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Annotation Multilingual and Disambiguation of Discourse Connectives for Machine Translation Thomas Meyer and Andrei Popescu-Belis Idiap Research Institute Rue Marconi 19, 1920 Martigny, Switzerland Thomas.Meyer@idiap.ch, Andrei.Popescu-Belis@idiap.ch Sandrine Zufferey and Bruno Cartoni Department of Linguistics, University of Geneva Rue de Candolle 2, 1211 Geneva 4, Switzerland Sandrine.Zufferey@unige.ch,...

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Annotation Multilingual and Disambiguation of Discourse Connectives for Machine Translation Thomas Meyer and Andrei Popescu-Belis Idiap Research Institute Rue Marconi 19, 1920 Martigny, Switzerland Thomas.Meyer@idiap.ch, Andrei.Popescu-Belis@idiap.ch Sandrine Zufferey and Bruno Cartoni Department of Linguistics, University of Geneva Rue de Candolle 2, 1211 Geneva 4, Switzerland Sandrine.Zufferey@unige.ch, Bruno.Cartoni@unige.ch Abstract spective helps to improve the accuracy of annotation, and how it helps to nd appropriate labels for automated processing and MT. Results from automatic annotation experiments, which are close to the state of the art, as well as feature analysis, help to assess the usefulness of the proposed labels. The paper is organized as follows. Section 2 explains the motivation of our experiments, and offers a wider perspective on our research goals, illustrating them with examples of translation problems which arise from ambiguous discourse connectives. Current resources and methods for discourse annotation are discussed in Section 3. Section 4 analyzes our experiments in manual annotation and in particular the inuence of the set of labels on the reliability of annotation. The automatic disambiguation experiments, the features used, the results and the analysis of features are described in Section 5. Section 6 concludes the paper and outlines future work. Many discourse connectives can signal several types of relations between sentences. Their automatic disambiguation, i.e. the labeling of the correct sense of each occurrence, is important for discourse parsing, but could also be helpful to machine translation. We describe new approaches for improving the accuracy of manual annotation of three discourse connectives (two English, one French) by using parallel corpora. An appropriate set of labels for each connective can be found using information from their translations. Our results for automatic disambiguation are state-of-the-art, at up to 85% accuracy using surface features. Using feature analysis, contextual features are shown to be useful across languages and connectives. 1 Introduction Discourse connectives are generally considered as indicators of discourse structure, relating two sentences of a written or spoken text, and making explicit the rhetorical or coherence relation between them. Leaving aside the cases when connectives are only implicit, the presence of a connective does not unambiguously signal a specic discourse relation. In fact, many connectives can indicate several types of relations between sentences, i.e. they have several possible senses in context. This paper studies the manual and automated disambiguation of three ambiguous connectives in two languages: alors que in French, since and while in English. We will show how the multilingual per- 2 2.1 Explicit Connectives and their Translation Three Multi-functional Connectives Discourse connectives form a functional category of lexical items that are used to mark coherence relations such as Cause or Contrast between units of discourse. Along with other function words, many connectives appear among the most frequent words, as shown for instance by counts (Cartoni et al., 2011) over the Europarl corpus (Koehn, 2005). The Penn Discourse Treebank (Prasad et al., 2008) (see Section 3.1 below) includes around 100 connective types, but the exact number varies across studies, 194 Proceedings of the SIGDIAL 2011: the 12th Annual Meeting of the Special Interest Group on Discourse and Dialogue, pages 194203, Portland, Oregon, June 17-18, 2011. c 2011 Association for Computational Linguistics depending on the discourse theory used to classify them. Among these types, Pitler et al.(2008) have shown that most of them are unambiguous and easy to identify, but others, especially temporal ones, often signal multiple senses depending on their context. Following the terminology of Petukhova and Bunt (2009, Section 2), we are interested here in sequential multi-functionality, i.e. the fact that the same connective can signal different relations in different contexts. We do not deal with simultaneous multi-functionality, i.e. the possibility for a single occurrence to signal several relations, which has been less frequently studied for connectives (see Petukhova and Bunt (2009) for the discourse usage of and). We identied the two English connectives while and since, along with the French connective alors que, as being particularly problematic because they are highly multi-functional, i.e. they can signal multiple senses. For alors que, a French database of connectives (LexConn (Roze et al., 2010), see Section 3 below) contains examples of sentences where alors que expresses either a Background or a Contrast relation. For the English connective since, Miltsakaki et al. (2005) identied three possible meanings: Temporal, Causal, and simultaneously Temporal/Causal. For while, even more senses are observed: Comparison, Contrast, Concession, and Opposition. In fact, in the Penn Discourse Treebank, the connective while is annotated with more than twenty different senses. 2.2 To support this hypothesis, we set up an experiment (Meyer, 2011) in which we constrained the translation of the three senses of the discourse connective while that were previously annotated as Temporal, Contrast and Concession. The system was forced to use predened French translations known to be correct, by directly modifying the phrase table of the trained MT system. This modication noticeably helped to improve translation quality and rose the B LEU score by 0.8 for a preliminary test set of 20 sentences. 2.3 Among the connectives that we plan to process in order to improve MT, the three connectives we focus on in this paper are frequent, ambiguous and therefore difcult to translate correctly by MT systems, as illustrated in the following examples. A rst reason why machine translation of connectives can be difcult is that there may be no direct lexical correspondence for the explicit source language connective in the target language, as shown in the reference translation of the rst example in Table 1, taken from the Europarl corpus (Koehn, 2005). EN FR EN FR Wider Research Objectives Our long-term goal is to identify automatically the senses of connectives for an application to machine translation (MT). Going beyond the labels provided by discourse theories, the goal is thus to nd the most appropriate labels in a new multilingual, empirical approach that makes use of parallel corpora to annotate and then learn the various senses of connectives. The disambiguation of such connectives in a source text is crucial for its translation, because each sense may be translated by a different connective and/or syntactical construct in the target language. More specically, we hypothesize that correctly labeled connectives are easier to learn and to translate by statistical MT systems than unlabeled ones. 195 Illustration of Mistranslations FR EN EN FR It is also important that we should not leave these indicators oating in the air while congratulating ourselves on the fact that we have produced them. Il est egalement important de ne pas laisser ces indicateurs otter, en nous f licitant de les avoir instaur s. e e Finally, and in conclusion, Mr President, with the expiry of the ECSC Treaty, the regulations will have to be reviewed since [causal] I think that the aid system will have to continue beyond 2002 . . . *Enn, et en conclusion, Monsieur le pr sident, a e ` lexpiration du trait ceca, la r glementation devra etre e e revu depuis que [temporal] je pense que le syst` me daides e devront continuer au-del` de 2002 . . . a Oui, bien entendu, sauf que le d veloppement ne se n gocie e e pas, alors que [contrast] le commerce, lui, se n gocie. e *Yes, of course, but development cannot be negotiated, so [causal] that trade can. Between 1998 and 1999, loyalists assaulted and shot 123 people, while [contrast] republicans assaulted and shot 93 people. *Entre 1998 et 1999, les loyalistes ont attaqu et abattu e 123 personnes, 93 pour les r publicains. e Table 1: Translation examples from Europarl. Discourse connectives, their translations, and their senses are indicated in bold. The rst example is a reference translation from EN into FR, while the others are wrong translations generated by MT (EN/FR and respectively FR/EN), hence marked with an asterisk. When an ambiguous connective is explicitly translated by another connective, the incorrect rendering of its sense can lead to erroneous translations, as in the second and third examples in Table 1, which are translated by the Moses SMT decoder (Koehn et al., 2007) trained on the Europarl corpus. The reference translation for the second example uses the French connective car with a correct causal sense, instead of the wrong depuis que generated by SMT, which expresses a temporal relation. In the third example, the French connective alors que, in its contrastive usage, is wrongly translated into the English connective so, which has a causal meaning (the reference translation uses whereas to express contrast). It may even occur that the system fails to translate a connective at all, as in the fourth example where the discourse information provided by while, namely a Contrast relation, is lost in the French translation, which is hardly coherent any longer. 3 3.1 Related Work Annotated Resources One of the very few available discourse annotated corpora is the Penn Discourse Treebank (PDTB) in English (Prasad et al., 2008). For this resource, one hundred types of explicit discourse connectives were manually annotated, as well as implicit relations not signaled by a connective. The sense hierarchy used for annotation consists of three levels, from four toplevel senses (Temporal, Contingency, Comparison, and Expansion), to 16 subsenses on the second level, and 23 further ones on the third level. The annotators were allowed to assign more than one sense to each occurrence, so 129 simple or complex labels are observed, over more than 18,000 explicit connectives. For French, the ANNODIS project (P rye Woodley et al., 2009) will provide annotation of discourse on an original corpus. Resources for Czech are also becoming available (Zik nov et al., 2010). aa For German, a lexicon of discourse markers named DiMLex exists since the 1990s (Stede and Umbach, 1998). An equivalent, more recent database for French is the LexConn lexicon of connectives (Roze et al., 2010) containing a list of 328 explicit connectives. For each of them, LexConn indicates and exemplies the possible senses, chosen from a list of 30 labels inspired from Rhetorical 196 Structure Theory (Mann and Thompson, 1988). 3.2 Automatic Disambiguation of Connectives The release of the PDTB had quite an impact on automatic disambiguation experiments. The stateof-the-art for recognizing all types of explicit connectives in English is therefore already high, at 97% accuracy for disambiguating discourse vs. nondiscourse uses (Lin et al., 2010) and 94% for disambiguating the four main senses from the PDTB hierarchy (Pitler and Nenkova, 2009). Lin et al. (2010) recently built the rst end-to-end PDTB discourse parser, which is able to parse unrestricted text with an F1 score of 38.18% for senses on the second level of the PDTB hierarchy. Other important contributions to automatic discourse connective classication and feature analysis has been provided by Wellner et al. (2006) and Elwell and Baldrige (2008). Fewer studies focus on the detailed analysis of specic discourse connectives. In Section 5.3, we will compare our results to Miltsakaki et al. (2005) who report classication results for the connectives since, while and when. In their study, as in the present one, the goal is to disambiguate senses from the second level of the PDTB hierarchy, a level which, as we will show, is appropriate for the translation of these connectives as well. 4 Connective Annotation in Parallel Corpora The resources mentioned above are either monolingual only (PDTB, LexConn) and/or not yet publicly available (ANNODIS, DiMLex). Moreover, our overall goal is related to multilingualism and translation, as explained in Section 2.2 above. Therefore, we performed manual annotation of connectives in a multilingual, aligned resource: the Europarl corpus (Koehn, 2005). We extracted from Europarl two subcorpora for each translation direction, EN/FR and FR/EN, to take into account the varying distribution of connectives in translated vs. original language, as explained in Cartoni et al. (2011). As the full PDTB hierarchy seemed too negrained given current capabilities for automatic labeling and the needs for translating connectives, we dened a simplied set of labels for the senses of connectives, by considering their usefulness and granularity with respect to translation, focusing on those that may lead to different connectives or syntactical constructs in the target language. 4.1 Method There are two major ways to annotate explicit discourse connectives. The rst approach is to label each occurrence of a connective with a label for its sense, similar to the PDTB or LexConn hierarchies of senses. However, as shown among others by Zikanova et al. (2010), this is a difcult and timeconsuming task even when the annotators are trained over a long period of time. This is conrmed by the rather low kappa scores resulting from the manual sense annotations as can be seen for each connective in detail below. The second approach to annotation, which is the one put forward in this paper, is based on translation spotting. In a rst step, human annotators work on bilingual sentence pairs, and annotate the translation of each connective in the target language. The translations are either a target language connective (signaling in principle the same sense(s) as the source one), or a reformulation, or a construct with no connective at all. In a second step of the annotation, all translations of a connective are manually clustered by the experimenters to derive sense labels, by grouping together similar translations. As demonstrated in the following subsections, for the three connectives under study, the second approach to connective annotation not only facilitates the annotation task, but also helps to derive the appropriate level of granularity for the sense labels. 4.2 Annotation of alors que This rst manual annotation involved two experienced annotators who annotated alors que in 423 original French sentences. The two main senses identied for alors que are Background (labeled B) Contrast (labeled C), as in the LexConn database. Annotators were also allowed to use the J label if they did not know which label to assign, and a D label for discarded sentences due to a nonconnective use of the two words which could not be ltered out automatically (e.g. Alors, que fera-t-on? ). The annotators found 20 sentences labeled with D, which were removed from the data. 15 sentences were labeled with J by one annotator (but none by 197 both), and it was decided to assign to them the label (either B or C) provided by the other annotator. The inter-annotator agreement on the B vs. C labels was quite low, showing the difculty of the task: kappa reached 0.43, quite below the 0.7 mark often considered as indicating reliability. The following example from Europarl illustrates the difculty of choosing between B and C. In particular, the reference translation into English also uses an ambiguous connective, namely while. FR EN La monnaie unique va entrer en vigueur au milieu de la tourmente nanci` re, alors que de nombreux e compl ments, logiques, mais que les Etats ne seme blaient pas avoir pr vus, nont pas encore et ape e port s. e The single currency is going to come into force in the midst of nancial turmoil, while a great many additional factors which were only to be expected, but which the states do not seem to have anticipated, have not been taken into consideration. Two methods were applied to deal with diverging manual annotations. To prepare the datasets for the automated disambiguation experiments, one solution (named A1, see Table 2) is to use the doublesense label B/C for sentences labeled differently by annotators (B vs. C). This label reects the difculty of manual annotation and preserves the ambiguity which might be genuinely present in each occurrence. The relevance of the B/C label is also supported by results from automatic labeling in Section 5.3 below. For comparison purposes, a second dataset named A2 was derived from translation spotting on the same French sentences aligned to English ones, as explained in Section 4.1. Alors que appeared to be mainly translated by the following English equivalents and constructs: although, whereas, while, whilst, when, at a time when. Through this operation, inter-annotator disagreement can sometimes be solved: when the translation is a clearly contrastive English connective (whereas or although), then the C label was assigned instead of B/C. Conversely, when the English translation was still ambiguous (while, whilst, or when), the experimenters made a decision in favor of either B or C by re-examining source and target sentences. 4.3 Annotation of since For since, 30 sentences were annotated by four experimenters in a preliminary round, with a kappa ID A1 A2 B1 B2 C1 Connective alors que alors que since since while Sent. 403 403 727 727 299 C2 while 299 Labels (nb. of occ.) B (92), C (191), B/C (120) B (126), C (277) T (375), C (341), T/C (11) T (375), C (352) T/C (92), CONC (134), C (43) T/CAUSAL (19), T/DUR (7) T/PUNCT (4) T (30), C (135), CONC (134) Table 2: The six datasets resulting from the manual annotation of the three connectives, with total number of sentences, possible labels and their number of occurrences. The explanations of the labels are given in Sections 4.2 through 4.4. score of 0.77, indicating good agreement. Then, each half of the entire dataset (727 sentences) was annotated by another person with three possible sense labels: T for Temporal, C for Causal and T/C for a simultaneously Temporal/Causal meaning. Two datasets were again derived from this manual annotation. To study the effects of a supplementary label, we kept the label T/C for dataset B1, but condensed it under label C in dataset B2, as shown in Table 2. 4.4 Annotation of while The English connective while is highly ambiguous. In the PDTB, occurrences of while are annotated with no less than 21 possible senses, ranging from Conjunction to Contrast, Concession, or Synchrony. We performed a pilot annotation of 30 sentences containing while with ve different experimenters, resulting in a quite low inter-annotator agreement, = 0.56. We therefore decided to perform a translation spotting task only, with two experienced annotators uent in English and French. The observed translations into French conrm the ambiguity of while, as they include several connectives and constructs, quite evenly distributed in terms of frequency: alors que, gerundive reformulations, other reformulations, si, tandis que, m me si, bien que, e etc. The translations were manually clustered to derive senses for while, in an empirical manner. For example, alors que signals Temporal/Contrast, which is also true for tandis que. Similarly, m me si e and bien que are clustered under the label Conces198 sion, and so forth. The translation spotting shows that at least Contrast, Concession, and several temporal senses are necessary to account for a correct translation. These distinctions are comparable to the semantic granularity of the PDTB second hierarchy level. To generate training sets for automated classication out of a total of 500 sentences, we discarded 201 sentences labeled by annotators with G (gerundive constructions), P (reformulations) or Z (no translation at all) these cases could be reconsidered in further work, as they represent valid translation problems. For the remaining 299 sentences, we created the following six labels by clustering the spotted translations: T/C (Temporal/Contrast), T/PUNCT (Temporal/Punctual), T/DUR (Temporal/Duration), T/CAUSAL (Temporal/Causal), CONC (Concession) and C (Contrast). These were used to tag the remaining 299 sentences, forming dataset C1. A second dataset (C2) with fewer senses was obtained from C1 by merging T/C to C (Contrast only) and all T/x to T (Temporal only). 5 Disambiguation Experiments The features for connective classication, the results obtained and a detailed feature analysis are discussed in this section. We show that an automated disambiguation system can be used to determine the most appropriate set of labels, and thus to corroborate the selection we made using translation spotting. 5.1 Features For feature extraction, all the datasets described in Section 4 were processed as follows. The English texts were parsed and POS-tagged by Charniak and Johnsons (2005) reranking parser. The French texts were POS-tagged with the MElt tagger (Denis and Sagot, 2009) and parsed with MaltParser (Nivre, 2003). As the English parser provides constituency trees, and the parser for French generates dependency trees, the features are slightly different in the two languages. The other features below were extracted using elementary pre-processing of the sentences. For English sentences, we used the following features: the sentence-initial character of the connec- tive (yes/no); the POS tag of the rst verb in the sentence; the type of rst auxiliary verb in the sentence (if any); the word preceding the connective; the word following the connective; the POS tag of the rst verb following the connective; the type of the rst auxiliary verb after the connective (if any). For French sentences, the features were the following: the sentence-initial character of the connective (yes/no); the dependency tag of the connective; the rst verb in the sentence; its dependency tag; the word preceding the connective; its POS tag; its dependency tag; the word following the connective; its POS tag; its dependency tag; the rst verb after the connective; its dependency tag. The cased connective word forms from the corpus were not lower-cased, thus keeping the implicit indication of the sentence-initial character of the occurrence, i.e. whether it starts a sentence or not. The output of the POS taggers was used for neighboring words, but not for the connectives, which almost always received the same tag. Charniaks parser for English provides POS tags which differentiate the verb tenses, such as VBD (past), VBG (gerund), and so on. These were considered for the verb directly preceding and the one directly following the connective. Tense was believed to be potentially relevant because since and while can have temporal meanings. The occurrence of auxiliary verbs (be, have, do, or need) may give additional indications about temporal relations in the sentence. We therefore used the types of auxiliary verbs as features, including the elementary conjugations, represented for to be as: be present, be past, be part, be inf, be gerund and similarly for the other auxiliary verbs, as in (Miltsakaki et al., 2005). As shown by Lin et al. (2010), duVerle and Prendinger (2009) or Wellner et al. (2006), the context of a connective is very important. We therefore extracted the words preceding and following each connective, the verbs and the rst and the last word of the sentences. These may include numbers, sometimes indicating a numerical comparison, time expressions, or antonyms, which could indicate contrastive relations, such as rise vs. fall (e.g. It is interesting to see the fundamental stock pickers scream foul on program trading when the markets decline, while hailing the great values still abounding 199 as the markets rise.). For French, we likewise extracted the words immediately preceding and following each connective, supplemented by their POS tags. In contrast to constituents, dependency structures contain information about the grammatical function of each word (heads) and link the dependents belonging to the same head. However, as the dependency parser provides no differentiated verb tags, we extracted the verb word forms themselves and added their dependency tags. The same applies to the connective itself, and preceding and following words and their dependency tags. The dependency tag of the non-connectives varies between subj (subject), det (determiner), mod (modier) and obj (object). The rst verb in the sentence often belongs to the root dependency while the verb following the connective most often belongs to the obj dependency. For alors que, the most frequent dependency tags were mod mod and mod obj, indicating the connectives main function as a modier of its argument. 5.2 Experimental Setting Our classication experiments made use of the WEKA machine learning toolkit (Hall et al., 2009) to run and compare several classication algorithms: Random Forest (sets of decision trees), Naive Bayes, and Support Vector Machine. The results are reported with 10-fold cross validation on the entire data for each connective, using all features. Table 3 lists for each method including the majority classier as a baseline the percentage of correctly classied instances (or accuracy, noted Acc.), and the kappa values. Signicance above the baseline is computed using paired t-tests at 95% condence. When a score is signicantly above the baseline, it is shown in italics in Table 3. The best scores for each dataset, across classiers, are indicated in boldface. When these scores were not signicantly above the baseline, at least they were never signicantly below either. 5.3 Results and Discussion Overall, the SVM classier performed best, which may be due to the large number of textual features (3 for EN data and 5 for FR data), as SVMs are known to handle them well (Joachims, 1998; du- ID Connective # Labels A1 A2 B1 B2 C1 alors que alors que since since while 403 B, C, B/C C2 while B, C 727 T, C , T / C T, C 299 T/C, T / PUNCT, T / DUR , Baseline Acc. 46.9 68.7 51.6 51.6 44.8 R. Forest Acc. 53.1 0.2 69.2 0.1 79.8 0.6 80.7 0.6 43.2 0.1 N. Bayes Acc. 55.7 0.3 68.3 0.2 82.3 0.7 84.0 0.7 49.9 0.2 SVM Acc. 54.2 0.3 64.7 0.1 85.4 0.7 85.7 0.7 52.2 0.2 T / CAUSAL , CONC , C T, C , CONC 43.5 60.5 0.3 59.9 0.3 60.9 0.3 Table 3: Disambiguation scores for three connectives (number of occurrences in the training sets), with two sets of labels each, for various classication algorithms. Accuracy (Acc.) is in percentage (%), and kappa is zero for the baseline method (majority class). The best scores for each data set are in boldface, and scores signicantly above the baseline (95% t-test) are in italics. Verle and Prendinger, 2009). The maximum accuracy for alors que is 55.7%, for since it is 85.7%, and for while it is 60.9%. While close to other reported values, there is still potential for improvement in the future. The analysis of results for each data sets leads to observations that are specic to each connective. The high improvement of over the baseline for A1, as opposed to no improvement for A2, conrms the usefulness of the double-sense B/C label for alors que, showing that in this case the three-way classication is probably better adapted to the linguistic properties of alors que than a two-way classication. Indeed, alors que, just as its frequently spotted translation while, is linguistically ambiguous in some contexts (see for instance the example in Section 4.2), in which the temporal and the contrastive meaning are likely to co-exist. In the case of A2, where the labels were forced to B or C only, automatic classiers do not signicantly outperform the baseline. While more elaborate features might help, these low scores can be related to the difculties of human annotators (Section 4.2), and make a strong case against using a two-label schema for alors que. The features used so far lead to high scores for since in datasets B1 and B2. The results are comparable to those from Miltsakaki et al. (2005), who used similar features and labels, though with a Maximum Entropy classier. Moreover, they provide results for individual connectives, and not, as most of the related work for the PDTB, on the whole set of ca. 100 discourse connective types. However, 200 Miltsakaki et al. (2005) used their own datasets for each connective, which are different from the PDTB, because the PDTB was not available at that time. Our SVM classier outperforms considerably the Maximum Entropy classier on the three-way classication task (with T, C, T/C), with an accuracy of 85.4% vs. 75.5%, obtained however on different datasets. For the two-way classication (T, C), again on different datasets, our accuracy of 85.7% is slightly lower than the 89.5% given in Miltsakaki et al. (2005).1 For while, when comparing C1 to C2, it appears that reducing the number of labels from six to three increases accuracy by 8-10%. This is probably due to the small number of training instances for the labels T/PUNCT and T/DUR in C1 for example. However, even for the larger set of labels, the scores are signicantly above baseline (52.2% vs. 44.8%), which indicates that such a classier might still be useful as input to an MT system, possibly improved thanks to a larger training set. The performance obtained by Miltsakaki et al. (2005) on while is markedly better than ours, with an accuracy of 71.8% compared to ours of 60.9% with three labels. 5.4 Feature Analysis The relevance of features can be measured using WEKA by computing the information gain (IG) brought by each feature to the classication task, 1 In another experiment (Meyer, 2011), we also applied our classiers to the PDTB data, with less features however. The results were in the same range as those from Miltsakaki et al. (2005), i.e. 75.3% accuracy for since and 59.6% for while. R 1 2 3 4 5 5 5 8 8 10 10 12 Feature preceding word following verb rst verb following word preceding words POS tag rst verbs dep. tag following words POS tag preceding words dep. tag connectives dep. tag following words dep. tag following verbs dep. tag sentence initial IG A1 1.12 0.81 0.74 0.68 0.15 0.14 0.19 0.10 0.09 0.13 0.04 0.05 R Feature 1 2 3 4 5 6 7 preceding word following word following verbs POS tag type of following aux. verb type of rst aux. verb rst verbs POS tag sentence initial IG B1 0.83 0.56 0.24 0.13 0.11 0.02 0.00 preceding word following word type of rst aux. verb following verbs POS tag rst verbs POS tag type of following aux. verb sentence initial IG C1 C2 1.02 0.65 0.83 0.55 0.12 0.07 0.16 0.04 0.07 0.09 0.12 0.05 0.08 0.07 Table 6: Information gain (IG) of features for EN connective while, ordered by decreasing average ranking (R) in experiments C1 and C2. The rst two features are considerably more relevant than the remaining ones. Table 4: Information gain (IG) of features for French connective alors que, ordered by decreasing average ranking (R) in experiments A1 and A2. Features 14 are considerably more relevant than the following ones. R Feature 1 2 3 4 5 5 7 A2 0.64 0.51 0.42 0.23 0.05 0.06 0.03 0.03 0.04 0.013 0.03 0.001 B2 0.75 0.52 0.21 0.12 0.11 0.01 0.00 Table 5: Information gain (IG) of features for EN connective since, ordered by decreasing average ranking (R) in experiments B1 and B2. i.e. the reduction in entropy with respect to desired classes (Hall et al., 2009) the higher the IG, the more relevant the feature. Features can be ranked by decreasing IG, as shown in Tables 4, 5 and 6, in which ranks were averaged over the rst and the second data set in each series. The tables show that across all three connectives and the two languages, the contextual features are always in the rst positions, thus conrming the importance of the context of a connective. Following these are verbal features, which are, for these connectives, of importance because the temporal meanings are additionally established by verbal tenses. POS and dependency features seem the least help201 ful for disambiguation. 6 Conclusion and Future Work We have described a translation-oriented approach to the manual and automatic annotation of discourse connectives, with the goal of identifying their senses automatically, prior to machine translation. The manual annotation of the senses of connectives has been enhanced through parallel corpora and translation spotting. This has lead to tag sets that improved both inter-annotator agreement and automatic labeling, which reached state-of-the-art scores. The analysis of relevant features has shown the utility of contextual information. To improve over these initial results, we will use more semantic information, such as relations found in WordNet between words in the neighborhood of connectives e.g. word similarity measures and semantic relations such as antonymy. To generate more training instances of the labels found, manual annotation will continue in order to see whether the senses found through translation spotting can improve automatic disambiguation of many more connectives. The annotation of a large parallel corpus will then help to train disambiguation tools along with statistical MT systems that use their output. Acknowledgments We are grateful for the funding of this work by the Swiss National Science Foundation (SNSF) under the COMTIS Sinergia Project, n. CRSI22 127510 (see www.idiap.ch/comtis/). References Bruno Cartoni, Sandrine Zufferey, Thomas Meyer, and Andrei Popescu-Belis. 2011. How comparable are parallel corpora? Measuring the distribution of general vocabulary and connectives. In Proceedings of 4th Workshop on Building and Using Comparable Corpora, Portland, OR. Eugene Charniak and Mark Johnson. 2005. Coarse-tone n-best parsing and maxent discriminative reranking. In Proceedings of ACL 2005 (43rd Annual Meeting of the ACL), pages 173180, Ann Arbor, MI. Pascal Denis and Benot Sagot. 2009. Coupling an anno tated corpus and a morphosyntactic lexicon for stateof-the-art POS tagging with less human effort. In Proceedings of PACLIC 2009 (23rd Pacic Asia Conference on Language, Information and Computation), pages 110119, Hong Kong, China. David duVerle and Helmut Prendinger. 2009. A novel discourse parser based on support vector machine classication. In Proceedings of ACL-IJCNLP 2009 (47th Annual Meeting of the ACL and 4th International Joint Conference on NLP of the AFNLP), pages 665673, Singapore. Robert Elwell and Jason Baldridge. 2008. Discourse connective argument identication with connective specic rankers. In Proceedings of ICSC 2008 (2nd IEEE International Conference on Semantic Computing), pages 198205, Santa Clara, CA. Mark Hall, Eibe Frank, Geoffrey Holmes, Bernhard Pfahringer, Peter Reutemann, and Ian H. Witten. 2009. The WEKA data mining software: An update. ACM SIGKDD Explorations Newsletter, 11:1018. Thorsten Joachims. 1998. Text categorization with support vector machines: Learning with many relevant features. In Proceedings of ECML 1998 (10th European Conference on Machine Learning), pages 137 142, Chemnitz, Germany. Philipp Koehn, Hieu Hoang, Alexandra Birch, Chris Callison-Burch, Marcello Federico, Nicola Bertoldi, Brooke Cowan, Wade Shen, Christine Moran, Richard Zens, Chris Dyer, Ondrej Bojar, Alexandra Constantin, and Evan Herbs. 2007. Moses: Open source toolkit for statistical machine translation. In Proceedings of ACL 2007 (45th Annual Meeting of the ACL), Demonstration Session, pages 177180, Prague, Czech Republic. Philipp Koehn. 2005. Europarl: A parallel corpus for statistical machine translation. In Proceedings of MT Summit X, pages 7986, Phuket, Thailand. Ziheng Lin, Hwee Tou Ng, and Min-Yen Kan. 2010. A PDTB-styled end-to-end discourse parser. Technical Report TRB8/10, School of Computing, National University of Singapore, Singapore. 202 William C. Mann and Sandra A. Thompson. 1988. Rhetorical Structure Theory: towards a functional theory of text organization. Text, 8(3):243281. Thomas Meyer. 2011. Disambiguating temporalcontrastive discourse connectives for machine translation. In Proceedings of ACL-HLT 2011 (49th Annual Meeting of the ACL: Human Language Technologies), Student Session, Portland, OR. Eleni Miltsakaki, Nikhil Dinesh, Rashmi Prasad, Aravind Joshi, and Bonnie Webber. 2005. Experiments on sense annotations and sense disambiguation of discourse connectives. In Proceedings of the TLT 2005 (4th Workshop on Treebanks and Linguistic Theories), Barcelona, Spain. Joakim Nivre. 2003. An efcient algorithm for projective dependency parsing. In Proceedings of IWPT 2008 (8th International Workshop on Parsing Technologies), pages 149160, Tokyo, Japan. Marie-Paule P ry-Woodley, Nicholas Asher, Patrice e Enjalbert, Farah Benamara, Myriam Bras, C cile e Fabre, St phane Ferrari, Lydia-Mai Ho-Dac, Anne e Le Draoulec, Yann Mathet, Philippe Muller, Laurent Pr vot, Josette Rebeyrolle, Ludovic Tanguy, Marianne e Vergez-Couret, Laure Vieu, and Antoine Widl cher. o 2009. Annodis: une approche outill e de lannotation e de structures discursives. In Proceedings of TALN 2009 (16` me Conf rence sur le Traitement Automae e tique des Langues Naturelles), Paris, France. Volha Petukhova and Harry Bunt. 2009. Towards a multidimensional semantics of discourse markers in spoken dialogue. In Proceedings of IWCS-8 (8th International Conference on Computational Semantics), pages 157168, Tilburg, The Netherlands. Emily Pitler and Ani Nenkova. 2009. Using syntax to disambiguate explicit discourse connectives in text. In Proceedings of ACL-IJCNLP 2009 (47th Annual Meeting of the ACL and 4th International Joint Conference on NLP of the AFNLP), Short Papers, pages 1316, Singapore. Emily Pitler, Mridhula Raghupathy, Hena Mehta, Ani Nenkova, Alan Lee, and Aravind Joshi. 2008. Easily identiable discourse relations. In Proceedings of Coling 2008 (22nd International Conference on Computational Linguistics), Companion Volume: Posters, pages 8790, Manchester, UK. Rashmi Prasad, Nikhil Dinesh, Alan Lee, Eleni Miltsakaki, Livio Robaldo, Aravind Joshi, and Bonnie Webber. 2008. The Penn Discourse Treebank 2.0. In Proceedings of LREC 2008 (6th International Conference on Language Resources and Evaluation), pages 29612968, Marrakech, Morocco. Charlotte Roze, Laurence Danlos, and Phillippe Muller. 2010. LEXCONN: a French lexicon of discourse connectives. In Proceedings of MAD 2010 (Multidis- ciplinary Approaches to Discourse), pages 114125, Moissac, France. Manfred Stede and Carla Umbach. 1998. DiMLex: a lexicon of discourse markers for text generation and understanding. In Proceedings of ACL 1998 (36th Annual Meeting of the ACL), pages 12381242, Montreal, Canada. Ben Wellner, James Pustejovsky, Catherine Havasi, Roser Sauri, and Anna Rumshisky. 2006. Classication of discourse coherence relations: An exploratory study using multiple knowledge sources. In Proceedings of 7th SIGDIAL Workshop on Discourse and Dialogue, pages 117125, Sydney, Australia. S rka Zik nov , Lucie Mladov , Ji Mrovsk , and a aa a r y Pavlina Jnov . 2010. Typical cases of annotators a disagreement in discourse annotations in Prague Dependency Treebank. In Proceedings of LREC 2010 (7th International Conference on Language Resources and Evaluation), pages 20022006, Valletta, Malta. 203
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Santa Barbara City - ENG - 110
English 110 The Ku Klux Klan in the 1920's The Ku Klux Klan (also known as The KKK), is an organization of white protestants who were mainly prejudiced towards African Americans, with exceptions of other religions or race groups (Simkin). Other groups dis
Santa Barbara City - ENG - 110
A Thin Society Anorexia has transformed from a psychiatric eating disorder into a lifestyle. In "A Secret Society of the Starving", Mim Udovitch interviews multiple girls from different blog websites who are "Pro-Ana" or "Pro- Mia" (Udovitch 557). Pro Ana
Santa Barbara City - ENG - 110
A Thin Society Anorexia has transformed from a psychiatric eating disorder into a lifestyle. In "A Secret Society of the Starving", Mim Udovitch interviews multiple girls from different blog websites who are "Pro-Ana" or "Pro- Mia" (Udovitch 557). Pro Ana
Santa Barbara City - ENG - 110
Compton Cookout Gone Wrong At University California San Diego, a fraternity's intention to host a ghetto themed party named "Compton Cookout" was held to support black history month although it turned into an utter disaster. In "Racist Frat Boys Will Be R
Santa Barbara City - ENG - 110
Compton Cookout Gone Wrong At University California San Diego, a fraternity's intention to host a ghetto themed party named "Compton Cookout" was held to support black history month although it turned into an utter disaster. In "Racist Frat Boys Will Be R
Santa Barbara City - ENG - 110
Life in the Hard TimesAn abundant amount of soldiers in the recent Iraq war are surviving more than any previous war in history. Thanks to medical advancements in the last 20 years, the survival rate is higher than ever before, although the survivor's li
Santa Barbara City - ART - 100
Artist BiographyArtemisia Gentileschi was born in Rome the year of 1593. (1) The artist genes ran in the family, with her father being Orazio Gentileschi, a well know roman artist. Prudentia Gentileschi was her mother, who died when Artemisia was twelve.
Santa Barbara City - ART - 100
Interpretation EssayArtemisia Gentilesch Judith & her maidservant w/head of Holofernes (1625) After Artemisia's piece, Judith beheading Holofernes, the artwork masterpiece, Judith and her Maidservant was created. Originally in 1614, Artemisia created the
Santa Barbara City - ENG - 100
With the economy taking the downfall not showing much room for change, Google's business is doing just fine. The article "Brisk Ad Sales Spur Google in Third Quarter" found from the New York Times talks about how advertisers are promoting products or serv
Santa Barbara City - ENG - 100
A Female's Plump Nightmare Getting ready to check out at your local grocery store, you usually encounter the magazines with juicy headline stories about how your favorite actress gained 10 pounds and has cellulite on her thighs. In "Fat is a Feminist Issu
Santa Barbara City - ENG - 100
Just a Click Away Every time I go to the airport, the number of people on their cell phone astounds me but it makes me wonder what would happen if this privilege wasn't available. "What's the Matter with Kids Today" is an article which supports the argume
Santa Barbara City - ENG - 100
A Thin Society Anorexia has transformed from a psychiatric eating disorder into a lifestyle. In "A Secret Society of the Starving", Mim Udovitch interviews multiple girls from different blog websites who are "Pro-Ana" or "Pro- Mia" (Udovitch 557). Pro Ana
Santa Barbara City - ENG - 100
Obvious Intellectualism Throughout life some people learn material easily by reading a book and others by going through obstacles. Two types of smarts are street smarts and book smarts which are talked about in `Hidden Intellectualism' written by Gerald G
Santa Barbara City - ENG - 100
The Union's Best Friend In the past, Wal-Mart has had a bad reputation for treating employees poorly. Karen Olsson, author of "Up against Wal-Mart" documents how Wal-Mart employees are underpaid and unfairly treated. She gives examples of unhappy employee
Santa Barbara City - ENG - 100
`Don't be SelfishIn the article "It Doesn't Add Up", Michael Shermer writes about the idea of loss aversion and how people react. Various experiments tested insinuate how people act towards money and what people have around them. Michael says "research
Santa Barbara City - ENG - 100
A Female's Plump Nightmare Getting ready to check out at your local grocery store, you usually encounter the magazines with juicy headline stories about how your favorite actress gained 10 pounds and has cellulite on her thighs. In "Fat is a Feminist Issu
Santa Barbara City - ENG - 100
Extra CreditAccording to Yahoo news minorities are anticipated to be the new U.S majority in the next 40 years. Many Hispanics conceive more children than the average white family would, which constitutes the population difference the country is facing.
Santa Barbara City - POLY SCI - 101
Extra Credit ArticleIn the New York Times science section online the article, "Disaster awaits Cities in Earthquake zones", informs readers within the further decades, major cities in the Middle East could possibly result a tragedy earthquake- perhaps mo
Santa Barbara City - POLY SCI - 101
Checks and balances: throughout each branch of government is able to participate in the influence of the activities of other branches. Tyranny: oppressive government that employs cruel and unjust use of power and authority. Confederation: a system of gove
Santa Barbara City - POLY SCI - 101
Currently overseas in our world today, the Israelis and Arabs are fights over a strip of land called Gaza. David Makovsky and Ghaith Al-Omari are two men very much involved in the subject who presented to our lecture hall about "How America Can Bring Arab
Santa Barbara City - POLY SCI - 101
"The New Grand Old Party" At the age of seven or eight, I remember waiting in a doctor's office glancing at the magazine next to me. The headline read "Clinton's affair with Monica Lewinsky". Sadly enough, the first political event I remember was Clinton'
Santa Barbara City - POLY SCI - 101
Question 1 Marks: 1 An important reason for why public policy and public opinion may not coincide in the United States is that Choose one answer. a. the American system of government was designed to account for the elite's needs and demands. b. American s
Santa Barbara City - BMS - 128
Regulation of Energy Intake by-hunger, satiation, satiety, appetite Hunger-Prompts eating; physiological desire Satiation-Signals to stop eating Satiety-Lack of hunger Appetite-Psychological desire Hunger, Satiation, and Appetite Stimulants-Diet Compositi
Santa Barbara City - BMS - 128
INTRODUCTION The article "5 Strange Ways Chocolate Keeps You Healthy", published in Prevention in January 2012, presents claims that consumption of chocolate is not only beneficial for cardiovascular health and reduces the risk of stroke but also suggests
Santa Barbara City - BMS - 128
Quiz 1Chapter 11. Nutrition a. Science that links food to health & disease b. Process of ingestion, digestion, absorption, transportation, excretion 2. Factors that affect food choices a. Environmental b. Health status c. Sensory d. Cognitive e. Genetic
Santa Barbara City - BMS - 128
Carbohydrates-Formed during photosynthesis; Photosynthesis-6CO2 + H2O + energy=C6H12O6 + 6O2; Condensation-water is formed;hydrolysis-water is a reactant; Monosaccharides glucose, fructose, galactose; Glucose-Found in fruits, vegetables, honey; Fructose-F
Cal Poly - CHEM - 124
\Computer Number 14Using ExcelInstructions: This assignment is to be completed ON YOUR OWN OUTSIDE OFCLASS and is due at the beginning of class on Tuesday September 27, 2011.You are to fill in this form using Microsoft Word to create a clear and info
Cal Poly - CHEM - 124
Chem 124Computer # 27Assigned Metal: MagnesiumThe Heat of Combustion of MetalsInstructions: Each person is to submit an individual report after performing the experiment with your partner.This report is due at the beginning of class on Tuesday, Octob
Cal Poly - CHEM - 124
Chem 124Computer Number 27Falll 2011Dr. NeffThe Heat of Sublimation of Dry IceInstructions: This report is to be completed by each of you INDIVIDUALLY after performing theexperiment with your partner. This report is due at the beginning of class on
Cal Poly - CHEM - 124
Chem 124Name:Partner:Fall 2011Dr. NeffComputer #: 27Conductivity: LED ExperimentInstructions: Each person is to submit an individual report after performing the experiment. This report is dueat the beginning of class on Tuesday November 8th. You a
Cal Poly - BRAE - 216
Lab 2-Series and Parallel CircuitsBRAE 216Fall 2011Date Performed_9/29/11_Lab 2Series and Parallel Circuits1. Objectives:Build simple series circuit and simple parallel circuitAnalyze circuit with the following:o Digital mulitmetero Computer-Mul
Cal Poly - BRAE - 216
Lab 4 Battery CapacityBRAE 216Fall 2011Date Performed 10/13/11_Lab 4Battery Capacity ExperimentObjectives:Assemble and carry out experimentDownload and examine data collectedReceive an introduction to acquiring electronic data from experimentEqu
Cal Poly - BRAE - 216
Lab 6 Basic WiringBRAE 216Fall 2011_Date Performed 10/27/11_Lab 6Basic WiringObjectives:Learnoooobasic wiring procedureConduit installationWiring 3-way circuitsWiring duplex outletsGroundingEquipment:Electricity Project BoardEMT and fi
Cal Poly - BRAE - 216
Lab 7 3 phase Motor ControlBRAE 216Fall 2011Date Performed 11/3/11Lab 73-phase Motor Control CircuitObjectives:Learn basic wiring principlesEquipment:Motor starter Hp 3-phase induction motorPushbutton controlsSJ wirePlugsProcedures and Metho
Cal Poly - BRAE - 236
Irrigation System Tour LabOn September 21, 2011, the BRAE 236 class went out to the Irrigation Practices Field for a tour.Border Strip Irrigation: One border strip was irrigated for about 50 minutes.Furrow Irrigation: Two furrows were irrigated at one
Cal Poly - BRAE - 236
10/31/11BRAE 236-02Lab 6: Soil and Plant Water Determination LabOn Wednesday, November 26, 2011, the BRAE 236 lab went out to the Irrigation PracticesField to measure the soil moisture depletion.Mr. Gaudi talked to us about the importance of understa
Cal Poly - BRAE - 236
9/23/11BRAE 236-02Lab 3: Basic Pipeline HydraulicsOn Wednesday, October 5, 2011, the BRAE 236 lab went out to the Water Resources Facility tobuild PVC pipeline and run tests on it. PVC pipe, fittings, primer andcement were used to construct a PVC wat
Cal Poly - ENGL - 149
Chapter 2 iFixit Audience Analysis QuizN ame:_Kerilyn Ambrosini_ _W atch the iFixit vid eo fou nd here: h ttp :/ / w w w .vim eo.com / 12841361 (p assw ord is stu d entw ithou t the qu otes) or ath ttp :/ / w w w .ifixit.com / Info/ Stu d ent_Delivera
Cal Poly - PHYS - 133
N am e_Final Exam A(You m ay x out one problem for it to not be grad ed , otherw ise, the last problem w ill notb e grad ed .)P hysics 133Spring 2011Z am m it1. (10) A m etal ball of rad ius 2.0 m has 3.2 m C of charge. Find the charge d ensityfor
Cal Poly - PHYS - 133
7. Current is flow ing in the d irection show n. It is increasing. Show them agnetic flux in the transform er core. Show the d irection of the current in the25 r esistor. If the pow er supply provid es a sine w ave of 150 v for the peakv oltage, w hat
Michigan State University - ADV - 843
The complexity of "brands" and "brandingPeopleIndividual Rolesa. Ownersb. Brand Committee - Related to Brand Charter.c. Retailersd. RepA brand rep is another way of saying Sales Associate. Basically yourjob will consist of representing the brand o
Michigan State University - ADV - 843
ConceptsBasicsBrandA brand is the identity of a specific product, service, or business[1][pageneeded]. A brand can take many forms, including a name, sign, symbol,color combination or slogan. The word brand began simply as a way totell one person's
Michigan State University - ADV - 843
Types of brand names Acronym: A name made of initials such as UPS or IBM Descriptive: Names that describe a product benefit or function likeWhole Foods or Airbus Alliteration and rhyme: Names that are fun to say and stick in themind like Reese's Piec
Michigan State University - ADV - 843
l. Voice(See story and: http:/brandstory.typepad.com/writer/2007/01/thinking_about_.html)m. Characters(See: http:/www.knowthis.com/blog/postings/can-you-guess-the-topbrand- characters/)n. Advertisingo. Slogans(See: http:/www.buzzle.com/articles/fam
Michigan State University - ADV - 843
4. Sustainable- A strong brand makes a business competitive. Asustainable brand drives an organization towards innovation and success.Example of sustainable brand is Marks and Spencers.5. Credibility- A strong brand should do what it promises. The way
Michigan State University - ADV - 843
h. LicensingLicensing means renting or leasing of an intangible asset. Examples ofintangible assets include a song (Somewhere Over The Rainbow), acharacter (Donald Duck), a name (Michael Jordan) or a brand (The RitzCarlton). An arrangement to license a
Michigan State University - ADV - 843
d. HierarchyPaws for ThoughtThe ADAMS BlogAugust 5th, 2009The importance of brand hierarchyComplicated brands often need to be architected to be understood. If anorganization has more than one brand or one brand with several subbrands, they must be
Michigan State University - ADV - 843
Effectsa. Essence(Brand Essence is a way of articulating the emotional connection andlasting impression - usually summed up with one simple statement orphrase - that defines the qualities, personality and uniqueness of a brand.Said another way, Brand
Michigan State University - ADV - 843
k. ReputationBrand Reputation is a discipline separate from that of traditional brandingcampaigns. Brand Reputation recognizes that due to increasedtransparency and access to information, traditional branding whetherthrough mission statements, marketi
Michigan State University - ADV - 843
Measures1. AwarenessBrand awareness means the extent to which a brand associated with aparticular product is documented by potential and existing customerseither positively or negatively. Creation of brand awareness is the primarygoal of advertising
Michigan State University - ADV - 843
Brand InsistenceThe stage of brand loyalty where the buyer will accept no alternative andwill search extensively for the required brand. See Brand Preference;Brand Recognition.(From:http:/www.babylon.com/definition/Brand_Insistence/English)11. Loyalt
Michigan State University - ADV - 843
16. KeywordsShould You Buy Your Brand?Nov 29, 2006 10:21 AM, By Brian QuintonIn a just and well-regulated world, buying your companys brand as asearch keyword would at least guarantee that the folks who searched onthat brand name would be herded to y
Michigan State University - ADV - 843
Processes1. Management/Strategya. MappingOften used to describe a set of techniques designed to represent brandsand their similarities in a visual "brand space". Useful for providinghighly intuitive representations in order to position brands ondime
Michigan State University - ADV - 843
2. Toolsa. Name generatorb. Gap(From: http:/www.brandbuzz.com/) Y & Rc. Glue(From: http:/www.slideshare.net/coolstuff/the-brand-gap )d. Hogs(From: http:/www.facebook.com/BrandGlueUK)(See Brand Hogs, The Word of Mouth Machine Find a company This is
FSU - PHY - 3900
Classical Mechanics (Escape Velocity) Problem 1Suppose the Moon were to have the same mass as the Earth, and you are trying to throw one of your physics books from the Earth to the Moon. With what minimum velocity must the book leave the surface of the E
FSU - PHY - 3900
Classical Mechanics SolutionsSolution 1 Conservation of energy given by the sum of potential energy due to gravity and kinetic energy can be used to determine escape velocity. In the case of Earth along the potential is given by: M m (r ) = -G E r where
FSU - PHY - 3900
Electrodynamics Problem 1Twelve wires, each of resistance r, are connected to form the edges of a cube. Calculate the effective resistance R of this network across a body-diagonal of the cube.Electrodynamics Problem 2Consider a capacitor connected to a
FSU - PHY - 3900
Electrodynamics SolutionsSolution 1-The AD-axis of the cube has threefold symmetry, i.e. the cube is invariant under rotations by 120 0 about that axis. -Hence, the corners B1 , B2 and B3 are equivalent and have the same potential. -Also, the corners C1
FSU - PHY - 3900
Physics Qualifying ExaminationProblems 16 Problems 7-12Thursday, September 1, 2011 Friday, September 2, 201115 pm 1-5 pm1. Solve each problem. 2. Start each problem solution on a fresh page. You may use multiple pages per problem. 3. At the top of eac
FSU - PHY - 3900
Physics Qualifying Examination Problems 16 Problems 7-12 1. Solve each problem. 2. Start each problem solution on a fresh page. You may use multiple pages per problem. 3. At the top of each solution page put the problem number (112) and your FSUID number,
FSU - PHY - 3900
Physics Qualifying Examination Problems 16 Problems 7-12 1. Solve each problem. 2. Start each problem solution on a fresh page. You may use multiple pages per problem. 3. At the top of each solution page put the problem number (112) and your FSUID number,