Related papers: The $G$-Noncommutative Minimal Model Program

We show that the minimal model program on any smooth projective surface is realized as a variation of the moduli spaces of Bridgeland stable objects in the derived category of coherent sheaves.

A version of quantum orbit method is presented for real forms of equal rank of quantum complex simple groups. A quantum moment map is constructed, based on the canonical isomorphism between a quantum Heisenberg algebra and an algebra of…

Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covariance matrices in high-dimensional spaces, spherical GMMs…

In a normed space setting, this paper studies the conditions under which the projected solutions to a quasi equilibrium problem with non-self constraint map exist. Our approach is based on an iterative algorithm which gives rise to a…

Over the years, computational imaging with accurate nonlinear physical models has garnered considerable interest due to its ability to achieve high-quality reconstructions. However, using such nonlinear models for reconstruction is…

Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, while maintaining interpretability through the…

In this work, we adopt the Gradient Projection Method (GPM) to problems of quantum control. For general $N$-level closed and open quantum systems, we derive the corresponding adjoint systems and gradients of the objective functionals, and…

This paper provides an overview and introduction to the development of non-ergodic ground-motion models, GMMs. It is intended for a reader who is familiar with the standard approach for developing ergodic GMMs. It starts with a brief…

Generalized approximate message passing (GAMP) is a promising technique for unknown signal reconstruction of generalized linear models (GLM). However, it requires that the transformation matrix has independent and identically distributed…

Learning to reason about relations and dynamics over multiple interacting objects is a challenging topic in machine learning. The challenges mainly stem from that the interacting systems are exponentially-compositional, symmetrical, and…

We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, "compression," of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate…

Neural networks are a promising tool for simulating quantum many body systems. Recently, it has been shown that neural network-based models describe quantum many body systems more accurately when they are constrained to have the correct…

Let $N$ be a normal subgroup of a group $G$. An $N$-module $Q$ is $G$-stable provided that $Q$ is equivalent to the twist $Q^g$ of $Q$ by $g$, for every $g\in G$. If the action of $N$ on $Q$ extends to an action of $G$ on $Q$, $Q$ is…

This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The…

Pairwise network models such as the Gaussian Graphical Model (GGM) are a powerful and intuitive way to analyze dependencies in multivariate data. A key assumption of the GGM is that each pairwise interaction is independent of the values of…

This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…

Let $G$ be a connected simple Lie group of real rank one and finite center, and let $K$ be a maximal compact subgroup. We study the families of spherical, ball, and uniform averages $(\sigma_t)_{t>0}$, $(\beta_t)_{t>0}$, and $(\mu_t)_{t>0}$…

We propose a unified approach to nonlinear modal analysis in dissipative oscillatory systems. This approach eliminates conflicting definitions, covers both autonomous and time-dependent systems, and provides exact mathematical existence,…

Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…

In this paper, we study the birational geometry of the Hilbert scheme of n points on P^2. We discuss the stable base locus decomposition of the effective cone and the corresponding birational models. We give modular interpretations to the…