## History and mission statement

Fields Institute for Mathematical Sciences: Founded in 1992, the Fields Institute plays a central role in "promoting contact and collaboration between professional mathematicians and the increasing number of users of mathematics". It supports research in pure and applied mathematics and statistics. Thematic programs of international interest, academic workshops, and prizes are organized by the Institute.

Of specific interest to the business community is the Commercial and Industrial Mathematics program. This program seeks to develop synergistic links between mathematicians and industrial partners. The Industrial Problem Solving Workshops are an initiative in this direction.

## What the workshop is about

**Objectives:**

The objective of the IPSW is to connect industries with faculty, postdocs and graduate students who have expertise in industrial case-studies. This interaction is fostered in the specific context of a problem-solving session over 5 days. The case-studies in question have a significant mathematical or statistical content and are focused on finance.

The interaction between industries or laboratories and academia has many potential benefits for both. Academics learn about interesting potential research problems and find application for their existing tools. Industries and labs get access to some of the most experienced mathematical modellers and problem-solvers on the continent.

**Format:**

The IPSW will occur over 5 days. Participants will include a group of academic experts (including mathematicians and statisticians) as well as experts from an industry or lab. On the first day, the problem posers will present their problem statements. The academic experts will divide into small teams, with one team assigned to each problem. The teams spend the next 3 days collaborating on solutions to their problem, and present their solution on the final day of the workshop.

**Deliverables:**

At the end of the week, the academic experts make a presentation consisting of the problem restatement and their solution. This is a summary of results; the teams also prepare reports for the problem posers.

## What's in it for the participating company or lab

The intellectual dedication of many expert problem-solvers during the workshop to the phenomenon of interest to the posers yields many benefits. These range from partial or complete solutions to the problem of interest, to long-term collaboration between the problem posers and the participating academics. The forum is an informal but intensive opportunity for companies or labs to take advantage of the mathematical and scientific computing expertise of participating researchers.

Often the academic reformulation and solution of the problem enables the problem poser to find inexpensive in-house strategies. Similar workshops in Europe and North America have saved participating companies hundreds of thousands of dollars.

In addition, the academic experts typically use state-of-the-art scientific and technological tools, which may prove useful to the problem poser in other contexts as well.

The workshop also serves as a mechanism for recruitment of talented graduate students; the problem poser sponsors can watch this pool of potential employees in action!

## Why do academic experts participate?

The potential benefits of the IPSW to professional mathematicians involved are myriad. They range from an exposure to interesting mathematical problems arising outside the confines of academia to an opportunity to try new scientific tools in novel application areas. Previous workshops have seen such involvement turn into long-term collaborations, often leading to journal publications and new research directions.

## Commitment of the IPSW

The Fields Institute will provide the academic expertise and infrastructure for this workshop. The recruitment of appropriate faculty and graduate students to best meet the needs of the problems will be done by the Fields Institute

## Commitment of industrial sponsors

Each participating company or lab contributes a problem with mathematical or statistical content for discussion during the workshop. They also commit a representative to participate in the workshop during the problem-solving phase. A company may sponsor part of the IPSW through a one-time or ongoing financial contribution.

Problems

**1. Develop a numerical tool for the depolluting effect of TiO2.**

Posed by the NRC Construction Research Centre, the goal is to model how concrete containing TIO2 will weather over time in a variety of local conditions for humidity, temperature, wind direction and speed, traffic volume, type of vehicles, sunlight, etc. TiO2 is used for NOx abatement, but large-scale photocatalytic oxidation experiments are expensive, and continuous air-quality monitoring in the field is challenging. Numerical modelling is potentially a valuable tool to complement such experiments, and to design optimal deployment.

**2. Improve effectiveness of spectral matching algorithms for unknown substance detection in portable Raman and FTIR spectrometers**

Posed by the NRC Measurement Science Research Centre, this is a pattern matching problem. Vibrational spectroscopy, and Fourier transform infrared absorption spectroscopies are increasingly in use via portable handheld spectrometers, eg by first responders for detection of hazardous materials, or to detect fentanyl in narcotics samples. Current algorithms compare the signal against a large database of known signals. These comparisons are complicated by the variety of ways samples may be presented. Also samples are rarely found in pure form, so signals are often superpositions of multiple signals from the database. As more and more of these devices are deployed, better matching algorithms are urgently needed.

Posed by the NRC Digital Technologies Research Centre, the problem is to estimate how informative a sample is, before applying machine learning or doing extensive modelling. Gamma statistics give a non-parametric approach to this, based on having a smooth response function for Euclidean data. This seems to work well with certain data sets (eg NRC has used this approach with radar data), but in other problems (eg job matching problems) the data is less structured and does not comply with the requirements of the original theory, developed for real-values scalar variables and continuous spaces. The goal would be to develop generalizations of the original mathematical theory in order to cover the case of heterogeneous, imprecise and incomplete data

**4. Real-time estimation of current building occupancy**

Posed by the NRC Construction Research Centre, the goal is to estimate the number of people in a specific building, for example, in order to manage building ventilation appropriately. Sensors or IoT devices can provide extensive data, eg. from motion detectors, CO2 sensors, lighting and electricity submeters, WiFi routers, etc. By calibrating this to ground-truth data (direct observation of the number of people in a building) or with data derived from cameras, the hope is to learn to make useful predictions based on less invasive sensing.

**5. Structure of disordered solids**

Posed by the NRC Nano Research Centre, the problem is to use nano beam electron diffraction (NBD) patterns to understand the structure of disordered solids. NBD patterns are usually used to study crystalline nanoparticles, but extending this to disordered materials would greatly expand the applicability of this technology. Patterns are typically collected from very small regions, but to handle larger regions the beam can be stepped across the sample, or the diameter or convergence angle can be varied. NBD provides information about the radial distribution or pair correlation functions for inter-atomic distances. Modelling how amorphous materials form and how this will manifest itself in NBD results would be very interesting.

**6. AI-driven interactive simulation solver running on mobile platforms**

Posed by the NRC Medical Devices Research Centre, the problem is to improve the real-time performance of interactive simulators, such as those used in surgical training. To address realism for deforming multibody scenes, simulators running on high-end computing platforms solve non-linear finite element (FE) equations at resolution rates of the order of 100Hz. The goal is to achieve equivalent realism on more affordable mobile platforms. Computing the FE pre-conditioner can be particularly time-consuming, so the hope is that a trained AI-predictor can help to more efficiently identify the pre-conditioner to use.

**7. Search and rescue probability of detection for the optimization of airborne sensor search**

Posed by the NRC Aerospace Research Centre, the problem involves modelling how sensor data should be incorporated into search and rescue (SAR) operations. Currently, SAR algorithms are optimized for naked eye observations. As electro-optical/infrared (EO/IR) sensors enter the SAR toolkit, it will be necessary to optimize both the configuration of the sensors, and how the search is then conducted. NRC has a large IR dataset of SAR trials to compare with. The goal is to understand how to model airborne IR-sensor-based searches correctly, from an operations research perspective.

## Schedule

To be announced.

## Room Locations

To be announced.

## Advisory Committee

Sean Bohun (UOIT)

Chris Budd (University of Bath)

Huaxiong Huang (York University and Fields)

Neal Madras (York University)

Odile Marcotte (UQAM and CRM)

Nilima Nigam (Simon Fraser University)

Pawel Prelat (Ryerson University and Fields)

Tom Witelski (Duke University)

## Previous Industrial Problem Solving Workshops

Auust 7-11, 2017

8th Montreal Industrial Problem Solving Workshop

May 8-12, 2017

Fields-China Joint Industrial Problem Solving Workshop

August 15-19, 2016

2016 Industrial Problem Solving Workshop

May 25-29, 2015

Big Data Industrial Problem Solving Workshop

August 11-14, 2014

Fields-MPrime Industrial Problem-Solving Workshop

August 20-24, 2012

Industrial Problem-Solving Workshop on Medical Imaging

August 16-20, 2010

Fields-MITACS Industrial Problem-Solving Workshop

June 22-26, 2009

OCCAM-Fields-MITACS, Math-in-Medicine Study Group

August 11-15, 2008

Fields-MITACS Industrial Problem-Solving Workshop

August 14-18, 2006

Fields-MITACS Industrial Problem-Solving Workshop