This article uses formal and usage-based data and methods to argue for a hybrid model of English tensed auxiliary contraction combining lexical syntax with a dynamic exemplar lexicon. The hybrid model can explain why the contractions involve lexically specific phonetic fusions that have become morphologized and lexically stored, yet remain syntactically independent, and why the probability of contraction itself is a function of the adjacent cooccurrences of the subject and auxiliary in usage, yet is also subject to the constraints of the grammatical context. Novel evidence includes a corpus study and a formal analysis of a multiword expression of classic usage-based grammar.

The present article provides a diachronic analysis of the negation and contraction patterns of will and would in British and American English. It contrasts nineteenth- and twentieth-century data from British and American fiction, comparing the collocational preferences of negated versus non-negated and contracted versus non-contracted modals. Utilising Configural Frequency Analysis, we explore frequency differences as well as variety-specific association patterns. Results reveal predominantly commonalities. The spread of the modal contractions ’ll and ’d as well as the spread of the contracted negator n’t proceeded at similar speeds in both varieties. The analysis at the level of cotextual configurations shows the emergence of several emancipated subschemas that are each differentially entrenched and conventionalised.

Two of the most well-known belief contraction operators are partial meet contractions (PMCs) and kernel contractions (KCs). In this paper we propose two new classes of contraction operators, namely the class of generalized partial meet contractions (GPMC) and the class of generalized kernel contractions (GKC), which strictly contain the classes of PMCs and of KCs, respectively. We identify some extra conditions that can be added to the definitions of GPMCs and of GKCs, which give rise to some interesting subclasses of those classes of functions, namely the classes of extensional and of uniform GPMCs/GKCs. In the context of contractions on belief sets the classes of partial meet contractions, uniform GPMCs and extensional GPMCs are all identical. Nevertheless, when considered as operations on belief bases, the class of uniform GPMCs coincides with the class of partial meet contractions, but the extensional GPMCs constitute a new kind of belief base contraction functions whose characterizing postulate of irrelevance of syntax is extensionality—the same postulate of irrelevance of syntax which occurs in the classical axiomatic characterization of partial meet contractions for belief sets—rather than the postulate of uniformity—which is the irrelevance of syntax postulate used in the axiomatic characterization for partial meet contractions on belief bases. Analogous results are obtained regarding the classes of extensional and of uniform GKCs. We present the interrelations in the sense of inclusion among all the new classes of operators presented in this paper and several well known classes of PMCs and of KCs.

Certain instances of contraction are provable in Zardini’s system $\mathbf {IK}^\omega $ which causes triviality once a truth predicate and suitable fixed points are available.

There is ample psycholinguistic evidence that speakers behave efficiently, using shorter and less effortful constructions when the meaning is more predictable, and longer and more effortful ones when it is less predictable. However, the Principle of No Synonymy requires that all formally distinct variants should also be functionally different. The question is how much two related constructions should overlap semantically and pragmatically in order to be used for the purposes of efficient communication. The case study focuses on want to + Infinitive and its reduced variant with wanna, which have different stylistic and sociolinguistic connotations. Bayesian mixed-effects regression modelling based on the spoken part of the British National Corpus reveals a very limited effect of efficiency: predictability increases the chances of the reduced variant only in fast speech. We conclude that efficient use of more and less effortful variants is restricted when two variants are associated with different registers or styles. This paper also pursues a methodological goal regarding missing values in speech corpora. We impute missing data based on the existing values. A comparison of regression models with and without imputed values reveals similar tendencies. This means that imputation is useful for dealing with missing values in corpora.

We prove the existence of common fixed points for monotone contractive and monotone nonexpansive semigroups of nonlinear mappings acting in Banach spaces equipped with partial order. We also discuss some applications to differential equations and dynamical systems.

In this paper we investigate gradient estimation for a class of contracting stochastic systems on a continuous state space. We find conditions on the one-step transitions, namely differentiability and contraction in a Wasserstein distance, that guarantee differentiability of stationary costs. Then we show how to estimate the derivatives, deriving an estimator that can be seen as a generalization of the forward sensitivity analysis method used in deterministic systems. We apply the results to examples, including a neural network model.

In 1968 Emmerick proposed the existence of a present stem type D. It is shown here from morphophonological patterning that his category contains two subtypes, temporarily labelled D1 and D2. By comparing vocalic contractions from the nominals with the D1 endings, it is clear that the D1 stems end synchronically in -a- and take the regular type A endings. The D2 stem vowel in contrast, behaves partly like nominal stems in -a-, and partly like stems in -i-. By reviewing contraction evidence relating to all vowels, it is shown that the D2 stems end synchronically, albeit abstractly, in -e- and take the regular type A endings. Two further verbs from Emmerick's type C are shown also to end in -e- and take the regular endings.

In this paper we prove Caristi’s fixed point theorem using only purely metric techniques.

Background: Short- (SICI) and long-interval intracortical inhibition (LICI) are involved in the control of movement and movement initiation. Alterations to the two circuits can result in direct alterations to the physiology of the muscles and can be used to explain the physiological changes to individuals with spinal cord injury (SCI). Objective: To probe changes in GABAergic function by characterizing the recruitment curves of SICI and LICI interval intracortical inhibition in an upper limb muscle in chronic SCI participants with injury between C3 and C7. Methods: Recruitment curves were elicited with conditioning stimulus intensities determined as a percentage of active motor threshold (AMT) (SICI, 60% to 110% AMT; LICI, 90% to 130% AMT) and recorded from the flexor carpi radialis muscle during an isometric contraction equal to 15% to 20% of maximum voluntary contraction. Results: AMT was greater and motor-evoked potential sizes were lower in SCI compared with uninjured controls. SICI magnitude was not different between groups, although the range of conditioning stimulus intensities to evoke SICI was unique to each group. LICI was reduced in the control group during active contraction and remained present in SCI. Discussion: LICI was increased in the actively contracted flexor carpi radialis muscle in individuals with SCI compared with age-matched controls. These findings indicate that GABAB function mediating LICI is different in SCI versus controls. Conclusions: Increased LICI in SCI may be attributed to the medication baclofen or to changes in the neural mechanisms controlling contraction-related modulation of the LICI circuit.

In this article, we prove convergence of the weakly penalized adaptive discontinuousGalerkin methods. Unlike other works, we derive the contraction property for variousdiscontinuous Galerkin methods only assuming the stabilizing parameters are large enoughto stabilize the method. A central idea in the analysis is to construct an auxiliarysolution from the discontinuous Galerkin solution by a simple post processing. Based onthe auxiliary solution, we define the adaptive algorithm which guides to the convergenceof adaptive discontinuous Galerkin methods.