Related papers: Hyperconnected Relator Spaces. CW Complexes and Co…
Starting from an array of four-leg Hubbard ladders weakly doped away from half-filling and weakly coupled by inter-ladder tunneling, we derive an effective low energy model which contains a partially truncated Fermi surface and a well…
The demand for higher data rates and the scarce spectrum resources drive the adoption of collaborative communication techniques. In this work we shown that the existing cluster based collaborative schemes can be greatly improved in terms of…
For decades, superconductivity in high-Tc cuprates has been viewed as a competitor that suppresses charge-density-wave (CDW) order by reducing its amplitude and spatial extent. Here, we show that this picture is incomplete, as…
We define a model for random (abstract) cell complexes (CCs), similiar to the well-known Erd\H{o}s-R\'enyi model for graphs and its extensions for simplicial complexes. To build a random cell complex, we first draw from an Erd\H{o}s-R\'enyi…
We develop the theoretical foundations of a generalized Gromov-Hausdorff distance between functions on networks that has recently been applied to various subfields of topological data analysis and optimal transport. These functional…
Most real-world networks are endowed with the small-world property, by means of which the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. The evidence sparkled a wealth of studies…
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…
The cortex is a very large network characterized by a complex connectivity including at least two scales: a microscopic scale at which the interconnections are non-specific and very dense, while macroscopic connectivity patterns connecting…
Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include…
In many hybrid quantum systems, a superconducting circuit is required that combines DC-control with a coplanar waveguide (CPW) microwave resonator. The strategy thus far for applying a DC voltage or current bias to microwave resonators has…
We present a family of complete acyclic Morse matchings on the face lattice of a hypersimplex. Since a hypersimplex is a convex polytope, there is a natural way to form a CW complex from its faces. In a future paper we will utilize these…
Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…
We present an analysis of a system of weakly coupled Hubbard chains based on combining an exact study of spectral functions of the uncoupled chain system with a renormalization group method for the coupled chains. For low values of the…
In this paper, we obtain a characterizations of the recurrence of a continuous vector field $w$ of a closed connected surface $M$ as follows. The following are equivalent: 1) $w$ is pointwise recurrent. 2)$w$ is pointwise almost periodic.…
Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal…
We introduce a notion of harmonic chain for chain complexes over fields of positive characteristic. A list of conditions for when a Hodge decomposition theorem holds in this setting is given and we apply this theory to finite CW complexes.…
Capacitors are typically connected together in one of two configurations: either in series, or in parallel. Here we study a capacitor-within-capacitor (CWC). Simulations and experiments indicate that the overall capacitance of the…
In this paper, we establish the rationality conjecture raised in \cite{FKS} for any $(r-1)$-connected ($r\geq 2$) $kr$-dimensional CW-complex $X$ ($k\geq 2$) having a unique spherical cohomology class $u\in \tilde{H}^r(X, \mathbb{Z})$ such…
We reformulate the inequalities among self-closeness numbers of spaces in cofibrations making use of homology dimension and show that the self-closeness number of a space is less than or equal to the homology dimension of the space. Then we…
We provide first a categorical exploration of, and then completion of the mapping of the relationships among, three fundamental perspectives on binary relations: as the incidence matrices of hypergraphs, as the formal contexts of concept…