University of Alberta

Curvature is one of the fundamental ingredients in differential geometry. People are increasingly interested in whether it is possible to think of combinatorial graphs as manifolds and a number of different notions of curvature have been proposed. I...

We consider the problem of learning an unknown function f from given data about f. The learning problem is to give an approximation fˆ to f that predicts the values of f away from the data. There are numerous settings for this learning problem...

About 100 years ago, William Henry Young and Felix Hausdorff provedthat, for a periodic L_p-integrable function, the sequence of its Fourier coefficients necessarily lies in the discrete \ell_{p'} space provided that p' is the conjugate of p and 1

Despite the promise of big data, inferences are often limited not by sample size but rather by systematic effects. Only by carefully modeling these effects can we take full advantage of the data -- big data must be complemented with big models and...

In many biological systems, it is essential for individuals to gain information from their local environment before making decisions. In particular, through sight, hearing or smell, animals detect the presence of other individuals and adjust their...

The development of precision medicine for cancer requires accurately quantifying the dynamics of tumor evolution. Two reasons this can be difficult are the limited number of times we can observe the tumor and intra-tumor heterogeneity that is...

I will begin by introducing the Penrose tiling -- the most famous example of a self-similar quasi-periodic pattern. In addition to its beauty and mathematical interest, this pattern has a famous physical application to exotic materials called...

Determining information about the state of a complex physical system from observations of its behavior is a fundamental problem in scientific inference and engineering design. Often, this can be formulated as the stochastic inverse problem of...

Biodegradation in soils has many implications for humankind. The importance of studying this process relies upon, for example, the impact of global warming, increasing food security and mitigating soil degradation. From the diverse problems to tackle...

This work describes how machine learning may be used to develop accurate and efficient nonlinear dynamical systems models for complex natural and engineered systems. We explore the sparse identification of nonlinear dynamics (SINDy) algorithm, which...