Cross-linguistic evidence for cognitive universals in the noun phrase

Noun phrase word order varies cross-linguistically, however, two distributional asymmetries have attracted substantial attention (i.a., Greenberg 1963, Cinque 2005). First, the most common orders place adjectives closest to the noun, then numerals, then demonstratives (e.g., N-Adj- Num-Dem). Second, exceptions to this are restricted to post-nominal position (e.g., N-Dem- Num-Adj, but not Adj-Num-Dem-N). These observations have been argued to reflect constraints on cognition. Here we report two experiments, following work by Culbertson & Adger (2014), providing additional support for this claim. We taught English- and Thai-speaking participants artificial languages in which the position of modifiers relative to the noun differed from their native order (post-nominal position in English, pre-nominal in Thai). We trained participants on single-modifier phrases, and asked them to extrapolate to multiple modifier phrases. We found that both populations infer relative orders of modifiers that conform to the tendency for closest proximity of adjectives, then numerals, then demonstratives. Further, we show that Thai participants, learning pre-nominal modifiers, exhibit a stronger such preference. These results track the typology closely and are consistent with the claim that noun phrase word order reflects properties of human cognition. We discuss future research needed to rule out alternative explanations for our findings, including prior language experience

Experimental evidence for the influence of structure and meaning on linear order in the noun phrase

Recent work has used artificial language experiments to argue that hierarchical representations drive learners’ expectations about word order in complex noun phrases like these two green cars (Culbertson & Adger 2014; Martin, Ratitamkul, et al. 2019). When trained on a novel language in which individual modifiers come after the Noun, English speakers overwhelmingly assume that multiple nominal modifiers should be ordered such that Adjectives come closest to the Noun, then Numerals, then Demonstratives (i.e., N-Adj-Num-Dem or some subset thereof). This order transparently reflects a constituent structure in which Adjectives combine with Nouns to the exclusion of Numerals and Demonstratives, and Numerals combine with Noun+Adjective units to the exclusion of Demonstratives. This structure has also been claimed to derive frequency asymmetries in complex noun phrase order across languages (e.g., Cinque 2005). However, we show that features of the methodology used in these experiments potentially encourage participants to use a particular metalinguistic strategy that could yield this outcome without implicating constituency structure. Here, we use a more naturalistic artificial language learning task to investigate whether the preference for hierarchy-respecting orders is still found when participants do not use this strategy. We find that the preference still holds, and, moreover, as Culbertson & Adger (2014) speculate, that its strength reflects structural distance between modifiers. It is strongest when ordering Adjectives relative to Demonstratives, and weaker when ordering Numerals relative to Adjectives or Demonstratives relative to Numerals. Our results provide the strongest evidence yet for the psychological influence of hierarchical structure on word order preferences during learning

Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

Boundedness of Pseudodifferential Operators on Banach Function Spaces

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on $X(\mathbb{R}^n)$ whenever the symbol $a$ belongs to the H\"ormander class $S_{\rho,\delta}^{n(\rho-1)}$ with $0<\rho\le 1$, $0\le\delta<1$ or to the the Miyachi class $S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)$ with $0\le\delta\le\rho\le 1$, $0\le\delta0$. This result is applied to the case of variable Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$.Comment: To appear in a special volume of Operator Theory: Advances and Applications dedicated to Ant\'onio Ferreira dos Santo

The integral homology of PSL2PSL_2 of imaginary quadratic integers with non-trivial class group

We show that a cellular complex described by Floege allows to determine the integral homology of the Bianchi groups $PSL_2(O_{-m})$, where $O_{-m}$ is the ring of integers of an imaginary quadratic number field \rationals[\sqrt{-m}] for a square-free natural number $m$. We use this to compute in the cases m = 5, 6, 10, 13 and 15 with non-trivial class group the integral homology of $PSL_2(O_{-m})$, which before was known only in the cases m = 1, 2, 3, 7 and 11 with trivial class group

The fundamental left-right asymmetry in the Germanic verb cluster

Cinque (2005, 2009, 2014a) observes that there is an asymmetry in the possible ordering of dependents of a lexical head before versus after the head. A reflection on some of the concepts needed to develop Cinque’s ideas into a theory of neutral word order reveals that dependents need to be treated separately by class. The resulting system is applied to the problem of word order in the Germanic verb cluster. It is shown that there is an extremely close match between theoretically derived expectations for clusters made up of auxiliaries, modals, causative ‘let’, a main verb, and verbal particles. The facts point to the action of Cinque’s fundamental left-right asymmetry in language in the realm of the verb cluster. At the same time, not all verb clusters fall under Cinque’s generalization, which, therefore, argues against treating all cases of restructuring uniformly