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A new method for constructing networks from binary data
Network analysis of multivariate data in psychological science
Denny Borsboom, Marie K. Deserno, … Lourens J. Waldorp
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Javier Alvarez-Galvez & Esteban Vegas-Lozano
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Rubén J. Sánchez-García
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Renaud Lambiotte, Martin Rosvall & Ingo Scholtes
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Jiachen Sun, Ling Feng, … Yanqing Hu
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Martina Contisciani, Eleanor A. Power & Caterina De Bacco
Cluster-based network proximities for arbitrary nodal subsets
Kenneth S. Berenhaut, Peter S. Barr, … Ryan L. Melvin
Claudia D. van Borkulo1,2,
Denny Borsboom2,
Sacha Epskamp2,
Tessa F. Blanken2,
Lynn Boschloo1,
Robert A. Schoevers1 &
Lourens J. Waldorp2
Scientific Reports volume 4, Article number: 5918 (2014) Cite this article
Mathematics and computing
Network analysis is entering fields where network structures are unknown, such as psychology and the educational sciences. A crucial step in the application of network models lies in the assessment of network structure. Current methods either have serious drawbacks or are only suitable for Gaussian data. In the present paper, we present a method for assessing network structures from binary data. Although models for binary data are infamous for their computational intractability, we present a computationally efficient model for estimating network structures. The approach, which is based on Ising models as used in physics, combines logistic regression with model selection based on a Goodness-of-Fit measure to identify relevant relationships between variables that define connections in a network. A validation study shows that this method succeeds in revealing the most relevant features of a network for realistic sample sizes. We apply our proposed method to estimate the network of depression and anxiety symptoms from symptom scores of 1108 subjects. Possible extensions of the model are discussed.
Research on complex networks is growing and statistical possibilities to analyse network structures have been developed to great success in the past decade1,2,3,4,5. Networks are studied in many different scientific disciplines: from physics and mathematics to the social sciences and biology. Examples of topics that have recently been subjected to network approaches include intelligence, psychopathology and attitudes6,7,8,9,10. Taking psychopathology as an example, nodes (elements) in a depression network may involve symptoms, whereas edges (connections) indicate to what extent symptoms influence each other. The structure of such a network, however, is unknown due to the absence of a sufficiently formalised theory of depression. Consequently, the network structure has to be extracted from information in data. The challenging question is how to extract it.
Methods that are currently used to discover network structures in the field of psychology are based on correlations, partial correlations and patterns of conditional independencies7,11,12,13. Although such techniques are useful to get a first impression of the data, they suffer from a number of drawbacks. Correlations and partial correlations, for example, require assumptions of linearity and normality, which are rarely satisfied in psychology and necessarily false for binary data. Algorithms like the PC-algorithm14,15, which can be used to search for causal structure, often assume that networks are directed and acyclic, which is unlikely in many psychological cases. Finally, in any of these methods, researchers rely on arbitrary cutoffs to determine whether a network connection is present or not. A common way to determine such cutoff-values is through null-hypothesis testing, which often depends on the arbitrary level of significance of α = .05. In the case of network analysis, however, one often has to execute a considerable number of significance tests. One can either ignore this, which will lead to a multiple testing problem, or deal with it through Bonferonni corrections, (local) false discovery rate, or other methods16,17,18, which will lead to a loss of power.
For continuous data with multivariate Gaussian distributed observations, the inverse covariance matrix is a representation of an undirected network (also called a Markov Random Field19,20). A zero entry in the inverse covariance matrix then corresponds to the presence of conditional independence between the relevant variables, given the other variables21. To find the simplest model that explains the data as adequately as possible according to the principle of parsimony, different strategies are investigated to find a sparse approximation of the inverse covariance matrix. Such a sparse approximation can be obtained by imposing an ℓ1-penalty (lasso) on the estimation of the inverse covariance matrix13,22,23. The lasso ensures shrinkage of partial correlations and puts others exactly to zero24. A different take involves estimating the neighborhood of each variable individually, as in standard regression with an ℓ1-penalty25, instead of using the inverse covariance matrix. This is an approximation to the ℓ1-penalised inverse covariance matrix. This Gaussian approximation method is an interesting alternative: it is computationally efficient and asymptotically consistent25.
In psychology and educational sciences, variables are often not Gaussian but discrete. Although discrete Markov Random Fields are infamous for their computational intractability, we propose a binary equivalent of the Gaussian approximation method that involves regressions and is computationally efficient26. This method for binary data, which we describe in more detail in the Methods section, is based on the Ising model19,27. In this model, variables can be in either of two states and interactions are at most pairwise. The model contains two node-specific parameters: the interaction parameter βjk, which represents the strength of the interaction between variable j and k and the node parameter τj, which represents the autonomous disposition of the variable to take the value one, regardless of neighbouring variables. Put simply, the proposed procedure in our model estimates these parameters with logistic regressions: iteratively, one variable is regressed on all others. However, to obtain sparsity, an ℓ1-penalty is imposed on the regression coefficients. The level of shrinkage depends on the penalty parameter of the lasso. The penalty parameter has to be selected carefully, otherwise the lasso will not lead to the true underlying network – the data generating network25. The extended Bayesian Information Criterion28 (EBIC) has been shown to lead to the true network when sample size grows and results in a moderately good positive selection rate, but performs distinctly better than other measures in having a low false positive rate29.
Using this approach, we have developed a coherent methodology that we call eLasso. The methodology is implemented in the freely available R package IsingFit (http://cran.r-project.org/web/packages/IsingFit/IsingFit.pdf). Using simulated weighted networks, the present paper studies the performance of this procedure by investigating to what extent the methodology succeeds in estimating networks from binary data. We simulate data from different network architectures (i.e., true networks; see Figures 1a and 1b) and then use the resulting data as input for eLasso. The network architectures used in this study involve random, scale-free and small word networks30,31,32. In addition, we varied the size of the networks by including conditions with 10, 20, 30 and 100 nodes and involve three levels of connectivity (low, medium and high). Finally, we varied the sample size between 100, 500, 1000 and 2000 observations. After applying eLasso, we compare the estimated networks (Figure 1c) to the true networks. We show that eLasso reliably estimates network structures and demonstrate the utility of our method by applying it to psychopathology data.
Examples of networks with 30 nodes in the simulation study.
(a) Generated networks. From left to right: random network (probability of an extra connection is 0.1), scale-free network (power of preferential attachment is 1) and small world network (rewiring probability is 0.1). (b) Weighted versions of (a) that are used to generate data (true networks). (c) Estimated networks.
The estimated networks show high concordance with the true networks used to generate the data (Figure 2). Average correlations between true and estimated coefficients are high in all conditions with 500 observations or more (M = .883, sd = .158, see Table 1). In the smallest sample size condition involving only 100 observations, the estimated networks seems to deviate somewhat more from the true networks, but even in this case the most important connections are recovered and the average correlation between generating and estimated networks remains substantial (M = .556, sd = .155). Thus, the overall performance of eLasso is adequate.
Table 1 Correlations as a measure of performance of eLasso. Correlations are computed between upper triangle of weighted adjacency matrix of data generating network and estimated network. Data is simulated under various conditions (ssize, nnodes, connectedness (p (probability of a connection), pa (preferential attachment), pr (probability of rewiring)) when the AND-rule and γ = .25 is applied. For networks with 100 nodes, deviating levels of connectedness are displayed between brackets. Results of applying eLasso with the OR-rule and γ = 0 are displayed between brackets
Mean correlations (vertical axes) of the upper triangles of the weighted adjacency matrices of true and estimated networks of 100 simulations with random, scale-free and small world networks for sample sizes ssize = 100, 500, 1000 and 2000, with number of nodes nnodes = 10, 20, 30 and 100.
We used three levels of connectivity (random networks: probability of an extra connection Pconn = .1, .2 and .3; scale-free networks: power of preferential attachment Pattach = 1, 2 and 3; small world networks: rewiring probability of Prewire = .1, .5 and 1). For the condition with 100 nodes, we used different levels of connectivity for random and scale-free networks in order to obtain more realistic networks (random networks: Pconn = .05, .1 and .15; scale-free networks: Pattach = 1, 1.25 and 1.5).
More detailed information about eLasso's performance is given by sensitivity and specificity. Sensitivity expresses the proportion of true connections which are correctly estimated as present and is also known as the true positive rate. Specificity corresponds to the proportion of absent connections which are correctly estimated as zero and is also known as the true negative rate. It has been shown that sensitivity and specificity tend to 1 when sample sizes are large enough29,33; the question is for which sample sizes we come close. Overall, specificity is very close to one across all conditions (M = .990, sd = .014) with somewhat lower specificity scores for the largest and most dense random networks (see Table 2). Overall, sensitivity is lower (M = .463, sd = .238) but becomes moderate for conditions involving more than 100 observations (M = .568, sd = .171). The reason that sensitivity is lower than specificity lies in the use of the penalty function (lasso); to manage the size of the computational problem, eLasso tends to suppress small but nonzero connections towards zero. Thus, lower sensitivity values mainly reflect the fact that very weak connections are set to zero; however, the important connections are almost aways correctly identified. In addition, the specificity results indicate that there are very few false positives in the estimated networks; thus, eLasso handles the multiple testing problem very well. Figure 1 nicely illustrates these results: almost all estimated connections in Figure 1c are also present in the generating network depicted in Figure 1b (high specificity), but weaker connections in the original network are underestimated (low sensitivity).
Table 2 Sensitivity and specificity, as a measure of performance of eLasso. Data is simulated under various conditions (ssize, nnodes, connectedness (p (probability of a connection), pa (preferential attachment), pr (probability of rewiring)) when the AND-rule and γ = .25 is applied. For networks with 100 nodes, deviating levels of connectedness are displayed between brackets. Results of applying eLasso with the OR-rule and γ = 0 are displayed between brackets
The above pattern of results, involving adequate network recovery with high specificity and moderately high sensitivity, is representative for almost all simulated conditions. The only exception to this rule results when the largest random and scale-free networks (100 nodes) are coupled with the highest level of connectivity. In these cases, the estimated coefficients show poor correlations with the coefficients of the generating networks, even for conditions involving 2000 observations (.222 and .681, respectively). For random networks, the reason for this is that the number of connections increases as the level of connectivity increases. For scale-free networks, the number of connections does not increase with increasing level of connectivity, but it does result in a peculiar arrangement of network connections, in which one node comes to have disproportionately many connections. Because eLasso penalises variables for having more connections, larger sample sizes are needed to overcome this penalty for these types of networks.
Although the lower level of sensitivity is partly inherent in the chosen method to handle the computational size of the problem and the solution to multiple testing through penalisation, it might be desirable in some cases to have a higher sensitivity at the expense of specificity. In eLasso, sensitivity can generally be increased in two ways. First, eLasso identifies the set of neighbours for each node by computing the EBIC28 (extended BIC). EBIC penalises solutions that involve more variables and more neighbours. This means that if the number of variables is high, EBIC tends to favour solutions that assign fewer neighbours to any given node. In this procedure, a hyperparameter called γ determines the strength of the extra penalty on the number of neighbours29,33. In our main simulation study, we used γ = .25. When γ = 0, no extra penalty is given for the number of neighbours, which results in a greater number of estimated connections. Second, we applied the so-called AND-rule to determine the final edge set. The AND-rule requires both regression coefficients βjk and βkj (from the ℓ1-regularised logistic regression of Xj on Xk and of Xk on Xj) to be nonzero. Alternatively, the OR-rule can be applied. The OR-rule requires only one of βjk and βkj to be nonzero, which also results in more estimated connections.
By applying the OR-rule and γ = 0, correlations between true and estimated coefficients are even higher in all conditions with 500 observations and more (M = .895, sd = .156; Table 1). Sensitivity also improved across all conditions (M = .584, sd = .221; Table 2). With more than 100 observations, average sensitivity is higher (M = .682, sd = .153). Applying the OR-rule and setting γ = 0 thus indeed increases the sensitivity of eLasso. As expected, this gain in sensitivity results in a loss of specificity; however, this loss is slight, as specificity remains high across all conditions (M = .956, sd = .039; Table 2).
Finally, it should be noted that with sparse networks, specificity partly takes on high values due to the low base rate of connections, since it is based on the number of true negatives. Therefore, we also investigated another measure, the so-called F1 score, that is not based on true negatives but on true positives, false positives and false negatives34; as such, it is independent of the base rate. For most conditions, the trends in the results are comparable. However, for larger and/or more dense random networks, the proportion of estimated connections that are not present in the true network is larger. More details about these results are provided in the online Supplementary Information.
To conclude, eLasso proves to be an adequate method to estimate networks from binary data. The validation study indicates that, with sample sizes of 500, 1000 and 2000, the estimated network strongly resembles the true network (high correlations). Specificity is uniformly high across conditions, which means there is a near absence of false positives among estimated network connections. Sensitivity is moderately high and increases with sample size. For the most part, sensitivity is lowered because of weak connections that are incorrectly set to zero; in these cases, however, eLasso still adequately picks up the most important connectivity structures. For larger networks with either higher connectivity or a higher level of preferential attachment, sensitivity becomes lower; in these cases, more observations are needed.
Application to real data
To demonstrate the utility of eLasso, we apply it to a large data set (N = 1108) containing measurements of depression of healthy controls and patients with a current or history of depressive disorder. We used 27 items of the Inventory of Depressive Symptomatology35, which was administered in the Netherlands Study of Depression and Anxiety36 (NESDA). Using eLasso, we investigate how individual depression symptoms are related, as this may reveal which symptoms are important in the depression network; in turn, this information may be used to identify targets for intervention in clinical practice.
The eLasso network for these data is given in Figure 3. To analyse the depression network, we focus on the most prominent properties of nodes in a network: node strength, betweenness and clustering coefficient (Figure 4). Node strength is a measure of the number of connections a node has, weighted by the eLasso coefficients37. Betweenness measures how often a node lies on the shortest path between every combination of two other nodes, indicating how important the node is in the flow of information through the network38,39. The local clustering coefficient is a measure of the degree to which nodes tend to cluster together. It is defined as how often a node forms a triangle with its direct neighbours, proportional to the number of potential triangles the relevant node can form with its direct neighbours38. These measures are indicative of the potential spreading of activity through the network. As activated symptoms can activate other symptoms, a more densely connected network facilitates symptom activation. Moreover, we inspect the community structure of the networks derived from the empirical data, to identify clusters of symptoms that are especially highly connected.
Application of eLasso to real data.
The resulting network structure of a group of healthy controls and people with a current or history of depressive disorder (N = 1108). Cognitive symptoms are displayed as ○ and thicker edges (connections) represent stronger associations.
Three centrality measures of the nodes in the network based on real data.
From left to right: node strength, betweenness and clustering coefficient. "Hypersomnia" (hyp) has no clustering coefficient, since it has only one neighbour.
Figure 3 reveals that most cognitive depressive symptoms (e.g., "feeling sad" (sad), "feeling irritable" (irr), "quality of mood" (qmo), "response of your mood to good or desired events" (rmo), "concentration problems" (con) and "self criticism and blame" (sel)) seem to be clustered together. These symptoms also seem to score moderate to high on at least two out of three centrality measures (Figure 4). For example, "rmo" has a moderate strength and a very high clustering coefficient, whereas it has a low betweenness. This indicates that activation in the network does not easily affect response of mood to positive events (low betweenness), but that, if the symptom is activated, the cluster will tend to stay infected because of the high interconnectivity (high clustering coefficient). Another interesting example is "energy level" (ene), which has a high node strength and betweenness, but a moderate clustering coefficient. Apparently, energy level has many and/or strong connections (high strength) and lies on many paths between symptoms (high betweenness), whereas it is not part of a strongly clustered group of symptoms (moderate clustering coefficient). This symptom is probably more important in passing information through the network, or between other clusters and might, therefore, be an interesting target for intervention.
As opposed to cognitive depressive symptoms, most anxiety and somatic symptoms (e.g., "panic/phobic symptoms" (pan), "aches and pains" (ach), "psychomotor agitation" (agi)) feature low scores on at least two centrality measures. Apparently, most anxiety and somatic symptoms either are less easily affected by other activated symptoms, do not tend to stay infected because of low interconnectivity (low clustering coefficient), or are less important for transferring information through the network (low betweenness). This is to be expected, since participants with a current or history of anxiety disorder are excluded from our sample. The item "feeling anxious" (anx), however, seems to be an important exception; feeling anxious does have a high node strength, a relatively high betweenness and a moderate clustering coefficient. Apparently, feeling anxious does play an important role in our sample of depressive and healthy persons: it can be activated very easily, since a lot of information flows through it (high betweenness), and, in turn, it can activate many other symptoms because it has many neighbours (high node strength, moderate clustering). The role of feeling anxious in our network is in line with high comorbidity levels of anxiety and depressive disorders found in the literature40,41,42. Still, feeling anxious is not a symptom of depression according to current classifications, even though recent adaptations in DSM-5 propose an anxiety specifier for patients with mood disorders43. In line with this, our data suggest that people with a depressive disorder experience depressive symptoms often also feel anxious, although they may not have an anxiety disorder. This supports criticisms of the boundaries between MDD and generalised anxiety, which have been argued to be artificial8.
Another interesting feature of networks lies in their organization in community structures: clusters of nodes that are relatively highly connected. In the present data, the Walktrap algorithm44,45 reveals a structure involving six communities (see Figure 5). The purple cluster contains mostly negative mood symptoms, such as "feeling sad" (sad) and "feeling irritable" (irr); the pink cluster contains predominantly positive mood symptoms, such as "capacity of pleasure" (ple) and "general interest" (int); the green cluster is related to anxiety and somatic symptoms, such as "anxiety" (anx) and "aches and pains" (ach); the blue and yellow clusters represent sleeping problems.
Community structure of the network based on real data, detected by the Walktrap algorithm44,45.
eLasso is a computationally efficient method to estimate weighted, undirected networks from binary data. The present research indicates that the methodology performs well in situations that are representative for psychology and psychiatry, with respect to the number of available observations and variables. Network architectures were adequately recovered across simulation conditions and, insofar as errors were made, they concerned the suppression of very weak edges to zero. Thus, eLasso is a viable methodology to estimate network structure in typical research settings in psychology and psychiatry and fills the gap in estimating network structures from non-Gaussian data.
Simulations indicated that the edges in the estimated network are nearly always trustworthy: the probability of including an edge, that is not present in the generating network, is very small even for small sample sizes. Due to the use of the lasso, more regression coefficients are set to zero in small sample sizes, which results in a more conservative estimation of network structure. For larger networks that are densely connected or that feature one node with a disproportionate number of connections, more observations are needed to yield a good estimate of the network. As the sample size grows, more and more true edges are estimated, in line with the asymptotic consistency of the method.
The model we presented may be extended from its current dichotomous nature to accommodate ordinal data, which are also prevalent in psychiatric research. For multinomial data, for example, the Potts model could be used46. This model is a generalisation of the Ising model with two states to a model with more than two states. Another straightforward extension of the model involves generalisation to binary time series data (by conditioning on the previous time point to render observations independent).
In this section we briefly explain the newly implemented method eLasso, provide the algorithm, describe the validation study and the real data we used to show the utility of eLasso.
eLasso
Let x = (x1, x2, …, xn) be a configuration where xi = 0 or 1. The conditional probability of Xj given all other nodes X\j according to the Ising model26,47 is given by
where τj and βjk are the node parameter (or threshold) and the pairwise interaction parameter respectively.
In practice, the graph structure of psychological constructs is unknown. Therefore, the estimation of the unknown graph structure and the corresponding parameters is of central importance. By viewing Xj as the response variable and all other variables X\j as the predictors, we may fit a logistic regression function to investigate which nodes are part of the neighbourhood of the response variable. The intercept τj of the regression equation is the threshold of the variable, while the slope βjk of the regression equation is the connection strength between the relevant nodes. In order to perform the logistic regression, we need multiple independent observations of the variables.
To establish which of the variables in the data are neighbours of a given variable and which are not, we used ℓ1–regularised logistic regression25,26. This technique is commonly called the lasso (least absolute shrinkage and selection operator) and optimises neighbourhood selection in a computationally efficient way, by optimising the convex function
in which i represents the independent observations {1, 2, .., n}, contains all βjk and τj parameters and ρ is the penalty parameter. The final term with ρ ensures shrinkage of the regression coefficients24,26. Parameter τj can be interpreted as the tendency of the variable to take the value 1, regardless of its neighbours. Parameter βjk represents the interaction strength between j and k.
The optimisation procedure is applied to each variable in turn with all other variables as predictors. To this end, the R package glmnet can be used48. The glmnet package uses a range of maximal 100 penalty parameter values. The result is a list of 100 possible neighbourhood sets, some of which may be the same. To choose the best set of neighbours, we used the EBIC28 (extended Bayesian Information Criterion). The EBIC is represented as
in which is the log likelihood (see below), |J| is the number of neighbours selected by logistic regression at a certain penalty parameter ρ, n is the number of observations, p − 1 is the number of covariates (predictors) and γ is a hyperparameter, determining the strength of prior information on the size of the model space33. The EBIC has been shown to be consistent for model selection and to performs best with hyperparameter γ = 0.25 for the Ising model29. The model with the set of neighbours J that has the lowest EBIC is selected. From equation (1), it follows that the log likelihood of the conditional probability of Xj given its neighbours Xne(j) over all observations is
At this stage, we have the regression coefficients of the best set of neighbours for every variable; i.e., we have both βjk and βkj and have to decide whether there is an edge between nodes j and k or not. Two rules can be applied to make the decision: the AND rule, where an edge is present if both estimates are nonzero and the OR rule, where an edge is present if at least one of the estimates is nonzero25,26.
Although we do have the final edge set by applying one of the rules, note that for any two variables j and k, we get two results: the result of the regression of j on k (βjk) and the result of the regression of k on j (βkj). To obtain an undirected graph, the weight of the edge between nodes j and k, ωjk, is defined as the mean of both regression coefficients βjk and βkj. All steps of the described method are summarised in the algorithm below and is incorporated in R package IsingFit (http://cran.r-project.org/web/packages/IsingFit/IsingFit.pdf).
Input data set X for p variables and n subjects
Output (weighted) edge set for all pairs Xj and Xk
Initialise: Select (randomly) one variable from the set of variables. This is the dependent variable.
Perform ℓ1-regularised logistic regression on all other variables (glmnet uses 100 values of penalty parameter ρ).
Compute the EBIC for ρ (i.e., each set of neighbours).
Identify the set of neighbours that yield the lowest EBIC.
Collect the resulting regression parameters in matrix Θ with τ on the diagonal and β on the off-diagonal.
Repeat steps a through d for all p variables.
Determine the final edge set by applying the AND rule: if both regression coefficients βjk and βkj in Θ are nonzero, then there is an edge between nodes j and k.
Average the weights of the regression coefficients βjk and βkj. Define Θ* as the averaged weighted adjacency matrix with thresholds τ on the diagonal. This is now a symmetric matrix.
Create a graph corresponding to the off-diagonal elements of the averaged weighted adjacency matrix Θ*. This can be done with qgraph in R49.
We generated data from the three most popular types of network architectures: random networks, scale-free networks and small world (clustered) networks30,31,32. Figure 1a shows illustrative examples of each type of networks. Network sizes were chosen to be comparable to the most common number of items in symptom checklists (10, 20 and 30 nodes), but also large networks were included (100 nodes). The level of connectivity of the networks was chosen to generate sparse networks. For this reason, in case of random networks, the probability of a connection (Pconn) between two nodes was set to 0.1, 0.2 and 0.3. For small world networks, the neighbourhood was set to 2 and for scale-free networks only one edge is added per node at each iteration in the graph generating process. To obtain a wide variety of well known graph structures, the rewiring probability (Prewire) in small world networks was set to 0.1, 0.5 and 1 and the power of preferential attachment (Pattach) in scale-free networks was set to 1, 2 and 3. For the condition with 100 nodes, we used different levels of connectivity for random and scale-free networks (random networks: Pconn = .05, .1 and .15; scale-free networks: Pattach = 1, 1.25 and 1.5). Otherwise, nodes will have too many connections.
The generated networks are binary: all connections have weight 1 or 0. To create weighted networks, positive weights were assigned from squaring values from a normal distribution with a mean of 0 and a standard deviation of 1 to obtain weights in a realistic range. Examples of resulting weighted networks are displayed in Figure 1b. Besides weights, thresholds of the nodes are added. To prevent nodes with many connections to be continuously activated and consequently having no variance, thresholds were generated from the normal distribution between zero and minus the degree of a node.
From the weighted networks with thresholds, data was generated according to the Ising model by drawing samples using the Metropolis-Hastings algorithm, implemented in R using the IsingSampler package50,51,52. Four sample size conditions were chosen that are realistic in psychology and psychiatry: 100, 500, 1000 and 2000. The generated data were used to estimate networks with eLasso. Examples of the resulting estimated networks are displayed in Figure 1c.
This setup led to a 3 × 4 × 3 × 4 quasi-factorial design, with the factors network type (random, small world, scale-free), level of connectedness, network size (10, 20, 30, 100) and sample size (100, 500, 1000, 2000). Thus, the total simulation study involved 144 conditions. Each of these conditions was replicated 100 times. For each condition, the mean correlation between data generating and estimated parameters, the mean sensitivity and the mean specificity is computed. These served as outcome measures, indicating the quality of network recovery. Sensitivity, or the true positive rate, is defined as SEN = TP/(TP + FN), in which TP is the number of true positives and FN is the number of false negatives. Specificity, or the true negative rate, is defined as SPE = TN/(TN + FP), in which TN is the number of true negatives and FP is the number of false positives. Note that, in order to compute sensitivity and specificity, the off-diagonal elements of the weighted adjacency matrix Θ* (βjk), have to be dichotomised.
Since specificity naturally takes on high values for sparse networks, also the F1 score is computed. For more details about the F1 score and the results, see Supplementary Information online.
We used data from the Netherlands Study of Depression and Anxiety36 (NESDA). This is an ongoing cohort study, designed to examine the long-term course and consequences of major depression and generalised anxiety disorder in the adult population (aged 18–65 years). At the baseline assessment in 2004, 2981 persons were included. Participants consist of a healthy control group, people with a history of depressive or anxiety disorder and people with current depressive and/or anxiety disorder.
To demonstrate eLasso, we selected individuals from NESDA with a current or history of depressive disorder and healthy controls. To this end, we excluded everyone with a current or history of anxiety disorder. The resulting data set contains 1108 participants. To construct a network we used 27 items of the self-report Inventory of Depressive Symptomatology35 that relates to symptoms in the week prior to assessment (IDS).
Data were dichotomised in order to allow the application of the Ising model. Therefore, the four response categories of the IDS items were recoded into 0 and 1. The first response category of each item indicates the absence of the symptom. In the case of "feeling sad", the first answering category is "I do not feel sad". This option is recoded to 0, since it indicates the absence of the symptom. The other three options ("I feel sad less than half the time", "I feel sad more than half the time" and "I feel sad nearly all of the time") are recoded to 1, indicating the presence of the symptom to some extent. Other items are recoded similarly.
Analysing the dichotomised data with our method and visualising the results with the qgraph package for R49, results in the network in Figure 3. The layout of the graph is based on the Fruchterman-Reingold algorithm, which iteratively computes the optimal layout so that nodes with stronger and/or more connections are placed closer to each other53. This network conceptualisation of depressive symptomatology might give new insights in issues that are still unexplained in psychology.
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Claudia D. van Borkulo, Lynn Boschloo & Robert A. Schoevers
Department of Psychology, Psychological Methods, University of Amsterdam,
Claudia D. van Borkulo, Denny Borsboom, Sacha Epskamp, Tessa F. Blanken & Lourens J. Waldorp
Claudia D. van Borkulo
Denny Borsboom
Sacha Epskamp
Tessa F. Blanken
Lynn Boschloo
Robert A. Schoevers
Lourens J. Waldorp
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder in order to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/4.0/
van Borkulo, C., Borsboom, D., Epskamp, S. et al. A new method for constructing networks from binary data. Sci Rep 4, 5918 (2014). https://doi.org/10.1038/srep05918
DOI: https://doi.org/10.1038/srep05918
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text:
Cardi B and Offset Know the Exact Night Their Baby Was Conceived
By Gabriel Pabon
Cardi B and Offset have quickly become one of Hip-Hop's biggest power couples. Their high-profile romance began back in early 2017 and they're sill going strong today. They first linked up on the remix of Cardi B's "Lick" and have collaborated on a number of tracks since then, including Migos' Gold hit "Motorsport." The two rappers are preparing for their biggest collaboration yet: they're expecting their first child together later this year.
After revealing her pregnancy this past weekend during her Saturday Night Live debut, Cardi B stopped by The Breakfast Club to dish out all the details behind the pregnancy… including the saucy details about the night, the baby was conceived. That's right: Cardi and Offset know the exact night their baby was conceived. When DJ Envy asked Cardi if the baby was planned, she began to laugh saying, "No it wasn't planned, it was just one night, it was a good night."
Charlamagne Tha God had to jump in, of course, to get even more revealing details about that "good night," asking the Bronx native if she "remember[s] when you got your club shot up?" Cardi continued to blush and laugh about the situation confirmed that she really does know the exact night the baby was conceived. "It couldn't have been any other night," she said.
T H A N K Y O U F O R A L L O F Y O U R S U P P O R T. W E F E E L S O B L E S S E D.
A post shared by OFFSET (@offsetyrn) on Apr 7, 2018 at 9:52pm PDT
Cardi also got extremely candid about her initial reaction to her unexpected pregnancy. She revealed she "kinda, sorta" considered getting an abortion after she found out she was pregnant, however, she didn't think about it for long. She said she's prepared for this next step in her personal life and that it frustrates her when people criticize her decision to keep her baby, especially when it comes from other women. "Why can't I have both, why do I have to choose between having a career and a baby, why can't I have both?" Cardi said, taking an empowering stand for women everywhere who might be struggling with a similar situation.
Cardi has definitely proven that she's a girl power icon, even if she shies away from referring to herself as a role model. She takes no shit from anybody, proving that she can and will do both, thanks very much. She'll continue to grind until her baby is born and she'll be back to her usual grind when her maternity leave is over.
The Bronx rapper is about to fly out to California to begin preparations for her set at Coachella, revealing that she'll be flying out this week and begin 10 hour day rehearsals for the festival. So if anybody has any doubts that Cardi can do anything, look no further. She's here to prove you wrong.
Check out the full interview with The Breakfast Club below…
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Chat About Cardi B and Offset Know the Exact Night Their Baby Was Conceived

redpajama_set_name: RedPajamaCommonCrawl


Author, activist, and conscious commerce expert Maggie Anderson, who lived exclusively off black businesses for an entire year in 2009, has announced a new venture called MAGGIESLIST.com.  An empowerment resource, it utilizes technology and social media to empower the black community through conscientious and collaborative commerce. The website, built by iSwop Networks, targets consumers whose habits, attitudes, and moral compass drive a duty and desire not only to buy from black-owned businesses but from institutions committed to supporting economic growth in the black community.
Anderson is best known for her family's history-making and highly publicized stand and economic experiment to spend an entire year purchasing goods and services only from black-owned businesses. 'This Empowerment Experiment' is chronicled in her book Our Black Year — One Family's Quest to Buy Black in America's Racially Divided Economy. Another major output of the experiment was the Northwestern University's Kellogg Graduate School of Management's study. The Kellogg study proved that nearly 1 million new jobs could be created if middle-class African American consumers would increase their spending within their community from the current 3% to 10%. Out of that book and study, MAGGIESLIST.com was born.
According to a released statement, the foundation for MAGGIESLIST.com is the same as for Anderson's extreme and, for some, controversial 'Rosa Parks-ian' stand–a cry for individual accountability and collective action toward resolving social ills disproportionately impacting the black community. "I made that sacrifice and bring MaggiesList.com now to prove that there are so many wonderful black-owned businesses out there, that we are not, shamefully, supporting them enough. And most of all, that we can counter poverty, recidivism, and violence; and create jobs, role models, and self-sustained neighborhoods just by supporting them a little more," states Anderson. To that end, MAGGIESLIST.com wants to inspire, facilitate, and track such increased spending, the social and financial impact on underserved communities, progress toward curing racial divides and disparities, and job creation.
Broderick Byers, CEO of iSwop Networks and managing partner of MAGGIESLIST.com, intends for the website to be the leading, innovative and transformational company in how conscious commerce is conducted and in facilitating increased economic activity, financial freedom and entrepreneurial excellence in the black community, according to the press statement. "Maggie's year brought intelligence and inspiration. Now MaggiesList.com harnesses the power of technology and social media to empower our community through conscious commerce and business development. That is why we will work hard to earn your trust, delivering actionable content, special offers, reputable local business, as well as black suppliers, franchisees, agents, independent reps, and black-manufactured products enabled by our partner brands and retailers," added Byers.
MAGGIESLIST.com is now registering users, businesses, advertisers, sponsors, and partners.


"I love lighthouses. The severe, uncompromising life of service lived by lonely lighthouse keepers possesses a special dignity. Poised between the last outcroppings of land and the vast expanse of the ocean, the lighthouse has become a profound symbol of human life, poised as it is between the transitory and the eternal."
Collect all of Thomas Kinkade Lighthouses!
A complete set is always more valuable.
This edition has been sold out for many years and is no longer available in the galleries or from the publisher. Now only found in private collections.
First of two paintings in Thomas Kinkade's Lighthouse Landmarks series. The other painting in the collection is Cape Hatteras Light.
++++ Thom created this painting in 2001.
++++ 20" x 24" CANVAS Framed in your choice of approx 28" x 32" Redwood Burl, Antique Gold or Brandy with fluted roses Museum Quality Frame ~~ ready to hang!
++++ Brass Plaque with legend "Split Rock Light ~~ Thomas Kinkade"
"I am intrigued by lighthouses. Erected in locations of great peril, they often stand in settings of remarkable beauty and drama as well. Where nature is most powerful, it can also be majestic.
That is especially true of Split Rock Light erected on the towering cliffs of Lake Superior's north shore in Minnesota to light the way for the massive ore carriers that moved a rich treasure of iron ore through from mines in Canada and the U.S. As I gaze on this beetling cliff, I begin to understand the legend of the Sirens, whose wild and beautiful song drew ships to wreck on their perilous rocks. Surely, beauty such as this might call even a plodding barge to its ruin.
Split Rock Light was built in 1910 and continued to guide ships through stormy waters until 1969 when the Minnesota park service took over its management. Now it is perhaps the most visited lighthouse in the U.S. Guests who make the long drive are rewarded by a breathtaking view of the rugged limestone light overlooking a majestic promontory.
I've employed artistic license in an effort to capture the drama in Split Rock Light - a romanticized moonlit portrayal of the glorious lighthouse - so you can enjoy this unparalleled view without having to drive the long, rural highway.
~~~ Shipwrecks from a mighty 1905 November gale prompted this rugged landmark's construction. Completed by the U.S. Lighthouse Service in 1910, Split Rock Light Station was soon one of Minnesota's best known landmarks. Restored to its 1920s appearance, the lighthouse offers a glimpse of lighthouse life in this remote and spectacular setting.
~~~ Two Harbors, Minnesota Split Rock Light is unusual, being a complete 20th century light station, with a tower, keeper's house, fog signal building, and oil house all constructed in 1910. The lens is a gorgeous Third Order bivalve Fresnel that looks like a big clamshell rather than the traditional beehive look. The lens contains 242 separate prisms, and was manufactured by Barbier, Bernard, and Turenne of Paris.
~~~ The light can be seen for 22 miles. The lens rotates, giving off a flashing white beam. The light was deactivated in 1969, and today is lit once a year on the anniversary of the wreck of the Edmund Fitzgerald. Part of the incentive for building Split Rock was the Lighthouse Board's concern that "the unusual magnetic attractions in the neighborhood make navigation difficult in thick weather." The tower stands atop a 130 foot high cliff.
~~~ The height of this site makes for a spectacular view out over Lake Superior and along the rocky shoreline. It is said to be the most visited Lighthouse in all of the US.
*Plus $35.00 for very secure packaging materials and shipping within the lower 48 States.
For current price and availability.


Jake Furr went 9-1 while Jon Spencer went 5-5 for the week. Furr now has a sizable advantage with a 48-10 record while Spencer is now 39-19.
Last week saw some separation between the Mansfield News Journal pickers.
Jake Furr went 9-1 while Jon Spencer went 5-5 for the week. Furr now has a sizable advantage with a 48-10 record, while Spencer is 39-19 on the year.
There is still plenty of time for Furr to fall on his face and Spencer to make a huge comeback, though. Let's see who the fellas picked in the Top 10 games of the weekend.
Jake Furr: I've had this one circled since the beginning of the season and wouldn't miss it for anything. Mansfield Senior is riding a 9-game winning streak into this one, but the Minutemen are coming off of a game where they demolished Upper Sandusky. Kyle Johnston tied the school record with eight threes. It is going to be a close one, but I am giving the advantage to the home team in overtime.
Jon Spencer: I also like the Minutemen at home, especially with Johnston heating up of late and Lex getting some strong play off the bench.
JF: The Colts saw their own 9-game winning streak snapped in a loss to Wooster Triway earlier this week. Harding did knock off Shelby earlier this year, but I think the Colts are going to run the table in the MOAC. Going with Clear Fork.
JS: Clear Fork gets back on the winning track.
JF: The Lucas Cubs just beat St. Peter's for the first time since 2011 last week. I think that is enough to give them the confidence to run the table in the Mid-Buckeye Conference. Logan Niswander is a matchup nightmare with his shooting ability and post moves. He will have a huge game.
JS: This is making it hard to make up ground on Jake, but I can't disagree with anything he said here.
JF: The Flames picked up their first win of the season this week, knocking off East Knox on Tuesday. St. Peter's brought an end to a 3-game skid, their first since 2011, by beating Plymouth. I think Cool Hand Luke Henrich cools off the Flames with his shooting ability.
JS: There have been some good games between these two schools, but the Spartans have too much firepower for the Flames this season.
JF: River Valley loves the run-and-gun style, but Shelby has way too many athletes for teams to try and test them with that. TJ Pugh is playing like a veteran instead of a sophomore and Uriah Schwemley is a stud. Tanner Stephens is stepping up big in Hunter Hoffman's absence and when Hoffman gets back from injury, Shelby is going to be hard to handle. Going with the Whippets here.
JS: Yeah, watch out for Shelby at full strength. Even now, the Whippets will be too much for River Valley to handle.
JF: The Clear Fork Lady Colts are just struggling to score the basketball, but I think they are going to be a tough second-half team. Saturday though, I am going with Buckeye Valley.
JS: I'll go with the Colts at home.
JF: I've had this one circled on my calendar since the beginning of the season, too. Lucas head coach Kathy Grover hosts her alma mater with her two daughters, Jessie and Jamie, leading the way. But the biggest X-factor is Morgan Spitler, who is starting to shoot the ball very well from three. Going with the Lady Cubs at home.
JS: No way Cubs cave at home.
JF: My alma mater only lost to St. Paul by 5 earlier in the year, but have since won just one game. I have to go with St. Paul on the road, but wouldn't be upset with a loss on my record in this one.
JS: That's OK Jake. I have your alma mater's back.
JF: I really like this matchup. Ontario has been playing some of the best basketball of any team in the area, but Shelby has been incredibly consistent and has a commanding lead in the MOAC standings. I have to go with Shelby here though, I think it is going to be closer than what many think.
JS: I like the home team here.
JF: This one is a no-brainer pick here. Crestview is 10-2 coming in and looking forward to a rematch with Western Reserve with the Firelands Conference title on the line. I think the Lady Cougars stay focused on that goal and win this one easily.
JS: Looks like I'm never going to catch Jake. I have to go with the Cougs here, too.


text:
De Samtgemeinde Eilsen is een Samtgemeinde in de Duitse deelstaat Nedersaksen. Het is een samenwerkingsverband van vijf kleinere gemeenten in het zuidwesten van de Landkreis Schaumburg. Het bestuur is gevestigd in Bad Eilsen.

Deelnemende gemeenten
 Ahnsen, oppervlakte 343 hectare, per 31 december 2021 987 inwoners
 Bad Eilsen, een kuuroord, oppervlakte 246 hectare, per 31 december 2021 2.569 inwoners
 Buchholz, oppervlakte 176 hectare, per 31 december 2021 742 inwoners
 Heeßen, oppervlakte 190 hectare, per 31 december 2021 1.419 inwoners
 Luhden, inclusief het dorpje Schermbeck, oppervlakte 435 hectare, per 31 december 2021 1.112 inwoners

Ligging en infrastructuur

De Samtgemeinde Eilsen ligt te midden van tot het Wezerbergland behorende heuvelruggen, waaronder de Bückeberg ten oosten van Bad Eilsen. Ten westen van Bad Eilsen ligt een beboste heuvel met de naam Harrl. Door de gemeente stroomt de Aue, een zijrivier van de Wezer.

Infrastructuur
Door de gemeente loopt, in west-oost-richting, de autosnelweg A2. Afrit 35 van deze Autobahn ligt vlakbij Luhden; de Autobahn kruist hier de van noordwest naar zuidoost lopende Bundesstraße 83 of B83. Ten noordwesten van Bad Eilsen, in Bückeburg, takt deze B83 van de belangrijke oost-westverbinding B65 af.

Door de gemeente loopt sinds 1900 een spoorlijn, die tot 1961 belangrijk was voor met name transport van gedolven steenkool uit mijnen bij Obernkirchen. Deze 20 km lange spoorlijn Rinteln-Stadthagen wordt sinds 1965 niet meer voor regulier reizigersvervoer gebruikt. Het is een goederen- en museumspoorlijn. Twee verschillende organisaties, waarvan er één over een stoomtrein beschikt (Dampfeisenbahn), verzorgen van tijd tot tijd toeristische ritten, waarbij ook het station van Bad Eilsen wordt aangedaan. Dichtbij dit station is verder een halteplaats voor bussen, waaronder streekbussen naar Rinteln, Stadthagen en Bückeburg. Vanuit Station Rinteln of Station Stadthagen kan men dan verder per trein reizen.

Buurgemeentes
In het westen, bij Luhden: o.a. Kleinenbremen, gemeente Porta Westfalica, deelstaat Noordrijn-Westfalen
In het noordwesten: Bückeburg
In het noordoosten: Obernkirchen
In het oosten, bij Buchholz: Bernsen, gemeente Auetal
In het zuiden: Rinteln.

Economie
De gemeentelijke economie steunt vooral op het toerisme, vanwege het natuurschoon in het omliggende heuvelland, en het kuurbedrijf in het kuuroord Bad Eilsen.

Geschiedenis

De in de huidige gemeente liggende plaatsen behoorden in de 16e en 17e eeuw oorspronkelijk tot het Graafschap Schaumburg, en werd bij de deling daarvan in 1640 toegewezen aan het Graafschap Schaumburg-Lippe. Deze situatie duurde tot aan de Napoleontische tijd.

Zie verder de artikelen over de vijf tot de Samtgemeinde behorende deelgemeenten.

Externe links
https://www.der-schaumburger-ferst.de/bahnhoefe-und-haltestellen/ Website museumspoorlijn 1
 www.dampfeisenbahn-weserbergland.de/fahrplan/regelfahrten-fahrplan/ Website museumspoorlijn 2 (Dampfeisenbahn)

Eilsen

redpajama_set_name: RedPajamaWikipedia


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Home › News › Paradiso Insurance Returns as Backer of Stafford's Late Model Division
Paradiso Insurance Returns as Backer of Stafford's Late Model Division
Posted on March 4, 2022 by Scott Running Posted in News
(Stafford Springs, CT)—After becoming a Stafford Speedway partner in 2021, Stafford Springs based Paradiso Insurance will once again sponsor the Paradiso Insurance Late Model 50 and provide a weekly $75 bonus for the third place finisher in each week's Late Model feature in 2022. The Paradiso Insurance Late Model 50, scheduled for September 2nd, has become a big event for Stafford's top full-fender division with over $10,000 in prize money.
"This brought the community together, our clients, our carrier representatives, and our employees which is everything Paradiso Insurance stands for," said Christopher Paradiso, Owner of Paradiso Insurance. "The 2021 race was better than we ever imagined."
"I thought it was awesome, very well put together," said Dori Wilson, Personal Lines Manager at Paradiso Insurance. "It was great to spend time with most of our employees outside of work, our carrier reps, and our clients! It was awesome to see all the kids go and say 'Drivers Start Your Engines!' and seeing one of our employees wave the green flag. We're looking forward to September 2nd!"
The Paradiso Insurance Late Model 50 is the longest and highest paying race on the schedule for the Late Model division. The race features posted awards in excess of $10,000 with the winner guaranteed to take home nearly $1,500 including contingency bonuses from iRacing and Broad Brook Brewing. The Paradiso Insurance Late Model 50 has seen 5 different winners in the last 5 seasons between Wayne Coury, Jr. in 2021, Tyler Leary in 2020, Ryan Fearn in 2019, Paul Arute in 2018, and Michael Bennett in 2017.
"The Late Model 50 was a great night, we were able to hand out some t-shirts right at the front gate which was getting our brand out there," said Hillary Palmberg, New Business Manager for Paradiso Insurance. "The infield experience was out of this world. The kids and all of us running into the infield and being able to step on the race track, so many people don't have that experience."
"Absolutely awesome time," said Brian O'Connor, Licensed Insurance Professional at Paradiso Insurance. "What a thrill to start the race!"
Much like the Paradiso Insurance Late Model 50 has seen parity among its winning drivers, the Late Model division itself continues to grow and flourish into one of the most competitive weekly divisions in the country. The shortened 2020 schedule saw 7 different drivers reach NAPA Victory Lane in only 14 races while the 2022 season hit double digits with a remarkable 10 different winners spread over 19 races.
About Paradiso Insurance
Located on Main Street in Stafford Springs, CT just a mile from Stafford Speedway, Paradiso Insurance is a local independent insurance agency that specializes in personal insurance, business insurance, and parcel delivery insurance. Owner Chris Paradiso leads the team in organizing the yearly community events that they put together, one being their annual flag day event. The Paradiso team prides themselves on giving back to the local community and believe that is the backbone of the agency.
For more information on Paradiso Insurance and their offerings visit www.paradisoinsurance.com or contact them at 860-684-5270.
The first $75 Paradiso Insurance contingency bonus of the 2022 season will be awarded on Sunday, April 24 as part of NAPA Spring Sizzler® Weekend. Tickets for the 50th running of the NAPA Auto Parts Spring Sizzler® are now available at staffordspeedway.com/tickets. The two day event begins Saturday, April 23rd with the NAPA Auto Parts Duel, two 40-lap qualifying races that will set the field for the 50th NAPA Spring Sizzler scheduled for April 24th. The PASS Super Late Models and all five of Stafford's weekly divisions as well as the Vintage All-Stars will also be on hand for the weekend.
‹ Family Tradition, Dana Wray Set For Limited Late Model Debut at Stafford
Chris Matthews Ready to Return to Victory Lane in Stafford's SK Lights ›


Aqualine-171 motorboat with seating capacity of no more than 4 persons (including steersman) is meant for pleasure, fishing and sailing along rivers, lakes, water-storage basins, coastal regions up to 5 km away from the waterfront with wave height up to 0.8 m and air temperature from -2º С to +45º С.
Aqualine-171 operation meets the requirements of the Russian River Registry and navigation security normative documents of the Russian Ministry of Transportation.
Despite small-scale size and low water displacement the boat is equipped with an engine of high power capacity. It's a high-speed boat with the high maneuverable characteristics: acceleration at the start of motion, turns and stops are performed at higher speed in comparison with the other boats.
Seating capacity, number of persons.
Maximal engine power capability, kW/ h.p.


text:
Huber Matos Benítez (26. listopadu 1918 Yara – 27. února 2014 Miami) byl kubánský politik, voják a spisovatel. Byl členem Partido Ortodoxo a aktivním odpůrcem režimu Fulgencia Batisty. Po vítězství kubánské revoluce se stal velitelem provincie Camagüey, záhy však začal kritizovat Fidela Castra za personální změny ve vedení státu a příklon ke komunistické ideologii. V říjnu 1959 byl zatčen a odsouzen jako zrádce a kontrarevolucinář ke dvacetiletému odnětí svobody. Po odpykání trestu v pevnosti La Cabaña se s rodinou vystěhoval ze země, žil v Kostarice a později v USA, kde vedl exilovou organizaci Cuba Independiente y Democrática a založil vlastní nadaci pro rozvoj demokracie na americkém kontinentu. Vydal vzpomínkovou knihu Když přišla noc.

Reference

Externí odkazy

Kubánští politici
Narození v roce 1918
Úmrtí v roce 2014
Narození 26. listopadu
Úmrtí 27. února
Úmrtí v Miami
Muži
Narození v provincii Granma


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The information below might be helpful for those living in Marseille and want to apply Vietnam visa if their nationality does not include in the Vietnam visa exemption list. There are two options to help them get Vietnam visa from Marseille.
How to get Vietnam visa on arrival from Marseille?


Sensational Summerlin Single Story! Bright and airy with loads of natural light. 2 bedrooms and a den with a open, flowing floorplan. Two car garage and a cute backyard area for afternoon lounging. Conveniently located near Downtown Summerlin, Red Rock Hotel/Casino and the 215 Freeway. Come and see today!


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Bristol Rovers v Cambridge United: Team news, kick-off, odds and more
The Gas are preparing for their first round clash in the freshly-named league cup
Luke Woodley Marshall
Jack Vittles
Bristol Rovers will be keen to get back to winning ways after a 1-0 defeat to Charlton on the weekend, the showing at The Valley will be a distant memory as the focus switches to Cambridge United in the first round of the Carabao Cup.
Rovers will be looking to progress to next round and be drawn amongst the top flight sides, like last year when they were drawn away to Chelsea.
What time is kick off and where can I follow it?
The match will be played at the Memorial Stadium and will kick off at 7:30pm. To follow the action, visit our live blog at www.bristolpost.co.uk/sport
What is there to play for?
A place in the Carabao Cup second round is up for grabs, where the teams will range from Premier League all the way down to League Two. Bristol Rovers claimed the scalp of second tier Cardiff City as the Pirates ran out 1-0 winners after extra time in last year's first round, before being eliminated next round by the eventual Champions of England, Chelsea. A win here would boost morale following a controversial defeat against Charlton Athletic, and help Rovers build momentum ahead of their clash with Peterborough United on Saturday.
What is the team news?
Tom Nichols
There hasn't been much injury news to report following the Charlton game, however, Rovers do find themselves on the wrong end of an injury crisis, with Daniel Leadbitter and James Clarke remaining doubtful for this clash. Meanwhile, new summer signings Tom Nichols and Sam Slocombe are fit to make their home debuts, with key players such as Billy Bodin and captain Tom Lockyer expected to start. Darrell Clarke still remains keen to add to his squad this summer, with a month until the transfer window slams shut. Clarke may be in the market for a right back, due to injury concerns.
Are there any tickets left?
Tickets remain very much available, with Cambridge United still advertising away tickets on their club website. Tickets are expected to be available on the evening at the Memorial Stadium.
Bristol Rovers 4/6; Draw 13/5; Cambridge United 4/1
Predicted line-up
Bristol Rovers celebrate Tom Nichols (2nd L) goal (Image: Neil Brookman/JMP)
Partington, Lockyer, Sweeney, Brown
Bodin, Sercombe, O Clarke, Broom
Gaffney, Nichols
Bristol Post verdict
A lot depends on the fitness of a few players for Rovers, with Byron Moore missing the Charlton match and defenders Joe Partington, James Clarke and Dan Leadbitter all carrying injuries. If none of them are fit, Sinclair made be used as a makeshift right back. Rovers will also hope to call on their on-loan Stoke duo of Ryan Sweeney and Dom Telford after an admin error stopped them playing against Charlton.
Whatever side Darrell Clarke picks, Rovers should have enough to overcome their league two opposition and progress to the next round.
Darrell Clarke
Bristol Rovers FCThe Leeds United and Aston Villa transfer news that could impact Bristol Rovers' January plansIt is one to keep an eye on


Happy Tuesday! I am itching to officially introduce you to my book, Patchwork Essentials: The Half-Square Triangle. Before I do that however, I'd like to share a little bit of the backstory on my journey that has led up to this moment.
Mini quilts from my first quilt along, found here.
I had "write a book" on my list of things I'd like to do for a while before I actually took steps towards doing it. I first started to think about writing a book back in late 2011/early 2012. I had just graduated from college and moved with Michael to Wisconsin. Instead of getting a traditional job I decided to try and turn my hobby into a job. It was not an easy time in my life. I was missing home, and had no routine. With Michael in his first semester of graduate school, I was spending all day alone. This gave me a lot of time to work on figuring things out. This included writing my very first sewing pattern, the Lined Drawstring Bag Pattern. I also wrote the second half of my Art of Choosing series during this time. Things were starting to pick up, and I thought that writing a book might be a good venture for me. I actually spoke with an agent about an interested publisher, but a week later I was approached by Art Gallery Fabrics. So, writing a book took a backseat for a while.
My first try at half-square triangles, a Starflower block, early 2010.
As time went on, I got discouraged about not writing a book sooner. Designing fabric and patterns kept me plenty busy and at times I thought my opportunity had passed. Then last year, I realized that I just needed to make it a priority. I didn't have time to write a book because I wasn't making time. Now the real question was what to write about? For a long time I thought I would write a book about color and choosing fabric. But honestly, I have no expert knowledge on the subject. I minored in Art in college, but most of my know-how is intuitive and pieced together. I feel comfortable discussing it on a basic level, but not in depth enough to fill a whole book. It took some serious consideration, but when I finally landed on writing a book about half-square triangles, it made perfect sense. Half-square triangles were one of the very first quilting techniques I tried. They have always been a favorite of mine, and I have made a lot of projects with them beyond the quilts in my book.
The first quilt I worked on for the book, Opposites Attract.
Once I decided on half-square triangles, everything started to fall into place. I wanted the book to be more than just a collection of half-square triangle quilts, I wanted there to be intention behind each design. Each quilt in the book explores a different way of playing with the basic block form. I'll go more into that in my next post!
Sunset Tiles, my quilt in Scraps, Inc.
After working with Lucky Spool on Scraps, Inc. and seeing the beautiful books set to be published by them, I knew that's who I wanted to work with. Shortly after Spring Quilt Market in 2014, I pitched my book, and by July I was busy starting on the projects. I completed nearly all of the writing and sewing that Fall and early Winter. Staying focused working on the book and projects almost exclusively was really challenging for me, both mentally and physically. As you may know, I have arthritis (for more on sewing with arthritis see my post here), so all the cutting and trimming definitely took it's toll.
Procrastinating comes naturally to me, so I tried to be as organized as possible throughout the process and set myself monthly and weekly deadlines. I still managed to save a lot of the writing for later, but stayed on track with the sewing. There were definitely times where I felt like I was in over my head, or that I was never going to be done. It was hard not having that "instant gratification" to keep me motivated. My biggest motivator ended up being a spreadsheet taped to my sewing room door. It had each project broken down by step (fabric selection, cutting, HST making, trimming, etc). So each time I'd finish a step, I could fill in that box, which gave me a sense of accomplishment along the way.
I wore a lot of different hats in the process of writing this book. I was able to have my hand in many of the decisions made about the structure, design, and even take a few of the photographs. While at times that meant extra work on my end, it makes me appreciate the finished product even more. In the end, I'm glad that I waited to write this book. Blogging, contributing to other books, working with magazines, and most importantly writing my self-published patterns has given me invaluable experience. It allowed me time to find my voice.
You are an inspiration! I just had a baby and am struggling to find time to quilt. I feel like I've lost a little bit of myself so I'm living vicariously through you..... Well done on the book and Hi from Scotland!
Congratulations on your book, I am looking forward to getting introduced to it!
Congratulations! What an accomplishment! I love your blog & sure your book is amazing as well. Can't wait to see it!
Congrats, Jeni, and it's so interesting to hear the road you took to where you are now. I love your Sunset Tiles quilt, such a beautiful way to showcase smaller cuts. Best of luck with book!
Congrats, Jeni! The book is due to arrive here today - can't wait to see it!
Thank you, Jeni, for sharing your story as well as your beautiful quilts. Your integrity shines through. Looking forward to seeing the book soon.
Congrats and I can't wait!
Congratulations! Looking forward to seeing your book!
So exciting Jeni!!! It was so fun to read your journey here, thanks for sharing ;) Can't wait for you book!!!!
Congratulations! Feels, good, doesn't it?!!!
I'm looking forward to owning your book & putting it to good use! I hope you bring some copies w/this wknd at your lecture in IL so I can purchase one!
Congratulations! Looking forward to seeing all the projects.
Congratulations! You are very accomplished!!
It's nice to hear some background. It's clear that writing a book is a MAJOR time commitment! I'm really looking forward to seeing it - I love HSTs. Congratulations on being a published author and hope it flies off the shelves.
I really enjoyed reading your story, thank you! Book writing is on my 'list' too, and it's good to hear of someone who waited for the right time. I know that's not now for me! And it's ok to wait till it is.
That is fantastic, I really need to buy this book and ym going to write a review about it for the Swiss Guild! I am sure that the members will love this new baby if yours!
Congratulations on your achievement and I admire your work ethic. I am looking forward to reading more.
Hey Jeni! I've been looking forward to your book since you mentioned it on your blog a while back! Congrats!!! I'm sure you are on a big cloud right now!! Can't wait to get my hands on your book!!!
Oh my goodness Jeni what a journey! Congrats on the publishing of your book. Thank you so much for sharing that w/us. I'm still practicing my HSTs:) Mostly I wanted to say thanks for the tips on crafting w/arthritis. I grew up in your area of Wisconsin , now live in the south-east USA in warmer winters. It still effects me the same tho regardless of climate. I'm indebted to you for sharing that also. I'll remember to rest while quilting, cutting and sewing. Same sappy high dollar iron story here....I just bought a cheapo at Target...best thing yet!
Congrats!!! What a fun journey!
I'm anxious to see what you've included in your book. Congrats.
Congratulations! I am so proud of you!!
Thanks for sharing the backstory. It was so interesting! I love the color of your new book and can hardly wait to see it in person.


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