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We describe new spaces and maps. Our graphical map is a visual and numerical correspondence between spaces of circular electrical networks and circular planar split systems. When restricted to the planar circular electrical case, this…
This paper investigates the capacity of a wireless two way relay channel in which two end nodes exchange information via a relay node. The capacity is defined in the information-theoretic sense as the maximum information exchange rate…
Using the theory of resolving classes, we show that if $X$ is a CW complex of finite type such that $\map_*(X, S^{2n+1})\sim *$ for all sufficiently large $n$, then $\map_*(X, K) \sim *$ for every simply-connected finite-dimensional CW…
Macrochains of topologically interlocked rings with unique physical properties have recently gained considerable interest in supramolecular chemistry, biology, and soft matter. Most of the work has been, so far, focused on linear chains and…
(Pre)closure spaces are a generalization of topological spaces covering also the notion of neighbourhood in discrete structures, widely used to model and reason about spatial aspects of distributed systems. In this paper we introduce an…
In this study we want to connect our previously proposed context-relevant topographical maps with the deep learning community. Our architecture is a classifier with hidden layers that are hierarchical two-dimensional topographical maps.…
It is well known that for many semilinear parabolic equations there is a global attractor which has a cell complex structure with finite dimensional cells. Additionally, many semilinear parabolic equations have equilibria with finite…
Relevant to top-down ${\cal M}$-theory dual of large-$N$ thermal QCD-like theories at intermediate coupling, induced by the $G_2$ structure supported by the closed $M_7$ - a warped product of the ${\cal M}$-theory circle and a…
Metabolism is a fascinating cell machinery underlying life and disease and genome-scale reconstructions provide us with a captivating view of its complexity. However, deciphering the relationship between metabolic structure and function…
The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is…
This article introduces a theory of proximal nerve complexes and nerve spokes, restricted to the triangulation of finite regions in the Euclidean plane. A nerve complex is a collection of filled triangles with a common vertex, covering a…
The gap symmetries of superconductivity are studied in this work. It is found that the gap symmetries are simply determined by the 4-fold rotational symmetries of the coupling potential on neighbor sites. A local on-site coupling potential…
In the context of cellular networks, users located at the periphery of cells are particularly vulnerable to substantial interference from neighbouring cells, which can be represented as a two-user interference channel. This study introduces…
A recurrent neural network model storing multiple spatial maps, or ``charts'', is analyzed. A network of this type has been suggested as a model for the origin of place cells in the hippocampus of rodents. The extremely diluted and fully…
A brief history of the discovery of new superconductors is given. Different types of pairing mechanisms are considered. By comparing Tcs in different cuprate families it is concluded that the pairing in the CuO2 layers must be supplemented…
Complex networks are used to depict topological features of complex systems. The structure of a network characterizes the interactions among elements of the system, and facilitates the study of many dynamical processes taking place on it.…
Complex numbers have long been favoured for digital signal processing, yet complex representations rarely appear in deep learning architectures. RNNs, widely used to process time series and sequence information, could greatly benefit from…
Let X be a (connected and reduced) complex space. A q-collar of X is a bounded domain whose boundary is a union of a strongly q-pseudoconvex, a strongly q-pseudoncave and two flat (i.e. locally zero sets of pluriharmonic functions)…
The main purpose of this paper is to introduce a new smooth version of a CW complex named a fat CW complex, and to show that it includes all closed manifolds, because existing smooth versions of CW complexes (e.g. [Iwa22]) do not have such…
We introduce notions of {\it upper chernrank} and {\it even cup length} of a finite connected CW-complex and prove that {\it upper chernrank} is a homotopy invariant. It turns out that determination of {\it upper chernrank} of a space $X$…