Semi-invariants of symmetric quivers of tame type

A symmetric quiver $(Q,\sigma)$ is a finite quiver without oriented cycles $Q=(Q_0,Q_1)$ equipped with a contravariant involution $\sigma$ on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form on a representation $V$ of $Q$. We shall say that $V$ is orthogonal if is symmetric and symplectic if $$ is skew-symmetric. Moreover, we define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. So we prove that if $(Q,\sigma)$ is a symmetric quiver of tame type then the rings of semi-invariants for this action are spanned by the semi-invariants of determinantal type $c^V$ and, when matrix defining $c^V$ is skew-symmetric, by the Pfaffians $pf^V$. To prove it, moreover, we describe the symplectic and orthogonal generic decomposition of a symmetric dimension vector

Semi-invariants of symmetric quivers of finite type

Let $(Q,\sigma)$ be a symmetric quiver, where $Q=(Q_0,Q_1)$ is a finite quiver without oriented cycles and $\sigma$ is a contravariant involution on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form on a representation $V$ of $Q$. We shall call the representation orthogonal if is symmetric and symplectic if $$ is skew-symmetric. Moreover we can define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. For symmetric quivers of finite type, we prove that the rings of semi-invariants for this action are spanned by the semi-invariants of determinantal type $c^V$ and, in the case when matrix defining $c^V$ is skew-symmetric, by the Pfaffians $pf^V$

Self-care of heart failure patients: practical management recommendations from the Heart Failure Association of the European Society of Cardiology.

Self-care is essential in the long-term management of chronic heart failure. Heart failure guidelines stress the importance of patient education on treatment adherence, lifestyle changes, symptom monitoring and adequate response to possible deterioration. Self-care is related to medical and person-centred outcomes in patients with heart failure such as better quality of life as well as lower mortality and readmission rates. Although guidelines give general direction for self-care advice, health care professionals working with patients with heart failure need more specific recommendations. The aim of the management recommendations in this paper is to provide practical advice for health professionals delivering care to patients with heart failure. Recommendations for nutrition, physical activity, medication adherence, psychological status, sleep, leisure and travel, smoking, immunization and preventing infections, symptom monitoring, and symptom management are consistent with information from guidelines, expert consensus documents, recent evidence and expert opinion

Biofluid Biomarkers in Huntington's Disease

Huntington's disease (HD) is a chronic progressive neurodegenerative condition where new markers of disease progression are needed. So far no disease-modifying interventions have been found, and few interventions have been proven to alleviate symptoms. This may be partially explained by the lack of reliable indicators of disease severity, progression, and phenotype.Biofluid biomarkers may bring advantages in addition to clinical measures, such as reliability, reproducibility, price, accuracy, and direct quantification of pathobiological processes at the molecular level; and in addition to empowering clinical trials, they have the potential to generate useful hypotheses for new drug development.In this chapter we review biofluid biomarker reports in HD, emphasizing those we feel are likely to be closest to clinical applicability