Math and Computing Research Discovery Days

Reference in Structured Data Integration for Data Science

For any enterprise whether it is a business or research organization, making better decisions is extremely important for success but that requires handling huge amounts of data analytics from diverse sources which is again a big technical challenge. Data integration helps in this regard by bringing data from disparate sources together to provide users with a unified view where they can run queries easily to obtain the required information. In this research, we discuss semantic data modelling and reference issues in structured data integration. Our work will explore and establish the theoretical foundations for related data models, reference issues, query language grammar, semantics, and constructs for the integration mechanisms as well.

Predicting Measles Outbreaks from Vaccine Sentiments on Social Media

Vaccinating decisions for childhood diseases such as measles have been studied using coupled
models of disease dynamics and individual behaviors. Such models applied evolutionary game
theory to model people’s vaccination strategies as they are affected by social norms.

The popularity of social media has provided convenience for the spread of pro- and anti-vaccine
sentiments. High-frequency social media data also brings new ideas to study population dynamics
of infectious diseases.

This project aims to build a bridge directly from social media data to potential disease outbreaks
through deep learning models and provide novel methods for disease outbreak prediction
near thresholds. We improved existing coupled behavior-disease models by considering different
social groups and investigated the effect of homophily on disease dynamics near tipping points. We
generated realizations from our developed stochastic model. After being trained with enough theoretical
data, we showed that a deep learning model (e.g. a CNN-LSTM model) could capture EWS
directly from real-world social media data and predict a potential disease outbreak in the future.

GradXcepUNet: Explainable AI Based Medical Image Segmentation 

Medical images segmentation is an important research area. Physicians and radiologists can diagnose diseases in their patients by observing the visual features using various imaging methods like CT, MRI, X-ray, and Ultrasound. AI-based medical image segmentation models can help radiologists and experts analyze various ailments. However, the prediction results are only trustworthy when the results can be interpreted by a doctor. Our work utilizes “Explainable AI(XAI).” We propose GradXcepUNet, an XAI-based medical image segmentation model, that  couples the segmentation power of U-Net and explainability features of the Xception  classification network by Grad-CAM. The Grad-CAM trained images highlight the critical regions for the Xception classification network. Then, as the guidance, the visualized results for critical regions are combined with an existing segmentation model (U-Net) to produce the final segmentation results. With the assistance of XAI analysis and visualization, our GradXcepUNet outperforms the original U-Net and many state-of-the-art methods. The evaluation results show that we can reach a Dice coefficient of 97.73% and an Intersection over Union (IoU) score of 78.86% on the 3D-IRCADb-01 database.

Impact of pregnancy and lactation on maternal calcium homeostasis: Mathematical model and analysis

During pregnancy and lactation there are significant changes in the maternal body. In fact, physiological adaptations occur in almost all tissues and organs. In particular, calcium homeostasis is impacted due to the large demand for calcium by the fetus and breastmilk. Despite having a similar additional calcium demand, maternal adaptations in pregnancy and lactation are different. During pregnancy, the mother’s body increases intestinal absorption of calcium. However, during lactation, intestinal absorption returns to normal levels and the calcium needs of breastmilk are instead met by increased bone resorption and calcium reabsorption from the kidneys. The multitude of physiological processes involved in calcium homeostasis along with the complex and dynamic adaptations involved in lactation and pregnancy make this problem well-suited for investigation using mathematical modeling. In this project, we explore the differential impacts of pregnancy and lactation on calcium demand in the mother’s body. Understanding these mechanisms are key for understanding the complicated physiologies of pregnancy and lactation.

A PINN Approach to Symbolic Differential Operator Discovery with Sparse Data

Lena Podina, Brydon Eastman, Mohammad Kohandel

Given ample experimental data from a system governed by differential equations, it is possible to use deep learning techniques to construct the underlying differential operators.This small data regime in machine learning can be made tractable by providing our algorithms with prior information about the underlying dynamics. Physics Informed Neural Networks (PINNs) have been very successful in this regime (reconstructing entire ODE solutions using only a single point or entire PDE solutions with very few measurements of the initial condition). We modify the PINN approach by adding a neural network that learns a representation of unknown hidden terms in the differential equation. The algorithm yields both a surrogate solution to the differential equation and a black-box representation of the hidden terms. These hidden term neural networks can then be converted into symbolic equations using symbolic regression techniques like AI Feynman. In order to achieve convergence of these neural networks, we provide our algorithms with (noisy) measurements of both the initial condition as well as (synthetic) experimental data obtained at later times.

Investigating the role of circadian rhythm-based exercise and diet in type 2 diabetes

Justification of the importance of the work being presented 

We develop mathematical models of metabolism and its interactions with our body's internal clock, also known as the circadian clock. Circadian rhythm disruption can contribute to metabolic dysregulation (diabetes, hypertension) and memory issues. Although the brain centrally controls circadian rhythms, peripheral tissues like the liver and muscles impose their own rhythms. It is therefore important to conduct research that directly compares exercise at various times versus meal ingestion. We present a whole-body exercise and diet model that incorporates controls from the liver and skeletal muscle peripheral clocks. Our model predicts that post-meal exercise improves glycemia in patients with type 2 diabetes mellitus (T2DM), and that the benefits of morning or afternoon exercise vary according to chronotype. The model could be used to guide future experimental studies aimed at determining the effect of circadian rhythms on the efficacy of exercise and diet for T2DM. 

Adversarial machine learning focuses on studying attacks that target machine learning algorithms and the
defenses against worst-case attacks to strengthen the adversarial robustness of existing models.
Specifically for image classification tasks, it is often difficult to comprehend the underlying logic behind
adversarial examples even for machine learning practitioners due to key challenges such as 1) the attacks
exploiting ``non-robust" features that are not human-interpretable and 2) the perturbations applied being
almost imperceptible to human eyes. In this study, we propose an interactive web-based application that
aims to visualize the properties and consequences of evasion attacks for adversarial machine learning
learners and provide data and model performance analytics for more experienced practitioners. In
addition, we design the visualization to be informative in terms of robustness comparison evaluation
between different models and show how prediction results may alter when varying levels of perturbations
are applied to the data instances.

Spatial and Temporal Discounting in a Coupled Social-Climate Model
This research discovers the effects on mitigation and projected temperature anomalies through applying spatial and temporal discounting in human decision making in a coupled social – climate model. While past climate models have implemented a static human contribution to climate change through Representative Concentration Pathways and Shared Socioeconomic Pathways, this research develops and implements a dynamic social system coupled to the climate system. This idealizes a two-way feedback between human decision making, social norms, and human behaviour with changes in the climate. The spatial and temporal discounting addressed in this research is guided by the definition of judgemental discounting, such that individuals consider climate change conditions to be worse in other locations and further in time. We begin by implementing a coupled system of differential equations where a two-patch model for the human subsystem includes spatial discounting in the form of updated utility functions. The utilities determine the impacts of individuals in different populations taking up mitigative or non-mitigative strategies. Then temporal discounting is applied through percentage discounting per year within the system rather than a varied parameter. Results will be obtained through implementing the coupled feedback model with climate, social, and economic data. We hypothesize that the results will directly address the fundamental problem in dealing with climate change: where the negative effects of climate change are often portrayed as “there and later”, thus reducing the motivation to mitigate “here and now”.

Climate change mitigation efforts across the world are informed by results from mathematical models of climate change. These models, while immensely useful, have been criticized for assuming that anthropogenic carbon emissions are driven solely by demographic and economic forces, thus neglecting descriptions of human behaviour. Recently, social and behavioural frameworks have started making their way into models of climate change, resulting in ‘coupled social-climate models’. Results from these models show that the inclusion of human behaviour, driven by social and psychological forces, can significantly alter climate change projections.

We build on existing work by constructing a coupled social-climate model with country-level structure and parameterization. This allows us to introduce the element of diverse, dynamic human behaviour, which we model using tools from evolutionary game theory. Ultimately, if we are to leverage individual behavioural change to aid climate change mitigation, we need to develop mathematical models to understand the complex interactions between human behaviour and climate change. This effort could also benefit us by predicting outcomes, yet unforeseen, which may prove crucial in helping us prepare our response to climate change.

Beyond the Bones: Calcium Transport and Regulation in the Kidney
Calcium homeostasis is essential for the proper functioning of various cells and the kidney plays a vital role in this balance. The goal of this study is to expand our previous mathematical model of transepithelial transport along the male rat nephron to include the transport of calcium and to investigate the effects of inhibiting transepithelial sodium transport on urinary calcium excretion and its reabsorption along different nephron
segments. We simulated the effects of inhibiting the Na-K-2Cl transporter (NKCC2), reflecting the effects of the hypertensive drug, furosemide, the inhibition of the Na+/H+ exchanger (NHE3), the Na-Cl cotransporter (NCC), and the Epithelial Na channel (ENaC). Our results suggest that disruption in sodium transport significantly impacts renal calcium transport: NKCC2 inhibition significantly decreased calcium renal reabsorption along the thick ascending limb (TAL) and substantially increased calcium excretion by 8.7 folds in the case of complete inhibition. Our simulations of NHE3 inhibitions predicted reduced calcium reabsorption along the proximal tubule (PT) by ~46% and slightly increased calcium urine excretion. NCC inhibitions had slight effects on calcium reabsorption. The most notable effect of ENaC inhibition was the increased calcium reabsorption along the connecting tubule (CNT), resulting in a considerably reduced calcium excretion.

A longstanding problem in mathematical oncology is to accurately estimate the mathematical parameters which govern the growth of glioblastomas, a particularly aggressive form of brain tumour. While a method exists to derive these parameter estimates, it is plagued by problems including a high sensitivity to measurement error, a reliance on unrealistic mathematical assumptions, and a dependence on precise human measurements. Using deep learning techniques such as PINNs, it is possible to develop an algorithm that is capable of producing more accurate estimates of the key parameters while eliminating the shortcomings of the existing method. As part of my PhD research, I created a deep learning algorithm capable of making patient-specific predictions more accurately than the existing method. The data used in the research was collected by my collaborators at St. Michael’s Hospital and the University of Toronto. My computational approach allows for improved insight into the fundamental biological mechanisms that govern
tissue heterogeneity. This work has numerous implications in treatment planning, drug development, and patient survival.

Individual artificial intelligence (AI) agents learning to work together is an important problem in multiagent systems (MAS). We propose a model for multi-objective optimization, a credo, for agents in a system that are configured into multiple groups (i.e., teams). Our model of credo regulates how agents optimize their behavior for the groups they belong to. We evaluate credo in the context of challenging social dilemmas with reinforcement learning agents. Our results indicate that the interests of teammates, or the entire system, are not required to be fully aligned for achieving globally beneficial outcomes. We identify two scenarios without full common interest that achieve high equality and significantly higher mean population rewards compared to when the interests of all agents are aligned.

Kidneys: regulator of magnesium homeostasis

Magnesium plays an important role in several physiological functions and metabolic and biochemical processes within the cell and its deficiency has been associated with neurological disorders, heart disorders, hypertension, and type 2 diabetes. The kidneys play a central role in maintaining serum magnesium within a narrow range (0.70–1.10 mmol/L). In this study, an epithelial cell-based computational model of solute transport in rat kidneys was developed to understand the mechanism of magnesium transport along different nephron segments. Since magnesium transport is tightly coupled to sodium transport, the model was used to simulate the effects of different antihypertensive diuretics on renal magnesium reabsorption. The simulations showed that loop and thiazide diuretics result in increased magnesium excretion, whereas potassium-sparing diuretics favor magnesium retention.

Daneshbaz: Open Research, Open Problem, Open Ideas.

Publishing a paper can take a long time, and collaborating with someone you don't know can be challenging. Throughout their careers, researchers encounter these issues, but it is particularly crucial for those in their early stages and newcomers, such as graduate students. Their small network limits their ability to facilitate such collaborations due to their inexperience and lack of publications. In addition, because the status quo usually prevents publication updates, papers will no longer be subject to revisions. This can create a unique challenge for those just entering the research field, as they may not have the resources or experience to navigate these obstacles. Moreover, without periodic revisions, the integrity of the published work is put at risk. Daneshbaz.com supports current practices while improving the whole process, advocating for a transparent, fast, and hassle-free publication system. Our proposed approach creates a more efficient publishing ecosystem, facilitating collaboration among researchers, introducing an alternative to dead papers, and helping shape research's future. There is no doubt that Daneshbaz is a revolution in research.

Citizen-focused democratic processes where participants deliberate on alternatives and then vote to make the final decision are increasingly popular today. While the computational social choice literature has extensively investigated voting rules, there is limited work that explicitly looks at the interplay of the deliberative process and voting. In this paper, we build a deliberation model using established models from the opinion-dynamics literature and study the effect of different deliberation mechanisms on voting outcomes achieved when using well-studied voting rules. Our results show that deliberation generally improves welfare and representation guarantees, but the results are sensitive to how the deliberation process is organized. We also show, experimentally, that simple voting rules, such as approval voting, perform as well as more sophisticated rules such as proportional approval voting or method of equal shares if deliberation is properly supported. This has ramifications on the practical use of such voting rules in citizen-focused democratic processes.