Physics Commons^™

A Causal Inference Approach For Spike Train Interactions, Zach Saccomano

Dissertations, Theses, and Capstone Projects

Since the 1960s, neuroscientists have worked on the problem of estimating synaptic properties, such as connectivity and strength, from simultaneously recorded spike trains. Recent years have seen renewed interest in the problem coinciding with rapid advances in experimental technologies, including an approximate exponential increase in the number of neurons that can be recorded in parallel and perturbation techniques such as optogenetics that can be used to calibrate and validate causal hypotheses about functional connectivity. This thesis presents a mathematical examination of synaptic inference from two perspectives: (1) using in vivo data and biophysical models, we ask in what cases the …

Ongoing Calculus In The Cerebral Cortex, Luke Long

Physics Undergraduate Honors Theses

Various modes of neuronal computations have long been theorized to be possible based on the structure and geometry of the brain. These computations also seem necessary for many of the integral functions of the brain, like information processing and regulatory processes in the body. However, experimental data directly supporting these claims have been rare.

In this study, data collected in mice from a large number of neurons over a long period of time provided the opportunity to search for some of these computations, specifically change detection and squaring calculations. Using Matlab, the goal of this analysis was to find statistically …

Scale-Free Behavioral Dynamics Directly Linked With Scale-Free Cortical Dynamics, Sabrina Jones

Physics Undergraduate Honors Theses

In organisms, an interesting phenomenon occurs in both behavior and neuronal activity: organization with fractal, scale-free fluctuations over multiple spatiotemporal orders of magnitude (1,2). In regard to behavior, this sort of complex structure-- which manifests itself from small scale fidgeting to purposeful, full body movements-- may support goals such as foraging (3-6), visual search (4), and decision making (7,8). Likewise, the presence of this sort of structure in the cerebral cortex in the form of spatiotemporal cascades, coined “neuronal avalanches,” may offer optimal information transfer (9). Thus, when considering the functional relationship between the cerebral cortex and movements of the …

Mathematical Modelling Of Temperature Effects On The Afd Neuron Of Caenorhabditis Elegans, Zachary Mobille, Rosangela Follmann, Epaminondas Rosa

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Circuits With Broken Fibration Symmetries Perform Core Logic Computations In Biological Networks, Ian Leifer, Flaviano Morone, Saulo D. S. Reis, José S. Andrade Jr., Mariano Sigman, Hernán A. Makse

Publications and Research

We show that logic computational circuits in gene regulatory networks arise from a fibration symmetry breaking in the network structure. From this idea we implement a constructive procedure that reveals a hierarchy of genetic circuits, ubiquitous across species, that are surprising analogues to the emblematic circuits of solid-state electronics: starting from the transistor and progressing to ring oscillators, current-mirror circuits to toggle switches and flip-flops. These canonical variants serve fundamental operations of synchronization and clocks (in their symmetric states) and memory storage (in their broken symmetry states). These conclusions introduce a theoretically principled strategy to search for computational building blocks …

Analog Implementation Of The Hodgkin-Huxley Model Neuron, Zachary D. Mobille, George H. Rutherford, Jordan Brandt-Trainer, Rosangela Follmann, Epaminondas Rosa

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Calculating The Dimensionality Of The Brain, And Other Applications Of An Optimized Generalized Ising Model In Predicting Brain's Spontaneous Functions, Pubuditha M. Abeyasinghe

Electronic Thesis and Dissertation Repository

Understanding a system as complex as the human brain is a very demanding task. Directly working with structural and functional neuroimaging data has led to most of the understanding we have gained about the human brain. However, performing only the direct statistical comparisons on the empirical function and the structure does not fully explain the observed long-range functional correlations. Therefore, implementations of mathematical models to gain further understanding of the relationship between the structure and function of the brain is critical. Additionally, spontaneous functions of the brain can only be predicted using computer simulated models; which will be pivotal for …

A Critical Firing Rate In Synchronous Transitions Of Coupled Neurons, Annabelle Shaffer, Epaminondas Rosa, Rosangela Follmann

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Rules And Mechanisms For Efficient Two-Stage Learning In Neural Circuits, Tiberiu Teşileanu, Bence Ölveczky, Vijay Balasubramanian

Publications and Research

Trial-and-error learning requires evaluating variable actions and reinforcing successful variants. In songbirds, vocal exploration is induced by LMAN, the output of a basal ganglia-related circuit that also contributes a corrective bias to the vocal output. This bias is gradually consolidated in RA, a motor cortex analogue downstream of LMAN. We develop a new model of such two-stage learning. Using stochastic gradient descent, we derive how the activity in ‘tutor’ circuits (e.g., LMAN) should match plasticity mechanisms in ‘student’ circuits (e.g., RA) to achieve efficient learning. We further describe a reinforcement learning framework through which the tutor can build its teaching …

Failure Of Surface Color Cues Under Natural Changes In Lighting, David H. Foster, Iván Marín-Franch

MODVIS Workshop

Color allows us to effortlessly discriminate and identify surfaces and objects by their reflected light. Although the reflected spectrum changes with the illumination spectrum, cone photoreceptor signals can be transformed to give useful cues for surface color. But what happens when both the spectrum and the geometry of the illumination change, as with lighting from the sun and sky? Is it possible, as a matter of principle, to obtain reliable cues by processing cone signals alone? This question was addressed here by estimating the information provided by cone signals from time-lapse hyperspectral radiance images of five outdoor scenes under natural …

Experimental And Computational Studies Of Cortical Neural Network Properties Through Signal Processing, Wesley Patrick Clawson

Graduate Theses and Dissertations

Previous studies, both theoretical and experimental, of network level dynamics in the cerebral cortex show evidence for a statistical phenomenon called criticality; a phenomenon originally studied in the context of phase transitions in physical systems and that is associated with favorable information processing in the context of the brain. The focus of this thesis is to expand upon past results with new experimentation and modeling to show a relationship between criticality and the ability to detect and discriminate sensory input. A line of theoretical work predicts maximal sensory discrimination as a functional benefit of criticality, which can then be characterized …

A Principle Of Economy Predicts The Functional Architecture Of Grid Cells, Xue-Xin Wei, Jason Prentice, Vijay Balasubramanian

Publications and Research

Grid cells in the brain respond when an animal occupies a periodic lattice of ‘grid fields’ during navigation. Grids are organized in modules with different periodicity. We propose that the grid system implements a hierarchical code for space that economizes the number of neurons required to encode location with a given resolution across a range equal to the largest period. This theory predicts that (i) grid fields should lie on a triangular lattice, (ii) grid scales should follow a geometric progression, (iii) the ratio between adjacent grid scales should be √e for idealized neurons, and lie between 1.4 and 1.7 …

Dynamics Of The Fitzhugh-Nagumo Neuron Model, Zechariah Thurman

Physics

In this paper, the dynamical behavior of the Fitzhugh-Nagumo model is examined. The relationship between neuron input current and the firing frequency of the neuron is characterized. Various coupling schemes are also examined, and their effects on the dynamics of the system is discussed. The phenomenon of stochastic resonance is studied for a single uncoupled Fitzhugh-Nagumo neuron.

Resiliency To Bistability In The Neurons From The Pre-Bötzinger Complex, Treadwell D. Singfield Ii

Georgia State Undergraduate Research Conference

No abstract provided.