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We propose an optimization problem to minimize the base stations transmission powers in OFDMA heterogeneous networks, while respecting users' individual throughput demands. The decision variables are the users' working bandwidths, their association, and the base stations transmission powers. To deal with wireless channel uncertainty, the channel gains are treated as random variables respecting a log-normal distribution, leading to a non-convex chance constrained mixed-integer optimization problem, which is then formulated as a mixed-integer Robust Geometric Program. The efficacy of the proposed method is shown in a real-world scenario of a large European city.

Heterogeneous networks have emerged as a popular solution for accommodating the growing number of connected devices and increasing traffic demands in cellular networks. While offering broader coverage, higher capacity, and lower latency, the escalating energy consumption poses sustainability challenges. In this paper a novel optimization approach for OFDMA heterogeneous networks is proposed to minimize transmission power while respecting individual users throughput constraints. The problem is formulated as a mixed integer geometric program, and optimizes at once multiple system variables such as user association, working bandwidth, and base stations transmission powers. Crucially, the proposed approach becomes a convex optimization problem when user-base station associations are provided. Evaluations in multiple realistic scenarios from the production mobile network of a major European operator and based on precise channel gains and throughput requirements from measured data validate the effectiveness of the proposed approach. Overall, our original solution paves the road for greener connectivity by reducing the energy footprint of heterogeneous mobile networks, hence fostering more sustainable communication systems.

In this paper we present spin-to-charge current conversion properties in the Weyl semimetal TaP by means of the inverse Rashba-Edelstein effect (IREE) with the integration of this quantum material with the ferromagnetic metal Permalloy $(Py=Ni_{81}Fe_{19})$. The spin currents are generated in the Py layer by the spin pumping effect (SPE) from microwave-driven ferromagnetic resonance and are detected by a dc voltage along the TaP crystal, at room temperature. We observe a field-symmetric voltage signal without the contamination of asymmetrical lines due to spin rectification effects observed in studies using metallic ferromagnets. The observed voltage is attributed to spin-to-charge current conversion based on the IREE, made possible by the spin-orbit coupling induced intrinsically by the bulk band structure of Weyl semimetals. The measured IREE coefficient ${\lambda}_{IREE}=(0.30 \pm{0.01})$ nm is two orders of magnitude larger than in graphene and is comparable to or larger than the values reported for some metallic interfaces and for several topological insulators., Comment: 15 pages, 4 figures

Using kinetic Monte Carlo simulations, we develop a framework to relate morphological properties and microscopic dynamics during island growth, coalescence, and initial formation of continuous heteroepitaxial films. The average island width is controlled by adatom mobility on the substrate. Subsequent evolution strongly depends on the Ehrlich-Schw\"{o}ebel energy barrier $E_{ES}$ of the deposited material. As $E_{ES}$ decreases, islands becomes taller and their coalescence is delayed. For small islands and large $E_{ES}$, the global roughness increases as $W\sim{\text{thickness}}^{1/2}$ and the local roughness increases at short scales (apparent anomalous scaling) before and after island coalescence. If the islands are wide, $W$ may have a plateau for large $E_{ES}$ and has a maximum for small $E_{ES}$ when the islands coalesce. This framework is applied to atomic-force microscopy data of the initial stages of CdTe deposition on Kapton: a maximum of $W$ during island coalescence indicates negligible ES barrier, consistently with scaling properties of much thicker films, and the diffusion coefficient ${10}^{-7}{\text{--}}{10}^{-5}{\text{cm}}^2/{\text s}$ on the Kapton surface at $150\,^{\circ}\mathrm{C}$ is estimated. Applications of the framework to other materials are suggested, in which the expected roles of ES barriers are highlighted.

Let $k$ be a field of characteristic different from $2$ and let $G$ be a nonabelian residually torsion-free nilpotent group. It is known that $G$ is an orderable group. Let $k(G)$ denote the subdivision ring of the Malcev-Neumann series ring generated by the group algebra of $G$ over $k$. If $\ast$ is an involution on $G$, then it extends to a unique $k$-involution on $k(G)$. We show that $k(G)$ contains pairs of symmetric elements with respect to $\ast$ which generate a free group inside the multiplicative group of $k(G)$. Free unitary pairs also exist if $G$ is torsion-free nilpotent. Finally, we consider the general case of a division ring $D$, with a $k$-involution $\ast$, containing a normal subgroup $N$ in its multiplicative group, such that $G \subseteq N$, with $G$ a nilpotent-by-finite torsion-free subgroup that is not abelian-by-finite, satisfying $G^{*}=G$ and $N^{*}=N$. We prove that $N$ contains a free symmetric pair., Comment: 14 pages

The Kardar-Parisi-Zhang (KPZ) class is a paradigmatic example of universality in nonequilibrium phenomena, but clear experimental evidences of asymptotic 2D-KPZ statistics are still very rare, and far less understanding stems from its short-time behavior. We tackle such issues by analyzing surface fluctuations of CdTe films deposited on polymeric substrates, based on a huge spatio-temporal surface sampling acquired through atomic force microscopy. A \textit{pseudo}-steady state (where average surface roughness and spatial correlations stay constant in time) is observed at initial times, persisting up to deposition of $\sim 10^{4}$ monolayers. This state results from a fine balance between roughening and smoothening, as supported by a phenomenological growth model. KPZ statistics arises at long times, thoroughly verified by universal exponents, spatial covariance and several distributions. Recent theoretical generalizations of the Family-Vicsek scaling and the emergence of log-normal distributions during interface growth are experimentally confirmed. These results confirm that high vacuum vapor deposition of CdTe constitutes a genuine 2D-KPZ system, and expand our knowledge about possible substrate-induced short-time behaviors., Comment: 13 pages, 8 figures, 2 tables

In this letter, we have constructed and experimentally investigated frustrated arrays of dipoles forming two-dimensional artificial spin ices with different lattice parameters (rectangular arrays with horizontal and vertical lattice spacings denoted by $a$ and $b$ respectively). Arrays with three different ratios $\gamma =a/b = \sqrt{2}$, $\sqrt{3}$ and $\sqrt{4}$ are studied. Theoretical calculations of low-energy demagnetized configurations for these same parameters are also presented. Experimental data for demagnetized samples confirm most of the theoretical results. However, the highest energy topology (doubly-charged monopoles) does not emerge in our theoretical model, while they are seen in experiments for large enough $\gamma$. Our results also insinuate that magnetic monopoles may be almost free in rectangular lattices with a critical ratio $\gamma = \gamma_{c} = \sqrt{3}$, supporting previous theoretical predictions.

Some general criteria to produce explicit free algebras inside the division ring of fractions of skew polynomial rings are presented. These criteria are applied to some special cases of division rings with natural involutions, yielding, for instance, free subalgebras generated by symmetric elements both in the division ring of fractions of the group algebra of a torsion free nilpotent group and in the division ring of fractions of the first Weyl algebra., Comment: 11 pages