Related papers: Effective nonvanishing, effective global generatio…

Generating point clouds, e.g., molecular structures, in arbitrary rotations, translations, and enumerations remains a challenging task. Meanwhile, neural networks utilizing symmetry invariant layers have been shown to be able to optimize…

Deep generative models parametrised by neural networks have recently started to provide accurate results in modelling natural images. In particular, generative adversarial networks provide an unsupervised solution to this problem. In this…

In this work, we provide some novel results that establish both the existence of Henig global proper efficient points and their density in the efficient set for vector optimization problems in arbitrary normed spaces. Our results do not…

We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a…

We introduce a notion of singular hermitian metrics (s.h.m.) for holomorphic vector bundles and define positivity in view of $L^2$-estimates. Associated with a suitably positive s.h.m. there is a (coherent) sheaf 0-th kernel of a certain…

We present LiDARGen, a novel, effective, and controllable generative model that produces realistic LiDAR point cloud sensory readings. Our method leverages the powerful score-matching energy-based model and formulates the point cloud…

We study torus-equivariant vector bundles $E$ on a complex projective variety $X$ which is either a Bott-Samelson-Demazure-Hansen variety or a wonderful compactification of a complex symmetric variety of minimal rank. We show that $E$ is…

We formalize the main approach for showing Zariski descent-type statements for strong generation of triangulated categories associated to algebro-geometric objects. This recovers various known statements in the literature. As applications…

The purpose of this paper is to establish an effective non-vanishing theorem for the syzygies of an adjoint-type line bundle on a smooth variety, as the positivity of the embedding increases. Our purpose here is to show that for an adjoint…

Consider the critical Galton-Watson branching system with infinite variance of the offspring law. We provide an alternative arguments against what Slack~{\cite{Slack68}} did when it seeked for a local expression in the neighborhood of point…

We give a complete classification of globally generated vector bundles of rank 3 on a smooth quadric threefold with $c_1\leq 2$ and extend the result to arbitrary higher rank case. We also investigate the existence of globally generated…

This treats the base-point-freeness of the adjoint bundles on normal surfaces with a boundary. This is an extension of the non-relative version of the theorem of Ein-Lazarsfeld-Masek and the theorem of Kawachi-Masek.

We give a moduli-theoretic treatment of the existence and properties of moduli spaces of semistable quiver representations, avoiding methods from geometric invariant theory. Using the existence criteria of Alper--Halpern-Leistner--Heinloth,…

We study the effective action for gravity obtained after the integration of scalar matter fields, using the local momentum representation based on the Riemann normal coordinates expansion. By considering this expansion around different…

In this paper we construct strong exceptional collections of vector bundles on smooth projective varieties that have a prescribed endomorphism algebra. We prove the construction problem always have a solution. We consider some applications…

In this note we contribute to the study of Seshadri constants on abelian and bielliptic surfaces. We specifically focus on bounds that hold on all such surfaces, depending only on the self-intersection of the ample line bundle under…

Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…

In machine learning, stochastic gradient descent (SGD) is widely deployed to train models using highly non-convex objectives with equally complex noise models. Unfortunately, SGD theory often makes restrictive assumptions that fail to…

Generative Adversarial Networks (GANs) have shown immense potential in fields such as text and image generation. Only very recently attempts to exploit GANs to statistical-mechanics models have been reported. Here we quantitatively test…

Generative models based on invertible transformations provide a physics-aware route to sample equilibrium configurations directly from the Boltzmann distribution, enabling efficient exploration of complex thermodynamic landscapes. Here, we…