Abstract: Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision and natural language processing. Along with its empirical success, deep learning has been theoretically shown to be […]
Abstract: The operadic structure on the moduli spaces of algebraic curves encodes in a combinatorial way how nodal curves in the boundary can be obtained by glueing smooth curves along marked […]
Abstract: Matroids are combinatorial abstractions of vector spaces embedded in a coordinate space. Many fundamental questions have been open for these classical objects. We highlight some recent progress that arise from the […]
Abstract: Bott periodicity relates vector bundles on a topological space X to vector bundles on X “times a sphere”. I’m not a topologist, so I will try to explain an algebraic […]
Abstract: A main challenge in analyzing single-cell RNA sequencing (scRNA-seq) data is to reduce technical variations yet retain cell heterogeneity. Due to low mRNAs content per cell and molecule losses during […]
Abstract: Encryption is the backbone of cybersecurity. While encryption can secure data both in transit and at rest, in the new era of ubiquitous computing, modern cryptography also aims to […]
Abstract: Let X be a compact hyperbolic surface. We can see that there is a constant C(X) such that the intersection number of the closed geodesics is \leq C(X) times the […]
Abstract: Although everyone talks about AI + healthcare, many people were unaware of the fact that there are two possible outcomes of the collaboration, due to the inherent dissimilarity between the […]
Abstract: Many statistical and computational tasks boil down to comparing probability measures expressed as density functions, clouds of data points, or generative models. In this setting, we often are unable to […]
Abstract: Conditional independence (CI) is an important tool instatistical modeling, as, for example, it gives a statistical interpretation to graphical models. In general, given a list of dependencies among random variables, […]
Abstract: In spatial population genetics, it is important to understand the probability of extinction in multi-species interactions such as growing bacterial colonies, cancer tumor evolution and human migration. This is because […]
Abstract: The recent success of neural networks enables a better interpretation of 3D point clouds, but processing a large-scale 3D scene remains a challenging problem. Most current approaches divide a large-scale […]