Generation of representation models for complex systems using Lagrangian functions

In this article, a new methodology is presented to obtain representation models for a priori relation z = u(x1, x2, . . . ,xn) (1), with a known an experimental dataset zi; x1i ; x2i ; x3i ; . . . ; xni i=1;2;...;p· In this methodology, a potential energy is initially defined over each possible model for the relationship (1), what allows the application of the Lagrangian mechanics to the derived system. The solution of the Euler–Lagrange in this system allows obtaining the optimal solution according to the minimal action principle. The defined Lagrangian, corresponds to a continuous medium, where a n-dimensional finite elements model has been applied, so it is possible to get a solution for the problem solving a compatible and determined linear symmetric equation system. The computational implementation of the methodology has resulted in an improvement in the process of get representation models obtained and published previously by the authors.

Inherited Photoreceptor Degeneration Causes the Death of Melanopsin-Positive Retinal Ganglion Cells and Increases Their Coexpression of Brn3a

Purpose: To study the population of intrinsically photosensitive retinal ganglion cells (melanopsin-expressing RGCs, m+RGCs) in P23H-1 rats, a rat model of inherited photoreceptor degeneration. Methods: At postnatal (P) times P30, P365, and P540, retinas from P23H dystrophic rats (line 1, rapid degeneration; and line 3, slow degeneration) and Sprague Dawley (SD) rats (control) were dissected as whole-mounts and immunodetected for melanopsin and/or Brn3a. The dendritic arborization of m+RGCs and the numbers of Brn3a+RGCs and m+RGCs were quantified and their retinal distribution and coexpression analyzed. Results: In SD rats, aging did not affect the population of Brn3a+RGCs or m+RGCs or the percentage that showed coexpression (0.27%). Young P23H-1 rats had a significantly lower number of Brn3a+RGCs and showed a further decline with age. The population of m+RGCs in young P23H-1 rats was similar to that found in SD rats and decreased by 22.6% and 28.2% at P365 and P540, respectively, similarly to the decrease of the Brn3a+RGCs. At these ages the m+RGCs showed a decrease of their dendritic arborization parameters, which was similar in both the P23H-1 and P23H-3 lines. The percentage of coexpression of Brn3a was, however, already significantly higher at P30 (3.31%) and increased significantly with age (10.65% at P540). Conclusions: Inherited photoreceptor degeneration was followed by secondary loss of Brn3a+RGCs and m+RGCs. Surviving m+RGCs showed decreased dendritic arborization parameters and increased coexpression of Brn3a and melanopsin, phenotypic and molecular changes that may represent an effort to resist degeneration and/or preferential survival of m+RGCs capable of synthesizing Brn3a.