July 10-31, 2023
In July 2023 PIMS is holding a virtual workshop called Math to Power Industry(M2PI 2022) which will run from July 10 - 30. More information about applications for industry partners and participants will appear here soon.
We suggest that organizations provide a $1000 stipend for each of the four students on their team, similar to an intern salary. This will help to recruit exceptional teams of students. This is not a requirement for participating in M2PI, and there is no other cost for employer partners to participate in the program.
The intended outcome is that partner organizations will have the opportunity to engage with highly skilled talent, while also receiving innovative solutions to the math challenge submitted to the workshop. You can see examples of successful projects on the 2022 M2PI website.
If you have questions please contact the organizers through the contact form below.
Explore the projects and reports from previous editions
Math to Power Industry 2022 (M2PI 2022) will take place July 11-29, 2022. We are now inviting non-academic partner organizations to consider particpation in this workshop.
The final-report for m2pi 2021 is now available. It features projects from
Projects, reports, team members and other details are available on the MathIndustry 2020 page. .
Certified training programs
Agile software development, virtual collaboration, open source toolchains
communication skills, project management, effective teams & ethics
Mitacs will offer their Leadership Skills course to our workshop participants. You will need to enroll for this course on the EDGE portal and complete the (approx. 90 minute) asynchronous portion of the course prior to the workshop. On completion of the asynchronous part of the course and signing up for the facilitated session you will receive a Zoom link from Mitacs for the facilitated part of the course taking place on July 11th, 2022, from 1pm until 3:30 pm MDT.
The ability to detect man-made objects in vegetation would aid many fields of industry including – but not limited to – search and rescue as well as agriculture. The ability to locate man-made objects such as damaged modes of transportation, camping or hiking equipment, parachutes, etc. in said vegetation aids the chances of locating missing individuals involved in these cases. While much imagery of these objects exists, imagery of them in varying degrees of repair within vegetation is limited at best making standard machine learning detection methods difficult. In such cases, focusing on the vegetation may enable the detection of such objects through machine learning methods where imagery is limited. In agriculture, farming equipment may require repair while in the field where it is easily possible to misplace equipment in vegetation. This lost equipment could damage other farming equipment while work is being done. Locating lost equipment will help limit further damage of farming equipment saving not only money, but time and production as well.
For this project, the team will be given access to aerial multispectral imagery containing a variety of man-made objects located in vegetation. The goal of this project is to develop a method which can detect these random man-made objects using machine learning and computer vision techniques while investigating the benefits of multispectral data to solving this problem. The machine learning field of focus for this problem is that of anomaly detection.
At Awesense we’ve been building a platform for digital energy, with the goal of allowing easy access to and use of electrical grid data in order to build a myriad of applications and use cases for the decarbonized grid of the future, which will need to include more and more distributed energy resources (DERs) such as rooftop solar, batteries as well as electric vehicles (EVs).
Awesense has built a sandbox environment populated with synthetic but realistic data and exposing APIs on top of which such applications can be built. As such, what we are looking for is to create a collection of prototype applications demonstrating the power of the platform. Given the synthetic nature of the dataset we can make available, this would be more of a “deliver a method (and implementation of it)” type project than a “deliver insights” type project.
This involves coding some analyses and visualizations on top of said data and APIs. It would require good data wrangling + statistics + data visualization skills to design and then implement the best way to transform, aggregate and visualize the data for the use case at hand (see below). The data access APIs are in SQL form, so SQL querying skills would also be required. Beyond that, the tools and programming languages used to create the analyses and visualizations would be up to the students. Typical ones we have used include BI tools like Power BI or Tableau and notebooking applications like Jupyter or Zeppelin combined with programming languages like python or R.
If the participants don’t have any electrical background, we can teach enough of it to allow handling the given use case. For this year’s project, we have chosen a use case entitled “EV charger capacity study”. At a high level, this entails determining how many new EV chargers could be installed in a particular portion of the electrical distribution grid without overloading the capacity of the grid infrastructure at that location. This would allow distribution grid planners to determine whether or not to approve requests for “interconnection” of EV chargers; it would also allow them to plan for needed infrastructure upgrades to support more EV chargers in the future.
Local labour market information (LMI), including employment, unemployment, and participation rates, are important for planning activities conducted by municipal and First Nation governments, service providers, and many more organizations. Census of Population (Census) data, published by Statistics Canada (StatCan), provides LMI at the Census Division (CD) and Census Subdivision (CSD) levels. However, the Census is only conducted every five years. This project asks participants to build a model which estimates intercensal LMI at the CD and CSD levels.
LMI are not publicly available at the CD and CSD levels of geography for years when the Census is not conducted. StatCan’s Labour Force Survey provides data on a monthly basis. However, StatCan does not publish Labour Force Survey data at the CD or CSD levels. As such, LMI at the Economic Region level are often used in the place of intercensal data on CDs or CSDs. Figure 1 shows the CSD of the District of Kitimat, as well as the larger CD and Economic Region it is within, as an example illustrating how Economic Regions may not serve as good proxies for CSDs.
Cedar Academy Society is building a digital representation or “digital twin” of a Lower Mainland city, powered by Unity3D engine. During the summer of 2022, we aim to complete the integration of real-time traffic data into such model to better reflect the dynamic nature of the communities we live in. Through previous studies, we have been able to associate traffic camera-captured images to object counts. This year, we intend to drive further and to project those object counts into visualized traffic in a virtual world.
Residential radon progeny exposure is the second leading cause of lung cancer, after smoking. The two main radon isotopes are Rn-222, which is part of the uranium-238 decay chain, and Rn-220, also called thoron, which is part of the thorium-232 decay chain. There is currently much interest in the Rn-220 contribution to radon progeny exposure, which has so far been largely ignored. (Rn-220 has a relatively short half life and usually decays before it reaches the living areas in a house and it usually doesn’t show up in radon measurements. But, Rn-220 has a longer lived decay product which does reach living areas and contributes to radon progeny exposure. It can even exceed the Rn-222 contribution.)
Environmental Instruments Canada (EIC) produces a Radon Sniffer (see https://radonsniffer.com/ ), which is used by radon mitigators and building scientists to find radon entry points. These sniffers currently assume all radon is Rn-222. See the appendix for a more detailed description of how the sniffer works. We want to extend the functionality to Rn-220.
In a 2020 M2PI project, we came up with a dedicated sampling and counting sequence and developed the math to determine how much Rn-222 vs Rn-220 was in the air. This report is available to the team.
In this project, we wish to develop a method by which we can determine the presence of Rn-220 in the air, while the Radon Sniffer is continually sampling air and without having to run a dedicated thoron measurement sequence.
Principal Component Analysis (PCA), as well as Factor Analysis, are a couple of techniques used to increase data value by making data more interpretable while simultaneously preserving as much variability and information possible . Given large topic-indexed datasets reflecting activity by parliamentarians such as chamber interventions, committee interventions, bills, motions, and chamber votes how might such analytical techniques be used to reduce the dimensionality of these sets while increasing their interpretability? Can useful and efficient graphical displays for the public be generated through the application of such techniques to political data? What other types of data analysis methods may be used alongside such techniques to extract meaning from political data? What measures of similitude or difference between individual politicians or parties might be derived? How might such features help to measure political performance? How can topic indexes be aggregated to reflect similarities in political concern?
The stormwater infrastructure in many cities is facing challenges as the climate changes, rainfall patterns change and sea levels rise. To meet these challenges, cities are installing green infrastructure (GI) systems to absorb and retain rainfall where it lands and reduce sewer overflow. Across North America alone, cities are investing over $56.2 billion dollars in green infrastructure. By doing so, communities are becoming more resilient against climate change and are achieving environmental, social and economic benefits. Novion’s Climate Intelligence Platform helps cities monitor their green infrastructure for performance optimization, regulatory compliance, and maintenance.
Once green infrastructure has been constructed, monitoring the changes in water level after a rainfall event is required to verify its performance and net impact. This project will investigate aspects of this monitoring.
Long-distance dispersal of insects in fast moving air currents is increasingly recognized as an important driver of their dynamics at a landscape scale. Moreover, this type of dispersal has important implications for forest and agricultural crops impacted by insects. Because the detection and tracking of populations of flying insects remains challenging, it is rarely possible to determine where insects originated after they have dispersed long distances. Data from weather radars designed to detect precipitation may be useful tools for gaining insight into insect long distance dispersal because insect bodies and rain drops are often similar in size. Thus, within radar scans there is potential to quantify the density of insects departing to start long-distance dispersal as well as the movement trajectories of swarms–at least until they pass beyond the range of the radar. However, because Doppler weather radars are extremely sensitive and capable of detecting water vapor in clouds, it can be difficult to distinguish between potential insect signals and weather signals even when it is not ostensibly raining.
This project has two distinct objectives. First, we will investigate classification of radar images, based on motion, to identify insect swarms. Second, we will develop a mathematical model and numerical simulations to more easily distinguish distinguish meteorological and biotic signals.
Perfit is currently working on a virtual fitting room app that allows online shoppers to get a virtual preview of the fit of garments in their cart. The virtual fit is accomplished via simulations of cloth interacting with a customer avatar through particle collisions. Specifically, each piece of cloth is modeled using a mesh of interconnected particles. The company has made progress on collisions between cloth and avatar. However, there is a need for collisions between cloth and cloth that has remained a significant challenge for the company. For example, the capability for a virtual garment to interact with itself via cloth-on-cloth collision would allow improved wrinkle quality, and garments with pleats, such as a pleated skirt. The technical challenge facing the company is to enable the handling of cloth-on-cloth collisions in near real time. In a mathematical sense, an algorithm for cloth-on-cloth collisions would need to be developed that minimizes the number of operations required (e.g., avoids brute force particle searches) while maintaining sufficient accuracy.
Topics in geometry, physics, computational methods, and computer graphics are expected to arise while working on this problem. The preferred implementation of the solution is the Fortran programming language in order to facilitate integration with the existing physics engine. During the workshop, meshes for both customer avatar and cloth will be made available through GitHub for testing.
Cancer is a disease that affects 14M people each year. While we have had some success with specific cancers, many patients are put on a roller coaster of emotion through cycles of remission and relapse. There is abundant scientific evidence which tells us cancer is driven by multiple genes working in concert. CSTS Healthcare has developed a computational system which identifies personalized cancer therapy for every cancer patient given their unique set of DNA and RNA. In practice, the therapy a patient actually receives may not exactly match what our system has identified as the best therapy. In this project we will develop therapy similarity measures to allow us to compare our therapies with those actually given by to a patient by their oncologists.
Performance metrics in sports have seen remarkable growth and development. What if we turned some of these mathematical tools on political performance? Building on last year’s M2PI project, the goal of this year’s project is to analyze data related to the activities of legislators in Canada and the USA with a view to developing engineered features which might reflect political performance. These engineered features should be granular enough to significantly inflect during the course of a parliamentary or legislative session, providing quantitative and comparative performance insight.
Realtime simulators in virtual reality are a leading-edge technology to provide standardized training and evaluation that contribute to heavy-equipment operator safety. They aim to reduce accidents due to operator inexperience by training an operator in scenarios before they are expected to perform these same tasks in reality. To satisfy the high frame-rate requirements of real-time simulation, algorithms to solve these models must be extremely efficient and yield predictable and reproducible results.
The simulation of heavy equipment involves simulating both physical bodies in motion and hydraulic pressures. The goal of this project is to develop an approach to the simulation of fluid pressure volumes that can be interfaced with a position-based dynamics (PBD) simulation, improving performance and providing a more realistic experience.
Among the renewable and clean energy technologies, wind energy is one of the most efficient, costing 1–2 cents per kilowatt-hour after the production tax credit by governments. While natural wind speeds over various continents in the world span from 0 to 20 m/s, Vertical Axis Wind Turbines (VAWT) placed on highway medians make it possible to utilize consistently higher wind speeds due to vehicle motion. Additionally, the energy generated by these wind turbines is reported to increase multi-fold due to the shearing winds generated on both sides of the medians by the on-going traffic. In this project, we will seek to optimize the positioning of turbines to achieve optimal results using criteria determined to be important, such as output power, ease of installation/repair, proximity to consumers, additive effects from positioning etc. We will use real-life traffic, geographical and weather data, and subsequently investigate economic feasibility of implementation of this technology.
The City of Winnipeg’s Insect Control Branch (ICB) of the Public Works Department provides services to Winnipeg residents to control insects, including mosquitoes. The mosquito control program is based on an environmentally mindful insect control strategy, and includes: (1) A larviciding program that is 100% biological and uses four larviciding helicopters, (2) Monitoring and treating over 31,500 hectares of water area on an ongoing basis based on weather conditions, and (3) Monitoring for adult nuisance mosquitoes in New Jersey Light Traps beginning early May.
In this project, we will examine some of the key challenges facing the ICB such as (1) Predictive modelling of adult mosquito populations subject to changes in rainfall/soil moisture content and wind speed (2) Preditictive modelling of larval development subject to changes in spring and summer temperatures.
McMillan-McGee have developed induction heating technology for in-situ soil remediation. As such, we have developed heater casings, work coils, and inverters which generate high frequency alternating current. We have also developed a great amount of the analytical work for engineering this equipment.
An important aspect of our inverter design (or for that matter any high frequency inverter in general) is to have a good understanding of the electrical properties (resistance and inductive reactance) of the DC bus bar that supplies current to the high speed switching devices (IGBTs and SiC Mosfets). Knowing this would allow us to design a suitable bus bar system that can absorb energy caused by switching transients from these semiconductor devices as a result of commuting current through the work coil. The problems in this project centre on solving certain boundary value problems involving Maxwell’s equations and linking these to the laws of thermodynamics.
Insect dispersal is often divided into two classes: local and long distance. Local dispersal is the most common dispersal mode and because many individuals disperse this way, it is well described by dispersal kernels. Long distance dispersal is more stochastic and difficult to model using dispersal kernels because only a small proportion of insects are thought to disperse long distances. For the mountain pine beetle for example, most individuals disperse between five and fifty meters from where they were born but about 0.2 percent of individuals end up above tree canopies where they can be pulled upwards by updrafts and then transported laterally by higher wind speeds in the lower atmosphere.
Long-distance dispersal is likely the dominant determinant of the speed of mountain pine beetle invasions, but estimation of invasion speeds using standard mathematical approaches are impeded by the strong Allee effect. In this project, we will explore theoretical dispersion distributions and models to better estimate mountain pine beetle invasion speed.
Existing techniques for insect mark and recapture studies can result in unnatural dispersal patterns. We have developed a new technique for marking insects as the emerge from which offers a much more natural dispersal pattern.
The technique involves coating trees with a special paper which glows under ultra-violet light. The insects are marked with paper dust as they chew through the paper to emerge. Following recapture, they can be examined for traces of the paper under ultra-violet light.
In this project we will work with images of insects marked using this technique and control images of unmarked insects. The problem is to conduct batch analysis of the images and classify them as marked and unmarked to validate the new technique.
Producing food and other goods sustainability is the greatest challenge of our generation. To produce food sustainably there are many factors to consider including the types of crops, the inputs, organic vs. non-organic, use of fertilizer, food waste, transportation to market and other factors. The goal of this project is to develop a model which can take into account factors end-to-end in the food supply chain to inform decisions on methods (organic, traditional, vertical, etc.) and sustainability indicators (green house gases, etc.).
Roads are a vital component of today’s society. They not only connect us to different cities, towns, provinces, and countries, but they also provide of a means of transporting goods and services. Typically, roads are constructed using materials such as concrete, or asphalt. Between the cold winter temperatures and hot summer temperatures, as well as settling earth, cracks and potholes are bound to occur on roads.
Alberta spent over 1.6 billion dollars in transportation related needs in 2020-21. Over 26% of this money went towards road construction and maintenance related expenditures. Roads undergo regular inspection; a detailed Surface Condition Rating occurs every two years in Alberta. This helps determine the priority in which maintenance should occur on roads in the province. One method of conducting these inspections could be done via aerial imagery. While an individual could go through these images to inspect the roads for cracks and potholes, is there a way that machine learning and computer vision could not only detect cracks but also classify their severity?
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.
MathIndustry (Math to power industry) is a professional development school positioned to benefit Canadian industry because:
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 MathIndustry 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.