Mathematical modeling model neurons

McCarley, R. W. Hobson, J. A. (1975). Neuronal excitability modulation over the sleep cycle a structural and mathematical model. Science 189, 58-60. 

To complete the list of what we need to know to really understand a cell, there are the issues of adaptive processes—those mechanisms by which cells maintain viability in the face of changing environmental circumstances—and specialized functions that may be unique to a certain cell type such as nerve conduction in neurons. Finally, when we really understand a cell, we will be able to make a definitive mathematical model for it. 

McCance SL, Cohen PR, Cowen PJ Dthium increases 5-HT-mediated prolactin release. Psychopharmacology 99 276-281, 1989 McCann U, Hatzidimitriou G, Ridenour A, et al Dexfenfluramine and serotonin neurotoxicity further prechnical evidence that chnical caution is indicated. J Pharmacol Exp Ther 269 792-798, 1994 McCarley RW REM sleep and depression common neurobiological control mechanisms. Am J Psychiatry 139 565-570, 1982 McCarley RW, Hobson JA Neuronal excitability modulation over the sleep cycle a structural and mathematical model. Science 189 58-60, 1975... 

Control based on neural network. Similar to fuzzy logic modeling, neural network analysis uses a series of previous data to execute simulations of the process, with a high degree of success, without however using formal mathematical models (Chen and Rollins, 2000). To this goal, it is necessary to define inputs, outputs, and how many layers of neurons will be used, which depends on the number of variables and the available data. 

Simply expressed, an ANN is a collection of mathematical processing units (neurons), interconnected into a network that is capable of learning relationships within data. ANNs are data driven that is to say, they require data from which they can learn, but they do not require any assumptions about the model to be learned. 

The ANN is mathematical model that simulates many characteristics of actual neurons in the brain. Generally, an ANN is a structurally multi-layered network which links aTarge number of nodes (the neuron-like computational elements) and operates dynamically. Although mathematical neurons were conceived as early as 1943, only recently have large-scale real-world applications become practical. 

Artificial Neural Networks (ANN) are computational systems that emerged as an attempt to better understand neurobiology and cognitive psychology by means of simplified mathematical models of real neurons (Hassoun 1995 Fine 1999). The initial interest on these systems arose from the hope that they may enable us to increase our knowledge about brain, human cognition, and perception (Garson 2007). 

Berezetskaya, N.M., V.N. Kharkyanen, and N.I. Kononenko (1996). Mathematical model of pacemaker activity in bursting neurons of snail. Helix pomatia. J. Theor. Biol. 183,207-218. 

Miftakhov, RN. and D.L. Wingate (1994a). Mathematical modelling of the enteric nervous network 1 cholinergic neuron. Med. Eng. Phys. 16,67-Ti. 

Pitts [1943] proposed neuron models in the form of binary threshold devices and stochastic algorithms involving sudden 0-1 and 1-0 changes of states in neurons as the bases for modeling neural system. Subsequent work by Hebb [1949] was based on mathematical models that attempted to capture the concept of learning by reinforcement or association. 

An artificial neural network (ANN), usually called neural network (NN), is a mathematical model or computational model that is inspired by the structure and/or functional aspects of biological neural networks. A neural network consists of an interconnected group of artificial neurons, and it processes information using a connectionist... 

Neural network models in artificial intelligence definitions are usually referred to as artificial neural networks (ANNs) these are essentially simple mathematical models defining a function or a distribution over or both and, but sometimes models are also intimately associated with a particular learning algorithm or learning rule. A common use of the phrase ANN model really means the definition of a class of such functions (where members of the class are obtained by varying parameters, connection weights, or specifics of the architecture such as the number of neurons or their connectivity). 

The importance of dendritic spines in the establishment of neuronal connections, and the results obtained from the above mentioned study of the effect of darkness on the development of the mouse visual cortex, lead us to think that this mathematical model could be used, as a tool, to study the effects of hypothyroidism on the development of the cerebral cortex. 

The results obtained from this study showed that T, performed on rats at 10 days of age, produces, from 10 to 30 days, a smaller increase in the total number of spines counted along the apical shafts than during normal development. From 30 days of age onwards T produces an arrest of the increment of the total number of dendritic spines along the shafts. Furthermore, while it was possible to fit with the mathematical model the distribution of dendritic spines along the apical shafts of pyramidal cortical neurons of T rats 10, 20 and 30 days old, it was no longer possible to find this fitting for T animals older than 30 days. Therefore, T performed on rats at 10 days of age produces, not only an arrest in the production of dendritic spines in their C.C., but also (and what probably is more important) distortion of the distribution of these elements along the apical shafts of pyramidal neurons of layer V of the cerebral cortex ... 

Effect of thyroidectomy at 10 days of age (T q), and of treatments, started at 12,20 and 40 days of age, on the distribution of spines along the apical shafts of pyramidal neurons. The left-hand panel shows the experimental distributions corresponding to C, T and treated rats. Vertical bars represent 95% confidence intervals. The values of indicate the degree of fit of the distributions to the mathematical model, a value >4.5 indicating lack of fit. The right-hand panel shows the differences between the number of spines of equivalent segments of the distribution of T and treated rats and those of C animals. Data are from Ruiz-Marcos et al.27. 

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