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Direct calculation of cryo-EM and crystallographic model maps for real-space refinement

ACTA CRYSTALLOGRAPHICA SECTION D-STRUCTURAL BIOLOGY 2022年第12期78卷 1451-1468页

作者： Urzhumtsev, Alexandre G. Urzhumtseva, Ludmila M. Lunin, Vladimir Y. UdS Inst Genet & Biol Mol & Cellulaire Ctr Integrat Biol CNRSINSERM 1 Rue Laurent FriesBP 10142 F-67404 Illkirch Graffenstaden France Univ Lorraine Fac Sci & Technol BP 239 F-54506 Vandoeuvre Les Nancy France IBMC Inst Mol & Cellular Biol CNRS Architecture & Reactivite ARN UPR 9002 15 Rue R Descartes F-67084 Strasbourg France Univ Strasbourg F-67000 Strasbourg France RAS Keldysh Inst Appl Math Inst Math Problems Biol Pushchino 142290 Russia

This work addresses the problem of the calculation of limited-resolution maps from an atomic model in cryo-electron microscopy and in X-ray and neutron crystallography, including cases where the resolution varies from one molecular region to another. Such maps are necessary in real-space refinement for comparison with the experimental maps. For an appropriate numeric comparison, the calculated maps should reproduce not only the structural features contained in the experimental maps but also the principal map distortions. These model maps can be obtained with no use of Fourier transforms but, similar to density distributions, as a sum of individual atomic contributions. Such contributions, referred to as atomic density images, are atomic densities morphed to reflect distortions of the experimental map, in particular the loss of resolution. They are described by functions composed of a central peak surrounded by Fourier ripples. For practical calculations, atomic images should be cut at some distance. It is shown that to reach a reasonable accuracy such a distance should be significantly larger than the distance customarily applied when calculating density distributions. This is a consequence of the slow rate with which the amplitude of the Fourier ripples decreases. Such a large distance means that at least a few ripples should be included in calculations in order to obtain a map that is sufficiently accurate. Oscillating functions describing these atomic contributions depend, for a given atomic type, on the resolution and on the atomic displacement parameter values. To express both the central peak and the Fourier ripples of the atomic images, these functions are represented by the sums of especially designed terms, each concentrated in a spherical shell and depending analytically on the atomic parameters. In this work, the strength of the dependence of the accuracy of resulting map on the accuracy of the atomic displacement parameters and on the truncation distance

关键词： real-space refinement map calculation atomic images Fourier ripples truncation distances resolution atomic displacement parameters shell decomposition interference functions

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Connections Between Spectral Properties of Asymptotic Mappings and Solutions to Wireless Network Problems

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2019年第10期67卷 2747-2760页

作者： Cavalcante, Renato L. G. Liao, Qi Stanczak, Slawomir Tech Univ Berlin Fraunhofer Heinrich Hertz Inst D-10623 Berlin Germany Nokia Bell Labs D-70435 Stuttgart Germany

In this study, we establish connections between asymptotic functions and properties of solutions to important problems in wireless networks. We start by introducing a class of self-mappings (called asymptotic mappings) constructed with asymptotic functions, and we show that spectral properties of these mappings explain the behavior of solutions to some max-min utility optimization problems. For example, in a common family of max-min utility power control problems, we prove that the optimal utility as a function of the power available to transmitters is approximately linear in the low power regime. However, as we move away from this regime, there exists a transition point, easily computed from the spectral radius of an asymptotic mapping, from which gains in utility become increasingly marginal. From these results we derive analogous properties of the transmit energy efficiency. In this study, we also generalize and unify existing approaches for feasibility analysis in wireless networks. Feasibility problems often reduce to determining the existence of the fixed point of a standard interference mapping, and we show that the spectral radius of an asymptotic mapping provides a necessary and sufficient condition for the existence of such a fixed point. We further present a result that determines whether the fixed point satisfies a constraint given in terms of a monotone norm.

关键词： Utility optimization fixed point algorithms interference functions asymptotic mappings nonconvex optimization power control interference management

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FIXED POINT ITERATION FOR MAX-MIN SIR BALANCING WITH GENERAL interference functions

FIXED POINT ITERATION FOR MAX-MIN SIR BALANCING WITH GENERAL...

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Vucic, Nikola Schubert, Martin Fraunhofer German Sino Lab Mobile Commun MCI D-10587 Berlin Germany

ISBN: (纸本)9781457705397

This paper studies the convergence of a fixed point iteration algorithm for the problem of max-min signal-to-interference ratio (SIR) balancing. Differently from the existing work on the subject, the interference in the system is assumed to fall into the axiomatic framework of general interference functions. Monotonicity of the extremal SIR values during the iterations of the algorithm is shown. In the case of strictly monotonic interference functions, a novel sufficient condition for the convergence of the algorithm to an optimal solution is derived. The obtained condition is easily verifiable, and presents a generalization of a related requirement for the power method from matrix analysis. It is also shown how the results transfer to the power-constrained case and standard interference functions.

关键词： interference management power control fixed point iteration interference functions power method

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Coordinate Update Algorithms for Robust Power Loading for the MU-MISO Downlink With Outage Constraints

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2016年第11期64卷 2761-2773页

作者： Sohrabi, Foad Davidson, Timothy N. McMaster Univ Dept Elect & Comp Engn Hamilton ON L8S 4K1 Canada Univ Toronto Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada

We consider the problem of power allocation for the single-cell multi-user (MU) multiple-input single-output (MISO) downlink with quality-of-service (QoS) constraints. The base station acquires an estimate of the channels and, for a given beam-forming structure, designs the power allocation so as to minimize the total transmission power required to ensure that target signal-to-interference-and-noise ratios at the receivers are met, subject to a specified outage probability. We consider scenarios in which the errors in the base station's channel estimates can be modelled as being zero-mean and Gaussian. Such a model is particularly suitable for time division duplex (TDD) systems with quasi-static channels, in which the base station estimates the channel during the uplink phase. Under that model, we employ a precise deterministic characterization of the outage probability to transform the chance-constrained formulation to a deterministic one. Although that deterministic formulation is not convex, we develop a coordinate descent algorithm that can be shown to converge to a globally optimal solution when the starting point is feasible. Insight into the structure of the deterministic formulation yields approximations that result in coordinate update algorithms with good performance and significantly lower computational cost. The proposed algorithms provide better performance than existing robust power loading algorithms that are based on tractable conservative approximations and can even provide better performance than robust precoding algorithms based on such approximations.

关键词： Broadcast channel downlink beamforming robust power loading chance constraints interference functions

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Stability and Performance of Continuous-Time Power Control in Wireless Networks

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2014年第8期59卷 2012-2023页

作者： Feyzmahdavian, Hamid Reza Charalambous, Themistoklis Johansson, Mikael KTH Royal Inst Technol Dept Automat Control ACCESS Linnaeus Ctr Sch Elect Engn SE-10044 Stockholm Sweden

This paper develops a comprehensive stability analysis framework for general classes of continuous-time power control algorithms under heterogeneous time-varying delays. Our first set of results establish global asymptotic stability of power control laws involving two-sided scalable interference functions, and include earlier work on standard interference functions as a special case. We then consider contractive interference functions and demonstrate that the associated continuous-time power control laws always have unique fixed points which are exponentially stable, even under bounded heterogeneous time-varying delays. For this class of interference functions, we present explicit bounds on the decay rate that allow us to quantify the impact of delays on the convergence time of the algorithm. When interference functions are linear, we also prove that contractivity is necessary and sufficient for exponential stability of continuous-time power control algorithms with time-varying delays. Finally, numerical simulations illustrate the validity of our theoretical results.

关键词： interference functions positive systems power control time-varying delays wireless networks

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The Structure of General interference functions and Applications

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IEEE TRANSACTIONS ON INFORMATION THEORY 2008年第11期54卷 4980-4990页

作者： Boche, Holger Schubert, Martin Heinrich Hertz Inst Nachrichtentech Berlin GmbH Fraunhofer Inst Telecommun D-10587 Berlin Germany Fraunhofer German Sino Lab Mobile Commun MCI D-10587 Berlin Germany Tech Univ Berlin D-10587 Berlin Germany

This paper provides a theoretical framework for the analysis of interference-coupled multiuser systems. The fundamental behavior of such a system is modeled by interference functions, defined by axioms "nonnegativity, "scale-invariance" and "monotonicity." It is shown that every interference function has an interpretation as the optimum of a min-max problem, where the optimization is over a closed comprehensive positive coefficient set. This provides new insight into the structure of general interference functions and its elementary building blocks. Conversely, it is shown that every closed comprehensive positive set can be expressed as a level set of an interference function. This shows a close connection between the analysis of interference functions and multiuser performance regions, which are typically closed comprehensive. The generality of this framework allows for a wide range of potential applications. As an example, we analyze the problem of interference balancing.

关键词： Feasible set interference functions multiuser interference power control wireless communications

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ADMISSION CONTROL FOR AUTONOMOUS WIRELESS LINKS WITH POWER CONSTRAINTS

ADMISSION CONTROL FOR AUTONOMOUS WIRELESS LINKS WITH POWER C...

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2010 IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Kaliszan, Michal Stanczak, Slawomir Bambos, Nicholas Mobile Commun MCI Fraunhofer German Sino Lab Einsteinufer 37 D-10587 Berlin Germany Stanford Univ Dept Elect Engn Stanford CA 94305 USA

ISBN: (纸本)9781424442966

An admission control algorithm for power-controlled wireless networks, proposed previously for the case of linear interference functions, is considered in this paper. We analyze the properties of the algorithm using the framework of standard interference functions, which makes it applicable to many system designs. Furthermore, we introduce individual power constraints into the system. The key property of the algorithm is the protection of active users, which guarantees that as new users attempt to join the network, the quality of the established links is sustained. We present conditions under which this key property is preserved under power constraints and analyze the convergence properties of the scheme.

关键词： Admission control power control interference functions cognitive radio

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ADMISSION CONTROL FOR AUTONOMOUS WIRELESS LINKS WITH POWER CONSTRAINTS

ADMISSION CONTROL FOR AUTONOMOUS WIRELESS LINKS WITH POWER C...

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IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Michal Kaliszan Slawomir Stanczak Nicholas Bambos Fraunhofer German-Sino Lab for Mobile Communications MCI Einsteinufer 37 10587 Berlin/Germany Department of Electrical Engineering 350 Serra Mall Stanford University Stanford CA 94305

ISBN: (纸本)9781424442959

关键词： Admission control power control interference functions cognitive radio Admission control Power control Cognitive radio Individual Power Constraint Standing Orders

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A Tractable Method for Chance-Constrained Power Control in Downlink Multiuser MISO Systems With Channel Uncertainty

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IEEE SIGNAL PROCESSING LETTERS 2009年第5期16卷 346-349页

作者： Vucic, Nikola Boche, Holger Heinrich Hertz Inst Nachrichtentech Berlin GmbH Fraunhofer Inst Telecommun D-10587 Berlin Germany Tech Univ Berlin Heinrich Hertz Chair Mobile Commun D-10587 Berlin Germany

We consider a downlink wireless system with a multi-antenna base station (BS) and single-antenna users. The error in the channel knowledge at the BS is assumed to have Gaussian distribution. Power allocation strategies are designed in order to satisfy the users' quality-of-service targets with certain probabilities. Conservative solutions of the problems are found by applying the Vysochanskii-Petunin inequality in combination with the theory of interference functions. Significant performance improvements are obtained comparing with methods based on the worst-case optimization.

关键词： Imperfect channel knowledge interference functions multiple-antenna systems stochastic programming

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Convergence of Distributed Power Control with Full-Duplex Amplify-and-Forward Relays

Convergence of Distributed Power Control with Full-Duplex Am...

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International Conference on Wireless Communications and Signal Processing

作者： Song, Young-Keum Kim, Dongwoo Hanyang Univ Dept Elect Engn & Comp Sci Ansan 426791 South Korea

ISBN: (纸本)9781424448562

In this paper, we introduce a power control algorithm for cooperative cellular networks consisting of multiple sources, multiple full-duplex amplify-and-forward relays, and a destination. The objective of this algorithm is to allocate the available power of each source so that it can achieve the required transmission quality. The full-duplex relays receive the signal amplified by themselves and re-amplify it sequentially. We derive the SINR and interference function, and then a simplified analysis of convergence is given by using a standard techniques. We evaluate the power controlled system in terms of the outage probability as well as the average power consumption, and compare it with the system without a relay and with half-duplex relays, respectively. The simulation results illustrates potential advantages of the power controlled system with full-duplex relays, the performance of which is limited by an isolation factor.

关键词： Power control full duplex distributed algorithm standard techniques convergence interference functions

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