2018 Summer REU Program

Site Leader: Julia Arciero 

• Project 1: Using a Mathematical Model to Understand How Pairs of Red Blood Cells Interact in Linear Shear Flow
  Mentor: Dr. Jared Barber
  Description: Blood is composed of mainly red blood cells (45%) and plasma.  As blood flows through vessels, cells near walls are pushed towards the vessel center by wall interactions but pushed away from the vessel center by interactions with other cells.  These competing effects have a primary role in how cells are distributed across the vessel which, in turn, affect distribution of other important quantities like oxygen.  We have developed a two-dimensional computational model of red blood cell motion to investigate how two isolated cells interact near vessel walls.  The project will be use a previously-developed model to consider different types of interactions that pairs of cells undergo in this environment, how these interactions affect diffusion and mixing of cells, and the effects of various parameters like cell flexibility and size on these results.
   
• Project 2: Implementation of Advanced Topology Optimization Methods
  Mentor: Dr. Andres Tovar
  Description: In applied mathematics and engineering, topology optimization is known as the most effective material distribution numerical approach for synthesizing structures without any preconceived shape. Currently, a number of topology optimization algorithms is freely available in Matlab and other programming languages. Most of these algorithms use so-called density-based method, which can be used in 2D and 3D structures. The objective of this work is to implement more advanced topology optimization methods such as the level set-based and/or the phase field-based method. The student participating in this project will gain a complete understanding of the mathematics behind topology optimization and exposed to all related Matlab tools. The result of this research experience is the numerical implementation, analysis, and application of advanced topology optimization methods in structural optimization.
   
• Project 3: Using a Mathematical Model of Sepsis to Predict Survivability Conditions
  Mentor: Dr. Julia Arciero
  Description: Sepsis is a very serious and life-threatening illness caused by the body’s response to an infection.  Experiments conducted in rats have shown that once a bacteria load exceeds a certain level, the rats do not survive.  The presence of bacteria in the blood leads to a significant inflammatory response which in turn causes rapid damage to the body’s tissues that triggers a self-sustaining loop of damage and inflammation, eventually leading to either septic (bacteria-driven) or aseptic (inflammation-driven) death.  The objective of this study is to use a mathematical model to predict the survivability range for an infection given varying doses or degrees of virulence of a bacterial infection.  A model of ordinary differential equations will be used to simulate interacting populations of the bacteria and immune system.  Experimental data from rat sepsis studies will be used to estimate several model parameters.  The model will be used to predict conditions that lead to disease or health outcomes.

Site Leader: Simon Garnier

• Project 1: Modeling Slime Mold Decision-Making as Systems of Coupled Oscillators
  Mentors: Simon Garnier and Jason Graham
  Description: In a complex and dynamic world, how do you choose the best of multiple options when you do not possess a brain, or even the beginnings of a nervous system? From bacteria and immune cells to fungi and plants, the large majority of living beings face this problem every day. Nevertheless our knowledge of decision-making mechanisms is mostly limited to those of neuronal animals, and in particular vertebrates. The goal of this project is for students to explore with University of Scranton Assistant Professor Jason Graham and NJIT Assistant Professor Simon Garnier the choice-making abilities of a non-neuronal model organism: the slime mold Physarum polycephalum. Using models of coupled oscillators, the students will study the integration of noisy and contradictory information and the role of memory during decision-making by P. polycephalum. They will also compare their results to experimental data collected by Garnier’s lab as part of an IOS NSF-funded research effort. The results of this work will help understand information pro- cessing in organisms without a brain, thereby advancing our comprehension of the emergence of cognitive processes in biological systems.
   
• Project 2: Emergent oscillations in electrically coupled neuronal networks
  Mentors: Jorge Golowasch and Farzan Nadim
  Description: Electrical coupling of neurons via gap junctions can produce network oscillatory activity in the absence of any oscillatory components. Such oscillations depend on network activity spreading through closed loops (re-entry) through which action potentials can spread, thus producing periodic potential firing patterns of the component neurons (Gansert et al, 2007, J. Neurophysiol).  The properties of these re-entrant loops and the types of activity they can generate are mostly unknown. This project will combine computational modeling and mathematical analysis to characterize the types of activities that such networks can produce. Specific questions that will be addressed are: 1) What role does the size of the network play in the activity generated; 2) What is the role of electrical coupling strength; 3) What is the network output capacity; 4) How do intrinsic properties of neurons, specifically membrane potential resonance, influence network output.

Site Leader: Dennis Pearl

• Project 1: Assessing the Value of ChIP Data
  Mentor: Qunhua Li
  Description: ChIP-exo is a high-throughput technology for identifying protein binding sites on DNA. It has near single-bp resolution, providing detailed structural information on the organization of protein-DNA complexes at a fine scale. However, robust measures for assessing its quality and reproducibility are still lacking. While there are quality measures for similar but lower-resolution technologies, such as ChIP-seq data, these measures do not work well for ChIP-exo due to its high resolution. This project aims to use machine learning techniques to build a predictive model for automatically classify quality and reproducibility of ChIP-exo experiments and extract predictive features. 
   
• Project 2: Space-Time Models for Infectious Diseases
  Mentor: Murali Haran
  Description: Space-time models for infectious diseases: Infectious diseases like rotavirus, pertussis, measles, and meningitis have a major impact on populations all over the world,  particularly on children in sub-Saharan Africa. These disease present a number of important challenges including estimating the current burden and anticipating the future burden of these diseases, as well as studying the impact of different vaccination strategies on controlling their spread. These research problems involve developing models for the diseases and combining disparate sources of information such as surveillance data and hospital records. In these projects students will be introduced to infectious disease modeling via susceptible-infected-recovered (SIR) models. They will learn simulation techniques, as well as estimation and computational methods for fitting these models to data, both via maximum likelihood and Bayesian methods. They will learn these methods through simulated examples and by applying them to real data sets obtained from collaborators at the Center for Infectious Disease Dynamics (CIDD) at Penn State.
   
• Project 3: Nonparametric Models for Animal Movement
  Mentor: Ephraim Hanks
  Description: Movement is a fundamental process underlying the spread of infectious disease, the spread of invasive species, and the flow of information and resources in social species.  Understanding and predicting realistic movement of humans and animals can lead to improved surveillance of disease and more accurate predictions of the effects of changing landscapes.  Animal movement is highly complex, exhibiting dependence in time, correlation in movements between conspecifics, changing behavior across seasons, hard constraints such as rivers and cliffs, and response to local environmental cues.  Current statistical models for animal movement fail to capture this complexity fully.  Based on Taken's theorem (Taken 1981), complex dynamical systems such as animal movement can often be well-represented by a lower-dimensional dynamical system, and the dynamics are often captured well by considering lagged time observations of the system.  This suggests a nonparametric approach for modeling movement based on (1) the current local environment, (2) the animal's current movement state, and (3) the animal's state at multiple previous time steps.  In this project, students will use modern machine learning approaches to build models that capture and replicate the complexity of animal movement, and will apply these models to various animal systems, including social movements of ants in a nest, sea lion foraging trips, and elk migrations.
   
• Project 4: Estimating the Distribution of Amino Acids in the Pre-biotic Period
  Mentor: Dennis Pearl
  Description: Estimating the Distribution of Amino Acids in the Pre-biotic period.  When reconstructing phylogenetic histories from highly conserved sequences in all domains of life, recent evidence in several ancient enzymes shows that the distribution of amino acids is different at the root of the "tree of life" than in more rapidly changing newer enzymes. This provides a signal for the distribution of amino acids associated with a pre-biotic era (Pollack et al., 2013). In this project students will develop estimates of the pre-biotic distribution of amino acids from a variety of perspectives and combine evidence from phylogenetic and laboratory assessments. They will also develop and apply a new model of molecular evolution that allows for the amino acid distribution to vary with the level of site conservation. Students will advance their knowledge of stochastic evolutionary processes, and become skilled in aspects of probability and statistic inference associated with their use.