相关论文: Computing higher direct images in Macaulay2

Neural Networks require large amounts of memory and compute to process high resolution images, even when only a small part of the image is actually informative for the task at hand. We propose a method based on a differentiable Top-K…

Analysis of human sketches in deep learning has advanced immensely through the use of waypoint-sequences rather than raster-graphic representations. We further aim to model sketches as a sequence of low-dimensional parametric curves. To…

The woylier package implements tour interpolation paths between frames using Givens rotations. This provides an alternative to the geodesic interpolation between planes currently available in the tourr package. Tours are used to visualise…

In this paper, we present StrucTexTv2, an effective document image pre-training framework, by performing masked visual-textual prediction. It consists of two self-supervised pre-training tasks: masked image modeling and masked language…

Currently, transformer-based algorithms are making a splash in the domain of image deblurring. Their achievement depends on the self-attention mechanism with CNN stem to model long range dependencies between tokens. Unfortunately, this…

In this paper we present a new two-level iterative algorithm for tomographic image reconstruction. The algorithm uses a regularization technique, which we call edge-preserving Laplacian, that preserves sharp edges between objects while…

The analysis of digital images using homological procedures is an outstanding topic in the area of Computational Algebraic Topology. In this paper, we describe a certified reduction strategy to deal with digital images, but preserving their…

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial…

We present MRPC, an R package that learns causal graphs with improved accuracy over existing packages, such as pcalg and bnlearn. Our algorithm builds on the powerful PC algorithm, the canonical algorithm in computer science for learning…

This is a collection of results on the topology of toric symplectic manifolds. Using an idea of Borisov, we show that a closed symplectic manifold supports at most a finite number of toric structures. Further, the product of two projective…

Generating human portraits is a hot topic in the image generation area, e.g. mask-to-face generation and text-to-face generation. However, these unimodal generation methods lack controllability in image generation. Controllability can be…

We derive an original direct imaging method of an object. It is based on topological derivatives, and aims at inverting the amplitude of waves that are retropropagated after laser illuminations.

We present in this work a new methodology to design kernels on data which is structured with smaller components, such as text, images or sequences. This methodology is a template procedure which can be applied on most kernels on measures…

We construct a Fourier--Mukai transform for smooth complex vector bundles $E$ over a torus bundle $\pi:M \to B,$ the vector bundles being endowed with various structures of increasing complexity. At a minimum, we consider vector bundles $E$…

We present a complete reimplementation of the LinearSystem package of Magma, with substantial improvements in design and performance. The resulting efficiency enables computations that were previously out of reach. We briefly describe the…

When studying a graded module $M$ over the Cox ring of a smooth projective toric variety $X$, there are two standard types of resolutions commonly used to glean information: free resolutions of $M$ and vector bundle resolutions of its…

We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of (Lie) algebroids as vector bundle comorphisms - differential relations of a…

We give a new description of the data needed to specify a morphism from a scheme to a toric Deligne-Mumford stack. The description is given in terms of a collection of line bundles and sections which satisfy certain conditions. As…

Many well-known graph drawing techniques, including force directed drawings, spectral graph layouts, multidimensional scaling, and circle packings, have algebraic formulations. However, practical methods for producing such drawings…

In the first part of this paper we prove a vanishing criterion for higher direct images of projective families of line bundles on a Cohen-Macaulay variety X. The result involves certain first-order deformations of certain curves on X, and…