Networks often exhibit structure at disparate scales. We propose a method for identifying community structure at different scales based on multiresolution modularity and consensus clustering. Our contribution consists of two parts. First, we propose a strategy for sampling the entire range of possible resolutions for the multiresolution modularity quality function. Our approach is directly based on the properties of modularity and, in particular, provides a natural way of avoiding the need to increase the resolution parameter by several orders of magnitude to break a few remaining small communities, necessitating the introduction of ad-hoc limits to the resolution range with standard sampling approaches. Second, we propose a hierarchical consensus clustering procedure, based on a modified modularity, that allows one to construct a hierarchical consensus structure given a set of input partitions. While here we are interested in its application to partitions sampled using multiresolution modularity, this consensus clustering procedure can be applied to the output of any clustering algorithm. As such, we see many potential applications of the individual parts of our multiresolution consensus clustering procedure in addition to using the procedure itself to identify hierarchical structure in networks. Community detection is an ill-defined problem where one typically identifies community structure as approximate solutions to difficult optimization problems . Heuristics for identifying good community structure based on these optimization problems are often stochastic in nature, returning different structures for different runs of the algorithm. These different structures, even though they tend to be similar in quality based on the optimization criterion, can be rather different . Furthermore, networks often exhibit structure at different scales and multiresolution community detection methods , which identify structure at different scales based on a resolution parameter, have been developed to address this problem. For Stochastic Block Models, the number of blocks acts as a natural resolution parameter.Community detection13 attempts to mitigate this problem by identifying common features of an ensemble of partitions. The combination of the partitions of the ensemble yields a consensus partition, which is representative of the ensemble, in that it is more similar, on average, to all network divisions than any one of them. We stress that consensus clustering is essentially a noise-reduction technique, that delivers robust results, but not necessarily a better solution of the problem. For instance, if we deal with partitions generated by the optimization of some objective function , the best solution, according to the method, is the one corresponding to the largest value of the objective function, by definition. The issue of the relation between the solution provided by an algorithm and the ground truth(s) hidden in the data is much debated17. Consensus clustering approaches have been applied to the community detection problem previously21. As in these existing approaches, we use the pairwise co-classification of nodes as the basis for our consensus clustering procedure. This approach is natural in the case of community detection, as co-classification defines a network and one can thus use existing community detection algorithms for the consensus clustering step.As a result, when attempting to identify communities in a network, one is often confronted with the problem that one has a large number of potential partitions  and often no good way to select a single best partition. Consensus clustering et al.21 but without the need of setting an arbitrary threshold). We also exploit this property to obtain hierarchical consensus structures by recursively applying the procedure to clusters obtained at the previous step, stopping once a cluster has no significant sub-clusters. This recursive procedure results in much simpler (and thus easier to interpret) hierarchical structures than sweeping all possible threshold values18 and avoids the computationally expensive sorting step needed by the procedure suggested by Sales-Pardo et al.19.The key distinguishing feature of our consensus clustering procedure compared to these existing approaches is that we use a modified version of modularity with a null model based on the ensemble of partitions for the consensus clustering step. This null model allows us to assess statistical significance of co-classification. In particular, this means that our consensus clustering procedure does not identify communities in random networks  by Zhang and Mooreevent sampling. Event sampling directly exploits the behavior of the modularity quality function to provide good coverage of different scales in a network. We describe both the event sampling procedure and our Hierarchical Consensus procedure in Methods. Our Matlab implementation is available at https://github.com/LJeub/HierarchicalConsensus.The hierarchical aspect of our procedure is of particular interest for the application to ensembles of partitions obtained from multiresolution modularity that we focus on in this paper. In this application, one expects to see structure at different scales and a single consensus partition is unlikely to be particularly meaningful. In addition to the clustering method, the ensemble of input partitions itself is very important for consensus clustering to be successful. In the application to multiresolution modularity this means that we want our input partitions to cover all possible scales in the network as equally as possible. This is a non-trivial task as the possible values for the resolution parameter can often span several orders of magnitude and the sensitivity of obtained community structure on the value of the resolution parameter varies widely depending on the value of the resolution parameter itself. To address these problems, we propose a novel sampling strategy for the resolution parameter which we call 20 (the LF procedure). The LF procedure also uses the co-classification matrix to identify consensus clusters. It iteratively applies the same community detection algorithm that was used to obtain the original ensemble to a thresholded co-classification matrix for the ensemble of partitions generated at the previous iteration. The algorithm stops once all partitions in the ensemble are identical. At each iteration the co-classification matrix is thresholded, zeroing out small elements below a threshold τ ∈ .In this section we compare the performance of our Hierarchical Consensus (HC) procedure with the iterative procedure proposed by Lancichinetti and Fortunato24 to compare the performance of the two consensus clustering procedures. The parameter choices for the benchmark networks in Fig. 20. These parameter choices produce networks with many small communities where modularity-based community detection methods  run into the resolution limit of the measure26, typically merging some of the communities in the output partitions. However, given that partitions merging different communities are of similar quality, one would expect that different partitions in an ensemble generated by a stochastic modularity based community detection algorithm may merge different small communities. Thus a consensus clustering algorithm may be able to recover the planted communities in this example.We use LFR benchmark networksγ = 1, which corresponds to the standard modularity4 to sample the partitions. In Fig. γ to sample each partition. In Fig. 27 to sample the partitions. In each case we generate ensembles with 250 partitions. In Fig. γ = 1.In Fig. adjusted mutual information (AMI)28. We choose AMI  instead of the more popular normalized mutual information (NMI)29, as the latter tends to overstate the similarity between partitions with many small clusters (see methods). We will be using AMI throughout this work. On the x-axis we have the mixing parameter μ, that expresses how mixed the clusters are with each other . As a result, one expects the performance of community detection algorithms to decline as μ increases.The similarity between the planted partition of the benchmark and the consensus partition(s) is estimated via the τ. In this example, we get the best results for large values of τ. The best value of τ is situation dependent20 and it is not obvious how to choose τ in the absence of ground-truth information. While our recursive consensus clustering method also depends on a parameter α, this has an intuitive interpretation as a statistical significance level and setting it to a reasonable value such as α = 0.05 usually provides good results. Furthermore, our method can detect when a network does not have significant community structure. In particular, we do not identify any communities in the LFR networks with μ ≥ 0.8 in Fig. The results for the LF consensus procedure are very dependent on the value of the threshold μ is large.For any consensus clustering algorithm, the main goal is to return an output partition that is more representative of the underlying data than the input partitions. This baseline is represented by the performance of the partition in the initial ensemble that most closely resembles the planted partition (ensemble max) in Fig. μ is large. However, one should keep in mind that in the case of a multiresolution ensemble, the best partition corresponds to the partition at the optimal value of the resolution parameter. Identifying this optimal resolution a priori without knowledge of the planted partition is difficult . As such, the HC procedure comes close to identifying the optimal resolution.The situation for the multiresolution ensemble in Fig. α) but outperforms the LF procedure for larger ensembles. This is particularly impressive given that we avoid the arbitrary thresholding of the co-classification matrix which is key to the performance of the LF procedure in this example. The minimum ensemble size for the HC method arises from the fact that for small ensembles even zero co-classification can no longer be considered significant evidence that two nodes are not in the same community. This results in a resolution limit that depends on the number of partitions in the initial ensemble and the desired significance level α. Increasing the number of partitions in the initial ensemble allows one to identify smaller communities. Alternatively, increasing α also allows one to detect smaller communities given the same number of partitions in the initial ensemble at the cost of increasing α also increasing the risk of over-fitting. However, the results in Figs α  can improve the results and is a viable strategy if increasing the size of the initial ensemble is not possible.A key parameter for the performance of the HC procedure is the size of the initial ensemble. In Fig. 6 with power-law degree distribution, with exponent 2, minimum degree 5 and maximum degree 70. Each of the networks has 1000 nodes and a 2-level hierarchical community structure, where a fraction p0 of edges is allocated at random, only based on node degrees, a fraction p1 of edges is constrained to lie within groups of the first level partition p2 of edges is constraint to lie within groups of the second level partition p0 + p1 + p2 = 1. The community assignments are generated as follows:All nodes are in a single community in the base level partition.c of new communities from a Poisson distribution with mean 4 and minimum cutoff 2 (to ensure each community is split).Sample the number σ = 1.5. The probabilities determine the size of the clusters.Sample assignment probabilities for each of the new communities from a symmetric Dirichlet distribution with concentration parameter Assign to each node a community label based on these probabilities.Subsequent levels are generated by splitting communities from the previous level:We illustrate the effectiveness of our consensus clustering procedure to extract hierarchical structure on the example of artificial benchmark networks with two-level hierarchical community structure. The benchmark networks are based on a degree-corrected stochastic block modelγ and different null models for the consensus clustering in Fig. γ) and we use a significance level of α = 0.05 to identify the consensus hierarchy. We see that using event sampling and the local permutation model  memory requirements and more suited to the detailed exploration of smaller networks.In Fig. Overall, our HC procedure can successfully identify hierarchical structure based on a multiresolution ensemble of partitions. One limitation of our HC procedure is that it tends to be conservative when splitting communities. As a result, we often see spurious intermediate levels in the consensus hierarchy which are the result of merging ground-truth clusters.32: Social network between the 34 members of a Karate club with ground truth partition given by the split of the original club into two new clubs that occurred during the original study.Zachary Karate Club34: Network of American football games between the 115 Division IA colleges during regular season  with ground truth partition given by conference membership.American College Football (corrected)35: Network of hyperlinks between 1224 blogs on US politics with ground truth partition given by political orientation .Political Blogs36: Co-purchasing network of 105 books about US politics with ground truth partition given by political orientation .Political Books37: Undirected, weighted connections derived from diffusion imaging and tractography between 998 regions of interest of the human cerebral cortex (averaged over 5 participants). Ground truth is lacking for this network as the community structure of brain networks is generally unknown. In place of ground truth partitions, we provide hemispheric ordering as a reference.Human Structural Brain Network38: Directed, weighted connections derived from histological tract tracing data between 73 nodes in the rat cerebral cortex. As with the human network, we do not have a notion of ground truth for this network. Instead, we compare our results to a previously published38 single scale partition.Rat Structural Brain NetworkIn addition to artificial benchmark networks, we also use our consensus clustering procedure to identify community structure in networks with some notion of ground truth community structure see Fig. , a humanγ in our ensemble. At the same time, our consensus hierarchy provides a much simpler and easier to interpret description of the underlying structure than the entire ensemble of partitions. With the exception of the College Football network, the notion of ground truth corresponds most closely to the coarsest identified partition for these networks. In all these networks  we identify structure that is smaller-scale than the ground truth partition.As we can see from Fig. 39. In the case of the human brain network in Fig. ρ = −0.654). The rat multiscale analysis recovers most of the modules that were extracted earlier38 based on a single-scale analysis, while also revealing new associations that were previously missed and are functionally meaningful, for example the association of somatosensory areas  with other primary sensory  areas. In addition to retrieving larger modules similar to those described earlier, the multiscale consensus approach provides a detailed hierarchical view of how modules at different scales are arranged, a central objective for analyses of modular brain networks40.For the consensus partitions of the structural brain networks in Figs α = 0.05 and ensembles with 1000 partitions. In general, increasing the number of partitions in the ensemble allows one to potentially resolve finer-scale structure and smaller values of α reduce the risk of identifying spurious structure. However, we observe very similar structure at a significance level of α = 0.01 in these examples, suggesting that our results are reasonably robust to these parameter choices.In Figs 20 to achieve good results. This is important, as the value of the threshold strongly influences the results of these algorithms and the optimal value of the threshold is situation dependent and usually cannot be inferred from the available data. In artificial examples, where one can optimize the threshold to maximize recovery of the planted community structure, our hierarchical algorithm is competitive with the consensus clustering algorithm of20 for this optimized value of the threshold. Furthermore, our hierarchical consensus clustering algorithm does not identify communities in random networks that do not have community structure.Our goal for this paper was to address two key issues that frequently arise in the context of community detection in networks. One often obtains many different community structure solutions  and one often expects networks to have meaningful community structure at different scales. To address these problems, we develop a hierarchical consensus clustering algorithm that can identify hierarchical community structure in networks based on an ensemble of input partitions. Our hierarchical consensus algorithm eliminates the need to select an arbitrary threshold for the co-classification matrix that is necessary with existing consensus clustering procedures8 to sample the initial ensemble. We suggest a sampling strategy for the resolution parameter that ensures good coverage of all scales and should also be useful in other contexts . We then use our hierarchical consensus algorithm to identify a consensus hierarchical community structure which automatically identifies relevant scales in the network without the need of selecting a particular value of the resolution parameter. Furthermore, the consensus hierarchy can combine features from partitions obtained at different resolutions, thus potentially avoiding the resolution limit problems inherent in the use of modularity. In both artificial and real-world examples with a notion of ground truth communities, the best partition identified by the consensus hierarchy is usually comparable to the best partition of the original ensemble. However, the consensus hierarchy typically only consists of a few levels of nested community structures and is thus much easier to interpret and provides a much simpler representation of network community structure than the original ensemble of partitions.To identify hierarchical structure in networks, we use multiresolution modularityWhile we only considered multiresolution modularity to generate the initial ensemble, one could, in principle, use any multiresolution method instead. However, our event-sampling technique is specific to quality functions that can be decomposed as a sum over vertex pairs. Exponential and linear sampling, while not a good fit for multiresolution modularity, are general and may be good choices for other techniques.i  isWe use cluster assignment vectors 42 to optimize Q for all experiments in this paper.We use this null model for clustering the original networks. For the consensus clustering step we use a different null model which we introduce later. We use the iterated version of the GenLouvain algorithmγmin, γmax] of γ values that covers all possible resolutions, whereFor multiresolution modularity Eq.  one can γmax can be computed exactly by noting that γmax is the smallest value of γ such that Aij − γPij ≤ 0 for all i and j. However, γmin has to be determined numerically. To estimate γmin we use that modularity is a linear function of γ for a fixed partition. This means that we can directly compute the minimum value of γ for which a given partition is better than the trivial partition where all nodes are in the same community. This is effectively a special case of the CHAMP algorithm43. We can use this observation to iteratively estimate γmin. The iterative algorithm proceeds by first estimating γmin using a small sample of partitions at γ = 1. We then sample a new set of partitions using γ = γmin − ε  and use the new sample to update γmin. We repeat this process until the new sample consists only of the trivial partition.The upper bound γ values in a way that ensures that we give equal coverage to different scales in the network. Obvious sampling strategies would be linear sampling and exponential sampling. For linear sampling one would use equally spaced values of γ between γmin and γmax and for exponential sampling one would use values that are equally spaced on a logarithmic scale. However, these sampling strategies do not work well in practice when considering the entire range of gamma values. In particular, for many networks there is a large range of gamma values where the network is almost completely fragmented into singletons with a few small communities remaining that take extremely large values of γ to split apart. Especially for linear sampling  many of the sampled partitions will be from this regime and thus carry very little information about the network structure.We want to sample from this range of et al.41 to produce mesoscopic response functions that are comparable across different networks. As in Onnela et al.41 we split the contributions of node pairs to the modularity into ferromagnetic interactions E+(γ) = {|i ≠ j, Aij − γPij > 0} and antiferromagnetic interactions E−(γ) = {|i ≠ j, Aij − γPij < 0. Onnela et al.41 used the fraction of antiferromagnetic interactions, however we found this not to give a good coverage of the different scales in a network. Noting that the behavior of modularity depends on the relative magnitudes of ferromagnetic and antiferromagnetic interactions, as a single strong interaction can compensate for many weak interactions, we instead propose to use the relative magnitude of antiferromagnetic interactionsβ(γ) = 0 for γ ≤ 0 and β(γ) = 1 for To avoid this issue we introduce a new sampling strategy that we dub event sampling. The event sampling strategy is inspired by an idea used by Onnela γ, we invert the relationship between γ and βγ(β) at equally spaced values of β between βmin and βmax, where βmin = β(γmin) and βmax = β(γmax)  and E−(β), note that these change only at a discrete set of values  for a set of partitions The idea behind consensus clustering is to combine multiple partitions for the same network to obtain a  consensus partition for the network. We use an approach that is based on the co-classification matrix 20. However, the co-classifcation matrix has a peculiar structure that we would like to exploit. One of the strengths of the modularity quality function is that it is often straightforward to input prior knowledge about the structure of a network by using an appropriate null model to compute P.The co-classification matrix defines a new network. As a result one can in principle apply any network clustering method that can handle weighted networks to the co-classification matrix to obtain a consensus partitiong0 as a normalized sum of independent Bernoulli-distributed random variablesFor the consensus clustering problem we can define appropriate null models based on the input partitions. Assuming that under the null model different partitions are independently sampled from different distributions, we can write the entries This means that Pij = μij in Eq. , gi(t)) = 1 for any partition and hence i ≠ j from now on.To determine the g:The permutation model is perhaps the most common null model for ensembles of partitions. Its null assumptions are that for each sampled partition the number and sizes of clusters are fixed but nodes are otherwise assigned to clusters at random. Under these assumptions one obtains the following formula for Cij has the same distribution for any pair of nodes such that i ≠ j. It is hence a constant null model and thus in a sense resolution free45. While the simplicity of this model is appealing, we find that it does not work well in practice, in particular in the recursive application. It often results in splitting of individual nodes or small groups of nodes from clusters in the artificial networks and real networks  less frequently co-classified than could be explained by the local permutation model where the community assignment of one of the nodes remains fixed.This choice of null matrix means that the only negative contributions to the sum in Eq.  are from20. First, we obtain a new ensemble of partitions by optimizing Eq. . We do not use any thresholding on the co-classification matrices as the GenLouvain procedure is designed to handle full matrices.To obtain a consensus partition we use the iterative procedure suggested by Lancichinetti and Fortunatozing Eq.  using it25. We propose a recursive strategy for generating a hierarchical cluster tree to extract more information.A single partition is often not a good consensus summary for a sample of partitions. In the case of multiresolution modularity, this may be because of multiple meaningful scales in a network or because of the resolution limit problems of the modularity quality functionFor each cluster of the partition apply modularity based consensus clustering at a given significance level (so that we do not split clusters that could result at random) restricted to the nodes that are in the clusterrepeat the procedure for each newly generated clusterStarting from a partition where all nodes are in the same community, we apply the following procedure:This procedure stops once there are no more clusters that can be split into subclusters at the given significance level and results in a tree of clusters. We refer to this procedure as the hierarchical consensus (HC) procedure.O(n2) memory requirement and also limits the efficiency of the community detection algorithms used to cluster the co-classification matrix. The computational complexity of the hierarchical consensus procedure itself is largely determined by the the time needed to identify the first level of the hierarchy. The computational complexity of the Louvain-like community detection algorithm we use to cluster the co-classification matrix is approximately O(m) where m is the number of positive entries of the consensus modularity matrix (see Eq. (O(lm) for the hierarchical consensus procedure, where l is the number of partitions in the initial ensemble. Given that the hierarchical consensus procedure is trivially parallelizable, as one can sample partitions independently, scalability is typically memory-limited in practice.The computational complexity of the hierarchical consensus procedure is largely determined by the need to store and manipulate the co-classification matrix which is typically dense. This results in an (see Eq. ). This rG is the node-cluster adjacency matrix for the initial ensemble. Note that G is sparse with exactly nl non-zero entries, one for each node-partition pair. The current version of the GenLouvain code does not exploit this type of structure efficiently.It is in principle possible to reduce the memory requirements and thus potentially improve scalability by noting that the coclassification matrix can be written as42 with weighted random moves. This algorithm is similar to the original Louvain algorithm46 and uses the same two-phase structure. The algorithm starts with all nodes in their own community. During the first phase, the algorithm tries to move single nodes between communities, choosing between moves that increase modularity at random with probability proportional to the resulting increase in modularity. When there are no more single-node moves that increase modularity, the identified communities are aggregated to form new supernodes in phase two. Phase one and two are repeated with the supernodes until no further increase in modularity is identified. The algorithm is then restarted repeatedly using the new communities as the initial partition until no further increase in modularity is identified. This restarting of the algorithm can often yield significant improvements in modularity.We use the iterated variant of the GenLouvain codei is a random node. The mutual information can be normalized in different ways, e.g., by noting that Normalized variants of the mutual information 28. The adjusted mutual information28However, this measure and other variants of normalized mutual information are badly behaved for partitions with many clustersThe network data sets used to illustrate our consensus clustering method are available at 10.6084/m9.figshare.5876064.v1.


In this paper, we propose an agent-based model for investigating possible scenarios of genetic and cultural language evolution based on an integrated gene-culture coevolutionary framework. We focused on the following problems: (1) how communicative ability can evolve directionally under positive frequency-dependent selection and (2) how much of the directional effect there is between language and biological evolution. In our evolutionary experiments and analysis, we discovered a coevolutionary scenario involving the biological evolution of phenotypic plasticity and a cyclic coevolutionary dynamic between genetic and cultural evolution that is mediated by phenotypic plasticity. Furthermore, we discovered that the rates of cultural change are usually faster than the biological rates and fluctuate on a short time scale; on a long time scale, however, cultural rates tend to be slow. This implies that biological evolution can maintain the pace with language evolution. Finally, we analyzed the transfer entropy for a quantitative discussion of the directional effects between both evolutions. The results showed that biological evolution appears to be unable to maintain the pace with language evolution on short time scales, while their mutual directional effects are in the same range on long time scales. This implies that language and the relevant biology could coevolve. However, the vocal communication of such animals lacks the complex grammar and high expressiveness that characterize human language. Why do only humans have sophisticated language? This is one of the core questions to understanding human identity. In this study, we explored the evolution of language in the context of the biological evolution of the fundamental traits underlying communicative interaction. We focused on two fundamental problems concerning language evolution: how communicative ability can evolve directionally under frequency-dependent selection and whether the cultural evolution of language and biological evolution of traits underlying communicative interactions can coevolve.The possession of language distinguishes humans from other animals. It is true that other animals also engage in vocal communication; for example, vervet monkeys can convey some simple information by using alert calls2.One of the fundamental assumptions of most studies on language evolution from the biological viewpoint is that the fundamental traits underlying communicative interactions evolved under directional selection. These traits can be modified incrementally to increase the benefit from communicative interactions. At the same time, it has been assumed that such traits must be shared between individuals for communication to succeed. Accordingly, at least some of the selection is positively frequency-dependent. This may obstruct evolution based on directional selection. We believe that this captures a fundamental and general problem in the evolution of communicative traits. For example, in the context of language evolution, it has been pointed out that mutations in grammar cannot be beneficial because the peers of an individual with a grammar mutation may not understand the mutant form3. Phenotypic plasticity refers to the variability in a phenotype obtained from a given genotype resulting from development in different environments4. In the field of evolutionary biology, ontogenetic adaptation  based on phenotypic plasticity has recently been recognized as one of the key factors that bring about the adaptive evolution of novel traits6. Wund summarized eight hypotheses on how plasticity may influence evolution , focusing mainly on the adaptation to new environments7. For example, it has been suggested that phenotypic plasticity promotes persistence in a new environment and that a change in the environment can release cryptic genetic variations via phenotypic plasticity which in turn impact the rate of the evolutionary response. Zollman and Smead8 analyzed simple models of language evolution based on Lewis’s signaling game and the prisoner’s dilemma game. They observed that the presence of plastic individuals alters the trajectory of evolution by directing the population away from non-adaptive signalling and toward optimal signalling. They termed this the “Baldwin optimizing effect.” Suzuki and Arita showed that such an adaptive shift can occur repeatedly by using a computational model of the evolution of communicative traits  that incorporate behavioral plasticity. These studies have indicated that learning may be an important driving force for adaptive evolution in the context of communicative interactions, although they did not explicitly deal with the cultural evolution of language.Nature’s solution to this challenging problem can be found in the evolution of phenotypic plasticity12. Evolutionary scholars have converged on the idea that the cultural and innate aspects of language were tightly linked in a process of gene-culture coevolution13. However, the relationship between genes and language is extremely complex and shrouded in controversy because these mechanisms interact with each other despite the difference in their time scales14. Substantial knowledge regarding gene–culture coevolution in general has been acquired from the viewpoint of genetic analysis15. One seemingly common argument is that language changes rapidly and is a “moving target;” therefore, it does not provide a stable environment for biological adaptations16. This argument is almost parallel with the assumption that biological evolution has become “frozen” as if language evolution works on a “fixed” biological background17. For example, Chater et al.18 used a computational model to show that there are strong restrictions on the conditions under which the Baldwin effect  can embed arbitrary linguistic constraints and that the effect emerges only when language provides a stable target for natural selection.The second problem that we considered is the relationships between two different evolutionary processes: biological evolution and cultural evolutionet al.20 summarized several ways in which natural selection can adapt to moving targets. The simplest way is genetic evolution. In general, the ability of a population to keep pace with change depends on both the size of the population and the variation present. There are indeed many examples showing that adaptation can be very fast if variability is present. Furthermore, it has been reported that the rate of genomic evolution during the last 40,000 years has been more than 100 times higher than the characteristic rate for most of human evolution21. The second way is again the phenotypic plasticity. When natural selection acts to preserve adaptive phenotypes, it can lead to genetic change and to the fixation of the preserved adaptive phenotype by several evolutionary processes, including the Baldwin effect22. The third way is by means of systems and organs that have evolved to cope with fast-changing environments, much like the immune system being capable of tracking most pathogens.However, problems have been posed for the underlying assumptions of the “moving target argument.” With regard to biological evolution, Számadó et al.20 summarized two possible reasons why cultural evolution may not present a moving target that cannot be tracked by biological evolution; this is partly due to the fact that the rate of linguistic change depends on the frequency of use and population size. First, even contemporary linguistic changes need not be that fast. Second, past rates of linguistic change may have been much slower. There is also a seemingly counterintuitive claim23 that a “moving target” should increase the rate of evolution because temporally varying goals have been shown to substantially accelerate evolution compared with evolution under a fixed goal.With regard to cultural evolution, Számadó 24. We discuss this factor in detail later in the section Evolutionary Rates.Another factor is the measurement of the evolutionary rates. In general, there is an inverse correlation between the rates of evolution and the time interval used to measure the rates. This can explain why the pace of cultural evolution appears faster, that is usually measured with shorter intervals25. These studies tend to be one-sided. Indeed, there has been relatively little work on investigating the two types of adaptations within a single framework26. Based on the above considerations and hypotheses, in this study we used a coevolutionary framework that allows us to integrate biological and cultural evolution to develop a comprehensive understanding of language evolution. Figure Rather than viewing language as a monolithic and independent entity, modern researchers typically break it down into its component mechanisms and analyze these independently29. This sophistication could realize our quantitative analysis on the model using evolutionary rates and transfer entropy in this paper.We present a minimum computational model with a one-dimensional linguistic space, in which biological evolution, cultural evolution and individual learning can evolve language. It is a sophistication of our previous models with a two-dimensional linguistic spaceWe propose an integrated computational framework for investigating possible scenarios of the genetic and cultural evolution of language. This framework allowed us to study coevolutionary interactions between languages and agents who use the languages for communication.N and does not change through a trial, while the number of languages can vary.There are a finite number of agents and languages in a one-dimensional space, and agents can communicate with each other by using their shared languages Fig. . Note thlx (≥0) of a language x in the space represents the expressiveness of the language, which is the expected fitness benefit of a successful communication using that language.Each language is defined as a point in the space. The position i is also represented as a point in the same space and the interval surrounding the point. This point represents the agent’s innate language ability, for which the position is determined by its genotype ai (≥0). ai also represents a possible language that can be learned by the agent i with the minimum innate cost. In other words, the agent can use the corresponding language located at ai in the linguistic space without learning if it exists in the current population of languages. The area represents the agent’s linguistic plasticity determined by its genotype pi. The agent can use any languages that exist in its plasticity interval  through the learning processes of the languages by paying a certain cost (explained below in detail).Each agent SLi,j between agents i and j is defined as follows:In each generation, there is a chance for communication between two agents in each of all possible pairs of agents. If there are one or more languages that can be used by both agents, the agents can communicate successfully by using one of their shared languages. Specifically, the set of shared languages SLi,j ≠ /0.The agents can communicate successfully if i is defined as follows:W1 and W2 are the weights for the two components of the fitness function. The first component represents the benefit from successful communicative interactions. SCi is the set of agents with which the focal agent i successfully communicates by using the shared language with the position li,j. Note that, if the communicating agents share two or more languages in their communication, one of the shared languages is randomly selected and used for calculating the fitness. The second component represents the cost of linguistic plasticity. It is determined by the size of the interval of its plasticity (pi). The cost increases exponentially as the agents’ innate ability increases. This reflects a situation in which a greater innate ability makes it more costly to maintain the learning ability . Overall, this definition of the fitness means that agents who can communicate with more other agents by using more expressive languages that are acquired with less linguistic plasticity will have higher fitness.The fitness of each agent is determined by summing the expressiveness of the languages used in its successful communication with others and the cost of the linguistic plasticity. The fitness of an agent N times: a parent agent for the next generation is selected by using a roulette wheel selection that is proportional to the fitness , which produces an offspring that has the same genotypes as the ones of its parent. Each genotype of the offspring is mutated with the probability Pm. A mutation process adds a small random value R to the original genetic value of an offspring i (ai and pi), where R is a normal random number with the mean μ and variance σ2.After communicative interactions among agents, the biological evolution of agents occurs. The population of the next generation is generated by repeating the following procedures Subsequently, the population of languages evolves according to the following four cultural processes: cultural change, division, extinction, and fusion.We define a cultural change in languages as a change in the position of the language in the linguistic space due to the use of the language during successful communication among agents. Basically, a successful communication between a pair of agents moves the language used in the communication toward the agents’ innate linguistic abilities, as shown in Fig. dx) of a language x is calculated as follows:Specifically, the direction and amount of displacement  > Fd. Instead of the focal language x being removed, new two languages are created and placed at lx + dx+ and lx + dx− in the linguistic space.Each language is divided into two languages if it is pulled dramatically toward opposite directions simultaneously. Specifically, the language Any languages that are not used by any agents in the current generation will not appear in the next generation; in other words, they are removed from the linguistic space. This represents language extinction.Tf. The united language is placed in the midpoint between these two languages.When the distance between two languages is fairly close, these languages are united into a single language. This process occurs when the difference between the two languages is smaller than the threshold Through the above processes, the populations of the agents and languages coevolve.30. We can also assume that, in general, the collective adaptivity of language is related with not only communicative but also cognitive aspects. If so, the one dimensional space in the model might include the cognitive aspects of language (e.g. recursive ability or ability to merge), although we focus on the communicative aspect of language and define the dimension as expressiveness in this paper.Language is a communication tool but also a cognitive tool. Indeed, in the brain, utilizing language-related circuits, some form of linguistic knowledge is linked to the external world by producing/perceiving sounds and gestures, and at the same time, is connected to the inner mental world composed of concepts, intentions and reasoning29, we constructed a two-dimensional model based on a polar coordinate system in which the distance from a language to the origin represents its expressiveness, and its angle represents its structural character. The similarity in the structural character determines a communication success between agents but does not affect the fitness value from that successful communication. We observed a “linguistic burst” in that many languages with structural differences emerged from successful communication among agents sharing a few languages in the initial population located at the origin. However, after a few hundred generations, the structural properties of languages converged to a certain value and a cyclic coevolutionary process began to occur, which is similar to the one discussed in this paper. This paper proposed a more simplified model to focus more on evolutionary rates of biological and cultural processes and their directional effects, using transfer entropy.In our previous studyN = 2000, W1 = 3, W2 = 10, Pm = 0.001, Fd = 0.008, Tf = 0.02, and F = 0.001. The initial values of ai, pi, and lx were randomly selected from . We selected these values so that division and fusion of languages continuously occurred. Especially, the effects of changing parameters W2, F, Fd and Tf are described later in this section.We conducted evolutionary experiments for 10,000 generations. The following parameters were used: Figure W2. We found that the duration until the population reached the coevolution phase increased with W2. A higher cost of learning placed the population under stronger selection pressure at low plasticity. Because individuals with low plasticity were less robust against mutations and often failed to leave offspring, the evolution speed dropped. The rate of increase in the expressiveness of languages was inversely proportional to W2 due to the increased duration until the start of the coevolutionary phase. For example, in the case of no cost (W2 = 0), the duration was quite short: the coevolutionary phase started after about 100 generations. In the case of a huge learning cost (W2 = 100000), the evolution of the language and population stagnated around the origin because individuals could not increase their plasticity at all. Note that higher values of W2 led to a shorter cycle period. This is thought to be because the rapid decrease in phenotypic plasticity (ii) tended to occur more often as the cost of plasticity increased.We conducted experiments to study the effects of the model’s parameters on the evolutionary process. First, to investigate the effect of the learning cost, we conducted experiments with various weights for the learning cost F, which determines the amount of displacement of languages. Because this parameter is used in the processes of cultural change and language division, we assumed the condition that the threshold for the division Fd is proportional to F (Fd = F × 300) in order to mainly focus on the effects of change in F on the cultural change process. Experiments with different settings of F (from 1.0 × 10−7 to 1.0 × 10−4) showed that the chances of all languages dying off during the early generations increased with F. This is because, at large F when there are many individuals changing language, the amount of displacement of languages tends to be so large that languages are displaced outside the plasticity range of the agent population. Especially in trials with high F (1.0 × 10−5), successful evolution was only observed when the initial population had high plasticity by chance. At extremely high F (1.0 × 10−4), all trials failed in about 10 generations.We also investigated the effects of Fd and Tf, the thresholds for division and fusion of language, respectively, Fd is smaller, the less frequently division happens, and Tf is bigger, the more frequently fusion happens. In this case, the evolution goes stagnate because few languages can mediate communication between agents. Inversely, when Fd is too large, or Tf is too small, many languages tend to appear in one simulation step, leading to interesting behavior such as “linguistic burst”. We do not focus on this to simplify the following analyses in this paper.Concerning 18. However, the rate of evolution is known to depend on the time interval over which the rates are measured31. Rates of evolution can be measured in darwins (d), which is a standardized unit of change in factors of e, the base of the natural logarithm, per million years31.v1, v2, and Δt are the mean trait value calculated at the time t1, the mean value calculated at the time t2, and the time interval between v1 and v2, respectively. Figure 24. This has never been tested empirically before this study. We focused on this comparison in the context of language evolution, where the main challenge is the lack of empirical data. It is unclear as to what extent his findings can be extended to other domains of human cultures including language. Language evolution has at least two features which restrict the evolutionary rate: (1) Language evolution is restricted by the capacity of the human brain or organs that are related to language use, which differs from general cultural evolution. (2) Language speakers must share the conventions of language to communicate with each other, which restricts language evolution. Our model reflects these features. Thus, we were able to consider the relationship between both evolutionary processes in this context by performing informational analysis on our simulation results.Cultural linguistic change is often assumed to be significantly faster than biological changeai of agents being used as the trait value. The cultural rates were calculated by focusing on each occurrence of the cultural process as follows. (a) Cultural change: lx of the changed language was regarded as v2, and the corresponding value before its change was regarded as v1. (b) Division: in this case, two rates were calculated because one language was divided into two. The two different lx values of the divided languages were regarded as v2, and lx of the language before division was regarded as v1. (c) Fusion: this event also generated two rates because two languages fused into one. The lx value of the fused language was regarded as v2, and the two different lx values of the languages before fusion were regarded as v1. (d) Extinction: no rate was calculated. Here, we used the various lengths in generations of our model as Δt in order to observe the effects of the measurement interval on the evolutionary rates of languages and agents.We measured the evolutionary rates of languages and agents to clarify the relationship between the rates of both evolutions by focusing on their measurement-interval dependence. Here, we calculated biological rates by using the agent’s mean trait values in the population in each generation with t for ten intervals. The x-axis represents the time interval (Δt), and the y-axis represents the evolutionary rates of language and biological evolution (darwins).Figure The rates of language evolution tended to be higher than those of biological evolution. However, the rates of language evolution slowed with the time interval. This implies that the evolutionary rate of language has a stronger measurement-interval dependence than the rate of biological evolution. We propose that this is due to the lack of directionality in cultural evolution. This implies that biological evolution is more directional than cultural language evolution and can therefore maintain the pace with language evolution.32, which is able to quantify the asymmetric impact between multiple sequences. To put it simply, the TE from a process X to another process Y is the amount of uncertainty reduced in future values of Y by knowing the past values of X given past values of Y.We believe that it is important to investigate the directional effects for both evolutions in gene–culture coevolution to understand the complex relationship between them. In order to do this, we used transfer entropy (TE)TY→X from the sequence Yt = {yt}t=1,2,... to another sequence Xt = {xt}t=1,2,... indicates the amount of uncertainty reduced in the state xt + 1 by knowing the past l states of m states of TY→X is calculated as follows32:The TE Yt to the sequence Xt.This measure reflects the directional effect from the sequence lx and ai in each generation. The sequence was generated as follows: We separated the time series of lx (or ai) into periods with a specific time interval (Δt) and generated a sequence composed of the average of lx (or ai) in each separated period. Then, we replaced each value in the sequence with one of the five equally divided levels according to its rate of change from the previous value.In this analysis, we generated discrete sequences from the continuous data in evolutionary experiments that consisted of the time series of average values of TY→X33 by comparing it to the one when Yt was randomized  as follows:In addition, we calculated the effective transfer entropy (ET) to verify the significance of the effects of the calculated m = l = 1. We measured the entropies of 38 experiments while changing Δt for 10 intervals. The entropies were plotted as points for each trial. The X-axis represents the time interval (Δt) used for generating sequences, and the Y-axis represents the effective transfer entropy with the corresponding Δt. Each red point represents the effective entropy from language to biological evolution (ETL→B), and each blue point represents the ET from biological evolution to language evolution (ETB→L). The lines show their median values with the corresponding setting of (Δt). The mark above each interval indicates the significance level of the difference between the median values of ETL→B and ETB→L . We used Wilcoxon rank-sum test to calculate the significance34.Figure ETL→B and ETB→L when 10 ≤ Δt ≤ 110. This is because the directional effect from language to biological evolution was weak relative to that from biological to language evolution when we took measurements at short time scales. We think that this is due to the high evolutionary speed of language in short time scales. When we measured the evolutionary rate of language in short time scales, the rate tended to be high because of the measurement-interval dependence described in the Introduction. Biological evolution seems to be unable to keep pace with language evolution because of such high-speed changes in language at short time scales, which is the “moving target” problem18. However, at long time scales (Δt > 110), we found that the difference between them tended to be small. This implies that the directional effects on each other are comparable. This means that at long time scale, biological evolution can track language evolution, and coevolution occurs thanks to both phenotypic plasticity and a constraint imposed on dynamics of language evolution by language ability of agents.We observed a statistically significant difference between 35 and “opaque thought experiments” as an alternative methodology, where the consequences follow from the premises in such a non-obvious manner that the consequences can be understood only through systematic enquiry36).Investigating the evolutionary changes of language directly is difficult; as often stated, “language does not fossilize”. Therefore, researchers have relied on inferring the evolution of linguistic ability on the basis of fossil remains of human ancestors or analyzing cultural evolution , which has been observed over a short time scale. We believe that further investigating the cultural and biological evolutions of language in a comprehensive manner requires “emergent computational thought experiments”From this viewpoint, in this paper we proposed an integrated framework for investigating genetic and cultural language evolution. Based on this framework, we first constructed an agent-based model that captures both the cultural evolution of languages and biological evolution of linguistic faculties, which are expressed in a one-dimensional linguistic space. Second, we analyzed the evolutionary rates of cultural evolution and biological evolution by using our simulation results. Finally, we analyzed the directional effects between cultural evolution and biological evolution by using the transfer entropy calculated from our simulation results.et al. constructed several coevolutionary models for biological evolution of innate cognitive biases on language acquisition and cultural learning of languages based on Bayesian inference37. They showed that culture facilitates rapid biological adaptation yet rules out nativism. In other words, behavioral universals arise that are underpinned by weak biases rather than strong innate constraints. However, it should be noted that such reduced selection pressures brought about the genetic diversity in the innate genotypes  Diversity across language groups increases the fitness variance, which accelerates the rate of biological evolution. (2) The rate of cultural evolution tends to be restricted by the plasticity of individuals because languages cannot survive outside the linguistic plasticity range of individuals. (3) The rate of cultural change can be slow, especially when individuals reduce their learning cost as they cluster around existing languages with sufficient expressiveness for communication. In contrast to situations with no linguistic conventions among speakers, this tends to cause language evolution to stagnate. We think that the rate of cultural change may be faster when there are no linguistic conventions among speakers and slower when some shared conventions exist among them.These results partly support Számadó


The detailed characterization of non-trivial coherence properties of composite quantum systems of increasing size is an indispensable prerequisite for scalable quantum computation, as well as for understanding non-equilibrium many-body physics. Here, we show how autocorrelation functions in an interacting system of phonons as well as the quantum discord between distinct degrees of freedoms can be extracted from a small controllable part of the system. As a benchmark, we show this in chains of up to 42 trapped ions, by tracing a single phonon excitation through interferometric measurements of only a single ion in the chain. We observe the spreading and partial refocusing of the excitation in the chain, even on a background of thermal excitations. We further show how this local observable reflects the dynamical evolution of quantum discord between the electronic state and the vibrational degrees of freedom of the probe ion. An exhausting characterization of the coherence properties of quantum system becomes challenging with increasing system size. Here the authors demonstrate that phonon autocorrelation functions and quantum discord can be measured with local control, and validate it in a string of 42 trapped ions. The faithful description of the state of an interacting many-particle quantum system turns ever more difficult as the system size increases12456789101113141516176On the other hand, a microscopic approach where not only global observables but also the local ones as well as their correlations become an essential part of the description will at some point hit a complexity threshold. In particular, the increasing number of interacting degrees of freedom implies a rapidly proliferating number of possible defects, which induce disorder and/or noise; with finite temperature effects as one of the most fundamental and ubiquitous perturbations. Consequently, there is a conceptual and practical need to develop scalable and experimentally feasible approaches192021To contribute to this endeavour, we present a tagging method which can be used to track single quantum excitations in warm quantum many-body systems. We achieve this by coupling an auxiliary qubit in form of the electronic state of a probe ion to the motion of an ion chain of variable length23242228x, y) of an ion string aligned along the z axis can be described by the Hamiltonian of a chain of coupled quantum harmonic oscillators31The dynamics of the transverse motion  of length θ and phase 0 creates a superposition of the form αn and βn are specific for each Fock state π with respect to the first pulse.For the probe ion initially in the state As long as the system has not evolved between both pulses, we expect full contrast. However, if the phonon created by the preparation pulse is no longer localized at the probe ion, the second pulse  cannot mMore specifically, the phase contrast or visibilityPD is the probability that after the Ramsey sequence with free evolution time t the ion is found in the excited v(t) is closely connected to both the autocorrelation function of the probe ion's vibrational degree of freedom and to the discord between the electronic and the motional degrees of freedom of the probe ion (equations (19), (29) and (32) of where To make a quantitative connection, we assume that the density matrix describing the ion string after laser cooling is diagonal in the collective mode basis and that all modes are equally populated. This is justified by noting that laser cooling acts on the individual ions on timescales faster than the coupling between ions and that the spread of the eigenmode frequencies are nearly degenerate.With these assumptions, we find in where θ/2≈0.3, including contributions of first and second order, and used the additional assumption that the initial phonon state may be approximated by an equilibrium state of the local phonon modes  for each value of the free evolution time t. For the experiments, we first determine the time it takes to excite the probe ion to the gth tπ/2  and sepat, we observe a large phase contrast as the phonon excitation is still localized at the site of the probe ion. After a few tens of microseconds, the phonon excitation couples to the other sitesTo gather sufficient statistics, we repeat the experiment 500–750 times per data point. For short times T2∼2 ms. Instead, we attribute the reduced contrast mainly to a broad incoherent background of the laser light (see Methods section).Common to all measurements is a rapid loss of phase contrast followed by a specific revival pattern. Comparison with theory shows that the revival pattern is governed by the phonon dynamics in the ion chain. However, we also observe a reduction of the maximally expected visibility from 1 to values between 0.66 and 0.80. The reduction is independent of the Ramsey gap time, consistent with the measured Gaussian qubit decoherence with We expect that suitable extensions of the scheme to protocols consisting of more than one ion or two pulses are in fact capable of extracting higher-order phonon correlation functions both in space and time. This way, the methods of non-linear spectroscopy, which are typically employed to study dynamical and spectral features of molecular aggregates and semiconductors20In this context, it is also interesting to note that the method tracks an excitation in a bath of substantial size. In the example of a 42-ion string cooled down to the Doppler limit of about five local transverse quanta, there are about 42 × 5≈200 phonons present. Our method generates a single phonon and tags it with a specific phase relationship to the electronic state of the probe ion, allowing us to re-identify this excitation when it returns to its origin. Hence, the method allows to follow the dynamics of single phonons in a finite temperature environment.Our measurements also show that quantum coherence of motional excitations can be preserved even in long ion strings. Direct extensions of this work are to measure how phonons scatter off impurities and how this affects the transport dynamics in a finite temperature environmentMore generally, it would be interesting to study how this method could be applied to other systems, for example, interacting spin chains, where individual excitations could be coherently traced via an auxiliary probe spin.Finally, our method is scalable in the sense that the control of the subsystem is independent of the size of the total system. Thus, the discussed method can be applied or adapted to large coherent systems where suitable single particle control is available, such as for instance for neutral atoms in optical latticesB=−40 dB below the carrier of the laser light, however, peaking to around B=−28 dB near the bandwidth of 700 kHz of our servo loop to stabilize the laser frequency. This incoherent background drives other transitions than the blue sideband, and in particular the strong atomic carrier transitions between the S1/2(mJ=−1/2) and D5/2 levels. Our geometry was not optimized to drive only the S1/2(mJ=−1/2) and D5/2 (mJ=−1/2) transition, and hence we assume that all carrier transitions have a similar coupling strength of Ω0≈150 kHz when driving effective π-pulses on the blue sideband in tπ=20 μs. Thus, the population of the D-state will increase by B=−40 dB) and 0.06 (B=−28 dB) for each πeff/2-pulse and transition. We estimate that this effect accounts for 0.2 of the loss of contrast for both pulses and all five atomic carrier transitions.We observe a reduction of the maximally expected visibility from 1 to between 0.66 and 0.80. The reduced contrast is mainly due to a broad incoherent background on the laser light on the order of Another concern is motional heating during the free evolution time. In our trap, motional heating almost exclusively stems from voltage noise at the trap electrodes resulting in common noise to all ions. Thus, the centre-of-mass mode heats with about 0.2 quanta per ms while all other modes heat with less than 0.01 quanta per ms. Because the heating is predominantly common mode, motional heating will not influence the intrinsic dynamics of the ion string.All relevant data are available from the authors.How to cite this article: Abdelrahman, A. et al. Local probe of single phonon dynamics in warm ion crystals. Nat. Commun.8, 15712 doi: 10.1038/ncomms15712 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Supplementary Notes and Supplementary References


In the Prior to 2012, the biomedical applications of LOAC resided mainly within academic research laboratories and much innovative work continues there; however, with the National Institute of Health’s partnership with the Defense Advanced Research Projects Agency and the US FDA there was a major acceleration and step change. The initial investment of $13 million, part of a $70 million 5-year plan, supported 17 projects to both develop the technology for maintaining tissue and reconstruct one or more organs. The principal aim of this initiative was to provide new models that could be used for screening drugs in a cost-effective manner and thereby reduce the high drop-out and overall drug pipeline costs . Over thIn this special issue, colleagues have provided reviews of various applications of OOAC including work on stem cells, spheroids and tissue biopsies; there is novel research using bespoke devices for maintaining tumor biopsies as well as a user survey and two perspectives giving expert insight into the future of the OOAC field.in vivo tissues, with relatively minor treatments of scaffolds or polymers resulting in major differences in organ formation and function. Following logically from the generation of organs, the article by Rogal and colleagues has reviewed the multiorgan field which has developed significantly since the big NIH-led investment in 2012 [in vivo cardiac tissue has in my opinion resulted in on-chip heart research falling a little behind that of the oncology applications.First, the review by Zhang and colleagues focuses on the use of embryonic stem cells and reprogrammed human-induced pluripotent stem cells and how these cells can be differentiated on chip to form organs . This ar in 2012 . The app in 2012 . Many siThe ascendance of microphysiological systems to solve the drug testing dilemma” looks at the topic from an industry perspective and importantly highlights the role that regulatory bodies play [The reviews herein highlight the potential use of OOAC devices by the pharmaceutical industry in drug development. The fourth article by Eva-Marie Dehne and colleagues entitled, “ies play ; as any ies play . The revies play . DespiteThe article by Van Gent and colleagues describes the use of organotypic cultures and focuses on how these can be used in a high-throughput setting for drug screening . A key pin vivo environment and also acknowledge that this remains a challenge. Finally, John Wikswo said in an answer to the question “If you had unlimited funding, what would you do with it to further OOAC research?”, to which he replied “… What I would try to do is launch a program of intense characterization of the organs to try to understand the extent to which the in vitro cells on plastic and OOACs in humans and animal replicate real physiology”. I agree wholeheartedly that there needs to be a comparison of technologies to provide a rational basis on which researchers and end-users can select particular models.Finally, this special edition contains two perspectives from Alexander Mosig, a life scientist  and John


Management of lead malposition is crucial to avoid complications and is carried out on case‐by‐case bases. The 12‐lead ECG during pacing and chest X‐ray are essential during initial workup and recommended for new patients to the device clinic. Echocardiography and CT scan are important to confirm the location and plan appropriate therapy. The patient was a 42‐year‐old male with coronary artery disease and ischemic cardiomyopathy who underwent right‐sided single‐chamber Medtronic Protecta implantable cardioverter defibrillator (ICD)  placement for primary prevention by cardiothoracic surgery in August of 2012. Patient presented to our device clinic in June of 2014. He had no ICD shocks, and he leads a very active lifestyle. On device interrogation, he was found to have multiple asymptomatic tachycardia episodes. The device intracardiac electrograms (EMG) were reviewed and showed multiple runs of short V‐V tachycardia, which was interpreted as nonsustained ventricular tachycardia (NSVT)  T wave oversensing We tried pacing the ICD lead at the maximum output as part of workup to evaluate the possible diagnosis, which resulted in atrial capture only and morphology of the P wave was consistent with left atrial capture Fig. A and conDue to the young age of the patient and higher risk of complication if lead extraction is to be needed in the future, we elected to attempt lead removal and repositioning instead of just abandoning that lead.Lead revision was done in July of 2014 (23 months after implantation) under fluoroscopy guidance in the operating room due to concern about possible perforation and pericardial effusion with the lead removal from the CS. The lead was removed from the header, and a stylet was placed. After unscrewing the lead and with gentle traction, the lead came out without any difficulty. The lead was then positioned in the right ventricle apex and was screwed in with no complications and good pacing numbers. Transthoracic echocardiogram was obtained, and no pericardial effusion was detected.Patient was seen during follow‐up at 1 and 6 months, and ICD interrogation showed normal sensing, pacing, and no more episodes of short V‐V tachycardia.The patient was a 63‐year‐old male with symptomatic bradycardia who underwent dual chamber pacemaker (Medtronic Advisa DR MRI A2DR01) in February of 2006 by cardiothoracic surgery. Patient was referred to our EP clinic for generator change due to ERI on device check 9 years later. Patient reported no complaints and has been asymptomatic. He has past medical history significant for diabetes and hypertension. On review of the EKG, P wave axes and morphology were abnormal and consistent with left atrial pacing  pacing versus tip to can (unipolar) pacing. There was left atrial capture with the unipolar pacing as well, and it was with a lower threshold compared to bipolar (0.5 V @ 0.5 msec versus 0.75 V @ 0.5 msec) making the possibility of anodal capture with the lead ring unlikely. This could have been an indication that the atrial lead tip was actually in direct contact with, or at least very close to, the left atrial wall, which a good‐quality CT scan failed to show. The second possibility is that there was noncontact capture, which to the best of our knowledge has not been reported before. However, higher output to capture will be expected.As mentioned above, the patient denied any symptoms of CVA or TIA since device implant 9 years before, which created a long discussion with the patient about whether he would consider anticoagulation, especially because only a small portion of the atrial lead was present in the left atrium. Ultimately, we elected to start the patient on oral anticoagulation, and he was agreeable with that.Cardiac device therapy is being used increasingly to treat heart rhythm disorders. Transvenous implantation of a pacemaker or implantable cardioverter defibrillator lead into the left atrium or ventricle is a rare complication of cardiac pacing Patients with lead malposition in the left heart chamber may be asymptomatic or may present with complications secondary to arterial embolization. The traditional management has mainly focused on systemic anticoagulation with warfarin in order to minimize TE complications. The use of antiplatelet therapy as a sole means of preventing TE complications is not advisable The type and material of the lead can affect thrombogenicity The detection of an unusual arrhythmia pattern on EKG or device interrogation should always promote the workup of lead malposition, migration, perforation, or dysfunction Once the diagnosis of malposition is confirmed, the patient may simply be managed with anticoagulation or by properly reinserting the leads, considering the benefits and potential risks In our first case, the short V‐V tachycardia was actually an atrial tachycardia due to lead malposition. The pacing morphology of the P wave, the lateral X‐ray, and echocardiography were all very helpful to confirm the diagnosis of lead misplacement within the CS. Chest CT can help distinguish lead placement in the CS versus left atrium. However, based on the good image quality of the echocardiography in this patient, we did not feel that chest CT was indicated in his case.Previous series of coronary sinus pacemaker lead extraction have been published. The largest study to date by Bongiorni et al. In the second case, lead misplacement was suspected from P wave morphology on surface EKG and confirmed with the CXR. Echocardiography was suggestive of lead in the left atrial and not the CS, but a CT scan was crucial to confirm the finding and measure the portion of the lead in the left atrium. We decided to anticoagulate the patient at the end even though he had no symptoms for 9 years.Management of leads with chronic misplacement/malposition to avoid inappropriate device therapy, thromboembolic events, and complications if extraction was considered is typically a challenge and should be carried out on a case‐by‐case basis and includes extraction, abandoning the lead, and/or anticoagulation. 12‐lead ECG during pacing and PA & LA Chest X‐ray are extremely helpful to suspect or to confirm the diagnosis of lead misplacement/malposition and perhaps they need to be done routinely for all new patients to the device clinic with implanted device besides the device interrogation. Echocardiography and/or CT scan are typically the next step to confirm the location of the leads.AA: wrote the main manuscript. AA: helped writing the manuscript. HP: revised the manuscript. WP: participated in optimization of images. WM: revised the manuscript and obtained the consent from patients and clinical care of both cases.None of the authors has any conflicts of interest.


This study aimed to investigate, by means of finite element analysis, the effect of a drill hole at the end of a horizontal osteotomy to reduce the risk of lateral cortex fracture while performing an opening wedge high tibial osteotomy (OWHTO). The question was whether drilling a hole relieves stress and increases the maximum correction angle without fracture of the lateral cortex depending on the ductility of the cortical bone.Two different types of osteotomy cuts were considered; one with a drill hole (diameter 5 mm) and the other without the hole. The drill holes were located about 20 mm distally to the tibial plateau and 6 mm medially to the lateral cortex, such that the minimal thickness of the contralateral cortical bone was 5 mm. Based on finite element calculations, two approaches were used to compare the two types of osteotomy cuts considered: (1) Assessing the static strength using local stresses following the idea of the FKM-guideline, subsequently referred to as the “FKM approach” and (2) limiting the total strain during the opening of the osteotomy wedge, subsequently referred to as “strain approach”. A critical opening angle leading to crack initiation in the opposite lateral cortex was determined for each approach and was defined as comparative parameter. The relation to bone aging was investigated by considering the material parameters of cortical bones from young and old subjects.The maximum equivalent (von-Mises) stress was smaller for the cases with a drill hole at the end of the osteotomy cut. The critical angle was approximately 1.5 times higher for the specimens with a drill hole compared to those without. This corresponds to an average increase of 50%. The calculated critical angle for all approaches is below 5°. The critical angle depends on the used approach, on patient’s age and assumed ductility of the cortical bone.Drilling a hole at the end of the osteotomy reduces the stresses in the lateral cortex and increases the critical opening angle prior to cracking of the opposite cortex in specimen with small correction angles. But the difference from having a drill hole or not is not so significant, especially for older patients. The ductility of the cortical bone is the decisive parameter for the critical opening angle. Valgus-producing high tibial osteotomy is recognized as an effective surgical procedure for the treatment of unicompartmental osteoarthritis (OA) of the knee in the presence of axial malalignment in active patients. Precise preoperative planning  and the other without the hole. The osteotomy cut had a thickness of 2 mm. The starting point of the horizontal osteotomy was located on the medial side at 35 mm distally to the tibia plateau and the end point was located in the lateral cortical bone at 20 mm distally to the tibia plateau and 6 mm from the lateral cortex. The minimal thickness of the contralateral cortical bone was 5 mm. Two types of drill holes were considered: one directly at the end of the osteotomy cut as an extension and the second also at the end of the osteotomy, but above it. The drill holes were located about 20 mm distally to the tibial plateau and 6 mm medially to the lateral cortex. The specimen without hole or “Specimen with No Hole” has been designated by the abbreviation SNH Fig. . The “SpThe software HyperMesh  was used to generate the 3D geometries of the specimens from the mesh of the finite element model of the Lower Limb Model for Safety  and three dimensional finite element analysis (FEA) were performed. For the 2D analyses, a section along the frontal plane of each of the three tibias was considered, and an offset of 10 mm from that section was made to build 2D geometries of the three specimens.σSK) of the lateral cortex of the tibia were assessed following the ideas of the FKM-guideline for metals /3 is the hydrostatic stress and σV the equivalent (von-Mises) stressσ1, σ2 and σ3 being the principal stresses.The degree of multiaxiality is calculated by means of principal stresses at the reference point, i.e. the critical point to be assessed with maximum equivalent (von-Mises) stress.The local stresses were estimated by performing linear static FEA of opening the osteotomy cut by 10° because this value was considered as a median of the correction angles applied for HTO.Kp characterises the load bearing reserve from the first yielding at the reference point (the elastic limit load (ELL)) up to the plastic limit load (PLL). It is hence defined as the ratio of PLL to ELL.The factor The PLL was estimated by performing nonlinear FEA with the cortical bone as an ideal elastic–plastic material Fig. . The ostσSK) exceeded the existing combined stress. Relying on the FKM guidelines, the used combined stress is based for ductile material on the von Mises yield criterion and isgiven by Eq. (σGH) and the combined stress based on the normal stress hypothesis (σNH):The used failure criterion assumed that the specimen failed when the assessed static strength . The combined stress according to the normal stress hypothesis is given byThe weighting factor q is between 0 and 1 and depends on the ductility. Here it was chosen once as q = 0 for ductile and once as σSK based on a linear elastic calculation. The following flowchart  was hence the critical opening angle.Re) and ultimate tensile (σult) strength of the cortical bone of the femur are 114 MPa and 135 MPa respectively, while the maximum elongation at break is A = εult = 3.1% .Average values of the strength properties of the cortical bone were found in the literature and are summarised in Table Only Reilly and Burstein  related εult from this study  and the oldest (more than 80 years) patients from the study by Ott Ott . The youAll the material parameters that were chosen to be used in the present study were retrieved from the experimental studies of Reilly and Burstein  and McCaσy = (Re + σult)/2. The tangent modulus has been chosen as ET = 0.001 ⋅ E according to the FKM-guidelines  is decisive for the assessment of the static strength  and for semi-ductile material (A < 6%). The values of elongation at break A of the cortical bone from literature are smaller than 4%; this means that the cortical bone should be considered as semi-ductile according to this norm. But as the FKM-norm is conservative and addresses steel and aluminium only, hence the ductile material case was additionally investigated for reasons of comparison. The value of 6% was chosen for the elongation at break of the cortical bone considered as ductile. Therefore both material behaviours were taken into account while performing the FKM approach as indicated in Table According to FKM and Eq. , εref iσT) in the tensile test is the instantaneous applied load divided by the instantaneous cross-sectional area of the considered specimen. The engineering stress or stress (σ) is given by the quotient of the applied load to the original cross-s ectional area of the considered specimen. The engineering strain or strain (ε) is the total elongation divided by the initial length of the considered specimen. The true stress ( σT) is related to the stress (σ) by the relation σT = σ ⋅ (1 + ε) and the true strain (εT) to the engineering strain (ε) by the relation εT = ln(1 + ε).The multilinear true stress - strain curves Fig.  were app2D and 3D FEA were performed. For each of analysis type, in total 27 numerical simulations were done for the 3 chosen constitutive material laws , for the 3 different analysed specimens according to Figs. The mesh of the 2D models consisted of quadrilateral elements with a size of 0.5 mm. The 3D models were meshed with tetrahedral solid elements. The mesh size of the 3D models depended on the material behaviours that were considered. For linear analyses a fine mesh size varying between 0.2 and 2 mm was used in the vicinity of the hole at the end of the osteotomy open wedge, and a mesh size varying between 2 and 5 mm was used to mesh the rest of the tibia. For nonlinear analyses the mesh size of the region in the vicinity of the hole at the end of the osteotomy open wedge was 1 mm, and the mesh size of the rest of the tibia varied between 1 and 5 mm.The stress distributions after performing static linear analysis of opening the osteotomy cut by 10° were similar for any specimen independently of the case study Table . The equThe maximum values of the equivalent (von-Mises) and principal stresses for the 2D linear FEA are summarized in Table For the 2D FEA the maximum equivalent (von-Mises) stress was located at the tip of the osteotomy cut of the specimen SNH. The corresponding value was smaller for specimens with a drill hole at the end of the osteotomy cut  stress was located at the tip of the notch more on the inside of the osteotomy cut. The maximum values of the principal equivalent stresses are summarised in Table Kp was calculated according to Eq.   h and thnpl calculated according to Eq.  the critical angle was higher for specimens with drill hole (SWHE and SWHA) than for specimens without. For all specimens the critical angle decreases when we go from case study M (young patients) to case study L (old patients) with the lower ultimate strength.Figures crit was 1.1° on average for semi-ductile  was more important than its strength, as can be seen by comparing case H (Tensile strength Re = 114 MPa and A = 3.1%) and case M (Tensile strength Re = 80 MPa and A = 3.7%). The maximal critical angle of 4.5°obtained for young patients (case M) is approximately the double of that for old patients (case L).For any specimen the critical angle decreased with the elongation at break corresponding to an increasing of the age of the patient increases Fig. . The higA < 6%) and the strain approach with the more realistic 3D FEA were chosen for final comparison. The critical angles are shown in Fig. The FKM approach with semi-ductile material , a specimen with a drill hole centrically in line with, and at the end of, the osteotomy (SWHE) and a specimen with the drill hole located at the proximal end of the osteotomy (SWHA). The simulated surgical technique and the geometric characteristics of the osteotomy height, obliquity and minimal distance to the opposite cortex was the same for all specimens.Three material cases have been considered to reflect the physical variety depending mainly on the age of the patients. Case H was designed with the highest mean strength values found in literature. For cases M and L the material parameters used were those of young (20–29 years) and old (more than 80 years) patients respectively. While using the FKM approach, the cortical bone was considered firstly as semi-ductile and secondly as ductile following the differentiation proposed by the FKM-guidelines  of the osteotomy gap. Regardless of the analysis type, the stress concentration was located in the zone near to the tip of the osteotomy cut. The maximum equivalent (von-Mises) stress was smaller for specimens with a drill hole at the end of the osteotomy cut.The reference stress at the hot-spot was comparable for specimens SWHE and SWHA Table . This meThe specimens with a hole  yielded more slowly than those with no hole (SNH). This means that the hole enlarges the volume of highly charged material and hence leads to a smaller strain for a given opening angle or in larger values for the critical angle.For all specimens the critical angle leading to crack initiation decreased when the patient age increased. The absolute difference between the critical angle of the specimens with a drill hole and the specimens with no hole decreased with the patient age. This means that drilling a hole in order to reduce the critical angle is more advantageous in case of young patients. This is correlated to the fact that the cortical bone of old patients is less ductile. By comparing the results obtained with the FKM approach of semi-ductile Fig.  and of dIn specimens with larger correction angles exceeding approximately 4.5° cracks are initiated and material segregation is started even with relative ductile bone behaviour, i.e. in case of younger patients. Large correction angles hence always lead at least to micro-cracking in the zone of the tip of the osteotomy cut. The clinical relevance of micro-cracking in the zone of the tip of the osteotomy cut was not investigated here. In case of older people with reduced ductility and strength of the cortical bone, the cracking starts earlier, i.e. at smaller angles.The assessment was based on crack initiation only and hence complete dislocation was not investigated here. But as the wall thickness from the drilled hole to the outer surface of the bone is small, it can be concluded by simple engineering reasoning that complete rupture of the opposite cortex follows soon after crack initiation. These data suggest that the hinge pin offers no relevant benefit for the treatment of malalignment since the need for correction in patients with varus alignment is frequently above 8° of correction. It is well documented that the risk of revarisation in the presence of the opposite cortex fracture increases with every degree of valgus correction  cortex fissures can vary significantly among patients and bone stability does not allow an “all-or-nothing principle”. Nevertheless, the data of the present study indicate that a correctly placed hinge pin at the end of the horizontal and ascending tibial osteotomy does not prevent opposite cortex fracture in larger corrections. The data suggest that bone ductility is an important factor for the crack initiation and hence integrity of opposite cortex, especially for higher corrections.The current study suggests that the drill hole (hinge pin) at the end of the horizontal osteotomy reduces the stresses in the contralateral cortex and hence increases the critical opening angle prior to cracking of the opposite cortex in specimen with small correction angles. But the difference from having a drill hole or not is not so significant, especially for older patients. The ductility of the cortical bone is the decisive parameter for the calculated critical opening angle. Transferred to clinical practice, these data suggest that the hinge pin is an asset, but not the decisive parameter, and it cannot avoid cracking and rupture of the opposite cortex in cases of larger correction angles.