# Applied Mathematics

## PIMS-SFU 20th Anniversary Celebration: Nataša Pržulj - Data Driven Medicine

The Pacific Institute for the Mathematical Sciences (PIMS) was founded in 1996, and Simon Fraser University is a founding member. The members of PIMS now include all the major Canadian research universities west of Ontario, as well as universities in Washington and Oregon. Please join us to celebrate 20 years of productive collaboration, with a lecture by SFU alumna and professor at UCL Nataša Pržulj on Data Driven Medicine followed by a reception.

We are faced with a flood of molecular and clinical data. Various biomolecules interact in a cell to perform biological function, forming large, complex systems. Large amounts of patient-specific datasets are available, providing complementary information on the same disease type. The challenge is how to model and mine these complex data systems to answer fundamental questions, gain new insight into diseases and improve therapeutics. Just as computational approaches for analyzing genetic sequence data have revolutionized biological and medical understanding, the expectation is that analyses of networked “omics” and clinical data will have similar ground-breaking impacts. However, dealing with these data is nontrivial, since many questions we ask about them fall into the category of computationally intractable problems, necessitating the development of heuristic methods for finding approximate solutions.

We develop methods for extracting new biomedical knowledge from the wiring patterns of large networked biomedical data, linking network wiring patterns with function and translating the information hidden in the wiring patterns into everyday language. We introduce a versatile data fusion (integration) framework that can effectively integrate somatic mutation data, molecular interactions and drug chemical data to address three key challenges in cancer research: stratification of patients into groups having different clinical outcomes, prediction of driver genes whose mutations trigger the onset and development of cancers, and re-purposing of drugs for treating particular cancer patient groups. Our new methods stem from network science approaches coupled with graph-regularised non-negative matrix tri-factorization, a machine learning technique for co-clustering heterogeneous datasets.

## About Irreversibility in Rarefied Gas Dynamics

## 2016 Graduate Mathematical Modelling in Industry Workshop

## A glamorous Hollywood star, a renegade composer, and the mathematical development of spread spectrum communications.

## Bayesian study design for nonlinear systems: an animal disease transmission experiment case study

## Optimal Strategic Sizing of Energy Storage Facilities in Restructured Electricity Markets

## The long road to 0.075: a statistician’s perspective of the process for setting ozone standards

## Conference on the Mathematics of Sea Ice

Interesting mathematics arises in many areas of the study of sea ice and its role in climate. Partial differential equations, numerical analysis, dynamical systems and bifurcation theory, diffusion processes, percolation theory, homogenization and statistical physics represent a broad range of active fields in applied mathematics and theoretical physics which are relevant to important issues in climate science and the analysis of sea ice in particular.

## Sparse Recovery Using Quantum Annealing - Final Report

## Deducing Rock Properties from Spectral Seismic Data - Final Report

### Seismic Data in Exploration Geoscience

The recovery and production of hydrocarbon resources begins with an exploration of the earth’s subsurface, often through the use of seismic data collection and analysis. In a typical seismic data survey, a series of seismic sources (e.g. dynamite explosions) are initiated on the surface of the earth. These create vibrational waves that travel into the earth, bounce off geological structures in the subsurface, and reflect back to the surface where the vibrations are recorded as data on geophones. Computer analysis of the recorded data can produce highly accurate images of these geological structures which can indicate the presence of reservoirs that could contain hydrocarbon fluids. High quality images with an accurate analysis by a team of geoscientists can lead to the successful discovery of valuable oil and gas resources. Spectral analysis of the seismic data may reveal additional information beyond the geological image. For instance, selective attenuation of various seismic frequencies is a result of varying rock properties, such as density, elasticity, porosity, pore size, or fluid content. In principle this information is present in the raw data, and the challenge is to find effective algorithms to reveal these rock properties.

### Spectral Analysis

Through the Fourier transform, frequency content of a seismic signal can be observed. The Short Time Fourier transform is an example of a time-frequency method that decomposes a signal into individual frequency bands that evolve over time. Such time-frequency methods have been successfully used to analyze complex signals with rich frequency content, including recordings of music, animal sounds, radio-telescope data, amongst others. These time-frequency methods show promise in extracting detailed information about seismic events, as shown in Figure 1, for instance.

Figure 1: Sample time-frequency analysis of a large seismic event (earthquake). From Hotovec, Prejean, Vidale, Gomberg, in J. of Volcanology and Geothermal Research, V. 259, 2013.

### Problem Description

Are existing time-frequency analytical techniques effective in providing robust estimation of physical rock parameters that are important to a successful, economically viable identification of oil and gas resources? Can they accurate measure frequency-dependent energy attenuation, amplitude-versus-offset effects, or other physical phenomena which are a result of rock and fluid properties?

Using both synthetic and real seismic data, the goal is to evaluate the effectiveness of existing time-frequency methods such as Gabor and Stockwell transforms, discrete and continuous wavelet transforms, basis and matching pursuit, autoregressive methods, empirical mode decomposition, and others. Specifically, we would like to determine whether these methods can be utilized to extract rock parameters, and whether there are modifications that can make them particularly effective for seismic data.

The source data will include both land-based seismic surveys as well as subsurface microseismic event recordings, as examples of the breadth of data that is available for realistic analysis.

Figure 2: (a). Seismic data set from a sedimentary basin in Canada. The erosional surface and channels are highlighted by arrows. The same frequency attribute are extract from short time Fourier transform (b), continuous wavelet transform (c) and empirical mode decomposition (d).