Hyper-symplectic structures on integrable systems

We prove that an integrable system over a symplectic manifold, whose symplectic form is covariantly constant w.r.t. the Gauss-Manin connection, carries a natural hyper-symplectic structure. Moreover, a special Kaehler structure is induced on the base manifold.Comment: LaTeX file, 7 pages; to be published in Journal of Geometry and Physic

A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver

We show that there exists a morphism between a group $\Gamma^{\mathrm{alg}}$ introduced by G. Wilson and a quotient of the group of tame symplectic automorphisms of the path algebra of a quiver introduced by Bielawski and Pidstrygach. The latter is known to act transitively on the phase space $\mathcal{C}_{n,2}$ of the Gibbons-Hermsen integrable system of rank 2, and we prove that the subgroup generated by the image of $\Gamma^{\mathrm{alg}}$ together with a particular tame symplectic automorphism has the property that, for every pair of points of the regular and semisimple locus of $\mathcal{C}_{n,2}$, the subgroup contains an element sending the first point to the second

Insertion and Elimination Lie Algebra: the Ladder case

We prove that insertion-elimination Lie algebra of Feynman graphs, in the ladder case, has a natural interpretation in terms of a certain algebra of infinite dimensional matrices. We study some aspects of its representation theory and we discuss some relations with the representation of the Heisenberg algebraComment: LaTex, 17 pages, typos corrected, to appear in LM

A structured strategy of concept definition in measurement: the case of sensitivity

The paper emphasizes the importance that fundamental concepts in measurement science are defined according to a structured strategy, which provides both a general, qualitative characterization and a specific, type-related, quantitative definition. As a significant case, the concept 'sensitivity' is discussed and a definition for it proposed

Continuous Estimation of Emotions in Speech by Dynamic Cooperative Speaker Models

Automatic emotion recognition from speech has been recently focused on the prediction of time-continuous dimensions (e.g., arousal and valence) of spontaneous and realistic expressions of emotion, as found in real-life interactions. However, the automatic prediction of such emotions poses several challenges, such as the subjectivity found in the definition of a gold standard from a pool of raters and the issue of data scarcity in training models. In this work, we introduce a novel emotion recognition system, based on ensemble of single-speaker-regression-models (SSRMs). The estimation of emotion is provided by combining a subset of the initial pool of SSRMs selecting those that are most concordance among them. The proposed approach allows the addition or removal of speakers from the ensemble without the necessity to re-build the entire machine learning system. The simplicity of this aggregation strategy, coupled with the flexibility assured by the modular architecture, and the promising results obtained on the RECOLA database highlight the potential implications of the proposed method in a real-life scenario and in particular in WEB-based applications

Post-Lie Algebras and Isospectral Flows

In this paper we explore the Lie enveloping algebra of a post-Lie algebra derived from a classical $R$-matrix. An explicit exponential solution of the corresponding Lie bracket flow is presented. It is based on the solution of a post-Lie Magnus-type differential equation