All Stable Characteristic Classes of Homological Vector Fields

An odd vector field $Q$ on a supermanifold $M$ is called homological, if $Q^2=0$. The operator of Lie derivative $L_Q$ makes the algebra of smooth tensor fields on $M$ into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator $L_Q$ and are represented by $Q$-invariant tensors made up of the homological vector field and a symmetric connection on $M$ by means of tensor operations.Comment: 17 pages, references and comments adde

The role of cardiac biomarkers and epicardial fat in the diagnosis of heart failure in patients with various types of atrial fibrillation

Aim. To assess the level of various cardiac biomarkers and the volume of epicardial adipose tissue (EAT) in patients with heart failure (HF) depending on the type of atrial fibrillation (AF).Material and methods. This prospective observational study included 69 patients with symptomatic AF, as well as with manifestations of New York Heart Association (NYHA) class II-III HF. All patients were examined before catheter ablation for AF. The following investigations were performed: echocardiography, computed tomography, myocardial perfusion scintigraphy, immunochemical analysis of cardiac biomarkers (brain natriuretic peptide (BNP), high-sensitivity troponin I (hs-TnI)), as well as biochemical analysis of high-sensitivity C reactive protein (hsCRP). Patients were divided into 2 groups, depending on the AF type, into paroxysmal and non-paroxysmal (persistent and long-standing persistent).Results. The analysis included 69 patients with various AF types and symptomatic HF. There were significantly more patients with HF confirmed by an elevated BNP level in the group with non-paroxysmal type (27 (71%) vs 5 (16%), p<0,00001). Comparison analysis showed that in group 2 the mean BNP level was significantly higher than in group 1 (135,5 pg/ml [75,2;303,2] vs 40 pg/ml [20,7;56,9], respectively, p<0,00001). The hs-TnI level was higher in group 2 (2,5 [1,7;5,1] vs 1,9 [0,8;3,9], respectively, p=0,19), but there was no significant difference between the groups. The level of hsCRP did not differ in both groups. In group 1, the EAT volume was 139 [117,5;171] vs 169 [130;209,5] in group 2 (p=0,03).Conclusion. The type of AF plays a role in the interpretation of cardiac specific enzymes, and BNP levels and EAT volume are higher in patients with the non-paroxysmal form

Effect of promoter architecture on the cell-to-cell variability in gene expression

According to recent experimental evidence, the architecture of a promoter, defined as the number, strength and regulatory role of the operators that control the promoter, plays a major role in determining the level of cell-to-cell variability in gene expression. These quantitative experiments call for a corresponding modeling effort that addresses the question of how changes in promoter architecture affect noise in gene expression in a systematic rather than case-by-case fashion. In this article, we make such a systematic investigation, based on a simple microscopic model of gene regulation that incorporates stochastic effects. In particular, we show how operator strength and operator multiplicity affect this variability. We examine different modes of transcription factor binding to complex promoters (cooperative, independent, simultaneous) and how each of these affects the level of variability in transcription product from cell-to-cell. We propose that direct comparison between in vivo single-cell experiments and theoretical predictions for the moments of the probability distribution of mRNA number per cell can discriminate between different kinetic models of gene regulation.Comment: 35 pages, 6 figures, Submitte