Abstract
Ground breaking application of mathematics and biochemistry to explain formation of non-canonical bases, islands, G-quadruplex structures, and analog bases in DNA and mRNA at or near the transcription with connection to neural networks is implemented using statistical and stochastic methods apparatus with the addition of quantum principles. As a result the usual transience of Poisson spike trains (PST) becomes very instrumental tool for finding periodical type of solutions to Fokker-Plank (FP) stochastic differential equation (SDE). The present study develops new multidimensional methods of finding solutions to SDE. This is based on more rigorous approach to mathematical apparatus through Kolmogorov-Chentsov continuity theorem (KCCT) that allows the stochastic processes with jumps under certain conditions to have γ-Holder continuous modification, which is used as basis for finding analogous parallels in dynamics of formation of CpG and non-CpG islands (CpGI or non CpGI), repeats of G-quadruplexes, and non canonical bases during DNA (de)- methylation and neural networks.
Highlights
Ground breaking application of mathematics and biochemistry to explain formation of non-canonical bases, islands, G-quadruplex structures, and analog bases in DNA and messenger RNA (mRNA) at or near the transcription with connection to neural networks is implemented using statistical and stochastic methods apparatus with the addition of quantum principles
Recent numerous applications of FP stochastic differential equation (SDE) for flux rate to the to describe the mathematics of neural networks were introduced more than 60 years ago [21]
Focus on development of kinetic and dynamical theory for integrate and fire (I&F) neurons with application to simple and complex cells (determined by balance between cortico-cortical input and lateral geniculate nucleus (LGN)) in visual cortex provided qualitative intuition for dynamic phenomena related to transitions to bistability and hysteresis, where system jumps back and forth between the two branches of stable states for different, critical values of some control parameter that can result in optical binding
Summary
“Thousands of diseases are produced by genetic defects in channels, including many diseases of profound importance, like cystic fibrosis, epilepsy, atrial and ventricular fibrillation, and so on, as documented in many papers. Many of these diseases are caused by problems in the construction of channels, or the. Michael Fundator insertion of channels in the wrong places in the wrong cells, or in the regulation and control of channels”. Recent numerous applications of FP SDE for flux rate to the to describe the mathematics of neural networks were introduced more than 60 years ago [21]. FitzHugh’s consideration of stochasticity in neural networks was based on earlier works including Hodkin’s article after Kramers introduced FP SDE to the theory of rate of chemical reactions. He used notions of equilibrium, energy barrier, and memory friction. Focus on development of kinetic and dynamical theory for integrate and fire (I&F) neurons with application to simple (with inhibitory usually linear responses) and complex (characterized by strong cortical nonlinear and significant second harmonic responses excitation) cells (determined by balance between cortico-cortical input and lateral geniculate nucleus (LGN)) in visual cortex provided qualitative intuition for dynamic phenomena related to transitions to bistability and hysteresis, where system jumps back and forth between the two branches of stable states for different, critical values of some control parameter that can result in optical binding
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