Geometric Measure of Indistinguishability for Groups of Identical Particles

The concept of p-orthogonality (1=< p =< n) between n-particle states is introduced. It generalizes common orthogonality, which is equivalent to n-orthogonality, and strong orthogonality between fermionic states, which is equivalent to 1-orthogonality. Within the class of non p-orthogonal states a finer measure of non p-orthogonality is provided by Araki's angles between p-internal spaces. The p-orthogonality concept is a geometric measure of indistinguishability that is independent of the representation chosen for the quantum states. It induces a new hierarchy of approximations for group function methods. The simplifications that occur in the calculation of matrix elements between p-orthogonal group functions are presented

Biomarkers ST2 and interleukin 33 for assessing the severity of cardiac inflammation and fibrosis in patients with chronic heart failure

Chronic heart failure (CHF) is a pathology that affects more than 37 million people worldwide. Despite the introduction of new drugs into practice, that have proven their effectiveness in the treatment of patients with CHF, the life expectancy of these patients is growing at a slow pace. At the same time, the insufficient effect of neurohormonal blockers for the treatment of patients with CHF with preserved ejection fraction (CHFpEF), which prevails in the general structure of CHF, indicates a significant role of unidentified pathological processes in the development of this form of the disease. In recent years, the role of cardiac fibrosis has been actively studied within the framework of the investigation of the pathogenesis of CHFpEF, the probable biomarkers of which are interleukin (IL) 33 and suppression of tumorigenicity 2 (ST2). This literature review examines the influence of the IL-33/ ST2 interaction as a biomarker of cardiac fibrosis on the course of CHF and the possibilities of its practical application