dataesr/scientific-paragraphs-categorization huggingface dataset:
The result of our calculations are shown in Figure  10 , where the two black lines correspond to the two coloron acceptances, and the CMS excluded region in yellow is based on a 7 TeV dataset of 2. 2 fb -1. The curves show that in the asymmetric case, this search is potentially relevant due to the fairly large cross sections obtained in this case. Assuming the coloron acceptance, the bound on m KK is expected to range from 380 to 540 GeV, a region which is close to the dilepton channel. Moreover, this bound is only based on half of the total 2011 dataset. The blue dashed lines in the plot show the predicted cross section at 8 TeV. In the symmetric case, the prospect is much more difficult: in fact, the cross section is heavily suppressed because it only receives contribution from the pair production channels, and we expect a bound in the 300 GeV mass region, thus well below the dilepton channel.
III. THE PROPOSED OPTIMIZATION METHODOLOGY FOR MAKING THE SIMULTANEOUS DESIGN OF TWO MACHINES SHARING COMPONENTS: In this paper we propose to use of the OM with an optimization algorithm able to solve the following generic problem:  Minimizing an objective function that is one of the outputs of our OM:  (2)   With the outputs of the OM that can be constrained or fixed:  With the inputs of the OM that can be constrained or fixed: From a theoretical and practical point of view, the difficulty is that the number of inputs and outputs can be quite high, especially when we want to make the simultaneous design of several machines sharing components, since the number of parameters will increase with this number of machines and this even if some parameters are shared. That is why we propose here to use the methodology described in  [3]  and implemented in the CADES software  [4].
This methodology is particularly efficient for solving optimization problems of electromagnetic devices with a high number of input and output parameters and constraints. The principle is: 1° The designer has to give the model as a "white box" to a generator (a kind of compiler). "White box" means that the designer will give all the algebraic equations of the model of the device in a declarative language (called in CADES the SML language for System Modeling Language). Then the generator, thanks to an automated process, creates a code that computes the model. Moreover, as the generator produces computation code, it also obtains the derivatives of the equations and produces the sensitivity computation code. This has been done with sophisticated approaches likes symbolic computation, or Automatic Code Differentiation.
VI. VALIDATION OF THE DESIGN Since the optimization model is an analytical, or semi analytical model, a verification of the optimal design produced must be made. This can be done efficiently by using a finite element model. Here, we used the EFCAD software as a validation model considering the 6 pole pairs 3 kW /350 rpm PMG  [11]. shows that the flux densities defined in the project (see Table  I ) are achieved. The main input specifications of the 3 kW/350 rpm generator that will be checked are the phase-tophase voltage, the electromagnetic torque and the load power. To verify these specifications we used a module of EFCAD that connects the finite elements model to an external three-phase resistive load, star connected. This is a time varying simulation at fixed speed; hence steady state results are attained after only a few cycles.
Protein structure prediction from intra-protein contacts Transmembrane (TM) proteins are important targets for computational modeling methods, as they are -despite recent progress -significantly underrepresented in the Protein Data Bank  [44]. It has been estimated that around 25-30% of proteins in human body are TM proteins  [45, 46]. Unfortunately, since TM proteins are usually very large water insoluble molecules anchored in the lipid bilayer, their extraction, crystalization and analysis are difficult tasks. Currently only 2% of structures stored in PDB belong to transmembrane proteins, according to PDBTM service  [47] , as of April 2012. The lack of experimental structures cannot be compensated by template-based modeling (homology and threading), which is estimated to cover no more than 10% of all human TM proteins  [46].
Widely-used de novo approaches to structure prediction usually rely on exploration of protein conformational space by utilizing existing knowledge (such as database of fragments), and evaluation of candidate solutions by minimizing energy functions  [45, [48] [49] [50] [51] [52]. Successful predictions by these methods are currently limited to proteins up to 200-300 amino acids long because computational power limits the size of the conformational phase space that can be searched, typically 20,000-200,000 models per protein  [53, 54]. It was suggested that prediction of larger protein domains would become possible upon introduction of additional constraints to the conformational space  [55] , such as accurately predicted residue contacts  [56, 57]. Since contacts between distant residues tend to determine the overall global protein structure, prediction of these molecular contacts has been recognized early as a promising strategy in predicting the three-dimensional structures of proteins  [48, [58] [59] [60].
Recently, Marsico et al. [90]  developed a database of sequential motifs in transmembrane proteins using a structural fragment clustering method. While they found 213 statistically significant non-redundant motifs specific to α-helical transmembrane proteins, only 5 of them were assigned a role in helix-helix packing. Helices have smaller crossing angles in membrane proteins than in water soluble proteins, which is consistent with the requirements of structural compactness and membrane spanning  [88]. The helix-helix packing mode in transmembrane proteins was quantitatively studied by  [83]. They represented the mutual orientations of local axes by a single parameter. It was showed that a specific range of parameter values is preferred for helices of anti-parallel orientation. However, interactions between helices of parallel orientation appeared to be less constrained.
Probabilistic model of general protein sequences Since a protein is generally defined by a string composed of 20 different characters (amino acids), a protein grammar is expected to rely on a large set of terminals. We proposed to utilize physico-chemical properties of amino acids, collected from the Amino Acid index database (AAindex)  [121] [122] [123] [124] , to reduce significantly the number of possible combinations of the Right-Hand Side symbols in production rules  [37, 115]. Relations expressed by these rules refer to 3 levels of a quantitative property instead of 20 amino acid types, e. g. small, medium or large van der Waals volume. In this way, a number of rules, which is maintainable in the learning process, is kept. For each given property, our method relies on defining all the rules of the form A → a (called terminal rules) and associating them with proper probabilities, which are calculated using the known quantitative values pval associated with the amino acid identities.
Overview The Walters and DeGrado dataset of transmembrane helix-helix contacts  [91] , referred as WDG, contains 445 interacting transmembrane helix-helix pairs whose length varies from 10 to 14 residues per helix. In this study, we only considered the 4 most populous (67% of all cases) types of contact sites out of 14 created by the authors. Those 4 classes, that are referred as c1-c4, contain 300 pairs  (130, 71, 57, 42  in classes 1-4, respectively). The other classes were omitted because they do not include sufficient number of members for automated training of classifiers. We define a helix pair as anti-parallel if residues in the N-terminus of the first helix interact with residues in the C-terminus of the other helix. Analogically, if residues in the N-terminus of the first helix interact with residues in the N-terminus of the other helix, we call such a helix pair parallel.
Class 3 (13% of the dataset) is the parallel version of class 2. It has the largest average crossing angle (38 • ±8), while the average geometrical distance is the shortest (7. 9±0. 9 Å) among the four classes. Similarily to class 2, GxxxG motif is typically present on one of the two helices. Finally, class 4, which accounts for 9% of the helix pairs, has a parallel configuration resembling class 1. Reversely to class 3, it has the smallest average crossing angle (14 • ±17) and the largest average geometrical distance (9. 8±1. 2 Å). Interestingly, no position specific propensities for small residues were found in this class by  [91]. The number of transmembrane protein structures in the PDB database  [44]  has increased significantly since mid 2006, when  [91]  research was completed. Therefore, we created a new PDBTM dataset based on the PDBTM database  [47].
To avoid closely homologous structures, only 285 non-redundant (at 40% identity) alpha-helical chains were extracted from the PDBTM database (as of 30th November 2009). Note that contacts between helices from two chains in homo-oligomeric proteins are not represented in this dataset. Helix pairs with at least 1 residue in contact, according to Promotif3  [134]  definition, were searched. This procedure resulted in the dataset, referred as PDBTM, containing 641 whole helices involved in contacts.
Construction of datasets For each of the four main classes c1-c4, the helix-helix pair acting as centroid (3D template) in the WDG dataset was selected as class representative. Since processing helix pair sequences of varying lengths introduces an extra level of complexity, which may lead to a decrease in performance, we first truncated those templates to the length of 10-10 residues using a criterion of the most concise geometrical representation (least sum of inter-helical spatial distances between Cα atoms), see Additional file 2: Figure  S2. Then we aligned all WDG and PDBTM pairs to the WDG class centroids and the best match over 10-10 residue length was calculated according to RMSD. Then the fragments were assigned to the four classes according to a RMSD cutoff threshold of 1. 50 Å, as in  [91] , in order to keep only the best pairs.
While helical pairs in the PDBTM datasetwere assigned to Walters and DeGrado classes, the acceptance rate of helix pairs to a given WDG contact site class, in function of the RMSD cutoff, appeared to be almost linear for the range of thresholds from 1 to 2. 5 Å(see Additional file 3: Figure  S3 ). We surmise that the conformation space of transmembrane helix-helix contact sites may be continuous with classes c1 and c2, respectively c3 and c4, merging into a unique anti-parallel, respectively parallel, class. Therefore, the WDG classes could be seen as a way of quantitizing the space of helical pair configurations. This resulted in two datasets: In order to evaluate this, we counted the number of sequences in WDG150NR having at least one intra-class or inter-class neighbor whose identity was between 20% and 40%.
We found that 70% of sequences have an intraclass neighbor, while 86% have an inter-class neighbor in that identity range. This shows that sequence identity with the 20-40% range does not implicate contact class membership, although we observed that shared sequence identity increased grammar performance (see Analysis and discussion). • WDG150NR: A set The datasets are summarized in Table  1. Note that percentages of helix-helix contact sites from WDG and PDBTM datasets assigned to the four classes were similar for the most populous classes 1 and 2. Class 4 was overrepresented in the PDBTM at the expense of class 3 (see Additional file 2: Figure  S2 ).
Leave-one-out cross-validation Performance of single grammar classifiers was analysed in the Leave-One-Out Cross-Validation scheme with the WDG150NR dataset. The correctness of the leave-oneout procedure was assured by the non-redundant design of the set. Only one grammar was trained for each subset and amino acid property using all but one positive sample of a given class of helix pairs. The performance of the classifiers was tested on the one remaining positive sequence from that class and all negative sequences from the 3 other classes (class-vs-3 classification). The classifiers were evaluated on the basis of their average AUC ROC which in the case of LOOCV is equal to Specificity at the threshold equal to the score of the only positive sample (Table  2 ). The best average AUC ROC in the WDG150NR ranged from 0.
Four-fold cross-validation (4-fold CV) was carried out on the same dataset. The division was made according to alphabetical order of helix pair identifiers derived from the PDB codes. For each of the 4 helix-helix contact site classes and 2 selected amino acid properties (8 cases in total), 3 grammars were generated using 3/4 of positive samples (Note that, despite using the same set of parameters, GA usually produces different solutions in each run). Moreover, combined grammar classifiers were created by averaging scores (log probabilities) assigned to helix pairs by 3 grammars trained for the same class and amino acid property. Performance of the single and combined classifiers was tested on the remaining 1/4 positive sequences and all negative sequences in the dataset. The predictive power was assessed in class-vs-3-other-classes classification.
Test on independent dataset Grammars infered in 4-fold CV using the WDG150NR dataset were applied to classification of helix-helix contact fragments in the PDBTM150NRdataset, created by us independently (Table  1 ). Multiple grammar classifiers, combined single grammars and best single grammars according to 4-fold CV were evaluated (Table  4 ). The best results were obtained by the combined van der Waals-based grammar of class 3 (AUC ROC of 0. 60) and the combined accessibility-based grammar of class 4 (AUC ROC of 0. 57). In these cases performance in the PDBTM150NR matched performance in the WDG150NR. Single grammars which performed best inWDG150NR achieved ca. 20% worse results in the PDBTM150NR. All grammar classifiers trained for class 1 and 2 performed poorly in the PDBTM150NR. There was no significant benefit when the multiple grammar classifiers were applied.
Training on PDBTM dataset Noticeably worse results, when the PDBTM150NR was used for testing, could indicate some incoherence between the WDG150NR and PDBTM150NR datasets. The hypothesis was investigated in the opposite scenario, where the whole PDBTM150NR was used for training and the whole WDG150NR was used for testing (Table  5 , left). If PDBTM150NR's sequence patterns coverage is wider than WDG150NR's, performance similar to 4-fold CV (Table  3 ) is expected. Indeed, the classifiers obtained in this way showed better performance in the WDG150NR than combined grammars trained in the WDG150NR and tested in the PDBTM150NR datasets for classes 1 and 2 (10-20%, Table  4 ). Performance of grammars for classes 3 and 4 was similiar. In general, these results support the hypothesis that PDBTM150NR, while coherent with WDG150NR in terms of spatial similarity (RMSD), covers a wider space of sequence patterns.
The idea behind this test was to demonstrate that the helix-helix contact site classification could not be solved trivially by applying BLASTP to find similar sequences. For each helix-helix contact site class, its training set was used as a query and respective test set as a subject (or database). Subject sequences belonging to the same contact site class as the query sequences were considered as positive, while the others were considered as negative. For each subject sequence (positive or negative), the highest scoring hit (in terms of bit score  [136] ) to a query sequence was recorded. Where BLASTP did not find any hit (despite practically unlimited E-value), a bit score equal to zero was assigned. Subject sequences were ranked according to bit scores so that ROC curves could be calculated analogously to usage of grammar scores in the case of PCFGs.
Processing In our previous tests, sequences were preprocessed so that fragments from each helix of the pair were flanked by special symbols that were exploited by our method (see a rule for non-terminal Turn in Eq. 22). This information is redundant for the closest neighbor method which is based on complete alignments. On the contrary, the flanking could have been potentially useful for BLASTP and HMMER, however non-FASTA symbols had to be removed from datasets processed by these tools. Thus, the BLASTP and HMMER methods worked on concatenated sequences of helix fragments. In addition, we tested an approach where after initial processing of each helix independently, bit scores for two parts (fragments) forming the pair were summed. Moreover, it was possible to modify HMMER 2. 3. 2 source code to allow a special divider symbol between helix fragments; thus the amount of alignment information used by the tool was identical to that exploited by our grammars.
This demonstrates that the helix-helix contact site classification problem is out of scope of a simple sequence similarity search and requires a more powerful solution. Figure  3  shows that combined PCFGs outperformed Profile HMMs from HMMER packages, especially when trained on the PDBTM150NR dataset. In the most direct comparison, the combined PCFGs were better than HMMER2s divider by 5 to 10% in both dataset configurations. In thePDBTM150NR training and WDG150NR testing setups, the combined grammar classifiers outscored HMMER3 local 2-parts by ca. 10%. Moreover, in the same setups, PCFG best of 3 achieved about 20% larger AUC ROC than HMMER3 local 2-parts best of 3. Finally, performance of PCFGs and Profile HMMs are compared to results of the MSAbased strategy. In the case of 4-fold CV, the combined grammars and the HMMs matched the closest neighbor reference approach despite lacking complete alignment information.
Analysis and discussion We have demonstrated the capability of grammar classifiers to learn helix-helix contact site classes from sequences in the WDG150NR dataset. The results were consistent between LOO and 4-fold CV. While the average performance in terms of AUC ROC was moderate (approximately 0. 60), this improved to 0. 65 when the helix pair classification problem was treated explicitely as a 4-way classification (multiple grammar classifiers, Table  4 ). Testing in the independent PDBTM150NR dataset has shown 20% worse performance. This could indicate that sequence based features, distinctive to the four helix-helix contact site classes, may not be as well defined in the PDBTM150NR as in the original WDG150NR dataset (see also Additional file 1: Figure  S1 ). We demonstrated that the helix-helix contact site classification problem cannot be solved by a simple BLAST search and requires a more powerful solution.
The combined grammar classifiers outperformed state-of-the-art Profile HMMs from the HMMER2 and HMMER3 packages in the 4-fold CV in WDG150NR dataset. Moreover, our PCFG method was the only which learnt from PDBTM150NR to classify the WDG150NR sample for all four contact site classes. Comparison with reference results of the MSA-based closest neighbor in the training set approach demonstrated the grammar induction ability of generalization over the training sample. http://www. almob. org/content/8/1/31 In the next section, we will investigate the foundations of grammar classifiers performance and their relations to helix pair features. Moreover, correspondence between grammar structures and spatial configuration of helix pairs is assessed.
Therefore, grammar descriptors generated for classes 3 and 4 cannot be directly interpreted as in the case of anti-parallel pairs. Alternative strategy could rely on reversing of sequence direction in one helix of the parallel pair. Then, for an unknown pair of helices, both cases (normal and reversed direction of one of the helices) could be evaluated. Learning scheme Noticeable better performance of the best single grammars, in comparison to combined (averaged) grammars (Tables  9  and 5 ), suggests that our framework could benefit from further development of the evolutionary inference scheme in order to assure obtaining solutions consistently close to the global optimum. As an alternative, limitations of the current grammar induction process could be complemented by selecting the best grammar classifier from several trained candidates by means of validation, especially if more comprehensive datasets are available.
Dataset The Walters and DeGrado  [91]  classification of helical pairs in transmembrane proteins was the first attempt to systematic identification of helix-packing geometries with their encoding sequence motifs. Moreover, despite recent interest in helix packing in transmembrane proteins, their approach has not been superceded by up-to-date works  [90, [145] [146] [147]. Therefore, it was natural do adopt the WDG classification as the basis for our research. An apparent limitation of this dataset is its relatively small size. This did not allow us to induce grammar classifiers for less populous WDG classes of helix-helix arrangements which contain 1/3 of the sample. Moreover, interpretation of results for small classes 3 and 4 is less dependable. Therefore, we attempted to enlarge the available dataset using PDBTM database  [47].
Conclusions We presented an original probabilistic grammatical model of a protein language. The model covers the lexical (primary structure) and syntactical (secondary and tertiary structure) levels of protein linguistics. The core of the model consists of a probabilistic context-free grammar, whose rule probabilities are automatically inferred by a genetic algorithm from positive training samples only. In this process, an initially large generic set of rules is reduced to include only those rules which are relevant. We demonstrated the capability of the context-free framework for analysis of protein sequences. Sequence based grammar descriptors, which represented four classes of transmembrane helix-helix contact configurations, defined by Walters and DeGrado  [91] , were induced and tested using cross-validation on a modified non-reduntant version of their original dataset  [91].
The predictive power was assessed in class-of-interest versus other classes classification. The quality of the grammar classifiers was primarily evaluated in terms of Area Under ROC curves. The highest performance of the combined grammars (averaging over three single grammars) reached AUC ROC of 0. 68 (average over the four classes 0. 60). Moreover, best single http://www. almob. org/content/8/1/31 grammars achieved AUC ROC of 0. 71 (average over the four classes 0. 67). In addition, when the helix pair classification problem was treated explicitely as a 4-way problem of assigning a helix pair to one of the four most populous classes, our multiple grammar classifiers achieved an average AUC ROC of 0. 65. The grammar classifiers were then tested on a independent dataset obtained from the PDBTM database  [47].
The performance was 20% lower (best AUC ROC of 0. 60). We found that the sequence-based features distinctive to the four helix-helix contact classes in the Walters and DeGrado dataset are likely to be less well defined in the PDBTM-derived dataset. However, when PDBTMderived dataset was used for training and WDG-derived dataset served as the test sample, grammar classifiers achieved an average AUC ROC of 0. 58. This result is significant since all standard approaches, including Profile HMMs, obtained in this setting AUC ROC below 0. 55. The advantage of our probabilistic context-free framework for analysis of protein sequences over the current state of the art seems to be grounded in representing helix periodicity. While this feature does not require modeling long range dependencies, its implementation is facilitated by the context-free framework.