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A General Introduction to Lexical Databases Emmanuel Keuleers Department of Experimental Psychology Ghent University EMLAR 2015 - Utrecht, April 15-17, 2015 • What can you find in a lexical database? • How can you find it? Lexical Databases • Like a dictionary • Lexical properties of interest to psycholinguists • Frequency, orthography, phonology, morphology, syntax, … • Subjective ratings of those words • Behavioural responses to those data Lexical Databases • No standard: each database has its own format, peculiarities, ... • Text files, web interfaces, e-mail services, etc ... • In essence, a lexical database is just a list with a bunch of information about words. Lexical Databases • The truth: you'll have to find out where to find something and be prepared to do some processing work. CELEX: the big and complex lexical database History • Centre for Lexical Information • Founded in Nijmegen in 1986 • Max Planck Institute for Psycholinguistics & Interfaculty Research Unit for Language and Speech of the University of Nijmegen (now CLS) • Project ended in 2000 • Three large databases with lexical information for Dutch, English, and German • Dutch Database • 124,136 lemmata • 381,292 wordforms • 211,389 corpus types • English Database • 52,446 lemmata • 160,594 wordforms • 220,271 corpus types • German database • 51,728 lemmata • 365,530 wordforms • 290,712 corpus types Wordforms, lemmas, and corpus types Corpus types • Letter strings, regardless of part of speech • a walk in the park = to walk slowly = i walk alone = you walk alone Wordforms • Letter strings disambiguated for part of speech (and sometimes meaning) • a walk in the park ≠ to walk slowly ≠ i walk alone ≠ you walk alone • (walk, noun, singular), (walk, verb, infinitive), (walk, verb, 1p), (walk, verb, 2p) Lemmas • Headwords • (walk, noun): a walk in the park = the • long walks (walk, verb): I'm walking slowly = i walk alone = he walks too fast Celex Build Up • Information from dictionary sources • Corpus counts or correlation with existing frequency counts • Almost completely biased towards written language Dutch Database Sources • Van Dale's Comprehensive Dictionary of Contemporary Dutch (1984) • 80,000 lemmata • Word List of the Dutch Language ('Het Groene Boekje') • (1954), plus later revisions, including the 1994 spelling reform 65,000 lemmata The most frequent lemmata from the text corpus of the Institute for Dutch Lexicology (INL) 42,380,000 words in all • • 15,000 lemmata English Database Sources • Oxford Advanced Learner's Dictionary (1974) • 41,000 lemmata • Longman Dictionary of Contemporary English (1978) • 53,000 lemmata German Database Sources • Bonnlex, supplied by the Institute for Communication Research and Phonetics in Bonn • Molex, supplied by the Institute for German Language in Mannheim • Noetic Circle Services (MIT) German spelling lexicon Dutch Frequency Sources • INL Corpus (42 million tokens) • 930 entire fiction and non-fiction books (approx. 30% fiction, 70% non-fiction) published between 1970 and 1988. Newspapers, magazines, children's books, textbooks and specialist literature do not feature in the collection. English Frequency Sources • COBUILD/Birmingham corpus (17.9 million tokens) • 16.6 million tokens from written texts • 1.3 million tokens from transcribed dialogue German Frequency Sources • Mannheimer Korpus I, Mannheimer Korpus II and Bonner Zeitungskorpus 1 • 5.4 million tokens • written texts like newspapers, fiction and nonfiction • Freiburger Korpus • 600,000 tokens • transcribed speech • Corpus Types • Frequency • Orthography • Lemma lexica • Frequency • Orthography • Phonology • Derivational Morphology • Grammatical information • Wordform Lexica • Frequency • Orthography • Phonology • Inflectional Morphology Frequency Verb Frequency Deviation Freq/Million accept 3712 0 207.37 accord 2010 12 112.29 achieve 2121 0 118.49 act 2212 430 123.58 add 4190 0 234.08 agree 3424 0 191.28 Lexicon Form Frequency Deviation Frequency/ million lemma act 2212 430 123.58 wordform act 269 1233 15.03 wordform acted 92 366 5.14 wordform acting 489 103 27.32 wordform acts 187 80 10.45 wordform act 269 1233 15.03 wordform acted 92 366 5.14 wordform act 269 1233 15.03 wordform acted 92 366 5.14 wordform act 269 1233 15.03 wordform acted 92 366 5.14 wordform acted 92 366 5.14 • Lemma frequency • Frequency over all wordforms of the lemma • Wordform frequency • Deviation == 0 : exact count • Deviation > 0 : result of disambiguation • Less than 100 tokens • Manual disambiguation • More than 100 tokens • Disambiguation on a sample of 100 tokens • Frequency ± deviation = 95 % confidence interval • No disambiguation for verbal flection • Frequency divided between forms • Frequency Deviation > Frequency • No disambiguation for German • Frequency divided between forms • English and German databases have separate fields for written and spoken frequencies • Spoken frequencies based on very small corpora • 1.3 million for English • 0.4 million for German • What does it mean when an entry in CELEX has a frequency of zero • Many entries in the database sources were not found in the frequency sources • A few entries do not come from database sources but are left with a zero frequency after disambiguation • will have deviation > zero • Many entries added to CeLex for morphological decomposition of other lemmas have a frequency of zero Word frequency distributions Word frequency distributions word frequency rank the of and to a in that it i 1 093 546 540 085 514 946 483 428 422 334 337 995 217 376 199 920 198 139 1 2 3 4 5 6 7 8 9 • Let's plot the rank of each word in the COBUILD corpus against its frequency. • The word with the highest frequency gets the highest rank (1), the word with the lowest frequency gets the lowest rank (220,270). • In total there are 17.9 million word tokens in the COBUILD corpus. • Not very clear. • Let's plot it again so that the difference between a frequency of 1 and a frequency of 10 is the same as the difference between a frequency of 10 and a frequency of 100 106=1,000,000 the of and to a in 103=1,000 all these words have frequency 1 100=1 • Word frequency lists are composed of very few words with a very high frequency • Most words (corpus types) occur only once in the corpus! • The relation between word frequency and rank is log linear. Comparing frequencies • Word frequencies from different databases cannot be easily compared because of different corpus sizes • Example: Celex Dutch ±42m vs Celex English ±18million • Solution: frequency per million words Frequency per million word frequency frequency per million rank the of and to a in that it i 1 093 546 540 085 514 946 483 428 422 334 337 995 217 376 199 920 198 139 60 955.74 30 105.07 28 703.79 26 946.93 23 541.47 18 840.30 12 116.83 11 143.81 11 044.54 1 2 3 4 5 6 7 8 9 Comparing frequencies • Beware! Some frequency lists contain words with a frequency of 0 • Log10(0) is not something that can be computed • Solution: always add 1 to the raw frequencies when you are transforming to frequencies per million Formula Frequency per million = Raw Frequency +1 (adjusted) Corpus size in million FPM ('that') = 217 376 +1 =12116.89 17.94 log10(12116.89)=4.08 Zipf Values Van Heuven, Mandera, Keuleers, & Brysbaert (2014) Formula Freq. per billion = Raw Frequency +1 Corpus size in billion FPB ('that') = 217 376 +1 =12116889.63 .01794 log10(12116889.63)=7.08 word frequency Relative Frequency log10(fpm) zipf the of and to a in that it i 1 093 546 540 085 514 946 483 428 422 334 337 995 217 376 199 920 198 139 0.0602191 0.0297413 0.0283569 0.0266213 0.0232570 0.0186127 0.0119704 0.0110092 0.0109111 4.78 4.47 4.45 4.43 4.37 4.27 4.08 4.04 4.04 7.78 7.47 7.45 7.43 7.37 7.27 7.08 7.04 7.04 Orthography • Lemma and wordform lexica list orthographic variants with separate frequencies Status • Dutch: preferred, non-preferred, informal • preferred & non-preferred: in “Groene Boekje” non-standard forms occurring at least once in • informal: INL corpus • English: British, American • British: acceptable for British • American: occurs only in American • German • No orthographic variants Lemma ID Form Status Frequency 1070 aardappelcroquet preferred 0 1070 aardappelkroket non-preferred 0 1138 aardelektrode preferred 0 1138 aardelectrode non-preferred 0 1202 aardolieprodukt preferred 6 1202 aardolieproduct non-preferred 0 1357 abductie preferred 0 1357 abduktie non-preferred 0 Lemma ID Form Status Frequency 1359 anaesthesia British 12 1359 anesthesia American 1 1360 anaesthetic British 47 1360 anesthetic American 4 1361 anaesthetic British 8 1361 anesthetic American 0 1362 anaesthetist British 16 • Abstract stems for Dutch • if a stem with final s or f changes to z or v anywhere in its inflectional paradigm, an abstract stem is given ending with z or v. Type Stem Abstract Stem Adjective approximatief approximatiev Noun arbeidershuis arbeidershuiz Noun arbeidersparadijs arbeidersparadijz Noun arbeidsbeurs arbeidsbeurz Adjective arbeidsextensief arbeidsextensiev Adjective arbeidsintensief arbeidsintensiev Adjective arbeidsloos arbeidslooz Phonology • Canonical phonetic transcriptions for written forms • English: primary and secondary pronunciation • Dutch, German: no phonetic variants • Syllabified • Stress and CV patterns • IPA-like character sets • SAM-PA • CeLex • CPA • DISC character set • one character per phoneme • no ambiguity • unreadable Idnum Spelling Status DISC Syllables IPA Stress CV 42577 sleekness primary sliknIs sliːk-nɪs 10 CCVVCCVC 42577 sleekness secondary sliknIs sliːk-nəs 10 CCVVCCVC 42582 sleepily primary slipIlI sliː-pɪ-lɪ 100 CCVVCV-CV 42582 sleepily secondary slipIlI sliː-pə-lɪ 100 CCVVCV-CV 42584 sleepiness primary slipInIs sliː-pɪ-nɪs 100 CCVVCV-CVC 42584 sleepiness secondary slipInIs sliː-pɪ-nəs 100 CCVVCV-CVC • Dutch and German • Separate phonetic trancsriptions for headwords and stems • English • First variant is always the primary one, as listed in the English Pronouncing Dictionary • Newer versions use BBC English and Network English, transcriptions in CeLex are probably RP. • Phonological transcriptions for morphologically complex Dutch and German stems with indication of morpheme boundaries • Only with CELEX and CPA character sets Stem Phonological Transcription Phonetic Transcription Arbeiter arbait+@r [ar][bai][t@r] Arbeitsplatz arbait+s#plats [ar][baits][plats] Arbeitgeber arbait#ge:b+@r [ar][bait][ge:] [b@r] arbeitsamkeit arbait#za:m#kait [ar][bait][za:m] [kait] Morphology • Lemma Morphology • Morphstatus: indicates if the lemma has a relevant morphological decomposition • Segmentation • Immediate, Flat, Hierachical Immediate Segmentation aansprakelijkheidsverzekering aansprakelijkheid s verzekering Flat Segmentation aansprakelijkheidsverzekering aan spreek elijk heid s ver zeker ing Hierachical Segmentation aansprakelijkheidsverzekering aansprakelijkheid aansprakelijk verzekering aanspreek aan spreek verzeker elijk heid s ver zeker ing • Wordform morphology • Inflectional Features Form Flection Frequency adjusted past,1p,singular 35 adjuster singular 5 adjusters plural 1 adjusting present,participle 71 adjustment singular 150 adjustments plural 84 adjusts present,3p,singular 14 Grammatical Information • Syntactic class for lemmas • Dutch: Expression, Noun, Adjective, Quantifier/Numeral, Verb, Article, Pronoun, Adverb, Preposition, Conjunction, Interjection • English: Noun, Adjective, Numeral,Verb, Article, Pronoun, Adverb, Preposition, Conjunction, Interjection, Single, Complex, Letter, Abbreviation, Infinitival • German • Noun, Adjective, Quantifier/Numeral, Verb, Article, Pronoun, Adverb, Preposition, Conjunction, Interjection • Additional subclassification Form Class Subclasses videotape Noun uncountable videotape Verb transitive vide supra Interjection vie Verb linking Vietnam Noun proper Vietnamese Adjective ordinary Vietnamese Noun countable Form Class Subclasses magnetisch Adjective magnetiseren magnetiseerb aar magnifiek Verb Adjective nonadverbial lexical intransitive transitive nonadverbial Adjective adverbial Magyaars Adjective adverbial maharadja Noun maharishi Noun Mahdi Noun Mahler Noun propername How to get information from CeLex • Option 1: CeLex CD with textfiles • Typical ‘text processing’ languages (AWK, Perl) • Elegant language (Python) • Import in spreadsheet application • Option 2: Public web interface at MPI (WebCeLex) • Good tool for selection • Process with scripting language Examples cued by the orthography. Thus both MOUTH and TENTH end in TH but differ in voicing; although both form the plural by adding S in the orthography, the inflections are pronounced differently. The mappings between spelling and pronunciation for these words are therefore rather complex. In summary, the words we excluded differ in some respects from the words in the training corpus and raise additional challenges for our approach that need to be addressed. tates performance o age of the space of Performance o and on inflected w comparison we als feedforward netwo feedforward model these words, with models’ capacities To explore these questions, we conducted a replicaing them on nonwo tion simulation using a much larger corpus. Monosyllables Here the attractor 132 A. Albright, B. Hayes / Cognition 90 (2003) 119–161 were extracted from the CELEX electronic corpus (Baayen, than the feedforwa Table 2 Piepenbrock, & van Rijn, 1993). All items fitting a CCwith the conclusion Past tenses for gleed derived by the analogical model CVVCCC template were used, yielding 7,839 words. Most learning complex Output Score Analogs of the additional words are inflected items. The phonologlearning of the larg gleeded 0.3063 plead, glide, bleat, pleat, bead, greet, glut, need, grade, gloat, and 955 others in our ical network was expanded from 66 to 88 units to accommotion. The larger m learning set gled 0.0833 bleed, lead, breed, read, feed, speed, meet, bottle-feed gleed 0.0175 bid, beat, slit, let, shed, knit, quit, split, fit, hit, and 12 others gleet M. W. & Seidenberg, 0.0028 M. S. lend, build, bend, send, spend Harm, (1999). Phonology, reading acquisition, and dyslexia: insights from connectionist models. glade Rev, 106(3), 0.0025 Psychol 491-528. eat glode 0.0017 weave, freeze, steal, speak glud 0.0005 sneak [skraI dt] are phonologically filtered; the remaining candidates are submitted to the core GCM algorithm for evaluation, as described above. As an illustration of how the model works, Table 2 shows the outcomes it derives for gleed, along with their scores and the analog forms used in deriving each outcome. To conclude, we feel that a model of this sort satisfies a rigorous criterion for being “analogical”, as it straightforwardly embodies the principle that similar forms influence one another. The model moreover satisfies the criteria laid out in Section 2.1: it is fully susceptible to the influence of variegated similarity, and (unless the data accidentally help it to do so) it utterly ignores the structured-similarity relations that are crucial to our rulebased model. 2.5. Feeding the models We sought to feed both our rule-based and analogical models a diet of stem/past tense pairs that would resemble what had been encountered by our experimental participants. We took our set of input forms from the English portion of the CELEX database (Baayen, Piepenbrock, & Gulikers, 1995), selecting all the verbs that had a lemma frequency of 10 or greater. In addition, for verbs that show more than one past tense (like dived/dove), we included both as separate entries (e.g. both dive-dived and dive-dove). The resulting corpus consisted of 4253 stem/past tense pairs, 4035 regular and 218 irregular. Verb forms were listed in a phonemic transcription reflecting American English pronunciation. A current debate in the acquisition literature (Bybee, 1995; Clahsen & Rothweiler, 1992; Marcus, Brinkmann, Clahsen, Wiese, & Pinker, 1995) concerns whether prefixed forms of the same stem (e.g. do/redo/outdo) should be counted separately for purposes Albright, A. & Hayes, B. (2003). Rules vs. analogy in English past tenses: A computational/experimental of learning. We prepared a version of our learning set from which all prefixed forms study. Cognition, 90(2), 119-161. were removed, thus cutting its size down to 3308 input pairs (3170 regular, 138 irregular), and ran both learning models on both sets. As it turned out, the rule-based model did slightly better on the full set, and the analogical model did slightly better on the edited set. The results below reflect the performance of each model on its own best learning set. Feeding the models B. New et al. / 2.5. Journal of Memory and Language 51 (2004) 568–585 573 withboth Baayen al.!s findings Dutch, but models deviates afrom s We sought to feed ouretrule-based andin analogical diet of stem/past Serenoresemble and Jongman!s findings rds were selected from Lexique and 44that would tense pairs what had beenin English. encountered by our experimental the two experiments reported thusof the CELEX rds were constructed. Selection andWe took So, participants. ouron setthe ofbasis inputofforms from the English portion far, it seems that Dutch and French plurals are ria were the same as in Experiment 1, database (Baayen, Piepenbrock, & Gulikers, 1995), selecting all theproverbs that had a the same way, and both differ significantly quencies of the word forms. One list lemma frequency ofcessed 10 oringreater. In addition, for verbs that show more than one past from the findings in English. In addition, there is some singular frequency of 16, and a plural tense (like dived/dove), we included both as separate entries (e.g. both dive-dived and suggestive evidence that the Dutch/French pattern could he other list had a singular frequency The resulting 4253 stem/past tenseand pairs, also becorpus presentconsisted in Italianof(Baayen et al., 1996) in 4035 regular frequency of 4. The twodive-dove). lists of words irregular. Spanish Verb forms were listed in a phonemic reflecting (Dominguez et al., 1999), making thetranscription English the number of letters (6.4and and 218 6.3) and American English pronunciation. finding even more isolated. Therefore, we decided to relables (1.7 and 1.7). A complete list of A currentB debatepeat in the (Bybee, 1995; Clahsen & Rothweiler, the acquisition Sereno and literature Jongman experiments. in Appendix A (see also Appendix 1992; Marcus, Brinkmann, Clahsen, Wiese, & Pinker, 1995) concerns whether prefixed ). forms of the same stem (e.g. do/redo/outdo) should be counted separately for purposes Experiment 3 of learning. We prepared a version of our learning set from which all prefixed forms e was identical to thatwere described in thus cutting its size down to 3308 input pairs (3170 regular, 138 removed, A closer look at Sereno and Jongman revealed cept that in this experiment only the irregular), and ran both learning models on both sets. As (1997) it turned out, the rule-based a number of methodological differences between rms were presented. Because of this, model did slightly better on the full set, and the analogical model didthat slightly better on study and all of the other studies. For a start, Sereno ed in -s. the edited set. The results below reflect the performance of each model on its own best and Jongman presented their singular and plural stimuli learning set. in two different experiments (their Experiments 2A and 2B). This blocked presentation may have encouraged Albright, A. & Hayes, B. (2003). Rules vs. analogy in English past tenses: A computational/experimental participants to ignore the end -s in the experiment with ys mean reaction time and percentage study. Cognition, 90(2), 119-161. the plural stimuli. Another problem is that Sereno and ent 2. Extreme reaction times were reJongman!s word frequencies were based on the Brown to the procedure described in Expericorpus which only includes one million words. This is 5.5% of the RT data in the subjects a quite limited corpus if we compare it to the French s 4.7% in the item analysis were discorpus used in Lexique (31 million tokens) and the Enwith one repeated measure revealed glish corpus used in Celex (17.9 million tokens). For he frequency of the plural form both these reasons, we decided to repeat the Sereno and Jongover participants (F1(1,14) = 24.09, man experiments, following the same procedure as in < .001) and in the analysis over items our French studies (and in the Dutch studies). Mse = 1371.50, p < .001). Participants to singular word forms with high-freMethod n to singular word forms with low-fre- ng of Experiment 2 was the presence of effect when the singular forms were ce frequency. When two singular forms rface frequency but differ in the freural forms, the singular with the more processed faster. This result agrees (in ms), standard deviation and percentage 2 m Presented forms: singular M SD %ER al 540 50 2.1 al r] 596 63 3.6 Participants Thirty-eight students from Royal Holloway, University of London, took part in the experiment in return for course credits. They were all native English-speakers and had normal or corrected-to-normal vision. Stimulus materials The word stimuli were two lists of 24 nouns drawn from the Celex database (Baayen, Piepenbrock, & Gulikers, 1995), based on a corpus of 16.6 million written words and 1.3 million spoken words. The first list consisted of singular dominant items, with an average frequency of 25 per million for the singular forms and eight for the plural forms. The second list consisted of plural dominant items with average frequencies of 9 and 26, respectively. The base frequencies (34 vs. 35) did not differ between the lists. The stimuli were further matched on the number of letters (6.3 and 6.3) and the number of syllables (2 and 2). A complete list of the stimuli is presented in Appendix A. As in Experiment 1, two versions of the word list were created, so that each participant saw only one form of a word. New, B., Brysbaert, M., Segui, J., Ferrand, L., & Rastle, K. (2004). The processing of singular and plural nouns in French and English. Journal of Memory and Language, 51(4), 568-585. Appendix A (continued) Word [in English] Mean reaction time pavilion [bungalow] perruque [wig] prêtre [priest] 582 [river] rivière sculpteur [sculptor] tige [stem] A (continued) Appendix torse [chest] Word [in English] vallée [valley] 491 71 17 536 58 4 635 178 20 B. New et al. / Journal of Memory 584 107 and Language 34 51 (2004) 568–585 625 95 5 578 84 12 618 113 12 Mean reaction time SD Singular frequency 520 76 26 pavilion [bungalow] perruque [wig] prêtre [priest] rivière [river] Materials used in Experiment 3 sculpteur [sculptor] Word Singular tige [stem] Mean reaction torse [chest] vallée [valley] Singular dominant items 491 536 635 584 625 578 time 618 520 beast 468 belief 439 cathedral 476 clinic 480 Materials used in Experiment 3 dragon 482 famine 525 Word Singular hat 422 Mean reaction time journal 495 Singular dominant603 items lieutenant monument 547 beast 468 moustache 519 belief 439 prophet 532 cathedral 476 regiment 586 clinic 480 salad 490 dragon 482 sister 463 famine 525 studio 450 hat 422 sum 480 journal 495 sword 467 lieutenant 603 talent 473 monument 547 task 473 moustache 519 texture 433 prophet 532 tribe 478 regiment 586 valley 483 salad 490 sister Plural dominant items463 studio 450 acre 584 sum 480 ancestor 569 biscuit 434 sword 467 critic 546 talent 473 disciple 560 task 473 dollar 514 texture 433 glove 455 tribe 478 heel 490 valley 483 ingredient lip Plural dominant molecule acre neighbour ancestor nostril biscuit sandal critic shoe disciple sock dollar soldier glove heel ingredient lip molecule neighbour nostril sandal shoe sock soldier SD SD 68 43 68 65 43 52 33 SD 78 67 112 68 88 43 90 68 126 65 78 43 59 52 67 33 90 78 73 67 67 112 68 45 88 65 90 85 126 78 59 67 90 73 67 68 45 65 85 Singular frequency 71 58 178 107 95 84 Frequency113 76 17 4 20 34 5 Plural 12 Mean reaction time 12 26 17 67 15 15 8 7 53 18 14 11 16 10 10 16 82 22 32 13 24 65 11 23 49 516 477 553 548 495 642 439 456 609 588 547 606 572 470 489 498 483 490 506 468 490 505 495 Frequency 17 67 15 15 8 7 53 18 14 11 16 10 10 16 82 22 32 13 24 65 11 23 49 535 444 items 498 584 466 569 562 434 536 546 438 560 434 514 466 101 77 43 92 114 65 59 94 75 50 57 101 67 71 77 81 43 64 92 56 114 35 65 15 6 5 12 4 15 5 11 4 17 5 15 19 2 6 1 5 14 12 3 4 26 15 455 490 535 444 498 466 562 536 438 434 466 59 94 75 50 57 67 71 81 64 56 35 5 11 4 17 5 19 2 1 14 3 26 559 568 458 534 533 503 441 479 553 482 515 475 551 516 448 441 448 Plural frequency 559 568 458 534 533 503 441 479 553 482 515 475 551 516 448 441 448 85 95 85 85 137 76 50 48 110 67 83 61 87 111 84 64 42 Plural frequency 4 2 13 8 3 8 Frequency 2 6 SD 96 58 83 77 80 145 Plural 51 Mean reaction time 52 132 110 516 106 477 108 553 133 548 63 495 52 642 81 439 98 456 78 609 107 588 74 547 65 606 78 572 91 470 489 498 483 490 506 468 490 505 495 4 2 13 8 3 8 2 6 SD 96 58 83 77 80 145 51 52 132 110 106 108 133 63 52 81 98 78 107 74 65 78 91 85 95 85 85 137 76 50 48 110 67 83 61 87 111 84 64 42 11 24 3 5 2 1 15 6 1 6 2 6 2 4 32 6 17 4 12 17 2 15 7 23 22 11 23 13 53 15 18 11 61 12 31 10 8 65 16 57 Frequency 11 24 3 5 2 1 15 6 1 6 2 6 2 4 32 6 17 4 12 17 2 15 7 23 22 11 23 13 53 15 18 11 61 12 31 10 8 65 16 57 Exercises and practical applications http://crr.ugent.be/emlar2015