Lie integrability for time-independent and time-dependent Hamiltonian systems

In this paper we present the theorem on Lie integrability by quadratures for time-independent Hamiltonian systems on symplectic and contact manifolds, and for time-dependent Hamiltonian systems on cosymplectic and cocontact manifolds. We show that having a solvable Lie algebra of constants of motion for a Hamiltonian system is equivalent to having a solvable Lie algebra of symmetries of the vector field defining the dynamics of the system, which allows us to find the solutions of the equations of motion by quadratures.Comment: Comments are welcome. arXiv admin note: text overlap with arXiv:2211.0297

Scaling symmetries and canonoid transformations in Hamiltonian systems

We investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case we pay special attention to non-standard (non-canonical) symmetries, in particular scaling symmetries and canonoid transformations, as they provide new interesting tools for the qualitative study of these systems. Our main results are the characterizations of these non-standard symmetries and the analysis of their relation with conserved (or dissipated) quantities.Comment: 22 pages. Comments are welcom

Canonical and canonoid transformations for Hamiltonian systems on (co)symplectic and (co)contact manifolds

In this paper we present canonical and canonoid transformations considered as global geometrical objects for Hamiltonian systems. Under the mathematical formalisms of symplectic, cosymplectic, contact and cocontact geometry, the canonoid transformations are defined for (co)symplectic, (co)contact Hamiltonian systems, respectively. The local characterizations of these transformations is derived explicitly and it is demonstrated that for a given canonoid transformation there exist constants of motion associated with itComment: 18 page

Transforming growth factor β receptor 1 is a new candidate prognostic biomarker after acute myocardial infarction

<p>Abstract</p> <p>Background</p> <p>Prediction of left ventricular (LV) remodeling after acute myocardial infarction (MI) is clinically important and would benefit from the discovery of new biomarkers.</p> <p>Methods</p> <p>Blood samples were obtained upon admission in patients with acute ST-elevation MI who underwent primary percutaneous coronary intervention. Messenger RNA was extracted from whole blood cells. LV function was evaluated by echocardiography at 4-months.</p> <p>Results</p> <p>In a test cohort of 32 MI patients, integrated analysis of microarrays with a network of protein-protein interactions identified subgroups of genes which predicted LV dysfunction (ejection fraction ≤ 40%) with areas under the receiver operating characteristic curve (AUC) above 0.80. Candidate genes included transforming growth factor beta receptor 1 (TGFBR1). In a validation cohort of 115 MI patients, TGBFR1 was up-regulated in patients with LV dysfunction (P < 0.001) and was associated with LV function at 4-months (P = 0.003). TGFBR1 predicted LV function with an AUC of 0.72, while peak levels of troponin T (TnT) provided an AUC of 0.64. Adding TGFBR1 to the prediction of TnT resulted in a net reclassification index of 8.2%. When added to a mixed clinical model including age, gender and time to reperfusion, TGFBR1 reclassified 17.7% of misclassified patients. TGFB1, the ligand of TGFBR1, was also up-regulated in patients with LV dysfunction (P = 0.004), was associated with LV function (P = 0.006), and provided an AUC of 0.66. In the rat MI model induced by permanent coronary ligation, the TGFB1-TGFBR1 axis was activated in the heart and correlated with the extent of remodeling at 2 months.</p> <p>Conclusions</p> <p>We identified TGFBR1 as a new candidate prognostic biomarker after acute MI.</p

Coordinated modular functionality and prognostic potential of a heart failure biomarker-driven interaction network

<p>Abstract</p> <p>Background</p> <p>The identification of potentially relevant biomarkers and a deeper understanding of molecular mechanisms related to heart failure (HF) development can be enhanced by the implementation of biological network-based analyses. To support these efforts, here we report a global network of protein-protein interactions (PPIs) relevant to HF, which was characterized through integrative bioinformatic analyses of multiple sources of "omic" information.</p> <p>Results</p> <p>We found that the structural and functional architecture of this PPI network is highly modular. These network modules can be assigned to specialized processes, specific cellular regions and their functional roles tend to partially overlap. Our results suggest that HF biomarkers may be defined as key coordinators of intra- and inter-module communication. Putative biomarkers can, in general, be distinguished as "information traffic" mediators within this network. The top high traffic proteins are encoded by genes that are not highly differentially expressed across HF and non-HF patients. Nevertheless, we present evidence that the integration of expression patterns from high traffic genes may support accurate prediction of HF. We quantitatively demonstrate that intra- and inter-module functional activity may be controlled by a family of transcription factors known to be associated with the prevention of hypertrophy.</p> <p>Conclusion</p> <p>The systems-driven analysis reported here provides the basis for the identification of potentially novel biomarkers and understanding HF-related mechanisms in a more comprehensive and integrated way.</p

Predictive integration of gene functional similarity and co-expression defines treatment response of endothelial progenitor cells

<p>Abstract</p> <p>Background</p> <p>Endothelial progenitor cells (EPCs) have been implicated in different processes crucial to vasculature repair, which may offer the basis for new therapeutic strategies in cardiovascular disease. Despite advances facilitated by functional genomics, there is a lack of systems-level understanding of treatment response mechanisms of EPCs. In this research we aimed to characterize the EPCs response to adenosine (Ado), a cardioprotective factor, based on the systems-level integration of gene expression data and prior functional knowledge. Specifically, we set out to identify novel biosignatures of Ado-treatment response in EPCs.</p> <p>Results</p> <p>The predictive integration of gene expression data and standardized functional similarity information enabled us to identify new treatment response biosignatures. Gene expression data originated from Ado-treated and -untreated EPCs samples, and functional similarity was estimated with Gene Ontology (GO)-based similarity information. These information sources enabled us to implement and evaluate an integrated prediction approach based on the concept of <it>k</it>-nearest neighbours learning (<it>k</it>NN). The method can be executed by expert- and data-driven input queries to guide the search for biologically meaningful biosignatures. The resulting <it>integrated kNN </it>system identified new candidate EPC biosignatures that can offer high classification performance (areas under the operating characteristic curve > 0.8). We also showed that the proposed models can outperform those discovered by standard gene expression analysis. Furthermore, we report an initial independent <it>in vitro </it>experimental follow-up, which provides additional evidence of the potential validity of the top biosignature.</p> <p>Conclusion</p> <p>Response to Ado treatment in EPCs can be accurately characterized with a new method based on the combination of gene co-expression data and GO-based similarity information. It also exploits the incorporation of human expert-driven queries as a strategy to guide the automated search for candidate biosignatures. The proposed biosignature improves the systems-level characterization of EPCs. The new integrative predictive modeling approach can also be applied to other phenotype characterization or biomarker discovery problems.</p

An effective non-parametric method for globally clustering genes from expression profiles

Clustering is widely used in bioinformatics to find gene correlation patterns. Although many algorithms have been proposed, these are usually confronted with difficulties in meeting the requirements of both automation and high quality. In this paper, we propose a novel algorithm for clustering genes from their expression profiles. The unique features of the proposed algorithm are twofold: it takes into consideration global, rather than local, gene correlation information in clustering processes; and it incorporates clustering quality measurement into the clustering processes to implement non-parametric, automatic and global optimal gene clustering. The evaluation on simulated and real gene data sets demonstrates the effectiveness of the algorithm. <br /