Convergence in the Malabar

The Indo-Portuguese creole languages that formed along the former Malabar Coast of southwestern India, currently seriously endangered, are arguably the oldest of all Asian-Portuguese creoles. Recent documentation efforts in Cannanore and the Cochin area have revealed a language that is strikingly similar to its substrate/adstrate Malayalam in several fundamental domains of grammar, often contradicting previous records from the late 19th-century and the input of its main lexifier, Portuguese. In this article, this is shown by comparing Malabar Indo-Portuguese with both Malayalam and Portuguese with respect to features in the domains of word order (head-final syntax and harmonic syntactic patterns) and case-marking (the distribution of the oblique case). Based on older records and certain synchronic linguistic features of the Malabar Creoles, this article proposes that the observed isomorphism between modern Malabar Indo-Portuguese and Malayalam has to be explained as the product of either a gradual process of convergence, or the resolution of historical competition between Dravidian-like and Portuguese-like features.

TRUNCATED AFFINE SPRINGER FIBERS AND ARTHUR’S WEIGHTED ORBITAL INTEGRALS

We explain an algorithm to calculate Arthur’s weighted orbital integral in terms of the number of rational points on the fundamental domain of the associated affine Springer fiber. The strategy is to count the number of rational points of the truncated affine Springer fibers in two ways: by the Arthur–Kottwitz reduction and by the Harder–Narasimhan reduction. A comparison of results obtained from these two approaches gives recurrence relations between the number of rational points on the fundamental domains of the affine Springer fibers and Arthur’s weighted orbital integrals. As an example, we calculate Arthur’s weighted orbital integrals for the groups ${\textrm {GL}}_{2}$ and ${\textrm {GL}}_{3}$ .

Malle's conjecture for for

We propose a framework to prove Malle's conjecture for the compositum of two number fields based on proven results of Malle's conjecture and good uniformity estimates. Using this method, we prove Malle's conjecture for $S_n\times A$ over any number field $k$ for $n=3$ with $A$ an abelian group of order relatively prime to 2, for $n= 4$ with $A$ an abelian group of order relatively prime to 6, and for $n=5$ with $A$ an abelian group of order relatively prime to 30. As a consequence, we prove that Malle's conjecture is true for $C_3\wr C_2$ in its $S_9$ representation, whereas its $S_6$ representation is the first counter-example of Malle's conjecture given by Klüners. We also prove new local uniformity results for ramified $S_5$ quintic extensions over arbitrary number fields by adapting Bhargava's geometric sieve and averaging over fundamental domains of the parametrization space.

Toward Liberal Immigration Control

Can contemporary liberal states formulate and pursue a “liberal” immigration control policy? Set against the backdrop of the experience of immigrant-receiving Western liberal democracies, this article examines this question by focusing on Japan. Its main objective is to map the under-studied case of Asia’s most liberal democracy, which is conventionally associated with an “at best illiberal” stance on immigration. I contend, first, that liberal immigration control policy is inevitably defined by approximation, and second, that Japanese policy outputs have become, albeit to varying degrees, more liberal in three fundamental domains of immigration control: the admission policy is increasingly open and unambiguous; the selection policy is gradually being racially decentered; and the removal policy is more attuned to migrants’ rights. However, this case also demonstrates that such an evolution generates inconsistencies across, and tensions within, the different policy domains, which underscores the contemporary liberal state’s general incoherence on immigration affairs.

CLARIAH: Enabling Interoperability Between Humanities Disciplines with Ontologies

One of the most important goals of digital humanities is to provide researchers with data and tools for new research questions, either by increasing the scale of scholarly studies, linking existing databases, or improving the accessibility of data. Here, the FAIR principles provide a useful framework. Integrating data from diverse humanities domains is not trivial, research questions such as “was economic wealth equally distributed in the 18th century?”, or “what are narratives constructed around disruptive media events?”) and preparation phases (e.g. data collection, knowledge organisation, cleaning) of scholars need to be taken into account. In this chapter, we describe the ontologies and tools developed and integrated in the Dutch national project CLARIAH to address these issues across datasets from three fundamental domains or “pillars” of the humanities (linguistics, social and economic history, and media studies) that have paradigmatic data representations (textual corpora, structured data, and multimedia). We summarise the lessons learnt from using such ontologies and tools in these domains from a generalisation and reusability perspective.

Generalized Dual-Root Lattice Transforms of Affine Weyl Groups

Discrete transforms of Weyl orbit functions on finite fragments of shifted dual root lattices are established. The congruence classes of the dual weight lattices intersected with the fundamental domains of the affine Weyl groups constitute the point sets of the transforms. The shifted weight lattices intersected with the fundamental domains of the extended dual affine Weyl groups form the sets of labels of Weyl orbit functions. The coinciding cardinality of the point and label sets and corresponding discrete orthogonality relations of Weyl orbit functions are demonstrated. The explicit counting formulas for the numbers of elements contained in the point and label sets are calculated. The forward and backward discrete Fourier-Weyl transforms, together with the associated interpolation and Plancherel formulas, are presented. The unitary transform matrices of the discrete transforms are exemplified for the case A 2 .

Mathematical aspects of molecular replacement. V. Isolating feasible regions in motion spaces

This paper mathematically characterizes the tiny feasible regions within the vast 6D rotation–translation space in a full molecular replacement (MR) search. The capability to a priori isolate such regions is potentially important for enhancing robustness and efficiency in computational phasing in macromolecular crystallography (MX). The previous four papers in this series have concentrated on the properties of the full configuration space of rigid bodies that move relative to each other with crystallographic symmetry constraints. In particular, it was shown that the configuration space of interest in this problem is the right-coset space Γ\G, where Γ is the space group of the chiral macromolecular crystal and G is the group of rigid-body motions, and that fundamental domains F Γ\G can be realized in many ways that have interesting algebraic and geometric properties. The cost function in MR methods can be viewed as a function on these fundamental domains. This, the fifth and final paper in this series, articulates the constraints that bodies packed with crystallographic symmetry must obey. It is shown that these constraints define a thin feasible set inside a motion space and that they fall into two categories: (i) the bodies must not interpenetrate, thereby excluding so-called `collision zones' from consideration in MR searches; (ii) the bodies must be in contact with a sufficient number of neighbors so as to form a rigid network leading to a physically realizable crystal. In this paper, these constraints are applied using ellipsoidal proxies for proteins to bound the feasible regions. It is shown that the volume of these feasible regions is small relative to the total volume of the motion space, which justifies the use of ellipsoids as proxies for complex proteins in MR searches, and this is demonstrated with P1 (the simplest space group) and with P212121 (the most common space group in MX).