MMathSci Theses Presentations

This semester’s MMathSci Theses Presentations will take place Thursday, 1 June in the
AGR (Level 8) Carslaw and on zoom:

https://uni-sydney.zoom.us/j/81570621760

The schedule and talk details are below.  All are welcome to
attend.  

10:30 - Ye Tian (supervisor: Jennifer Chan) 
11:00 - Jiawang Lin (supervisor: Pengyi Yang) 
11:30 - Ben Tran (supervisor: Ben Goldys) 
12:00 - Jing Zhang (supervisor: Jie Yen Fan) 

1:30 - Xiaoyue Wen (supervisor: Linh Nghiem) 
2:00 - Thomas Gavrielatos (supervisor: Zsuzsanna Dancso) 
2:30 - Finn Kinley (supervisor: Kevin Coulembier) 
3:00 - Erchun Liu(supervisor: Milena Radnovic) 

Name: Thomas Malliaras Gavrielatos

Title: A Reidemeister theorem for solid ribbon torus links in R^4 

Abstract: Reidemeister-type theorems form a cornerstone of knot theory, as they enable
the combinatorial study of knots as equivalence classes of knot diagrams.  In this talk
I will outline a proof for a Reidemiester theorem for solid ribbon torus links in R^4.
Ribbon torus links are embedded tori in R^4, characterised by the existence of a
"filling" so that the resulting immersed solid tori have only restricted, "ribbon" type
singularities.  For these objects, Reidemeister theorems are not yet known: the
difficulty is the combinatorial description of filling changes.  Building on work by
Audoux and others, we prove a Reidemeister theorem for solid ribbon torus links
(combinatorially described as welded links), where the filling is included in the data.
The proof relies on the construction of two inverse maps: the enhanced Tube map from
diagrams to solid ribbon links, and the Conn map from solid ribbon links to diagrams.
This talk is based on joint work with Zsuzsanna Dancso.  

Name: Finn Kinley 

Title: The Category O of a Periplectic Lie Superalgebra through the Quivers of Blocks 

Abstract: In the study of the BGG category O of semi-simple Lie algebras, an object of
great interest is the endomorphism algebra A of all morphisms between indecomposable
projective modules in O.  It is well known that the category of A-modules is equivalent
to O, and so understanding A (and its representations) enables us to answer many
questions about O.  Block-wise descriptions of A for low rank Lie algebras have been
given by way of quivers and relations, thanks to Soergel and Stroppel.  

This same story holds in the world of Lie superalgebras which admit triangular
decompositions (for example, classical Lie superalgebras), but there is comparably
little work done on computing these algebras.  We find explicitly quivers and relations
for two of the three blocks of O(pe(2)) (up to equivalence), where pe(2) is the
periplectic Lie superalgebra of rank 2.  The story for one of these blocks had
previously not been told.  These quivers exhibit quite a lot of symmetry and are
relatively easy to draw.  

Through our descriptions, one recovers results known previously about equivalences
between the blocks of O(pe(2)).  Moreover, the endomorphism algebras of these two blocks
are seen to be quadratic.  This begs the question of whether they are Koszul, a fact
that was known previously for one of these blocks and is now answerable for the other
using our findings.  

Name: Jiawang Lin 

Title: Reclassification of multimodal single-cell dataset by DeepReclassify 

Abstract: This thesis aim to reclassify mislabelled cell type to correct classification
based on single-cell omics dataset.  To accomplish this goal, original data is applied
on autoencoder model to reduce the dimentionality and passed result into a
semi-supervised deep learning framework called DeepReclassify.  DeepReclassify is a
feedforward neural network that use Adasampling techniques to filter negative effects
caused by mislabelled cell.  Once DeepReclassify is successfully trained, it can map
potentially mislabelled cell type to the right label.  

Name: Erchun Liu 

Title: Pencil of conics 

Abstract: The thesis mainly focused on the elementary concept of comics and the
derivative pencils of conics.  The background of this study is the introduction of
ellipses, parabolas, hyperbolas, degenerate conics, and some famous theorems.  For
better understanding, we introduced the geometry significance in R^3 .  Two
discriminants are used to classify each conic section into different conic types.  In
the rest of the thesis, the main purpose is to calculate and classify pencils of conics
for any four fixed points from some particular shapes and analyze how the graph of
pencils of conics will look like.  The main methodology through the whole calculation is
the classification via discriminants of conics.  Based on the examples of pencils of
conics in this thesis, the topic can be extended to a broader study with any four fixed
points, randomly but not limited to form an exact shape.  

Name: Ye Tian 

Title: Research on Neural Network Models for Skewed Data to Solve Auto Insurance
Problems.  

Abstract: At present, in the auto insurance industry, in order to better classify the
safety of drivers, it is necessary to build a suitable neural network model for
prediction.  In order to build a model that can deal with skewed data, several models
were built for research.  First, use different packages to compare whether the model
accuracy is affected by the packages.  Second, set different parameters to build
different models.  Third, four different methods are used to deal with skewed data.
Then, classify the drivers using a mixture Poisson model.  Finally, multiple models are
compared and the best model in this situation is choosed.  

Name: Ben Tran

Title: An Ornstein-Uhlenbeck Process on the Wasserstein Space of
Probability Measures 

Abstract: In this thesis, we construct and analyse the properties
of an Ornstein-Uhlenbeck type process on a space of probability measures, the
Wasserstein space $\cP_2(\Rd)$.  Taking a separable Hilbert space of vector fields known
as the \emph{tangent space}, we construct an Ornstein-Uhlenbeck process on this space
using classical stochastic analysis, then define a related process on $\cP_2(\Rd)$ using
the theory of generators and Dirichlet forms.  We then analyse these objects and the
$L^2$ spaces upon which they are defined.  

Name: Xiaoyue Wen

Title: Analysis of Dimension Reduction Algorithms in Linear Regression Models 

Abstract: In the information age, where the volume of data is growing, and the types of
data are becoming increasingly diverse, the professional requirements of various
industries are becoming more and more refined.  The massive emergence of data makes the
organization and interdependencies of data increasingly complex.It is an essential
aspect for industry data analysis to reduce the dimensions of these data to improve
analysis efficiency.  In this thesis, we attempt to construct linear regression models
based on data and investigate the feasibility of different dimension reduction
algorithms within this context.  We introduce Principal Component Analysis(PCA), the
Sliced Inverse Regression (SIR) algorithm and the Principal Fitted Component (PFC)
algorithm, and compare the performance of these models.  We apply these algorithms to
various data types and evaluate their feasibility of dimension reduction by fitting
different parameters.  To assess the reduction quality and ascertain the reliability and
fidelity of the algorithms, we measure the correlation between vectors before and after
dimension reduction, represented by the angles between the vectors.  By conducting
simulations, we can assess the reduction, reliability, and fidelity of different
algorithms.  

Name: Jing Zhang

Title: Epidemic Compartment Model with Applications in COVID-19 

Abstract: The compartment model serves as a valuable tool for epidemic prediction,
offering insights into the dynamics of infectious diseases and facilitating timely
decision-making.  In this project, we introduce an overview of the compartment model and
its application in the field of epidemics, focusing specifically on the SIR model.
Additionally, we provide a brief introduction to the SIR-BD model, which incorporates
birth and death rates into the classical SIR model.  Under the background of the
COVID-19 pandemic, we delve into an exploration of diverse strategies for combating the
epidemic.  Our study involves the adaptation of the SIR model to incorporate testing and
quarantine, vaccination, and lockdown measures.  By employing real-world COVID-19 data
from the United States, we estimate the parameters of the SIR model and generate
predictions under various intervention scenarios.