Using the conventional Haberkorn approach, it is evaluated the recombination of the radical pair (RP) singlet spin state to study theoretically the cytoprotective effect of an extremely-low-frequency electromagnetic field (ELF-EMF) on early stages of hepatic cancer chemically induced in rats. The proposal is that ELF-EMF modulates the interconversion rate of singlet and triplet spin states of the RP populations modifying the products from the metabolization of carcinogens. Previously, we found that the daily treatment with ELF-EMF 120 Hz inhibited the number and area of preneoplastic lesions in chemical carcinogenesis. The singlet spin population is evaluated diagonalizing the spin density matrix through the Lanczos method in a radical pair mechanism (RPM). Using four values of the interchange energy, we have studied the variations over the singlet population. The low magnetic field effect as a test of the influence over the enzymatic chemical reaction is evaluated calculating the quantum yield. Through a bootstrap technique the range is found for the singlet decay rate for the process. Applying the quantum measurements concept, we addressed the impact toward hepatic cells. The result contributes to improving our understanding of the chemical carcinogenesis process affected by charged particles that damage the DNA.

The most suitable mechanism of action of electromagnetic fields (EMF) on biological systems is the effect on the radical pair (RP) recombination through the Zeeman effect and hyperfine interaction, which changes the rate of reactions or the product distribution. Enzyme reactions with RP intermediates can be altered by EMF, like those catalyzed by cytochrome P450 enzymes (CYP450), a heme-thiolate family protein that detoxifies xenobiotics and involved in chemical carcinogenesis. CYP450 activate chemical carcinogens producing an enormous amount of free radicals, which damage the DNA resulting in the malignant transformation of cells. During the activation, CYP450 produce spin-correlated RP intermediates that can either go to recombination or to continue the catalytic process. As CYP450 are electron carrier proteins, it is possible that RP intermediates may be affected by EMF. It was previously found that periodic treatment with extremely low frequency electromagnetic fields (ELF-EMF) inhibits more than 50% the number and area of preneoplastic lesions in rats with chemically induced hepatocarcinogenesis through reduction of cell proliferation. In this work, we developed a quantum mechanical model based on RP mechanism in order to explain the experimental effects of ELF-EMF on the free radicals produced in the early stages of chemical carcinogenesis.

Power series solution method has been traditionally used to solve ordinary and partial linear differential equations. However, despite their usefulness the application of this method has been limited to this particular kind of equations. In this work we use the method of power series to solve nonlinear partial differential equations. The method is applied to solve three versions of nonlinear timedependent Burgers-type differential equations in order to demonstrate its scope and applicability.

Resumen: La dinámica de sistemas, la simulación de eventos discretos y la simulación basada en agentes son tres formas de modelamiento ampliamente usadas para la toma de decisiones empresariales. Estos paradigmas están enfocados en representar el comportamiento de los sistemas en el tiempo, aunque con perspectivas distintas. En este artículo se presenta una comparación de los tres paradigmas en 10 aspectos, comparación que puede servir como referente para elegir la técnica más apropiada para un problema requerido. Palabras clave: teoría de sistemas / métodos de simulación / modelos matemáticosA qualitative comparison of system dynamics, discrete event simulation, and agent-based simulation AbstRAct: Systems dynamics, discrete event simulation, and agent-based simulation are three widely used forms of modeling for business decision making. These paradigms are focused on representing the behavior of systems over time, although in different perspectives. This paper compares the three paradigms in 10 aspects and it can serve as an indicator to choose the most appropriate technique to a required problem.