A Mathematical Model of a Neuron with Synapses based on Physiology

The neuron, when considered as a signal processing device, itsinputs are the frequency of pulses received at the synapses, and its output is the frequency of action potentials generated- in essence, a neuron is a pulse frequency signal processing device. In comparison, electrical devices use either digital or analog signals for communication or processing, and the mathematics behind these subjects is well understood. However, in regards to pulse frequency processing devices, there has not yet been a clear and persuasive mathematical model to describe the functions of neurons. It goes without saying that such a model is very important, not only for understanding neuron and neural system behavior, but also for undeveloped potential applications in industry. This paper proposes a method for obtaining the mathematical relationship between the input and output signals of a neuron based on physiological facts. The proposed method focuses on the currents across the postsynaptic membrane of each synapse, and the key is to recognize that the net charge across the whole membrane of a neuron over each action potential cycle must equal to zero. By analyzing the relationship between the input of a synapse and the currents across the postsynaptic membranes, a dynamic pulse frequency model of the neuron can be obtained. Here, we show that the transfer function of a neuron depends on the function of thepostsynaptic current of each synapse in resting state, which can be found by detecting the postsynaptic current when a pulse is received at the synapse. The transfer function of a typical neuron generally includes addition and subtraction of feedthrough terms and/or first order lag functions. To focus on the most basic characteristics of a neuron, accommodation, adaptation, learning, etc. are not discussed in this paper

Cognitive Deficit of Deep Learning in Numerosity

Subitizing, or the sense of small natural numbers, is an innate cognitive function of humans and primates; it responds to visual stimuli prior to the development of any symbolic skills, language or arithmetic. Given successes of deep learning (DL) in tasks of visual intelligence and given the primitivity of number sense, a tantalizing question is whether DL can comprehend numbers and perform subitizing. But somewhat disappointingly, extensive experiments of the type of cognitive psychology demonstrate that the examples-driven black box DL cannot see through superficial variations in visual representations and distill the abstract notion of natural number, a task that children perform with high accuracy and confidence. The failure is apparently due to the learning method not the CNN computational machinery itself. A recurrent neural network capable of subitizing does exist, which we construct by encoding a mechanism of mathematical morphology into the CNN convolutional kernels. Also, we investigate, using subitizing as a test bed, the ways to aid the black box DL by cognitive priors derived from human insight. Our findings are mixed and interesting, pointing to both cognitive deficit of pure DL, and some measured successes of boosting DL by predetermined cognitive implements. This case study of DL in cognitive computing is meaningful for visual numerosity represents a minimum level of human intelligence.Comment: Accepted for presentation at the AAAI-1

Investigation of 3D electrical impedance mammography systems for breast cancer detection

Breast cancer is a major disease in women worldwide with a high rate of mortality, second only to lung cancer. Hence, there is considerable interest in developing non-invasive breast cancer detection methods with the aim of identifying breast cancer at an early stage, when it is most treatable. Electrical impedance mammography (EIM) is a relatively new medical imaging method for breast cancer detection. It is a safe, painless, non-invasive, non-ionizing imaging modality, which visualizes the internal conductivity distribution of the breast under investigation. Currently some EIM systems are in clinical trials but not commercialized, as there are still many challenges with sensitivity, spatial resolution and detectability. The research in this thesis aims to enhance and optimize EIM systems in order to address the current challenges. An enhanced image reconstruction algorithm using the duo-mesh method is developed. Both in simulations and real cases of phantoms and patients, the enhanced algorithm has proven more accurate and sensitive than the former algorithm and effective in improving vertical resolution for the EIM system with a planar electrode array. To evaluate the performance of the EIM system and the image reconstruction algorithms, an image processing based error analysis method is developed, which can provide an intuitive and accurate method to evaluate the reconstructed image and outline the shape of the object of interest. Two novel EIM systems are studied, which aim to improve the spatial resolution and the detectability of a tumour deep in the breast volume. These are: rotary planar-electrode-array EIM (RPEIM) system and combined electrode array EIM (CEIM) system. The RPEIM system permits the planar electrode array to rotate in the horizontal plane, which can dramatically increase the number of independent measurements, hence improving the spatial resolution. To support the rotation of the planner electrode array, a synchronous mesh method is developed. The CEIM system has a planar electrode array and a ring electrode array operated independently or together. It has three operational modes. This design provides enhanced detectability of a tumour deep within the tissue, as required for a large volume breast. The studies of the RPEIM system and the CEIM system are based on close-to-realistic digital breast phantoms, which comprise of skin, nipple, ducts, acini, fat and tumour. This approach makes simulations very close to a clinical trial of the technology