We are offering three openings for unpaid internship, and two MSc thesis projects starting January 2021. The subject area is mathematical modeling with applications in Systems Biology and Computational Ecology. Each internship project can also be extended to a MSc thesis.
The projects are jointly organized and supervised by the Computational Biology Unit (Univ. of Bergen), the Department of Computer Science and Mathematical Sciences (Western Norway Univ. of Sciences) and the Fisheries Dynamics dept. (Institute of Marine Research) Norway.
Prospective candidates will work on developing and analysing mathematical models that describe the dynamics of biological and ecological systems. The project tasks will include bifurcation analysis, parameter estimation (optimization), uncertainty quantication and mathematical programming in Matlab, Python, or C.
Time and Duration:
Internship: The start time and duration is negotiable but a 3 months (minimum) is expected, with a weekly workload of 40 hours.
MSc thesis: Approximately 6 months, with negotiable start time, and in consultation with home institution.
For applications, attach:
a copy of your academic records (transcripts)
a letter of motivation (max. 1 page)
name and email address of an academic reference
Special Covid-19 Considerations:
Depending on the state of the pandemic situation in 2021-2022, remote supervision
(via, e.g., Zoom/Teams) may be considered.
Detailed project descriptions
MSc Project 1 – Linking Population Size and Vital Rates to System State in a Single-Species Model
Background: Modeling how population size and vital rates (e.g., growth, mortality) are linked to dynamic population state is challenging, as the process involves several nonlinear steps, which regulate both population growth rate and stability via a feedback loop.
Goal: To develop a single species mathematical (ordinary/delay differential equation) model to study how population size and vital rates are linked to switches in population states. We obtain realistic scenarios by extending the approach to a stochastic framework, which is to be validated using empirical observations.
Keywords: Nonlinear, Deterministic/Stochastic models, Multi-stability, Bifurcation and Sensitivity analysis, Feedback loops.
MSc Project 2 – A Comparison of Polynomial Chaos (PC) Approaches in Parameter and Uncertainty Estimation
Background: Most descriptions of dynamical system involves Ordinary or Delay differential equations with uncertain/random parameters. Exploring the full range of the random parameters and the impact of parameter uncertainty on the state variables can be challenging. Polynomial Chaos (PC) theory is a fast concept of stochastic analysis, which allows us to explore the space of the random parameters and quantify uncertainty, without resorting to rigorous Monte-Carlo simulations.
Goal: To apply and compare three variants of the PC approach to quantifying uncertainty. We use a model described by a set of highly nonlinear ordinary differential equations with time-invariant random parameters of arbitrary probability distributions. There is a choice between an ecological, and a systems biological model.
Keywords: Polynomial Chaos, Stochastic, Uncertainty, Prediction
Internship Project 1 – Nonlinear Models with Unknown Intermediate Process Equations
Background: Many biological systems evolve through several intermediate (non- linear and complex) stages. Data for the intermediate stages may be unavailable at the required scale and accuracy, and system dynamic knowledge may be limited. Predicting the system dynamic behavior based solely on data from an initial, and end stage is challenging when the end-stage observations are strongly influenced by the dynamics of the intermediate stages.
Goal: We examine a mathematical modeling approach that uses a compact functional description of the unknown intermediate stages. The appropriateness of the approach will be validated using empirical observations. Finally, we use numerical simulations to investigate extension of the framework to account for stochasticity in the intermediate stages.
Internship Project 2 – Inferring System Dynamic Models from Empirical Data
Background: Deriving the governing equations of dynamic systems from noisy observation data is inherently complex and challenging. The observations may represent different states of the system, and these states must be captured by the model parameters. Complex models may overt the observation data, which results in poor model prediction performance. Hence, there is a need to derive parsimonious models that balance accuracy with model complexity.
Goal: To analyse an algorithm that combines sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. We aim at applying the algorithm to data generated using a system of nonlinear (ordinary and delay) differential equations, and to empirical observations for which the underlying dynamics are modestly known.
Internship Project 3 – Model Reduction Techniques Applied to Dynamical System Models
Background: Mathematical model reduction procedures derive reduced-order models that are close to the original (full-scale) model and preserve some of its key properties (e.g., stability).
Goal: To examine the performance of a number of model reduction techniques when applied to two spefic (discrete-time, and continuous-time) dynamic system models. We evaluate how reduction may affect some scale-dependent attributes of the model, and suggest a methodology for addressing the challenge.