Conventional deep neural networks capture essential information processing stages in perception. Deep neural networks often require very large volume of training examples, whereas children can learn concepts such as hand-written digits with few examples. The goal of this project is to develop a deep spiking neural network that can learn from few training trials. Using known neuronal mechanisms, a spiking neural network model is developed and trained to recognize hand-written digits with presenting one to four training examples for each digit taken from the MNIST database. The model detects and learns geometric features of the images from MNIST database. In this work, a novel biological back-propagation based learning rule is developed and used to a train the network to detect basic features of different digits. For this purpose, randomly initialized synaptic weights between the layers are being updated. By using a neuroscience inspired mechanism named 'synaptic pruning' and a predefined threshold, some of the synapses through the training are deleted. Hence, information channels are constructed that are highly specific for each digit as matrix of synaptic connections between two layers of spiking neural networks. These connection matrixes named 'information channels' are used in the test phase to assign a digit class to each test image. As similar to humans' abilities to learn from small training trials, the developed spiking neural network needs a very small dataset for training, compared to conventional deep learning methods checked on MNIST dataset.
In this paper, a numerical solution of an inverse non-dimensional heat conduction problem will be considered. By using a sensor located at a point inside the body and measuring the temperature at a point x = x 1 , 0 < x 1 < 1, and applying the Chebyshev polynomials base function to the inverse heat conduction problem, we determine a stable numerical solution to this problem.
Mathematics Subject Classification: 35R30
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