Group Analysis of the Novikov Equation

We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilations symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigat the invariant solutions

Natural History of MYH7-Related Dilated Cardiomyopathy

BACKGROUND: Variants in myosin heavy chain 7 (MYH7) are responsible for disease in 1% to 5% of patients with dilated cardiomyopathy (DCM); however, the clinical characteristics and natural history of MYH7-related DCM are poorly described. OBJECTIVE: We sought to determine the phenotype and prognosis of MYH7-related DCM. We also evaluated the influence of variant location on phenotypic expression. METHODS: We studied clinical data from 147 individuals with DCM-causing MYH7 variants (47.6% female; 35.6 ± 19.2 years) recruited from 29 international centers. RESULTS: At initial evaluation, 106 (72.1%) patients had DCM (left ventricular ejection fraction: 34.5% ± 11.7%). Median follow-up was 4.5 years (IQR: 1.7-8.0 years), and 23.7% of carriers who were initially phenotype-negative developed DCM. Phenotypic expression by 40 and 60 years was 46% and 88%, respectively, with 18 patients (16%) first diagnosed at <18 years of age. Thirty-six percent of patients with DCM met imaging criteria for LV noncompaction. During follow-up, 28% showed left ventricular reverse remodeling. Incidence of adverse cardiac events among patients with DCM at 5 years was 11.6%, with 5 (4.6%) deaths caused by end-stage heart failure (ESHF) and 5 patients (4.6%) requiring heart transplantation. The major ventricular arrhythmia rate was low (1.0% and 2.1% at 5 years in patients with DCM and in those with LVEF of ≤35%, respectively). ESHF and major ventricular arrhythmia were significantly lower compared with LMNA-related DCM and similar to DCM caused by TTN truncating variants. CONCLUSIONS: MYH7-related DCM is characterized by early age of onset, high phenotypic expression, low left ventricular reverse remodeling, and frequent progression to ESHF. Heart failure complications predominate over ventricular arrhythmias, which are rare

Symmetry analysis for a Fisher equation with exponential diffusion

In this paper, we consider a generalized Fisher equation with exponential diffusion from the point of view of the theory of symmetry reductions in partial differential equations. The generalized Fisher-type equation arises in the theory of population dynamics. These types of equations have appeared in many fields of study such as in the reaction-diffusion equations, in heat transfer problems, in biology, and in chemical kinetics. By using the symmetry classification, simplified by equivalence transformations, for a special family of Fisher equations, all the reductions are derived from the optimal system of subalgebras and symmetry reductions are used to obtain exact solutions