidity from this disease. Health workers must actively take up mass education campaigns to clarify misconceptions about the disease and its risk factors.


The purpose of the present study was to use a commercially available grayscale phantom to compare two ultrasound systems regarding their ability to reproduce clinically relevant low‐contrast objects at different sizes and depths, taking into account human observer variability and other methodological issues related to observer performance studies. One high‐end and one general ultrasound scanner from the same manufacturer using the same probe were included. The study was intended to simulate the clinical situation where small low‐contrast objects are embedded in relatively homogeneous organs. Images containing 4 and 6.4 mm objects of four different contrasts were acquired from the grayscale phantom at different depths. Six observers participated in a 4‐alternative forced‐choice study based on 960 images. Case sample and human observer variabilities were taken into account using bootstrapping. At four of sixteen depth/size/contrast combinations, the visual performance of the high‐end scanner was significantly higher. Thus, it was possible to use a grayscale phantom to discriminate between the two evaluated ultrasound systems in terms of their ability to reproduce clinically relevant low‐contrast objects. However, the number of images and number of observers were larger than those usually used for constancy control.PACS number(s): 87.57.C‐, 87.63.dh The purpose of the medical ultrasound system is to reproduce the echogenicity of the patient as accurately as possible. There are many steps involved from the actual examination to the outcome of the same. The acoustic properties of the patient, the transmitter unit, how the beams are formed, the properties of the transducer, the receiver, how the signals and the image are processed, the quality of the display, and finally the ability of the user to drive the scanner and probe and interpret the displayed information all affect the probability for a correct diagnosis. One of the quantitative objectives in the B‐mode image is to detect and, if possible, identify the presence of limited‐size tissue masses (lesions) within or adjacent to a reference tissue.Quantifying the performance of medical imaging modalities can be done either by using human or model  observers. Since model observers generally involve simple detection and discrimination tasks — in which a known target profile embedded in noise is discriminated from a known alternative profile — the development of models has typically considered diagnostic features in terms of signal and noise characteristics.It is tempting to use a model observer instead of human observers also to measure differences in performance between systems or to assess the impact of a change for a given system. However, when, for example, new techniques  are released in a new model, the correlation between the human and model observer, even if shown for previous existing conditionsHuman observer studies are often based on receiver operating characteristics (ROC) analysisIntra‐ and interobserver variability is always present in studies involving human observers. The outcome of a study based on a small number of images and observers may therefore be of limited value. This is also of relevance when trying to assess low‐contrast detectability, regardless whether methods such as ROC and MAFC studies or subjective assessments are used. Always using human observers in control of the low‐contrast detectability may therefore be impractical, as described by Thilander‐Klang et al.Despite the reliability problems associated with human observer studies, such studies may nevertheless be needed when validity is essential. The highest validity is normally obtained if the images included are images of humans, as this results in a test situation most resembling the clinical situation. However, as patient anatomy varies much, acquiring an image material providing a fair comparison between systems may be difficult even if the patients are their own test and control. An additional difficulty of detection studies is that they rely on a known truth. If phantoms are used instead of patients, the experimenter has complete control over the ground truth and the acquisition conditions. However, for results based on phantom studies to be valid, the images produced by the phantom need to be relevant in terms of the appearance of the image background and the objects used to represent signals. Nevertheless, if the size, contrast, and depth of the objects in the phantom are clinically relevant, such studies may be of value in the comparison of different systems.The purpose of the present study was to use a commercially available grayscale phantom to compare two ultrasound systems regarding their ability to reproduce clinically relevant low‐contrast objects at different sizes and depths, taking into account human observer variability and other methodological issues related to observer performance studies. The study was intended to simulate the clinical situation where small low‐contrast objects are embedded in relatively homogeneous organs.‐9dB,‐6dB,‐3dB,+3dB,+6dB, and +9dB. The depth possible for scanning varies for the different sizes: 1–6 cm for 2.4 mm, 2–9 cm for 4 mm, and 3–12 cm for 6.4 mm, according to the specifications. The maximum depth for the 2.4 mm objects is 6 cm and in abdominal examinations, the depth of the region of interest (ROI) is often deeper. Regarding the clinical relevance of lesion size, a retrospective clinical study of liver lesionsAs described above, the present work was restricted to simulate the situation where small low‐contrast objects  are embedded in relatively homogeneous organs in the abdomen , where speckle is the dominating image property affecting detection. The best way to perform a comparison of low‐contrast lesion detectability with real observers would be to choose a tissue mimicking phantom that makes it possible to acquire many statistically independent views of each targetTwo ultrasound systems were included in the present study, a high‐end GE Logiq9 (L9) and the more general GE Logiq P5 (LP5) . In order to isolate the capability of the scanner itself, the same probe was used for both scanners (curved array C4 standard probe (2–5 MHz)). The probe was tested and approved by the standards of Sonora FirstCall test system . The default Abdomen settings, presented in Using MATLAB , the acquired images were used to produce a dataset suitable for a 4‐alternative forced‐choice (4‐AFC) study. Around each signal, three background regions were extracted from the image .+6,+3,+3, and +6dB were extracted from the same image for every combination of scanner, object size, and depth. The position of the signal image was randomized for each of the 4‐AFC images. As an aid, a reference square containing an object of the same size and contrast as the signal was shown on top of each imageThe four regions  were used to produce 4‐AFC images. Each of the contrast levels 960(2object sizes×4contrast levels×2depths×2scanners×30images) 4‐AFC images. The observers were not blinded to the design of the experiment, but they were blinded to the origin of the images in the experiment.Six observers participated in the 4‐AFC study, five medical engineers and one medical physicist. All observers had experience of ultrasound imaging and four of them regularly performed image quality control of medical imaging systems. The instruction to the observers was to determine which of the four squares contained the signal. No time limitation was set, the viewing distance was free, and the observers were free to alter zoom and window/level. Nearest‐neighbor pixel value interpolation was used and the default zoom level was twice as many pixels along one side as the original size. ViewDEXn=6) and images (n=30) was determined as figure‐of‐merit (FOM). In order to correctly take all sources of uncertainty into account, bootstrapping was used to determine the uncertainty of the FOM. No assumptions about the underlying distribution are needed when using nonparametric bootstrapping.FOM=1). Additionally, for some of the confidence intervals PC=1 was included. In these cases it is impossible to numerically transform PC to d’ since the value of d’ that corresponds to PC=1 is plus infinity. For this reason, only PC is presented in the results, as in the study of Miéville et al.<0.01 was considered indicating a statistically significant difference.For each combination of contrast, size, and depth, PC averaged over observers . The CV for the single observer was determined based on this expression of the variance. To demonstrate the necessity of taking possible dependencies in the data into account in the statistical analysis, as a comparison the result of using the product of the number of images and the number of observers as N was calculated — as if every new image/observer combination was a unique trial . This result was compared with the CV determined from bootstrapping, as described above.where ±3dB vs. ±6dB, in total four comparisons) were made for the eight combinations of fixed scanner (n=2), size (n=2) and depth (n=2). Thus, this resulted in 32 comparisons where it was expected to obtain a significant difference in PC. Since the result was expected to be better for the ±6dB contrast levels, a one‐sided p‐value <0.01 was used to evaluate if the differences were significant. Additionally, comparisons where no difference in PC was expected were also performed: the positive and negative contrasts for 3 and 6 dB were compared to each other when scanner, size, and depth were fixed. This resulted in 16 comparisons and a two‐sided p‐value of 0.01 was set as a limit for significant difference. Finally, the observers’ results were compared to each other pairwise. In this comparison, all data from each observer were included and a two‐sided p‐value <0.01 was used to determine a significant difference in PC between each observer pair.To put the obtained results between the scanners in perspective, comparisons between different contrast levels  showed significant differences (p<0.01) when the scanner, size, and depth were fixed. For the 16 comparisons between the positive and negative contrast levels of the same strength, three comparisons showed significant differences when the scanner, size, and depth were fixed.All 32 comparisons between the different contrast levels (p<0.01) than Observer 1, Observers 3–6 significantly better than Observer 2, and Observer 6 significantly better than Observer 3.Differences among the observers were seen. Observers 2–6 performed significantly better  with increasing frequency but that the attenuation was nonlinear, which could affect penetration depth at higher frequencies. As long as the compared objects are far from the penetration depth, this effect would probably be minimal. The backscatter properties of the tissue‐mimicking material in the CIRS 047 are not mentioned in the specification from the manufacturer other than “scatter controlled independently from attenuation”. The backscatter coefficient is difficult to measure accurately and is therefore rarely reported in the literature.Regarding the clinical relevance of the background, the properties of different tissue‐mimicking materials in ultrasound phantoms have previously been studied by Browne et al.±6dB were the highest contrasts used in the present study. Regarding producing accurate images, another difference between using spherical and cylindrical objects is that phantoms containing spherical objects are more sensitive to the position of the probe. The beam has to align very accurately with the plane intersecting the center of the spheres. The position is important for the cylindrical objects as well, but an error in position affects what is being reproduced much more with the spheres. The presented method is a compromise between acquiring many independent images of the same objects of different contrasts and the bias of the partial volume effect when using cylinders instead of spheres, when using a commercially available ultrasound phantom.Regarding the phantom properties, to use objects formed as cylinders to evaluate the ability to detect spherical lesions has been questioned, since the effect of the slice thickness on the image is not taken in account.Another issue is the angle between the vertical line from the center of the probe and the line from the center of the probe to the center of the object. Hall et al.Regarding the study design, the images in a multiple‐alternative forced‐choice study should be statistically independent.A significant problem when comparing ultrasound systems is to choose what the settings should be. One single set of settings may be preferred to keep the amount of images at a reasonable level, even if this is not the way ultrasound is used in the clinical situation where the user instead often optimizes the settings depending on the task. There are mainly three ways to handle a single set of settings when comparing ultrasound systems. The first is to have standardized settings for the systems, which to some extent simplifies the comparison. However, some of the features may have to be suspended if those features are not available for all of the compared systems, leading to an unfair comparison and somewhat invalid results. The second way is to allow a representative of each manufacturer to optimize the system for the task. Although this probably makes the best use of the systems, the outcome becomes dependent on the expertise of the representatives and it may thus be difficult to remap the results for general use. The third way, and the one chosen for the present feasibility study, is to use the default setting for a certain and relevant examination.  The reason for this approach was to compare the systems using the settings that the manufacturer finds appropriate for a given type of examination using a certain combination of probe and scanner. In the present study the L9 used some (low) crossbeam  for the Abdomen setting while the LP5 did not. This may have contributed to better visibility at shallower depths for the L9. Regarding the frequency the default setting was used here as well, which in this case was different for the two compared systems even if the same multifrequency probe was used. Kofler et al.A large issue of observer performance studies is the statistical uncertainty. The use of nonparametric bootstrap as a plug‐in principleIt may be surprising that a significant difference between the scanners was found in only four of sixteen comparisons even if the number of images and number of observers were relatively large. This indicates that it may be hard to detect differences when all the sources of variability are correctly taken into account, especially when the variability of the observers is introduced. When comparing performance, it may nevertheless be necessary to base the study on human observers, even if it is laborious, to achieve a high clinical validity of the results. For quality control, on the other hand, the present study indicates that other methods may be meritorious. However, the quality control may be intended to take the clinical effect of a detected change into account. For example, a malfunctioning probe element may be acceptable as long as it does not affect the clinical use of the probe. In such instances, it may be of value to employ methods with a high clinical validity also for quality control.−6dB at the ground depth for the two scanners. All observers got all answers right for the negative contrast, whereas one observer missed two and five answers for the positive contrast for the two scanners. When the PC values are so close to 1 as these are, some missed values have large influence on the difference. These points using the largest sizes of the positive and negative 6 dB objects turned out to be too easy to see to get desired differentiation for a 4‐AFC study. The third point that showed a difference was the 4 mm objects at ±3dB signal at ground depth for L9. Studying +3dB signal is unexpectedly high, which is the reason for the significant difference found. That type I or type II errors may be committed in studies is an unavoidable effect of hypothesis testing, and that a few type I errors assumingly have occurred here is not unexpected given the multitude of comparisons being made. In general, though, these results indicate that the method is robust and that it does not result in an unexpectedly high rate of type I or type II errors. That the method found four significant differences between the two scanners, and that it in all cases was the same scanner that performed better, should strengthen the confidence that the method may be used to discriminate between ultrasound scanners in terms of their ability to reproduce clinically relevant low‐contrast objects.To put the results between the scanners in perspective, 32 comparisons were made where a significant difference in PC was expected, since all comparisons were made between higher and lower contrast levels and everything else was constant. All of the comparisons showed the expected difference. Thus, the method resulted in no false‐negatives (or type II errors) in these comparisons. When the positive and negative values of the same contrast levels were compared when everything else was constant, 3 out of 16 comparisons showed significant differences. Assuming that there should be no difference in detection between the positive and negative contrasts of the same magnitude, this means that the method resulted in three false‐positives (or type I errors). Two of them were the 6.4‐mm objects at signal levels + and In the present study the purpose of using several observers was mainly to get a result that was representative for a general observer, but by using several observers a better statistical uncertainty was also expected. Finally, a preliminary analysis of some of the data in the present study has been presented by Lorentsson et al.The purpose of the present study was to use a commercially available grayscale phantom to compare two ultrasound systems regarding their ability to reproduce clinically relevant low‐contrast objects at different sizes and depths, taking into account human observer variability and other methodological issues related to observer performance studies. A four‐alternative forced‐choice experiment was conducted in which the detectability of details of different size, contrast and depth was compared between two ultrasound scanners from the same manufacturer. The study was intended to simulate the clinical situation where small low‐contrast objects are embedded in relatively homogeneous organs. A bootstrapping technique was used to take case‐sample and human‐observer variabilities into account. For four of sixteen combinations statistically significant differences were obtained, in favor of the high‐end machine. Thus, it was possible to use a grayscale phantom to discriminate between the two evaluated ultrasound systems in terms of their ability to reproduce clinically relevant low‐contrast objects. However, the number of images and number of observers were larger than those usually used for constancy control.This work is licensed under a Creative Commons Attribution 3.0 Unported License.Supplementary MaterialClick here for additional data file.


The availability of more data of dynamic gene expression under multiple experimental conditions provides new information that makes the key goal of identifying not only the transcriptional regulators of a gene but also the underlying logical structure attainable.We propose a novel method for inferring transcriptional regulation using a simple, yet biologically interpretable, model to find the logic by which a set of candidate genes and their associated transcription factors (TFs) regulate the transcriptional process of a gene of interest. Our dynamic model links the mRNA transcription rate of the target gene to the activation states of the TFs assuming that these interactions are consistent across multiple experiments and over time. A trans-dimensional Markov Chain Monte Carlo (MCMC) algorithm is used to efficiently sample the regulatory logic under different combinations of parents and rank the estimated models by their posterior probabilities. We demonstrate and compare our methodology with other methods using simulation examples and apply it to a study of transcriptional regulation of selected target genes of Arabidopsis Thaliana from microarray time series data obtained under multiple biotic stresses. We show that our method is able to detect complex regulatory interactions that are consistent under multiple experimental conditions.https://github.com/giorgosminas/TRS and at http://www2.warwick.ac.uk/fac/sci/systemsbiology/research/software.Programs are written in MATLAB and Statistics Toolbox Release 2016b, The MathWorks, Inc., Natick, Massachusetts, United States and are available on GitHub Bioinformatics online. Elucidating the structure of gene regulation from biological data is a key task of systems biology with applications spanning across biology and biomedicine , ChIP-chreverse-engineering or network inference methods focus on inferring interactions between a large number of genes from high-throughput expression profiles  model that employs ordinary differential equations (ODEs) linking the transcription of the target gene to the observed activation states of a set of potential regulators by means of a piecewise linear transcription rate function which jumps to a different value when at least one regulator in the set changes its activation (ON/OFF) state. This form of transcription function is a simple and flexible model that can also be seen as an approximation of the commonly used S-shaped (e.g. Hill type) functions  algorithm , of the target gene is hence described byδ is the mRNA degradation rate and is, iτ, which we will refer to as activation (deactivation).Consider the regulation of the mRNA transcription of a target gene by an unknown set iτ, t in Extending the univariate approach of δ, the ODE solution of our model has the form of a linear regression with coefficients M(0), For given threshold levels, see also .The aim is to identify the subset Let The resulting log-likelihood function for the parameter set Mπ, Sπ, Bπ and Dπ, respectively, where Draw and perform one of the following moves with probabilities M Move a threshold: randomly draw S Swap a regulator: randomly draw B Add a regulator (Birth): randomly draw D Remove a regulator (Death): randomly draw To address the trans-dimensional nature of our model, we developed a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm based on 2. Compute the likelihood  a. Use the updated regulator set and threshold levels to derive the observed activation states  b. Use least squares to estimate the transcription function  c. Compute the updated mRNA expression, 3. Compute the acceptance ratio4. Propose k = 1,…,K.5. Draw Steps 4 and 5 are standard Metropolis Gaussian random-walk and Gibbs steps, respectively, while the moves in step where c is a constant set as large as possible subject to BDπ set to control the number of attempted trans-dimensional moves during MCMC sampling. The probabilities of (M) and (S), respectively, are chosen as Following A truncated normal distribution is used for the proposal probability of the regulator threshold level et al. (1998) and To derive the initial values kψ. The latter results in a full conditional posterior distributions that can be numerically computed. Alternatively, a full conditional least squares estimate of kψ can be derived (see SI section 4). A gamma prior distribution is used for the degradation rate δ, while the number of regulators, ν, is assumed to be Poisson with parameter λ.A natural conjugate choice of prior distribution for the error variance Prior distributions are also formulated for the set of transcription factors, L = 10 hours with measurements recorded every about 0.5–1.5 hours and 4 replicates per experiment to reflect a realistic sample size scenario. The simulated profiles of the TFs and the target gene are the sum of a deterministic profile, In this simulation study, a target gene is assumed to be observed simultaneously with six candidate TFs in two experimental conditions over a period of h(t), of the first two candidate TFs, f1 and f2, are the same as in f3 has the same profile as f2 in experiment 2, but unlike f2, its profile is also the same in experiment 1. The fourth TF f4 has constant low levels in the first experiment and constant high levels in the second experiment and could potentially explain differences between all transcription rates of the target gene of each experiment. Candidate f5 is a reflection of f2 and thus it provides an alternative regulation model in which f1 and f5 are AND activators (i.e. both are present for activation) of the target. Finally, the profile of f6 has a similar form to f1 but with a smaller range.The regulation of the target gene is the repressed activation shown in h(t), described above are derived as solutions of an ODE system with transcription of the target being regulated by f1 and f2 through Hill Functions of the nuclear concentration of the TF protein levels (for more details see SI section 5.1). However, we need to adapt to the case that only the mRNA expression levels of the candidate TFs and the target are observed as is the case in many current experimental protocols including microarrays. In order to apply the TRS methodology to these datasets, it is necessary to approximate the protein profiles of the candidate TFs from their mRNA expression levels. We do this by fitting splines to derive a continuous mRNA expression profile and using Wild bootstrap  have much smaller posterior probabilities. The set The algorithm assigns the largest posterior probability 0.79 to models with two TFs and a probability of 0.18 to models with three TFs. The estimate of the posterior probability of TF t see SI .λ = 1) are given in the SI. They demonstrate the importance of using a small parameter value for the Poisson prior to avoid overfitting and the use of informative priors on the TF set and their thresholds for attaining more robust results.Results for the case of non-informative priors applied to the same choice of TF and their threshold and for a Poisson prior on the number of TFs with larger mean parameter . A large coefficient (–1.3) is allocated to the target gene, but the tool cannot conclude whether this is due to degradation or self-regulation. The tool also fails to detect the repression of this activation caused by f2 with all coefficients except for the target and f6 in We also apply the GRNInfer tool  gene in the system related to flowering time published in h(t) corresponds to solutions of an ODE system (see SI sect. 5.2) and normal measurement error with In a similar fashion to the example in the previous section, we simulate data in four experimental conditions where the system is assumed to be observed for 10 days with 0.5–1.5 days observation frequency. The simulated profiles are again the sum of The algorithm detects the true TFs with very high probabilities with some of the other genes also being sampled. The most likely model is the true regulator set with the regulator set that does not include SOC1 also receiving higher probability  than other regulator sets. The true interactions can be correctly deduced from the TRS algorithm and the data fit is again excellent see SI .We also apply the GRNInfer tool to the same data. The tool incorrectly allocates the largest coefficient (1.59) to the FD gene that is not a TF. The repressor SVP and AP1, which is not a TF, receive a relatively large negative coefficient . The other genes receive smaller coefficients with exception the target gene SOC1 (–0.80), but the tool is unable to infer whether this is due to auto-suppression or degradation .A.thaliana.The two simulation studies clearly demonstrate that the TRS algorithm is well able to detect the correct regulation model, along with possible alternative regulation models, under realistic noise levels and sample sizes compatible with our observed data for A.thaliana to multiple biotic stresses, namely Botrytis cinerea  (h is used to specify the degradation rate δ (sd 0.1543). The trans-dimensional MCMC algorithm described in earlier sections is run for 1M iterations (execution times 2.6 and 3.2 hours).To approximate the protein profiles of the candidate TFs from their mRNA expression observed in the microarray experiments, we fitted splines and used the wild bootrstap method as above (see SI sect. 2). We constructed informative prior distributions, as described in previous sections see SI , for theBotrytis and P.syringae DC3000 and GBF6 acting as a repressor. The candidates TCP21, ANAC025, ANAC064, Rap2.6L are sampled alternatively to block the repression caused by GBF6. Such hypothesized interactions could be tested by biologists in additional experiments.The following results were obtained for posterior inference. For gene ANAC092 see  the postRegarding the SCL3 gene see , the posIn this study we suggest the use of the TRS model as a simple biologically interpretable model to draw inference about possible regulatory logics between a set of putative TFs and a gene of interest. Assuming that any interactions are consistent across different experiments and over time imposes constraints that, in principle, allows us to identify the set of regulatory TFs and to deduce their dynamic regulation logic. The algorithm for Bayesian inference on the TRS model parameters is trans-dimensional and is efficiently solved by the suggested RJMCMC. The advantage of this methodology is that different combinations of parents are sampled within the algorithm allowing us to identify a set of all plausible regulation models that are compatible with the data and to rank them according to their posterior model probabilities.We showed that the methodology works well for two simulation studies with realistic sample sizes and noise levels, and present results of its application to the transcriptional regulation of two target genes of Arabidopsis Thaliana under multiple biotic stresses. The algorithm indeed suggests a few alternative regulation models and it is clear that despite its simplicity it can infer regulation logics to a greater degree of complexity than existing methods.A. thaliana data examples the clusters of interest only contained very few TFs with jointly similar profiles and most of them could be ruled out on the basis of other biological information. However, if combined with a cluster analysis of the TFs across experiments as a pre-processing step, the TRS methodology has the potential to be applied to very large sets of putative TFs.We note that further checks against a potentially much larger set of parents can be carried out to see if other potential TFs exist, which may not have been included in the set of candidate parents and which may have similar transcription profiles across experiments. Such genes can be identified by performing a cluster analysis across experiments as, for example, suggested in In order for the methodology to work well it is essential that the magnitude of the observations between experiments has comparable scales. In cases where the measurements are not comparable, an additional computation is necessary to bring them to some relative measurement unit.Finally we note that an extension to a network methodology with multiple targets considered simultaneously is within reach and can be built on the suggested TRS approach.Supplementary DataClick here for additional data file.


Analytical expressions are given for the properties of the crystal and liquid above 200 °K. For the crystal, a modified Einstein function was used to adjust the melting temperature to 414.3 °K. Values between 975 and 1025 cal/mole for the heat of fusion were found to be the ones most consistent with the data. Comparison of the results with polyethylene data shows reasonable agreement.Thermodynamic data on the  This analysis is intended to circumvent the inherent difficulties involved in measuring polyethylene directly since (so far) even the most carefully crystallized polyethylene samples are not large, well defined CH2-chain systems, and measurements necessarily reflect the nonnegligible effects of chain folds and “amorphous” inclusions. Wunderlich /[H liquid)-H ]. The values of H (liquid) -H  calculated in this study are significantly larger than those given by Wunderlich , but botH) between the enthalpies of the solid and liquid is quite constant in the melting region and the tendency of ΔH to become negative at low temperatures is not pronounced. Even though ΔS appears to tend toward zero between 100 and 150 °K, the necessity for polyethylene to form a glass to maintain a positive ΔH and ΔS is not as obvious as in most substances. It seems likely that the discontinuity in the ΔH versus temperature curve at the glass transition would be so small that it would be difficult to detect. In accord with the above, ΔF is well approximated by ΔfhΔMT/T over an unusually large range of temperatures. This simple linear approximation to Δf is in error by only 1.5 percent for ΔT=50 degrees and by less than 5 percent for ΔT= 100 degrees. One would expect Δf to be much less linear than this for most substances [The thermodynamic properties represented in figures 1bstances . From thn-paraffins for predicting the properties of the polyethylene glassy state would be to have data on the glassy state of the n-paraffins.There is no indication in the data derived from the liquid paraffins above 200 °K of the existence of the glassy state in polyethylene, and yet the glass is generally considered to be the stable amorphous state in polyethylene below about 237 °K . One may2 in the n-paraffin thermodynamic properties is not as constant in the liquid state as in the solid. This result seems consistent with the following argument. In the solid, even for chains with less than 10 CH2 units, the intermolecular forces are strong enough compared to the intramolecular forces to isolate the motions of a central CH2 unit from those of the chain ends. In the liquid the intermolecular forces are weaker and less regular so that the CH2 behavior is sensitive to chain end effects. The nonlinearity of the incremental increase per CH2 in the liquid thermodynamic properties with reciprocal chain length possibly indicates the presence of “entire chain” vibrational modes in the liquid even for very long chain lengths.7As shown in n-paraffin specific heat data for longer chain lengths and higher temperatures in order to increase the accuracy and temperature range of the predicted higher temperature solid and liquid thermodynamic values.The departure of the predicted specific heat from that measured for polyethylene in the 10 to 80 °K temperature range should be investigated further. Since all polyethylenes so far measured seem to show the same higher than predicted specific heats in this range, the anomaly would seem to be associated with some nonideal feature which all samples have in common—e.g., chain folded surfaces. It would be interesting to examine the changes in specific heat of polyethylene with lamellar thickness to see if the discrepancy could be resolved. It might also be useful to attempt to analyze the data in this paper in the manner reported recently by Wunderlich [


Re-entrant ionization chambers or, “dose calibrators”, are the standard equipment used to assay radiopharmaceuticals in clinical practice. These devices consist of a gas-filled , pressurized ionization chamber surrounding a well in which the source is placed. When calibrated they can provide a measurement of radioactivity with a linear response over a very wide range of values . The rea99mTc the difference in activity reading is less than 5% when the volume of the source changes from ~ 0.5 ml in syringe to 9 ml in syringe [125I than for 99mTc [125I by 20% or more [90Y was shown to lead to twice the variation in activity reading [Most radionuclides used in nuclear medicine have a characteristic gamma emission so that the current being measured is predominantly caused by photons ionizing in the chamber without interacting within the source itself. For this reason, the size and shape of the source will have less of an impact on the activity reading of the calibrator for a gamma emitter than for an isotope with no characteristic gamma emission. Controlled experiments have shown that for  syringe . Such a  syringe , it may  or more . Variati or more . The equ reading  which is reading . The spe90Y is a radionuclide of increasing importance in nuclear medicine due to its growing frequency of use in a variety of therapies. Whilst generally regarded as a pure beta emitter, it does produce a very small quantity (32 ppm) of positrons during the 0+→0+ de-excitation of 90Zr, to which 90Y decays, from pair production (β+–β−) and subsequent annihilation radiation [90Y radioactivity in a vial to within an accuracy of 5% [90Y have been studied and the results demonstrate that for 90Y the chamber response is highly dependent on the geometry in use and care should be taken to calculate the dial setting or calibration factor for each geometry and volume being used [adiation , 9. The cy of 5% , 11. Theing used .90Y labelled microspheres are now widely used in the treatment of primary and metastatic liver cancer. The microspheres are typically shipped in a glass vial and suspended in aqueous solution to a total volume of 5 ml. The amount of radioactivity can be measured in a dose calibrator both before and after a pre-determined volume of the suspension has been withdrawn for administration to the patient . The resin microspheres are denser than water and, after agitation, settle to the bottom of the vial. Measurement of radioactivity for 90Y-labelled microspheres will be affected by not only the volume to be dispensed for the treatment, the choice of vessel and the variability of the geometry of the vessel, but also the concentration of the microspheres in the sample and the concentration of the suspension. This work presents a novel method for comparing the relative sensitivity of an ionization chamber to changes in the volume and concentration of suspended 90Y resin microspheres measured in the glass vial provided by the manufacturer.Resin-based 90Y microspheres were obtained from Sirtex Medical . Weights were measured using a precision balance , calibrated within the previous 12 months by a certified authority. Radioactivity was measured in a CRC 55 TW dose calibrator  using the “48 × 10” calibration setting which is recommended by the dose calibrator manufacturer for the measurement of 90Y. This calibration factor is specific for 5 g of solution in a standard source ampoule made of about 0.6 mm thick borosilicate glass. It is noted by the instrument manufacturer that this setting is for estimation purposes only.Ten unused glass shipping vials used for dispensing of resin-based The dry weight of each of the ten glass vials was measured using the balance without the rubber stopper and metal crimp that are normally part of the vial. Uncertainty in the measurement of weight was estimated by repeated measurement of a sample glass vial with 5 g water inside.90Y in solution. A carrier free sample of 90Y chloride  with a calibrated radioactivity level of 4620 MBq in 1 ml was obtained. Assay of the sample was performed by the supplier without an uncertainty estimate and the only radioactive impurity reported was Sr-90 which compromised < 0.0001% of the sample at the time of calibration. The activity was transferred via a syringe to a 10 ml Wheaton vial and the activity was diluted by the addition of 5 g of sterile water for injection. Into each of the six Sirtex shipping vials was transferred 1 g of 90Y solution. Assay of the activity in the six vials indicated that less than 5% of the activity was lost in the transfer process. The vials were weighed using the balance mentioned previously and assayed using the CRC 55 TW calibrator by placing the vial manually in the centre of the “dipper” which was lowered into the dose calibrator as shown in Fig. The effect of changing volume for this combination of dose calibrator and measurement vessel was examined using ionic y is the reading of the dose calibrator as a function of the weight of solution in the vessel, k is an exponential decay constant and x is the weight of the solution. The fitted curves were normalized to the assay reading at 5 g to provide the vial-specific weight-response correction factors for measurements at weights of less than 5 g.− 7 g which is considered to have a negligible effect on the density of the solution in this situation. There is also a slight variation in water density based on impurities found in water for injection and changes in room temperature. These affects are considered negligible in comparison to the other affects considered in the uncertainty budget for the measurement of 90Y solution.Taking the density of the solution to be 1 g/ml, the dose calibrator response as a function of volume can be derived. It is recognized that to maintain a constant density, carrier added solution must be added to the solution instead of ordinary water however the lack of a carrier added solution will cause only negligible distortions of the solution density. The mass of yttrium chloride in the initial sample would have been less than 2 × 1090Y solution was made. A standard reference material was obtained from ANSTO with a stated uncertainty of 1.8% which was directly traceable to the work reported by Mo et al. [In order to gauge the significance of the response of the chamber an estimate of the uncertainty in clinical assay of o et al. . Other c90Y was also removed in the process. The vial of microspheres was weighed before suspending the spheres and then measuring the activity in the CRC 55 TW. Water was added to the vial in approximately 0.25 g increments by syringe with the vial weighed, microspheres suspended and activity measured after each addition of water. The total weight of the suspension was increased to more than 5 g by the addition of the water. In this way the total activity in the vial remained constant but the concentration of microspheres varied fourfold. The volume of the suspension can be derived from the mass of added water as in the previous section and by using the manufacturer reported volume of 5 ml for the dose before the water was removed. The response of the chamber to varying quantity of water added to the microspheres was plotted alongside the response curve described previously.As we were unable to change the density of the resin microspheres directly, the combined effect of microsphere concentration and source volume was measured using a sample of SIR-Spheres . The sample of SIR-Spheres was obtained with a calibrated activity of 1.8 ± 0.2 GBq as measured by the supplier. To estimate the uncertainty in the assay of the radioactive sample in our dose calibrator, the radioactivity in the vial was measured 10 times with the microspheres allowed 2 min to settle between measurements before being re-suspended and remeasured. Measurements were taken by placing the vial in the centre of the plastic “dipper”  immediatThe empty vials had an average weight of 20.013 g (range 19.960–20.293 g). The difference between vials gave rise to a variation in ionization chamber response which is included in the uncertainty budget assuming a rectangular distribution.Five of the six vials that were previously prepared were used to calculate vial-specific radioactivity/volume response curves with one vial being excluded from the study when its walls became contaminated with radioisotope. There was little variation in the volume curves between vials with the greatest discrepancy being observed at small volumes Table .V is the volume of the source. The correlation coefficient for the one-phase decay curve with the measured dose calibrator reading was greater than 0.99 for all five vials. The fitted curve is shown in Fig. The response of the dose calibrator  was given by entclass1pt{minimaDose calibrator readings were plotted as a function of volume Fig.  while ke90Y-labelled microspheres will make negligible difference to the shape of the volume correction curve. The variation in mass of the vials was consistent with other publications [90Y solution and microspheres has not previously been reported in the literature and it may be the case that this model is less affected by these issues. The volume of the vial’s contents cannot be measured by weight because the density of the microspheres in suspension is unknown. No validated methods of measuring the volume of the vial contents are available so the uncertainty due to the volume cannot be overcome.The small variation in the characteristics of the five Sirtex shipping vials suggests that using a single volume adjustment curve for all vials of resin-based ications , 15 but ications  and lessications . The relThe volume curve is similar to that previously reported for 10 ml glass vials  and is s− 3 [90Y microspheres in the glass shipping vial can be obtained using a calibration factor derived from 90Y in solution. The estimate of uncertainty that we obtained for 90Y chloride solution is smaller than what was estimated by Ferreira et al. which is attributed to a smaller change in chamber response between vials [The good fit between the volume effect and the combined volume and concentration effect means that any error caused by the concentration of microspheres in the suspension will be negligible in the clinical context. It has been suggested that this can be attributed to the similar densities between the resin microspheres and water  with the− 3 . This faen vials . MeasureIt should be noted that Mo et al. , Lourenc90Y-labelled resin microspheres, with a change in volume from 5 ml down to 1 ml leading to a 12% error in the reading. This paper has demonstrated a novel method for comparing the relative effect of density changes with variation of volume changed. In this example, using the case of resin based microspheres, the ionization chamber calibration factor is not dependent on microsphere density. An accurate assay of resin-based 90Y labelled microspheres is possible if the glass shipping vial is used as the calibration vessel and the volume effect is corrected, or the volume returned to the original 5 ml by adding water assuming the residual activity does not fall below the region of linear response of the dose calibrator.Dose calibrators are sensitive to changes in the volume of the source when measuring