Research Grant Awarded to JAC Physics Teacher
Congratulations to Chris Larnder of the John Abbott College Physics department.
He was awarded a research grant from FRQNT’s Programme de recherche pour les chercheurs de collège for his project entitled “Accelerometer-based inference of constrained motions”.
To read the summary of the research click on the link below.
“Accelerometer sensors, originally developed in the 1960’s to provide inertial-navigation capabilities for aircraft, ships and spacecraft, have now, with the advent of micro-electromechanical (MEMS) technology, become ubiquitous low-cost components providing motion-sensing capability in a wide variety of areas. In the field of biomedical applications alone, a partial list includes behavioural biometrics; gesture recognition; surgical skills; detection of gait disorders; iOT-enabled systems for rehabilitation, assisted living and elderly care; and physiological monitoring.
The challenge for researchers lies no longer in the collection of the data but in its interpretation. One fundamental difficulty is the separation of the gravitational contribution to the accelerometer signal. This is often alleviated by the addition of a gyroscope to the system. Typically, the gyroscope is used to detect changes in orientation and the accelerometer is relegated to the detection of changes in linear velocity. The analysis is still vulnerable to another widely-recognized problem, viz. the drift error that accumulates when the orientation or position of an object is reconstructed through single or double- integration techniques.
For completely arbitrary unconstrained motions, such as in the free motion of an aircraft, there is no means of overcoming these limitations. However, when there are known constraints imposed on the motion paths, they can be exploited in the reconstruction of the remaining degrees of freedom. Although this can reduce error and problem complexity, there does not appear to be a systematic study of such strategies. A simple starting point is a circular-motion investigation that demonstrates, without the use of gyroscopes, the ability to recover both the radial and angular position of accelerometers with respect to the axis of rotation. This contrasts with gyroscope-free techniques for unconstrained motions which requires anywhere from 12 to 18 accelerometers for a single body.
In the proposed project, we will identify and explore simple low-degree-of-freedom systems that are sufficiently constrained so as to allow the motion to be fully and reliably inferred using only a single 3-axis accelerometer. The development of such techniques also promises broad applicability as a low-level classification layer in machine-learning (ML) architectures for motion in complex systems such as the human body. Recognizing that traditional ML systems suffer from inflexibility and poor transfer to related domains, there is increasing interest in hybrid systems that incorporate domain-specific knowledge. Automated detection or ruling-out of simple low-level constraints in a motion signal can serve as a universal feature extractor converting a complex time series into a low-dimensional feature vector, into a single classification or some type of interval-dependent qualifier. Different deep networks specialized for distinct application domains can re-use the same early stage, thus decreasing development time, increasing learning transfer opportunities and comprehensibility of the internal representations.”
Research Grant Awarded to JAC Math Teacher
Congratulations to Ferenc Balogh of the John Abbott College Mathematics department. He was awarded a research grant from the Fonds de recherche du Québec – Nature et technologies (FRQNT).
Ferenc’s research project: “Asymptotiques des statistiques des valeurs propres dans les matrices aléatoires planaires“, proposes to include two JAC students to help in this research project.
To read the summary of this research proposal, click on the link below.
“A random matrix is an array of random numbers drawn from a prescribed probability distribution. The classical models of Hermitian random matrices are defined by densities on the space of Hermitian matrices that are invariant under the action of the unitary group.
The statistics of Hermitian matrices are well understood: the correlation functions of their eigenvalues are expressible in terms of orthogonal polynomials, and their asymptotic expansion in the large matrix size limit is governed by the equilibrium measure that minimizes the energy in an electrostatic variational problem. The supports of the orthogonality measure and the equilibrium measure are both real when the model is Hermitian. The eigenvalues behave like electrically charged particles on the real line, and by this analogy one can use them to model various systems with a built-in repulsion between its components, like the distribution of cars parked on a street, perched birds on a wire, the departure times of autobuses in a self-managing transport network, or the boarding times of passengers of an aircraft.
Thanks to the Riemann-Hilbert method, developed by Deift and Zhou, it is possible to find the asymptotic expansions of the orthogonal polynomials which may be used to obtain universal limits of the correlation functions in different scaling limits, which only depend on the underlying symmetries of the model. My research work focuses on the relation between the asymptotics of orthogonal polynomials and the equilibrium measures for planar random matrix models for which the eigenvalues are not confined to the real axis. These models are motivated by their potential applications to phenomena on land or sea where a repulsive force is present between the components of a system.
The Riemann-Hilbert approach for Hermitian matrices is not directly applicable to planar matrix models, a general method to get the asymptotic expansions of the correlation functions is yet to be found. To date, this problem is solved only in a handful of very special examples.
With my previous work on the subject as starting point, I propose the present project using various techniques from potential theory, conformal mappings, orthogonal polynomials, quadrature domains, and Fredholm determinants to find new universal statistical laws for planar random matrices.”
The Fonds de recherche du Québec – Nature et technologies (FRQNT) Award
2 Winners from John Abbott College
First year students Zoë Deskin and David Toharia have each been selected to receive a $5000 summer internship award from the Fonds de recherche du Québec – Nature et technologies (FRQNT).
Zoë is an Arts and Sciences student with an interest in conservation ecology and environmental science. This award will allow her to work in Professor Jacqueline Bede’s laboratory at McGill University (Macdonald Campus) for 10 weeks this summer on: Plant-Insect Interactions: The impact of herbivory on the expression of plant defensive compounds.
David is an Honours Science student and will be working in Professor Peter Grutter’s Physics lab at McGill (downtown campus) on: The development of machine learning approaches to find and determine the position and radius of rings in images. This opportunity will allow him to pursue his passion for Physics.
Dr. Roberta Šilerová and Dr. Simon Daoust were instrumental in finding the stage locations and participated in the selection process along with Teresa Hackett (JAC Research Officer) and Joanne Ross (Program Deans’ Office). Forty- four JAC students responded to the call for this award. Congratulations to Zoë and David. They will be back at JAC in the fall – ask them about their experience!