Noncommutative Khintchine inequalities in interpolation spaces of LpL_p-spaces

We prove noncommutative Khintchine inequalities for all interpolation spaces between $L_p$ and $L_2$ with $p<2$. In particular, it follows that Khintchine inequalities hold in $L_{1,\infty}$. Using a similar method, we find a new deterministic equivalent for the $RC$-norm in all interpolation spaces between $L_p$-spaces which unifies the cases $p > 2$ and $p < 2$. It produces a new proof of Khintchine inequalities for $p<1$ for free variables. To complete the picture, we exhibit counter-examples which show that neither of the usual closed formulas for Khintchine inequalities can work in $L_{2,\infty}$. We also give an application to martingale inequalities.Comment: 33 pages, published versio

A Crevice on the Crane Beach: Finite-Degree Predicates

First-order logic (FO) over words is shown to be equiexpressive with FO equipped with a restricted set of numerical predicates, namely the order, a binary predicate MSB$_0$, and the finite-degree predicates: FO[Arb] = FO[<, MSB$_0$, Fin]. The Crane Beach Property (CBP), introduced more than a decade ago, is true of a logic if all the expressible languages admitting a neutral letter are regular. Although it is known that FO[Arb] does not have the CBP, it is shown here that the (strong form of the) CBP holds for both FO[<, Fin] and FO[<, MSB$_0$]. Thus FO[<, Fin] exhibits a form of locality and the CBP, and can still express a wide variety of languages, while being one simple predicate away from the expressive power of FO[Arb]. The counting ability of FO[<, Fin] is studied as an application.Comment: Submitte

Continuity of Functional Transducers: A Profinite Study of Rational Functions

A word-to-word function is continuous for a class of languages~$\mathcal{V}$ if its inverse maps $\mathcal{V}$_languages to~$\mathcal{V}$. This notion provides a basis for an algebraic study of transducers, and was integral to the characterization of the sequential transducers computable in some circuit complexity classes. Here, we report on the decidability of continuity for functional transducers and some standard classes of regular languages. To this end, we develop a robust theory rooted in the standard profinite analysis of regular languages. Since previous algebraic studies of transducers have focused on the sole structure of the underlying input automaton, we also compare the two algebraic approaches. We focus on two questions: When are the automaton structure and the continuity properties related, and when does continuity propagate to superclasses

The effects of stimulation of the anterior cingulate gyrus in cats with freedom of movement

Stimuli of varying strength, frequency and duration were applied to the anterior cingulate gyrus in unanesthetized cats with freedom of movement. The motor, vegetative and electrical effects of these stimuli, although inconstant, lead to a consideration of the role of this structure in the extrapyramidal control of motricity

Revealing otherness : a comparative examination of French and English medieval hagiographical romance

This dissertation is an analysis of three hagiographical romances written in France around the thirteenth century and later adapted into English. The texts are Ami et Amile, Robert le Diable and Florence de Rome and their English counterparts Amis and Amiloun, Sir Gowther and Le bone Florence of Rome. All six texts have been understudied, with the possible exception of Ami et Amile. They are linked in many ways, some thematic, some generic. They have all caused confusion and arguments as to what their genre is (Epic? Saint’s life? Romance? A combination of two or three genres?) and feature the defining notions of otherness, exile and penance. In spite of appearances, this work shows that the French and English authors prove to have quite different takes on the same stories. Drawing on Lacanian psychoanalysis and postcolonial theory, the chapters discuss the presence of otherness in the texts, in all its manifestations and offer new readings of the poems as well as possible solutions to the difficult question of genre in the middle ages. The many shapes taken by the other/Other (physical and emotional otherness; hybridity and gender) are exposed and utilised to uncover the meanings and ideological complexities of these multidimensional poems. This approach also reveals that the English texts propose a more conservative reading of common material than did their French originals. It is therefore suggested that the generic tendencies of these medieval texts be correlated with the importance of the Other in the respective redactions of the tales. Reading without consideration of these two factors produces a lopsided comparative view, while reading with both in mind leads to a better appreciation of rewriting and adaptation in the Middle Ages

Association between patient outcomes and key performance indicators of stroke care quality: A systematic review and meta-analysis

Purpose: Translating research evidence into clinical practice often uses key performance indicators to monitor quality of care. We conducted a systematic review to identify the stroke key performance indicators used in large registries, and to estimate their association with patient outcomes. Method: We sought publications of recent (January 2000–May 2017) national or regional stroke registers reporting the association of key performance indicators with patient outcome (adjusting for age and stroke severity). We searched Ovid Medline, EMBASE and PubMed and screened references from bibliographies. We used an inverse variance random effects meta-analysis to estimate associations (odds ratio; 95% confidence interval) with death or poor outcome (death or disability) at the end of follow-up. Findings: We identified 30 eligible studies (324,409 patients). The commonest key performance indicators were swallowing/nutritional assessment, stroke unit admission, antiplatelet use for ischaemic stroke, brain imaging and anticoagulant use for ischaemic stroke with atrial fibrillation, lipid management, deep vein thrombosis prophylaxis and early physiotherapy/mobilisation. Lower case fatality was associated with stroke unit admission (odds ratio 0.79; 0.72–0.87), swallow/nutritional assessment (odds ratio 0.78; 0.66–0.92) and antiplatelet use for ischaemic stroke (odds ratio 0.61; 0.50–0.74) or anticoagulant use for ischaemic stroke with atrial fibrillation (odds ratio 0.51; 0.43–0.64), lipid management (odds ratio 0.52; 0.38–0.71) and early physiotherapy or mobilisation (odds ratio 0.78; 0.67–0.91). Reduced poor outcome was associated with adherence to swallowing/nutritional assessment (odds ratio 0.58; 0.43–0.78) and stroke unit admission (odds ratio 0.83; 0.77–0.89). Adherence with several key performance indicators appeared to have an additive benefit. Discussion: Adherence with common key performance indicators was consistently associated with a lower risk of death or disability after stroke. Conclusion: Policy makers and health care professionals should implement and monitor those key performance indicators supported by good evidence

A metric characterization of freeness

Let $\mathcal{M}$ be a finite von Neumann algebra and $u_1,\dots,u_N$ be unitaries in $\mathcal{M}$. We show that $u_1,\dots,u_N$ freely generate $L(\mathbb{F}_N)$ if and only if $$\left\|\sum_{i=1}^N u_i \otimes (u_i^{\mathrm{op}})^* + u_i^*\otimes u_i^{\mathrm{op}}\right\|_{\mathcal{M}\overline{\otimes}\mathcal{M}^{\mathrm{op}}} = 2\sqrt{2N - 1}.$$Comment: 9 page