Related papers: Witness structures and immediate snapshot complexe…

We give a universal recipe for constructing nonlinear entanglement witnesses able to detect non-classical correlations in arbitrary systems of distinguishable and/or identical particles for an arbitrary number of constituents. The…

Information systems with witnesses have been introduced in [D. Spreen. Generalised information systems capture L-domains. arXiv:1610.02260v2] as a logic-style representation of L-domains: The category of such information systems with…

Shellings of simplicial complexes have long been a useful tool in topological and algebraic combinatorics. Shellings of a complex expose a large amount of information in a helpful way, but are not easy to construct, often requiring deep…

Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…

In this paper, we propose a novel ensembling technique for deep neural networks, which is able to drastically reduce the required memory compared to alternative approaches. In particular, we propose to extract multiple sub-networks from a…

Scene graph prediction --- classifying the set of objects and predicates in a visual scene --- requires substantial training data. However, most predicates only occur a handful of times making them difficult to learn. We introduce the first…

We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…

This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…

Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…

In this paper we introduce a method which allows us to study properties of the random uniform simplicial complex. That is, we assign equal probability to all simplicial complexes with a given number of vertices and then consider properties…

We elaborate on a general method that we recently introduced for characterizing the "natural" structures in complex physical systems via a multiscale network based approach for the data mining of such structures. The approach is based on…

In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…

The goal of this paper is to perform object detection in satellite imagery with only a few examples, thus enabling users to specify any object class with minimal annotation. To this end, we explore recent methods and ideas from…

A crucial step in the analysis of persistent homology is the transformation of data into an appropriate topological object (in our case, a simplicial complex). Modern packages for persistent homology often construct Vietoris--Rips or other…

We propose a new framework for object detection based on a generalization of the keypoint correspondence framework. This framework is based on replacing keypoints by keygraphs, i.e. isomorph directed graphs whose vertices are keypoints, in…

A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like ``holonomy'', ``parallel transport'', ``bundles'', ``combinatorial curvature'' etc. in the context of simplicial (polyhedral) complexes, posets,…

The paper describes clustering problems from the combinatorial viewpoint. A brief systemic survey is presented including the following: (i) basic clustering problems (e.g., classification, clustering, sorting, clustering with an order over…

Visual recognition tasks are often limited to dealing with a small subset of classes simply because the labels for the remaining classes are unavailable. We are interested in identifying novel concepts in a dataset through representation…

When light travels through scattering media, speckles (spatially random distribution of fluctuated intensities) are formed due to the interference of light travelling along different optical paths, preventing the perception of structure,…