Maximal Rank Correlation

The Maximal Rank Conjecture

Let C be a general curve of genus g, embedded in Pr via a general linear series of degree d. In this paper, we prove the Maximal Rank Conjecture, which determines the Hilbert function of C ⊂ Pr.

Dynamic Rank-Maximal Matchings

We consider the problem of matching applicants to posts where applicants have preferences over posts. Thus the input to our problem is a bipartite graph G = (A ∪ P , E), where A denotes a set of applicants, P is a set of posts, and there are ranks on edges which denote the preferences of applicants over posts. A matching M in G is called rank-maximal if it matches the maximum number of applican...

The Maximal Rank Conjecture and Rank Two Brill-Noether Theory

We describe applications of Koszul cohomology to the BrillNoether theory of rank 2 vector bundles. Among other things, we show that in every genus g > 10, there exist curves invalidating Mercat’s Conjecture for rank 2 bundles. On the other hand, we prove that Mercat’s Conjecture holds for general curves of bounded genus, and its failure locus is a Koszul divisor in the moduli space of curves. W...

Multivariate Maximal Correlation Analysis

Correlation analysis is one of the key elements of statistics, and has various applications in data analysis. Whereas most existing measures can only detect pairwise correlations between two dimensions, modern analysis aims at detecting correlations in multi-dimensional spaces. We propose MAC, a novel multivariate correlation measure designed for discovering multidimensional patterns. It belong...

Spearman Rank Correlation Coefficient