Higher-Dimensional Algebra III: n-Categories and the Algebra of Opetopes

We give a definition of weak n-categories based on the theory of operads. We work with operads having an arbitrary set S of types, or `S-operads', and given such an operad O, we denote its set of operations by elt(O). Then for any S-operad O there is an elt(O)-operad O+ whose algebras are S-operads over O. Letting I be the initial operad with a one-element set of types, and defining I(0) = I, I(i+1) = I(i)+, we call the operations of I(n-1) the `n-dimensional opetopes'. Opetopes form a category, and presheaves on this category are called `opetopic sets'. A weak n-category is defined as an opetopic set with certain properties, in a manner reminiscent of Street's simplicial approach to weak omega-categories. Similarly, starting from an arbitrary operad O instead of I, we define `n-coherent O-algebras', which are n times categorified analogs of algebras of O. Examples include `monoidal n-categories', `stable n-categories', `virtual n-functors' and `representable n-prestacks'. We also describe how n-coherent O-algebra objects may be defined in any (n+1)-coherent O-algebra.Comment: 59 pages LaTex, uses diagram.sty and auxdefs.sty macros, one encapsulated Postscript figure, also available as a compressed Postscript file at http://math.ucr.edu/home/baez/op.ps.Z or ftp://math.ucr.edu/pub/baez/op.ps.

Authorship attribution in portuguese using character N-grams

For the Authorship Attribution (AA) task, character n-grams are considered among the best predictive features. In the English language, it has also been shown that some types of character n-grams perform better than others. This paper tackles the AA task in Portuguese by examining the performance of different types of character n-grams, and various combinations of them. The paper also experiments with different feature representations and machine-learning algorithms. Moreover, the paper demonstrates that the performance of the character n-gram approach can be improved by fine-tuning the feature set and by appropriately selecting the length and type of character n-grams. This relatively simple and language-independent approach to the AA task outperforms both a bag-of-words baseline and other approaches, using the same corpus.Mexican Government (Conacyt) [240844, 20161958]; Mexican Government (SIP-IPN) [20171813, 20171344, 20172008]; Mexican Government (SNI); Mexican Government (COFAA-IPN)

A proof of strong normalisation using domain theory

Ulrich Berger presented a powerful proof of strong normalisation using domains, in particular it simplifies significantly Tait's proof of strong normalisation of Spector's bar recursion. The main contribution of this paper is to show that, using ideas from intersection types and Martin-Lof's domain interpretation of type theory one can in turn simplify further U. Berger's argument. We build a domain model for an untyped programming language where U. Berger has an interpretation only for typed terms or alternatively has an interpretation for untyped terms but need an extra condition to deduce strong normalisation. As a main application, we show that Martin-L\"{o}f dependent type theory extended with a program for Spector double negation shift.Comment: 16 page

On the relative expressiveness of higher-order session processes

By integrating constructs from the λ-calculus and the π-calculus, in higher-order process calculi exchanged values may contain processes. This paper studies the relative expressiveness of HOπ, the higher-order π-calculus in which communications are governed by session types. Our main discovery is that HO, a subcalculus of HOπ which lacks name-passing and recursion, can serve as a new core calculus for session-typed higher-order concurrency. By exploring a new bisimulation for HO, we show that HO can encode HOπ fully abstractly (up to typed contextual equivalence) more precisely and efficiently than the first-order session π-calculus (π). Overall, under session types, HOπ, HO, and π are equally expressive; however, HOπ and HO are more tightly related than HOπ and π