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In this paper, we introduce a novel model for random hypergraphs based on weighted random connection models. In accordance with the standard theory for hypergraphs, this model is constructed from a bipartite graph. In our stochastic model,…
A small-world topology characterizes many complex systems including the structural and functional organization of brain networks. The topology allows simultaneously for local and global efficiency in the interaction of the system…
We prove existence of extension dimension for paracompact spaces. Here is the main result of the paper: \proclaim{Theorem} Suppose X is a paracompact space. There is a CW complex K such that {a.} K is an absolute extensor of X up to…
To better understand the structure and function of complex systems, researchers often represent direct interactions between components in complex systems with networks, assuming that indirect influence between distant components can be…
In this paper, we introduce and study the class of {\it enriched strictly pseudocontractive mappings} in Hilbert spaces and extend the corresponding convergence theorem (Theorem 12) in [Browder, F. E., Petryshyn, W. V., {\it Construction of…
When two periodic potentials compete in materials, one may adopt the other, which straightforwardly generates topological defects. Of particular interest are domain walls in charge-, dipole-, and spin-ordered systems, which govern…
Road network is a critical infrastructure powering many applications including transportation, mobility and logistics in real life. To leverage the input of a road network across these different applications, it is necessary to learn the…
High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…
We compare two properties for a CW-space $X$ of finite type: (1) being homotopy equivalent to a CW-complex without $j$-cells for $k\leq j\leq \ell$ (($k,\ell$)-cellfree) and (2) $H^j(X;R)=0$ for any $\mathbb Z\pi_1(X)$-module $R$ when…
Web services represent a system with a huge number of units and many various and complex interactions. Complex networks as a tool for modelling and analyzing natural environments seem to be well adapted to such a complex system. To describe…
High-throughput techniques are leading to an explosive growth in the size of biological databases and creating the opportunity to revolutionize our understanding of life and disease. Interpretation of these data remains, however, a major…
We present several new results on the feasibility of inferring the hidden states in strongly-connected trackable weak models. Here, a weak model is a directed graph in which each node is assigned a set of colors which may be emitted when…
Complex reasoning over text requires understanding and chaining together free-form predicates and logical connectives. Prior work has largely tried to do this either symbolically or with black-box transformers. We present a middle ground…
In this paper we consider the hyperspace $C_{n}(X)$ of non-empty and closed subsets of a base space $X$ with up to $n$ connected components. We consider a class of base spaces called finite ray-graphs, which are a noncompact variation on…
We consider complements of standard Seifert surfaces of special alternating links. On these handlebodies, we use Honda's method to enumerate those tight contact structures whose dividing sets are isotopic to the link, and find their number…
A phenomenological model of self-organization explaining the emergence of a complexity with features that apparently satisfy the specific criteria usually required for recognizing the appearance of life in laboratory is presented. The…
Herein, a methodology is developed to replicate functions, measures and stochastic processes onto a compact metric space. Many results are easily established for the replica objects and then transferred back to the original ones. Two…
The controlled growth of nanowires (NWs) with dimensions comparable to the Fermi wavelengths of the charge carriers allows fundamental investigations of quantum confinement phenomena. Here, we present studies of proximity-induced…
This paper considers the two-way relay channel (TWRC) where two users communicate via a relay. For the restricted TWRC where the uplink from the users to the relay is any deterministic function and the downlink from the relay to the users…
It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones. Despite the vast…