In this paper, we aim to develop alternative methods to backpropagation that more closely resemble biological computation. While backpropagation has been an extremely valuable tool in machine learning applications, there is no evidence that neurons can back propagate errors. We propose two methods intended to model the intrinsic selectivity of biological neurons to certain features. Both methods use selectivity matrices to calculate error and to update synaptic weights in different ways, either by comparing neuronal firing rate to a threshold - firing rate algorithm - or computing error from a generated score - scoring algorithm. We trained and tested networks that used either of the two algorithms with the MNIST database. We compared their performance with a multilayer perceptron network with 3 hidden layers that updated synaptic weights through typical error backpropagation. The backpropagation algorithm had a test error of 1.7%. Networks that updated synaptic weights based on the scoring method gave a test error of 2.0%, and networks using the firing rate method 4.3%. We were thus able to develop more biologically plausible models of neural networks in the brain while obtaining performance comparable to typical backpropagation algorithms.

Demyelination has a detrimental impact on conduction of nerve signals. The purpose of this paper is to understand the impact of demyelination and build a mathematical model for it. We will model the impact of demyelination on neuronal characteristics, including capacitance and ion leakage. We will then create a small network of demyelinated nerves and study the impact on various types of connections, such as propagation through the network and inhibition. Performance of the demyelinated network will be compared with a network of standard neurons. This model can help us further understand the medical implications of demyelination-causing diseases.

To investigate neural correlates of collaborative actions between parents and their children, EEG data was recorded during a social interaction. Four dyads of one parents and one of their children (mean age: 4.6 years) played a turn taking game with high and low reward outcomes. After learning the rule of the game, the reward contingency was reversed in 20% of trials, thereby eliciting a prediction error. Independent component analysis (ICA) was used to determine and exclude non-brain components. The children’s data is inconclusive, possibly because of the small number of subjects. The parents’ event related potential show P3a positivity dependent on reward outcome during their own actions. During observation of their child’s action, the P3a component is effected by the reward expectation, not the actual outcome. Interestingly, this is in contrast with event related potentials of two unacquainted adults recorded during the same experiment.

Because of its energy efficiency and biological plausibility, spiking neural network is getting more and more attention recently, especially in the fields of neuromorphic engineering. Although several researchers have proved the feasibility of spiking neural networks in machine learning fields, we present a more biologically plausible network. In this project, we demonstrate the viability of Spiking-Time Dependent Plasticity of Spiking Neural Networks in unsupervised machine learning fields by digit recognition. With 100 excitatory neurons, we obtained an accuracy of 80%.

A Hodgkin-Huxley model was constructed in MATLAB with seven neurons that collectively represent each of the main regions of the brain. One model affected by Parkinson’s Disease (PD) and a Machado-Joseph Disease (MJD) model were developed using the orignal healthy model as a basis. To simplify the model given the limited resources regarding MJD activity, all conductance values and equilibrium potentials are standard across all regions of the brain. The bulk current and behaviors between the regions are represented through synaptic or inhibitory connections. Therefore, adjusting the synaptic strengths and/or inhibitory power between the neurons within the healthy model such that the brain mimics PD and MJD, created the two unique disease models. In order to accurately compare the behaviors of the networks, we used uniformly scaled current across the disease models. Given an external current to the Substantia Nigra at the beginning of the network, we observed the spiking frequencies of the cortex, represented as the final neuron in the network. The cortex neuron is presumed to excite the motor cortex, thus causing the motor deficit symptoms. Our hypothesis was that we can infer whether the network resembles a PD or MJD by observing the output spiking behavior in response to known currents.

CCK connections to pyramidal cells exhibit an interesting phenomena termed "Depolarization- Induced Suppression of Inhibition (DSI)." During DSI, depolarization of the pyramidal cell (PC) releases cannabinoids that bind to the CB1 receptor on CCK cells. This initiates a molecular cascade in the CCK basket cell that results in decreased release of GABA onto the pyramidal cell. Thus, when a pyramidal cell is excited, the perisomatic inhibition from CCK cells is reduced and the pyramidal cell is capable of becoming even more excited. Since CA1 pyramidal cells often act as place cells, it seems likely that DSI would play a role in place cell behavior. Here, DSI is modeled in a Hodgkin-Huxley neuron microcircuit and its spike timing relative to theta is quantified. Using this model, we are able to show that the CCK-PC connections contribute to phase precession in CA1 pyramidal cells.

Recent work has suggested that dendrites act as a key organization unit of pyramidal neurons, integrating local inputs to generate complex neural response properties. In computational models of cortical networks, incorporating the integrative properties ofdendrites, for instance by directing the landing of synapses to particular compartments on the dendritic arbor, and can increase the accuracy of a model at describing the input-output functions of realistic neurons. In this study, we sought to determine how the concentration of local inhibitory synapses on either the proximal or distal portion of dendrites of primary visual cortex neurons would modify the gain of the network. We used a model of exponential integrate and fire neurons to simulate the network, and found that landing of inhibitory synapses on the proximal portion of the dendrite resulted in an increased network gain relative to distal landing. These observations suggest that the spatial patterning of synapses is an essential component in generating cortical models that accurately capture biological data.

Valproic acid (VPA), one type of antiepileptic drugs (AEDs), is widely used as a treatment for epilepsy. The exact mechanism of this drug remains elusive. However, studies have found that the drug could cause both positive and negative effects on the hippocampus. Temporal lobe epilepsy is a type of epilepsy that originates in the hippocampus, and it is often marked by the occurrence of abnormal voltage patterns such as high frequency oscillations (HFOs) in the hippocampus. HFOs are local field potential (LFP) patterns measured in the hippocampus and they primarily occur in the CA1 region of the hippocampus, which receives excitatory input from the CA3 region. Mathematical models of the hippocampal regions and simulations of the drug effect on the regions could help us validate in-vivo and in-vitro experimental recordings of ripple phenomena in the hippocampus, and allow for a deeper level of understanding of the drug effect of VPA on the hippocampal area, respectively. In this project, three representative hippocampal models were investigated including a modified model of the CA1 region and two models of the CA3 region to study the relationship of the drug effect of VPA and the resulting neural activities.

In neuro-circuits, the ow of information is regulated by a diverse population of inhibitory neurons. Previous studies(Bloodgood (2013), Lin (2008)) have shown that NPAS4, the activity-dependent transcription factor, regulates the number of inhibitory synapse and functions in the cell. When information is travelling through the hippocampus, two kinds of perisomatic inhibitory interneurons, PV(Parvalbumin) basket cell and CCK(Cholecystokinin) basket cell, are re-cruited to transfer inhibition signals to the pyramidal cell(Freund (2012)). Previous experi-ments(Bartos (2012)) have shown that the output signaling properties of those two kinds of cells are dierent. While the output signal of PV basket cells is fast recruited, uniformed and with high frequency, that of CCK basket cells is slowly recruited, asynchronous, uctuating and with less timed inhibitory output. Our study focuses on modeling the whole mechanism of how NPAS4 affects the informa- tion ow in the hippocampus. Specifcally, the genetic circuit approach is applied to model the recruitment of PV/CCK basket cells regulated by NPAS4. Meanwhile, the signal that is transferred inside the pyramidal cell(action potential spikes) is modeled by using the neural circuits. As the result, we created a model which is able to recreate the spiking pattern of both basket cell by taking account of the interneural inhibition/excitation, as well as the regulation of NPAS4.

Transcutaneous electrical nerve stimulation (TENS) has been commonly used for non-invasive pain relief in patients. Two potential mechanisms by which TENS induces analgesia are investigated: (1) opioid receptor activation (2) interruption of action potential propagation. Results indicate that opioid receptor activation significantly reduces pain signal activity through several biochemical pathways and mechanisms of action, while an applied electrical current with medium frequency (~20 Hz), high amplitude (>= 30 μA/cm2), and low duty cycles (<= 10%) provided the most amount of impediment to pain signal propagation for the modeled neuron.

The modeling of the biophysical and bioelectromagnetic mechanisms underlying the noninvasive technique of Transcranial Magnetic Stimulation (TMS) is undertaken to better understand the excitatory and inhibitory neurodynamics within the cortical regions of the brain. After twenty years, TMS empirical results have been both encouraging and effective for both science and medical treatments, yet the foundations of the fundamental biophysical and electrophysiological models are only beginning to be understood. Several advancements are proposed which potentially offer enhanced focality by reducing the beam of magnetic field and induced electric field to a smaller target area of the cortex (< 2mm^2) in lieu of the state-of-the-art at approximately 2cm2. Also, novel techniques are formulated for reconfigurable beam steering, multiple beams and the synthesis of "custom" shape profiles in the targeted cortical region. Neuronal modeling using the active nonuniform cable equation validates the nonuniform nature of spatial excitability along nerve fibers. Thus, greater control of focality and patterning will lead to great efficacy of TMS.

Neuromodulation has been implicated in the induction and modulation of synaptic plasticity, and thus provides a potential vehicle for local reinforcement learning within a defined neural network. Specifically, the neuromodulator dopamine has been shown to encode reward-prediction error, the amount that an agent’s received reward deviates from its expected reward. Furthermore, dopamine has been demonstrated to modulate synaptic plasticity based on novelty or uncertainty. Additional evidence exists supporting the parallel role of acetylcholine in the induction of plasticity via a gating mechanism, as well as the modulation of learning rates within discrete neural networks. We endeavor to understand the calculus underlying these interactions, and propose the possibility that neuromodulators act combinatorially to modulate synaptic plasticity. We evaluate the validity of our model with respect to parameters such as reward prediction error encoding, learning rate, and inducibility to spiking, conditioned on single layer neural networks with a bipartite graph connectivity scheme. Within this model we contrast the results of combinatorial modulation with that of classical reward-based training on canonical reinforcement learning tasks. We hope to extend our investigation by further quantifying the effect of potentially correlated activity amongst the stated parameters, particularly regarding task performance. Through iterative regression on the linearly separable as well as the nonlinear interactions of these neuromodulators, we ultimately hope to gain a more complete understanding of their collective dynamics and interactions as well as their evoked synaptic changes underlying reinforcement learning.

Feedforward connections from one visual cortical area to another have been used to organize the cortex into a hierarchy. In addition to direct corticocortical projections, primary and secondary visual cortex are connected via an indirect pathway through the pulvinar, a higher order thalamic nucleus. These two feedforward pathways from V1 to V2 have the potential to differentially affect downstream activity through their connection strengths and conduction delays. To investigate the contributions of corticocortical and cortico-thalamocortical pathways to downstream population activity, these areas are modeled with linear rate variables which take into account the network architecture of cortex and thalamus. Synaptic weights are varied to assess the affects of driver and modulator afferent strengths. Pulvinar inactivation is simulated to provide a prediction for future experiments. Finally, the effects of conduction delays are considered on the dynamics of network activity.

Recent publications on neural networks on VLSI chips show various neuromorphic circuits featuring spike-time-dependent (STDP) plasticity. These circuits are built in both analog and mixed-domain fashions: sophisticated transistor level circuits, synaptic weights memory look-up tables, digital counters etc. A lot of advancements have been made to mimic the neural networks with the highest number of neurons and interconnecting synapses. The techniques include minimization of the circuit topologies and maximization of energy efficiency. HP Lab’s discovery of novel memristive elements resulted in very compact and energy efficient memristive synapse implementations. The paper introduces conceptual STPD circuit implementations in neural VLSI chips, then develops mathematical foundations of novel memristive synapse and provides simulation results and discussion.

Top-down feedback has been proposed to play an important role in extracting salient features in our environment. This process involves selectively increasing the activity of specific sensory neurons. Though top-down feedback has been proposed as a mechanism involved in attention, its involvement in unsupervised learning is still relatively unknown. Here, we explore the role of top-down feedback in unsupervised learning in biologically realistic neurons. To do this, we used the Brian neuron simulation environment to construct a small network of leaky integrate and fire neurons and tested the effect of top-down feedback on the changes synaptic strengths of simulated sensory neurons. In our simplified network with synaptic weights regulated by spike-timing dependent plasticity, our network could learn to discriminate between two different input types. The addition of stable top-down feedback, however, did not affect the learning rate. Additionally, we found a prominent role for inhibitory activity in the ability of our network to learn to discriminate between inputs types. Overall, our study explores the roles of top-down feedback and inhibition in unsupervised learning.

In this project, we implemented models for serotonin modulation in biological neural networks, motivated by the findings of reduced serotonin neurotransmission as a consequence of Diabetes Mellitus. Because the effects of serotonin on the human nervous system are widely varying and poorly quantified, we used models based on experimental data for the model organism Aplysia. These models were used to investigate modified neurotransmission of serotonin in a single sensory neuron and in small neural networks. We also examined the effect on excitability and network performance. Finally, we investigated its implications on memory in a simple two-neuron circuit by experimenting with Hebbian learning rules and synaptic strengths. Our simulations indicate that reduced serotonin neurotransmission reduces the excitability of single neurons and impairs the function of simple neural networks. Our simulations involving synaptic plasticity indicate that reduced serotonin neurotransmission reduced or negated synaptic strengthening based on the implemented learning rules. The results provide basis for further experimental investigation to quantify the effect of serotonin in its varied roles in the human nervous system.

The Hippocampal regions CA3 and CA1 have been demonstrated to play a role in memory consolidation and spatial navigation. Recurrent Collaterals (RC) in CA3 Pyramidal cells serve as a feedback mechanism onto CA3 cells while Schaffer Collaterals (SC) directly project synaptic inputs from CA3 to CA1. The neuronal activity from RC and SC have been associated with Long-term Potentiation, gamma frequencies, and Sharp-Wave Ripples oscillations (SWR), activities present during events believed to be related to long-term memory storage. This project explored the effects of altering the number of synaptic connections within each region and between the two regions. By varying the probability that synaptic connections will form in CA3’s RC and the SC, it was determined that there was a non-obvious and non-linear effect for each region’s ability to be engaged in a particular firing frequency. It was found that approximately a ten percent connection between both the Schaffer collaterals and the recurrent collaterals best engaged CA3 and CA1 in gamma and ripple frequencies.