THE RESONATE-AND-FIRE NEURON: TIME DEPENDENT AND FREQUENCY SELECTIVE NEURONS IN NEURAL NETWORKS

The means through which the nervous system perceives its environment is one of the most fascinating questions in contemporary science. Our endeavors to comprehend the principles of neural science provide an instance of how biological processes may inspire novel methods in mathematical modeling and engineering. The application ofmathematical models towards understanding neural signals and systems represents a vibrant field of research that has spanned over half a century. During this period, multiple approaches to neuronal modeling have been adopted, and each approach is adept at elucidating a specific aspect of nervous system function. Thus while bio-physical models have strived to comprehend the dynamics of actual physical processes occurring within a nerve cell, the phenomenological approach has conceived models that relate the ionic properties of nerve cells to transitions in neural activity. Further-more, the field of neural networks has endeavored to explore how distributed parallel processing systems may become capable of storing memory. Through this project, we strive to explore how some of the insights gained from biophysical neuronal modeling may be incorporated within the field of neural net-works. We specifically study the capabilities of a simple neural model, the Resonate-and-Fire (RAF) neuron, whose derivation is inspired by biophysical neural modeling. While reflecting further biological plausibility, the RAF neuron is also analytically tractable, and thus may be implemented within neural networks. In the following thesis, we provide a brief overview of the different approaches that have been adopted towards comprehending the properties of nerve cells, along with the framework under which our specific neuron model relates to the field of neuronal modeling. Subsequently, we explore some of the time-dependent neurocomputational capabilities of the RAF neuron, and we utilize the model to classify logic gates, and solve the classic XOR problem. Finally we explore how the resonate-and-fire neuron may be implemented within neural networks, and how such a network could be adapted through the temporal backpropagation algorithm.

Extensive clonal spread and extreme longevity in saw palmetto, a foundation clonal plant

The lack of effective tools have hampered our ability to assess the size, growth and ages of clonal plants. With Serenoa repens (saw palmetto) as a model, we introduce a novel analytical framework that integrates DNA fingerprinting and mathematical modelling to simulate growth and estimate ages of clonal plants. We also demonstrate the application of such life-history information of clonal plants to provide insight into management plans. Serenoa is an ecologically important foundation species in many Southeastern United States ecosystems; yet, many land managers consider Serenoa a troublesome invasive plant. Accordingly, management plans have been developed to reduce or eliminate Serenoa with little understanding of its life history. Using Amplified Fragment Length Polymorphisms, we genotyped 263 Serenoa and 134 Sabal etonia (a sympatric non-clonal palmetto) samples collected from a 20 X 20 m study plot in Florida scrub. Sabal samples were used to assign small field-unidentifiable palmettos to Serenoa or Sabal and also as a negative control for clone detection. We then mathematically modelled clonal networks to estimate genet ages. Our results suggest that Serenoa predominantly propagate via vegetative sprouts and 10000-year-old genets may be common, while showing no evidence of clone formation by Sabal. The results of this and our previous studies suggest that: (i) Serenoa has been part of scrub associations for thousands of years, (ii) Serenoa invasion are unlikely and (ii) once Serenoa is eliminated from local communities, its restoration will be difficult. Reevaluation of the current management tools and plans is an urgent task.

Extensive clonal spread and extreme longevity in saw palmetto, a foundation clonal plant

The lack of effective tools has hampered our ability to assess the size, growth and ages of clonal plants. With Serenoa repens (saw palmetto) as a model, we introduce a novel analytical frame work that integrates DNA fingerprinting and mathematical modelling to simulate growth and estimate ages of clonal plants. We also demonstrate the application of such life-history information of clonal plants to provide insight into management plans. Serenoa is an ecologically important foundation species in many Southeastern United States ecosystems; yet, many land managers consider Serenoa a troublesome invasive plant. Accordingly, management plans have been developed to reduce or eliminate Serenoa with little understanding of its life history. Using Amplified Fragment Length Polymorphisms, we genotyped 263 Serenoa and 134 Sabal etonia (a sympatric non-clonal palmetto) samples collected from a 20 x 20 m study plot in Florida scrub. Sabal samples were used to assign small field-unidentifiable palmettos to Serenoa or Sabal and also as a negative control for clone detection. We then mathematically modelled clonal networks to estimate genet ages. Our results suggest that Serenoa predominantly propagate via vegetative sprouts and 10000-year-old genets maybe common, while showing no evidence of clone formation by Sabal. The results of this and our previous studies suggest that: (i) Serenoa has been part of scrub associations for thousands of years, (ii) Serenoa invasions are unlikely and (ii) once Serenoa is eliminated from local communities, its restoration will be difficult. Reevaluation of the current management tools and plans is an urgent task.

Monitoring and Modeling of the Hydraulic and Sediment Processes at In-Stream Restoration Structures in the Vicinity of a Bridge Crossing

The long-term performance of infrastructure depends on reliable and sustainable designs. Many of Pennsylvania’s streams experience sediment transport problems that increase maintenance costs and lower structural integrity of bridge crossings. A stream restoration project is one common mitigation measure used to correct such problems at bridge crossings. Specifically, in an attempt to alleviate aggradation problems with the Old Route 15 Bridge crossing on White Deer Creek, in White Deer, PA, two in-stream structures (rock cross vanes) and several bank stabilization features were installed along with a complete channel redevelopment. The objectives of this research were to characterize the hydraulic and sediment transport processes occurring at the White Deer Creek site, and to investigate, through physical and mathematical modeling, the use of instream restoration structures. The goal is to be able to use the results of this study to prevent aggradation or other sediment related problems in the vicinity of bridges through improved design considerations. Monitoring and modeling indicate that the study site on White Deer Creek is currently unstable, experiencing general channel down-cutting, bank erosion, and several local areas of increased aggradation and degradation of the channel bed. An in-stream structure installed upstream of the Old Route 15 Bridge failed by sediment burial caused by the high sediment load that White Deer Creek is transporting as well as the backwater effects caused by the bridge crossing. The in-stream structure installed downstream of the Old Route 15 Bridge is beginning to fail because of the alignment of the structure with the approach direction of flow from upstream of the restoration structure.