Twelve Offertory Sentences

Comparing Offertory Melodies of Five Medieval Christian Chant Traditions

In this study, we compare the melodies of five medieval chant traditions: Gregorian, Old Roman, Milanese, Beneventan, and Mozarabic. We present a newly created dataset containing several hundreds of offertory melodies, which are the longest and most complex within the total body of chant melodies. For each tradition, we train ngram language models on a representation of the chants as sequence o...

"Linguistic" sentences and "real" sentences

This p~$r Id~ntift~ iwe klr¢ds of sentences: "llngulsUc" sentences ~ J "r~al" a~-ntence~. "l't~,~ former is a kind of sentel~'~,e~ that ar~ often discussed in (cemputatkmal) Ungulstlc literatures, sucll as the:re In i:lgure 1. The latter, on the other hand, is a kind of senteace=~ that appear in practical applications, such as those In Flgu='e 2. Where~ts both are grammatical English sentences,...

Clustering Sentences - Making Sense of Synonymous Sentences

Twelve Publications

We prove a complexity classification theorem that classifies all counting constraint satisfaction problems (#CSP) over Boolean variables into exactly three categories: (1) Polynomial-time tractable; (2) #P-hard for general instances, but solvable in polynomial-time over planar graphs; and (3) #P-hard over planar graphs. The classification applies to all sets of local, not necessarily symmetric,...

Some Sentences on Our Consciousness of Sentences

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