2024-25 Department of Mathematics and Statistics Events |
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July, 2025 |
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Thursday |
Ph.D. Defense
Speaker: Daniel Gray, Ph.D. Candidate TItle: Analysis of the 2-Person Combinatorial Games Split-S-Nim and Chomp on 2 Rows Abstract: Split-S-Nim is a variant of Nim in which each player on their turn can choose to make any legal move in the traditional version of Nim or add q coins to a heap, where q is some element of a predetermined subset of integers, S. We classify all sets that have the property in which the winning strategy is equivalent to the winning strategy for a version of the game with a set that has cardinality 1. If S has a smallest non-negative even value, q, then we conclude that it must either have a winning strategy identical to a version of the game with the set S = {q} or must have a general winning strategy that differs from any general winning strategy appropriate for a version of the game such that S has one element. This winning strategy is found by calculating the Sprague-Grundy numbers for the game with one heap. If S has no non-negative even elements, we show that the winning strategy is the same as the traditional game of Nim. Similarly, we show that if there is an odd integer in S greater than or equal to −1, then the winning strategy must differ, with the exception of the odd value of 1 when 0 is in S. Finally, we show subsets with smallest non-negative even elements of the form 2n +4s or 2n +4s+2 will only have a winning strategy identical to a singleton set version of the game if all other even values have certain properties. We complete our study of Split-S-Nim by considering the winning strategy for a game where S = Z. This version of the game is a logical extension of the game Nim in which the player can replace a heap of any size with up to two heaps of a size smaller than the original heap. Chomp is a combinatorial game attributed to Frederik Shue and David Gale in which players take turns removing rectangular pieces from an n × m grid. While a winning strategy for the first player has been shown to exist, the strategy is not known. We analyze the case where the starting position has 2 rows, finding the Sprague-Grundy numbers for all subgames of that starting position. |
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Thursday |
MS Exam Presentation Speaker: Shalini Perera, MS candidate Title: Learning Compact Representations for Medical Imaging: Autoencoding-Based Embeddings for Enhanced Classification Abstract: Nonparametric density estimation is studied for spherical data that may arise in manyscientifi c and practical fi elds. In particular, nonparametric mixture models based on likelihoodmaximization are used. A nonparametric mixture has component distributions mixed togetherwith a mixing distribution that is completely unspecifi ed and needs to be determined from data.For mixture components, a two-parameter distribution family can be used, with one parameter asthe mixing variable and the other to control the smoothness of the density estimator. Forexample, the popular von Mises-Fisher distributions can be readily used for this purpose.Numerical studies with various spherical data sets show that the resultant mixture-based densityestimators are strong competitors with the best of the other density estimators. |
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Friday |
MS Exam Presentation Speaker: Bimal Kumar Datta. MS candidate Title: Single-Cell RNA-Seq Data Analysis Using 'Seurat' Abstract: In this project, we present a comprehensive workflow to analyze scRNA-Seq data using the‘Seurat’ package in R. Our approach includes data normalization, identification of highly variablegenes, dimensionality reduction using PCA, t-SNE, and UMAP, clustering, and identification ofcell-type-specific markers. This case study also demonstrates how standard computational toolscan be used to identify significant immune cell populations and explore their gene expressionprofile. |
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Monday |
MS Exam Presentation Speaker: Ganesh Siwakoti, MS candidate Title: Learning Compact Representations for Medical Imaging: Autoencoding-Based Embeddings for Enhanced Classification Abstract: This study presents a framework for enhancing medical image classification through the use of compact representations learned via convolutional autoencoders (AEs). Using the MedMNIST benchmark, specifically the PathMNIST and BloodMNIST datasets, we first evaluate baseline classifiers including Linear, Multi-Layer Perceptron (MLP), and Convolutional Neural Networks (CNN). We then integrate latent embeddings generated from AEs into these classifiers to assess performance improvements. Experiments are conducted across multiple latent dimensions (32, 64, 128) to identify optimal embedding sizes. Quantitative metrics such as accuracy, F1 score, and AUC, along with qualitative tools like t-SNE and UMAP visualizations, are used for evaluation. Results show that autoencoder-augmented models consistently outperform their non-augmented counterparts, with CNN+AE achieving the highest accuracy and robustness across both datasets. This approach demonstrates the value of unsupervised representation learning in improving the efficiency and effectiveness of medical image classification tasks. |
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August, 2025 |
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August |
CryptoTeens in South Florida summer camp is a five - day camp for high-school students who want to discover the technology and the science behind cryptography. Participants will be introduced to the fundamental principles of c ryptography and learn how to apply conceptual knowledge to real-world situations. The camp will focus on Post-Quantum Cryptography, the area of math that is in charge of protecting our information in the era of quantum technology. The program includes stimulating lectures, inspiring talks by alumni and speakers from industry and government , and engaging exercise sessions. |
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March 2026 |
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March 2-6 |
57th Southeastern International Conference on Combinatorics, Graph Theory, and Computing Regsiter Here! |
