相关论文: From 9-IM Topological Operators to Qualitative Spa…

Many works in the recent literature introduce semantic mapping methods that use CNNs (Convolutional Neural Networks) to recognize semantic properties in images. The types of properties (eg.: room size, place category, and objects) and their…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

With its boundary tracing out a link or knot in 3D, the Seifert surface is a 2D surface of core importance to topological classification. We propose the first-ever experimentally realistic setup where Seifert surfaces emerge as the boundary…

We define higher quantum Airy structures as generalizations of the Kontsevich-Soibelman quantum Airy structures by allowing differential operators of arbitrary order (instead of only quadratic). We construct many classes of examples of…

Neural Tensor Networks (NTNs), which are structured to encode the degree of relationship among pairs of entities, are used in Logic Tensor Networks (LTNs) to facilitate Statistical Relational Learning (SRL) in first-order logic. In this…

Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails…

Different classes of communication network topologies and their representation in the form of adjacency matrix and its eigenvalues are presented. A self-organizing feature map neural network is used to map different classes of communication…

Collision detection is essential to virtually all robotics applications. However, traditional geometric collision detection methods generally require pre-existing workspace geometry representations; thus, they are unable to infer the…

A set of fixed points of the Hopfield type neural network is under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter…

Dense indoor scene modeling from 2D images has been bottlenecked due to the absence of depth information and cluttered occlusions. We present an automatic indoor scene modeling approach using deep features from neural networks. Given a…

Current theoretical and empirical research in neural networks suggests that complex datasets require large network architectures for thorough classification, yet the precise nature of this relationship remains unclear. This paper tackles…

Hypergraph is a topological model for networks. In order to study the topology of hypergraphs, the homology of the associated simplicial complexes and the embedded homology have been invented. In this paper, we give some algorithms to…

The aim of this paper is to combine several Ivlev-like modal systems characterized by 4-valued non-deterministic matrices (Nmatrices) with IDM4, a 4-valued expansion of Belnap-Dunn's logic FDE with an implication introduced by Pynko in…

To solve more complex things, computer systems becomes more and more complex. It becomes harder to be handled manually for various conditions and unknown new conditions in advance. This situation urgently requires the development of…

Networks are ubiquitous structure that describes complex relationships between different entities in the real world. As a critical component of prediction task over nodes in networks, learning the feature representation of nodes has become…

We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible…

Amorphous solids remain outside of the classification and systematic discovery of new topological materials, partially due to the lack of realistic models that are analytically tractable. Here we introduce the topological Weaire-Thorpe…

Topological Deep Learning (TDL) has emerged as a paradigm to process and learn from signals defined on higher-order combinatorial topological spaces, such as simplicial or cell complexes. Although many complex systems have an asymmetric…

Topological order in solid state systems is often calculated from the integration of an appropriate curvature function over the entire Brillouin zone. At topological phase transitions where the single particle spectral gap closes, the…

The paper explains the connection between topological theories for one-manifolds with defects and values in the Boolean semiring and automata and their generalizations. Finite state automata are closely related to regular languages. To each…