A Riemann-Roch-Hirzebruch formula for traces of differential operators

Let D be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an n-dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, for the Lefschetz number of D as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator of the Hochschild cohomology of the algebra of differential operators in a formal neighbourhood of a point. If D is the identity, the formula reduces to the Riemann--Roch--Hirzebruch formula.Comment: 31 pages, 1 figure. Misprints corrected and appendix with analytical details added in v

Binnendifferenzierte Sachtexte als Unterstützung für den Erwerb von domänenspezifischen Wissensbeständen und Konzepten: Executive Summary

Les textes dans les livres d’école sont souvent trop difficiles même pour des élèves de niveau moyen. Pour des apprenants plus faibles et des enfants pour qui l’allemand est une langue seconde, ces textes sont trop exigeants sur le plan linguistique. La mise à disposition de textes de niveaux différenciés est dès lors une nécessité pour une école inclusive.Texts in the social sciences at schools are often difficult even for children with average scholastic abilities; weak learners or children who speak German as a second language are over-challenged. Consequently, internally differentiated texts – i.e. different versions of the same content – are necessary to create an inclusive learning environment.Sachtexte in Schulbüchern sind oft selbst für durchschnittlich begabte Kinder zu schwer; für schwächere Lernende und für Kinder mit Deutsch als Zweitsprache sind sie sprachlich überfordernd. Binnendifferenzierte Sachtexte sind deshalb eine Notwendigkeit für eine inklusive Schule.I testi contenuti nei libri scolastici sono spesso troppo difficili persino per gli allievi di livello medio; per gli studenti più deboli e per i bambini per i quali il tedesco è una seconda lingua, questi testi sono troppo esigenti dal punto di vista linguistico. L’offerta di testi che variano dal punto di vista della difficoltà di lettura diventa perciò una necessità per una scuola inclusiva.Il project „Texts tematics differenziads a l’intern sco med per sustegnair l’acquisiziun dal savair e da concepts da domenas specificas“ sa basa sin la constataziun che meds d’instruir e d‘emprender (ed ils texts tematics cuntegnids en quels) stattan anc adina en il center da l’instrucziun, ma na satisfan betg a las pretensiuns per in’instrucziun individualisanta. Questa constataziun stat en connex cun las exigenzas ad ina scola inclusiva ed a las consequenzas organisatoricas da la differenziaziun interna

Cue-induced cocaine craving enhances psychosocial stress and vice versa in chronic cocaine users.

Stress and craving, it has been found, contribute to the development and maintenance of and relapse in cocaine use disorder. Chronic cocaine users (CU), previous research has shown, display altered physiological responses to psychosocial stress and increased vegetative responding to substance-related cues. However, how psychosocial stress and cue-induced craving interact in relation to the CU's physiological responses remains largely unknown. We thus investigated the interaction between acute psychosocial stress and cocaine-cue-related reactivity in 47 CU and 38 controls. In a crossed and balanced design, the participants were randomly exposed to a video-based cocaine-cue paradigm and the Trier Social Stress Test (TSST) or vice versa to investigate possible mutually augmenting effects of both stressors on physiological stress responses. Over the course of the experimental procedure, plasma cortisol, ACTH, noradrenaline, subjective stress, and craving were assessed repeatedly. To estimate the responses during the cocaine-cue paradigm and TSST, growth models and discontinuous growth models were used. Overall, though both groups did not differ in their endocrinological responses to the TSST, CU displayed lower ACTH levels at baseline. The TSST did not elevate craving in CU, but when the cocaine-cue video was shown first, CU displayed an enhanced cortisol response to the subsequent TSST. In CU, cocaine-cues robustly evoked craving but no physiological stress response, while cue-induced craving was intensified after the TSST. Taken together, though CU did not show an altered acute stress response during the TSST, stress and craving together seemed to have mutually augmenting effects on their stress response

Cue-induced cocaine craving enhances psychosocial stress and vice versa in chronic cocaine users

Stress and craving, it has been found, contribute to the development and maintenance of and relapse in cocaine use disorder. Chronic cocaine users (CU), previous research has shown, display altered physiological responses to psychosocial stress and increased vegetative responding to substance-related cues. However, how psychosocial stress and cue-induced craving interact in relation to the CU’s physiological responses remains largely unknown. We thus investigated the interaction between acute psychosocial stress and cocaine-cue-related reactivity in 47 CU and 38 controls. In a crossed and balanced design, the participants were randomly exposed to a video-based cocaine-cue paradigm and the Trier Social Stress Test (TSST) or vice versa to investigate possible mutually augmenting effects of both stressors on physiological stress responses. Over the course of the experimental procedure, plasma cortisol, ACTH, noradrenaline, subjective stress, and craving were assessed repeatedly. To estimate the responses during the cocaine-cue paradigm and TSST, growth models and discontinuous growth models were used. Overall, though both groups did not differ in their endocrinological responses to the TSST, CU displayed lower ACTH levels at baseline. The TSST did not elevate craving in CU, but when the cocaine-cue video was shown first, CU displayed an enhanced cortisol response to the subsequent TSST. In CU, cocaine-cues robustly evoked craving but no physiological stress response, while cue-induced craving was intensified after the TSST. Taken together, though CU did not show an altered acute stress response during the TSST, stress and craving together seemed to have mutually augmenting effects on their stress response

Self-regulation of the dopaminergic reward circuit in cocaine users with mental imagery and neurofeedback

BACKGROUND Enhanced drug-related reward sensitivity accompanied by impaired sensitivity to non-drug related rewards in the mesolimbic dopamine system are thought to underlie the broad motivational deficits and dysfunctional decision-making frequently observed in cocaine use disorder (CUD). Effective approaches to modify this imbalance and reinstate non-drug reward responsiveness are urgently needed. Here, we examined whether cocaine users (CU) can use mental imagery of non-drug rewards to self-regulate the ventral tegmental area and substantia nigra (VTA/SN). We expected that obsessive and compulsive thoughts about cocaine consumption would hamper the ability to self-regulate the VTA/SN activity and tested if real-time fMRI (rtfMRI) neurofeedback (NFB) can improve self-regulation of the VTA/SN. METHODS Twenty-two CU and 28 healthy controls (HC) were asked to voluntarily up-regulate VTA/SN activity with non-drug reward imagery alone, or combined with rtfMRI NFB. RESULTS On a group level, HC and CU were able to activate the dopaminergic midbrain and other reward regions with reward imagery. In CU, the individual ability to self-regulate the VTA/SN was reduced in those with more severe obsessive-compulsive drug use. NFB enhanced the effect of reward imagery but did not result in transfer effects at the end of the session. CONCLUSION CU can voluntary activate their reward system with non-drug reward imagery and improve this ability with rtfMRI NFB. Combining mental imagery and rtFMRI NFB has great potential for modifying the maladapted reward sensitivity and reinstating non-drug reward responsiveness. This motivates further work to examine the use of rtfMRI NFB in the treatment of CUD

Effect of normobaric hypoxic exercise on blood pressure in old individuals

Purpose To test the hypothesis that the combination of endurance training and hypoxia leads to greater improvements in resting and exercise blood pressure in old sedentary individuals compared to endurance training only. Methods We randomly assigned 29 old overweight participants (age: 62 +/- 6 years, body mass index (BMI): 28.5 +/- 0.5 kg/m(2), 52% men) to single blind 8-week bicycle exercise in hypoxia (fraction of inspired oxygen (FIO2) = 0.15) or normoxia (FIO2 = 0.21). Brachial blood pressure was measured at rest, during maximal incremental exercise testing, and during a 30 min constant work rate test, at baseline and after the training period. Results Work rate, heart rate and perceived exertion during training were similar in both groups, with lower oxygen saturation for participants exercising under hypoxia (88.7 +/- 1.5 vs. 96.2 +/- 1.2%, t(27) = - 13.04, p < 0.001, |g|= 4.85). Office blood pressure and blood pressure during incremental exercise tests did not change significantly in either group after the training program. Systolic blood pressure during the constant work rate test was reduced after training in hypoxia (160 +/- 18 vs. 151 +/- 14 mmHg, t(13) = 2.44 p < 0.05, |d|= 0.55) but not normoxia (154 +/- 22 vs. 150 +/- 16 mmHg, t(14) = 0.75, p = 0.46, |d|= 0.18) with no difference between groups over time (F = 0.08, p = 0.77, eta(2) = 0.01). Conclusion In old individuals hypoxia in addition to exercise does not have superior effects on office or exercise blood pressure compared to training in normoxia

Impaired glutamate homeostasis in the nucleus accumbens in human cocaine addiction

Cocaine addiction is characterized by overwhelming craving for the substance, which drives its escalating use despite adverse consequences. Animal models suggest a disrupted glutamate homeostasis in the nucleus accumbens to underlie addiction-like behaviour. After chronic administration of cocaine, rodents show decreased levels of accumbal glutamate, whereas drug-seeking reinstatement is associated with enhanced glutamatergic transmission. However, due to technical obstacles, the role of disturbed glutamate homeostasis for cocaine addiction in humans remains only partially understood, and accordingly, no approved pharmacotherapy exists. Here, we applied a tailored proton magnetic resonance spectroscopy protocol that allows glutamate quantification within the human nucleus accumbens. We found significantly reduced basal glutamate concentrations in the nucleus accumbens in cocaine-addicted (N = 26) compared to healthy individuals (N = 30), and increased glutamate levels during cue-induced craving in cocaine-addicted individuals compared to baseline. These glutamatergic alterations, however, could not be significantly modulated by a short-term challenge of N-acetylcysteine (2400 mg/day on two days). Taken together, our findings reveal a disturbed accumbal glutamate homeostasis as a key neurometabolic feature of cocaine addiction also in humans. Therefore, we suggest the glutamatergic system as a promising target for the development of novel pharmacotherapies, and in addition, as a potential biomarker for a personalised medicine approach in addiction