相关论文: Phantom depth and stable phantom exactness

Matched asymptotic expansion is a useful technique in General Relativity and other fields whenever interaction takes place between physics at two different length scales. Here matched asymptotic expansion is argued to be equivalent quite…

The notion of phantom extension of order a given ordinal $\alpha $ has been introduced in collaboration with Casarosa, as an algebraic analogue of the order of a phantom map in topology, to study the structure of flat modules. In this…

Weakly approximable triangulated categories, introduced by Neeman, provide a powerful framework for studying localization phenomena in triangulated categories. In this paper, we establish new localization theorems showing that, under mild…

Weak proregularity of an ideal in a commutative ring is a subtle generalization of the noetherian property of the ring. Weak proregularity is of special importance for the study of derived completion, and it occurs quite often in…

Fedorchuk's fully closed (continuous) maps and resolutions are applied in constructions of non-metrizable higher-dimensional analogues of Anderson, Choquet, and Cook's continua. Certain theorems on dimension-lowering maps are proved for…

The self-supervised learning of depth and pose from monocular sequences provides an attractive solution by using the photometric consistency of nearby frames as it depends much less on the ground-truth data. In this paper, we address the…

This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…

We develop a new numerical technique for approximating solutions of the Navier-Stokes equations on moving domains. The method aims at simulating an incompressible fluid past an object whose motion is assigned a priori using a level-set…

From the output produced by a memoryless deletion channel from a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that…

In this paper, we introduce and study relative phantom morphisms in extriangulated categories defined by Nakaoka and Palu. Then using their properties, we show that if $(\C,\E,\s)$ is an extriangulated category with enough injective objects…

We investigate the infinite-distance properties of families of unstable flux vacua in string theory with broken supersymmetry. To this end, we employ a generalized notion of distance in the moduli space and we build a holographic…

We consider a model with two real scalar fields which admits phantom domain wall solutions. We investigate the structure and evolution of these phantom domain walls in an expanding homogeneous and isotropic universe. In particular, we show…

Most existing methods often rely on complex models to predict scene depth with high accuracy, resulting in slow inference that is not conducive to deployment. To better balance precision and speed, we first designed SmallDepth based on…

In this note, a condition (\emph{open persistence}) is presented under which a (pre)closure operation on submodules (resp. ideals) over rings of global sections over a scheme $X$ can be extended to a (pre)closure operation on sheaves of…

We consider approximations of general continuous functions on finite-dimensional cubes by general deep ReLU neural networks and study the approximation rates with respect to the modulus of continuity of the function and the total number of…

In this paper, we tackle the problem of estimating the depth of a scene from a monocular video sequence. In particular, we handle challenging scenarios, such as non-translational camera motion and dynamic scenes, where traditional structure…

In this article, we study the relationship between notions of depth for sequences, namely, Bennett's notions of strong and weak depth, and deep $\Pi^0_1$ classes, introduced by the authors and motivated by previous work of Levin. For the…

Fuzzy closure spaces are an extension of classical closure spaces in topology, where the concept of closure is defined in terms of fuzzy sets. This article introduces interior operators and neighborhood systems in fuzzy closure spaces.…

Self-supervised monocular depth estimation methods have been increasingly given much attention due to the benefit of not requiring large, labelled datasets. Such self-supervised methods require high-quality salient features and consequently…

Several important measures of quantum correlations of a state of a finite-dimensional composite system are defined as linear combinations of marginal entropies of this state. This paper is devoted to the infinite-dimensional generalizations…