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Search Results (548)

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Keywords = asymptotic convergence

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19 pages, 1771 KiB  
Article
Steady Radial Diverging Flow of a Particle-Laden Fluid with Particle Migration
by C. Q. Ru
Fluids 2025, 10(8), 200; https://doi.org/10.3390/fluids10080200 - 1 Aug 2025
Abstract
The steady plane radial diverging flow of a viscous or inviscid particle-fluid suspension is studied using a novel two-fluid model. For the initial flow field with a uniform particle distribution, our results show that the relative velocity of particles with respect to the [...] Read more.
The steady plane radial diverging flow of a viscous or inviscid particle-fluid suspension is studied using a novel two-fluid model. For the initial flow field with a uniform particle distribution, our results show that the relative velocity of particles with respect to the fluid depends on their inlet velocity ratio at the entrance, the mass density ratio and the Stokes number of particles, and the particles heavier (or lighter) than the fluid will move faster (or slower) than the fluid when their inlet velocities are equal (then Stokes drag vanishes at the entrance). The relative motion of particles with respect to the fluid leads to particle migration and the non-uniform distribution of particles. An explicit expression is obtained for the steady particle distribution eventually attained due to particle migration. Our results demonstrated and confirmed that, for both light particles (gas bubbles) and heavy particles, depending on the particle-to-fluid mass density ratio, the volume fraction of particles attains its maximum or minimum value near the entrance of the radial flow and after then monotonically decreases or increases with the radial coordinate and converges to an asymptotic value determined by the particle-to-fluid inlet velocity ratio. Explicit solutions given here could help quantify the steady particle distribution in the decelerating radial flow of a particle-fluid suspension. Full article
(This article belongs to the Special Issue 10th Anniversary of Fluids—Recent Advances in Fluid Mechanics)
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19 pages, 503 KiB  
Article
Dynamic Value at Risk Estimation in Multi-Functional Volterra Time-Series Model (MFVTSM)
by Fatimah A. Almulhim, Mohammed B. Alamari, Ali Laksaci and Mustapha Rachdi
Symmetry 2025, 17(8), 1207; https://doi.org/10.3390/sym17081207 - 29 Jul 2025
Viewed by 188
Abstract
In this paper, we aim to provide a new algorithm for managing financial risk in portfolios containing multiple high-volatility assets. We assess the variability of volatility with the Volterra model, and we construct an estimator of the Value-at-Risk (VaR) function using quantile regression. [...] Read more.
In this paper, we aim to provide a new algorithm for managing financial risk in portfolios containing multiple high-volatility assets. We assess the variability of volatility with the Volterra model, and we construct an estimator of the Value-at-Risk (VaR) function using quantile regression. Because of its long-memory property, the Volterra model is particularly useful in this domain of financial time series data analysis. It constitutes a good alternative to the standard approach of Black–Scholes models. From the weighted asymmetric loss function, we construct a new estimator of the VaR function usable in Multi-Functional Volterra Time Series Model (MFVTSM). The constructed estimator highlights the multi-functional nature of the Volterra–Gaussian process. Mathematically, we derive the asymptotic consistency of the estimator through the precision of the leading term of its convergence rate. Through an empirical experiment, we examine the applicability of the proposed algorithm. We further demonstrate the effectiveness of the estimator through an application to real financial data. Full article
(This article belongs to the Section Mathematics)
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7 pages, 263 KiB  
Proceeding Paper
Recent Progress on Conjecture O and Its Variants: A Survey
by Xiaobin Li, Yuhui Peng, Yamin Xu and Bin Zhu
Proceedings 2025, 123(1), 2; https://doi.org/10.3390/proceedings2025123002 - 28 Jul 2025
Viewed by 64
Abstract
Conjecture O (and the Gamma Conjectures), introduced by Galkin, Golyshev, and Iritani stand as pivotal open problems in the quantum cohomology of Fano manifolds, bridging algebraic geometry, mathematical physics, and representation theory. These conjectures aim to decode the structural essence of quantum multiplication [...] Read more.
Conjecture O (and the Gamma Conjectures), introduced by Galkin, Golyshev, and Iritani stand as pivotal open problems in the quantum cohomology of Fano manifolds, bridging algebraic geometry, mathematical physics, and representation theory. These conjectures aim to decode the structural essence of quantum multiplication by uncovering profound connections between spectral properties of quantum cohomology operators and the underlying geometry of Fano manifolds. Conjecture O specifically investigates the spectral simplicity and eigenvalue distribution of the operator associated with the first Chern class c1 in quantum cohomology rings, positing that its eigenvalues govern the convergence and asymptotic behavior of quantum products. Full article
(This article belongs to the Proceedings of The 5th International Conference on Symmetry (Symmetry 2025))
20 pages, 768 KiB  
Article
Convergence and Stability of the Truncated Stochastic Theta Method for McKean-Vlasov Stochastic Differential Equations Under Local Lipschitz Conditions
by Hongxia Chu, Haiyan Yuan and Quanxin Zhu
Mathematics 2025, 13(15), 2433; https://doi.org/10.3390/math13152433 - 28 Jul 2025
Viewed by 93
Abstract
This paper focuses on McKean-Vlasov stochastic differential equations under local Lipschitz conditions. We first introduce the stochastic interacting particle system and prove the propagation of chaos. Then we establish a truncated stochastic theta scheme to approximate the interacting particle system and obtain the [...] Read more.
This paper focuses on McKean-Vlasov stochastic differential equations under local Lipschitz conditions. We first introduce the stochastic interacting particle system and prove the propagation of chaos. Then we establish a truncated stochastic theta scheme to approximate the interacting particle system and obtain the strong convergence of the continuous-time truncated stochastic theta scheme to the non-interacting particle system. Furthermore, we study the asymptotical mean square stability of the interacting particle system and the truncated stochastic theta method. Finally, we give one numerical example to verify our theoretical results. Full article
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15 pages, 3131 KiB  
Article
Real-Time Experiments for Decentralized Adaptive Synchronized Motion Control of a Closed-Kinematic Chain Mechanism Robot Manipulator
by Charles C. Nguyen, Tri T. Nguyen, Tu T. C. Duong, Tuan M. Nguyen, Ha T. T. Ngo and Lu Sun
Machines 2025, 13(8), 652; https://doi.org/10.3390/machines13080652 - 25 Jul 2025
Viewed by 193
Abstract
This paper presents the results of real-time experiments conducted to evaluate the performance of a developed adaptive control scheme applied to control the motion of a real closed-kinematic chain mechanism (CKCM) robot manipulator with two degrees of freedom (DOFs). The developed control scheme, [...] Read more.
This paper presents the results of real-time experiments conducted to evaluate the performance of a developed adaptive control scheme applied to control the motion of a real closed-kinematic chain mechanism (CKCM) robot manipulator with two degrees of freedom (DOFs). The developed control scheme, referred to as the decentralized adaptive synchronized control scheme (DASCS), was the result of the combination of model reference adaptive control (MRAC) based on the Lyapunov direct method and the synchronization technique. CKCM manipulators were considered in the experimental study due to their advantages over their open-kinematic chain mechanism (OKCM) manipulator counterparts, such as higher stiffness, better stability, and greater payload. The conducted computer simulation study showed that the DASCS was able to asymptotically converge tracking errors to zero, with all the active joints moving synchronously in a prescribed way. One of the important properties of the DASCS is the independence of robot manipulator dynamics, making it computationally efficient and therefore suitable for real-time applications. The present paper reports findings from experiments in which the DASCS was applied to control the above manipulator and carry out various paths. The DASCS’s performance was compared with that of a traditional adaptive control scheme, namely the SMRACS, when both schemes were applied to track the same paths. Full article
(This article belongs to the Section Automation and Control Systems)
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18 pages, 6211 KiB  
Article
Managing Redundancy in a Multiple-Robot Orienteering Problem for Equilibrium and Robustness
by Zengzhen Mi, Tong Jiang, Wenwen Leng and Yuchengzhi Lei
Appl. Sci. 2025, 15(15), 8217; https://doi.org/10.3390/app15158217 - 24 Jul 2025
Viewed by 203
Abstract
In our work, the Robust Multiple-robot Orienteering Problem with Workload Balancing is constructed for the first time. Our primary contribution lies in the rigorous formulation of this problem as a three-stage optimization task. It leverages the Robust Multiple-robot Orienteering Problem (RMOP) as the [...] Read more.
In our work, the Robust Multiple-robot Orienteering Problem with Workload Balancing is constructed for the first time. Our primary contribution lies in the rigorous formulation of this problem as a three-stage optimization task. It leverages the Robust Multiple-robot Orienteering Problem (RMOP) as the initial stage. The Path Replanning stage and the workload balancing stage are introduced to minimize walk redundancy and achieve workload equilibrium. The resultant solution upholds the optimality inherent to the original RMOP. Additionally, we craft a suite of heuristic strategies to mitigate redundancy and employ Monte Carlo sampling to tackle the problem. Our algorithm analysis indicates that the method has asymptotic convergence properties and a feasible time complexity under certain conditions. Local parallelization of the algorithm can further improve its performance. Our simulation studies demonstrate that our approach can efficaciously attain a balance between robustness and workload without compromising performance in the presence of adversarial challenges. Full article
(This article belongs to the Special Issue Embodied Intelligence and Its Application in Robotics)
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25 pages, 1507 KiB  
Article
DARN: Distributed Adaptive Regularized Optimization with Consensus for Non-Convex Non-Smooth Composite Problems
by Cunlin Li and Yinpu Ma
Symmetry 2025, 17(7), 1159; https://doi.org/10.3390/sym17071159 - 20 Jul 2025
Viewed by 206
Abstract
This paper proposes a Distributed Adaptive Regularization Algorithm (DARN) for solving composite non-convex and non-smooth optimization problems in multi-agent systems. The algorithm employs a three-phase iterative framework to achieve efficient collaborative optimization: (1) a local regularized optimization step, which utilizes proximal mappings to [...] Read more.
This paper proposes a Distributed Adaptive Regularization Algorithm (DARN) for solving composite non-convex and non-smooth optimization problems in multi-agent systems. The algorithm employs a three-phase iterative framework to achieve efficient collaborative optimization: (1) a local regularized optimization step, which utilizes proximal mappings to enforce strong convexity of weakly convex objectives and ensure subproblem well-posedness; (2) a consensus update based on doubly stochastic matrices, guaranteeing asymptotic convergence of agent states to a global consensus point; and (3) an innovative adaptive regularization mechanism that dynamically adjusts regularization strength using local function value variations to balance stability and convergence speed. Theoretical analysis demonstrates that the algorithm maintains strict monotonic descent under non-convex and non-smooth conditions by constructing a mixed time-scale Lyapunov function, achieving a sublinear convergence rate. Notably, we prove that the projection-based update rule for regularization parameters preserves lower-bound constraints, while spectral decay properties of consensus errors and perturbations from local updates are globally governed by the Lyapunov function. Numerical experiments validate the algorithm’s superiority in sparse principal component analysis and robust matrix completion tasks, showing a 6.6% improvement in convergence speed and a 51.7% reduction in consensus error compared to fixed-regularization methods. This work provides theoretical guarantees and an efficient framework for distributed non-convex optimization in heterogeneous networks. Full article
(This article belongs to the Section Mathematics)
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21 pages, 962 KiB  
Article
Modal Regression Estimation by Local Linear Approach in High-Dimensional Data Case
by Fatimah A. Almulhim, Mohammed B. Alamari, Ali Laksaci and Zoulikha Kaid
Axioms 2025, 14(7), 537; https://doi.org/10.3390/axioms14070537 - 16 Jul 2025
Viewed by 165
Abstract
This paper introduces a new nonparametric estimator for detecting the conditional mode in the functional input variable setting. The estimator integrates a local linear approach with an L1-robust algorithm and treats the modal regression as the minimizer of the quantile derivative. [...] Read more.
This paper introduces a new nonparametric estimator for detecting the conditional mode in the functional input variable setting. The estimator integrates a local linear approach with an L1-robust algorithm and treats the modal regression as the minimizer of the quantile derivative. As an asymptotic result, we derive the theoretical properties of the estimator by analyzing its convergence rate under the almost complete consistency framework. The result is stated under standard conditions, characterizing both the functional structure of the data and the local linear approximation properties of the model. Moreover, the expression of the convergence rate retains the usual form of the stochastic convergence rate in functional statistics. Simulations and real-data applications demonstrate the algorithm’s effectiveness, showing its advantage over existing methods in high-dimensional prediction tasks. Full article
(This article belongs to the Special Issue Advances in Statistical Simulation and Computing)
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23 pages, 1065 KiB  
Article
Modeling and Neural Network Approximation of Asymptotic Behavior for Delta Fractional Difference Equations with Mittag-Leffler Kernels
by Pshtiwan Othman Mohammed, Muteb R. Alharthi, Majeed Ahmad Yousif, Alina Alb Lupas and Shrooq Mohammed Azzo
Fractal Fract. 2025, 9(7), 452; https://doi.org/10.3390/fractalfract9070452 - 9 Jul 2025
Viewed by 318
Abstract
The asymptotic behavior of discrete Riemann–Liouville fractional difference equations is a fundamental problem with important mathematical and physical implications. In this paper, we investigate a particular case of such an equation of the order 0.5 subject to a given initial condition. We establish [...] Read more.
The asymptotic behavior of discrete Riemann–Liouville fractional difference equations is a fundamental problem with important mathematical and physical implications. In this paper, we investigate a particular case of such an equation of the order 0.5 subject to a given initial condition. We establish the existence of a unique solution expressed via a Mittag-Leffler-type function. The delta-asymptotic behavior of the solution is examined, and its convergence properties are rigorously analyzed. Numerical experiments are conducted to illustrate the qualitative features of the solution. Furthermore, a neural network-based approximation is employed to validate and compare with the analytical results, confirming the accuracy, stability, and sensitivity of the proposed method. Full article
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31 pages, 417 KiB  
Article
On the Properties of Iterations Generated with Composition Maps of Cyclic Contractive Self-Mappings and Strict Contractions in Metric Spaces
by Manuel De la Sen
Mathematics 2025, 13(14), 2224; https://doi.org/10.3390/math13142224 - 8 Jul 2025
Viewed by 196
Abstract
This paper studies the convergence of distances between sequences of points and that of sequences of points in metric spaces. This investigation is focused on the iterative processes built with composed self-mappings of a cyclic contraction, which can involve more than two nonempty [...] Read more.
This paper studies the convergence of distances between sequences of points and that of sequences of points in metric spaces. This investigation is focused on the iterative processes built with composed self-mappings of a cyclic contraction, which can involve more than two nonempty closed subsets in a metric space, which are combined with compositions of a strict contraction with itself, which operates in each of the individual subsets, in any order and any number of mutual compositions. It is admitted, in the most general case, the involvement of any number of repeated compositions of both self-maps with themselves. It is basically seen that, if one of the best-proximity points in the cyclic disposal is unique in a boundedly compact subset of the metric space is sufficient to achieve unique asymptotic cycles formed by a best-proximity point per each adjacent subset. The same property is achievable if such a subset is strictly convex and the metric space is a uniformly convex Banach space. Furthermore, all the sequences with arbitrary initial points in the union of all the subsets of the cyclic disposal converge to such a limit cycle. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems, 2nd Edition)
13 pages, 2098 KiB  
Article
A Prescribed-Time Consensus Algorithm for Distributed Time-Varying Optimization Based on Multiagent Systems
by Yanling Zheng, Siyu Liu and Jie Zhong
Mathematics 2025, 13(13), 2190; https://doi.org/10.3390/math13132190 - 4 Jul 2025
Viewed by 325
Abstract
This paper presents a distributed optimization algorithm for time-varying objective functions utilizing a prescribed-time convergent multi-agent system within undirected communication networks. Departing from conventional time-invariant optimization paradigms with static optimal solutions, our approach specifically addresses the challenge of tracking dynamic optimal trajectories in [...] Read more.
This paper presents a distributed optimization algorithm for time-varying objective functions utilizing a prescribed-time convergent multi-agent system within undirected communication networks. Departing from conventional time-invariant optimization paradigms with static optimal solutions, our approach specifically addresses the challenge of tracking dynamic optimal trajectories in evolving environments. A novel continuous-time distributed optimization algorithm is developed based on prescribed-time consensus, guaranteeing the consensus attainment among agents within a user-defined timeframe while asymptotically converging to the time-dependent optimal solution. The proposed methodology enables explicit predetermination of convergence duration, representing a significant advancement over existing asymptotic convergence methods. Moreover, two simulation examples on the rendezvous problem and multi-robots control are presented to validate the theoretical results, exhibiting precise time-controlled convergence characteristics and effective tracking performance for time-varying optimization targets. Full article
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27 pages, 913 KiB  
Article
On the Exact Asymptotic Error of the Kernel Estimator of the Conditional Hazard Function for Quasi-Associated Functional Variables
by Abdelkader Rassoul, Abderrahmane Belguerna, Hamza Daoudi, Zouaoui Chikr Elmezouar and Fatimah Alshahrani
Mathematics 2025, 13(13), 2172; https://doi.org/10.3390/math13132172 - 3 Jul 2025
Viewed by 662
Abstract
The goal of this research is to analyze the mean squared error (MSE) of the kernel estimator for the conditional hazard rate, assuming that the sequence of real random vector variables (Un)nN satisfies the quasi-association condition. By [...] Read more.
The goal of this research is to analyze the mean squared error (MSE) of the kernel estimator for the conditional hazard rate, assuming that the sequence of real random vector variables (Un)nN satisfies the quasi-association condition. By employing kernel smoothing techniques and asymptotic analysis, we derive the exact asymptotic expression for the leading terms of the quadratic error, providing a precise characterization of the estimator’s convergence behavior. In addition to the theoretical derivations and a controlled simulation study that validates the asymptotic properties, this work includes a real-data application involving monthly unemployment rates in the United States from 1948 to 2025. The comparison between the estimated and observed values confirms the relevance and robustness of the proposed method in a practical economic context. This study thus extends existing results on hazard rate estimation by addressing more complex dependence structures and by demonstrating the applicability of the methodology to real functional data, thereby contributing to both the theoretical development and empirical deployment of kernel-based methods in survival and labor market analysis. Full article
(This article belongs to the Section D1: Probability and Statistics)
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23 pages, 6299 KiB  
Article
Multi-Valve Coordinated Disturbance Rejection Control for an Intake Pressure System Using External Penalty Functions
by Louyue Zhang, Duoqi Shi, Chao Zhai, Zhihong Dan, Hehong Zhang, Xi Wang and Gaoxi Xiao
Actuators 2025, 14(7), 334; https://doi.org/10.3390/act14070334 - 2 Jul 2025
Viewed by 240
Abstract
Altitude test facilities for aero-engines employ multi-chamber, multi-valve intake systems that require effective decoupling and strong disturbance rejection during transient tests. This paper proposes a coordinated active disturbance rejection control (ADRC) scheme based on external penalty functions. The chamber pressure safety limit is [...] Read more.
Altitude test facilities for aero-engines employ multi-chamber, multi-valve intake systems that require effective decoupling and strong disturbance rejection during transient tests. This paper proposes a coordinated active disturbance rejection control (ADRC) scheme based on external penalty functions. The chamber pressure safety limit is formulated as an inequality-constrained optimization problem, and an exponential penalty together with a gradient based algorithm is designed for dynamic constraint relaxation, with guaranteed global convergence. A coordination term is then integrated into a distributed ADRC framework to yield a multi-valve coordinated ADRC controller, whose asymptotic stability is established via Lyapunov theory. Hardware-in-the-loop simulations using MATLAB/Simulink and a PLC demonstrate that, under ±3 kPa pressure constraints, the maximum engine inlet pressure error is 1.782 kPa (77.1% lower than PID control), and under an 80 kg/s2 flow-rate disturbance, valve oscillations decrease from ±27% to ±5%. These results confirm the superior disturbance rejection and decoupling performance of the proposed method. Full article
(This article belongs to the Special Issue Actuation and Robust Control Technologies for Aerospace Applications)
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59 pages, 1417 KiB  
Article
Symmetrized Neural Network Operators in Fractional Calculus: Caputo Derivatives, Asymptotic Analysis, and the Voronovskaya–Santos–Sales Theorem
by Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales and Gislan Silveira Santos
Axioms 2025, 14(7), 510; https://doi.org/10.3390/axioms14070510 - 30 Jun 2025
Viewed by 264
Abstract
This work presents a comprehensive mathematical framework for symmetrized neural network operators operating under the paradigm of fractional calculus. By introducing a perturbed hyperbolic tangent activation, we construct a family of localized, symmetric, and positive kernel-like densities, which form the analytical backbone for [...] Read more.
This work presents a comprehensive mathematical framework for symmetrized neural network operators operating under the paradigm of fractional calculus. By introducing a perturbed hyperbolic tangent activation, we construct a family of localized, symmetric, and positive kernel-like densities, which form the analytical backbone for three classes of multivariate operators: quasi-interpolation, Kantorovich-type, and quadrature-type. A central theoretical contribution is the derivation of the Voronovskaya–Santos–Sales Theorem, which extends classical asymptotic expansions to the fractional domain, providing rigorous error bounds and normalized remainder terms governed by Caputo derivatives. The operators exhibit key properties such as partition of unity, exponential decay, and scaling invariance, which are essential for stable and accurate approximations in high-dimensional settings and systems governed by nonlocal dynamics. The theoretical framework is thoroughly validated through applications in signal processing and fractional fluid dynamics, including the formulation of nonlocal viscous models and fractional Navier–Stokes equations with memory effects. Numerical experiments demonstrate a relative error reduction of up to 92.5% when compared to classical quasi-interpolation operators, with observed convergence rates reaching On1.5 under Caputo derivatives, using parameters λ=3.5, q=1.8, and n=100. This synergy between neural operator theory, asymptotic analysis, and fractional calculus not only advances the theoretical landscape of function approximation but also provides practical computational tools for addressing complex physical systems characterized by long-range interactions and anomalous diffusion. Full article
(This article belongs to the Special Issue Advances in Fuzzy Logic and Computational Intelligence)
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19 pages, 437 KiB  
Article
Mutual Information-Oriented ISAC Beamforming Design for Large Dimensional Antenna Array
by Shanfeng Xu, Yanshuo Cheng, Siqiang Wang, Xinyi Wang, Zhong Zheng and Zesong Fei
Electronics 2025, 14(13), 2515; https://doi.org/10.3390/electronics14132515 - 20 Jun 2025
Viewed by 267
Abstract
In this paper, we study the beamforming design for multiple-input multiple-output (MIMO) ISAC systems, with the weighted mutual information (MI) comprising sensing and communication perspectives adopted as the performance metric. In particular, the weighted sum of the communication mutual information and the sensing [...] Read more.
In this paper, we study the beamforming design for multiple-input multiple-output (MIMO) ISAC systems, with the weighted mutual information (MI) comprising sensing and communication perspectives adopted as the performance metric. In particular, the weighted sum of the communication mutual information and the sensing mutual information is shown to asymptotically converge to a deterministic limit when the number of transmitting and receiving antennas grow to infinity. This deterministic limit is derived by utilizing the operator-valued free probability theory. Subsequently, an efficient projected gradient ascent (PGA) algorithm is proposed to optimize the transmit beamforming matrix with the aim of maximizing the weighted asymptotic MI. Numerical results validate that the derived closed-form expression matches well with the Monte Carlo simulation results and the proposed optimization algorithm is able to improve the weighted asymptotic MI significantly. We also illustrate the trade-off between asymptotic sensing and asymptotic communication MI. Full article
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