Related papers: The Solution of the Kadison-Singer Problem
Several recent polyphonic music transcription systems have utilized deep neural networks to achieve state of the art results on various benchmark datasets, pushing the envelope on framewise and note-level performance measures. Unfortunately…
We introduce a new approach to the anisotropic Calder\'on problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large…
Recently in graph theory several authors have studied the spectrum of the Cayley graph of the symmetric group S_n generated by the transpositions (1, i) for 2 <= i <= n. Several conjectures were made and partial results were obtained. The…
The uncovering of new structure on the Cuntz semigroup of a C*-algebra of stable rank one leads to several applications: We answer affirmatively, for the class of stable rank one C*-algebras, a conjecture by Blackadar and Handelman on…
What makes a computational problem easy (e.g., in P, that is, solvable in polynomial time) or hard (e.g., NP-hard)? This fundamental question now has a satisfactory answer for a quite broad class of computational problems, so called…
We have seen remarkable success in representation learning and language models (LMs) using deep neural networks. Many studies aim to build the underlying connections among different modalities via the alignment and mappings at the token or…
This paper addresses the challenges and advancements in speech recognition for singing, a domain distinctly different from standard speech recognition. Singing encompasses unique challenges, including extensive pitch variations, diverse…
As music streaming services dominate the music industry, the playlist is becoming an increasingly crucial element of music consumption. Con- sequently, the music recommendation problem is often casted as a playlist generation prob- lem.…
This paper introduces the Simultaneous assignment problem. Let us given a graph with a weight and a capacity function on its edges, and a set of its subgraphs along with a degree upper bound function for each of them. We are also given a…
In this paper, we study a generalization of the classical minimum cut prob- lem, called Connectivity Preserving Minimum Cut (CPMC) problem, which seeks a minimum cut to separate a pair (or pairs) of source and destination nodes and…
In this set of lectures I review recent developments in string theory emphasizing their non-perturbative aspects and their recently discovered duality symmetries. The goal of the lectures is to make the recent exciting developments in…
This paper is based on my talk at ICM on recent progress in a number of classical problems of linear algebra and representation theory, based on new approach, originated from geometry of stable bundles and geometric invariant theory.
Many applications of cross-modal music retrieval are related to connecting sheet music images to audio recordings. A typical and recent approach to this is to learn, via deep neural networks, a joint embedding space that correlates short…
The algebraic approach to the Constraint Satisfaction Problem (CSP) uses high order symmetries of relational structures -- polymorphisms -- to study the complexity of the CSP. In this paper we further develop one of the methods the…
We investigate a series of learning kernel problems with polynomial combinations of base kernels, which will help us solve regression and classification problems. We also perform some numerical experiments of polynomial kernels with…
In this paper two related simplification problems for systems of linear inequalities describing precedence relation systems are considered. Given a precedence relation system, the first problem seeks a minimum subset of the precedence…
This paper investigates the spectral norm version of the column subset selection problem. Given a matrix $\mathbf{A}\in\mathbb{R}^{n\times d}$ and a positive integer $k\leq\text{rank}(\mathbf{A})$, the objective is to select exactly $k$…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: {\em give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\subset GL(n,{\bf C})$ or $c_j\subset gl(n,{\bf C})$ so that there…