A system-theoretic approach to global and local regulation in neuron morphologies

Synaptic plasticity is a crucial neuronal mechanism for learning and memory. It allows synapses to change their strength over time. This dissertation focuses on a particular form of synaptic plasticity called synaptic scaling, a homeostatic mechanism that preserves relative synaptic strengths in an activity-dependent manner. Synaptic scaling is fundamental for neuronal stability, regulating other plasticity mechanisms like Hebbian plasticity or long-term potentiation (LTP). The aims of this dissertation are to explore the implications of synaptic scaling (and other forms of plasticity, such as structural plasticity) on the overall behavior of neurons. This is done using system-theoretic tools and feedback control. We first formulate a biophysical closed loop model of synaptic scaling. We then study how synaptic scaling affect neurons’ behavior in both abstract and reconstructed morphologies. This study reveals important tradeoffs between robustness, convergence rate, and accuracy of scaling. We first look at synaptic scaling as a “global control action” whose main role is to guarantee a steady level of neural activity. We then consider activity-dependent degradation as a “local control action” whose role is to assist the neuron in fine-tuning different desirable spatial concentration profiles. We show that, in extreme scenarios, it can promote a level of competition between synapses that has a destabilizing effect on the overall behavior. At the methodological level, we use compartmental modeling and we focus on the in- teraction between feedback and transport, in linear and nonlinear settings. Using classical system-theoretic tools like Bode and Nyquist analysis and singular perturbation arguments, and more recent tools like contraction and dominance theory, we derive parameter ranges under which synaptic scaling is stable and well-behaved (slow regulation), stable and oscilla- tory (aggressive regulation), and unstable (pathological regulation). We also study the system robustness against static and dynamics uncertainties. Finally, to understand how different plasticity mechanisms simultaneously affect the neuron behavior, we study synaptic scaling in the presence of activity-dependent growth (mimicking a structural plasticity mechanism). This is a third layer of control action shaping the neuron morphology. We find that activity-dependent growth improves the neuron’s performance when synaptic scaling is insufficient

Consistent and fast inference in compartmental models of epidemics using Poisson Approximate Likelihoods

Addressing the challenge of scaling-up epidemiological inference to complex and heterogeneous models, we introduce Poisson Approximate Likelihood (PAL) methods. In contrast to the popular ODE approach to compartmental modelling, in which a large population limit is used to motivate a deterministic model, PALs are derived from approximate filtering equations for finite-population, stochastic compartmental models, and the large population limit drives consistency of maximum PAL estimators. Our theoretical results appear to be the first likelihood-based parameter estimation consistency results which apply to a broad class of partially observed stochastic compartmental models and address the large population limit. PALs are simple to implement, involving only elementary arithmetic operations and no tuning parameters, and fast to evaluate, requiring no simulation from the model and having computational cost independent of population size. Through examples we demonstrate how PALs can be used to: fit an age-structured model of influenza, taking advantage of automatic differentiation in Stan; compare over-dispersion mechanisms in a model of rotavirus by embedding PALs within sequential Monte Carlo; and evaluate the role of unit-specific parameters in a meta-population model of measles

Modeling and Visualization of Competing Escalation Dynamics: A Multilayer Multiagent Network Approach

Recent advances in military technology, such as hypersonic missiles, which can travel at more than five times the speed of sound and descend quickly into the atmosphere, give world nuclear superpowers a new edge. These advances up the game for nuclear superpowers with an extremely rapid, intense burst of military striking capability to secure upfront gains before encountering potentially overwhelming military confrontation. However, this so-called fait accompli has not been systematically studied by the United States in the perspective of the escalation philosophies of nuclear power competitors, or the mathematical modeling and visualization of multi-modal escalation dynamics. This gap may hamper any further command and control for nuclear deployment and decision making for strategic planning in preparation of such scenarios. This thesis aims to bridge the gap by implementing a network approach to model the escalation dynamics among competing nuclear superpowers

Reconfigurable Filtering of Neuro-Spike Communications Using Synthetically Engineered Logic Circuits.

High-frequency firing activity can be induced either naturally in a healthy brain as a result of the processing of sensory stimuli or as an uncontrolled synchronous activity characterizing epileptic seizures. As part of this work, we investigate how logic circuits that are engineered in neurons can be used to design spike filters, attenuating high-frequency activity in a neuronal network that can be used to minimize the effects of neurodegenerative disorders such as epilepsy. We propose a reconfigurable filter design built from small neuronal networks that behave as digital logic circuits. We developed a mathematical framework to obtain a transfer function derived from a linearization process of the Hodgkin-Huxley model. Our results suggest that individual gates working as the output of the logic circuits can be used as a reconfigurable filtering technique. Also, as part of the analysis, the analytical model showed similar levels of attenuation in the frequency domain when compared to computational simulations by fine-tuning the synaptic weight. The proposed approach can potentially lead to precise and tunable treatments for neurological conditions that are inspired by communication theory

GPU-based implementation of real-time system for spiking neural networks

Real-time simulations of biological neural networks (BNNs) provide a natural platform for applications in a variety of fields: data classification and pattern recognition, prediction and estimation, signal processing, control and robotics, prosthetics, neurological and neuroscientific modeling. BNNs possess inherently parallel architecture and operate in continuous signal domain. Spiking neural networks (SNNs) are type of BNNs with reduced signal dynamic range: communication between neurons occurs by means of time-stamped events (spikes). SNNs allow reduction of algorithmic complexity and communication data size at a price of little loss in accuracy. Simulation of SNNs using traditional sequential computer architectures results in significant time penalty. This penalty prohibits application of SNNs in real-time systems. Graphical processing units (GPUs) are cost effective devices specifically designed to exploit parallel shared memory-based floating point operations applied not only to computer graphics, but also to scientific computations. This makes them an attractive solution for SNN simulation compared to that of FPGA, ASIC and cluster message passing computing systems. Successful implementations of GPU-based SNN simulations have been already reported. The contribution of this thesis is the development of a scalable GPU-based realtime system that provides initial framework for design and application of SNNs in various domains. The system delivers an interface that establishes communication with neurons in the network as well as visualizes the outcome produced by the network. Accuracy of the simulation is emphasized due to its importance in the systems that exploit spike time dependent plasticity, classical conditioning and learning. As a result, a small network of 3840 Izhikevich neurons implemented as a hybrid system with Parker-Sochacki numerical integration method achieves real time operation on GTX260 device. An application case study of the system modeling receptor layer of retina is reviewed