Weyl quantization of degree 2 symplectic graded manifolds

Let $S$ be a spinor bundle of a pseudo-Euclidean vector bundle $(E,\mathrm{g})$ of even rank. We introduce a new filtration on the algebra $\mathcal{D}(M,S)$ of differential operators on $S$. As main property, the associated graded algebra $\mathrm{gr}\mathcal{D}(M,S)$ is isomorphic to the algebra $\mathcal{O}(\mathcal{M})$ of functions on $\mathcal{M}$, where $\mathcal{M}$ is the symplectic graded manifold of degree $2$ canonically associated to $(E,\mathrm{g})$. Accordingly, we define the Weyl quantization on $\mathcal{M}$ as a map $\mathcal{WQ}_\hbar:\mathcal{O}(\mathcal{M})\to\mathcal{D}(M,S)$, and prove that $\mathcal{WQ}_\hbar$ satisfies all desired usual properties. As an application, we obtain a bijection between Courant algebroid structures $(E,\mathrm{g},\rho,[\cdot,\cdot])$, that are encoded by Hamiltonian generating functions on $\mathcal{M}$, and skew-symmetric Dirac generating operators $D\in\mathcal{D}(M,S)$. The operator $D^2$ gives a new invariant of $(E,\mathrm{g},\rho,[\cdot,\cdot])$, which generalizes the square norm of the Cartan $3$-form of a quadratic Lie algebra. We study in detail the particular case of $E$ being the double of a Lie bialgebroid $(A,A^*)$.Comment: 41 page

E-participation with social media in Science, Technology and Innovation: Brazilian States Research Support Foundations case

The use of social media has advanced in all social strata with effect on citizen participation in political discussions. In the context of Science, Technology and Innovation (ST&I) policies, bringing citizens closer together is a challenge for scientific and governmental institutions. The Brazilian States Research Support Foundations (RSF) show interest in promoting this approach to legitimize investments in science. Studies on the effects of social media on the relations between science, society and government are scarce. This research analyzed how e-participation, through social media, promotes citizen participation in the ST&I policies and actions of the RSFs. Nine organizations, including at least one Foundation from each Brazilian region, participated in this study. The main contribution of social media was the ability to intensify the interactions between government, researchers and citizens, using an informal and accessible language

The Roman Catholic Ordinary Mass from circa 1750 to circa 1820: A Selected Bibliography

Orchestrated masses from the 18th century and early years of the 19th century provide a valuable source of repertoire for contemporary choral conductors. This project will explore composers and works from circa 1750 to 1820 to provide choral conductors with a list of works suitable for programming based on the practical size of vocal and instrumental forces. Western choral music was born in a church setting. Among all choral genres, the mass is the only genre composed throughout all eras, from medieval until the 20th century. The mass remained a prominent genre during the 18th century despite the secularizing influence of the Enlightenment. Unlike earlier choral masses, these masses reflected the growing interest in and influence of orchestral music. According to Chester L. Alwes (2015) “The dominant genre of Classic-Romantic period is undoubtedly that of the Mass ordinary for chorus, soloists, and orchestra.” This paper will compile a catalog of masses featuring choir and orchestra as well as supplemental scholarly materials useful for interpretation and performance. The inventory will focus on the Roman Catholic Ordinary Masses from circa 1750 to circa 1820, using exclusively the Latin and Greek texts. In this document, the reader will also find a guide to research resources such as articles, theses, dissertations, books, and other written materials related to the collected works

Cognitive control is quickly adapted to actual task requirements despite misleading context cues—Evidence from the N2, CRN, and ERN

Cognitive control is flexibly adapted to task requirements in healthy individuals. Medio-frontal negativities in the event-related potential of the electroencephalogram can serve as indicators of cognitive control. With increasing conflict frequency, stimulus-locked control, as indexed by the N2, is increased and response-locked control, as indexed by the correct-related negativity, is reduced. On the behavioral level, this shift is associated with improved conflict resolution as evident in reduced response times and error rates in incompatible trials and a reduced response time congruency effect. Cognitive control adaptation might be implemented through experience-based task sets specifying advantageous processing strategies. Here, we investigated whether the cognitive control task set will be sustained when coupled with a contextual cue, even when the initial task requirements are no longer present. A flanker task with two conflict frequency conditions (25% incompatible and 75% incompatible trials) was presented. In the training phase, the conflict frequency conditions were paired with a distinct context cue (i.e., background color). In the test phase, the previously associated cues were again presented, but conflict frequency was identical in both conditions (50% incompatible trials). Although typical cognitive control adaptation was observed in the training phase on the behavioral and event-related potentials level, this pattern was not sustained in the test phase. Thus, the present study provides further evidence that cognitive control is flexibly adapted to task requirements even in the presence of misleading cues

Effects of a three-week executive control training on adaptation to task difficulty and emotional interference

Intact executive functions are characterized by flexible adaptation to task requirements, while these effects are reduced in internalizing disorders. Furthermore, as executive functions play an important role in emotion regulation, deficits in executive functions may contribute to symptom generation in psychological disorders through increased emotional interference. Thus, the present study investigated transfer effects of a three-week executive control training on adaptation to task difficulty and emotional interference in healthy participants (n = 24) to further explore the training’s suitability for clinical application. To assess the adaptation to task difficulty, the proportion congruency effect on behavioral data (response times, error rates) and ERP measures (N2, CRN) was assessed in a flanker task with varying frequency of incompatible trials (25%, 75%). To quantify emotional interference, flanker stimuli were superimposed on neutral or negative pictures. Replicating previous results, the training increased interference control as indexed by decreased response times and errors rates, increased N2 amplitude and decreased CRN amplitude in incompatible trials after training. Proportion congruency effects were weaker than expected and not affected by the training intervention. The training lead to a shift in the time-point of emotional interference: before training negative pictures lead to a reduction in CRN amplitude, while after training this reduction was observed for the N2. This pattern illustrates that the training leads to a change in task processing mode from predominant response-related cognitive control to predominant stimulus-related cognitive control (N2), indicating a proactive processing mode.Peer Reviewe

The Pontryagin Class for Pre-Courant Algebroids

In this paper, we show that the Jacobiator $J$ of a pre-Courant algebroid is closed naturally. The corresponding equivalence class $[J^\flat]$ is defined as the Pontryagin class, which is the obstruction of a pre-Courant algebroid to be deformed into a Courant algebroid. We construct a Leibniz 2-algebra and a Lie 2-algebra associated to a pre-Courant algebroid and prove that these algebraic structures are isomorphic under deformations. Finally, we introduce the twisted action of a Lie algebra on a manifold to give more examples of pre-Courant algebroids, which include the Cartan geometry.Comment: 26 page