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31 pages, 1361 KB

Open AccessArticle

Ground User Clustering for Adaptive Multibeam GEO Satellite Networks

by Heba Shehata, Hazer Inaltekin and Iain B. Collings

Sensors 2026, 26(8), 2384; https://doi.org/10.3390/s26082384 - 13 Apr 2026

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This paper considers geometry-aware ground user clustering and Cluster Center Optimization for beam pointing and scheduling in adaptive multibeam Geostationary Earth Orbit (GEO) satellite networks. By grouping ground users, beams can be directed toward user clusters to maximize satellite throughput. We propose GeoClust, a polynomial-time geometric user clustering algorithm for adaptive multibeam GEO satellite networks, using a geometric set-cover approach that explicitly balances link signal-to-interference-plus-noise ratio (SINR) and hopping overhead. The algorithm employs a Boyle–Dykstra projection-based cluster center update within an alternating optimization framework, combined with nearest-center membership updates, to enforce the cluster-radius constraint while ensuring feasibility and provable convergence. It also achieves near-linear throughput scaling with increasing number of RF chains. Numerical evaluations on real-world population data show that, under heavy traffic conditions, our approach more than doubles the zero outage and median user rates compared to benchmark schemes. Full article

(This article belongs to the Special Issue Feature Papers in Communications Section 2025–2026)

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10 pages, 927 KB

Open AccessArticle

On-Line Prediction of the Quantum Density Matrix

by Mehrzad Soltani and Mark J. Balas

Quantum Rep. 2026, 8(1), 1; https://doi.org/10.3390/quantum8010001 - 22 Dec 2025

Viewed by 1188

Abstract

Time evolution of open quantum systems is governed by the master equation. The master equation, which is a matrix formalism, is the time derivative of the density matrix, which contains the complete information on the state of a quantum system. Instead of implementing successive measurements on repeated identically prepared systems, which are inevitably imperfect and can only be performed a limited number of times, a state estimator can be designed to obtain the whole information about the state of a quantum system represented in a density matrix. Trace-one and positive semi-definite properties of the density matrix arising from physical constraints have to be preserved during state estimation in quantum systems. To address this challenge, we present a projection technique that incorporates Dykstra’s algorithm and physical constraints into state estimation. This technique, which is an iterative method, ensures convergence and includes a designed oracle that projects the estimated state into intersections of admissible closed convex sets. The oracle structure is constructed using Hilbert projection, which looks for the best approximation of the projected estimated state within a Hilbert space into a closed convex set. According to the Hilbert projection theorem, this proposed oracle guarantees the existence and uniqueness of the best approximation of the projected state. Full article

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24 pages, 821 KB

Open AccessFeature PaperArticle

Stochastic Proximal Gradient Algorithms for Multi-Source Quantitative Photoacoustic Tomography

by Simon Rabanser, Lukas Neumann and Markus Haltmeier

Entropy 2018, 20(2), 121; https://doi.org/10.3390/e20020121 - 11 Feb 2018

Cited by 10 | Viewed by 5785

Abstract

The development of accurate and efficient image reconstruction algorithms is a central aspect of quantitative photoacoustic tomography (QPAT). In this paper, we address this issues for multi-source QPAT using the radiative transfer equation (RTE) as accurate model for light transport. The tissue parameters are jointly reconstructed from the acoustical data measured for each of the applied sources. We develop stochastic proximal gradient methods for multi-source QPAT, which are more efficient than standard proximal gradient methods in which a single iterative update has complexity proportional to the number applies sources. Additionally, we introduce a completely new formulation of QPAT as multilinear (MULL) inverse problem which avoids explicitly solving the RTE. The MULL formulation of QPAT is again addressed with stochastic proximal gradient methods. Numerical results for both approaches are presented. Besides the introduction of stochastic proximal gradient algorithms to QPAT, we consider the new MULL formulation of QPAT as main contribution of this paper. Full article

(This article belongs to the Special Issue Probabilistic Methods for Inverse Problems)

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