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In this paper we consider the problem of communication scheduling in wireless networks with respect to the SINR(Signal to Interference plus Noise Ratio) constraint in metric spaces. The nodes are assigned linear powers, i.e. for each sender…
Recent empirical investigations suggest a universal scaling law for the spatial structure of social networks. It is found that the probability density distribution of an individual to have a friend at distance $d$ scales as $P(d)\propto…
Many engineered systems, such as energy and transportation infrastructures, are networks governed by non-linear physical laws. A primary challenge for operators of these networks is to achieve optimal utilization while maintaining safety…
We propose to optimize the activation functions of a deep neural network by adding a corresponding functional regularization to the cost function. We justify the use of a second-order total-variation criterion. This allows us to derive a…
In this work, we conduct a comparative study on two deep unfolding mechanisms to efficiently perform power control in the next generation wireless networks. The power control problem is formulated as energy efficiency over multiple…
The support of a flow $x$ in a network is the subdigraph induced by the arcs $uv$ for which $x(uv)>0$. We discuss a number of results on flows in networks where we put certain restrictions on structure of the support of the flow. Many of…
Let $c_n = c_n(d)$ denote the number of self-avoiding walks of length $n$ starting at the origin in the Euclidean nearest-neighbour lattice $\mathbb{Z}^d$. Let $\mu = \lim_n c_n^{1/n}$ denote the connective constant of $\mathbb{Z}^d$. In…
The AC Optimal Power Flow (AC-OPF) is a key building block in many power system applications. It determines generator setpoints at minimal cost that meet the power demands while satisfying the underlying physical and operational…
Non-orthogonal multiple access (NOMA) is considered as one of the predominant multiple access technique for the next-generation cellular networks. We consider a 2-user pair downlink NOMA system with imperfect successive interference…
Given the dynamic nature of traffic, we investigate the variant of robust network design where we have to determine the capacity to reserve on each link so that each demand vector belonging to a polyhedral set can be routed. The objective…
Rapid technological advances in the domain of Wireless Power Transfer (WPT) pave the way for novel methods for power management in systems of wireless devices and recent research works have already started considering algorithmic solutions…
In [Q. Liao et al., Commun. Math. Sci., 20(2022)], a linear-time Sinkhorn algorithm is developed based on dynamic programming, which significantly reduces the computational complexity involved in solving optimal transport problems. However,…
The degree distributions of many real world networks follow power-laws whose exponents tend to fall between two and three. Within the framework of the Barabasi-Albert model (BA model), we explain this empirical observation by a simple fact.…
This paper examines the behavior of the price of anarchy as a function of the traffic inflow in nonatomic congestion games with multiple origin-destination (O/D) pairs. Empirical studies in real-world networks show that the price of anarchy…
The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a…
We address the problem of interference management and power control in terms of maximization of a general utility function. For the utility functions under consideration, we propose a power control algorithm based on a fixed-point…
When data is plentiful, the loss achieved by well-trained neural networks scales as a power-law $L \propto N^{-\alpha}$ in the number of network parameters $N$. This empirical scaling law holds for a wide variety of data modalities, and may…
Solving the shortest path and the min-cut problems are key in achieving high performance and robust communication networks. Those problems have often beeny studied in deterministic and independent networks both in their original…
We prove discrete-to-continuum convergence for dynamical optimal transport on $\mathbb{Z}^d$-periodic graphs with energy density having linear growth at infinity. This result provides an answer to a problem left open by Gladbach, Kopfer,…
We study temporal logics and automata on multi-attributed data words. Recently, BD-LTL was introduced as a temporal logic on data words extending LTL by navigation along positions of single data values. As allowing for navigation wrt.…