An Abstract Morimoto Theorem for Generalized FF-structures

We abstract Morimoto's construction of complex structures on product manifolds to pairs of certain generalized $F$-structures on manifolds that are not necessarily global products. As applications we characterize invariant generalized complex structures on product manifolds in which one factor is a Lie group and we generalize a theorem of Blair, Ludden and Yano on Hermitian bicontact manifolds.Comment: 26 page

Abstract structures for moods in Greek

It is my intention to make two major points in this paper: 1. The first has to do with finding a frame within which the modal expressions of one particular Ancient IE [Indoeuropean] language – I have chosen Classical Greek – can be best described. I shall try to point out that the regularities which we find in these expressions must depend on an underlying principle, represented by abstract structures. These structures are semanto-syntactic, which means that the semantic properties or bundles of properties are arranged not in a linear order but in a hierarchical order, analogous to a bracketing in a PS structure. The abstract structures we propose have, of course, a very tentative character. They can only be accepted as far as evidence for them can be furnished. 2. My second point has to do with the modal verb forms that were the object of the studies of most Indo-Europeanists. If in the innermost bracket of a semanto-syntactic structure two semantic properties or bundles of properties can be exchanged without any further change in the total structure, and if this change is correlated with a change in verbal mood forms and nothing else, then I think we are faced with a case where these forms can be said to have a meaning of their own. I shall also try to show how these meanings are to be understood as bundles of features rather than as unanalyzed terms. In my final remarks: I shall try to outline the bearing these views have on comparative IE linguistics

Rewriting Abstract Structures: Materialization Explained Categorically

The paper develops an abstract (over-approximating) semantics for double-pushout rewriting of graphs and graph-like objects. The focus is on the so-called materialization of left-hand sides from abstract graphs, a central concept in previous work. The first contribution is an accessible, general explanation of how materializations arise from universal properties and categorical constructions, in particular partial map classifiers, in a topos. Second, we introduce an extension by enriching objects with annotations and give a precise characterization of strongest post-conditions, which are effectively computable under certain assumptions

Construction of Negatively Curved Cubic Carbon Crystals via Standard Realizations

We constructed physically stable sp2 negatively curved cubic carbon structures which reticulate a Schwarz P-like surface. The method for constructing such crystal structures is based on the notion of the standard realization of abstract crystal lattices. In this paper, we expound on the mathematical method to construct such crystal structures

Generalized Strong Preservation by Abstract Interpretation

Standard abstract model checking relies on abstract Kripke structures which approximate concrete models by gluing together indistinguishable states, namely by a partition of the concrete state space. Strong preservation for a specification language L encodes the equivalence of concrete and abstract model checking of formulas in L. We show how abstract interpretation can be used to design abstract models that are more general than abstract Kripke structures. Accordingly, strong preservation is generalized to abstract interpretation-based models and precisely related to the concept of completeness in abstract interpretation. The problem of minimally refining an abstract model in order to make it strongly preserving for some language L can be formulated as a minimal domain refinement in abstract interpretation in order to get completeness w.r.t. the logical/temporal operators of L. It turns out that this refined strongly preserving abstract model always exists and can be characterized as a greatest fixed point. As a consequence, some well-known behavioural equivalences, like bisimulation, simulation and stuttering, and their corresponding partition refinement algorithms can be elegantly characterized in abstract interpretation as completeness properties and refinements

An exemplar model should be able to explain all syntactic priming phenomena : a commentary on Ambridge (2020)

The authors argue that Ambridge’s radical exemplar account of language cannot clearly explain all syntactic priming evidence, such as inverse preference effects (greater priming for less frequent structures), and the contrast between short-lived lexical boost and long-lived abstract priming. Moreover, without recourse to a level of abstract syntactic structure, Ambridge’s account cannot explain abstract priming in amnesia patients or cross-linguistic priming. Instead, the authors argue that abstract representations remain the more parsimonious account for the wide variety of syntactic priming phenomena