Student project mentoring
Below is a list of various past student projects I have supervised. Some are semester-long independent research experiences, others are longer projects culminating in a written senior thesis. This list give you a flavor of the kinds of topics possible, but I’m open to supervising a project in any area of application that has a computational or statistical component to it. Students who are interested in completing an honors thesis, senior thesis, or independent research project are encouraged to come talk to me.
Honors thesis by Halley Dante ('23). A comparison of stastical methods used to analyze data collected on the "spatial decision making" movements of zebrafish. Data was collected by Halley in the neurobiology laboratory of Armin Bahl at the University of Konstanz in Germany
Abstract: Real world data is inherently noisy and data analysis can be especially complex when noise is compounded in hierarchical and multilevel data structures. Since such data structures can be described using multiple approaches, the way data is collapsed and grouped within these structures can influence its resulting interpretation and analyses. To avoid discrepancies in data collapsing and grouping, multiple statistical approaches have been developed specifically to analyze multilevel data structures. Examples of multilevel statistical models are the two-factor ANOVA and the general linear model with repeated-measures (GLM-RR) which is typically used in the context of looking at change over time. Unlike simple summary-statistics such as t-tests, multilevel models allow for precision in the effect of each level on the observed data. In this study, analyses will be done using both simple statistical models and multilevel models with a dataset from a behavioral decision-making assay that aims to see whether phototactic preference changes over 24 hours in larval zebrafish. The simple and multilevel analyses will be compared through the descriptive analyses and hypothesis testing. The descriptive analyses will provide insight into the practicality of collapsing levels of data in hierarchical data structures and the hypothesis testing will provide comparative insight into the use of both simple and multilevel statistical models.
See her honors thesis here.
Abstract: Real world data is inherently noisy and data analysis can be especially complex when noise is compounded in hierarchical and multilevel data structures. Since such data structures can be described using multiple approaches, the way data is collapsed and grouped within these structures can influence its resulting interpretation and analyses. To avoid discrepancies in data collapsing and grouping, multiple statistical approaches have been developed specifically to analyze multilevel data structures. Examples of multilevel statistical models are the two-factor ANOVA and the general linear model with repeated-measures (GLM-RR) which is typically used in the context of looking at change over time. Unlike simple summary-statistics such as t-tests, multilevel models allow for precision in the effect of each level on the observed data. In this study, analyses will be done using both simple statistical models and multilevel models with a dataset from a behavioral decision-making assay that aims to see whether phototactic preference changes over 24 hours in larval zebrafish. The simple and multilevel analyses will be compared through the descriptive analyses and hypothesis testing. The descriptive analyses will provide insight into the practicality of collapsing levels of data in hierarchical data structures and the hypothesis testing will provide comparative insight into the use of both simple and multilevel statistical models.
See her honors thesis here.
Honors thesis by Taylor Flanagan ('21). A Python-based computational project using Markov models to randomly generate compositions of Balinese gamelan gong kebyar improvisations on the reyong. Each of the reyong's four players can play only some of the gamelan's five tones and must use specific patterns. The model's probability values come from a combination of top-down and bottom-up techniques, making extensive use of Leslie Tilley's work on the grammar of *reyong norot* and example patterns from her concurrent study of musician Dewa Ketut Alit's improvisation. The model outputs MIDI files for audio playback of the constructed songs.
Read his thesis here
Read his thesis here
Honors thesis by Joshua Mariz ('21). An algorithm written in Javascript to estimate the distribution of "compactness scores" in a grid model of electoral voting districts. The algorithm randomly generates districts of equal size in an n x n grid using a novel square-by-square growth method.
Read his thesis here.
Read his thesis here.
Honors thesis by Kayla Pietruszka ('11). This project used numerical simulation of differential equations to investigate a model of calcium and glucose dynamics in the beta cells of the pancreas.
Abstract: Pancreatic beta cells are triggered to release insulin into the bloodstream by fast oscillations (“bursting”) of their internal calcium (Ca), which can be mathematically modeled using a system of nonlinear ordinary differential equations. In the original Chay and Keizer model (1983), the dynamics of Ca depend on Ca currents flowing into and out of the cell, which are modified by changes in the cell’s electrical potential (itself a function of Ca and potassium in the cell). Keizer and Magnus (1989) and Bertram and Sherman (2004) updated the model to include an ATP-sensitive potassium current as well as an internal Ca compartment (the endoplasmic reticulum). However, none of these models account for changing levels of blood glucose (which is important, for instance, during a meal). Fridlyand and Philipson (2010) present modelling that connects the ADP/ATP ratio in the beta cells to blood glucose. We integrate their observations into the Bertram and Sherman model via a two-dimensional sigmoid function to establish a relationship between calcium bursting in pancreatic beta cells and glucose concentration. Through computer simulation, we demonstrate a bifurcation to periodic bursting behavior as glucose increases (and ADT/ATP decreases). We also find that there is a linear decreasing relationship between calcium conductance and the critical glucose concentration for the onset of bursting.
See her research poster here and her honors thesis here.
Abstract: Pancreatic beta cells are triggered to release insulin into the bloodstream by fast oscillations (“bursting”) of their internal calcium (Ca), which can be mathematically modeled using a system of nonlinear ordinary differential equations. In the original Chay and Keizer model (1983), the dynamics of Ca depend on Ca currents flowing into and out of the cell, which are modified by changes in the cell’s electrical potential (itself a function of Ca and potassium in the cell). Keizer and Magnus (1989) and Bertram and Sherman (2004) updated the model to include an ATP-sensitive potassium current as well as an internal Ca compartment (the endoplasmic reticulum). However, none of these models account for changing levels of blood glucose (which is important, for instance, during a meal). Fridlyand and Philipson (2010) present modelling that connects the ADP/ATP ratio in the beta cells to blood glucose. We integrate their observations into the Bertram and Sherman model via a two-dimensional sigmoid function to establish a relationship between calcium bursting in pancreatic beta cells and glucose concentration. Through computer simulation, we demonstrate a bifurcation to periodic bursting behavior as glucose increases (and ADT/ATP decreases). We also find that there is a linear decreasing relationship between calcium conductance and the critical glucose concentration for the onset of bursting.
See her research poster here and her honors thesis here.
Independent research project by Kevin McKay ('13). Simulations and visuaslization in C++ and MATLAB of a discrete-time probabilistic model of cardiac physiology dynamics.
Abstract: Probabilistic Cellular Automata (PCA) are mathematical models that represent spatially discrete systems as two-dimensional grids of neighboring lattice nodes. We used a PCA with nearest-neighbor interactions to simulate calcium release inside cardiac myocytes to model cardiac instability, a precursor to heart attacks. The states of the nodes are either “on” or “off” according to rules that incorporate randomness. The number of “on” states represents the overall activation of the system, and oscillations in this value indicate instability. The amplitude of these oscillations was studied as a function of the strength of nearest neighbor interactions. For small lattice size, there was a steady, gradual increase in amplitude as interaction strength grew. For large lattice size, the amplitude increase was sudden and sharp. Similar patterns were observed with changes in aspect ratio of the lattice. The results suggest that as the lattice became larger and less oblong, a critical value threshold for onset of oscillations became defined. These simulations helped us understand the dynamics of cardiac myocytes under actual conditions of biological variability and can lead to new hypotheses for future trials.
See his research poster here.
Abstract: Probabilistic Cellular Automata (PCA) are mathematical models that represent spatially discrete systems as two-dimensional grids of neighboring lattice nodes. We used a PCA with nearest-neighbor interactions to simulate calcium release inside cardiac myocytes to model cardiac instability, a precursor to heart attacks. The states of the nodes are either “on” or “off” according to rules that incorporate randomness. The number of “on” states represents the overall activation of the system, and oscillations in this value indicate instability. The amplitude of these oscillations was studied as a function of the strength of nearest neighbor interactions. For small lattice size, there was a steady, gradual increase in amplitude as interaction strength grew. For large lattice size, the amplitude increase was sudden and sharp. Similar patterns were observed with changes in aspect ratio of the lattice. The results suggest that as the lattice became larger and less oblong, a critical value threshold for onset of oscillations became defined. These simulations helped us understand the dynamics of cardiac myocytes under actual conditions of biological variability and can lead to new hypotheses for future trials.
See his research poster here.
Independent research project by Ashely Rhoades ('14). A statistical analysis of demographic predictors of diabetes using data compiled by zip code in Los Angeles County, examining the link between diabetes and other health outcomes with regional availability and distribution of fast food restaurants.
Independent research project by Niko Victoria ('17). We simulated large-scale differential equation models in c++ on a high-performance computing platform.
Abstract: The primary function of pancreatic beta-cells is to release insulin to control blood glucose levels. When beta-cells synchronize their electrochemical bursting patterns via gap junctions that physically connect the cells into a cluster, insulin release is enhanced. Diabetes mellitus is an endocrine disorder characterized by poor insulin release which may arise from electrochemical desynchronization between cells due to cellular dysfunction. Islet amyloid polypeptide (IAPP), a byproduct of insulin secretion, is thought to be a possible source of this dysfunction. One possible mechanism by which IAPP acts is membrane disruption via pore formation; but how do these pores affect the electrical activity and overall function of cell clusters?
Simulations were run using the 190-core parallel computing cluster using code written in C++. We developed a differential equation model, based on a Hodgkin-Huxley-type equation for a single cell, with multiple cells coupled by a "gap current", which simulates beta-cells islets of multiple electrically coupled cells primarily dependent on [Ca2+], [K+], and voltage. Synchrony among cells was measured using a synchronization index: a minimum average correlation between bursting patterns of neighboring cells in the cluster. With this model we showed (1) bursting patterns of neighboring cells can be synchronized via electrical coupling with a coupling conductance of 0.4 S in a three-cell model; (2) bursting could be induced in non-bursting cells by neighbor cells; and (3) leak currents with a conductance of 3.5 S in only 10% of cells can drastically reduce synchrony throughout the cluster. Given these results, pore formation can be a viable mechanism by which IAPP contributes to diabetes.
See his research poster here.
Abstract: The primary function of pancreatic beta-cells is to release insulin to control blood glucose levels. When beta-cells synchronize their electrochemical bursting patterns via gap junctions that physically connect the cells into a cluster, insulin release is enhanced. Diabetes mellitus is an endocrine disorder characterized by poor insulin release which may arise from electrochemical desynchronization between cells due to cellular dysfunction. Islet amyloid polypeptide (IAPP), a byproduct of insulin secretion, is thought to be a possible source of this dysfunction. One possible mechanism by which IAPP acts is membrane disruption via pore formation; but how do these pores affect the electrical activity and overall function of cell clusters?
Simulations were run using the 190-core parallel computing cluster using code written in C++. We developed a differential equation model, based on a Hodgkin-Huxley-type equation for a single cell, with multiple cells coupled by a "gap current", which simulates beta-cells islets of multiple electrically coupled cells primarily dependent on [Ca2+], [K+], and voltage. Synchrony among cells was measured using a synchronization index: a minimum average correlation between bursting patterns of neighboring cells in the cluster. With this model we showed (1) bursting patterns of neighboring cells can be synchronized via electrical coupling with a coupling conductance of 0.4 S in a three-cell model; (2) bursting could be induced in non-bursting cells by neighbor cells; and (3) leak currents with a conductance of 3.5 S in only 10% of cells can drastically reduce synchrony throughout the cluster. Given these results, pore formation can be a viable mechanism by which IAPP contributes to diabetes.
See his research poster here.
Independent research project by Brian Joerger ('18). A computational project to simulate a three-dimensional probabilistic lattice model of state dynamics in discete time. of calcium release in a human heart cells (using c++) and to effectively visualize the results of those simulations (using MATLAB).