In a number of estimation problems in bioinformatics, accuracy measures of the target problem are usually given, and it is important to design estimators that are suitable to those accuracy measures. However, there is often a discrepancy between an employed estimator and a given accuracy measure of the problem. In this study, we introduce a general class of efficient estimators for estimation problems on high-dimensional binary spaces, which represent many fundamental problems in bioinformatics. Theoretical analysis reveals that the proposed estimators generally fit with commonly-used accuracy measures  as well as it can be computed efficiently in many cases, and cover a wide range of problems in bioinformatics from the viewpoint of the principle of maximum expected accuracy (MEA). It is also shown that some important algorithms in bioinformatics can be interpreted in a unified manner. Not only the concept presented in this paper gives a useful framework to design MEA-based estimators but also it is highly extendable and sheds new light on many problems in bioinformatics. In estimation problems in bioinformatics, the space of solutions is generally large and often high-dimensional. Among them, a number of fundamental problems in bioinformatics, such as alignment of biological sequences, prediction of secondary structures of RNA sequences, prediction of biological networks, and estimation of phylogenetic trees, are classified into estimation problems whose solutions are in a high-dimensional binary space. Such problems are generally difficult to solve, and the estimates are often unreliable.centroid estimator, which represents an ensemble of all the possible solutions and minimizes the expected Hamming loss of the prediction The popular solutions for these problems, such as for the secondary structure of RNA with minimum free energy, are the maximum likelihood (ML) estimators. The ML estimator maximizes the probability that the estimator is exactly correct, but that probability is generally very small. Noticing the drawbacks of the ML estimators, Carvalho and Lawrence have proposed the In this paper, we conduct a theoretical analysis of estimation problems in high-dimensional binary space, and present examples and solutions in bioinformatics. The theories in this paper provide a unified framework for designing superior estimators for estimation problems in bioinformatics. The estimators discussed in this paper, including the ML estimator and the centroid estimator, are formalized as maximum expected gain (MEG) estimators, which maximize the estimator-specific gain functions with respect to the given probability distribution. The objective of the estimation is not always to find the exact solution with an extremely small probability or to find the solution with the minimum Hamming loss, but rather to find the most accurate estimator. Therefore, we adopt the principle of maximum expected accuracy (MEA), which has been successfully applied to various problems in bioinformatics, such as the alignment of biological sequences Theoretical analysis, however, shows that those MEA estimators are not always robust with respect to accuracy measures. To address this, we previously proposed the Problem 1 Given a pair of biological  sequences  and , predict their alignment as a point in , the space of all the possible alignments of  and .Problem 2 (Prediction of secondary structures of RNA sequences)Given an RNA sequence , predict its secondary structure as a point in , the space of all the possible secondary structures of .A point in Problem 3 (Estimation problem on a binary space)Given a data set  and a predictive space  , which is a subset of -dimensional binary vectors , that is, , predict a point  in the predictive space .Not only Problem 1 and Problem 2 but also a number of other problems in bioinformatics are formulated as Problem 3, including the prediction of biological networks and the estimation of phylogenetic trees (Problem 4).To discuss the stochastic character of the estimators, the following assumption is introduced.Assumption 1 (Existence of probability distribution)In Problem 3, there exists a probability distribution  on the predictive space .For Problem 3 with Assumption 1, we have the following Bayesian maximum likelihood (ML) estimator.Definition 1 (Bayesian ML estimator )For Problem 3 with Assumption 1, the estimatorwhich maximizes the Bayesian posterior probability , is referred to as a Bayesian maximum likelihood (ML) estimator.For problems classified as Problem 3, Bayesian ML estimators have dominated the field of estimators in bioinformatics for years. The classical solutions of Problem 1 and Problem 2 are regarded as Bayesian ML estimators with specific probability distributions, as seen in the following examples.Example 1 In Problem 1 with a scoring model , the distribution  in Assumption 1 is derived from the Miyazawa model  (See “Probability distributions  in ), and the Bayesian ML estimator is equivalent to the alignment that has the highest similarity score.Example 2 (RNA structure with minimum free energy)In Problem 2 with a McCaskill energy model , the distribution  in Assumption 1 can be obtained with the aid of thermodynamics (See “Probability distributions  on ” in  for details), and the Bayesian ML estimator is equivalent to the secondary structure that has the minimum free energy (MFE).When a stochastic model such as a pair hidden Markov model (pair HMM) in Problem 1 or a stochastic context-free grammar (SCFG) in Problem 2 is assumed in such problems, the distribution and the ML estimator are derived in a more direct manner.gain function that gives the gain for the prediction, and the maximum expected gain (MEG) estimator that maximizes the expected gain.The Bayesian ML estimator regards the solution which has the highest probability as the most likely one. To provide more general criteria for good estimators, here we define the Definition 2 (Gain function)In Problem 3, for a point  and its prediction , a gain function is defined as , .Definition 3 (MEG estimator)In Problem 3 with Assumption 1, the maximum expected gain (MEG) estimator is defined asaccuracy measures of the target problem, the MEG estimator is considered as the maximum expected accuracy (MEA) estimator, which has been successfully applied in bioinformatics In Problem 3, for a point  and its prediction , a gain function  written aswhere, is referred to as a pointwise gain function.Definition 5 (Centroid estimator )In Problem 3 with Assumption 1, a centroid estimator is defined as an MEG estimator for the pointwise gain function given in Eq. (1) by defining .consensus estimator, which can be easily computed.Throughout this paper, Definition 6 (Consensus estimator )In Problem 3 with Assumption 1, the consensus estimator for a pointwise gain function is defined asnot contained within the predictive space The consensus estimator is generally Theorem 1In Problem 3 with Assumption 1 and a pointwise gain function, let us suppose that a predictive space  can be written as is defined as for an index-set . If the pointwise gain function in Eq. (1) satisfies the conditionfor every  and every  , then the consensus estimator is in the predictive space , and hence the MEG estimator contains the consensus estimator.The above conditions are frequently satisfied in bioinformatics problems  and negative scores for those of false predictions (FP and FN):To design a This gain function is naturally compatible with commonly used accuracy measures such as sensitivity, PPV, MCC and F-score In Problem 3 with Assumption 1 and a fixed , the -centroid estimator is defined as the MEG estimator for the pointwise gain function given in Eq. (1) by Theorem 2The MEG estimator for the gain function in Eq. (4) is equivalent to a -centroid estimator with .Theorem 2  does not depend on Theorem 3In Problem 3 with Assumption 1, the predictive space  satisfies the following condition: if , then  where  for all . Then, the -centroid estimator is equivalent to the estimator that maximizes the sum of marginalized probabilities  that are greater than  in the prediction.The condition is necessary to obtain Corollary 1 (-centroid estimator for )In Problem 3 with Assumption 1, the predictive space  is given in the same form in Eq. (2) of Theorem 1. Then, the -centroid estimator for  contains its consensus estimator. Moreover, the consensus estimator is identical to the following estimator :where .Here, Corollary 1 does not hold for Example 3 In Problem 1 with Assumption 1, the -centroid estimator maximizes the sum of the alignment probabilities which are greater than  (Theorem 3), and for  it can be given as the consensus estimator calculated from Eq. (8) (Corollary 1). For , the -centroid estimator is obtained by using a dynamic programming algorithm with the same type of iterations as in the Needleman-Wunsch algorithm:where  stores the optimal value of the alignment between two sub-sequences,  and  (see “Secondary structure prediction of an RNA sequence (Problem 2)” in  for detailed descriptions).Example 4 (-centroid estimator for prediction of secondary structures)In Problem 2 with Assumption 1, the -centroid estimator maximizes the sum of the base pairing probabilities that are greater than  (Theorem 3), and for  it can be given as the consensus estimator calculated from Eq. (8) (Corollary 1). For , the -centroid estimator is obtained with the aid of a dynamic programming algorithm with the same type of iterations as in the Nussinov algorithm: where  stores the best score of the sub-sequence  ” in  for the detail descriptions).The Problem 4 (Estimation of phylogenetic trees)Given a set of operational taxonomic units , predict their phylogenetic trees (unrooted and multi-branched trees) as a point in , the space of all the possible phylogenetic trees of .The phylogenetic tree in Example 5 (-centroid estimator of phylogenetic estimation)In Problem 4 with Assumption 1, the -centroid estimator maximizes the number of the partitioning probabilities which are greater than  (Theorem 3), and for  it can be give as the consensus estimator calculated from Eq. (8) (Corollary 1) (see “Estimation of phylogenetic trees (Problem 4)” in  for details).Because the Hamming distance between two trees in Predictions based on probability distributions on the predictive space were discussed in the previous sections. However, there are certain even more complex problems in bioinformatics, as illustrated by the following example.Problem 5 (Prediction of common secondary structures of RNA sequences)Given a set of RNA sequences  and their multiple alignment of length  and the same energy model for each RNA sequence, predict their common secondary structure as a point in , which is the space of all possible secondary structures of length .In the case of Problem 5, although the probability distribution is not implemented in the predictive space, each RNA sequence Assumption 2In Problem 3 there exists a probability distribution  on the parameter space  which might be different from the predictive space .Definition 8 In Problem 3 with Assumption 2, for a point  and a prediction , a generalized gain function is defined as , .It should be emphasized that the MEG estimator (Definition 3), pointwise gain function (Definition 4) and Theorem 1 can be extended to the generalized gain function.In the case of Problem 5, for example, the parameter space is the product of the spaces of the secondary structures of each RNA sequence, and the probability distribution is the product of the distributions of secondary structures of each RNA sequence. Here, the general form of the problem of representative prediction is introduced.Problem 6 (Representative prediction)In Problem 3 with Assumption 2, if the parameter space is represented as a product space  and the distribution of  has the form , predict a point  in the predictive space .The generalized gain function for the representative prediction should be chosen such that the prediction reflects as much as each data entry. Therefore, it is natural to use the following generalized gain function that integrates the gain for each parameter.Definition 9 In Problem 6, a homogeneous generalized gain function is defined aswhere  is the gain function in Definition 2.Definition 10 (Representative estimator)In Problem 6, given a homogeneous generalized gain function , the MEG estimator defined as is referred to as the representative estimator.Proposition 1The representative estimator is equivalent to an MEG estimator with averaged probability distribution on the predictive space :and a gain function .This proposition shows that a representative prediction problem with any homogeneous generalized gain function can be solved in a manner similar to Problem 3 Given a data set , where  and  are two biological sequences to be aligned and  is a sequence that is homologous to both  and , predict a point  in the predictive space  .The precise probabilistic model of this problem might include the phylogenetic tree, ancestor sequences and their alignments. Here, we assume a simpler situation where the probability distribution of all possible multiple alignments of Problem 8 (Prediction in a subspace of the parameter space)In Problem 3 with Assumption 2, if the parameter space  is represented as , predict a point  in the predictive space .For the problem of representative prediction (Problem 6), generalized gain functions on From the above MEG estimator, it might appear that Problem 8 is trivial. However, it is not a simple task to calculate the marginalized distribution in Eq. (11) in actual problems.To reduce the computational cost, we change Problem 8 by introducing an approximated probability distribution on the product space Problem 9 (Prediction in product space)In Problem 3 with Assumption 2, if the parameter space  is represented as  and the probability distribution on  is defined as predict a point  in the predictive space .This factorization of spaces and probability distributions creates a number of inconsistencies in the parameter space with respect to the original Problem 8. In other words, the approximated distribution yields non-zero values for a point that is not included in the original Definition 11 (-type pointwise gain function)In Problem 8, a -type pointwise gain function is defined as  in Eq. (1) in Definition 4 havingwhere the valuein the gain function should be designed to reduce the inconsistencies resulting from the factorization.Definition 12 (Approximated -type estimator)In Problem 9, with a -type pointwise gain function with  in Eq. (13) on , an approximated -type estimator is defined as an MEG estimator:Example 6 We obtain the approximate estimator for Problem 7 with the following settings. The parameter space is given as , where and the probability distribution on the parameter space  is given as for . The  in Eq. (13) of the -type pointwise gain function is defined asThe approximated -type estimator for this -type pointwise gain function is employed in a part of probabilistic consistency transformation (PCT) , which is an important step toward accurate multiple alignments. See “Pairwise alignment using homologous sequences” in  for precise descriptions.It is easily seen that Theorem 3 applies to the approximated generalized (pointwise) gain function: see Theorem 4.)Moreover, to confirm whether approximated bias with respect to the accuracy measures for the problem (see Eqs. (20) and (22)), and are therefore inappropriate from the viewpoint of the principles of MEA. Moreover, these estimators cannot be introduced in a general setting, that is, Problem 3. It has been also shown that the In this paper, general criteria for designing estimators are given by the maximum expected gain (MEG) estimator (Definition 3). The Bayesian ML estimator is an MEG estimator with the delta function The parameter The reader might consider that it is possible to design estimators that maximize the expected MCC or F-score which balances sensitivity (SEN) and positive predictive value (PPV). However, it is much more difficult to compute such estimators in comparison with the The expected value of the gain function of the multiplication and/or division of TP, TN, FP and FN, while the gain function of the sums of these values . Two types of estimators for such problems, for example, estimators for representative prediction and estimators based on marginalized distribution, have been discussed.alignments of biological sequences” in Prediction of the common secondary structure from an alignment of RNA sequences (Problem 5) is an example of representative prediction. The probability distribution is not implemented in the predictive space, the space of common secondary structure, but each RNA sequence has a probability distribution for its secondary structure. Because the “correct” reference for the common secondary structure is not known in general, direct evaluation of the estimated common secondary structure is difficult. In the popular evaluation process for this problem, the predicted common secondary structure is mapped to each RNA sequence and compared to its reference structure. Using the homogeneous generalized gain function exactly implements this evaluation process and the MEG estimator for the averaged probability distribution is equivalent to the MEG estimator for homogeneous generalized gain function. Therefore, we can use the averaged base pairing probabilities according to the alignment as the distribution for the common secondary structure . If we can calculate the marginalized distribution on the predictive space from the distribution on the parameter space, all general theories apply to the predictive space and the marginalized distribution. In actual problems, such as pairwise alignment using homologous sequences (Problem 7), however, computational cost for calculation of the marginalized probability is quite high. We introduced the factorized probability distribution (Eq. (12)) for approximation, the et al.cluster centroid, which is computed by the centroid estimator with a given cluster in a predictive space. We emphasize that the extension of cluster centroid by using In case probability distribution on the predictive space is multi-modal, In this work, we constructed a general framework for designing estimators for estimation problems in high-dimensional discrete (binary) spaces. The theory is regarded as a generalization of the pioneering work conducted by Carvalho and Lawrence, and is closely related to the concept of MEA. Furthermore, we presented several applications of the proposed estimators .We define a space of the alignments of two biological  sequences Then Here at most one position in the sequence at most one position in the sequence not crossing. Note that The inclusion We define a space of the secondary structures of an RNA sequence Then Here at most one base-pair in a secondary structure pseudo-knot are not allowed in The inclusion We define a space of phylogenetic trees (unrooted and multi-branch trees) of a set of Then Lemma 1The number of elements in  (i.e. ) is equal to  where .Lemma 2The topological distance  between two phylogenetic trees  and  in  iswhere  is the indicator function.Remark 1If we assume the additional condition , then  is a set of binary trees.We use three probability distributions in this paper.For two protein sequences partition function.Miyazawa model Pair Hidden Markov Model (pair HMM) CONTRAlign (pair CRF) model Remark 2Strictly speaking, the alignment space in the pair hidden Markov model and the CONTRAlign model consider the patterns of gaps. In these cases, we obtain the probability space on  by a marginalization.For an RNA sequence partition function.McCaskill model Stochastic Context free grammars (SCFGs) model CONTRAfold  model A probability distribution There are several evaluation measures of a prediction in estimation problems for which we have a reference (correct) prediction in Problem 3. The Sensitivity (SEN), Positive Predictive Value (PPV), Matthew's correlation coefficient (MCC) and F-score for a prediction are defined as follows. It should be noted that these measures can be written as a function of TP, TN, FP and FN. See The schematic diagrams of the MEG estimator (Definition 3), the representative estimator (Definition 10) and the approximated In this section we describe several applications to bioinformatics of the general theories. Some of these applications have already been published. In those cases, we briefly explain the applications and the readers should see the original paper for further descriptions as well as the computational experiments. All of the applications in this section are summarized in The pairwise alignment of biological  sequences (Problem 1) is another fundamental and important problem of sequence analysis in bioinformatics cf. .The Estimator 1 For Problem 1, we obtain the -centroid estimator where the predictive space  is equal to  and the probability distribution on  is taken by .First, Theorem 2 and the definition of Property 1 (A relation of Estimator 1 with accuracy measures)The -centroid estimator for Problem 1 is suitable for the accuracy measures: SEN, PPV, MCC and F-score with respect to the aligned-bases in the predicted alignment.Note that accurate prediction of aligned-bases is important for the analysis of alignments, for example, in phylogenetic analysis. Therefore, the measures in above are often used in evaluations of alignments e.g. aligned-base (matching) probability in this paper. The aligned-base probability matrix The marginalized probability Property 2 (Computation of Estimator 1)The pairwise alignment of Estimator 1 is found by maximizing the sum of aligned-base probabilities   that are larger than . Therefore, it can be computed by a Needleman-Wunsch-style dynamic programming (DP) algorithm  after calculating the aligned-base matrix :where  stores the optimal value of the alignment between two sub-sequences,  and .The time complexity of the recursion of the DP algorithm in Eq. (19) is equal to By using Corollary 1, we can predict the pairwise alignment of Estimator 1 with Property 3 (Computation of Estimator 1 with ) The pairwise alignment of the -centroid estimator can be predicted by collecting the aligned-bases whose probabilities are larger than .http://last.cbrc.jp/) The genome alignment software called LAST  is one of the most important problems of sequence analysis in bioinformatics. Its importance has increased due to the recent discovery of functional non-coding RNAs (ncRNAs) because the functions of ncRNAs are closely related to their secondary structures Estimator 2 (-centroid estimator for Problem 2)For Problem 2, we obtain the -centroid estimator (Definition 7) where the predictive space  is equal to  and the probability distribution on  is taken by .The general theory of the Property 4 (A relation of Estimator 2 with accuracy measures)The -centroid estimator for Problem 2 is suitable for the widely-used accuracy measures of the RNA secondary structure prediction: SEN, PPV and MCC with respect to base-pairs in the predicted secondary structure.Because the base-pairs in a secondary structure are biologically important, SEN, PPV and MCC with respect to base-pairs are widely used in evaluations of RNA secondary structure prediction, for example, base-pairing probability. The base-paring probability matrix The marginalized probability Property 5 (Computation of Estimator 2)The secondary structure of Estimator 2 is found by maximizing the sum of the base-pairing probabilities  (of the base-pairs in the predicted structure) that are larger than . Therefore, it can be computed by a Nussinov-style dynamic programming (DP) algorithm  after calculating the base-pairing probability matrix :where  stores the best score of the sub-sequence .foldstructureIf we replace “By using Corollary 1, we can predict the secondary structure of Estimator 2 with Property 6 (Computation of Estimator 2 with )The secondary structure of the -centroid estimator with  can be predicted by collecting the base-pairs whose probabilities are larger than .entroidFoldfold and McCaskill models.The software CRelations of Estimator 2 with other estimators are summarized as follows:foldfold program.A relation with the estimator used in Sfold: For Problem 2, Do et al.false predictions of base-pairs For Problem 4, we obtain the -centroid estimator (Definition 7) where the predictive space  is equal to  and the probability distribution on  is taken by .The following property is easily obtained by Theorem 2 and Property 7 The -centroid estimator with  (i.e. centroid estimator) for Problem 4 minimizes expected topological distances.partitioning probability. However, it is difficult to compute For Property 8 (Computaion of Estimator 3)The phylogenetic tree of Estimator 3 is found by maximizing the sum of the partitioning probabilities  (of the partitions given by the predicted tree) that are larger than .In contrast to Estimator 1 (the Property 9 (Estimator 3 with )The -centroid estimator with  for Problem 4 contains its consensus estimator.In this section we consider the problem of the alignment between two multiple alignments of biological sequences , which iProblem 10 The data is represented as  where  and  are alignments of biological sequences and the predictive space  is equal to , that is, the space of the alignments of  and .In the following, Estimator 4 (Representative estimator for Problem 10)For Problem 10, we obtain the representative estimator (Definition 10). The gain function  is the gain function of the -centroid estimator. The parameter space  is represented as a product space  where  is defined in the previous section. The probability distribution on the parameter space  is given by  for  where  is given in the previous section .Corollary 2 proves the following properties of Estimator 5.Property 10 (A Relation of Estimator 4 with accuracy measures)Estimator 4 is consistent with the accuracy process for Problem 10 that is shown in . We compare every pairwise alignment of  and  with the reference alignment. These comparisons are made using TP, TN, FP and FN with respect to the aligned-bases .Property 11 (Computation of Estimator 4)Estimator 4 can be given by maximizing the sum of probabilities  that are larger than  whereTherefore, the pairwise alignment of Estimator 4 can be computed by the Needleman-Wunsch-type DP algorithm of Eq. (19) in which we replace  with Eq. (24).Property 12 (Computation of Estimator 4 with )The Estimator 4 with  contains the consensus estimator. Moreover, the consensus estimator is identical to the estimator :where  is defined in Eq. (24).averaged aligned-base (matching) probability matrix of The probability matrix The estimator used in ProbCons is identical to Estimator 4 in the limit Common secondary structure prediction from a given multiple alignment of RNA sequences plays important role in RNA research including non-coding RNA (ncRNA) Problem 11 (Common secondary structure prediction)The data is represented as  where  is a multiple alignment of RNA sequences and the predictive space  is identical to  .The representative estimator (Definition 10) directly gives an estimator for Problem 11.Estimator 5 (The representative estimator for Problem 11)For Problem 11, we obtain the representative estimator (Definition 10) as follows. The gain function  is the gain function of the -centroid estimator. The parameter space is equal to  where  is the space of secondary structures. The probability distribution on  is given by  where  is the probability distribution of the secondary structures of  after observing the alignment .For example, Corollary 2 proves the following properties of Estimator 5.Property 13 (A relation of Estimator 5 with accuracy measures)Estimator 5 is consistent with an evaluation process for common secondary structure prediction: First, we map the predicted common secondary structure into secondary structures in the multiple alignment, and then the mapped structures are compared with the reference secondary structures based on TP, TN, FP and FN of the base-pairs using, for example, SEN, PPV and MCC .Much research into common secondary structure prediction employs the evaluation process in Property 14 (Computation of Estimator 5)The common secondary structure of Estimator 5 is given by maximizing the sum of the averaged base-pairing probabilities  whereTherefore, the common secondary structure of the estimator can be computed using the dynamic programming algorithm in Eq. (10) if we replace  with .Also, we can predict the secondary structure of Estimator 5 without conducting Nussinov-style DP:Property 15 (Computation of Estimator 5 with )The secondary structure of Estimator 5 with  can be predicted by collecting the base-pairs whose averaged base-paring probabilities are larger than .alifoldfoldcCaskill-MEA It should be noted that the tools of common secondary structure prediction, RNAAs in the previous application to RNA secondary structure prediction using homologous sequences, if we obtain a set of homologous sequences and  see , we woulProblem 12 The data is represented as  where  and  are two biological sequences that we would like to align, and  is a set of homologous sequences for  and . The predictive space  is given by  which is the space of the pairwise alignments of two sequences  and .The difference between Problem 1 and this problem is that we can use other biological sequences (that seem to be homologous to We can introduce the probability distribution (denoted by The Estimator 6 (Approximated -type estimator for Problem 12)We obtain the approximated -type estimator (Definition 12) for Problem 12 with the following settings. The parameter space is given by  whereand the probability distribution on the parameter space  is defined by for . The pointwise gain function (see Definition 4) in Eq. (11) is defined by where  is the length of the sequence .Property 16 (Computation of Estimator 6)The alignment of Estimator 6 is equal to the alignment that maximizes the sum of  larger than  whereTherefore, the recursive equation of the dynamic program to calculate the alignment of Estimator 6 is given by replacing  in Eq. (19) with Eq. (30).Moreover, by using Theorem 1, we have the following proposition, which enables us to compute the proposed estimator for Property 17 (Computation of Estimator 6 for )The pairwise alignment of Estimator 6 with  can be predicted by collecting the aligned-bases whose probability  in (30) is larger than .probability consistency transformation (PCT) of It should be noted that If we obtain a set of homologous RNA sequences for the target RNA sequence, we might have a more accurate estimator Problem 13 (RNA secondary structure prediction using homologous sequences)The data  is represented as  where  is the target RNA sequence for which we would like to make secondary structure predictions and  is the set of its homologous sequences. The predictive space  is identical to , the space of the secondary structures of an RNA sequence .common secondary structures. The common secondary structure is naturally modeled by a structural alignment , and the probability distribution We obtain the approximated -type estimator (Definition 12) for Problem 13 with the following settings. The parameter space is given by  whereand the probability distribution on  is defined by for . Moreover, Eq. (11) in the pointwise gain function is defined by for .It should be noted that Estimator 13 is equivalent to the estimator proposed in Property 18 (Computation of Estimator 7)The secondary structure of Estimator 7 is computed by maximizing the sum of  larger than  whereHere,  and . Therefore, the secondary structure of Estimator 7 can be computed by the Nussinov-type DP of Eq. (10) in which we replace  by Eq. (33).entroidHomfold. See The computational cost with respect to time for computing the secondary structure of Estimator 7 is Property 19 (Computation of Estimator 7 with )Estimator 7 with  can be predicted by collecting the aligned-bases where the (pseudo-)base-paring probability of Eq. (33) is larger than .not mean the structural alignment In this section, we focus on the pairwise alignment of structured RNAs. This problem is formulated as Problem 1, so the output of the problem is a usual alignment  into the space The probability distributions Then, the Estimator 8 (Approximated -type estimator for Problem 1 with two RNA sequences)In Problem 1 where  and  are RNA sequences, we obtain the approximated -type estimator (Estimator 2) with the following settings. The parameter space is given by  whereand the probability distribution on the parameter space  is defined by for . The pointwise gain function of Eq. (11) is defined by whereand ,  and  are positive weights that satisfy .This approximated Property 20 (Computation of Estimator 8)The alignment of Estimator 8 can be computed by maximizing the sum of probabilities  that are larger than  whereHere, we defineTherefore, the pairwise alignment of Estimator 8 can be computed by a Needleman-Wunsch-type dynamic program of Eq. (19) in which we replace  with Eq. (35).pseudo-aligned base probability where Note that By checking Eq. (14), we obtain the following property:Property 21 (Computation of Estimator 8 with )The pairwise alignment of Estimator 8 can be predicted by collecting aligned-bases where the probability in Eq. (35) is larger than .In this section, we give the proofs of the theorems, propositions and corollary.We will prove a more general case of Theorem 1 where the parameter space Theorem 4In Problem 3 with Assumption 1 and a pointwise gain function, suppose that a predictive space  can be written aswhere  is defined asfor an index-set . If the pointwise gain function in Eq. (1) (we here think  is in a parameter space  which might be different from ) satisfies the condition for every  and every  , then the consensus estimator is in the predictive space , and hence the MEG estimator contains the consensus estimator.(proof)It is sufficient to show that the consensus estimator  is contained in the predictive space  because  for all  in the MEG estimators, whereIf we assume that  is not contained in the predictive space,  that is,  such that  is a binary vector, there exist indexes  such that ,  and . By the definition of , we obtainTherefore, we obtainIn order to prove the last inequality, we use Eq. (??). This leads to a contradiction and the theorem is proved.Remark 3It should be noted that the above theorem holds for an arbitrary parameter space including continuous-valued spaces.Proof of Theorem 2. (proof)Because  for arbitrary , we obtain, using the definitions given in equations (15),(16),(17) and (18),Therefore, we have and this leads to the proof of the theorem.Proof of Theorem 3. (proof)The expectation of the gain function of the -centroid estimator is computed as whereis the marginalized probability. Therefore, we should always predict  wheneverbecause the assumption of Theorem 3 ensures that the prediction  never violate the condition of the predictive space . Theorem 3 follows by using those facts.Proof of Corollary 1. (proof)For every , , , , we have and the condition of Eq. (3) in Theorem 1 is satisfied . Therefore, by Theorem 1, the -centroid estimator contains its consensus estimator.The last half of the corollary is easily proved using the equation where .Proof of Proposition 1. (proof) 5The representative estimator in Definition 10 can be written asThen, we finish the proof of Proposition 1.The equation is easily derived from the equality


Then, the asymmetric selenofunctionalization occurred at the 3-substituted tryptamine and subsequently the proton of the phosphoric acid protonates the phthalimide anion to release phthalimide. Finally, the amide on the side chain of the tryptamine derivatives attacks the resultant iminium cation leading to the formation of the product in an enantioselective manner.On the basis of experimental observations, we proposed a reaction mechanism . The phob]indoline core structure  to 1.5 equiv by using 5 mol % of catalyst (R)-3b. After a single recrystallization from methanol, the product 4a was obtained in 50% yield and with 97% ee. The oxidative deselenation of 4a with MCPBA afforded the corresponding alcohol 5 in 95% yield. The stereochemistry of the alcohol was found to be identical to that of the parent selenide, as demonstrated previously [Finally, we demonstrate the synthetic application of this reaction in the construction of the 3a-(phenylselenyl)bispyrrolidino[2,3-tructure . Under teviously .N-phenylselenophthalimide (N-PSP) catalyzed by chiral phosphoric acids (up to 89% ee). In this context, we used this protocol to prepare the key chiral precursor of the (+)-alline.In summary, we have developed a reaction for the enantioselective selenofunctionalization of tryptamine derivatives with File 1Experimental procedures and characterization data for new compounds. In addition, confirmatory crystallographic data are included.


Despite their importance in self-assembly processes, the influence of charged counterions on the geometry of self-assembled organic monolayers and their direct localisation within the monolayers has been given little attention. Recently, various examples of self-assembled monolayers composed of charged molecules on surfaces have been reported, but no effort has been made to prove the presence of counterions within the monolayer. Here we show that visualisation and exact localisation of counterions within self-assembled monolayers can be achieved with scanning tunnelling microscopy (STM). The presence of charges on the studied shape-persistent macrocycles is shown to have a profound effect on the self-assembly process at the liquid–solid interface. Furthermore, preferential adsorption was observed for the uncharged analogue of the macrocycle on a surface. Ordered monolayers formed by the self-assembly of molecular building blocks on solid surfaces have recently attracted considerable attention –4, due t1 and its charged analogue 2  solution of 1 onto a freshly cleaved HOPG surface. 1, separated by domain boundaries. Regularly spaced bright columns are tilted 30° away from the main crystallographic directions of the underlying graphite and comprise the aromatic parts of the molecule. High resolution images  over the charged macrocycle 2. However, co-assembly of 2 and 1 constitutes an ideal system to identify, unambiguously, the counterions by STM, where macrocycle 1 can be considered as an internal standard for the evaluation of different STM contrasts. The STM contrasts of both molecular species are distinct from the STM contrasts exhibited by the self-assembly of macrocycle 1  of the self-assembled structures formed differs from the structures exclusively formed by macrocycle 1  the appearance of the molecules within the monolayer changed . Two typ1 and 2 and to the iodide counterions, the same areas were scanned while scanning conditions were modified. For the duration of these experiments no dynamic exchange (desorption–readsorption) of molecules adsorbed on the surface was observed. 2 and 1. The area highlighted by the red rectangle  on top of the charged nitrogen atoms. As STM contrast is a convolution of the physical height and the local density of states [In order to assign, unambiguously, particular STM contrast to macrocycles ectangle  shows electangle . The remectangle . The appectangle . By compf states , the larf states . This st2, causes variation in the self-assembly of the macrocycle molecules. This is evidenced from the differences in the packing of pure 1 and mixed monolayers of 2 and 1. Steric effects can be excluded as the shapes and sizes of 1 and 2 are effectively unaltered. The formation of the mixed monolayer suggests that the molecule–substrate interactions are considerably stronger for macrocycle 1 than for macrocycle 2. No separation of 1 and 2 into different domains was observed. A tentative explanation for the different packing of pure 1 and the mixed monolayers of 1 and 2 is the tendency of the same charges, positive on the molecules and negative on the counterions, to be separated by the maximum possible distance while still preserving the high density of packing. The same tendency applies for the local interfacial dipoles that are formed upon adsorption of the molecule on the surface [2 in the co-assembly of 2 and 1  were prepared, and for each experiment a drop of the appropriate solution was applied onto a freshly cleaved surface of HOPG . The STM investigations were then performed at the liquid–solid interface within 1.5 h of the initial dropcasting of the solution. The HOPG lattice was recorded by lowering the bias immediately after obtaining images of the 2D structure. Images were corrected for drift effects using the HOPG lattice as calibration grid (Scanning Probe Image Processor (SPIP) 4.1.7 software (Image Metrology ApS)).All STM experiments were carried out at 20–24 °C. Experiments were performed using a PicoSPM microscope (Agilent). Tips were mechanically cut from PtIr wire . Prior to imaging, solutions of File 11 and 2.Experimental details of synthesis and characterisation of macrocycles


Objective. To determine the most effective and biodegradable dispersant of spilled oil in water surrounding two Persian Gulf provinces. Methods. This study compared the effects of three dispersants, Pars 1, Pars 2, and Gamlen OD4000 on removal of oil in two Persian Gulf provinces' water. Overall, 16 stations were selected. Using the Well method, the growth rate of isolated bacteria and fungi was identified. To specify the growth rate of microorganisms and their usage of oil in the presence of the above-mentioned dispersants, as exclusive sources of carbon, the bacteria were grown in culture medium for 28 days at 120 rpm, 30°C, and their optical density was measured by spectrophotometry. Then, we tested biological oxygen demand (BOD) and chemical oxygen demand (COD) in microorganisms. Results. The highest growth rate was documented for the growth of microorganisms on either Pars 1 or Pars 2 dispersants or their mixtures with oil. However, the culture having microorganisms grown on Pars 1 had higher BOD and COD than the other two dispersants . Mixture of oil and Pars 2 as well as oil and Pars 1 dispersants showed the highest BODs and CODs, respectively. In the Bahregan province, microorganisms grown on Pars 2 had maximum amount of BOD and COD in comparison with Pars 1 and Gamlen dispersants . Conclusion. Pars 1 and Pars 2 were the most effective dispersants with highest degradability comparing Gamlen. In each region, the most suitable compound for removing oil spill from offshores with least secondary contamination should be investigated. The main causes of oil pollution in the oceans are extraction of oil, transportation with ballast water release and tanker accidents, and also war-related incidents . UnfortuThe use of dispersants in nearshore areas is expected to increase the exposure of aquatic organisms to petroleum . If not Considering the lack of ability of any bacterial strain for complete catabolism and biodegradation of crude oil, finding appropriate strains is necessary. Even microorganisms which are consumers of non-hydrocarbonate components occasionally play important roles in removal of crude oil from the environment .Many methods have been used to remove oil spills from water including physical removal of crude oil, chemical remediation of the spills using dispersants and so-called “sinking agents,” and, in some cases, intentionally burning floating petroleum slicks. Using chemical dispersants as an oil spill countermeasure is the most frequently employed clean-up method because such liquids can be readily applied to large oil spills, and also this method is generally more cost effective than physical remediation methods , 4.Furthermore, the exclusive property of these dispersants to make oil spills dispersed into water will enhance the biodegradability of crude oil due to the increased exposed surface of the spills to such agents .Chemical dispersion of an oil slick increases the petroleum toxicity, When the meteorological conditions induce the dispersion of the oil slick such as wave, the application of dispersant does not rise the petroleum toxicity . The sigDispersants contain surfactants, which are surface-active agents with molecules composed of groups of opposing polarity and solubility; that is, surfactants usually have both an oil-soluble hydrocarbon chain and a water-soluble group. The synthetic surfactants can be anionic, cationic, nonionic, or amphoteric; however, only anionic or nonionic surfactants are utilized as crude oil dispersants. Surfactant mixtures often include other chemical agents, such as solvents, which enhance the dispersing capability of the surfactant .Chemical surfactants are amphiphilic compounds which can reduce surface and interfacial tensions by accumulating at the interface of immiscible fluids and increase the solubility and mobility of hydrophobic or insoluble organic compounds –13.Chemical surfactants can increase the pseudosolubility of petroleum components in water , 15.They are effective in reducing the interfacial tensions of oil and water in situ, and they can also reduce the oil viscosity and remove water from the oil prior to processing , 17.Nevertheless, not all surfactant compositions are efficient in dispersing spilled oil products, and many of the effective ones have the drawbacks of being toxic and/or not biodegradable . BiodegrThis study was conducted to determine the most effective and biodegradable dispersant of spilled oil in water surrounding two Persian Gulf provinces.We selected two provinces in Persian Gulf because of their location in one of the biggest offshore oil drilling rig and high traffic density of oil vessels in the sea lanes of Persian Gulf; Siri and Bahregan provinces were studied because of their numerous shorelines contaminated by oil spills. We compared the effects of the dispersants produced by Iranian Offshore Oil Company, that is, Pars 1 Pars 2 in comparison with Gamlen, which is actually used in the Persian Gulf water. Biodegradability of Gamlen and its effects on dispersing of oil had already been studied , 19.The culture used in the investigation was originally isolated from 16 sampling stations located at different longitude and latitude in the Siri and Bahregan province offshore .Microorganisms were isolated through common microbiological experiments under the sterile condition. They were cultured in the presence of Pars 1, Pars 2, and Gamlen separately and also the combination of each with oil at a dispersant-to-oil ratio of 1/20 , 20. Dis2PO4 (170), K2HPO4 (435), Na2HPO4 7H2O (668), NH4Cl (850), MgSO4·7H2O (22.5), CaCl2·2H2O (27.5), and FeCl3 (0.25)) and 2 mL of fresh overnight culture of each microorganisms were poured into six 500 mL flasks. Dispersants as an exclusive source of carbon were added to each flask as follows: flask 1: Pars 1, flask 2: Pars 2, flask 3: Gamlen, flask 4: Pars 1 and oil, flask 5: Pars 2 and oil, flask 6: Gamlen and oil.In this regard, isolated microorganisms, which were able to grow at the side of wells, were individually cultured overnight. 100 mL of manual culture media ((concentration in 1/mg): KH It should be noted that the series of flasks containing both dispersant and oil was set up by preparing 1 : 20 dilution of the dispersant/crude oil . Six conIn order to identify the biodegradation of above-mentioned dispersants and their mixture with oil in the sampling stations, the BOD and the COD of each sample were measured in the presence of total microorganisms , 23. TheThe standard microbiological procedures were used to identify the species of the bacterium and fungus microorganisms.The obtained data was analyzed by the Statistical Package for Social Sciences software version 15.0  using analysis of variance (ANOVA) and post hoc Tukey statistical tests.Based on standard microbiological procedures, 4 genera of bacteria and 3 genera of fungus in Siri province and 4 genera of bacterium and 2 genera of fungus in Bahregan province were identified.The ability of bacteria and fungi to grow in the presence of dispersants individually or mixture of each with crude oil is presented in The highest number of bacteria and fungi in Siri Province were those cultured in the presence of Pars 1, Pars 2 or separate mixture of each with crude oil, whereas in Bahregan Province, the bacteria around Pars 1 and Pars 2, had better growth rate compared with Gamlen.In Siri province, the microorganisms isolated from the sampling stations, which had the ability to grow at the side of wells in the Well method, were cultured 28 days for the purpose of biomass analysis. The bacteria and fungi were grown for 28 days, and their optical density was measured in different time intervals. The OD reading showed that the highest growth occurred in the presence of either Pars 1 or Pars 2 or their separate mixture with crude oil.The results of ANOVA and post hoc Turkey statistical tests are shown in P = 0.006) were documented in the effects of isolated microorganisms (4 bacteria and three fungi) on different dispersants  after 24 hours.As shown in P ≤ 0.046) and also between Gamlen and combination of crude oil with Pars 1 (P ≤ 0.005). In other words, the effect of microorganisms on Pars 1 dispersant is more than that on Gamlen dispersant.The comparison of the mean growth rate using hoc Tukey test exhibited that there is meaningful differences between Pars 1 and Gamlen dispersants ( This finding is in agreement with the result obtained from the Well method experiment.The results of ANOVA test on day 28 did not show significant difference in effects of microorganisms among each dispersant separately or their combination with crude oil.P ≤ 0.755) showed that there is no meaningful differences in effects of microorganisms among each dispersant separately or their combination with crude oil.The results of ANOVA test on day 28 , the highest growth rate is when Pars 1 and Pars 2 are the only sources of carbon in the environment. In 7-P bacterium the highest growth rate was observed in the presence of Pars 1 dispersant after one week. 8-E bacterium had the highest growth in the first week in the presence of Pars 1 dispersant and in 4th the week with presence of combination of Pars 1 and crude oil. Moreover, 5-C and 1-E showed the highest growth rate after four weeks in the presence of Pars 2 dispersant.The result of statistical calculations on isolated bacteria (4 genera) and fungi (3 genera) in Siri province showed that in the first 24 hours, noticeable growth has occurred in the presence of Pars 1 dispersant as well as its combination with crude oil showing significant difference compared to the growth of the same organisms in the presence of the other dispersants or their combination with Siri province crude oil. In Bahregan province, in all conditions the maximum growth rate was found in the presence of Pars 1 and Pars 2 in the environment. In 4 bacteria of Bahregan province, combination of crude oil with 2 bacteria of 5-E and 1-E which are related to These findings confirm that Pars 1 dispersant has more adaptability to both province ecosystems, and also they have more ability in biodegradation of crude oil compared with the other two dispersants. There was no significant differences in the effect of microorganisms on each dispersant and also on their combination with crude oil after 28 days. However, since the entered material to the ecosystem needs to be degraded fast, Pars 1 dispersant which shows more degradability in the first 24 hours comparing other dispersants, is more adaptable to the environment.Pseudomonas spp. bacteria in 4 weeks showed the highest growth rate of bacteria to the great extent in the presence of Pars 1 dispersant and slightly lower extent in the presence of Pars 2 dispersant. The growth peak was seen on day 14 in the presence of combination of Pars 1 dispersant and crude oil. The growth curve of Aureobasidium spp. fungus shows that on day 28, the highest optical density is observed when the microorganism is cultured in the presence of Pars 2 and its mixture with crude oil; also the growth peak occurred in the presence of the aforementioned mixture in the first 24 hours. However, the microorganisms had also enhanced growth in the presence of Pars 1 dispersant.In Siri province, The growth diagrams of  The optical density of microorganism cultures containing dispersants is indicating the usage of these components as the sole carbon source which leads to microorganism growth and catabolism of the carbohydrate , 25. The In agreement with results obtained from optical density reading and the Well method experiment, microorganism culture containing Pars 1 showed the highest level of BOD and COD. BOD is an indicator of biodegradation of organic components in water. BOD is measured by the amount of required oxygen for bacteria to metabolize organic components. The flasks are kept at 20°C for 5 days and the amount of dissolved oxygen is determined by chemical procedures. The BOD test identifies the approximate amount of required oxygen for biological oxidation of contaminated water, surplus water, and sewages. This is the only experiments determining the amount of required oxygen for bacteria in order to catabolize the organic components. Therefore, the higher BOD shows the increased amount of consumed oxygen which is consequently indicating the enhanced bacterial activity .The COD value indicates the amount of oxygen needed to chemically oxidize organic compounds present in wastewater and adjacent to oxidizing material. In fact, chemical oxygen demand determines the amount of organic compound present in the sample which has the ability to be oxidized by a strong chemical oxidizing agent . BOD and COD tests are well-known methods for assessment of biodegradability of organic materials such as surfactants; for instance, in a study in 1976, the percentage of biodegradation of 123 organic compounds was assayed [Previous studies showed that none of the bacterial species are able to catabolize all the components of crude oil, and its complete biodegradation depends on the presence of various bacterial species and microorganisms. Even microorganisms which are consumers of non-hydrocarbonate compounds can play important role in biodegradation of crude oil . Thus, i In this study, the highest BOD and COD in Siri province were related to culture containing Pars 1 in comparison with the two other dispersants studied. Likewise, BOD-COD test performed on different combinations of dispersants and crude oil showed highest score for the combination of Pars 1 and crude oil and secondly to the mixture of Pars 2 and crude oil. Moreover, in Bahregan province the maximum BOD and COD devoted to Pars 2 dispersant. These findings suggest that microorganisms with the presence of these compounds require the highest amount of oxygen for their activities including the biodegradation of such components. Furthermore, in oxidation and degradation reactions, in presence of oxidizing agents, the highest amount of chemical oxygen is demanded; therefore; Pars 1, mixture of Pars 2 and crude oil, and also mixture of Pars 1 and crude oil hold more degradability properties compared to the mixture of Gamlen and crude oil. In fact, Pars 1 and Pars 2 increased biodegradability of crude oil more than that of Gamlen dispersant. Since Pars 1 showed more degradability compared with the other two dispersants, the bioadaptability of this dispersant is high enough, so that it does not get accumulated in the region and does not make the environment contaminated.This study revealed that Pars 1 and Pars 2 dispersants are more biodegradable than Gamlen and have more effectiveness in biodegradation of crude oil. These findings suggest that, in each region, the most suitable compound for removing oil spill from offshores with least secondary contamination should be investigated.


Symmetry and regularity of gait are essential outcomes of gait retraining programs, especially in lower-limb amputees. This study aims presenting an algorithm to automatically compute symmetry and regularity indices, and assessing the minimum number of strides for appropriate evaluation of gait symmetry and regularity through autocorrelation of acceleration signals.Ten transfemoral amputees (AMP) and ten control subjects (CTRL) were studied. Subjects wore an accelerometer and were asked to walk for 70 m at their natural speed (twice). Reference values of step and stride regularity indices (Ad1 and Ad2) were obtained by autocorrelation analysis of the vertical and antero-posterior acceleration signals, excluding initial and final strides. The Ad1 and Ad2 coefficients were then computed at different stages by analyzing increasing portions of the signals . At each stage, the difference between Ad1 and Ad2 values and the corresponding reference values were compared with the minimum detectable difference, MDD, of the index. If that difference was less than MDD, it was assumed that the portion of signal used in the analysis was of sufficient length to allow reliable estimation of the autocorrelation coefficient.All Ad1 and Ad2 indices were lower in AMP than in CTRL (P < 0.0001). Excluding initial and final strides from the analysis, the minimum number of strides needed for reliable computation of step symmetry and stride regularity was about 2.2 and 3.5, respectively. Analyzing the whole signals, the minimum number of strides increased to about 15 and 20, respectively.Without the need to identify and eliminate the phases of gait initiation and termination, twenty strides can provide a reasonable amount of information to reliably estimate gait regularity in transfemoral amputees. Lower-limb amputees may present several gait deviations ,2, with The use of inertial sensors for analyzing gait has rapidly increased over the last few years. Recent advances in sensor manufacturing, computational power of portable systems, and wireless technology  have allowed extending the usage of inertial sensors (mainly accelerometers) beyond a merely clinical environment, to include also the home or outdoor environments, such as during activities of daily life or for long-term monitoring of signs and symptoms of specific pathologies -12.In our view, key elements for designing such portable system are: 1) identification of relevant gait features and methods to measure them; 2) appropriate signal processing and feature selection; 3) evaluation of reliability and usability of the approach; 4) provision of practical guidelines for an evaluation protocol; 5) clinical validation of the evaluation protocol and of the rehabilitation outcomes. In a previous study  we facedThe present work moves from the outcomes of study  and aimsThe subjects analyzed in this study are the same that were studied in . Briefly2. The unit was placed on the thorax at the xiphoid process, following the guidelines from our previous study [st order, cut-off frequency = 28 Hz) before digitalising the acceleration signals. Data processing and analyses were performed in Matlab .Acceleration signals were collected by the MEMS accelerometer of an XSens inertial measurement unit , which has a full scale of ± 50 m/sus study . The senSubjects were asked to walk straight ahead along a hallway of the INAIL Centre, for a distance of 70 m. They were initially asked to walk at their natural speed. Subsequently, they were asked to walk slower than their natural speed for a second test and then faster for a third test. The order of the tests was fixed . Each subject participated in two measurement sessions: after the first three tests, the operator removed the sensor from the thorax, and the subject was asked to rest for 15 minutes; then, a second operator placed the sensor on the thorax, and asked the subject to repeat the three gait tests in the same order. Thus, a total of 6 gait tests were acquired for each subject, two for each gait speed.x(i) can be computed by the following equation [The unbiased autocorrelation sequence of an acceleration signal equation :N is the total number of samples and m is the time lag expressed as number of samples. As shown in previous studies [m), Ad1, reflects the regularity of the acceleration between consecutive steps of the subject. This can be interpreted as a measure of the symmetry between steps performed by the prosthetic and the sound leg (or between left and right leg in CTRL). The second peak of Ad(m), Ad2, reflects the regularity of consecutive strides. Higher Ad1 (Ad2) values reflect higher step (stride) regularity . From the time lag between Ad1 and Ad2, given the sampling frequency, it is possible to compute the walking cadence  A search window, three samples wide, is applied to the autocorrelation sequence. The window starts from the first sample of the sequence, and is shifted sample-by-sample until the sequence ends  In each position of the search window, the maximum value of the autocorrelation sequence is considered: if it is in the second of the three samples of the window, the value and related position in the autocorrelation sequence (time shift) are saved in a vector of maxima. c) When the search of maxima is finished, the vector of maxima is analyzed; since, by definition, Ad2 shows a time shift that is twice that of Ad1, the vector is searched to identify a couple of maxima whose time shifts are in a ratio of 2, with a given tolerance (10%). If one couple is found that satisfies this criterion, and both maxima are positive, that couple is assumed as a candidate for Ad1 and Ad2 (Ad1 being the maximum with lower time shift). d) Since in some cases such couple of Ad1 and Ad2 candidates may not be the actual Ad1 and Ad2, another possible couple of maxima is searched within the vector of maxima, but now limiting the search to those maxima whose time lag does not exceed twice the time lag of the identified Ad2 candidate (within the accepted tolerance). This time interval limitation is necessary to avoid the identification of different peaks in the autocorrelation sequence . The limitation of twice the time lag of the first Ad2 candidate was empirically found adequate. e) If another couple of Ad1 and Ad2 candidates is identified, the new Ad2 candidate value is compared to the old Ad2 candidate value: if the former is greater, the new candidates are in fact assumed as being Ad1 and Ad2; otherwise, the old candidates are assumed as being Ad1 and Ad2.In this study we propose a new, simple algorithm capable of automatically identifying the peaks of the autocorrelation sequence corresponding to Ad1 and Ad2 coefficients. The algorithm operates as follows: This algorithm was used for the computation of Ad1 and Ad2 in all the analyses previously described. A block diagram of the algorithm is depicted in Figure ref, Ad2ref) for gait symmetry and regularity estimation in each test.For each of the gait tests, we initially considered only the central portion of the acceleration signals: we excluded from the analysis the first and last 1500 samples, so that we were highly confident that the transitional phases of gait initiation and termination were completely ignored . The obtained Ad1 and Ad2 coefficient values were assumed as the reference values .Firstly, we considered the central portion of the acceleration signals, as indicated above. For each signal, we performed the autocorrelation analysis for the computation of Ad1 and Ad2 coefficients beginning with a very small portion of the signal (100 samples). We then progressively enlarged the portion of the signal analyzed by steps of 100 samples. At each step of the procedure, Ad1 and Ad2 coefficients were calculated. Thus, for each acceleration signal we ended with a vector of Ad1 and Ad2 values that could be compared with the corresponding reference values previously obtained  vector of Ad1 and Ad2 values for each acceleration signal.V, Ad1AP, Ad2V, Ad2AP), SEM calculation was performed separately for AMP and CTRL subjects.As stated above, all subjects performed each gait test twice. This allowed us to calculate the standard error of measurement, SEM -16. We aSEM values were used to compute the minimum detectable difference, MDD, for each Ad1 and Ad2 coefficient. MDD indicates the minimum difference that must be observed between two measures of one variable to assume that the difference is "real", and not due to random errors, or systematic errors such as those, for instance, that are due to the incompetence of the operators (inter-rater variability). MDD was computed as EM×1.96×2.ref and Ad2ref. When the difference was lower than the corresponding MDD value, we assumed that the portion of the acceleration signal under analysis was sufficiently long to allow appropriate computation of the Ad coefficients. In fact, by definition, two measures of the same variable whose difference is less than the MDD have to be considered indistinguishable. From the calculated minimum length of the acceleration signal expressed in number of samples, with prior knowledge of the sampling frequency and the walking cadence of the subject  function, called rmaov1, which was downloaded at the URL http://www.mathworks.com/matlabcentral/fileexchange (last checked: 14 July 2011).The possible inter-rater variability in the computation of Ad1Repeated Measures ANOVA was also used to assess possible differences between AMP and CTRL groups in the mean value of the Ad1 and Ad2 coefficients and the main characteristics of the subjects . For sake of brevity, we present results related to Ad1interest ).AP and its reference value for increasing length of the acceleration signal portion considered. Similar information is reported for Ad2V . When the acceleration signals were examined excluding the transitional phases of walking the number of strides to properly compute Ad1AP was very small, and not different between AMP and CTRL subjects. The minimum number of strides for appropriate computation of Ad2V was still small but greater than that for computation of Ad1AP, for both AMP and CTRL , hence in this study we focused the analysis on these two coefficients. It should be noted that in other studies, such as [From our previous study , Ad1AP a such as ,17, the AP and Ad2V, we had to define to what extent a possible difference with the Ad1AP and Ad2V reference values could be acceptable. To this aim, we referred to the computation of SEM and MDD [To evaluate the minimal portion of the signal that was necessary for reliable computation of Ad1 and MDD -16.AP is very small, and not different between AMP and CTRL  is due to the reason that the assessment of the stride quality obviously requires, by definition, more information than that required for the step. In fact, it is not surprising that the minimum number of strides for Ad2V is not far, on average, from being double than for Ad1AP . We found that the two tests in each subject were not different, and hence there was no significant rater effect. Besides, this result also implicitly seems to suggest that test-retest variability, possibly due to fatigue effects, was not present as well.et al. seem to claim that the number of steps for adequate gait assessment through autocorrelation sequence is around ten . This is in relatively good agreement with our results obtained in ideal conditions , but not with those obtained in the non-ideal case. On the other hand, in another study [Our results are hardly comparable with previous results. To our knowledge, no previous study addressed the problem of the minimum number of strides that are necessary for reliable estimation of the quality of gait in subjects with lower-limb prosthesis, not even with approaches different from those based on inertial sensors and autocorrelation analysis. However, we can compare our results with a couple of previous studies, though not performed on amputees. In , Moe-Niler study  it was rWe addressed the problem of evaluating what the minimum number of strides is for reliable assessment of gait symmetry and regularity through accelerometry-based autocorrelation analysis in subjects with lower-limb prosthesis. We were able to reach the following conclusions and recommendations: when the gait includes transitional phases due to gait initiation, the number of strides to be performed over a rectilinear path should be around 15 for the assessment of step symmetry and 20 for stride regularity.i: i-th peak of the autocorrelation sequence; ANOVA: Analysis of variance; AMP: Subject with amputation; AP: Antero-posterior axis; CTRL: Control subject; MDD: Minimum detectable difference; ML: Medio-lateral axis; Ref: Reference; V: Vertical axis; SEM: Standard error of measurement.AdThe authors declare that they have no competing interests.AT has made substantial contributions to analysis and interpretation of data and has been involved in drafting the manuscript. LR has made substantial contributions to analysis and interpretation of data and has been involved in revising the manuscript. MR has made substantial contributions to acquisition, analysis and interpretation of data. AGC has made substantial contributions to conception and design, analysis and interpretation of data, and has been involved in revising the manuscript. LC has made substantial contributions to conception and design of the study and has been involved in revising the manuscript. All authors read and approved the final manuscript


Objectives. To demonstrate the feasibility of the prenatal diagnosis of partial androgen insensitivity syndrome by 3D-4D ultrasound. Methods. To report prenatal diagnosis of partial androgen insensitivity syndrome at 32nd week of gestation by 3D-4D ultrasound in a fetus with a 46XY karyotype, testing negative to the mutation analysis of SRY gene and the 5α-reductase 2 gene (SRD5A2). Results. 3D-4D surface rendering allows the detection of external and internal genital malformations and can address the prenatal diagnosis of PAIS and can exclude associated complications. Conclusions. Prenatal diagnosis of PAIS allows an adequate parental counseling and an early optimal management of the condition, not only for the psychological and social reflections but also for the avoidance of complications and postnatal morbidity due to misdiagnosis or delays in the treatment of the genital ambiguity. Androgen insensitivity syndrome  represents the most common identifiable cause of male pseudohermaphroditism, accounting for as many as 1 : 20.000 births [α-reductase 2 gene (SRD5A2) to exclude other causes of hermaphroditism or pseudohermaphroditism. Both analyses did not reveal any mutation. To clarify the discrepancy between the male karyotype and the female genital phenotype, an amniocentesis was performed and the fetal DNA extracted from the cultured amniocytes was tested by direct sequencing for mutations in the SRY gene and in the 5Therefore, the presence of female external genitalia without the uterus, in association with normal SRY and SRD5A2 genes, led us to the diagnostic hypothesis of  (CAIS/PAIS), that was tested through the sequence analysis of the AR gene which did not show any mutation. A multidisciplinary counseling session was scheduled with the parents to address the issue of the female sex assignment at birth. Delivery was at the 39th gestational week. The female external genitalia with clitoromegaly at birth are shown in In the present report, we show how the prenatal diagnosis of PAIS allows an adequate parental counseling and an optimal management of the condition, not only for the relevant psychological and social implications of an early diagnosis but also for the reduction of the chance of complications and postnatal morbidity due to misdiagnosis or delays in the treatment of the genital ambiguity. The contribution of US in prenatal sex determination is well known, and its role in detecting sexual differentiation disorders has been previously established . In addiα-reductase 2 deficiency), and the confirmation of the diagnosis through the identification of a molecular defect in AR gene. In our case, direct sequencing of all of the 8 exons of the AR gene did not detect any mutation, consistent with the mutation rate of 28% to 73% for the incomplete, milder phenotypes [The mainstay of the diagnosis of PAIS is the presence of a 46 XY karyotype, the determination of the normality (baseline or after hCG stimulation) of testosterone and dihydrotestosterone levels  has given the possibility of a reassuring prenatal counseling session about the excellent prognosis of the condition, contributing to improve the quality of life and health for both the child and the parents.


AbstractWe studied cytogenetic reactions of Scots pine seedlings to heavy metals – lead, cupric and zinc nitrates applied at concentrations 0.5 to 2000 µM. We determined the range of concentrations of heavy metals that causes mutagenic effect. Lead was found to cause the strongest genotoxicity as manifested by significant increase in the frequency of pathological mitosis, occurrence of fragmentations and agglutinations of chromosomes, various types of bridges, and a significant number of the micronuclei which were absent in the control. Possible cytogenetic mechanisms of the cytotoxic action of heavy metals are discussed. PageBreakimpact their growth, development and productivity. Apart from the toxic effect, HMs have a mutagenic (genotoxic) effect which is still not sufficiently studied  have become the most dangerous and widely spread pollutants of the biosphere and especially soil . Increas studied .Pinus sylvestris L.) is one of the most common forest forming species in Palaearctic. The investigation of cytogenetic responses of Scots pine seedlings to various HMs will help to estimate the genotoxicity and cytotoxicity of these metals as well as the metal resistance of the plants and develop criteria for selection of tolerant trees for reforestation in anthropogenically polluted areas.The influence of HMs on plants  has been intensively studied by morphological, physiological, and biochemical methods . There aPinus sylvestris L.) from the Usmansky forest  were used. The conditions in this site are dry forest (A1); the composition is 100% Scots pine. The Usmansky forest is a secondary forest, located along the watersheds of the Voronezh River and the Usman River, Voronezh province, Russia. The quantity of HMs in soil is not excessive (The seeds of pine trees (xcessive . Accordixcessive .3)2, zinc nitrate hexahydrate Zn(NO3)2∙6H2O, cupric nitrate trihydrate Cu(NO3)2∙3H2O and potassium nitrate KNO3 of different concentrations (from 0.5 to 2000 µM) for 18 hours. Then the seeds were germinated in the same solutions in Petri dishes on moist filter paper at a room temperature for 5–7 days. The selected concentrations of HMs are stressful and correspond approximately to: Pb(NO3)2 – from 3.5 to 14 000 MAC , Zn(NO3)2∙6H2O – from 3.3 to 13 000 MAC, Cu(NO3)2∙3H2O – from 32 to 128 000 MAC (Pinus sylvestris L. in our conditions) in ethanol-acetic mixture . The preparations for cytogenetic analysis stained in aceto-hematoxylin were made according to the technique describedPageBreak earlier  and placed in Petri dishes on moist filter paper and then germinated at room temperature. In the experimental variants the seeds were pre-soaked in the solutions of lead nitrate Pb the mitotic activity of meristematic tissue (which was estimated by the mitotic index (MI)) calculated as a percentage of the number of dividing cells in prophase, meta-, ana-and telophase of mitosis to the total number of counted cells), 2) the percentage of cells in each mitosis phase to determine the duration of these phases, 3) the frequency and spectrum (types) of mitotic abnormalities (MPs) , 4) the presence and frequency of cells with micronuclei was calculated as the percentage of cells with micronuclei to the total number of interphase cells counted, and 5) the proportion of cells with Statistical processing of the data was performed with the help of the statistical program package Stadia and Statistica. The procedure of grouping the data and their treatment are described in the work of Variation of cytogenetic parameters in the root meristem of Scots pine seedlings from the control and experimental samples is presented in Mitotic activity. Mitotic activity determines growth energy. Since the mitotic index (MI) is a rather stable parameter at a given time, its change may reflect a mutagenic influence of environmental factors on studied objects  . HoweverPageBreakA comparison of the frequency of cells at different stages of mitosis revealed that under conditions of stress  there was an increase in the proportion of cells at metaphase, and especially the metaphase-anaphase transition (meta-anaphase) (naphase) , as illunaphase) . The inhnaphase) . For exanaphase) .1 cells to S-phase from G2 to mitosis and metaphase to anaphase are viewed as critical stages in which a temporary stop of the cell cycle and check of the genetic material’s integrity take place. Therefore, the “control point” of the cell cycle is a mechanism that protects the dividing cells against lethal mitosis by activation of repair systems for DNA damage or self-destruction of heavily damaged cells via apoptosis. Thus, it is possible to consider the change in duration of cells’ passage in mitosis (an increase in the number of cells in metaphase and meta-anaphase) as one of the mechanisms of adaptation to stressors and maintenance of homeostasis in cell populations of Scots pine seedlings under the influence of Pb, Zn and Cu.PageBreakThe change of the duration of cells’ passage through the stages of mitosis under the influence of HMs may be associated with the checkpoint activation. In cell cycle, transitions from GThe obtained data on the impact of equal concentrations of various HMs salts on the mitotic activity of root meristem cells allow us to estimate their cytotoxicity. For example, although the decrease in the MI was similar  for all Mitotic pathologies and the micronucleus test. It has been shown for Scots pine that the level and spectrum of mitotic pathologies (MPs), the frequency of cells with micronuclei and the number of nucleoli in the cell are the most sensitive cytogenetic parameters to the anthropogenic pollution, objectively reflecting the state of their genetic system  for Pb, 33 MAC for Zn and 320 MAC for Cu. The usage of so high concentration in our experiment is explained by the short duration of HMs infulence. Typically, the value of MAC on HMs-polluted territories is lower in natural conditions, but it can come up to 35 MAC for Pb  defined with ISSR markers depends on the degree of moistening of the soil containing the HMs group. The genetic variation was higher in the population of Picea mariana growing on the wet lands as compared to those growing on the dry land. But cytological analysis of black spruce seeds from metal-contaminated and uncontaminated areas showed normal mitotic behavior during prophase, metaphase, anaphase, and telophase. There is no research on the influence of the specific HMs on the mitosis under field conditions.A significant increase of MPs was found for all tested salts of HMs  starting from the concentration of 5 µM (selected as a threshold). C for Pb . In anthC for Pb . There aC for Pb  that genWith increase in HMs concentration the frequency of the MPs increased. Starting with the concentration 50 µM for Pb and Zn, the average value of the MPs exceeded normal values of spontaneous mutation level in central Russia by up to 5% . MoreoveThe spectrum of MPs in Scots pine seedlings of experimental samples was manifested by the same abnormalities as identified in control  as well as by the new ones such as chromosome fragments in prophase, metaphase, anaphase, chromosome agglutination; chromosome segregation in metaphase and anaphase; different types of bridges  . The preThe tested HMs generally caused similar cytogenetic response. Nevertheless, we noticed some specificity of the induced abnormalities. For example, Pb to a greater extent (from 0.4 to 19.8%) caused an appearance of chromosome fragments in prophase and metaphase. Zn had the widest range of induced MPs, including chromosome fragmentation (from 0.4 to 7.3%) and agglutination (0 to 3.6%) and multiple bridges. Cu mainly caused agglutination (0 to 8.8%) and less frequently chromosome fragmentation (from 0 to 3.7%) .The differences between the experimental variations were particularly clearly observed in the frequency of occurrence of micronuclei in interphase cells . MicronuThe seedlings treated with potassium nitrate showed no significant differences in MP frequency compared with the control . MicronuPageBreakAccording to the results Kruskall-Wallis nonparametric univariate analysis of variance test, lead had the greatest impact on the frequency of MPs  of its physical and chemical properties .It is well known that Cu and Zn are trace elements essential for cell metabolism, but their excess of the normal physiological level results to a negative impact. Several mechanisms of HM detoxification (including Cu and Zn) that ensure the maintenance of cellular homeostasis and metal resistance increase in plants have been described in a number of papers. These include an immobilization of the cell wall , formatiThe experiments with Scots pine showed  that cytNucleolar activity. The role of the nucleolus in metabolic processes is due to its involvement in the biosynthesis of cell rRNA which is necessary for protein biosynthesis. It is known that nucleolar activity in pines can vary within wide limits manifested by the varying number of nucleoli (1 to 12 nucleoli in one nucleus). The number of nucleoli increases under extreme conditions  due to an increase in cells with the maximum number of nucleoli (10–12) in the nucleus. 4) The data on MPs level and the micronuclei frequency indicate the strength of genotoxic (mutagenic) impact of HMs affecting Scots pine seedlings germination as Pb > Zn > Cu. We show that the most sensitive and suitable for assessing HMs genotoxicity in the early stages of development are the PM level and spectrum, the number of cells with micronuclei and the nucleolar activity.The presented data show the high genotoxic effect of zinc, cupric and, especially, lead nitrates on Scots pine seedlings. With an increase in HMs concentration (from 5 µM), there were significant changes in cytogenetic parameters. 1) There was a marked inhibition of mitosis manifested in a significant increase in the number of cells in metaphase and intermediate meta-anaphase, which may be caused by blocking the polymerization of tubulin spindle microtubules. However, a decrease in mitotic activity may provide additional time to repair damage  of chromosomal material in the transition of cells through the “checkpoint” cell cycle. 2) The rate (up to 5–27 fold depending on the concentration of HMs) increased and the spectrum of MPs expanded. Specific chromosome damage, not observed in controls appeared, such as a large number of chromosome fragments (up to 19.8%) and agglutination (8.8%) and a significant amount of micronuclei in interphase cells (up to 0.43%) which indicated the inhibiting impact of HMs on the enzymes of DNA repair systems. 3) The cytogenetic adaptive reactions of Scots pine to the


Lumbosacral transitional vertebra (LTV) is a common congenital and hereditary anomaly in many dog breeds. It predisposes to premature degeneration of the lumbosacral junction, and is a frequent cause of cauda equina syndrome, especially in German shepherd dogs. Ventrodorsal hip radiographs are most often used in diagnosis of LTV in screening programs. In this study, value of laterolateral lumbar spine radiographs as additions to ventrodorsal radiographs in diagnosis of LTV, and characteristics of LTV and the eighth lumbar vertebra (L8) in laterolateral radiographs were studied. Additionally, computed tomography (CT) features of different types of LTV were elucidated.χ2 statistics, generalized logit model for multinomial data, and one-way analysis of variance was used for statistical analyses.The ventrodorsal pelvic and laterolateral lumbar spine radiographs of 228 German shepherd dogs were evaluated for existence and type of LTV. Morphology of transverse processes was used in classification of LTV in ventrodorsal radiographs. The relative length of sixth (L6) and seventh (L7) vertebrae (L6/L7) was used in characterization of these vertebrae in laterolateral radiographs. CT studies were available for 16 dogs, and they were used for more detailed characterization of different types of LTV. Non-parametric In all, 92 (40%) dogs had a LTV, the most common type being separation of first spinous process from the median crest of the sacrum in 62 dogs (67% of LTV). Eight dogs had eight lumbar vertebrae. Those dogs with LTV had longer L7 in relation to L6 than dogs with normal lumbosacral junctions. When L6/L7 decreased by 0.1 units, the proportion of dogs belonging to the group with L8 was 14-fold higher than in the group with normal lumbosacral junctions. L8 resembled first sacral vertebra (S1) in length and position and was therefore classified as one type of LTV. With CT it was shown that categorizing LTV, based on shape and visibility of transverse processes seen in ventrodorsal radiographs, could be misleading.We suggest that L8 be included as a part of the LTV complex, and the laterolateral radiographs of the lumbar spine be considered as an addition to ventrodorsal projections in the screening protocols for LTV. The sacrum consists of three fused vertebrae and develops, as do the other vertebrae, from three primary ossification centers. The first and second segments have additional ossification centers laterally. They represent ancestral forms of ribs and develop into the ventral parts of the sacral wings . LumbosaThe definition of LTV varies in the veterinary literature. It has been described as a vertebra having features of both lumbar and sacral vertebrae, in which a disc space exists between the first (S1) and second (S2) sacral segments . SeveralLTV is usually diagnosed radiographically, using a ventrodorsal projection -8,10, buThe prevalence of LTV in German shepherd dogs is reported to be from 4.3% to 29.0% ,8,10 andThe aims of this study were to determine the diagnostic value of the laterolateral radiographic projection as an addition to ventrodorsal projection in diagnosing LTV in screening programs for German shepherd dogs, and to describe the features of LTV and L8 in laterolateral radiographs. An additional aim was to compare radiographic and CT features of different types of LTV. Our hypotheses were that L8 is part of the LTV complex, and that a laterolateral radiographic projection increases significantly the accuracy of the diagnosis of LTV in screening programs.The ventrodorsal pelvic and laterolateral lumbar spine radiographs of German shepherd dogs were collected from three sources: 1) Finnish Kennel Club hip dysplasia screening radiographs in 2007, when an additional laterolateral projection of the lumbar spine, as requested by the national breed club, was included in the screening radiographs, 2) radiographs from the Finnish Border Guard of dogs (born 1995–2006) withdrawn from active service, and 3) radiographs and CT studies collected from the database of the Veterinary Teaching Hospital of the University of Helsinki between May 2005 and March 2011 of dogs radiographed for various reasons. A CT study of the lumbosacral area was included in the study when available.Two of the authors evaluated the ventrodorsal and laterolateral radiographs for the existence and type of LTV independently, blinded to the findings of the other projection. Thereafter, the two authors evaluated both projections together, and a diagnosis of LTV was based on consensus. An LTV seen in the ventrodorsal projection was diagnosed and classified into three types based on the morphology of the transverse processes, according to the previously published scheme . In typeThe number of lumbar vertebrae was counted using the last thoracic vertebra as a reference point. The first lumbar vertebra (L1) was the vertebra caudal to this vertebra. To evaluate the appearance of the last presacral vertebra, the laterolateral radiographs were evaluated for position of seventh and length of sixth and seventh L6 - L7) vertebrae (and L8 when present). The position of L7 relative to the ilium was recorded. It was graded as caudal if the cranial border of the ilium was cranial to the cranial endplate of L7 Figure , interme - L7 verThe primary author evaluated the CT images. Multiplanar reconstructions (MPR) Figures  and 10 aχ2 statistics. A one-sided p-value was used to determine the statistical significance of the difference.The sensitivity was calculated for the ventrodorsal radiographic projection in diagnosis of LTV with a non-parametric The relationship between type of lumbosacral junction and relative length of L6/L7 was investigated with generalized logit model for multinomial data. The model included type of the lumbosacral junction as the response variable and the relative length of L6/L7 as a fixed effect. In the model, the differences between groups were quantified with odds ratios and 95% confidence intervals (CI). Dogs with normal lumbosacral junctions based on radiographs were used as the reference category. Since there were very few or no observations in many cells of the location of the L7 type, a generalized logit model could not be fitted to the data properly. Thus, only descriptive statistics of the relationship between the type of lumbosacral junction and location of L7 are provided. The difference between types of lumbosacral junction was analysed with one-way analysis of variance. Here, the response variable was the relative length of L6/L7 and the type of lumbosacral junction was used as a fixed factor. Statistical significance was set at the 5% level. SAS System for Windows version 9.2  was used for all statistical calculations.In all, 228 German shepherd dogs were included in the study, of which 79 were males and 149 were females. The mean age of the dogs was 42 months (range 5 months - 134 months). LTV was diagnosed in 92 dogs (40.4%), based on ventrodorsal and/or laterolateral radiographs. Ten dogs with eight vertebrae were included in the LTV group. In Six of these dogs, the only abnormal radiographic finding was a short and caudally positioned L8. In addition four dogs had L8 and nonfused S2-S3.Results regarding the type of LTV are presented in Table Of the 228 dogs, 217 (95.2%) had seven, ten dogs (4.3%) had eight, and one dog with LTV (0.4%) had six lumbar vertebrae. The caudal position of the L7 in relation to the ilium was the most common type. All dogs with L8, but none of the dogs with normal lumbosacral junctions had cranial position of the L7 in relation to the ilium Figure . Clear dA CT study was performed in 16 dogs, of which nine dogs had abnormal sacrum and seven were normal. The abnormal findings are presented in Table We compared ventrodorsal hip and laterolateral lumbar spine projections in the radiological diagnosis of LTV in German shepherd dogs, and scrutinized the radiographic and CT features of the LTV.The incidence of LTV is dependent on the definition. In the present study, dogs with eight lumbar vertebrae as the only abnormal finding were classified as to having a LTV, which contrasts with the previous studies. It has argued that L8 is a clinically irrelevant finding  and hencThe incidence of LTV was 40% in our study, which was markedly higher than in other studies ,10. In oIn our study, the relative length of L6/L7 was similar in dogs with separation of the S1 spinous process from the median crest as the only abnormality and dogs with LTV, suggesting similar morphology. From the results, we can also conclude that in all three LTV types the relative length of L6/L7 tended to be smaller than in the dogs with normal lumbosacral junctions; i.e. dogs with all types of LTV have a longer L7 in comparison to L6 than dogs with normal lumbosacral junctions. Separation of the S1 spinous process from the median crest as the only abnormality can be genetically a mild form of LTV, and selection against the trait could decrease the incidence of more serious forms of LTV in German shepherd dogs.The laterolateral projection made the diagnosis of L8 possible. A statistically significant increase in the diagnostic accuracy of LTV was detected when the laterolateral lumbar spine projection was included in the protocol in addition to the ventrodorsal projection. It would have been be possible to diagnose a short L8 with abnormally small transverse processes from the ventrodorsal projection used in hip dysplasia screening, but this would have been difficult if the second to the last lumbar vertebra was not included in the radiograph for comparison. This is seldom the case, because only the last lumbar vertebra is consistently seen in hip radiographs made according to the protocol of Fédération Cynologique Internationale (FCI) . Some of the radiographic signs, such as separation of the S1 spinous process from the median crest of the sacrum and separation of the sacral vertebrae were visible in only one of the two projections. Every missed case in the ventrodorsal projection had eight lumbar vertebrae. Surprisingly, five of six dogs with symmetrical intermediate or lumbar-type LTV had a normal sacrum based on a laterolateral radiograph. The existence of abnormal transverse processes was ensured with CT in two of these dogs (dog 3 and dog 9 in Table A limitation in our study was the lack of radiographs of the total spine, since it can be argued that a transitional vertebra in the thoracolumbar junction can cause the extra vertebra. However, the markedly caudal position of L8 speaks for an LTV. Another limitation was the low number of dogs; however, the results were statistically significant.We conclude that laterolateral radiographs of the lumbar spine would be a valuable addition in screening for LTV in German shepherd dogs. The laterolateral projection may, in addition, assist in screening for lumbosacral osteochondrosis and lumbosacral stenosis, two typical conditions in German shepherd dogs. We suggest that L8 be included in the LTV complex in the screening programs. Further studies are needed to elucidate the genetic basis for the different types of lumbosacral and sacral congenital malformations.The authors declare that they have no competing interests.AKL partly collected and analysed all the data and drafted the manuscriptRS partly collected and analysed the dataJJ performed the statistical analyses and revised the statistical sections of the manuscriptMS participated in the design of the study and revision of the manuscriptOL-V participated in the design of the study, helped to draft the manuscript, and revised itAll authors read and approved the final manuscript.