Many of the estimated topologies in phylogenetic studies are presented with the bootstrap support for each of the splits in the topology indicated. If phylogenetic estimation is unbiased, high bootstrap support for a split suggests that there is a good deal of certainty that the split actually is present in the tree and low bootstrap support suggests that one or more of the taxa on one side of the estimated split might in reality be located with taxa on the other side. In the latter case the follow-up questions about how many and which of the taxa could reasonably be incorrectly placed as well as where they might alternatively be placed are not addressed through the presented bootstrap support. We present here an algorithm that finds the set of all trees with minimum bootstrap support for their splits greater than some given value. The output is a ranked list of trees, ranked according to the minimum bootstrap supports for splits in the trees. The number of such trees and their topologies provides useful supplementary information in bootstrap analyses about the reasons for low bootstrap support for splits. We also present ways of quantifying low bootstrap support by considering the set of all topologies with minimum bootstrap greater than some quantity as providing a confidence region of topologies. Using a double bootstrap we are able to choose a cutoff so that the set of topologies with minimum bootstrap support for a split greater than that cutoff gives an approximate 95% confidence region. As with bootstrap support one advantage of the methods is that they are generally applicable to the wide variety of phylogenetic estimation methods. Bootstrap support or bootstrap probability (BP), A brief example is given in While methods to obtain a set of ranked trees based on minBP will be useful as supplementary information to BP for estimated splits, it is desirable to quantify the level of uncertainty associated with a set of trees through a confidence level. A (1 − α) × 100% confidence region for the true topology is a data-dependent, and hence random, set of topologies that contains the true topology with probability 1 − α. This differs from a Bayesian credible interval both in its construction and in that the true topology is treated as fixed but unknown, rather than random. Because of the duality between testing and confidence region construction, given a testing procedure, a (1 − α) × 100% confidence region can be constructed as the set of trees for which a test of the null hypothesis that the tree is correct gave a p-value ≥ α. Existing methods for testing whether topologies are correct include the the SH test , the SOWAs an alternative to using a set of trees ranked by minBP as input to an existing testing procedure, we can treat minBP as a test statistic of the null hypothesis that a given tree is correct. This interpretation of minBP as a test statistic differs from the conventional interpretation as a p-value. In any case, as with any other test statistic, bootstrapping can be used to approximate its distribution. In effect this results in a double bootstrap since for each bootstrap sample, additional bootstrap samples are required to obtain the minBP value. A 95% confidence region of trees is given by the set of trees with minBP larger than the 5th percentile of the bootstrap distribution.n is the number of sites. Considerable attention has been given to the question as to what constitutes large BP. http://www.mathstat.dal.ca/~tsusko that will produce files with the required bootstrapped data sets and, based upon the input estimated trees, will construct lists of a prespecified number of trees ranked according to minBP, calculate all trees with minBP at least as large as a cutoff and/or calculate the appropriate cutoff using the double bootstrap output.The methods presented here are generally applicable to the wide variety of phylogenetic estimation methods. Required as input is a set of trees estimated in some way for the original data set, bootstrapped data sets and possibly double bootstrapped data sets when minBP-based confidence regions are desired. Software will be made available at A and rabbit, opposum and mouse in the other set, Ac. A pair of splits S1 = A1 | A1c, S2 = A2 | A2c, are compatible if at least one of the pairwise intersections A1A2, A1A2c, A1c A2 and A1c A2c is the empty set. A phylogenetic tree satisfies that all of its splits are pairwise compatible and it is sufficient for a set of distinct splits to be pairwise compatible for it to define a tree. Since there are 2m-3 branches in an unrooted tree, where m is the number of taxa, 2m-3 distinct splits are required to define a tree.m − 3 distinct pairwise compatible splits corresponding to internal branches (at least two elements on both sides of the split).Given a set of splits the algorithms presented here find all subsets of splits that define a tree. Splits corresponding to terminal branches can be ignored since they are present in all trees and compatible with all splits. It thus suffices to determine all subsets of k < m − 3 compatible splits and we represent it as the collection of m − 3 splits that are compatible and contain the k compatible splits.The discussion above was for binary trees. To restrict attention to such trees we treat a multifurcating tree as the set of binary trees with 0 edge lengths that gives rise to it. In terms of splits, a multifurcating tree is defined by Si, i = 1,…,k a simple algorithm that can be used is to find all sets of r compatible splits successively for r = 1,…,m − 3. The sets of compatible splits with r = m − 3 gives the set of trees. Given the sets of r compatible splits, C1,…,Cs, the sets of r + 1 compatible splits are found by finding, for each of these sets, the set of splits compatible with it. The unions of the Cj with the sets of splits compatible with them give the sets of r + 1 compatible splits. The difficulty with this approach is that the number of sets of r compatible splits can get very large for intermediate r.Given a set of splits, C = {Si1,…, Sir} (i1 < … < ir) of splits as followsAn alternative algorithm updates a current set P, that are compatible with the splits in C.Obtain or update the set of splits, r < m − 4, add the first split in P to C and go to 1.If r = m − 4, each split in P together with C gives a tree. Store the trees and update C by setting Sir to the first split Si, i > ir compatible with the rest of the splits in C. Go to 1.If k × k compatibility matrix, assigning a 1 or a 0 to the ij position according to whether Si and Sj are compatible or not, can be constructed at the beginning so that further checks on compatibility require checking the ijth entry of the compatibility matrix alone. For the application of primary interest here, determining all trees with minBP at least as large as some threshold ζ(<0.5), any split with support larger than 1 − ζ, must be in the final tree and thus give a set of splits that can be placed in C initially and never removed.Much less storage is required for this algorithm but compatibility of splits requires checking more frequently. Some additional computational economies can be achieved. For instance, a C and compatibility set P. The worst case time-complexity would arise when all choices of k are compatible. In this case, each current set C of size r would have compatibility set P of size k − r. In addition, each of the possible r, r < m − 4, would arise in the algorithm. For each of these, the update step 2 would check compatibility of the first split in P with the rest of the k − r − 1 splits in P. Thus the number of comparisons considered would be Given a compatibility matrix, computation requires a sequence of binary comparisons to update the current set The approach we take here is to treat minBP not as a p-value but as a test statistic. A tree is included in a (1 − α) × 100% confidence region if its minBP is greater than the αth quantile of the distribution of minBP. Since the distribution of minBP is difficult to calculate analytically, a bootstrap must be used to approximate it.B nonparametric bootstrap samples are generated and, for each of these samples, the minBP value for the originally estimated tree is obtained giving B minBP values. The resulting αth quantile of the bootstrap distribution or α × Bth sorted minBP value from the bootstrap samples is used as the cutoff for splits to include in obtaining the confidence region.Given an estimated tree, F̂, that assigns probability 1/n to each of the observed vectors of character states . Since the bootstrap generates data from F̂, the proportion of bootstrap samples with minBP larger than ζ should be approximatelyTo outline why this use of the nonparametric bootstrapping gives a reasonable cutoff, it is useful to characterize the bootstrapping process as sampling of vectors of character states from the empirical distribution. Each bootstrapped data set is obtained by independently selecting vectors of character states  from the probability distribution, B can and should be chosen large enough that the proportion of minBP larger than ζ is equal to (1) up to a negligible error. In practice, particularly in the case of expensive phylogenetic estimation procedures, this is often not the case.In principle, F̂, the empirical distribution, converges to the actual distribution, F, of vectors of character states implied by the random substitution process and the true tree. We can usually think of the true tree in a variety of different ways as a function of F, T(F). For instance, T(F) is the tree that maximizes the expected log likelihood and T(F) is also the tree that minimizes the expected sum of squared pairwise distances. Which characterization is more appropriate depends on the estimation procedure under consideration. For instance, with likelihood estimation, thinking of T(F) as the maximizer of expected log likelihood is more appropriate, since the expected log likelihood for a single vector of character states from F̂ is just the log likelihood, T(F̂) is the maximum likelihood estimate of the tree for the data. Since F̂ ≈ F for large samples, the expectation is thatUnder quite general conditions, Since the left hand side of (2) is approximately the proportion of bootstrap samples with minBP larger than ζ, if the cutoff ζ is chosen as the αth quantile of the bootstrapped minBPs, we haveT(F), is in the confidence region if and only if all of its splits have BP greater than ζ. Thus the set of trees with minBP larger than the αth quantile of the bootstrap distribution gives an approximate (1 − α)×100% confidence region.where the last equality follows from the fact that the true tree, The use of bootstrapping actually requires a double bootstrap. For each bootstrap sample at the top level giving the minBP values for the estimated tree across bootstrap samples, additional bootstrap samples have to be taken to obtain the minBP values. This can quickly become costly. For the example applications here, we used 100 bootstrap samples in both levels of the bootstrapping process. Including the original data set, this requires 10101, estimations of trees.The first two examples that we consider have been considered previously in the literature on confidence regions estimation and testing  and invoTo determine a minBP cutoff for a 95% confidence region for the mammalian mitochondrial data considered earlier, 100 bootstrap samples were generated from the original data set. From each of these samples, another 100 bootstrap samples were generated to obtain the minBP value for the estimated tree. This resulted in 100 minBP values. The minBP cutoff was taken as the fifth percentile of the minBP values which turned out to be 6%; the minBP cutoff for a 90% confidence region was 15%. Based upon this, a 95% confidence region is given by the first 3 ranked trees with the third being a borderline inclusionpth quantile of the sample of bootstrapped minBPs then the p-value is p. For the mammalian mitochondrial data, the p-values are given in An alternative way of characterizing the support for a ranked set of minBP trees is through p-values. We can define a test of the null hypothesis that a given tree is the correct tree by rejecting that hypothesis at the α level if and only if the tree is not in a (1 − α)×100% confidence region. The p-value for this test is the smallest α level for which the null hypothesis can be rejected which, in the present case, is the smallest α for which the tree is not in a (1 − α)×100% confidence region. Since a tree is in the confidence region as long as its minBP is larger than the cutoff for that region, and the cutoffs are determined from the bootstrapped minBPs, the p-value is found by obtaining the largest bootstrapped minBP less than the minBP for the given tree. If this bootstrapped minBP is the gag and pol genes for isolates of HIV-1 subtypes A, B, D and E: A1 (Q23), A2 (U455), B (BRU), D (NDK), E1 (90CF11697) and E2 (93TH057). For the GLS test and the minBP p-values, the F84 model as implemented in the PHYLIP package, The HIV data set was considered previously in The particular null hypothesis of interest in Interesting features of this analysis include a comparatively large minBP p-value, a large minBP cutoff of 31% for a 95% confidence region and the possibility that the F84 model is not flexible enough for the data. Given the results from other tests and the large drop in minBP from the first topology to the second, it is expected that increased double bootstrap sampling would reduce the p-value for all topologies except the first; with 100 bootstrap samples p-values are necessarily in the set {0.01,0.02,…,1.00}. However, a large number of bootstrapped minBP values would clearly be required. Without very significant computational resources, obtaining a fine resolution for minBP p-values is infeasible.As discussed earlier, a double-bootstrap-free minBP cutoff is 5% and comes from the conventional interpretation of 1-BP as a p-value for the null hypothesis that a split is not present. In the present example this seems inappropriate. The results of the other tests indicate that there is very little support for the second and third topologies, which would have to be included with this cutoff, and the results of bootstrapping the minBP values indicate that values as small as 5% are quite unlikely.An alternative approach to the nonparametric bootstrap is a parametric bootstrap where the bootstrapped minBP values are obtained from bootstrap data sets simulated from the fitted model with estimated parameters. A possible advantage of the nonparametric bootstrap is that since data is being generated from the empirical distribution it should be giving reasonable accurate approximations to the probabilities that minBP is larger than a value, even if the assumed substitution process is incorrect. If the tree estimation procedure is used with a misspecified model that is still “close enough” to the generating process to allow distinctions between competing topologies, reasonable results can be obtained. In the present case, an F84 model was used where With 13 taxa, the number of possible trees for the archaebacterial data set is 13,749,310,575, so that this data set serves to illustrate some of the difficulties in inference with larger numbers of taxa. The data set, which had 269 sites, was considered previously in The ranked trees, the fourth in particular, give an indication of reasons that the number of trees can be expected to grow quickly with larger numbers of taxa. The second ranked tree indicates that there is significant support for Af being closer to the Tc, Tw, Ph split. The third ranked tree indicates that there is support for the positions of Ao and Pa being switched. The fourth tree, combines both of these alternative splits, placing Af closer to the Tc, Tw, Ph split and switching the positions of Ao and Pa from what they were in the estimated tree. Generally, if a number of alternative splits are supported in separated regions of the tree, as is increasingly likely with larger numbers of taxa, any combinations of those splits will produce a tree that is well supported.Based on a double bootstrap with 100 bootstrapped data sets at both levels, the cutoff minBP for a 95% confidence region was found to be 1% for this data set. Here, in contrast to the HIV data set, the cutoff was less than the 5% cutoff suggested by the BP test. Part of the reason for this has to do with the increased uncertainty about the tree for this data set. The small branch lengths and small BP suggest a generating tree that is closer to the “boundary” between trees in tree space, implying that BP is expected to be smaller for the generating tree. Even if the generating tree was a comparable distance from the boundary as for the HIV data set, because of the larger number of splits, the minimum BP over all splits can be expected to be smaller. The use of minBP as a test statistic adjusts for the multiple comparisons implied by considering a number of BPs instead of just one.The 264 trees with minBP greater than or equal to the 1% cutoff for a 95% confidence region is too large for easy presentation and some extraction of summary information from this set is required. A simple summary is provided by defining groups of taxa and presenting all trees in the confidence region that are compatible with those groups as trees of groups where taxa labels are replaced by group labels. An example is given in For each group, the split with the group on one side must be present in the tree for it to be compatible with the groups.If the tree is compatible with the groups, for each group, a single representative is selected and the splits between representatives are determined.The splits for the group representatives obtained in 2 give a tree for the groups with the names of the representatives replaced by the group names.In the set of 264 trees for all of the taxa, 72 were incompatible with the groups indicated. Many more of them corresponded to the same tree with groups as taxa but with some variation of splits within groups.Since the probability is 0.95 that the correct tree is contained in a 95% confidence region of trees, the probability that the correct tree of groups is contained in the set of distinct trees of groups corresponding to the trees in the region is 0.95 as well. Thus this set provides a confidence region for the trees of groups. This is true for confidence regions generally, not just those constructed using minBP. Note, however, that an assumption is being made about the existence of groups in the tree.T replaced by splits of groups. In the original approach, the minimum bootstrap support is over both within and between groups splits, while in this approach the minimum is only over between group splits. Consequently the 5% cutoff coming from a double bootstrap can be expected to be larger and thus the confidence region of trees of groups will be smaller than the set extracted from the confidence set of trees.The above approach provides a way of extracting summary information when the confidence region of trees is large. However, the knowledge that groups exist can be used to create smaller confidence regions. The same arguments as were given in (1) and (2) apply with In principle, estimation in this case should be constrained: trees should be estimated with the splits of groups present whether this is the case for the unconstrained estimated tree or not. As an approximation that avoids recomputing trees for every choice of groups, one can ignore bootstrap samples that give trees that are incompatible with the group splits. Since any samples where the groups were present in the tree give the same unconstrained estimate as the constrained estimate, and since these constitute a majority of the cases, the resulting minBP cutoff should be approximately the same as if the more appropriate constrained estimation had been used.For the EF-1α data, the cutoff was found to be 1% as it was for confidence regions for the original trees. Thus the confidence region for groups of trees is given in The methods presented here are most closely related to a variety of methods that use bootstrap support for topologies to construct confidence regions, including those discussed in Other BP methods rank bootstrap support for trees in order of some distance from the “best” tree cf , for insOther ways of using BP include constructing the bootstrap profile, or set of all topologies that arose in bootstrap sampling . CalculaIn theory, if it were possible to calculate the limiting BP for each topology as the number of bootstrap samples increases without bound, this value should be used as BP. The fact that this cannot be done leads to difficulties in high-uncertainty problems as has been noted in a and b. Each cumulative distribution was approximated through simulation. The BP and minBP values for the true tree was calculated for 1000 simulations with Jukes-Cantor maximum likelihood estimation being applied to sequences of 1000 nucleotides simulated under a Jukes-Cantor substitution process; 100 bootstrap samples were considered in each simulation. The cumulative distribution function, with the y-value giving the probability that BP (minBP) is less than or equal to the corresponding x value, was estimated based on the observed proportions in the simulations. The appropriate bootstrap cutoff value for a 95% confidence region is the value of BP (minBP) such that the probability of being less than or equal to it is 0.05. If every topology with BP (minBP) greater than this value is included in the confidence region, the probability of type I error, not including the true topology in the confidence region, is 0.05.High-uncertainty problems where large numbers of trees should be included in a confidence region can only arise with substantial numbers of taxa but difficulties with low BP can arise with small numbers of taxa as well if the true tree is poorly resolved. We illustrate this in a = 0.1 and b = 0.0001. In the language of a = 0.005, b = 0.001 and a = 0.001, b = 0.001, the probabilities that the true tree will be included in a 95% confidence region using a 5% cutoff for BP (minBP) are 0.80 (0.63) and 0.21 (0.49). While this suggests that the 5% cutoff is generally too large, the well resolved case when a = 0.01 and b = 0.01 saw BP (minP) values greater than 5% 1000 (999) times in the 1000 simulations.One interesting set of observations comes by comparison with the interpretation of BP as a first-order correct p-value . Accordia = 0.01, b = 0.0001, a = 0.005, b = 0.001 and a = 0.001, b = 0.001 the cutoffs for BP (minBP) were 1 (2), 0 (1) and 0 (1). Note that 100 bootstrap samples were being considered in each simulation. Each of these simulations gives an unbiased estimate of the limiting BP (minBP) with infinite bootstrap samples. However, if the 5th percentile of the distribution of the target limiting BP (minBP) is between 0 and 1%, which is almost certainly the case here, 100 bootstrap samples are not sufficient to determine it. In short, in each of these poorly resolved cases, more bootstrap samples are required to have enough resolution to determine an appropriate BP cutoff for a 95% confidence region. However, because the cumulative distribution of minBP moves away from 0 faster than the distribution for BP, less bootstrap sampling effort is required to obtain the same resolution.The other interesting observation comes from considering the cutoffs corresponding to a 95% confidence region: the 5th percentiles of the distributions. For the poorly resolved cases In practice, since the true topology is not known, the cumulative distribution functions of With or without a confidence region interpretation the bootstrap methods presented here provide useful supplementary information to bootstrap support values, indicating what kinds of alternative splits had reasonable levels of support. As a confidence region construction procedure, with smaller numbers of taxa the HIV and mammalian mitochondrial analyses gave results comparable to existing confidence region construction methods. Most such methods require input of sets of trees for construction of confidence regions. One alternative use of the sets of trees with minBP greater than a threshold is as input to some other confidence region construction method. It should be noted that in some cases this is not strictly justified. For instance, the theory motivating the SH and AU tests assume a fixed set of trees, not a data determined set. In contrast the SOWH and GLS methods include in their confidence sets all trees that have large likelihood or small generalized sum of squares respectively. While in principle these routines should include all trees meeting a certain criterion they can only recognize those trees that meet the criterion among the input trees. Using the set of trees with minBP larger than a fairly small threshold automates the search for trees that might be expected to be included.An undesirable attribute of the minBP confidence region construction method is that it fails to use additional information such as likelihood or branch lengths. However, this is unavoidable for any method that can be used in conjunction with a wide array of different methods including parsimony, likelihood and distance methods. Still it seems reasonable to expect that confidence region methods that use additional information will give smaller confidence regions; results for the HIV and mammalian mitochondrial data sets suggest comparable inferences however. Another potential drawback is that very large sets of trees can result with larger numbers of taxa. In this case a list of a fixed number of trees with top-ranked minBP can still be useful in providing supplementary information to bootstrap support.Inference with larger numbers of taxa generally requires careful consideration. A multiple comparisons issue arises in that with larger numbers of taxa there are larger numbers of splits and thus the probability of finding a false split with large bootstrap bootstrap support increases. The use of minBP adjusts for this multiple comparisons issue with the tradeoff that a larger region of trees result. An alternative approach to the nonparametric bootstrap is a parametric bootstrap where the bootstrapped minBP values are obtained from bootstrap data sets simulated from the fitted model with estimated parameters. A possible advantage of the nonparametric bootstrap is that it should give reasonably accurate approximations to the probabilities that minBP is larger than a value, if the approximation of independence across sites is not too rough but the substitution process is misspecified. The tradeoff is that if the modeling is correct, the parametric bootstrap distribution can be expected to give a less variable approximation to the true distribution of pattern probabilities. Assuming a large enough sample size, the empirical distribution and parametric bootstrap distribution should be comparable since they both consistently estimate the true distribution and so one expects comparable answers. From a practical standpoint, the main reason for not using parametric bootstrapping is that it requires clear model specification, which is not required for parsimony and some distance methods. In addition, some models, like the covarion models of The focus here has been on inference but the tree with maximum minBP might also be considered as an alternative estimate of topology. While in every example considered here, the tree with maximum minBP was the estimated tree this need not be the case. In fact the maximum minBP is interpretable as a majority rule consensus tree with data-dependent percentage equal to largest percentage for which a binary tree can be constructed (c.f.


During concept learning tasks, for example, it has been suggested that characteristic features are abstracted from a set of examples with the consequence that learning of similar tasks is facilitated—a process termed ‘learning to learn’. From a computational point of view such an extraction of invariants can be regarded as learning of an underlying structure. Here we review the evidence for structure learning as a ‘learning to learn’ mechanism, especially in sensorimotor control where the motor system has to adapt to variable environments. We review studies demonstrating that common features of variable environments are extracted during sensorimotor learning and exploited for efficient adaptation in novel tasks. We conclude that structure learning plays a fundamental role in skill learning and may underlie the unsurpassed flexibility and adaptability of the motor system. The same pair of stimulus-objects was repeatedly presented presented in randomized locations (i.e. left or right) for a block of trials. At the start of a new block two new stimulus-objects were used. Initially, the monkeys took many trials to learn the correct response, but in later blocks Harlow observed a greater than 95% success rate on the second trial of each block “describes the ability of animals to slowly learn a general rule which can then be applied in order to rapidly solve new problem sets”Harlow noted that most animal experiments had studied learning as an isolated episode on a single task and, therefore, did not reflect learning in everyday life which involves experience over many tasks intra-dimensional shifts compared to extra-dimensional shifts in learning problems Further investigations showed how the features of the training sets determined learning rates. Substantial facilitation was reported for Animals have also been shown to learn more complex rules by mastering conditional discriminations that depend on the presence of contextual stimuli 3‘Learning to learn’ has also been reported in both children and adults 4In sensorimotor control it is natural to think of regularities between motor output and sensory inputs. These are imposed by both the physical properties of the body and the regularities in the environment or set of task to be performed. Structural learning could exploit these regularities to facilitate learning.4.1parametric adaptive control, knowledge of the structure of the control task is presupposed (e.g. the form of the equations of motion governing the dynamics of the arm) and only unknown parameters of the structure that are currently in play have to be estimated (e.g. the mass of a hand-held object). Parametric adaptive control, therefore, consists of estimating the parameters of the system (using one of a number of optimization procedures) and then using these parameter estimates in the control process. However, when the structural form itself is unknown, adaptive control relies on structural learning to develop a representation of the control process. Such structural learning, in its most general form, needs to determine the relevant inputs and outputs of the system, the dimensionality and form of the control problem, the relation between the control variables, their range of potential values and the noise properties associated with them. The theoretical literature has primarily investigated parametric adaptive control as this allows, by design, the adaptive control problem to be turned into a parametric optimization problem for which established system identification techniques can be employed to determine the parameters of the fixed model structure—see, for example Adaptive control is a branch of control theory aimed at problems in which some of the properties of the system that we wish to control are unknown. This approach uses two levels of analysis: ‘structural adaptive control’ and ‘parametric adaptive control’ u, is driven as a function of sensory input, x, and the parameters of the system, μ such that u = f f represents the structure of the task and μ the relevant parameters which vary across tasks. Critically, the representation of μ, and hence f, depends on the task. For example, if across tasks the mass of a hand-held object varies then μ might represent the mass, whereas if the task involved wielding sticks of different lengths μ might represent the length of the stick. In adaptive control theory u = f is called a parametric adaptive control law, because it encapsulates the knowledge of how the unknown parameters μ are structurally related to the other control variables. Such parametric control laws can be used to study movement generation within the framework of optimal feedback control, and have been successful in explaining a wide range of human motor behaviour One control theoretic framework to study adaptive control is optimal feedback control theory in which the command, 4.2‘Learning to learn’ phenomena have also been observed in motor control tasks The importance of variability during training is also emphasized in another visuomotor displacement study While the motor studies described above have investigated ‘learning to learn’ effects, they have not directly tested structural learning as a basis for facilitation of learning. Recently, we have conducted a series of studies to directly test the idea of structural learning in motor control. In our tasks subjects had to learn visuomotor transformations between their actual and perceived hand movement in virtual reality reaching tasks—for example, a visuomotor rotation would induce the perceived hand movement to be a rotated version of the actual hand movement. Such visuomotor transformations can be chosen to have a particular structure  that requires the setting of specific parameters to be fully determined . By randomizing these parameter settings in our experiment we could test how random experience of a particular structure affects learning of a new visuomotor transformation. In The structural learning hypothesis also predicts that, when learning a new transformation, the motor controller should, at least initially, explore preferentially along the structure  and its direct causal antecedents denoted as parents (Xi). Thus, depending on a particular network structure S with model parameters μS the joint probability distribution S of the network determines the dependencies between the variables — that is the presence or absence of arrows — while the probabilities that specify the actual dependencies quantitatively are parameters of that structure. Therefore, ‘structural learning’ refers to learning the topology of such a network, whereas ‘parametric learning’ involves determining quantitatively the causal connections given by the structure. In particular, the problem of structural learning is exacerbated in the presence of hidden variables, because the hidden variables and the structure between them and the observables have to be inferred. This is the standard case in sensorimotor learning. For instance, in the rotation experiments described above the hidden variable is the rotation angle. If the nervous system can extract this hidden variable, the joint probability distribution over the sensorimotor space can be efficiently computed as μ represents a rotation-specific hidden variable (P(S|X) of a certain structural model S given the data X, and (b) computing the posterior probability P of the parameter μS given the structural model S and the data X. By using this formalism the concept of structural learning can be easily incorporated within the framework of Bayesian sensorimotor integration Structural learning can also be considered from a Bayesian point of view, in which the learner maintains a probability distribution over possible structures that could explain the data. Such structural learning is typically studied in the framework of Bayesian networks . Ultimatcessing) A. The devariable B. Formal6The hypothesis of structural learning as a ‘learning to learn’ mechanism can be applied to a large body of existing research. In experimental psychology ‘learning to learn’ phenomena have been reported when animals are exposed to different environments that belong to a particular class or type. Instead of talking about ‘class’ or ‘type’ we might equally say that these environments share a common structure. Harlow pioneered the hypothesis that animals form ‘learning sets’ of abstract solution strategies applicable to all environments that share the same class or structure. In addition, studies in cognitive science have investigated structure learning mainly in the context of inferring causal dependencies. So far these studies have rarely asked the question how such structure learning transfers to new learning problems, although some have reported ‘learning to learn’ effects


This is a retrospective study of 520 patients with lung cancer, seen at the Tata Memorial Hospital between 1963 and 1970. Matched controls were obtained from those patients who came to the hospital within the same period and who were diagnosed as not having cancer. The patients and controls were matched for age, sex and community. As reported in other studies, an association was found between smoking habit and lung cancer. The relative risk of all types of smokers to non-smokers is 2·45, of bidi smokers 2·64 and of cigarette smokers 2·23. There is a preponderance of the group of epidermoid carcinomata among smokers as against adenocarcinomata. The probable reasons for the reported low incidence of lung cancer in this population have been discussed.


On the Origin of Species. Now on the 150th anniversary of the publication of that seminal work, a study linking vestigial organs with molecular biology with paleontology has shown even more clearly how vestigial organs are of critical explanatory power in evolutionary theory. In the current issue of PLoS Genetics, Meredith et al. ENAM) gene in placental mammals that sheds light on the evolutionary process. What is different about this study from others in the literature using gene sequences in the study of evolution is that ENAM sequences and functionality directly mirror the evolution of teeth in living and extinct placental mammals.Charles Darwin was intrigued with vestigial organs and, in fact, made them a part of his “long argument” for the existence of evolution in the natural world in Chapter 13 of ENAM therefore becomes an important protein to follow in the transition of organisms with and without teeth, and teeth with and without enamel. What then becomes interesting is the distribution of enamel in living and extinct mammals , and pseudogene—by reconstructing the presence and absence of enamel  and silent substitutions  when comparing sequences. Using well-developed methods to correct these counts for molecular evolutionary processes, they then produce a ratio of the replacement site count to the silent site count called ω. This ratio can then be interpreted to indicate three kinds of selection pressure on molecules. If ω<1.0, then the molecule or sites being studied are under what is called “purifying selection”. When ω = 1.0, the sites are changing neutrally, and when ω>1.0 the sites are changing under what is called “positive Darwinian selection”. The first category simply retains amino acid sequence as a result of strong selection to stay the same. The latter category usually results in adaptation of the molecule to a changing external environment.ENAM genes in the phylogeny and more and more relaxed purifying selection on the premutation and mixed lineages. Finally, when we reach pseudogene lineages, the pattern of evolution is neutral or totally relaxed and leads to what the authors suggest is “molecular decay”—the accumulation of stop codons and frameshift mutations. The molecular decay is then easily correlated with the loss of phenotype .When the branches that are categorized as functional are examined, ω = 0.51 and is significantly less than the neutral expectation. Branches categorized as pseudogenes have an ω = 1.02, and branches categorized as premutation and mixed have intermediate values . These results indicate strong purifying selection on branches that lead to functional ENAM decay in the evolution of placental mammals, not a single instance of regain or re-evolution of enamel occurs once ENAM has decayed on an earlier branch of the tree. These observations are consistent with Dollo's Law that states that once a complex organ is lost it can never be regained in exactly the same form. Indeed, other workers ENAM recovering its function after 10 MY is only 0.014. The observed rapid demise of ENAM as demonstrated by the accumulation of stop codons and frameshifts in the genes of edentulous and enamelless mammals is entirely consistent with these calculations. As with decay and our own teeth, once an ENAM gene decays for a period of time, there is no resurrecting it. Any tooth that might evolve after a loss would not really be a tooth but rather an analogy of a tooth or a “false” tooth.While the Meredith et al. On the Origin of Species: “Rudimentary organs may be compared with the letters in a word, still retained in the spelling, but become useless in the pronunciation, but which serve as a clue in seeking for its derivation” Darwin created a stunning metaphor for vestigial organs in Chapter 13 of ENAM genes produces pseudogenes that are correlated with the loss or alteration of phenotype and the “decay” of teeth in certain lineages during mammalian evolution.The metaphor suggests that rudimentary organs are like words spelled the same as their antecedents that have become pronounced differently, and with the different pronunciation the unpronounced letters in the spelling become useless in communication. Meredith et al.


The classification system which employs a statistical procedure to obtain the final result gave a success rate of 100% to distinguish CHF patients from normal patients. For this study the Holter monitor data of 36 normal and 36 CHF patients were used. The classification system using standard deviation of RR intervals also performed well, although it did not match the 100% success rate using the features from SODP. However, the success rate for classification using this procedure for SDRR was many fold higher compared to using a threshold. The classification system in this paper will be a valuable asset to the clinician, in the detection congestive heart failure.A classification system to detect congestive heart failure (CHF) patients from normal (N) patients is described. The classification procedure uses the  The need to reach remote, underserved communities with life saving health care is an important area that warrants attention. Fast electronic communication and reliable automated classification systems will enhance this area of health care. In particular when cardiologists serving remote areas are few, reliable automated classification systems will not only free offsite cardiologists from routine visual analysis of electrocardiogram (ECG) data but also provide valuable specialized treatment to patients in remote areas from more experienced cardiologists elsewhere via electronic communication. The analysis and classification of large amount Holter monitor data is an aspect which is amenable to reliable automation. This paper concerns itself to develop such a system to distinguish congestive heart failure (CHF) subjects from normal (N) subjects. The patient measurements that are used for this automated analysis are the Holter monitor RR interval data. In the system that is being studied, these RR intervals are used in the construction of a second-order difference plot (SODP), whose features are then used as input in the classification algorithm. In addition the paper also looks at the results that are obtained using the standard deviation of RR intervals (SDRR) in the classification algorithm. Several attempts in this direction of automatic classification of CHF patients have been made with varying success. The use of power spectral densities of the RR intervals derived from autoregressive moving average (ARMA) with the artificial neural network (ANN)  is one oThe method presented in this paper is an alternate procedure to the methods mentioned above. It uses time domain information and it is easy to implement compared to the above methods. A reliable automated system in the future can be a fusion of the both time domain and a successful frequency domain method. In this respect, the method presented here can not only be used to provide an independent classification tool, but also be used as a complementary method to verify the frequency domain results. x(n + 1) is plotted against x(n) in a time series [x(n + 2) − x(n + 1)) is plotted against (x(n + 1) − x(n)). It is a plot of successive rates against each other. The graph displays the correlation between consecutive rate values in a time series. In this paper the focus is on SODP. It is a simple analytical technique which could be a valuable additional tool in the analysis of heart rate variability (HRV). The objective of this paper is to examine the potential of this additional tool in the analysis and classification of cardiac RR interval data collected via Holter monitors, in particular to identify congestive heart failure patients (CHF) from normal (N) patients. In the Poincare plot, a technique taken from nonlinear dynamics, each sample value e series . It dispe series , ) [r, around the origin, counting the number of points that fall within the radius, and dividing by the total number of points. Let n be the total number of points and r the radius of the central area. Then,Central Tendency Measure (CTM(r))  is a parr, CTM provides the fraction of the total number of points that lie within it. For a particular radius r, CTM counts the number of successive rates that have all sign combinations, without any distinction.r) as a function of r for a normal and CHF subject, whose SODP is shown in r in the range close to 0.015 provides the best separation in the value of CTM. However the optimum r to distinguish between CHF and N is chosen by examining the CTM for a bigger data set of 36 normal and 36 CHF subjects. This is carried out by evaluating CTM(r) for the CHF and N subjects and then determining the probability associated with the T statistic that is attributed to the differences in the means of the two data sets being due to chance. The chosen r value is the one which gives the smallest probability. This provides the best separation using CTM between the two data sets. This will be done later.r in an SODP is another parameter that is being studied here to characterize the differences between the two distributions. Each point in the SODP is characterized by a distance d(i) whereThe mean distance of the points within the circular radius D(r) is evaluated by determining the mean distance of the points which are within a circular radius r. The term distance is used here in reference to the SODP plot.D(r) as a function of r for the CHF and N subject, whose SODP is shown in r equal to 0.02. The optimum r is however chosen using the same procedure used for CTM with the expanded 36 CHF and 36 N subjects.r in SODP was evaluated. This number involved the counting the number of successive rates that have all sign combinations. On the other hand, the evaluation of  CCTM involves counting the number of points that are present in the four quadrants of the SODP separately, that lie within a circular radius r. Let xx(i) = x(i + 1) − x(i); yy(i) = x(i + 2) − x(i + 1); Then,In δ(dk(i)) = 0, k = 1,2, 3,4k(r), k = 1,…, 4, are plotted as a function of r for both CHF and N subject, whose SODP is shown in r in the range of 0.015 to 0.02. Again the optimal radius r for each component CTM is chosen using the same procedure used for CTM with the expanded 36 CHF and 36 N subjects.k-nearest neighbor where the object is classified by a majority vote of its neighbors, with the object being assigned to the class most common amongst its k nearest neighbors [k = 1, was used, where the subject is assigned to the class of its nearest neighbor. In the k-nearest neighbor classification algorithm, both the Euclidean and the Mahalanbois [k-nearest neighbor classification algorithm. The results presented in this paper use this classification algorithm.Three classification algorithms were investigated. One of them is the eighbors . In thisalanbois  distancealanbois . The othalanbois , 15 and alanbois –18. PrelCardiac RR interval data of 36 normal and 36 CHF patients was used in the analysis. The RR interval data was obtained from MIT-BIH Normal Sinus Rhythm database, BIDMC Congestive Heart Failure database, and congestive heart failure RR interval database posted on Physionet . Before The ages of the normal subjects in this study were 50.5 ± 17.6 while those of CHF patients were 56.5 ± 11.0. Both groups had both male and female subjects. The majority of the CHF subjects belonged to New York Heart Association (NYHA) classes 3 and 4. There were 2 who belonged to class 2  and 2 in class 1 . Subjects classified as belonging to classes 3 and 4 are subjects who suffer from severe congestive heart failure. Subjects in class 2 show mild limitation of activity while class 1 suffers no symptoms from ordinary activities . A plot r), D(r), CCTM1(r), CCTM2(r), and CCTM3(r), CCTM4(r) are obtained from their SODP for different r values. The values of r used were in the range shown Figures r values the t-test at significance level of 0.05 was performed to determine whether the samples from the normal and CHF distribution have the same mean. The result is given in terms of values for h, p, and ci. A value of h equals to one indicates that one can reject the null hypothesis at the 0.05 significance level. The p value indicates the probability of observing a t value s the pooled standard deviation) as large or larger by chance under the null hypothesis. A low value for p smaller than the significance level indicates that the null hypothesis is improbable. The ci range indicates the 95% confidence interval of the true difference in means. If it does not include zero, it indicates that there is a difference. In r  that gives the lowest value of p for the range of r values studied are given for each of these measures, along with values of ci. The value of h for all these reported cases is 1, implying that there is difference in the means at 95% confidence level. Also included in this table are the p and ci values for SDRR. The value of r given in table is not the only r value where the means are significantly different. There are a number of other r values where h = 1. The r value given is the one which has the smallest p in the range of r values tested here. This gives the best separation between the N and CHF subjects. The number of points (n) used is 30000. The table also includes values of p and ci for this r value for SODP plots where the number of points has been increased to 70000. In the last row of this table, the p and ci values for SDRR are shown for n = 30000 and 70000. The p values for SDRR are much greater compared to the measures used for SODP. The results for n = 70000 show that better distinction between N and CHF is obtained compared to n = 30000. Since they provide a better separation, the features from this data set will be used for training. In this section the SODP features discussed earlier are evaluated for the 36 normal and 36 CHF patients using the RR interval cardiac data. Also included in this section are the results of SDRR. For each of these 36 N and 36 CHF subjects CTM, as one of the SODP feature sets from the 36 N and 36 CHF subjects. The training set that is used in this case is the SODP features of the 71 subjects that exclude the test data. The feature set used for the training data is the SODP features obtained from the RR intervals where n = 70000. This set as seen from table provided the best separation between N and CHF patients. For the test data the SODP features using 30000 RR intervals is used. Instead of using the full data set of n = 70000 for the test data we use a shorter RR interval data set, so that classification can be carried out many times with different data sets of the same subject. This is done in order to minimize random errors in the algorithm. Thus the algorithm is repeated with different feature sets of the same subject obtained from different sets of 30000 RR intervals, within the n = 70000 RR intervals. These different 30000 RR interval data sets start at various positions within the 70000 data set. The classification algorithm is run for each of these test data which are different realizations of the feature set for the same subject. Suppose that the number of these different realizations is mc. In this study we had mc = 31. In every classification run the subject i is assigned a value of 1 for pi(l) if the subject is misclassified, and 0 when the classification is correct. The results of i refer to the subject and j to the feature set group. The above result is for a particular feature grouping. Suppose that we have fg feature groups. For example, if we use 6 features, then we can have 63 possible groups. Thus fg = 63. If we use only two of them then fg = 3. If only one feature is used fg = 1. The subject i is misclassified if k-NN classification system using features of the SODP obtained from RR intervals has performed very well, with 100% success rate, when the six feature set is used. In this case, the result is the same for both Euclidean and Mahalanbois distance measures. For the two feature set, the performance is better if the Mahalanbois distance measure is used. The Mahalanbois distance, unlike the Euclidean distance which depends only on the distance between two vectors, takes into account the correlation of the other vectors present. It is a statistical distance, and requires the covariance matrix of the vectors present. One would therefore expect that this classification system using this will be better than the Euclidean distance. This is seen here for the two feature set of the SODP. In fact a simpler two feature set of {CTM(r), D(r)} gives zero misclassification using the Mahalanbois distance. The performance using SDRR is also good, where only one subject is misclassified. If the performance of the classification system using SDRR is compared with the simple threshold used in The results of r; and the four component central tendency measures. These features are then used as input into a k-nearest neighbor algorithm, with k = 1, for classification. The final classification result is obtained using a statistical procedure which involves running the classification algorithm many times with different feature sets of the same subject and different groupings of the features. This has the effect of reducing random errors. The study focused on determining whether a patient is healthy or has congestive heart failure from the Holter monitor RR interval data. For this study the Holter monitor data of 36 normal and 36 CHF patients was used. The result of this study showed a 100% classification rate using the features obtained from the second-order difference plot. In this paper a classification scheme to separate N from CHF subjects is studied using the RR intervals obtained from the Holter monitor. This is carried out using the features from a second-order difference plot obtained from the RR intervals. The RR interval data was preprocessed to remove trends and any ectopic beats present in the time series before second-order difference plots were drawn and several features extracted. Six features were obtained from the second-order difference plot. These features are central tendency measure, mean distance of the points within the circular radius The study also showed that the standard deviation of RR intervals also performed well using this procedure, although it could not reach the 100% success rate achieved using the features from the second-order difference plot. However the success rate for classification was many fold higher compared to the simple procedure of using a threshold. The results of the classification procedure using both the SODP features and SDRR are encouraging and one would expect such consistent results with the use of larger training sets. The analysis outlined in this paper will be a valuable asset to the clinician, in addition to the clinical and history information of the subject, to provide a useful strategy in the detection congestive heart failure.


The pitfalls of experimental phasing are described. Phaser. Supplementary material includes animated probabilistic Harker diagrams showing how maximum-likelihood-based phasing methods can be used to refine parameters in the case of SIR and MIR; it is hoped that these will be useful for those teaching best practice in experimental phasing methods.Developments in protein crystal structure determination by experimental phasing are reviewed, emphasizing the theoretical continuum between experimental phasing, density modification, model building and refinement. Traditional notions of the composition of the substructure and the best coefficients for map generation are discussed. Pitfalls such as determining the enantiomorph, identifying centrosymmetry (or pseudo-symmetry) in the substructure and crystal twinning are discussed in detail. An appendix introduces combined real–imaginary log-likelihood gradient map coefficients for SAD phasing and their use for substructure completion as implemented in the software  Experimental phasing is required when there is no sufficiently good template for molecular replacement, which is the case when studying proteins with no (or low) sequence identity to proteins for which the structure is known; that is, proteins with new (or very different) folds. Since these structures tend to provide a wealth of novel biological information, experimental phasing remains a key tool in the crystallographer’s toolkit.http://www-structmed.cimr.cam.ac.uk/Course) and in journal articles  in the asymmetric unit of one of the crystals from which data have been collected. The initial set of atoms is found using Patterson, direct methods or dual-space methods [implemented in software such as et al., 1964et al., 2007A            Substructure atoms found independently in different derivatives need not have the same hand or be on the same origin for the space group. If multiple-wavelength isomorphous replacement (MIR) or MIR with anomalous scattering (MIRAS) phasing is undertaken with the sites in different derivatives having different hands  with density-modification methods. Density modification has the effect of selecting the correct phase from the two phase possibilities. Thus, in the case of SAD and SIR the improvements in the map can be very dramatic. Traditional density-modification methods include solvent flattening  or to the Wilson B factor of the data. The scattering factors f′ and f′′ can be estimated from the values given in the Sasaki tables , the area under the PDF curve  is optimized  the substructure parameters, which are not well determined by the initial substructure-location programs. Although the positions of the substructure atoms are relatively well determined, the occupancies are only poorly estimated from the relative Patterson peak heights . Individual atomic i.e. when the error model used in the derivation of the likelihood function correctly models the sources of error in the experiment. Errors that derive from, for example, non-isomorphism and radiation damage are not part of the error model and will degrade the quality of the phases. Where non-isomorphism and/or radiation damage is present it is important to optimize the set of data sets used in phasing and/or to exclude data at high resolution (where the errors will be greatest). An example of this was presented at the 2003 CCP4 Study Weekend on the topic of Experimental Phasing , V is the volume of the unit cell, h represents the reciprocal-space indices , |F            h| is the amplitude of the structure factor and ϕh is the phase of the structure factor F            h. Note that if Friedel’s law applies and |F            h| = |F            h−| and ϕh = −ϕ            h (i.e. the diffraction pattern has a centre of inversion at the origin) then the sine terms for h and −h cancel and the imaginary component is zero everywhere; the electron density is real. If Friedel’s law does not apply then the imaginary term is not zero. The imaginary component can be represented as a second real electron-density map. The peaks in this second map are the positions of the anomalously scattering atoms that cause Friedel’s law to break down.Electron density is calculated using the electron-density equation, which is the Fourier transform of the structure factors,vice versa. Using this theorem, it can be shown that the best structure factor (F            best) is the ‘centroid’ structure factor ; it is not the ‘most probable’ structure factor . The probabilistic approach puts the approximation of taking the average of the two phases for map calculation in the case of SAD and SIR onto a firm theoretical footing. It has the added advantage of showing how to up-weight the structure factors (high figure of merit) when the two possible phases are close together and down-weight the structure factors (low figure of merit) when the phases are further apart.What structure factor should be used in the electron-density equation in the probabilistic approach? We have to pick one phase and amplitude for substitution into the electron-density equation. The best structure factor will usually be the one that gives the lowest root-mean-square deviation between the calculated electron density and the true electron density. . Parseval’s theorem (of Fourier transforms) relates the root-mean-square error in real space to the root-mean-square error in reciprocal space and or Fig. 5. The ampmF            obs have the lowest noise. When the model is ‘nearly complete’, that is, the calculated structure factors are good approximations to the true structure factors and the phase error is low, then the map with coefficients mF            obs shows electron-density features that are present in the true structure but missing from the model at half-weight. To boost the peaks of the electron density at the places where the model is incomplete, crystallographers and model-building algorithms usually look at maps with coefficients 2mF            obs − DF            calc  and subtract one copy of the model, but at the expense of doubling the noise. In cases where the real scattering of the substructure is a significant fraction of the true structure factor, 2mF            obs − DF            calc maps may also be useful in experimental phasing before model building starts.The probabilistic approach thus shows that maps with coefficients 5.l-amino acids (i.e. left-handed amino acids) and right-handed α-helices, but a small number of proteins consisting of d-amino acids and left-handed α-helices have successfully been synthesized and their structures solved  is equal to the intensity of reflection  then the diffraction cannot show the hand: a structure and its mirror image fit the data identically.The handedness of the protein can be determined from the diffraction pattern when there is significant anomalous scattering and thus Friedel’s law is broken  from the normally scattering component on a Harker diagram  and the coordinate system for the reciprocal lattice  are both conventionally right-handed. There is a tricky step at the stage of the Fourier transform used to generate the electron density. Crystallographers use the forward Fourier transform to calculate structure factors and the inverse Fourier transform to calculate electron density. The inverse Fourier transform uses , which is a change-of-hand operation. If all these operations are kept track of correctly, then the Friedel differences will show l-amino acids for naturally occurring proteins.Tracking the hand of the protein through the diffraction experiment is nontrivial. The diffraction from either hand can be worked out from first principles using the Laue equations and the 90° phase lag of the anomalous scattering with respect to the incoming wave . Therefore, the hand of the initial substructure is arbitrary; both sets of sites satisfy the anomalous differences (whether through Patterson or ‘direct methods’) equally well. Part of the process of the diffraction experiment is to find which hand of the substructure is correct, i.e. is consistent with l-amino acids. Unfortunately, the Friedel diffraction information that can determine the hand is lost when initially determining the substructure by Patterson methods or so-called ‘direct methods’. These methods only use the magnitude of the anomalous difference |I41, I4122 and I4132), the substructure is converted to its other hand by the inversion operation through the origin →. For chiral space groups, in addition to inverting the coordinates of the substructure through the origin, the space group must also be changed to its chiral partner ; however, the crystallographic symmetry of these space groups  generates a 43 screw from the 41 screw operation (and vice versa). Thus, the chiral partners for these three space groups that ‘should’ exist are not distinct space groups. By convention → followed by shifting the sites in the unit cell to position them around the alternate screw symmetry axis. Alternatively, in these three space groups the change-of-hand operation can be considered to be an inversion through a point that is not the origin.For nonchiral space groups  over all the reflections and this statistical bias will indicate the correct hand. Therefore, it is possible to discover the hand from the anomalous differences alone (i.e. without inspecting the electron density) whenever the structure factors calculated from the substructure have Friedel differences. Unfortunately, this is not the case if the substructure consists of only one type of anomalous scatterer. For example, if the substructure consists of only the selenium sites of a selenomethionine protein then the substructure cannot predict the hand.  For the calculated structure factors to have a Friedel difference, the substructure must have more than one scattering type, at least one of which must be a significant anomalous scatterer  the hand can be found with anomalous differences even without density modification. To understand this, consider the case at the end of refinement when there is a good model for the structure . If there are anomalous differences, then there are anomalously scattering atoms in the model and the calculated structure factors have a Friedel difference between lc Fig. 6. For exaer Fig. 6. . For any experimental phasing method that includes an anomalous difference , if there is only one type of  scatterer in the substructure then only one hand need be refined . The other hand can be phased from the refined parameters from the first hand and density-modification statistics can be used to determine the correct hand. If there are two or more types of scatterer  in the substructure then the substructure parameters must be refined in both hands. The correct hand can be determined from the phasing statistics, since one hand will fit the observed direction of the anomalous differences in the data better than the other hand.Thus, with SIR and MIR, and any number of scatterers, the parameters of the model need only be refined with the substructure in one hand; the other hand can be phased using the refined parameters. The correct hand is found by inspecting the density (i.e. SIR). If the hand is incorrect then ‘the Fourier gives rise to negative holes at loci which are related by inversion through the origin to the anomalous scatterer.’ This is equivalent to looking at the SIRAS-phased electron density and finding mirror-image density in negative electron density, but is easier to identify by eye (the only method available in 1976) as the imaginary map is less noisy than the real map. The second SIRAS method (p. 182) involves calculating the phases twice ‘by combining isomorphous and anomalous scattering data once for each heavy-atom configuration’ and then inspecting the density for ‘recognisable features’. If more than one isomorphous derivative is available then Blundell & Johnson  the distribution of anomalous or heavy atoms in the substructure is centrosymmetric. If the space group is iϕsub), where ϕsub are the phases of the substructure. This map looks random for a noncentrosymmetric substructure. In SAD the ‘noise’ is the negative inverse of the true electron density convoluted with the Fourier transform of exp(2iϕsub), which also looks random for a noncentrosymmetric substructure. However, if the substructure is centrosymmetric then all the substructure phases are either 0 or π and thus exp(2iϕsub) = 1 and the ‘noise’ map does not look random. The SIR map becomes a superposition of the true electron density with its mirror-image density and the SAD map becomes the superposition of the true electron density with its mirror-image density in negative. Note that these maps have the same form as the maps calculated using the two hands of the substructure . Interpreting the maps thus becomes much more difficult as there are features above the noise level that are not attributable to the true electron density.Centrosymmetric substructures in SAD and SIR result in electron-density maps with very different properties to those calculated with noncentrosymmetric substructures. Recall that SAD and SIR give a phase ambiguity and that an electron-density map calculated with the average of the two possible phases is the superposition of the true electron density and ‘noise’. In SIR the ‘noise’ is the mirror image of the true electron density convoluted with the Fourier transform of exp(2i.e. inspecting the coordinates) will find atoms that are related by inversion through the origin. For exact centrosymmetry, all atoms must have a centrosymmetric partner. Since it is the scattering from the atoms that is the issue, another condition of exact centrosymmetry is that the B factors and occupancies of the atoms at positions inverted through the origin must be identical. However, it is highly unlikely that all the atomic parameters will be exactly centrosymmetric and the more the centrosymmetry is broken the less difficult structure solution will be. The disadvantage of the simple geometric approach is that it is unable to quantify how difficult a pseudo-centrosymmetric arrangement will make structure solution or how difficult structure solution will be when only a subset of the sites is centrosymmetric. The phase-o-phrenia algorithm  resembles a delta function . The phase-o-phrenia plot for one randomly placed atom in P1 generates a ‘δ-function’ plot clearly showing the centrosymmetry of this substructure. Conversely, four randomly placed atoms in P31 generate a ‘flat’ plot and therefore are not centrosymmetric. The phase-o-phrenia algorithm also shows that some maps will be more difficult to interpret than others even if the substructure is not centrosymmetric. For example, one randomly placed atom in P3 gives a phase-o-phrenia plot that is close to that of a δ-function, because the substructure has It is often not immediately obvious that a substructure is centrosymmetric. A simple geometrical approach to the problem (If the substructure for the reference structure has centrosymmetry (or pseudosymmetry) then difference Fourier maps for other derivatives will also have this higher symmetry, since the centrosymmetry (or pseudosymmetry) is encoded in the phases. Difference Fourier maps calculated with these phases will show fallacious high peaks which can be mistaken for real atoms. To avoid this problem, only one peak should be selected from the difference Fourier in the first instance and the computation of the phases should be repeated with the additional site. In this way, new sites will be consistent with one choice of hand. However, in our experience it can be very difficult to break the centrosymmetry by only adding one site in a new derivative at a time and it can be better to find the sites in the new derivative independently and then use this derivative as the reference for locating the substructure in other derivatives.7.i.e. estimating the untwinned intensities from the observed structure-factor intensities). Twinned protein structures have been solved using a range of experimental phasing methods: SIR  twinned data in the general case, including perfectly twinned data (Yeates & Rees, 1987Phaser software (McCoy et al., 2007A            In our experience with the 8.et al., 2002et al., 2003et al., 2000et al., 2005et al., 2004et al., 2007et al., 2006The development of automated pipelines (Adams 10.1107/S0907444910006335/ba5142sup1.gif            Animated version of Fig. 1.. DOI: 10.1107/S0907444910006335/ba5142sup2.gif            Animated version of Fig. 2.. DOI: 10.1107/S0907444910006335/ba5142sup3.gif            Animated version of Fig. 3.. DOI: 10.1107/S0907444910006335/ba5142sup4.gif            Animated version of Fig. 4.. DOI:


We report a Li-Fraumeni syndrome family in which we have detected a splice acceptor mutation in intron 3 of TP53. The mutation affects one of the invariant residues at the splice acceptor site, as a result of which two aberrant transcripts are produced. A child with Wilms' tumour aged 3 years in this family was shown not to be a mutation carrier.


Sir,The association between dietary acrylamide and cancer of the large bowel, kidney and bladder was assessed in a Swedish case–control study, with a total of 987 cases and 538 healthy controls, that originally had been created for evaluating the carcinogenic effects of heterocyclic amines from diet (μg among the controls and 28.4–29.4 μg among the cases), and that less than 2% of the population was estimated to have a daily intake as high as 1 μg acrylamide per kilogram body weight per day. If we assume an average body weight of 70 kg in the population, those 2% of the population with a ‘high’ exposure had an estimated excess intake of about 42.5 μg acrylamide per day; this corresponds to an increase in lifetime cancer mortality of 2.7 per 1000, based on the risk assessment model of the P<0.05), and with 80% statistical power, among those 2% with ‘high’ exposure. It can also be calculated that, assuming an exposure prevalence of 2%, the lowest possible relative risk that would have 80% chance of being significantly detected in a study of 987 cases and 538 controls is as high as 2.4; this type of power calculation assumes that there is no residual confounding or misclassification bias. However, the Swedish study is likely to suffer from considerable nondifferential misclassification of exposure to acrylamide, taking into account both lack of precision in food frequency questionnaire data and the sparse data on acrylamide levels in food products that were available for the intake calculations. Thus, it is not realistic that not even a ‘true’ relative risk as high as 2.4 could have been detected in the Swedish study.A basal aspect to consider when interpreting the Swedish results is the size both of the expected cancer risk enhancement and of the cancer risk possible to detect. The authors correctly state, ‘…a true association may be concealed if the level of exposure in the studied population is low and/or if the range of variation is limited.’ Unfortunately, the authors provide only limited information about the estimated daily intake of acrylamide among cases and controls, which makes it virtually impossible to get the full picture of absolute levels and interindividual variations in exposure. The interquartile comparisons given in cannot be interpreted in terms of absolute levels and variation of exposure. The only acrylamide dose figures given in the paper concern the estimated mean daily intakes (27.5 There is a need to validate the type of exposure assessments for acrylamide that were used in the Swedish study using biomarkers for acrylamide exposure, for example, haemoglobin adducts of acrylamide, which reflect the cumulative dose during the preceding months (


Antiviral agents have been hailed to hold considerable promise for the treatment and prevention of emerging viral diseases like H5N1 avian influenza and SARS. However, antiviral drugs are not completely harmless, and the conditions under which individuals are willing to participate in a large-scale antiviral drug treatment program are as yet unknown. We provide population dynamical and game theoretical analyses of large-scale prophylactic antiviral treatment programs. Throughout we compare the antiviral control strategy that is optimal from the public health perspective with the control strategy that would evolve if individuals make their own, rational decisions. To this end we investigate the conditions under which a large-scale antiviral control program can prevent an epidemic, and we analyze at what point in an unfolding epidemic the risk of infection starts to outweigh the cost of antiviral treatment. This enables investigation of how the optimal control strategy is moulded by the efficacy of antiviral drugs, the risk of mortality by antiviral prophylaxis, and the transmissibility of the pathogen. Our analyses show that there can be a strong incentive for an individual to take less antiviral drugs than is optimal from the public health perspective. In particular, when public health asks for early and aggressive control to prevent or curb an emerging pathogen, for the individual antiviral drug treatment is attractive only when the risk of infection has become non-negligible. It is even possible that from a public health perspective a situation in which everybody takes antiviral drugs is optimal, while the process of individual choice leads to a situation where nobody is willing to take antiviral drugs. Recent outbreaks of SARS and H5N1 influenza have underlined the threat that viruses in the animal reservoir pose to the human population. Fortunately, neither SARS nor H5N1 influenza have become endemic in humans. Nevertheless, these and other events have stressed the importance of being prepared for emerging and reemerging infectious diseases.For most infectious diseases vaccination is the preferred control measure. Indeed, vaccines generally have proven highly efficacious, providing strong and long-lasting immunity against infection, disease, and transmission. However, in case of a previously unknown infectious disease a vaccine may not be readily available. For such emerging infectious diseases the control options are limited. This is especially so for viral pathogens that cannot be treated by effective antimicrobial drugs. For these pathogens the control options are restricted to case isolation and contact tracing, promotion of changes in behavior, vaccination using vaccines with poor efficacy, and antiviral drugs. Although the efficacy of currently available antiviral drugs is also far from perfect and although antiviral drugs provide protection for a short amount of time only, an advantage of antiviral drugs over vaccines is their broad spectrum of action For a newly arising viral infectious disease it may be possible to contain an outbreak at an early stage by means of a large-scale antiviral control program if the control program is started early and has high compliance rates, if the efficacy of antiviral drugs is sufficiently high, and if the transmissibility of the pathogen is sufficiently low In this paper we employ population dynamical and game theoretical analyses to investigate (i) under which conditions an antiviral control program can prevent an epidemic, and (ii) when people should consider taking antiviral drugs. With regard to the latter question we take two perspectives. First, we focus on the public health officer whose goal it is to minimize the total amount of damage caused by both infection and prophylactic antiviral treatment. In a second step we then compare the strategy that is optimal from the point of view of the population as a whole with the strategy that would evolve if individuals pursue their own interest.The dilemma that an individual faces is the following. Should you take your chances and refuse antiviral prophylaxis? The price that you may have to pay upon infection may be high (death in its most extreme consequence). The potential reward is that once you have successfully recovered from infection you also reap the benefit of long-lasting immunity. The alternative is that you take antiviral drugs and so avoid the potentially high cost of infection. The drawback of this option is that you may have to take antivirals for a prolonged period of time. This has negative side-effects in the short term The situation is complicated by the fact that an individual's risk of infection does not only depend on whether or not the individual itself decides to take antiviral drugs but also on the decision of others. In the context of vaccination it is well known that in such a situation there can be a trend of decreasing willingness to participate in a control program, which will lead to strategies that are not optimal from the population perspective We would like to stress from the onset that we strive more for conceptual clarification than for the most precise representation of a specific system. In particular, all our analyses are based on the simplifying assumptions that individuals act rationally, have perfect information and foresight while they do not engage in projecting the epidemic, and that the details of population structure play a minor role. We are aware that these simplifying assumptions cannot be neglected in the real world, and we therefore do not believe that our model is suited to make quantitative predictions for any specific emerging infectious disease. Rather, our models serve a purpose by laying out, in an idealized context, the key factors shaping the interests of individuals and public health officers. In case of influenza vaccination others have investigated models with added layers of complexity with the goal to make quantitative predictions SIRV-type epidemic models in which individuals are susceptible (S), infected and infectious (I1 or I2), recovered and immune (R), or  protected against infection by antiviral prophylactic treatment (V) form the basis of the analyses. μ, and the excess mortality while on antiviral treatment is given by γ. Hence, life expectancy is μ−1 in the absence of infection and antiviral control, and (μ+γ)−1 while on antiviral drugs. In the infected classes (I1 and I2) the excess death rates resulting from infection are given by ν and ν(1−AVEI), where AVEI is the antiviral efficacy for infectiousness and virulence. In the following, γ and ν will be referred to succinctly as the cost of antiviral prophylaxis and infection. From the susceptible class individuals move to the protected and infected classes at rates σ and λ. The parameter λ is colloquially called the force of infection, and it depends on the prevalence of infection (V are infected at a reduced rate λ(1−AVES), where AVES denotes the antiviral efficacy for susceptibility. This implies that individuals in class V cannot be infected at all if AVES = 1, while the antiviral drug provides no protection against infection if AVES = 0. Finally, the rates of recovery and non-compliance are given by α and ρ, respectively. An overview of the model parameters and their default values is given in Stochastic and deterministic nfection . IndividR0), which gives the number of new infections caused by a single infected individual in a population of uninfected individuals in the early stages of an outbreak R0>1 the pathogen can invade a population in which it is not yet present, while it cannot if R0<1. In the case that the pathogen-induced mortality is such that it hardly affects the infectious period, the reproduction number is given byS) and relative infectiousness if infected (1−AVEI). Notice that the reproduction number increases with increasing pathogen transmissibility (β) and length of the infectious period ((μ+α)−1), and with increasing rate at which individuals leave the protected class (μ+γ+ρ). The reproduction number decreases with increasing rate of antiviral prophylaxis (σ).When will a prophylactic antiviral control program be able to prevent an epidemic? Several studies have addressed this question using simulations of metapopulation models that include household structure and other population and pathogen details c, which is given by the solution of the equation R0 = 1. For the default parameter values (cσ = 1.96 (yr−1) if antiviral drugs provide complete protection against infection (AVES = 1). This implies that approximately two-thirds of the population needs to be protected against infection by antiviral prophylaxis in order to prevent an epidemic. This fraction increases if antiviral drugs provide partial protection against infection and subsequent transmission.Equation (1) shows that the pathogen cannot invade the population if the rate of antiviral prophylaxis exceeds a certain critical rate of antiviral prophylactic therapy σr values  it turns6 individuals). If no control measures are put into place (top panel), epidemiological theory informs that a large epidemic will unfold with probability x) = −R0x) Is it possible to prevent a major epidemic with an antiviral response that is started quickly after an introduction of the pathogen? To answer this question we performed stochastic simulations in which an antiviral response is initiated after a certain number of individuals are infected  given that it is initially susceptible or  protected against infection by antiviral control. If the probability to remain alive is larger when initially susceptible than when under antiviral treatment, the best option is not to take antiviral drugs. Otherwise the reverse is true. The formal analyses are given in γ = 0.00001 (yr−1)), the critical force of infection ranges from 0.0005 (yr−1) to 0.0007 (yr−1) if the horizon is one month or longer. Assuming a standard relation between the the force of infection and the prevalence of infection ) the critical force of infection again increases by an order of magnitude, and taking antiviral drugs is the rational strategy if 400 or more individuals are infected.tion see  this impS = 1) the equilibrium prevalence of infection decreases monotonically with increasing rate of antiviral control, up to the point where the pathogen cannot persist , while the cost of antiviral prophylaxis is γ = 0.0001 (yr−1). Hence, in our default scenario excess mortality decreases with increasing rate of antiviral control up to the point where the pathogen is just unable to persist (σ = 1.96 (yr−1)).Although the risk of antiviral prophylaxis may have a negligible effect on the prevalence of infection, it does affect excess mortality at equilibrium induced by infection and antiviral treatment. In fact, in case of a perfect antiviral drug excess mortality decreases with increasing rate of antiviral prophylaxis ifNext we turn our attention to the different perspectives of the individual versus the public health officer. Our focus is on the antiviral treatment rate that minimizes excess mortality. Minimizing this quantity with respect to the antiviral treatment rate yields the strategy that is optimal from the population perspective. Throughout this section and the next we assume that the pathogen is endemically present at the population dynamical equilibrium. As we have argued above, the optimal population strategy is such that the pathogen is just unable to persist if the risk of antiviral prophylaxis is small (i.e. if (2) is satisfied). Otherwise, the optimal population strategy is not to take antiviral drugs at all yσ is calculated in a population where the majority of individuals take antiviral drugs at a rate xσ. This allows one to determine the antiviral treatment strategy that will evolve at the population level by the process of individual choice. The optimal population and individual rates of antiviral treatment at the population level will be denoted by In β<51 (yr−1)) the pathogen cannot persist, and there is no need to take antiviral drugs. If transmissibility is intermediate there is a positive population optimum (γ = 0) then both the population and individual optimal control rates are such that the pathogen is driven to extinction. For the default parameter values this is achieved if at least two-third of the population is on antiviral drug treatment (σ≥1.96). If there is a cost to antiviral treatment, then the best option is to drive the pathogen to extinction if one takes the population perspective, until the risk of antiviral prophylaxis exceeds the risk of infection at the endemic equilibrium with no antiviral control (γ>0.00025 (yr−1)). Alternatively, if all individuals are allowed to flexibly adjust their own strategy, the optimal rate of antiviral prophylaxis decreases gradually with increasing antiviral death rate. In this case the optimal rate of antiviral prophylaxis is zero if γ>0.00016 (yr−1). Notice that for intermediate cost of antiviral treatment the public health officer favours a strategy that is aimed at eradicating the disease, while the process of individual choice leads to a situation where nobody is willing to take antiviral drugs.The bottom panel of SAVE = 0.3 and IAVE = 0.8 as default parameter values Unfortunately, to date there are no antiviral drugs that provide complete protection against infection and disease. For instance, an analysis of two recent trials with the antiviral drug oseltamivir shows that it provides little protection against infection with influenza, and moderate protection against subsequent shedding and disease IAVE = 0.8. The fact that the optimal fractions taking antiviral drugs decrease with increasing antiviral efficacy for susceptibility can be understood as follows. A decrease in the antiviral efficacy for susceptibility renders the antiviral drug less effective. However, since the cost of antiviral treatment is low while the antiviral efficacy for infectiousness is relatively high the rational strategy is to eradicate the pathogen if one takes the population perspective. With decreasing antiviral efficacy for susceptibility this is achieved by increasing the rate of antiviral control. Interestingly, the top panel indicates that if one takes the individual perspective excess mortality is highest if antiviral drugs provide complete protection against infection, since then the optimal control rate is lowest.The relation between the antiviral efficacies for susceptibility and infectiousness, and the optimal rates of antiviral control is investigated in SAVE = 0.3. The picture in this panel is more complicated than in the top panel. In particular, eradication of the pathogen is not feasible if the antiviral efficacy for infectiousness drops below a critical value (IAVE<0.51). If the antiviral efficacy for infectiousness is just above this critical value it still is the best strategy to drive the pathogen to extinction if one takes the population perspective. However, this can only be achieved if almost all individuals are in the protected class (IAVE<0.07) it is better not to take antiviral drugs at all (IAVE<0.51) it is not possible to achieve eradication, but it may nevertheless be wise to take antiviral drugs. In fact, taking the population perspective, it is always better to be  protected by antiviral drugs than to be fully susceptible in this region of parameter space  frequently leads to nausea and a number of less frequent adverse effects such as hepatitis and skin reactions While we have used mortality as the currency to compare the costs and benefits of antiviral drug use, previous game theoretical studies of vaccination focused on the relative perceived risk of vaccination as compared to infection, and thereby also introduced a common currency to compare the costs and benefits of vaccination Throughout this paper we have made the simplifying assumptions that individuals and public health officer's act rationally, have perfect information and foresight, and that the details of population structure and antiviral drug action play a minor role. These assumptions were made in order to be able to keep the analyses manageable, and to be able focus in detail on the conflict of interest. We are, of course, aware that in the real world a variety of complicating factors play a role. Therefore, our study is not intended nor suited to make quantitative predictions, but it serves to explore how the public and individual interests are shaped by pathogen transmissibility, cost of antiviral treatment, and antiviral efficacy for susceptibility and infectiousness.It would be interesting to extend the model in a number of directions in order to be able to make specific predictions for specific viral threats. For this purpose several steps should be taken. First, depending on the precise research question some form of population structure would probably need to be taken into account. For instance, if the goal were to decide how a limited supply of antiviral drugs is best distributed across different risk groups, the model would need to include different risk groups and take into account that the stockpile of antiviral drugs or vaccines is not infinitely large Fortunately, none of the recent viral threats from the animal reservoir  has succeeded in getting a definitive foothold in the human population. As a consequence, the key epidemiological characteristics of the next emerging virus  remain unknown. This is also largely true for rare but serious side-effects of antiviral drugs. This has rendered attempts to provide realistic predictions of the effectiveness of control measures such as antiviral treatment somewhat speculative Text S1Model structure and details of the model analyses(0.10 MB PDF)Click here for additional data file.