**An Economic Stimulus Opportunity for Canada**

Explore projects and reports from the 2020 edition of M2PI

*Math ^{Industry}* (Math to power industry) is a professional development
school positioned to benefit Canadian industry because:

- Recent PhDs and Postdocs in the mathematical sciences are a national resource that is poised to be underutilized.
- Ideas from the mathematical sciences are vital to Canada’s industry sectors and are especially important during and after the pandemic.
- A cohort-based training and job placement program focused on key industry sectors will help advance Canada’s economy.

The drastic decrease in economic activity caused by the pandemic combined with cost explosions in other governmental programs will lead to significant cuts in higher education budgets. Reductions in the capacity of universities to hire new faculty and postdocs will essentially eliminate a career pathway for a generation of young researchers. This talent pool should be effectively redirected toward activities that drive Canada’s economic recovery.

The important role that mathematical scientists play in defining government
policy responses to the pandemic is analogous to the role these experts should
play across Canada’s industry sectors. Governmental decisions regarding when or
how to optimally implement policies to flatten the curve rely upon predictive
models, data analysis, and other mathematical insights. Effective business
decision-making similarly requires expertise in modeling, computation,
statistics, optimization (mathematical sciences). Studies by Deloitte have
revealed the enormous impact the mathematical sciences have on the UK Economy
and the Dutch Economy. Goals for the *Math ^{Industry}* include economic
stimulation during and after the COVID-19 pandemic, placement of recent
mathematical science PhDs into jobs in western Canada, and an ongoing
improvement to Canada’s Business Enterprise Research and Development capacity.

The Pacific Institute for the Mathematical Sciences (PIMS) and partners are offering a virtual rapid response program to train and place young mathematical scientists into jobs in important industry sectors in western Canada (agrifood, energy, forestry, health care, mining). This program will start with a training bootcamp (software best practices, business, communications, project management), group collaborations with industry partners, and create a funnel leading to job placements in industry.

Certified training programs

Agile software development, virtual collaboration, open source toolchains

communication skills, project management, effective teams & ethics

.js-id-2020#### Cenovus Energy

#### ATCO - Optimized Scheduling

#### Divi Project

#### BC Financial Services Authority

#### Environmental Instruments Canada

#### Fotech Solutions

#### Ioto International

#### Mcmillan Mcgee

#### Ovintiv

#### Aerium Analytics

This project concerns the transportation of heavy oil via pipeline, and the impact of congestion in transportation on pricing. Using stochastic transport optimization can we model and answer the following questions: When there are documented disruptions in the transport system, can we predict how large the congestion surcharge was and how prices responded to the disruption? Can we predict the occurrence of congestion by perturbing input factors in the system? How do shape and connections in the transport network contribute to the propensity for frequency of the congestion and magnitude of congestion surcharge?

Due to the outbreak of Covid-19 around the world, and government policies implemented as a response to the outbreak, many corporations have chosen to let their employees work from home to prevent the spread of the disease. In order to safely re-open the economy, one of the recommendations from health authorities is to allow only a limited percentage of workers in the workplace at any specific time. Given these constraints, it is useful for companies to arrange flexible work schedule so the employees go to offices during reasonable working hours, and at the same time reduce their commute time to improve their productivity. In this problem, you will help a model business to design and optimize their employees’ working-at-office schedule using a combination of criteria which you deem to be important, and real-life data such as traffic, limitation on work schedule hours, commuting time and others.

The main limitation of blockchains is storage requirements, which would be alleviated if one could reversibly compress the data in a blockchain or in its underlying transaction graph. Determine to what extent a transaction graph can be compressed (for later decompression) or what obstructions exist to its compression. What compression ratio can you achieve for an ordered sequence of cryptographic hashes? Pure Mathematics skills and experience with mathematical proof-writing are essential skills for this project. Knowledge of undergraduate-level cryptography or Python programming skills would be assets, but are not required.

The goal of this project is to develop a housing price estimate/forecast using publicly available data to inform evidence-based decision making for the benefit of government regulators, industry practitioners, and concerned citizens. Students will be expected to use Python 3.X for data acquisition, cleaning, organization, and manipulation. Working experience with libraries such as Pandas may be useful. Previous experience with other programming languages such as Matlab or R is useful but not required.

Environmental Instruments Canada (EIC) produces a Radon Sniffer which is used to find radon entry points. One method of determining the ratio of Radon 222 to Radon 220 (thoron) in the air is by implementing sampling and counting sequences and observing the change in the alpha count over time. The goal of this project is to develop an optimized sampling and counting sequence that results in the best statistical accuracy. Understanding radioactive decay and the coupled differential equations describing a decay series would be useful. A team with statistical expertise would be essential. Some familiarity with spreadsheets such as Excel would be helpful.

Consider a distributed acoustic sensing (DAS) system monitoring a fibre optic cable deployed along an active roadway. The goal of this project is to use data collected from the DAS system to develop a detection and tracking method capable of identifying individual vehicles and reporting their position and velocity as they move along the road/fibre. Once the position and velocity are determined, various metrics for traffic flow could be determined, allowing for prediction and optimization of traffic congestion.

Performance metrics in sports have seen remarkable growth and development. What if we turned some of these mathematical tools on political performance? The goal of this project is to analyze data which are related to the progression of a bill into law in the US. A background in statistics or graph theory would be helpful. Some background in computer programming or data science may be helpful, but not necessary.

The goal of this project is to develop a reasonably accurate and affordable design tool to model the performance of McMillan-McGee’s patented induction heaters, which are used for thermal conductive remediation of contaminated soil. A good design tool would be useful to assess the feasibility and cost of using different heater lengths, diameters, and materials. Working knowledge of Maxwell’s equations, vector analysis, boundary value problems, Green’s functions, complex variables, contour integration, residues, integral transformations and differential equations would be essential background for this project.

In March 2020, the WTI futures contract settled below zero for the first time in the contract’s history. Many market participants apply the Black 76 model or a variation of this model to calculate the value of the options on this futures contract. However, Black 76 requires positive underlying market prices. The goal of this project is to identify alternative models which can accept negative underlying pricing, and assess the suitability of the alternatives. People interested in quantitative finance, commodity training and marketing, and bridging the gap between quantitative experts and non-experts would be excellent team members for this project.

Standard procedure for building training sets for some machine learning models involves an individual going through hundreds of images and creating 2D binary matrices which reflects where the region of interest is in each image. Depending on the type of images, can we use RGB information or some other method to automate this process? The goal of this project is to develop a method which creates a mask of an image depicting where monochromatic objects occur in an image automatically and with limited user input.

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