Amalgamation and interpolation in ordered algebras

The first part of this paper provides a comprehensive and self-contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations. In particular, proofs are given of known equivalences between the amalgamation property and the Robinson property, the congruence extension property and the extension property, and the flat amalgamation property and the deductive interpolation property, as well as various dependencies between these properties. These relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice-ordered abelian groups and MV-algebras, and to determine important subvarieties of residuated lattices where these properties hold or fail. In particular, a full description is given of all subvarieties of commutative GMV-algebras possessing the amalgamation property.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

Because someone has recommended it - Patients’ reasons for choosing acupuncture or qigong

Question: Recent research has indicated a considerable contribution of placebo effects to the outcome of acupuncture treatments: especially patients’ expectations seem to have an influence [1] and [2]. In this context it is important to better understand the patient–practitioner relationship. The aim of this study was to investigate why patients in Switzerland choose acupuncture or qigong, and what they expect from the treatment and the practitioners [3]. Methods: A qualitative survey with open questions was performed among 38 patients newly enrolled for treatment in 7 different practices for Traditional Chinese Medicine ((TCM); 6 practices for acupuncture, 1 for qigong). Questions aimed to identify reasons for choosing TCM, knowledge about its range of indications, and patients’ expectations towards method and therapist. Answers were categorised and analysed by frequency. Results: The most common reasons for choosing TCM were recommendation by acquaintances, the idea of trying a new treatment and the perception of TCM as being a gentle method. The majority of respondents had poor knowledge about the range of conditions to be treated with TCM: pain of the musculoskeletal system, headaches and chronic problems were considered as main indications. Surprisingly, gynaecological or gastro-intestinal diseases were not mentioned by the respondents. Practitioners were expected to have professional competence, provide information, empathy and understanding. Conclusions: The most striking result of this survey was the fact that patients knew very little about TCM and its indications. Thus, more precise information about TCM and other complementary methods should be offered to the general public, which would help patients to decide whether to consider TCM for the treatment of their disease. And, on the other hand, for the therapists it is important to better understand and respond to patients’ expectations in order to achieve better treatment results. The results of this qualitative survey were briefly discussed with the participating practitioners, who found them remarkable and support further quantitative studies. We plan to further investigate this topic. References 1. J. Pariente, P. White, R.S.J. Frackowiak, G. Lewith. Neuroimage, 25 (2005), pp. 1161–1167 2. M. Karst, D. Schneidewind, D. Scheinichen. Forsch Komplementmed, 17 (2010), pp. 21–27 3. S.D. Klein. Dt Ztschr f Akup, 52 (2009), pp. 18–23

Evaluation of perpendicular reflection intensity for assessment of caries lesion activity/inactivity

The aim of this study was to evaluate, using visual assessment, an experimental optical sensor measuring perpendicular reflection intensity (PRI) as an indicator of enamel caries lesion activity/inactivity. Forty teeth with either an active or an inactive enamel lesion were selected from a pool of extracted teeth. Each tooth was cut into halves, with a clinically sound half and a half with a non-cavitated enamel lesion. After gentle plaque removal, the teeth were kept moistened. The lesions were then photographed and a defined measuring site per lesion was chosen and indicated with an arrow on a printout. Independently, the chosen site was visually assessed for lesion activity, and its glossiness was measured with PRI assessment. Surface roughness (SR) was assessed with optical profilometry using a confocal microscope. Visual assessment and PRI were repeated after several weeks and a reliability analysis was performed. For enamel lesions visually scored as active versus inactive, significantly different values were obtained with both PRI and SR. PRI values of the clinically sound control surfaces were significantly different only from active lesions. Generally, inactive lesions had the same glossiness and the same roughness as the sound control surfaces. The reliabilities for visual assessment (? = 0.89) and for PRI (ICC = 0.86) were high. It is concluded that, within the limits of this study, PRI can be regarded as a promising tool for quantitative enamel lesion activity assessment. There is scope and potential for the PRI device to be considerably improved for in vivo use.

Flow experience during Taiji practice - an oberservational study in healthy subjects

Background: Taiji is a mind-body practice, characterised by gentle and mindful body movements originating from Chinese martial arts. Studies investigating the reasons why people engage into Taiji and maintain their practice routine have emphasised extrinsic motivational outcome related aspects. The relevance of intrinsic motivation (i.e. motivation that comes from inside an individual and is driven by an interest or enjoyment in the performed activity itself) has not yet been examined. The autotelic aspect of intrinsic motivation is an essential precondition for experiencing flow, a state where subjects fully immersed into the performance of an activity report to be highly concentrated, optimally challenged and in control of the action. The aim of our study was to assess to which degree flow was experienced in the course of a 3 month Taiji-beginners class and to examine the relationship between the degree of flow experience at the end of the course and the Taiji practice behaviour. Materials and Methods: 28 healthy subjects participated in a Taiji beginners course (2 x 1h per week for 3 months). Flow values were measured at week 1, 6 and 12 by using the Flow-Kurz-Skala (FKS) questionnaire. Data were analysed by using ANOVA with repeated measurements, students t-Tests for comparison with normative values, and pearson correlation coefficients were calculated. Results: In the course of the 12 weeks Taiji training, mean flow values increased continuously (F(1.34, 8.92) = 19.49; p < .001). The mean value for experienced flow during Taiji practice at week 12 (M = 5.54; SD = ±.77) was significantly above the norm value (t = 3.705; df = 27; p < .01). Since average course attendance rate was high (86.8 %), a ceiling effect is assumed, thus flow values did not correlate with course adherence (r = .236; p = .227). However, a significant correlation was found between flow values at week 12 and practice at home (r = .439; p < .05). Conclusion: Our findings emphasise the potential value of intrinsic motivational aspects inherent in Taiji practice for developing a regular practice routine. The impact of increased flow experience on health related outcome measures, and its relevance in clinical trials is subject of further research.

Taiji practice attenuates psychobiological stress reactivity - A randomized controlled trial in healthy subjects

Background: Stress reducing effects of Taiji, a mindful and gentle form of body movement, have been reported in previous studies, but standardized and controlled experimental studies are scarce. The present study investigates the effect of regular Taiji practice on psychobiological stress response in healthy men and women. Methods: 70 participants were randomly assigned to either Taiji classes or a waiting list. After 3 months, 26 (8 men, 18 women) persons in the Taiji group and 23 (9 men, 14 women) in the waiting control group underwent a standardized psychosocial stress test combining public speaking and mental arithmetic in front of an audience. Salivary cortisol and α-amylase, heart rate, and psychological responses to psychosocial stress were compared between the study groups. (ClinicalTrials.gov number, NCT01122706.) Results: Stress induced characteristic changes in all psychological and physiological measures. Compared to controls, Taiji participants exhibited a significantly lower stress reactivity of cortisol (p = .028) and heart rate (p = .028), as well as lower α-amylase levels (p = .049). They reported a lower increase in perceived stressfulness (p = .006) and maintained a higher level of calmness (p = .019) in response to psychosocial stress. Conclusion: Our results consistently suggest that practicing Taiji attenuates psychobiological stress reactivity in healthy subjects. This may underline the role of Taiji as a useful mind–body practice for stress prevention.

Sleep deprivation before stroke is neuroprotective: A pre-ischemic conditioning related to sleep rebound

BACKGROUND AND AIM: We have previously shown in a rat model of focal cerebral ischemia that sleep deprivation after stroke onset aggravates brain damage. Others reported that sleep deprivation prior to stroke is neuroprotective. The main aim of this study was to test the hypothesis that the neuroprotection may be related to an increase in sleep (sleep rebound) during the acute phase of stroke. METHODS: Male Sprague Dawley rats (n=36) were subjected to continuous polygraphic recordings for baseline, total sleep deprivation (TSD), and 24h after ischemia. TSD for 6h was performed by gentle handling and immediately followed by ischemia. Focal cerebral ischemia was induced by permanent occlusion of distal branches of the middle cerebral artery. Control experiments included ischemia without SD (nSD) and sham surgery with TSD (n=6/group). RESULTS: Shortly after stroke, the amount of slow wave sleep (SWS) and paradoxical sleep (PS) increased significantly (p<0.05) in the TSD/ischemia, resulting in an increase in the total sleep time by 30% compared to baseline, or by 20% compared with the nSD/ischemia group. The infarct volume decreased significantly by 50% in the TSD/ischemia compared to nSD group (p<0.02). Removal of sleep rebound by allowing TSD-rats sleep for 24h before ischemia eliminated the reduction in the infarct size. CONCLUSION PRESTROKE: Sleep deprivation results in sleep rebound and reduces brain damage. Sleep rebound may be causally related to the neuroprotection.