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The steady-state degree of a chemical reaction network is the number of complex steady-states for generic rate constants and initial conditions. One way to bound the steady-state degree is through the mixed volume of the steady-state system…

We consider the downlink of a two-layer heterogeneous network, comprising macro cells (MCs) and small cells (SCs). The existing literature generally assumes independent placements of the access points (APs) in different layers; in contrast,…

Meeting the continued growth in data traffic volume, Dynamic Time Division Duplex (D-TDD) has been introduced as a solution to deal with the uplink (UL) and downlink (DL) traffic asymmetry, mainly observed for dense heterogeneous network…

In this work we give specific examples of competition models, with six and eight species, whose three-dimensional dynamics naturally leads to the formation of string networks with junctions, associated with regions that have a high…

Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…

As two major players in terrestrial wireless communications, Wi-Fi systems and cellular networks have different origins and have largely evolved separately. Motivated by the exponentially increasing wireless data demand, cellular networks…

We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatio-temporal dynamics on the range and strength of coupling, we uncover a…

To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein…

For solving unsteady hyperbolic conservation laws on cut cell meshes, the so called small cell problem is a big issue: one would like to use a time step that is chosen with respect to the background mesh and use the same time step on the…

We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…

We consider the downlink of a cellular network with multiple cells and multi-antenna base stations, including a realistic distance-dependent pathloss model, clusters of cooperating cells, and general "fairness" requirements. Beyond Monte…

Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However the investigation of their collective phenomena is only at its infancy. Here we…

The feasibility conditions of interference alignment (IA) are analyzed for reverse TDD systems, i.e., one cell operates as downlink (DL) but the other cell operates as uplink (UL). Under general multiple-input and multiple-output (MIMO)…

Balanced neural networks -- in which excitatory and inhibitory inputs compensate each other on average -- give rise to a dynamical phase dominated by fluctuations called asynchronous state, crucial for brain functioning. However, structural…

The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…

This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…

In this paper, the investigation is first motivated by showing two examples of simple regular symmetrical graphs, which have the same structural parameters, such as average distance, degree distribution and node betweenness centrality, but…

We consider infinite heterogeneous networks, consisting of input-to-state stable subsystems of possibly infinite dimension. We show that the network is input-to-state stable, provided that the gain operator satisfies a certain small-gain…

Chimera-like states are manifested through the coexistence of synchronous and asynchronous dynamics and have been observed in various systems. To analyze the role of network topology in giving rise to chimera-like states we study a…

Small cell networks with dynamic time-division duplex (D-TDD) have emerged as a potential solution to address the asymmetric traffic demands in 5G wireless networks. By allowing the dynamic adjustment of cell-specific UL/DL configuration,…