An iterative algorithm based on the Gerchberg-Saxton (GS) algorithm to control both the phase and amplitude of an optical beam in the output plane of a beam-shaping platform is proposed in this paper. In the proposed ...
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An iterative algorithm based on the Gerchberg-Saxton (GS) algorithm to control both the phase and amplitude of an optical beam in the output plane of a beam-shaping platform is proposed in this paper. In the proposed algorithm, both the phase and the amplitude in the non-zero optical intensity region of a beam in the output plane are constrained, whereas the phase in the other region in the output plane is constraint-free. Thus, both the amplitude and phase distributions in the desired region of the output beam can be controlled with a phase-only hologram. The effectiveness of the algorithm is verified with both the simulations and experiments. The algorithm converges fast and is easy to implement. With this algorithm, we can design various novel optical beams, specifically, the beams with a phase-gradient, which would have extensive applications in areas such as optical trapping.
Rotary parts are crucial to transmission equipment. Measuring and analyzing the eccentricity of rotary parts enables the monitoring of vibrations in machinery, ensures smooth operation, and reduces equipment maintenan...
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Rotary parts are crucial to transmission equipment. Measuring and analyzing the eccentricity of rotary parts enables the monitoring of vibrations in machinery, ensures smooth operation, and reduces equipment maintenance costs. The accurate measurement and modification of eccentricity are the premise to ensure rotary parts' quality, however, existing measurement methods are computationally inefficient, complex, and expensive to implement, and limited in scope. In this paper, a novel and generalized precision measurement method is proposed to accurately and efficiently evaluate rotary parts' eccentricity parameters, including attitude angle, eccentricity, and eccentric angle. This precision measurement method includes a lever measuring mechanism with a spherical probe and a corresponding efficient signal processing algorithm. The measuring mechanism has a simple structure and can effectively measure arbitrary cross-sections, and its design and optimization principles are investigated and presented thoroughly. The signal processing algorithm can efficiently extract eccentricity parameters of measured cross-sections. This proposed method has proven to overcome the limitations of literacy methods and exhibits generality and anti-interference. Simulation calculation and experimental verification are used to evaluate the effectiveness, computation efficiency, applicability, and repeatability. The proposed method exhibits tremendous potential in a diverse range of applications, such as detecting eccentricity and correcting errors for mechanical measurements, aerospace, equipment manufacturing, and other related fields.
In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged ...
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In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.
Interference alignment (IA) has been shown as an important technique to achieve a linear capacity scaling in wireless communications. However, the IA scheme over finite signaling dimensions for a general multiple-inpu...
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Interference alignment (IA) has been shown as an important technique to achieve a linear capacity scaling in wireless communications. However, the IA scheme over finite signaling dimensions for a general multiple-input-multiple-output (MIMO) X channel is still rarely studied. The main challenge of MIMO X channels is that the two sets of conditions for IA, namely the interference nulling conditions and the rank preservation conditions, get coupled. The usual IA methods for the interference channel and the broadcasting channel cannot be applied anymore. In this paper, we show that the rank preservation conditions can be replaced by a group of specific rank conditions, under which the IA problem is simplified. Then, based on this technique, an iterative algorithm of IA is designed for the MIMO X channel. The algorithm is designed with limited signaling dimensions. From the simulation results, we find that the algorithm has good performances even under limited signal-to-noise ratio.
The strong H-tensors have important applications in many areas of science and engineering, e.g., the determination of positive definiteness for an even-order homogeneous polynomial form in the real field. In this pape...
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The strong H-tensors have important applications in many areas of science and engineering, e.g., the determination of positive definiteness for an even-order homogeneous polynomial form in the real field. In this paper, we propose two iterative algorithms with non-parameter for identifying strong H-tensors, which overcome the drawback of choosing the best value of parameter ? in some existing algorithms given by Li et al. and Liu et al. (J. Comput. Appl. Math., 255, 1-14, 2014 and Comput. Appl. Math. 36, 1623-1635, 2017). Some numerical experiments are performed to illustrate the feasibility and effectiveness of our algorithms.
Railway traffic controllers face the problem that trains are often not operated as planned in timetables due to perturbations such as unexpected, degraded operations, and technical failures. This paper deals with the ...
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Railway traffic controllers face the problem that trains are often not operated as planned in timetables due to perturbations such as unexpected, degraded operations, and technical failures. This paper deals with the problem of train rerouting and rescheduling faced by the controllers of different regional railway control centers that must coordinate their decisions to minimize the impact of perturbations over the whole network. We split this real-time railway traffic management problem into two decision levels. At the lower level, the local area controllers, the dispatchers, manage train schedules and routes in their control areas from a microscopic perspective. At the higher level, a coordinator ensures the compatibility of dispatchers' decisions over two or more areas from a macroscopic perspective. To solve our problem, we propose an iterative optimization algorithm. The preliminary experimental results show that the proposed algorithm can reduce the delay propagation.
The National Basketball Association, also known as the NBA, is a professional basketball league composed of 30 professional teams in North America and one of the four major professional sports leagues in the United St...
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The National Basketball Association, also known as the NBA, is a professional basketball league composed of 30 professional teams in North America and one of the four major professional sports leagues in the United States. This research delves into predicting winning percentages in NBA games using a data-driven approach. It utilizes three years' worth of comprehensive game data from 30 NBA teams(2014-2016), including actual outcomes and expert predictions. The study aims to acquire valuable teamwork and data research skills while contributing to sports analytics. Data preparation involves cleaning and selecting recent seasons for model training. The prediction model utilizes an iterative algorithm to estimate team strength coefficients based on game results. Though the model shows promise, its accuracy falls slightly short compared to bookies' predictions. The research provides valuable insights for predicting NBA game outcomes and suggests avenues for improving the model's accuracy through additional variables
iterative phase retrieval algorithms from multiple diffraction patterns in the terahertz (THz) frequency range are a promising tool of computational imaging capable of providing high spatial resolution of reconstructe...
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iterative phase retrieval algorithms from multiple diffraction patterns in the terahertz (THz) frequency range are a promising tool of computational imaging capable of providing high spatial resolution of reconstructed phase images. One of the commonly used algorithms is SBMIR, which employs multiple intensity distributions of the diffraction object wavefield as input data. Com -pared with single-frame methods, the multi-plane approach allows for a faster convergence, but requires time-consuming data acquisition from a receiver positioned at a variety of distances from the object. Previously, we proposed a method for THz data acquisition in a single scan mode, which allows one to quickly obtain an exhaustive set of diffraction distributions. In this paper we evaluate an up-to-date phase retrieval algorithm based on the SBMIR/R-SBMIR method (which utilizes stochastic wavefront propagation) on the experimental data captured by a single-scan technique. Unlike a number of conventional phase retrieval algorithms, which may require a series of numerical experiments for determining optimal intensity distributions from a large dataset, disordered propagation of the estimation wavefront guarantees the high-contrast and high-resolution image reconstruction without pre-setting the parameters. It is shown that the package use of the single-scan technique with the subsequent data processing using the R-SBMIR algorithm has ap-plication potential for automation of the multi-plane phase retrieval in the THz range.
BackgroundWhereas filtered back projection algorithms for voxel-based CT image reconstruction have noise properties defined by the filter, iterative algorithms must stop at some point in their convergence and do not n...
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BackgroundWhereas filtered back projection algorithms for voxel-based CT image reconstruction have noise properties defined by the filter, iterative algorithms must stop at some point in their convergence and do not necessarily produce consistent noise properties for images with different degrees of heterogeneity. PurposeA least-squares iterative algorithm for proton CT (pCT) image reconstruction converges toward a unique solution for relative stopping power (RSP) that optimally fits the protons. We present a stopping criterion that delivers solutions with the property that correlations of RSP noise between voxels are relatively low. This provides a method to produce pCT images with consistent noise properties useful for proton therapy treatment planning, which relies on summing RSP along lines of voxels. Consistent noise properties will also be useful for future studies of image quality using metrics such as contrast to noise ratio, and to compare RSP noise and dose of pCT with other modalities such as dual-energy CT. MethodsWith simulated and real images with varying heterogeneity from a prototype clinical proton imaging system, we calculate average RSP correlations between voxel pairs in uniform regions-of-interest versus distance between voxels. We define a parameter r, the remaining distance to the unique solution relative to estimated RSP noise, and our stopping criterion is based on r falling below a chosen value. ResultsWe find large correlations between voxels for larger values of r, and anticorrelations for smaller values. For r in the range of 0.5-1, voxels are relatively uncorrelated, and compared to smaller values of r have lower noise with only slight loss of spatial resolution. Conclusionsiterative algorithms not using a specific metric or rationale for stopping iterations may produce images with an unknown and arbitrary level of convergence or smoothing. We resolve this issue by stopping iterations of a least-squares iterative algorithm when r reache
A new system of generalized mixed implicit equilibrium problems (SGMIEP) involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium pro...
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A new system of generalized mixed implicit equilibrium problems (SGMIEP) involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem (AMEP) is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems (SGEP) is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field.
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