Type: Seminar

Modified: Wed 24 May 2023 1503; Wed 24 May 2023 1640; Tue 30 May 2023 1625

Distribution: World

Expiry: 7 Jun 2023

Auth: oyacobi@p724m2.pc (assumed)

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.

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