Modification of a Reward-Modulated Hebbian Learning Rule as a Model of Working Memory [PDF]
In liquid state machines with generic cortical microcircuits, synaptic plasticity can be optimized by reward-modulated Hebbian learning, eliminating the need for supervised learning (Hoerzer, Legenstein, and Maass, 2014). Reward- modulated Hebbian learning can thus lead to autonomous emergence of task- specific working memory during the learning of computational rules. However, in Hoerzer, Legenstein, and Maass (2014), reward-modulated Hebbian learning was modeled with an all-or-none modulatory signal that permitted synaptic weight change only above a criterion level of learning. We use liquid computing models to investigate working memory emergence via Hebbian learning with non-binary modulatory signals. We implement a nonbinary, but discrete modulatory signal and an analog signal. In doing so, we model physiological conditions of tonic and phasic output of reward-mediating systems like the dopaminergic system. We find that the effects of analog modulatory signals on working memory emergence improve reward-modulated Hebbian learning in liquid state machines. We propose that reward-modulated Hebbian learning in generic microcircuits of neurons can abstractly model general cognitive processes.
Evaluating Single and Multi-Neuronal Dynamics under Ischemic Conditions [PDF]
It is necessary to examine the membrane dynamics of the neuron under ischemic conditions to understand the physiological changes that occur during metabolic perturbations. This would have far-reaching effects on exploring the brain metabolic activity following trauma. Any tissue in the body which has a metabolic demand requires the substrates for metabolism to be delivered, typically by the circulatory system. Of these substrates, molecular oxygen provides a means for cells to undergo aerobic respiration, which provides an abundance of ATP for further cellular activity. Our model is based on the single neuron approximation of the energy depleted state which exists under ischemic conditions. The original model was proposed by Zandt, first author of the reference paper Zandt et al. "Neural Dynamics during Anoxia and the 'Wave of Death'". This model features the dynamics of a single neuron operating under reduced depolarization conditions as a result of dynamic changes in the membrane potential and equilibrium concentrations of Na+ and K+ as a result of the reduced capacity of the ATP pump. The model we will be considering is strictly Hodgkin Huxley, since we need to consider the individual movements of sodium and potassium, and reduced models often eliminate the distinction between these variables to apply dimensionality reduction. For the small model simulations, we will evaluate dynamics of one and two neuron networks under ischemic conditions. In addition, we will investigate the effects of restoration of oxygen and glucose on our ischemic model to investigate the vitality of the neuron post-ischemia.
Effects of Betaxolol on Hodgkin-Huxley Model of Tiger Salamander Retinal Ganglion Cell [PDF]
Isolated retinal ganglion cells (RGC) elicit action potentials upon depolarization from upstream bipolar cells, which are modulated by horizontal and amacrine cells. The frequency and amplitude of action potential spikes are not only dependent on upstream input, but also the inherent intracellular and extracellular ion concentrations. The Hodgkin-Huxley model examined in this paper accounts calcium concentration changes within the cell, which has an appreciable effect due to the large changes in calcium reversal potential arising from the small intracellular calcium concentration and large extracellular calcium concentration. This paper studies the effects of a voltage gate inhibiting drug, Betaxolol, in a single cell Hodgkin-Huxley model of the tiger salamander retina. Betaxolol reduces both sodium current in an RGC, leading to reduced spiking frequency; however, calcium current is also reduced by the drug, which has an opposite effect of increasing spiking frequency. This study found that if the sodium conductance is reduced to one-third of the control value, the calcium conductance must be reduced less than one-third of its control value for the cell to have a reduced spiking frequency.
Optimizing the Synchronization of Two Neural Networks [PDF]
In this paper, we aim to provide a non-adaptive signal-preprocessing algorithm that enhances synchronization between two networks. The degree of synchronization of two networks can be a good indicator of the fidelity of signal delivered to the biological network, which is of increasing importance following the advent of sensory prosthetics. We propose that the channel-to-channel correlation matrix could serve as a way of gaining insights about a 'black box network', and that a pseudo network created based on the reverse correlation matrix can improve synchronization if the input signals are pre-processed through the pseudo network. We also investigate different intra- and inter-network connection topologies and their effects on efficiency of signal delivery in order to minimize the connections needed to completely drive a biological network.
Evaluation of Memristor based models of Neurons and Neural Networks [PDF]
This project aims to explore if neurons and neural networks can be modeled and simulated using Memristors. Recent literature shows a rigorous and comprehensive nonlinear circuit-theoretic foundation for the memristive Hodgkin-Huxley Axon Circuit model. Also analog hardware architecture of a memristor bridge synapse-based multilayer neural network and its learning scheme has been presented in. In order to analyze and design memristive circuits, a laplace domain expression has been derived in. This project combines these works together to analyze and derive equations for memristive Hodgkin-Huxley axons and memristive synapses. These equations can then be used for modeling and simulating simple neural networks and possibly associative learning.
Stochastic Gradient Descent Learning and the Backpropagation Algorithm [PDF]
Many learning rules minimize an error or energy function, both in supervised and unsupervised learning. We review common learning rules and their relation to gra- dient and stochastic gradient descent methods. Recent work generalizes the mean square error rule for supervised learning to an Ising-like energy function. For a specific set of parameters, the energy and error landscapes are compared, and con- vergence behavior is examined in the context of single linear neuron experiments. We discuss the physical interpretation of the energy function, and the limitations of this description. The backpropgation algorithm is modified to accommodate the energy function, and numerical simulations demonstrate that the learning rule captures the distribution of the network's inputs.
Computational Optogenetics: Reducing Hyperexcitability of neurons through the use of Channelrhodopsin 2 [PDF]
In the scope of this research project we implement a computational model for the dynamical characteristics of channelrhodopsin 2, which was developed by the Cardiac Optogenetics and Optical Imaging Lab at Stony Brook University. We aim to determine the feasibility of using ChR2 to control and decrease the hyper excitation of neural networks.
Influence of Aging and Aging-Related Neurodegenerative Disease: From Single Neuron Model to Simple Neural Network [PDF]
During normal aging, quite a lot of age-related changes happen like short-term memory, shakiness and muscle weakness occurring in human beings, and further affect the brain function, such as the altered calcium influx through the calcium ion channels, neural plasticity deficits, and other neurodegenerative processes. Some of them will even develop to a fatal neurodegenerative disorder like Alzheimer's disease (AD) or Parkinson's disease. By modeling the effects of these changes on both the single neuron level and neural network, we can understand how the neural properties are linked to the function loss and death of neurons in different scales. In this project, we employ the powerful biological neuron models, especially the Morris-Lecar model with different physiology parameters along aging. By simulating both single neuron model and simple synaptic motif model and comparing the different neurodynamics between the young and old individuals, as well as the healthy people and patients with neurodegenerative diseases especially AD, we show the results that aging process does hinder neural spiking activity, slow down and reduce the action potential propagation, weaken the sensitivity to stimulus, and so forth.
Effects of Inhibitory Synaptic Current Parameters on Thalamocortical Oscillations [PDF]
We explore the role of specific GABAergic current conductance and decay time in specific inhibitory synapses in driving macroscopic cortical oscillations based on two computational neuron models. Simulations using a previously established thalamocortical network model demonstrate that: 1) oscillation frequency changes due to increased inhibitory conductance are dependent on post-synaptic neuron type, 2) changes in inhibitory current decay time have no effect on oscillation frequency, and 3) large changes in inhibitory conductance can produce dynamic changes in the network behavior that is uncaptured by peak oscillation frequency. These results warrant careful treatment of different types of GABA recipients in computational models, and motivate further investigation in the effects of substances which promote GABAergic activity, such as propofol.
Modeling Depolatization Induced Suppression of Inhibition in Pyramidal Neurons [PDF]
Depolarization-Induced Suppression of Inhibition (DSI) is effectively a mechanism for feedback-inhibition of inhibition. Wilson and Nicoll  showed that its effect is mediated through a retrograde endocannabinoid signal. Here, we produced a simple model for DSI which matched the effects and kinetics of DSI found in empirical data. We then explored a possible function for DSI through examining its effects on shaping orientation tuning curves. DSI demonstrated a dramatic effect on the shape of the tuning curve, indicating that it may play a similar role in-vivo.
Analysis of a simple object oriented simulation of STDP in memristor synapse arrays for potential use in event-driven contrastive divergence [PDF]
Memristors are electrical devices whose conductance can be modulated by the charge and voltage flux through the two elements. Previous work has shown that memristors are good models of synapses, even reproducing learning behavior such as spike-time dependent plasticity (STDP). As such, there is widespread interest in understanding how large networks of memristor synapses might be trained to perform tasks such as visual perception or categorization. Our project aim is to simulate a small network of memristor synapses using an object-oriented programming language (Java) to create each element of the network, following previously published models. The main aim will be to demonstrate and characterize STDP behavior in our modeled cells. We expect that the results of this simulation will be similar to those reported by other groups. The secondary aim will be to use this form of plasticity to train weights in a deep learning network. This aim will be mainly exploratory.
Investigating dynamic neural representations of learning/memory in auditory cortex by sound reconstruction [PDF]
Songbirds rely on auditory processing of natural communication signals for the rare behavior of vocal learning - the ability to reproduce and recognize vocalizations through an adult model. For this project, we obtained depth electrode recordings of local field potential from the caudal medial nidopallium, the songbird equivalent of auditory cortex. Anesthetized songbirds were given novel and familiar auditory objects, and the neural responses elicited by each object were used to predict the auditory objects provided, via a MATLAB-based reconstruction model. We expected that, as the novel objects were repeatedly presented, neural responses to repeats from the later part of stimuli presentation periods would produce better reconstructions (i.e. more similar to the actual objects) than the responses to earlier repeats. The results are inconsistent across birds, with a greater number of repeated presentations associated with worse reconstructions, in support of previously observed passive learning-induced changes in the stimuli-responsive neural networks.