相关论文: A numerical toolkit for multiprojective varieties

A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden…

Suppose that X is a complex projective variety and L is a pseudo-effective divisor. A numerical reduction map is a quotient of X by all subvarieties along which L is numerically trivial. We construct two variants: the L-trivial reduction…

We describe a method for predicting a classification of an object given classifications of the objects in the training set, assuming that the pairs object/classification are generated by an i.i.d. process from a continuous probability…

A multi-scale greedy-based object proposal generation approach is presented. Based on the multi-scale nature of objects in images, our approach is built on top of a hierarchical segmentation. We first identify the representative and diverse…

We introduce a deep multitask architecture to integrate multityped representations of multimodal objects. This multitype exposition is less abstract than the multimodal characterization, but more machine-friendly, and thus is more precise…

For an interval finite quiver $Q$, we introduce a class of flat representations. We classify the indecomposable projective objects in the category $\mathrm{rep}(Q)$ of pointwise finite dimensional representations. We show that an object in…

A data structure and toolkit are presented here that allow for the description and manipulation of mathematical models of three-manifolds and their interactive display from multiple viewpoints via the OpenGL 3D graphics package. The data…

Consider an ideal $I \subset R = \bC[x_1,...,x_n]$ defining a complex affine variety $X \subset \bC^n$. We describe the components associated to $I$ by means of {\em numerical primary decomposition} (NPD). The method is based on the…

A new class of entanglement witnesses (EWs) called reduction type entanglement witnesses is introduced, which can detect some multi-qudit entangeled states including PPT ones with Hilbert space of dimension $d_{_{1}}\otimes…

We propose a framework to continuously learn object-centric representations for visual learning and understanding. Existing object-centric representations either rely on supervisions that individualize objects in the scene, or perform…

Unsupervised object discovery is commonly interpreted as the task of localizing and/or categorizing objects in visual data without the need for labeled examples. While current object recognition methods have proven highly effective for…

We are concerned with the problem of decomposing the parameter space of a parametric system of polynomial equations, and possibly some polynomial inequality constraints, with respect to the number of real solutions that the system attains.…

We describe in a rudimentary fashion how SVM(support vector machine) plays the role of classifier in a mathematical setting. We then discuss its application in the study of multiple SNP(single nucleotide polymorphism) variations. Also…

The paper introduces a methodology for visualizing on a dimension reduced subspace the classification structure and the geometric characteristics induced by an estimated Gaussian mixture model for discriminant analysis. In particular, we…

We consider the problem of learning a classifier from observed functional data. Here, each data-point takes the form of a single time-series and contains numerous features. Assuming that each such series comes with a binary label, the…

Prototypical part learning is emerging as a promising approach for making semantic segmentation interpretable. The model selects real patches seen during training as prototypes and constructs the dense prediction map based on the similarity…

We present a generalization of multiview varieties as closures of images obtained by projecting subspaces of a given dimension onto several views, from the photographic and geometric points of view. Motivated by applications in Computer…

We introduce a new architecture for unsupervised object-centric representation learning and multi-object detection and segmentation, which uses a translation-equivariant attention mechanism to predict the coordinates of the objects present…

We have deluge of data in time series format for numerous phenomena. The number of snapshots, resolution and many other factors come into play as we look to identify the dynamics in a given problem. The pre-processing and post-processing…

In this paper we present a new method for entanglement witnesses construction. We show that to construct such an object we can deal with maps which are not positive on the whole domain, but only on a certain sub-domain. In our approach…