Recent studies have revealed the importance of considering the entire distribution of possible secondary structures in RNA secondary structure predictions; therefore, a new type of estimator is proposed including the maximum expected accuracy (MEA) estimator. The MEA-based estimators have been designed to maximize the expected accuracy of the base-pairs and have achieved the highest level of accuracy. Those methods, however, do not give the single best prediction of the structure, but employ parameters to control the trade-off between the sensitivity and the positive predictive value (PPV). It is unclear what parameter value we should use, and even the well-trained default parameter value does not, in general, give the best result in popular accuracy measures to each RNA sequence.pseudo-expected accuracy, which can easily be computed from base-pairing probabilities, is introduced. It is shown that the pseudo-expected accuracy is a good approximation in terms of sensitivity, PPV, MCC, or F-score. The pseudo-expected accuracy can be approximately maximized for each RNA sequence by stochastic sampling. It is also shown that well-balanced secondary structures between sensitivity and PPV can be predicted with a small computational overhead by combining the pseudo-expected accuracy of MCC or F-score with the γ-centroid estimator.Instead of using the expected values of the popular accuracy measures for RNA secondary structure prediction, which is difficult to be calculated, the This study gives not only a method for predicting the secondary structure that balances between sensitivity and PPV, but also a general method for approximately maximizing the (pseudo-)expected accuracy with respect to various evaluation measures including MCC and F-score. To predict the secondary structure of an RNA sequence is a classic problem of sequence analysis in bioinformatics. The importance of accurate predictions of secondary structures has increased due to the recent finding of functional non-coding RNAs whose functions are closely related to their secondary structures -3. SeconThere are many tools and algorithms for secondary structure prediction -11. The et al. [et al. [Therefore, another approach that considers the entire distribution of possible secondary structures of a given sequence has been introduced. Ding et al.  proposed [et al.  proposed [et al. ,10,19-22 [et al. -25 and o [et al. -28.not employ the accuracy measures that are used in actual evaluation of RNA secondary structure, namely, sensitivity (SEN), positive predictive value (PPV), Matthews correlation coefficient (MCC) and F-score, with respect to predicted base-pairs. From a view- point of MEA, it is useful to consider the estimators that maximize expectation of those accuracy measures. Because the computation of those estimators generally demands huge computational time, the previous studies could not use those accuracy measures directly.For RNA secondary structure predictions, two MEA-based estimators have been proposed: (i) the estimator proposed by  and (ii)Moreover, the previous MEA-based estimators contain a parameter that controls the balance between SEN and PPV of base-pairs in a predicted secondary structure. It is, however, unclear how to select the parameter in order to obtain one reasonable secondary structure , although there are situations that only one predicted secondary structure is required. There is also a possibility that the optimal parameter might depend on the length of sequence and/or the type of RNA family, although the γ-centroid estimator (and the estimator proposed by ) employspseudo-expected accuracy of a secondary structure with respect to a given accuracy measure, which is a function of the number of true positive base-pairs (TP), true-negative base- pairs (TN), false-positive base-pairs (FP) and false- negative base-pairs (FN). The pseudo-expected accuracy is then defined by using expected TP, TN, FP and FN. As the accuracy measures, we utilize SEN, PPV, MCC and F-score with respect to base-pairs, which are commonly used in the evaluations of RNA secondary structure predictions, because the base- pairs are essential for forming secondary/tertiary structures, which are known to be biologically important.In this study, to address the drawbacks of the current MEA-based methods described above, We introduce the The pseudo-expected accuracy is easily calculated using the base-pairing probability matrix, and can be computed much more efficiently than the expected accuracy. Although the pseudo-expected accuracy is not equal to the expected accuracy of a predicted secondary structure, we found that the pseudo-expected accuracy gives a good approximation of the expected accuracy in our situation. Accordingly, we also introduce the approximated estimators that maximize the expected accuracy of a given accuracy measure. Moreover, by combining the pseudo-expected MCC/F-score with the γ- centroid estimator, it is possible to predict the balanced secondary structure between SEN and PPV (which seems to be a reasonable secondary structure in many situations when only one predicted secondary structure is required), although there is a small computational overhead.The techniques described in this paper will be extended to design the maximum expected accuracy estimator for various evaluation measures (cf. ).x as a triangular binary matrix:θ = {θij}i < j where θij = 1 means that i-th base xi and j-th base xj form a base-pair, and θij = 0 means that i-th base xi and j-th base xj do not form a base-pair. In this study, pseudo-knotted base-pairs are not allowed in a secondary structure. For an RNA sequence x, where |x| is the length of x. A probability distribution on S(x) (denoted by p(·|x)) is given by the McCaskill [x, {pi,j}i <j, has entries I(·) is the indicator function that returns 1 if the condition is true and 0 otherwise. The base-pairing probability matrix of a given RNA sequence x can be computed using the McCaskill (Inside-Outside) algorithm, whose complexities are O(|x|3) and O(|x|2) for time and space, respectively .θ = {θij}i < j ∈ S(x) and σ = {σij}i < j ∈ S(x) of an RNA sequence x, we defineFor two secondary structures θ is a reference (correct) secondary structure and is a predicted secondary structure of x, Eqs. (1), (2), (3), (4), (5), (6), (7), and (8) are the number of true positive base-pairs, the number of true negative base-pairs, the number of false positive base-pairs, the number of false negative base-pairs, the SEN, the PPV, the MCC and the F-score, respectively. Because the base-pairs in a secondary structure are biologically important, accuracy measures based on base-pairs are useful and SEN, PPV, MCC and F-score are widely-used accuracy measures for secondary structure predictions. Note that MCC and F-score are balanced measures between SEN and PPV.  In the following, Acc means one of the SEN, PPV, MCC and F-score.When p(θ|x) on S(x), we calculate the expected values of Eq. (1) to Eq. (4).Given a probability distribution pij} indicates the base-pairing probability matrix. Moreover, we calculate the expected accuracy of an accuracy measure Acc  of σ as follows:Where {Acc for a given secondary structure σ  has been reported. The number of candidate secondary structures increases exponentially with the length of the RNA sequence , so to compute the expected Acc is an intractable problem. Therefore, we approximate it using stochastic sampling: For N secondary structures In order to compute the expected sampling ,31 of seN is sufficiently large by the properties of stochastic sampling. It should be noted that the sample size N grows exponentially with the sequence length to Acc of σ.for Acc is generally written as a function of TP, TN, FP and FN:In our situation, Acc = fpseudo-expected Acc of is defined byThen, for a secondary structure σ, the For example, the pseudo-expected MCC is given byx, the pseudo-expected Acc of σ can be easily computed by using Eqs. (9), (10), (11) and (12) without employing sampling/enumerating algorithms. Although the pseudo-expected Acc is not equal to the expected Acc, we shall see later that the pseudo-expected Acc is a good approximation of the expected Acc when Acc is equal to SEN, PPV, MCC or F-score.If we have the base-pairing probability matrix of The γ-centroid estimator  for RNA >0 controls SEN and PPV of a predicted secondary structure. This estimator is suitable when we would like to predict more TP and TN and fewer FP and FN because Eq. (17) is equivalent towhere γ 1 + α4)/(α2 + α3) and αk ≥ 0. Hamada et al. [with γ =  indicates that the γ-centroid estimator is not optimized for the actual evaluation measures . It is useful to introduce the estimator that maximizes expected SEN, PPV, MCC or F-score directly:Acc efficiently for given σ and p(θ|x). Because Acc contains products or divisions of TP, TN, FP and FN, no efficient method to compute the estimator Eq. (19) has been found, in contrast to the γ-centroid estimator of Eq. (17). Instead, we consider estimators that maximize pseudo-expected Acc as follows.It is, however, difficult to compute the expected The pseudo-expected SEN and PPV of a secondary structure σ can be computed byTherefore, the secondary structure given by maximizing pseudo-expected SEN (Eq. (20) with SEN)) is equivalent to the secondary structure that maximizes the sum of base-paring probabilities of the predicted base-pairs. The secondary structure is, therefore, equivalent to the one given by the γ-centroid estimator with a sufficiently large γ . On the S(x). The number of secondary structures of a given RNA sequence, however, is so large that it is not practical to enumerate all of them. Therefore, we again employ the stochastic sampling of secondary structures and approximate the estimator of Eq. (20) byBecause of the computational difficulty of computing "argmax" in Eq. (20) with MCC and F-score (see "Discussion" section for more details), we need to evaluate all the secondary structures in S is a set of secondary structures given by stochastic sampling. Note that the computational cost of this estimator is much smaller than that of predictions based on maximizing the expected MCC/F-score. If the pseudo-expected MCC/F-score gives a good approximation of the expected MCC/F-score and we use a sufficiently large sample size, then the estimator in Eq. (23) should be a reliable approximation to the estimator in Eq. (19) that maximizes the expected MCC/F-score.where In the γ-centroid estimator  of Eq.  [g Sthat has the best pseudo-expected MCC/F-score:Eq. (18), which is equivalent in form to the γ- centroid estimator, indicates that the γ-centroid estimator can Acc is equal to MCC or F-score. The pseudo-expected MCC/F-score of each secondary structure σ ∈ g Sis easily computed because the base-pairing probability matrix has already been computed.where bias to MCC and F-score  of the secondary structures of RNA sequence x, we used the CONTRAfold model (version 2.02) [θ is a reference structure.For the dataset, we utilized the S-151Rfam dataset  that conon 2.02)  and the on 2.02)  (in the on 2.02) ). For evAcc (Eq. (15)) with the expected Acc (Eq. (13)) where Acc is SEN, PPV, MCC or F-score. First, we obtained a set of secondary structures from the S-151Rfam dataset in the following way. For each RNA sequence in the S-151Rfam dataset, we predicted the secondary structures using the γ-centroid estimator [k: -5 ≤ k ≤ 10} ∪ {6} and two models (the McCaskill [Acc (Eq. (13)) of a given secondary structure, because the number of possible secondary structures is immense. Therefore, we plotted Acc of; Eq. (15)) and Acc of σ approximated by 1 M  samples; Eq. (14)) for each secondary structure σ in the set of secondary structures.In this experiment, we compared the pseudo-expected stimator  (implemecCaskill  and CONTcCaskill  models).The result is shown in Figure We conducted the experiments on RNA secondary structure prediction by maximizing the pseudo-expected MCC/F-score of the predicted secondary structure with stochastic sampling (the estimator in Eq. (23)). Note that the results in the previous section suggest that the estimator of Eq. (23) with a sufficiently large sample size is a good approximation to the estimator of Eq. (19) that maximizes the expected MCC/F-score.The results are shown in Figure It should be noted that the performance of the estimator that maximizes the pseudo-expected SEN (PPV) corresponds to the leftmost (rightmost) point in the SEN-PPV curve of the γ-centroid estimators.Figure It is also much better than the performance of RNAfold, Sfold and Simfold, all of which return a single prediction. Note that Method M2 with a fixed probabilistic model  generally achieves performance that differs from that of the γ-centroid estimator with the same model for any γ value. This is because Method M2 automatically selects the secondary structure with the best pseudo-expected MCC/F-score from a set of secondary structures given by the γ-centroid estimator for 17 γ values, while each point in a SEN-PPV curve of the γ- centroid estimator comes from a fixed γ-value.Table The comparison between the 2nd and 3rd rows in Table In summary, by combining the pseudo-expected accuracy with the γ-centroid estimator, we successfully predict the well-balanced secondary structure between SEN and PPV  and the performance (with CONTRAfold model) is better than that of RNAfold, Simfold, Sfold and CentroidFold.pseudo-expected accuracy,  of a given RNA secondary structure under a probability distribution of possible secondary structures. The pseudo-expected accuracy can be computed much more easily than the expected accuracy, because it is computed using the base-pairing probability matrix of the RNA sequence. Although the pseudo-expected accuracy of a given secondary structure is not equal to the expected accuracy of the structure, our computational experiments have indicated that the pseudo-expected accuracy of a given secondary structure is a good approximation of the expected accuracy of the structure when SEN, PPV, MCC and F-score were used as the accuracy mea-sure. This finding is one of the contributions of this study, which has not been reported in previous research.In this study, we introduced the expected accuracy, it is still unacceptably slow. Therefore, we then proposed the combination of the pseudo-expected MCC/F-score and the γ-centroid estimator, which produces one well-balanced secondary structure with small computational overhead. The computational experiments indicate that this approach achieved the best accuracy among state-of-the-art tools. To employ the γ-centroid estimator in Method M2 is suitable because the γ-centroid estimator is able to represent a secondary structures with an arbitrary balance between the expected TP, TN, FP and FN by adjusting the parameter γ (see Eq. (18)). This, however, does not prove that there always exists a γ such that the γ-centroid estimator achieves the best pseudo-expected MCC or F-score. Note that the combination of the pseudo-expected MCC/F-score with the MEA-based estimator proposed by [bias to MCC and F-score, compared to the γ-centroid estimator [Based on this finding, we introduced the approximate estimator that maximizes the pseudo-expected accuracy of a prediction by stochastic sampling, which achieved favorable accuracy in our computational experiments. Although the computational cost of this estimator is much smaller than the estimator that maximizes the posed by  is not sstimator .Although the trade-ff between SEN and PPV is inherent, and MCC or F-score is not always the best choice of quality measure for predicted secondary structures, the proposed method (Method M2) can be applicable when only a single structure is required. The pseudo-expected MCC/F-score is also employed as a ranking measure of several predicted secondary structures.Y that contains all the possible candidate solutions of the target problem, a function Acc for θ ∈ Y and y ∈ Y , and a probability distribution p(θ|D) on Y given data D, then the estimatorAs we described in the Introduction section, the term "maximum (maximizing) expected accuracy" (MEA) has been used in a number of previous studies ,7,10,26 Acc is equal to an accuracy measure (or is designed according to an accuracy measure) for a reference θ and a prediction y. This also implies that p(θ|D) is considered to be a probability distribution of references, which is misleading because p(θ|D) does not usually represent the distribution. In RNA secondary structure prediction, for example, The McCaskill model provides not a probability distribution of reference secondary structures but rather a full ensemble of possible secondary structures [is introduced. When this estimator is called a "maximum expected accuracy" (MEA) estimator, ructures .Acc according to accuracy measures for a target problem and a probability distribution p(θ|D) of solutions empirically achieves better performance than other estimators such as the maximum likelihood estimator and the centroid estimator  in RNA secondary structure predictions [The estimator of Eq. 25) with a well-designed function dictions ,10 and i with a wEq. (20) with MCC and F-score can be rewritten asapproximation of Eq. (20) with MCC since TN  is much larger than the others in RNA secondary structure predictions.respectively. Note that Eq. (26) is an The denominators in both equations prevent division of this optimization problem into sub-problems, which is required to design a dynamic programming algorithm, and hence no efficient algorithms to compute Eqs. (26) and (27) have yet been devised. Note that the "argmax" operation for only the numerator can be efficiently solved by dynamic programming . .et al. [Recently, Lu et al.  proposedet al. ) with vaet al. ).global alignment problems, the balance between SEN and PPV with respect to aligned bases is important in local alignment problems.The method presented in this paper can be applied to local alignments for biological sequences be-cause the γ-centroid estimator was also introduced in the problem . In contMH and KA conceived the study. MH developed the algorithms, performed the experiments and wrote the manuscript. KS implemented the algorithm in the CentroidFold software. All authors have read and approved the final manuscript.Supplementary Information for the main text. This file includes supplementary information for the main text.Click here for file


According the Taqqu's law, 1/f noise has the properties of long-range dependence and heavy-tailed probability density function (PDF). The contribution of this paper is to exhibit that the prediction error of a biomedical signal of 1/f noise type is long-range dependent (LRD). Thus, it is heavy-tailed and of 1/f noise. Consequently, the variance of the prediction error is usually large or may not exist, making predicting biomedical signals of 1/f noise type difficult.A fractal signal  Theoretically speaking, in general, we cannot assume that Var[x(t)] always exists [α-stable distributions [x(t)] may be infinite. That Var[x(t)] does not exist is particularly true for signals in biomedical engineering and physiology, see Bassingthwaighte et al.  should be minimized. Thus, the premise that Var[e(m)] can be minimized is that it exists.Let e(m)] may be large if p(e) is heavy tailed. In a certain cases, Var[e(m)] may not exist. To explain the latter, we assume that e(m) follows a type of heavy-tailed distribution called the Pareto distribution.It is obviously seen that Var does not exist if a = 1 or a = 2 and if e(m) follows the Pareto distribution.Denote by on. Then , it is ie(m)] does not exist may not occur if e(m) is light-tailed. Therefore, the question in this regard is whether e(m) is heavy-tailed if a biomedical signal x(n) is of 1/f noise. The answer to that question is affirmative. We explain it below.Note that the situation that Var may in general be large. In some cases [e(m)] may not exist, making the prediction of biomedical signals of 1/f noise type difficult with the way of minimizing Var[e(m)].We have explained that the prediction error me cases , Var[e(m


Do humans prefer the self even over their favorite other person? This question has pervaded philosophy and social-behavioral sciences. Psychology’s distinction between explicit and implicit preferences calls for a two-tiered solution. Our evolutionarily-based Dissociative Self-Preference Model offers two hypotheses. Other-preferences prevail at an explicit level, because they convey caring for others, which strengthens interpersonal bonds–a major evolutionary advantage. Self-preferences, however, prevail at an implicit level, because they facilitate self-serving automatic behavior, which favors the self in life-or-die situations–also a major evolutionary advantage. We examined the data of 1,519 participants, who completed an explicit measure and one of five implicit measures of preferences for self versus favorite other. The results were consistent with the Dissociative Self-Preference Model. Explicitly, participants preferred their favorite other over the self. Implicitly, however, they preferred the self over their favorite other . Results are discussed in relation to evolutionary theorizing on self-deception. Is the self the most cherished entity that humans possess, preferred even over their most valued other person ? Alternatively, as cultural animals explicit level? Second, are preferences for self more or less prevalent than preferences for favorite other at an implicit level? Our answers to these two questions are guided by an evolutionary model that we outline next.Recent psychological advances call for a two-tiered solution to this age-old dilemma. Preferences, like self-oriented versus other-oriented ones, can be held at an explicit level; as such, they are conscious, reflective, and reasoning-based Explicitly, preferences for favorite other should prevail over preferences for self. Explicit other-preferences are evolutionarily adaptive, because they convey caring for others Implicitly, however, preferences for self should prevail over preferences for favorite other. Implicit self-preferences are also evolutionarily adaptive, because they facilitate self-favoring automatic behavior in live-or-die situations To address the above two pivotal questions, we propose the Dissociative Self-Preference Model. Its evolutionary backbone generates divergent hypotheses for explicit and implicit preferences. explicit level. However, preferences for self will predominate over preferences for favorite other at the implicit level. We test these hypotheses on a large and divergent sample, using five established implicit measures for generalizability purposes.We report a study in which we examine the two hypotheses derived from the Dissociative Self-Preference Model. Preferences for favorite other will predominate over preferences for self at the www.dfg.de) to the second author (grant identifier: GO 1107/4-1). The DFG's board of ethics passed the research proposal that underlies the present study. DFG-funded projects do not require additional approval by other ethics committees . Irrespective, we informed participants at the outset that the study concerns the psychological representation of their favorite person and that they therefore will be asked to complete corresponding self-report measures and sorting tasks. Participants were also informed that participation is anonymous, consented to participate in this study by clicking on a button, and were shown a debriefing screen at the conclusion of the study session.The study was run as part of a research grant awarded by the German Research Foundation . Following that, we wondered whether participants had chosen themselves as their favorite other. 42 participants (3%) had done so, and we excluded their data from our analyses. Next, participants reported their own name. Subsequently, participants completed one of five implicit self-other preference measures and one explicit self-other preference measure. For each participant, we determined randomly which implicit measure (s)he had to complete. Also, for each participant, we determined randomly whether (s)he received the implicit or the explicit measure first.We used a diverse internet sample in terms of age, occupation, and family status comprising 1,519 German volunteers  “…more positive feelings?”, (2) “…more negative feelings?” (reverse-scored), and “Who is more…” (3) “… worthy to you?”, (4) “…pleasant to you?”, (5) “…likable to you?”, (6) “…worthless to you?” (reverse-scored), (7) “…unpleasant to you?” (reverse-scored), and (8) “…unlikable to you” (reverse-scored) (α  = .89).Participants responded to the following eight items on rating scales ranging from 1 =  “[Different implicit measures may assess somewhat distinct facets of self-preference own full name]” and “[favorite person’s full name].” Attitude-stimuli of the stimuli-based measures  were idiosyncratically generated by each participant. Specifically, participants were instructed to provide “three words that clearly and spontaneously signify [favorite person’s full name], and three different words that clearly and spontaneously signify yourself.” The instructions set two additional constraints. First, the chosen words for self and favorite other had to be equivalent . Second, each word had to signify distinctively one attitude-category and not the other . Instructions also included examples suggesting the use of first names, last names, nicknames, or initials.Attitude-categories of the category-based measures  were “[Valence-categories of the category-based measures  were “Positive” and “Negative.” Valence-stimuli of the stimuli-based measures  were “worthy,” “pleasant,” and “likable” for the “Positive” category and “worthless,” “unpleasant,” and “unlikable” for the “Negative” category . These valence-stimuli were chosen to match the items of the explicit measure.In the IAT, the two halves of critical trials are administered in separate blocks, one after the other. The SBIAT is a variant of the IAT that administers all its critical trials randomly within a single block. This can address several alternative explanations of IAT effects In the APP, participants are instructed to indicate–as fast as possible–whether valence items are positive or negative. Shortly before a valence item is presented, however, an attitude item (here: from the categories “self” or “favorite other”) is presented. Presentations of valence items and attitude items are randomized, so that four types of trials emerge: self-positive trials, self-negative trials, favorite other-positive trials, and favorite other-negative trials. Comparison of the reaction times between self-positive and favorite other-negative trials with favorite other-positive and self-negative trials constitutes an implicit index of self-other preference. Specifically, the degree to which a person is faster at self-positive and favorite other-negative trials, compared to favorite other-positive and self-negative trials, is an indicator of self-preference over other-preference In the NLT, participants indicate, for all letters of the alphabet, how positive or negative they perceive them to be. The degree to which participants rate their initials more positive than the initials of their favorite other is an indicator of self-preference over other-preference r ≤.29, all ps <.05  as comparison value, t  =  -23.70, p<.001 . Implicitly, however, participants preferred self over their favorite other, as indicated by one-sample t-tests with the implicit measures' scale-midpoints  as comparison values, t  = 4.95, p  = .001 , t  = 3.04, p  = .003 , t  = 2.29, p  = .02 , t  = 2.59, p  = .01 , t  = 5.78, p  = .001 .Next, we tested the two hypotheses derived from the Dissociative Self-Preference Model. Results were fully in line with these hypotheses . ExpliciF  = 2.03, p  = .09, justifying their aggregation. In line with our results for each implicit measure, the aggregate implicit index revealed a clear preference for self over favorite other as indicated by a one-sample t-test with the implicit index's midpoint  as comparison value, t  = 8.48, p<.001 .Further, we wondered whether it is justified to treat the five implicit measures interchangeably in our subsequent analyses. Therefore, we conducted an ANOVA with type of implicit measure as the Independent Variable (IV) and standardized implicit self-preference as the Dependent Variable (DM) . Despite sufficiently large samples to detect reliably even small effects, this analysis revealed that the standardized effects did not differ significantly across implicit measures, t-test revealed a significant difference between standardized explicit preferences for favorite other  and standardized implicit preferences for self , t  = 25.53, p<.001. This result buttresses the substantial difference between explicit other-preferences and implicit self-preferences. Additionally, comparison of absolute means and effect sizes  and standardized implicit self-preference as the DV. Despite sufficiently large samples to detect reliably even small effects, this analysis revealed that the standardized effects did not differ significantly across type of favorite other, F  = .12, p  = .88. In contrast, an ANOVA with the three major types of favorite other as the IV and explicit other-preference as the DV was significant, F  = 22.05, p  = .001. Post-hoc analyses revealed significant differences between all three types of favorite other at ps <.003 (Scheffé-tests). Specifically, other-preferences were strongest for child as favorite other , weaker for spouse/partner as favorite other , and weakest for best friend as favorite other   .People share more genes with their child than with their partner/spouse or best friend. Thus, from an evolutionary standpoint, it is conceivable that implicit preferences for self should be diminished when favorite other is one's child, rather than one's spouse/partner or best friend. Such pattern may be expected because it may maximize the survival-chances of one's genes. However, implicit self-preferences did not vary as a function of type of favorite other and a closer examination of the prehistoric parent-child relationship may provide an evolutionary explanation for our results. Specifically, in prehistoric humans both, the fertility rate as well as the child death rate were high F  = 1.28, p  = .26, as well as for implicit preferences, F  = 1.08, p  = .30.We tested for sex differences in explicit and implicit preferences, using a MANOVA with sex as the IV and explicit and implicit preferences as simultaneous DVs. Despite sufficiently large samples to reliably detect even small differences, we found no sex differences for explicit preferences, r  =  -.03, p  = .23, as well as with implicit preferences, r  = .01, p  = .66.We also tested whether explicit and implicit preferences varied as a function of participant age. Despite sufficiently large samples to reliably detect even small effects, age was uncorrelated with explicit preferences, N1 = 520, N2 = 793) completed two prior studies, each including a different, well-validated measure of self-presentation (datasets were linked via anonymous key-strings). Comparison of correlation coefficients using Fisher z transformation revealed that the influence of self-presentation on implicit and explicit preferences did not differ significantly with regard to the first index, z  = .74, p  = .46 . Together, conscious self-presentational efforts to deceive others are unlikely to account substantially for other-preferences (Do explicit other-preferences reflect genuine beliefs or conscious self-presentational efforts to deceive others? Additional analyses suggest the former. First, internet studies minimize self-presentation ferences .Explicitly, humans prefer their favorite other over the self. Implicitly, however, they prefer the self over their favorite other–be it their spouse/partner, best friend, or child. We consistently documented these results across five subsamples using five divergent implicit measures. The uncovered dissociative preferences may reflect ancestral traces and confer, in distinct ways, evolutionary advantages to the individual: Explicit preferences establish and cement interpersonal ties Von Hippel and Trivers distal evolution-based predictions–namely, the general human tendency to hold explicit other-preferences, but implicit self-preferences. Future research could examine the proximate mechanisms underlying the reported findings. For example, humans seek self-awareness in positive situations, but avoid self-awareness in negative situations The present hypotheses tested In conclusion, the findings are pertinent to a long-standing controversy in philosophy and the social-behavioral sciences: the dilemma of self-love versus other-love. Offering a middle-ground solution, the findings favor the arguments by Rousseau, Mencius, and Botero at the explicit level, while favoring the arguments of Hume, Xunzi, and Machiavelli at the implicit level. In Aristotle’s


By the practical success of the COSMO-RS fluid phase thermodynamics model ,2 in manSince the same intermolecular interaction modes, which govern fluid phase thermodynamics, are also responsible for binding of ligands to receptors, it is most plausible that a σ-based description of of ligand-ligand similarity or of ligand-receptor interactions should be very promising. Yet, since in COSMO-RS theory the 3D- distribution of the polarization charge density σ on the molecular surface is reduced to a histogram, the σ-profile, the initial approaches in this direction [The same technique can be used to consistently align a set of ligand molecules based on their local σ-profiles. After such alignment, the local σ-profiles or the set of local σ-moments, which is a compressed representation of the σ-profiles, are available as a grid-based local descriptor set, which can be used for subsequent molecular field analysis (MFA). COSMO-RS theory even provides a rationale that the binding free energy, including desolvation, must be a linear function of this set of descriptors. First validation studies have proven that the COSMOsim3D based MFA yields very promising results.


In this article, we present a graph-based method using a cubic template for volumetric segmentation of vertebrae in magnetic resonance imaging (MRI) acquisitions. The user can define the degree of deviation from a regular cube via a smoothness value Δ. The Cube-Cut algorithm generates a directed graph with two terminal nodes (s-t-network), where the nodes of the graph correspond to a cubic-shaped subset of the image’s voxels. The weightings of the graph’s terminal edges, which connect every node with a virtual source s or a virtual sink t, represent the affinity of a voxel to the vertebra (source) and to the background (sink). Furthermore, a set of infinite weighted and non-terminal edges implements the smoothness term. After graph construction, a minimal s-t-cut is calculated within polynomial computation time, which splits the nodes into two disjoint units. Subsequently, the segmentation result is determined out of the source-set. A quantitative evaluation of a C++ implementation of the algorithm resulted in an average Dice Similarity Coefficient (DSC) of 81.33% and a running time of less than a minute. Lumbar stenosis (LS), a narrowing of any part of the lumbar spinal canal with encroachment on the neural structures by surrounding bone and soft tissue Sometimes, degenerative spondylolisthesis, an asymptomatic slipping forward of one lumbar vertebra on another one with an intact neural arch, can be linked to LS Several features of the spinal anatomy can be distinguished by their different grey values in an MR image. In most T1- and T2-weighted image slices, normal adult vertebral body bone marrow can be differentiated from the outer boundaries of the vertebral body by a homogeneously lighter grey value This, however, does not apply to slices that depict the pedicles. Several approaches for vertebra segmentation have been proposed in the literature Klinder et al. gold standard CT data and they regard their algorithm as robust. Furthermore, they point out that different threshold levels, within visually acceptable intervals, had very little effect on the registration results. The authors conclude that in general, the accuracy of the registration relies on the similarity between actual and automatically generated surfaces as well as the precision of the digitized points used for the registration.Hoad and Martel Štern et al. Aslan et al. Weese et al. Yao et al. Ghebreab and Smeulders Zukić et al. Kelm et al. Square-CutOur approach to solve the problem of three-dimensional vertebral body segmentation is a non-trivial enhancement of the previously introduced two-dimensional graph-based segmentation strategy Section 2 presents the methods behind the introduced algorithm, Section 3 presents the results of our experiments and Section 4 concludes the paper and outlines areas for future work.The rest of this contribution is organized as follows: Cube-Cut. Cube-Cut extends a two-dimensional approach, previously introduced by Egger et al. Cube-Cut have been presented on a workshop The new vertebral body segmentation algorithm presented here will be referred to as P, Cube-Cut first selects a subset P’P of the image's voxels and in a last step it tags each voxel pP’ with either one of the labels sL or tLGiven a volumetric MR image pP’ involves two penalties The labeling of a voxel p(t(p))≥0 is the penalty for assigning the label t(p) to p andDp,p’(t(p),t(p’))≥0 is the penalty for assigning t(p) to p when t(p’) is the label of the voxel p’VD describes a voxel's affinities to the labels sL and tL. For example, the higher p(t(p) = Lt)D, the more p is affiliated with sL. V on the other hand reflects a voxel's affiliation to another voxel. In practice, p,p’(t(p), t(p’))V is greater than zero only if t(p)≠t(p’). Thus, V indirectly describes p's affiliation with p’ by awarding a penalty for tagging the two voxels with different labels: The higher p,p’V, the more p is affiliated with p’. Nevertheless, note that p,p’(t(p), t(p’)) = 0 for t(p)≠t(p’)V does not necessarily mean that the two voxels p and p’ can be tagged differently without penalty costs. If, for instance, p,p’’(t(p), t(p”))>0V, for t(p)≠t(p’’) and p’’P’ and if p’’,p’(t(p’’), t(p’)) >0V for t(p’’)≠t(p’), then the penalty cost for assigning different labels to p and p’ is at least p,p’’, Vp’’,p’}min{V.L which minimizes.L = {t(p)|pP’} is a labeling of the subset P’Cube-Cut tags the voxels in a way such that the overall penalty cost is minimized. The overall cost is described by (2). Cube-Cut thus returns the argument P’ and implements D and V (on the basis of the predetermined subset P’) in a way such that the returned labeling is to be interpreted in the following manner (Cube-Cut selects g manner :pP’ for which st(p) = L inside the vertebral body andCube-Cut assumes all voxels pP’ for which tt(p) = L can be assumed outside the vertebral body.all voxels Hence, in a first step Cube-Cut selects a subset of voxels, and on the basis of this subset, implements two penalty functions which then determine a clustering of the subset into two disjoint units of voxels. One unit describes the vertebral body while the other describes the background (which may include other vertebrae). The following paragraphs will describe the implementation of the algorithm.pn rays that expand from a user-defined seed point in the MR image. Each ray consists of k equidistantly spread voxels, where for all rays, the first voxel is always the user-defined seed point, so that |P’| = n * (k - 1) +1. As the seed point, the number and the length of the rays as well as the number of voxels per ray can be determined by the user. It is assumed that each ray exceeds the vertebral body. In the following, let P’ denotes a voxel on ray r, where 1≤ r ≤ n and where the voxel 1p or r might be omitted. Furthermore, from now on, k will always denote the number of voxels per ray and n the number of rays).The voxels i = j ≠ 1 and m ≠ n, then the voxels k voxels on each ray, there are k-1 different sized cubes for which 1p is the center , E(G))), c, s, t), where G is a directed, two-terminal graph and |V (G)| = |P’| +2. Each vertex vV(G)\{s,t} corresponds to exactly one voxel pP’ and no two vertices correspond to the same voxel. In the following, pv will denote a mapping of the vertex vV(G)\{s,t} onto its corresponding voxel pP’ and vp will describe the reverse mapping. The source s and the sink t have no counterparts in P’ and thus they are referred to as virtual nodes. In E(G), there exist two types of edges Cube-Cut generates a network i-links (inter-links) connect vertices vV(G)\{s,t} with each other. The i-links are further subdivided into z-edges and xy-edges, where z-edges connect vertices corresponding to neighboring voxels of the same ray (e.g. (xy-edges connect vertices corresponding to voxels of different rays (e.g. (o-links (outward-links) connect all vertices vV(G)\{s,t} with the source s (s-links) and the sink t (t-links). Hence, there are two o-links for each vertex.i- and o-links reflect the penalty functions D and V in the following manner (The capacities of the g manner :(3)c = 0 is assumed, if / E (G). After the graph has been set up, Cube-Cut determines a minimal s-t-cut  by deploying the Boykov-Kolmogorov algorithm http://vision.csd.uwo.ca/code/, accessed: March 2014) and then it labels P’ as follows:Note that the skew symmetry constraint does not have an effect since by convention Since by definition, the capacity of a minimal s-t-cut is minimal among all possible s-t-cuts, the labeling above minimizes (2).z-edges is introduced that ensures that each ray is exactly cut one time by a minimal s-t-cut n is the user-defined number of rays and k the total number of voxels per ray, again . The set of z-edges connects each vertex iv with its predecessor (i-1)v on the same ray , a minimal s-t-cut  has to cut each ray at least once. Yet, it does not cut any ray more than once because that would cost at least 2·By making sure that the seed point is in , ) around the user-defined seed point (inside the vertebra) and determines its interval of grey values I = , where.thi element of a tuple. Furthermore, Cube-Cut also iterates over the cube to determine an average grey value avgg byA voxel o-links, the interval I and the average grey value avgg are used as frames of reference.o-links (note: Each ray r consists of k voxels):The following Pseudo-Code depicts the fundamental principle of how Cube-Cut assigns capacities to the 0 1 2 3 4 5 6 7 8 9 10 11 12 sL. The premise on which this is based is that the user defines the seed point within the vertebral body (in the center).The tL, the t-links  is consequently initialized to zero (line 4 - 6)Furthermore, it is assumed that the last voxel on each ray . This is in order to "mark" the outer boundaries.The capacities of all of the other, intermediate Introduction). Thus, on each ray, the difference in value between the last voxel in the vertebral body and the first voxel on the outer boundaries can be assumed high.As already mentioned above, the rays expand from the user-defined seed point in the center of the vertebral body and they eventually intersect with the outer boundaries. Ignoring occasional outliers and homogeneous object/background transition regions for now, the inner vertebral body is characterized by a homogeneous set of voxel grey values, which are all higher or lower than the grey values that make up the outer boundaries . Note that this makes a cut right in front of the corresponding vertices very probable. The next sections explain how peculiarities and anomalies in vertebral MRI data sometimes prevent a cut from happening right in front of the outer boundaries and how Cube-Cut addresses these adverse effects.Taking the condition in line 7 into account, the outer boundaries therefore implement high A cut right in front of the outer boundaries is a cut that separates the last vertex that corresponds to a voxel which is still located inside the vertebral body from the subsequent ones on the same ray. If, for each ray, the cut takes place right in front of the outer boundaries of the vertebral body, then Cube-Cut returns a satisfactory segmentation result.r that corresponds to a voxel on the outer boundaries/background. If a minimal s-t-cut  cuts the ray right in front of S and T, then.s-weights since behind the outer boundaries, the rays mostly penetrate homogeneous areas dissimilar from the vertebral body (compare lines 7 & 8 of the pseudo code). Let Nevertheless, there are exceptions. w, which loads the s-weights according to their distance from the seed point (see next section). Line 8 of the pseudo code is extended to:As a consequence, the condition in line 7 of the pseudo code holds true for a sufficient number of background voxels on each of the affected rays, which is why condition (8) is not satisfied. Thus, the overrun occurs. Observe that the same applies to homogeneous object/background transition regions. Among others, Cube-Cut tackles this problem by introducing a coefficient Another phenomenon that negatively affects the segmentation result is outliers. Outliers share all relevant properties  that distinguish the vertebra's boundaries except that they are part of the inner vertebral body.s-capacities and then the smoothness constraint will be discussed.To be specific, an outlier causes the violation of w(·) loads an s-capacity according to the corresponding voxel's  = mi+b, where kib = 1-m.The coefficient  the ray . For a rw = 1 for the seed point i = 1), w = 0.5 = 0 for the last voxel on each ray. A voxel far away from the seed point is more likely to be outside the vertebral body.Observe that since the voxels are distributed uniformly on each ray, on a ray  and w: The smoothness constraint, which also addresses a violation of condition (9), will be the subject matter in the next section.I = , where X, Y, Z0N, can be characterized by a bijection S : XYZ, where XYXY is a cohesive area. Li et al. refer to a surface as feasible if two smoothness constraints are satisfied:S and S as well as S and S are neighboring x- and y-positions. Thus, two neighbors on a feasible surface cannot be arbitrarily distant from each other. Hereby, the smoothness constraints assure what Li et al. refer to as "surface connectivity". Observe that for a plane The smoothness constraint is based on the optimal surface segmentation algorithm developed by Li et al. z-axis. The voxels that make up a ray do not necessarily have to lie on neighboring positions in the image. Furthermore, for convenience, assume that I is a binary image with only two possible values for each voxel: “colored” xor “white”. In addition, let all rays intersect with a colored surface S(XY) in I, which means that each ray extends from XY and shares exactly one colored voxel with the surface.Now consider a number of equidistant rays that consist of the same number of uniformly spread voxels and which all extend parallel to the x-direction , which extend parallel to the z-axis, as described above. Here, a smoothness parameter In this context, in which only a subset of the image's voxels is observed, the smoothness constraint has to be defined via the neighborhood relations of the rays. Cube-Cut allows the user to impose a smoothness constraint on the segmentation result. It interprets each of the six sides of a vertebral body's outer boundaries  as a feasible surface. Furthermore, it takes into account that the six surfaces are anatomically connected, which is why the neighborhood relations overlap at the "edges" of the boundaries.xy-edgesCube-Cut implements the smoothness constraint 4N denotes a 4-neighborhood and as already mentioned above, the neighborhood relations overlap at the "edges" of the cubic voxel subset that the algorithm observes.xy-edges ensures that a minimal s-t-cut cuts the rays in a way such that the vertebra is segmented within the boundaries of the user-defined smoothness constraint The infinity-weighting of the straint  . Note thxy-edges for a For a smoothness constraint www.mevislab.de). We used two T2-weighted, volumetric, pathological MR-images (512×512×16 and 512×512×10), both of which had an anisotropic voxel spacing in x- and y-directions of 0.63 millimeters and 4.4 millimeters along the z-axis. We obtained isotropic voxel sizing  by resampling the two images, using the MeVisLab Resample3D-module, which resulted in resolutions of 159×159×35 and 159×159×22 respectively. The first image contained a stenosis and a spondylolisthesis; the second image showed a slipped disc.A C++ implementation of Cube-Cut was tested within the medical image processing platform MeVisLab 2.2.1 . For initialization of the GrowCut algorithm, strokes have been drawn inside and outside the vertebral body on a two-dimensional, sagittal image, a two-dimensional axial image and a two-dimensional coronal image  operating system, version 6.1.7601, the most expensive parameter settings took Cube-Cut less than a minute  to terminate. The settings that resulted in a maximum DSC of over 86% only took 19 seconds to execute. Overall, we achieved a mean DSC-value of 81.33%.A novel approach towards the volumetric segmentation of vertebral bodies was presented. Cube-Cut is a non-trivial, three-dimensional extension of the previously introduced two-dimensional segmentation strategy Square-Cut development of a specific graph-based algorithm for vertebral body segmentation;algorithm bases on a cubic template which is a novelty in the segmentation domain;scale-invariant segmentation by an optimal mincut through cubic-shaped divergences;physicians performed slice-by-slice segmentations to obtain ground truth boundaries;segmentation quality of the algorithm has been evaluated via the Dice Coefficient.The proposed method only requires a single user seed, while other approaches In addition, contrary to most of the alternative approaches Furthermore, whereas other approaches 2e(G) |Cmin|)O(v(G), where v(G) is the number of vertices, e(G) the number of edges and min||C the capacity of a minimal cut, the algorithm is most effective for networks of low complexity, like the one Cube-Cut generates. In addition, we want to point out here that Boykov's graph cut model can support high dimensional data in its own settings.To summarize, Cube-Cut generates a two-terminal s-t-network where the vertices correspond to a cubic shaped subset of the image's voxels. By only observing a subset of the image’s voxels, the algorithm improves the theoretical runtime in comparison to other graph-based approaches that consult the whole voxel set. The capacities of the terminal edges reflect a voxel's affiliation with the object  and the background, while the topology of non-terminal ∞-weighted edges implements the smoothness-constraint. After network construction, a minimal s-t-cut, computed in polynomial time, determines the segmentation result. For the mincut computation, the Boykov-Kolmogorov algorithm is applied, since it was demonstrated For evaluation, Cube-Cut 3D-masks were compared to manual vertebral body segmentation results, obtained in a time-costly slice-by-slice manner, performed by trained physicians, achieving a promising mean DSC of 81.33%, which is on par with the state of the art (comparable to Moreover, we also used a spherical template instead of the cubic shaped one, to set up a graph and applied it to vertebra segmentation. As shown in Furthermore, we also compared the Cube-Cut masks with GrowCut results and found that Cube-Cut clearly outperformed GrowCut in this setup, regardless of the similar DSC values. Besides others, GrowCut regularly did not recognize the vertebral body’s outer boundaries in the pedicle-regions, which led to false boundary detections as shown in Nevertheless, visual evaluations of Cube-Cut's segmentation results indicate that the algorithm frequently segments the same specific areas of a vertebral body inaccurately. Recognizing the rectangle shape of a vertebral body, on sagittal slices, these areas could be referred to as the vertebral body's "vertices" . AlthougRegarding the robustness of Cube-Cut in general, we can report that the method only performs satisfactory if the cube’s volume is larger than the vertebral body’s , left siFurthermore, as already mentioned above, the seed has to be placed roughly around the center region of the vertebral body in order to obtain satisfactory segmentation results. Nevertheless, the algorithm proved itself relatively stable against small deviations and moreover, the replacement of the seed only takes a second which is one of the distinguishing advantages of Cube-Cut.


This paper is a comment on “Intra- and interday reliability of spine rasterstereography” . We thinIn research, validity is the extent to which a conclusion corresponds accurately to the reality. Differently, reliability is the overall consistency of a measure . ValiditIn conclusion, “Therefore, this study validated aspects of the rasterstereographic measuring system that potentially could replace X-rays in follow-up of spinal deformities helping to reduce X-rays irradiation” . DiscussWe should verify the data from this study with caution before suggesting such a clear indication , 9. Atte


A multi-labeled tree, or MUL-tree, is a phylogenetic tree where two or more leaves share a label, e.g., a species name. A MUL-tree can imply multiple conflicting phylogenetic relationships for the same set of taxa, but can also contain conflict-free information that is of interest and yet is not obvious.T as the set of all conflict-free quartet topologies implied by T, and define the maximal reduced form of T as the smallest tree that can be obtained from T by pruning leaves and contracting edges while retaining the same information content. We show that any two MUL-trees with the same information content exhibit the same reduced form. This introduces an equivalence relation among MUL-trees with potential applications to comparing MUL-trees. We present an efficient algorithm to reduce a MUL-tree to its maximally reduced form and evaluate its performance on empirical datasets in terms of both quality of the reduced tree and the degree of data reduction achieved.We define the information content of a MUL-tree Our measure of conflict-free information content based on quartets is simple and topologically appealing. In the experiments, the maximally reduced form is often much smaller than the original tree, yet retains most of the taxa. The reduction algorithm is quadratic in the number of leaves and its complexity is unaffected by the multiplicity of leaf labels or the degree of the nodes. Multi-labeled trees, also known as MUL-trees, are phylogenetic trees that can have more than one leaf with the same label-5 Figur. MUL-treMUL-trees, unlike singly-labeled trees, can contain conflicting species-level phylogenetic information due to biological processes such as whole genome duplications or incomHere we provide a way to extract this information; specifically, we have the following results. MUL-Trees and information content on page 3).• We introduce a new quartet-based measure of the information content of a MUL-tree, defined as the set of conflict-free quartets that the tree displays , and show that any two MUL-trees with the same information content have the same MRF (Theorem 3).• We introduce the concept of the maximally-reduced form (MRF) of a MUL-tree The reduction algorithm on page 7). Its running time is quadratic in the number of leaves and does not depend on the multiplicity of the leaf labels or the degrees of the internal nodes.• We present a simple algorithm to construct the MRF of a MUL-tree (see Results and discussion on page 8). In our test data, the MRF is often significantly smaller than the original tree, while retaining most of the taxa.• We present computational experience with an implementation of our MRF algorithm  of the leaf set, where each part is the set of leaves on one of the two sides of e. From , we derive a collection of bipartitions ab|cd of quartets, such that {a,b} ⊆ A and {c,d} ⊆ B. Clearly, if one edge in a singly-labeled tree implies some bipartition q = ab|cd of {a,b,c,d}, then there can be no other edge that implies a bipartition, such as ac|bd, that is in conflict with q. Indeed, the quartet topologies implied by a singly-labeled tree uniquely identify it[We now give the intuition behind our notion of information content, deferring the formal definitions of this and other concepts to the next section. Quartets  are a natural starting point, since they are the smallest subsets from which we can draw meaningful topological information. A singly-labeled tree implies exactly one topology on any quartet. More precisely, each edge ntify it.b and c — b(1) and b(2), and, c(1) and c(2) — leads to two conflicting topologies on the quartet {b,c,d,e}. Edge  implies the bipartition bc|de, corresponding to the labels {b(1),c(1),d,e}, while edge  implies bd|ce corresponding to the leaves {b(2),c(2),d,e}. On the other hand, the quartet topology af|bc, implied by edge , has no conflict with any other topology that the tree exhibits on {a,b,c,f}. We show that the set of all such conflict-free quartet topologies is compatible (Theorem 1). That is, for every MUL-tree T there exists at least one singly-labeled tree that displays all the conflict-free quartets of T — and possibly some other quartets as well. Motivated by this, we only view conflict-free quartet topologies as informative, and define the information content of a MUL-tree as the set of all conflict-free quartet topologies it implies.The situation for MUL-trees is more complicated, as illustrated in FigureWe should note that conflicting quartets may well provide valuable information, whether about paralogy, deep coalescence, or mistaken annotations. In some cases, species-level phylogenetic information can be recovered from conflicted quartets through application of, e.g., gene-tree species-tree reconciliation . Howevev,w) implies is either in conflict with some other topology  or is already implied by some other edge ). Thus,  can be contracted without altering the information content. In fact, the information content remains unchanged if we also contract  and remove the leaves labeled b(1) and c(1). We define the MRF of a MUL-tree T as the tree that results from applying information-preserving edge contraction and leaf pruning operations repeatedly to T, until it is no longer possible to do so. The MRF of the tree in FigureAn example on page 8). If the MRF is itself a MUL-tree, it is not possible to reduce the original to a singly-labeled tree without either adding at least one quartet that did not exist conflict-free in T or by losing one or more conflict-free quartets.A MUL-tree may have leaves that can be pruned and edges that can be contracted without altering the tree’s information content, i.e., without adding or removing conflict-free quartets. For example, in Figurelabeled b and c(1)Since any two MUL-trees with the same information content have the same MRF, rather than comparing MUL-trees directly, we can instead compare their MRFs. This is appealing mathematically, because it focuses on conflict-free information content, and also computationally, since an MRF can be much smaller than the original MUL-tree. Indeed, on our test data, the MRF was frequently singly-labeled. This reduction in input size is especially significant if the MUL-tree is an input to an algorithm whose running time is exponential in the label multiplicity, such as Ganapathy et al.’s algorithm to compute the contract-and-refine distance between two area cladograms or HuberFor our experiments, we also implemented a post-processing step, which converts the MRF to a singly-labeled tree, rendering it available for analyses that require singly-labeled trees, including supermatrix,15 and sPrevious work on MUL-trees has concentrated on finding ways to reduce MUL-trees to singly-labeled trees , and to MUL-tree is a triple , where (i) T is an unrooted treea with leaf setM is a set of labels, and (iii)T a label from M.  For brevity we often refer to a MUL-tree by its underlying tree T. In what follows, unless stated otherwise, by a tree we mean a MUL-tree.A u,v) in T is internal if neither u nor v belong topendant otherwise. A pendant node is an internal node that has a leaf as its neighbor.An edge  be an edge in T and T′ be the result of deleting  from T. ThenT′ that contains u (v).Cuv is the set of labels common to bothCuv partition M. For example, in FigureCuv = {b,c}.Let  in T withu,v) resolves ab|cd. For example, in Figuret,u) resolves af|bc.A (resolved) information content of an edge  of a MUL-tree T, denoted Δ, is the set of quartets resolved by . An edge  in tree T is informative if |Δ| > 0;  is maximally informative if there is no other edge  in T with Δ ⊂ Δ. The information content of T, denotedE denotes the set of edges in T.The The next result shows that the quartets inFor every MUL-tree T, there is a singly labeled tree T′such thatT has no multiply-occurring labels. Pick any multiply-occurring label ℓ in T, select an arbitrary leaf labeled by ℓ, and relabel every other leaf labeled by ℓ, by a new, unique, label. The resulting tree T′ is singly labeled, and all labels of T are also present in T′. Consider a quartet ab|cd in T, that is resolved by edge . Assume thata. Clearly, this also holds for the only occurrence of a in T′. Similar statements can be made about labels b, c, and d. Thus, the quartet ab|cd is resolved by edge  in T′, and, hence, T′ displays all quartets of T. □Repeat the following step until Note that there are examples where the containment indicated by the above result is proper.The reduction algorithm, beginning on page 7). In the next lemmas,  and  denote two edges in tree T that lie on the pathTo conclude this section, we give some results that are useful for the MUL-tree reduction algorithm  ⊆ Δ if and only ifΔ((Only if) Suppose Δ ⊆ Δ; therefore,(If) Supposeu,v) ⊆ Δ. □Suppose Δ ⊆ Δ. Then, for any edge  onPu,xsuch thatvis closer toythan toz, Δ ⊆ Δ ⊆ Δ.u,v) ⊆ Δ, we havey,z) on Pu,x. By definitionu,v) ⊆ Δ ⊆ Δ. □By Lemma 2, since Δ: Delete leaf v from T. If, as a result, v’s neighbor u becomes a degree-two node, connect the former two neighbors of u by an edge and delete u. Contract (e): Delete an internal edge e and identify its endpoints.Our goal is to provide a way to reduce a MUL-tree v in T is prunable if the tree that results from pruning v has the same information content as T. An internal edge e in T is contractible if the tree that results from contracting e has the same information content as T. T is maximally reduced if it has no prunable leaf and no contractible internal edge.A leaf Every internal edge in a maximally reduced tree T resolves a quartet that is resolved by no other edge.We rely on two facts. First, every internal node in the tree has degree at least three. Second, every internal edge in the tree resolves a quartet; otherwise, the edge would be contractible and the tree would not be maximally reduced.u,v) in the tree. To prove that  resolves a quartet not resolved by any other edge, we need to show that there exists a quartet ab|cd of the form shown in Figurea and b. Consider the following cases: Consider any edge  resolves. Without such a leaf,  would resolve the same set of quartets as , so one of these two edges would be contractible, contradicting the assumption that the tree is maximally reduced. We select this leaf as b and we select any2. u, except v, are leaves. Then, at least two of its neighbors must participate in a quartet, because  must resolve a quartet. We select the two neighbors as a and b.3. All neighbors of a and b. By a similar argument, we can also select the desired c and d. This proves the existence of the desired quartet ab|cd. Therefore, each internal edge of T uniquely resolve a quartet. □In every case, we can select the desired leaves The next result shows that the set of quartets resolved by a maximally reduced tree uniquely identifies the tree.Let T and T′be two maximally reduced trees such thatThen, T and T′are isomorphic.maximally reduced form (MRF) of a MUL-tree T is the tree that results from repeatedly pruning prunable leaves and contracting contractible edges from T until this is no longer possible. Theorem 3 shows that we can indeed talk about “the” MRF of T. Before proving Theorem 3, we mention some of its consequences.The Every MUL-tree has a unique MRF.Any two MUL-trees with the same information content have the same MRF.If a maximally reduced MUL-treeTis not singly-labeled, there does not exist a singly-labeled treeT′such thatf. However, doing so will also introduce quartets that are not resolved by the maximally reduced MUL-tree.Note that Corollary 3 does not contradict Theorem 1. If the MUL-tree in Theorem 1 is maximally reduced and not singly-labeled, the containment is proper; i.e.,The relation “sharing a common MRF” is an equivalence relation on the set of MUL-trees.The last result implies that MUL-trees can be partitioned into equivalence classes, where each class consists of the set of all trees with the same information content. Thus, instead of comparing MUL-trees directly, we can compare their maximally reduced forms.We now proceed to the proof of Theorem 3. We need two lemmas.There is a bijectionϕbetween the respective sets of internal edges of T and T′with the following property. Let  be an internal edge in T and let  = ϕ. Then,andTherefore, Δ = Δ.u,v) in T. By Theorem 2,  must resolve a quartet ab|cd not resolved by any other edge as shown in Figureu′,v′) in T′. Suppose not. Using arguments similar to those in the proof of Lemma 3, we can show that all edges that resolve ab|cd in T′ form a path , where possibly x′ = w′, as shown in FigureConsider an edge  resolves a quartet not resolved by any other edge, by Theorem 2 there exists a label ℓ as shown, whereab|ℓd is a quartet in T′ andT. Clearly, T does not resolve the quartet on {a,ℓ,d,c} in the same way, aℓ|cd, as T′. This contradicts the assumption thatu′,v′) must be an edge. Moreover, only one such edge exists in T′ as it uniquely resolves the quartet ab|cd.Since  = Δ.Now consider any labelϕ from edges in T to edges of T′ such that Δ(e) = Δ(ϕ(e)). To complete the proof, we show that ϕ is onto. Suppose that for some edge e′ in T′ there is no edge e in T such that ϕ(e) = e′. But then e′ must resolve a quartet not resolved by any other edge in T′. This quartet cannot be inWe have shown that there is a one-to-one mapping ϕ be the bijection between the edge sets of T and T′ from the preceding lemma.Let Let  and  be any two neighboring internal edges inT, and let  = ϕ and  = ϕ be the corresponding edges in T′such thatandThen,  and  are neighbors in T′with q = r.u,v) and  are neighbors, and each resolves a quartet that is not resolved by the other,p,q) and  can exist in T′ is as part of the pathq ≠ r, then consider the edge  on Pps such that p is closer to t than to r. Then, the following must hold:Since  = ϕ−1 be the edge in T corresponding to . Irrespective of the position of  in T, (1) and (2) cannot be simultaneously true with respect to edges ,  and  in T. Therefore, q = r, which proves the desired result. □Let  in T such that v is a pendant node andu′,v′) = ϕ be the corresponding edge in T′ such thatT nor T′ have prunable leaves. Thus, the same set of leaves must be attached at v and v′ respectively. In subsequent steps, we select an internal edge  in T such that v is a pendant node and all the other pendant nodes inu′,v′) = ϕ such thatv and v′ respectively. Proceeding this way, each pendant node in T can be paired with the corresponding pendant node in T′, and be shown to have the same set of leaves attached to them. This shows that T and T′ are isomorphic, as claimed. □Lemmas 4 and 5 show that In preparation for the MUL-tree reduction algorithm of the next section, we give some results that help to identify contractible edges and prunable leaves.u,v) and  are two edges in tree T that lie on the pathbranches out from the path Pu,x if y ∈ Pu,x−{u,x}, and z ∉ Pu,x.The setting for the next result is the same as for Lemmas 2 and 3:  ⊆ Δ thenevery internal edge on a subtree branching out from Pu,xis contractible, and1. if Δ = Δ, every leaf on a subtree branching out from Pu,xis prunable. Thus, the entire subtree can be deleted without changing the information content of the tree.2. Refer to FigureA,B) in a subtree branching out of Pu,x, as shown. We claim thatM appear inA,B) is uninformative.1. Consider any edge  ⊆ Δ, we haveTo prove the claim, observe first that, by definition,M. SinceNow,u,v) = Δ. By an argument similar to the one used in the proof of Lemma 3, we can show that any edge  on the path Pv,w = (v…w)  still resolves the same quartet in S because(a) c adds a quartet toS must be resolved by an edge  inℓ ∈ Cjk, but now hasℓ ∈ Cjk and the edge still cannot resolve the quartet, a contradiction.(b) c is prunable. □Hence, Suppose that T is a MUL-tree where no pendant node is adjacent to two or more leaves with the same label. Let ℓ be any multiply-occurring label in T and let T′be the minimal subtree of T that spans all the leaves labeled by ℓ. Then, any leaf in T labeled ℓ attached to a pendant node of degree at least three in T′is prunable.v of degree at least three in T′ attached to a leaf labeled ℓ. Clearly deleting the leaf does not change the information content of any edge in Tu or Ty. Now consider an edge  in T′ as shown. Note that ℓ ∈ Cwx, so ℓ does not contribute to Δ. After deleting the leaf, we still have ℓ ∈ Cwx, so Δ remains unchanged. Therefore, the leaf is prunable. □Refer to FigureO(n2) algorithm to compute the MRF of an n-leaf MUL-tree T. In the previous section, the MRF was defined as the tree obtained by applying information-preserving pruning and contraction operations to T, in any order, until it is no longer possible. For efficiency, however, the sequence in which these steps are performed is important. Our algorithm has three distinct phases: a preprocessing step, redundant edge contraction, and pruning of redundant leaves. We describe these next and then give an example.We now describe a u,v) in T, we computeO(n2) time as follows. First, traverse subtreesu,v) whereFor every edge  and  such that Δ ⊆ Δ or vice-versa, and contract the less informative of the two. By Lemmas 1 and 2, we can compare Δ and Δ in constant time using the precomputed values ofv or in the subtrees branching out of v. Further, by Lemma 6 (2), if Δ = Δ, we can in fact delete these subtrees entirely, since their leaves are prunable. Lemma 3 implies that all such edges must lie on a path, and hence can be identified in linear time. The total time for all these operations is linear, since at worst we traverse every edge twice.Next, we repeatedly find pairs of adjacent edges ,O(n2) time and O(n) space.The tree that is left at this point has no contractible edges; however, it can still have prunable leaves. We first prune any leaf with a label ℓ that share a common neighboring pendant node. Such leaves can be found in linear time. For each such set, we delete all but one element. Let T be the tree that results from removing such leaves. Now, the only prunable leaves with a given label ℓ that might remain are leaves attached to different pendant nodes. By Lemma 7, we can identify and prune such leaves by performing the following steps. Next, we consider sets of leaves with the same label ℓ, consider the subgraph on the leaves labeled by ℓ.1. For each label 2. In this subgraph, delete any leaf not attached to a degree 2 pendant node as it is a redundant leaf.O(n) time per label and O(n2) time total. The space used is O(n). Hence, the overall time and space complexities are O(n2) time and O(n), respectively.This takes The resulting tree has no contractible edges nor prunable leaves. Therefore, it is the MRF of the orginal MUL-tree.We illustrate the reduction of the unrooted MUL-tree shown in Figuret,u),  and  are uninformative. They are therefore contracted, resulting in the tree shown in Figure1. In the preprocessing step, we find thatu,v) ⊂ Δ, contract . The result is shown in Figure2. Since Δ = Δ, delete the subtree branching out at w from the path from v to y and contract . The result is shown in Figure3. Since Δ, which included a broad range of label-set sizes, from 4 to 1500 taxa.We implemented our MUL-tree reduction algorithm, as well as a second step that restricts the MRF to the set of labels that appear only once, which yields a singlylabeled tree. We tested our two-step program on a set of 110,842 MUL-trees obtained from the PhyLoTA database  were of this kind. Trees in set B were reduced to singly-labeled trees in the second step; 36,392 trees (32.8%) were of this kind. Reducing a tree to its MRF (step 1), led to an average taxon loss of 0.83% of the taxa in the input MUL-tree. The total taxon loss after the second step (reducing the MRFs in set B to singly-labeled trees), averaged 12.81%. This taxon loss is not trivial, but it is far less than the 41.27% average loss from the alternative, naïve, approach in which all MUL-taxa (taxa that label more than one leaf) are removed at the outset. Note that, by the definition of MRFs, taxa removed in the first step do not contribute to the information content, since all non-conflicting quartets are preserved. On the other hand, taxa removed in the second step do alter the information content, because each such taxon participated in some non-conflicting quartet. Information content, in this case, will be lost but new information is never introduced, so the algorithm can be considered conservative.There were 8,741 trees (7.8%) with essentially no information content; these lost all resolution either when reduced to their MRFs, or in the second step. The remaining trees fell into two categories. Trees in set Taxon loss is sensitive to the number of total taxa and, especially, MUL-taxa, as demonstrated in FigureIn addition to the issue of taxon loss, we investigated the effect of our reduction on edge loss, i.e., the level of resolution within the resulting singly-labeled tree. Input MUL-trees were binary and therefore had more nodes than twice the number of taxa , a phylogenetic tree search engine that takes a user-provided list of species names and finds matches with a precomputed collection of phylogenetic trees, more than half of which are MUL-trees, assembled from GenBank sequence data. The trees returned are ranked by a tree quality criterion that takes into account overlap with the query set, support values for the branches, and degree of resolution. We have added functionality to provide reduced singly-labeled trees as well as the MUL-trees based on the full leaf set and the label sets from the reduced singly-labeled trees are used in downstream supermatrix construction.We have integrated our reduction algorithm into STBase , result in relatively large MRF trees. Comparing the MRF to the original MUL-tree may well provide a method for efficiently assessing and segregating data sets with respect to the causes of multiple labels.It would be interesting to compare our results with some of the other approaches for reducing MUL-trees to singly-labeled trees  or, indaThe results presented here can be extended to rooted trees, using triplets instead of quartets, exploiting the well-known bijection between rooted and unrooted trees .The authors declare that they have no competing interests.MMM and DFB conceived the problem. AD, DFB and MMM designed the experiments and drafted the manuscript. AD designed and implemented the algorithms, and implemented the experiments. DFB coordinated the project. All authors read and approved the final manuscript.


This work presents a data-centric strategy to meet deadlines in soft real-time applications in wireless sensor networks. This strategy considers three main aspects: (i) The design of real-time application to obtain the minimum deadlines; (ii) An analytic model to estimate the ideal sample size used by data-reduction algorithms; and (iii) Two data-centric stream-based sampling algorithms to perform data reduction whenever necessary. Simulation results show that our data-centric strategies meet deadlines without loosing data representativeness. Examples of these applications include: surveillance systems, biometric sensing, and intrusion detection. These applications have soft real-time characteristics, i.e., environment is not controllable, applications usually use probabilistic models to process data, and communication does not have acknowledgment.Despite their potential application, wireless sensor networks (WSNs) -3 have set al.  and we have 10 equals histogram classes. To obtain such a sample, we choose the central elements of each histogram class, respecting the sample size | V′| and the class frequencies of the histogram. Thus, the resulting sample will be represented by the same histogram. Meanwhile, considering the sensor-stream reduction algorithm presented by Aquino et al  >V [fst]+wid or k = |V|- 1 then  9coln' ← ⌈n'col | V′|/|V| ⌉{number of elements per columns in V′}   10index ←f st+⌈(col-n'coln)/2⌉   11forl←0 colto n'do   12V′[w] ←V[index]    13w ← w + 1    14index ← nextIndex    15end   16col ←n 0   17fst ← k   18end  19col ← ncoln + 1  20end 21Sort(V′) {according to the original order} 22end6.(http://nsnam.isi.edu/nsnam/index.php/Main_Page). Each simulated scenario was executed with 33 random topologies. At the end, for each scenario we plot mean values with 95% (symmetric asymptotic) confidence intervals.This section presents the simulation study of our data-centric strategy in specific scenarios. We perform our evaluation by using the NS-2 (Network Simulator 2), version 2.33 V|). The evaluated parameters are the delay and error in data quality, specified by two statistical tests. The default parameters used in simulations are presented in To identify assess the network behavior, we variate the number of nodes and the stream size (| mmd) for each number of nodes and |V| being considered. To do this, we consider different network sizes , the |V| = {256, 512,1024, 2048{, and only one data source generating V. In our case, the mindvalues is determined by measuring the time between the first data packet sent by the source and the last packet received by the sink, i.e., the time for V to be entirely received by the sink. mindvalues for all scenarios being considered.To evaluate the delay in real-time scenarios, it is important to determine the minimum deadline  concurrent traffic; minimum deadlines with delay caused by relay nodes in each packet transmitted with(out) concurrent traffic. These study are discussed in the next subsections. For all scenarios, we evaluate the simplified and complex formulations, both using mulation  consider6.1.a = dmin/2d) without concurrent traffic in this case, the application cannot send V and meet ad. In this case, V is reduced by using our data-centric strategy. In Monte Carlo simulation, we change the number of nodes  and |V| . V| = 2048.The first scenario considers half of minimum deadlines per a/d10000 or 0.01% of the ad. In this scenario, the application cannot send V, because the relay nodes eventually can be executing another task, consequently, the deadline ad cannot be met. We change the number of nodes  and |V| . The objective of this scenarios is to identify the appropriate strategy when relay nodes have other high priority tasks.The second scenario, considers V| = 2048. In contrast to prior scenario, ad is always met. The complex formulation, in a more realistic scenario, presents a better time usage, i.e., the delay is closer to deadline values. This occurs because the Ψ-reduction estimation in sample case [a, i.e.d, if a > dmind reduction cannot be efficient, when we consider other delay aspects like concurrent traffic. Another important observation is that more data is received in the complex formulation strategy. When the number of nodes is 1024, nearly 20% of data are deliver, in the complex formulation, against 18%, in the simplified one. This fact indicates that, considering only the deadline achievement, the complex formulation is more appropriate to more realistic scenarios.ple case  is relatΨrandom, in both formulation, has a smaller ϒ-error, because the random choice improves data dispersion. However, the simplified formulation has a smaller ϒ-error. In Φ ≈ 5%. Again, Ψcentral, in both formulation, has a smaller Φ-error ecause the central elements choice improves the average test. Although, the simplified formulation has a smaller Φ-error with 128, 256 and 512 nodes, the complex formulation presents a better performance for 1024 nodes.Ψrandom is preferable when the dstR has higher priority compared to the valR, otherwise, Ψcentral should be chosen. However, the complex formulation is more appropriate when we have large scale networks. The partial conclusion, considering more realistic real-time scenarios, is that the complex formulation is more appropriate, because the deadlines are met in all cases and the data representativeness is kept.Error evaluations suggest that the simplified formulation is more appropriate for small networks and the complex formulation is more scalable. In general, 6.3.ad = min/d2) with concurrent traffic. We use a 128-node network (we do not consider more nodes due to NS limitations), and vary the percentage of nodes generating data traffic  and |V| . The objective of this scenario is to identify the best strategy in critical applications when the network traffic gradually increases.This scenario considers 50% of minimum deadlines . The reason is that the complex formulation executes fewer consecutive Ψ-reductions. Φ ≈ 20%, note the increase in terror, compared to previous scenarios (Φ ≈ 5%). The reason is that in both formulations there more consecutive Ψ-reductions affecting data quality. Therefore, considering the confidence interval, both Ψ-reductions have the same behavior. Again, when the percentage of nodes generating data is high, the simplified formulation has a smaller Φ-error.Ψ-reduction strategies.The data error evaluation suggests that the simplified formulation is slightly better than the complex one. However, the partial conclusion, considering this critical and realistic real-time scenario, is that the complex formulation is more appropriate, because deadlines are met and data representativeness is kept. Considering the sampling algorithms, the behavior is kept in both 6.4.ad = mind, concurrent traffic, and all relay nodes delay the stream fragments at 0.01% of the ad. Again, we use a 128-node network and vary the percentage of nodes generating traffic  and |V| . TheThe last scenario considers objective of this scenario is to identify the best strategy when the relay nodes have extra tasks with high priority and the network has a traffic that gradually increases.ad is met in most cases. The complex formulation presents a more scalable behavior considering the percentage of nodes generating data. This occurs because the Ψ-reduction estimation [ad, i.e., if a ≥ dmind the Ψ-reduction cannot be efficient, when we consider other delay aspects, like concurrent traffic.timation  is relatV| = 256. Simplified and complex formulation are presented by using Ψcentral and Ψrandom. ≤ 40%. The Ψ*central, in complex formulation, has a smaller ϒ-error. The reason is that the complex formulation performs the maximum Ψ-reduction sooner . This result shows that because fewer successive *-reductions are performed, more representativeness is kept in the reduced data, i.e., data degradation is mitigated.Φ ≤ 30%. The complex formulation with Ψcentral presents Φ ≈ 5%. The reason is that the Ψcentral has a smaller Φ-error because the central elements choice improves the average test and the complex formulation performs the maximum Ψ-reduction early.Ψcentral strategy. The partial conclusion, considering this scenario, is that the complex formulation is actually more appropriate, because the deadlines are met in all cases while keeping data representativeness. Considering the sampling algorithm, the Ψcentral strategy with complex formulation is always indicated.The errors evaluation suggest that the complex formulation is more appropriate with the 7.In real-time applications of wireless sensor networks, the time used to deliver sensor-streams from source to sink nodes is a major concern. The amount of data in transit through these constrained networks has a great impact on the delay. In this work, we presented a data-centric strategy to meet deadlines in soft real-time applications for wireless sensor networks. This work represents shows how to deal with time constraints at lower network levels in a data-centric way.With our data-centric strategy we met application deadlines in several scenarios. In additional, we showed how to design real-time sensor-stream reduction applications and a analytical model used to found the ideal sample size. Results showed the efficiency of the strategy by reducing the delay without losing data representativeness. If the application is not strongly dependent on data accuracy, or the network operates in exception situation , then data reduction algorithms are powerful tool for real-time applications for resource-constrained networks.O(n), by considering some rank selection algorithms.As future work, we intend to match the proposed application-level solution with lower-level ones, for example, by considering some real-time-enabled signal processing method. In this case, not only data from a source is reduced, but similar data from different sources is also reduced, resulting in a more efficient solution. Another future work is to use feedback information to enable the source nodes to perform the reduction sooner. However, we intend to improve the central sampling algorithm complexity to