The Schedule

Introduction

Title: A short introduction to arrangements of hyperplanes

Speaker: Tan Nhat Tran (Ruhr University Bochum, Germany)

Abstract: We give a short introduction to the theory of arrangements of hyperplanes. Some connection to the theory of arrangements of hypertori will also be discussed. 

Slides for the talk 

Title: Faster algorithms for the real root decision problem for

symmetric polynomial systems.  

Speaker: Thi Xuan Vu (UiT, The Arctic University of Norway, Tromsø, Norway).  

Abstract: The problem of deciding the emptiness of algebraic sets

over real fields is a fundamental algorithmic problem in effective

real algebraic geometry, which appears in many applications such as robotics and filter banks. In this talk we focus on an important

class of polynomials, the ones invariant under the action of the

symmetric group.  We construct and analyze an algorithm to solve this problem. Efficiency is obtained by taking advantage of the symmetry of the input polynomials.    

This is a joint work with George Labahn, Cordian Riener, Mohab Safey El Din, and Éric Schost.

Slides for the talk

Title: Newton polytope of good symmetric functions

Speaker: Khanh Nguyen Duc (State University of New York at Albany)

Abstract: We introduce a general class of symmetric functions that has saturated Newton polytope and their Newton polytope has integer decomposition property. The class covers numerous previously studied symmetric functions.

Slides for the talk

Title: Knight moves on infinite boards

Speaker: Quan Hoang (VNU University of Science)

Abstract: This talk discusses some recreational puzzles regarding knight moves on infinite boards. Given an arbitrary starting position, the question is whether a knight could visit every square on a two-dimensional infinite board exactly once. Besides the standard infinite board, we analyze the question on different board types, e.g., the board of the first quadrant of the Oxy plane. We then focus on the board of one-eighth of the Oxy plane. Based on insights from greedy solutions, we obtain intriguing patterns applied to construct a solution for a significant board region. Finally, the remaining area is solved by integer programming. This work is inspired by the video "The Trapped Knight" featuring Neil Sloane on the Youtube channel Numberphile.

Slides for the talk

Title: Stochastic Approximation with Discontinuous Dynamics, Differential Inclusions, and Applications

Speaker: Nhu Nguyen (University of Rhode Island) 

Abstract: This talk develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and non-smooth analysis, and stochastic differential inclusions. Under broad conditions, it is shown that a suitably scaled sequence of the iterates has a differential inclusion limit. In addition, it is shown for the first time that a centered and scaled sequence of the iterates converges weakly to a stochastic differential inclusion limit. The results are then used to treat several application examples including Markov decision process, Lasso algorithms, Pegasos algorithms, support vector machine classification, and learning.

Slides for the talk

Title: Clustering and visualization of large-scale and multimodal omics data

Speaker: Van Hoan Do (Le Quy Don Technical University) 

Abstract: Emerging single-cell genomics technologies such as single cell RNA sequencing provide new opportunities for discovery of previously unknown cell types and facilitating the study of biological processes such as cancer development. Clustering and visualization using dimensionality reduction techniques such as t-SNE and UMAP are the fundamental steps in analyzing high-dimensional data produced by the technologies. However, computational models have been challenged by the exponential growth of the data thanks to the growth of large-scale genomic projects such as the Human Cell Atlas. In this talk, we will introduce Specter, a computational method that utilizes recent algorithmic advances in fast spectral clustering and ensemble learning. Specter achieves a substantial improvement in accuracy over existing methods and identifies rare cell types with high sensitivity. Moreover, its speed allows Specter to scale to millions of cells and leads to fast computation times in practice. In addition, we will present j-SNE and as the generalization to the joint visualization of multimodal omics data, e.g., CITE-seq data that simultaneously measures gene and protein marker expression. The approach automatically learns the relative importance of each modality to obtain a concise representation of the data.

Slides for the talk