scholarly journals A note on overrelaxation in the Sinkhorn algorithm

2021 ◽  
Author(s):  
Tobias Lehmann ◽  
Max-K. von Renesse ◽  
Alexander Sambale ◽  
André Uschmajew
Keyword(s):  
Spectral Analysis ◽  
Global Convergence ◽  
Local Convergence ◽  
A Priori ◽  
Relaxation Parameter ◽  
Parameter Range ◽  
Linearized Problem

AbstractWe derive an a priori parameter range for overrelaxation of the Sinkhorn algorithm, which guarantees global convergence and a strictly faster asymptotic local convergence. Guided by the spectral analysis of the linearized problem we pursue a zero cost procedure to choose a near optimal relaxation parameter.

scholarly journals Characterisation of the Contribution of the GABA-Benzodiazepine α1 Receptor Subtype to [11C]Ro15-4513 PET Images

2012 ◽  
Vol 32 (4) ◽  
pp. 731-744 ◽  
Author(s):  
James FM Myers ◽  
Lula Rosso ◽  
Ben J Watson ◽  
Sue J Wilson ◽  
Nicola J Kalk ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
A Priori ◽  
Benzodiazepine Receptor ◽  
Brain Regions ◽  
Complex Model ◽  
Receptor Subtype ◽  
Receptor Subtypes ◽  
Time Activity ◽  
Positron Emission ◽  
The Impact

This positron emission tomography (PET) study aimed to further define selectivity of [11C]Ro15-4513 binding to the GABARα5 relative to the GABARα1 benzodiazepine receptor subtype. The impact of zolpidem, a GABARα1-selective agonist, on [11C]Ro15-4513, which shows selectivity for GABARα5, and the nonselective benzodiazepine ligand [11C]flumazenil binding was assessed in humans. Compartmental modelling of the kinetics of [11C]Ro15-4513 time-activity curves was used to describe distribution volume ( VT) differences in regions populated by different GABA receptor subtypes. Those with low α5 were best fitted by one-tissue compartment models; and those with high α5 required a more complex model. The heterogeneity between brain regions suggested spectral analysis as a more appropriate method to quantify binding as it does not a priori specify compartments. Spectral analysis revealed that Zolpidem caused a significant VT decrease (~10%) in [11C]flumazenil, but no decrease in [11C]Ro15-4513 binding. Further analysis of [11C]Ro15-4513 kinetics revealed additional frequency components present in regions containing both α1 and α5 subtypes compared with those containing only α1. Zolpidem reduced one component (mean ± s.d.: 71% ± 41%), presumed to reflect α1-subtype binding, but not another (13% ± 22%), presumed to reflect α5. The proposed method for [11C]Ro15-4513 analysis may allow more accurate selective binding assays and estimation of drug occupancy for other nonselective ligands.

scholarly journals A New Reservoir Operation Chart Drawing Method Based on Dynamic Programming

Energies ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 3355 ◽  
Author(s):  
Zhiqiang Jiang ◽  
Yaqi Qiao ◽  
Yuyun Chen ◽  
Changming Ji
Keyword(s):  
Power Generation ◽  
Dynamic Programming ◽  
Global Convergence ◽  
Local Convergence ◽  
Reservoir Operation ◽  
Optimization Methods ◽  
Simulation Results ◽  
Conventional Methods ◽  
Drawing Method ◽  
New Reservoir

A reservoir operation chart is an important tool in guiding actual reservoir operation at present. There are mainly two kinds of methods in drawing the operation chart, i.e., conventional methods and optimization methods, but each of them has some shortcomings, such as the repeated empirical inspection and correction of conventional methods, and the sensitivity to the initial trajectories of some optimization algorithms. In view of this, based on the principle of dynamic programming (DP), this paper coupled the reservoir operation chart drawing model and the DP model, and proposed a new reservoir operation chart drawing method which has no empirical inspection and correction, no requirement for initial solution, no problem of premature convergence and local convergence. In addition, this method can guarantee the global convergence of the results to a certain extent because of the global convergence of DP. Ya Yangshan reservoir in the Li Xianjiang River of China was selected as the research object to derive the operation chart by the drawing method. The simulation results show that the proposed method in this paper presents better performance compared with the conventional method on power generation, guaranteed output, and assurance rate, especially on the latter, which has a 2.68% increase. In addition, compared with the deterministic optimization results of DP, it is found that the results of the proposed method are very close to that of deterministic DP, the differences are only 1.8 GWh (0.36% decline) and 1.6 GWh (0.32% decline). So, the validity and rationality of the proposed method are further verified by the simulation results.

scholarly journals General Local Convergence Theorems about the Picard Iteration in Arbitrary Normed Fields with Applications to Super–Halley Method for Multiple Polynomial Zeros

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1599
Author(s):  
Stoil I. Ivanov
Keyword(s):  
Error Estimates ◽  
Local Convergence ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Sufficient Conditions ◽  
Posteriori Error ◽  
Picard Iteration ◽  
Polynomial Zeros ◽  
Convergence Theorems ◽  
Simple And Multiple Roots

In this paper, we prove two general convergence theorems with error estimates that give sufficient conditions to guarantee the local convergence of the Picard iteration in arbitrary normed fields. Thus, we provide a unified approach for investigating the local convergence of Picard-type iterative methods for simple and multiple roots of nonlinear equations. As an application, we prove two new convergence theorems with a priori and a posteriori error estimates about the Super-Halley method for multiple polynomial zeros.

scholarly journals On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and non-stationary data

2016 ◽  
Vol 374 (2065) ◽  
pp. 20150206 ◽  
Author(s):  
Norden E. Huang ◽  
Kun Hu ◽  
Albert C. C. Yang ◽  
Hsing-Chih Chang ◽  
Deng Jia ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
A Priori ◽  
Integral Transforms ◽  
Density Variation ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Wave Nonlinearity ◽  
Frequency Modulations ◽  
Multiplicative Processes

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time–frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities.

Choice of operator length for maximum entropy spectral analysis

Geophysics ◽  
1978 ◽  
Vol 43 (7) ◽  
pp. 1384-1391 ◽  
Author(s):  
James G. Berryman
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Maximum Entropy ◽  
Empirical Evidence ◽  
Discrete Time ◽  
Seismic Data ◽  
A Priori ◽  
Evidence Based ◽  
Maximum Entropy Spectral Analysis ◽  
Discrete Time Series

Empirical evidence based on maximum entropy spectra of real seismic data suggests that M = 2N/ln 2N is a reasonable a priori choice of the operator length M for discrete time series of length N. Various examples support this conclusion.

scholarly journals Projection Methods for Ill-Posed Problems Revisited

2016 ◽  
Vol 16 (2) ◽  
pp. 257-276 ◽  
Author(s):  
Stefan Kindermann
Keyword(s):  
Exact Solution ◽  
Global Convergence ◽  
Least Squares ◽  
Local Convergence ◽  
Sufficient Conditions ◽  
Projection Methods ◽  
Bounded Sequence ◽  
Oblique Projection ◽  
Ill Posed

AbstractWe consider the discretization of least-squares problems for linear ill-posed operator equations in Hilbert spaces. The main subject of this article concerns conditions for convergence of the associated discretized minimum-norm least-squares solution to the exact solution using exact attainable data. The two cases of global convergence (convergence for all exact solutions) or local convergence (convergence for a specific exact solution) are investigated. We review the existing results and prove new equivalent conditions when the discretized solution always converges to the exact solution. An important tool is to recognize the discrete solution operator as an oblique projection. Hence, global convergence can be characterized by certain subspaces having uniformly bounded angles. We furthermore derive practically useful conditions when this holds and put them into the context of known results. For local convergence, we generalize results on the characterization of weak or strong convergence and state some new sufficient conditions. We furthermore provide an example of a bounded sequence of discretized solutions which does not converge at all, not even weakly.

scholarly journals Spectrum analysis and prediction possibilities of the onset dates of southwest monsoon over Kerala (India)

MAUSAM ◽  
2022 ◽  
Vol 46 (1) ◽  
pp. 15-24
Author(s):  
R. P. KANE
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Zonal Wind ◽  
Monsoon Rainfall ◽  
Late Onset ◽  
A Priori ◽  
Southwest Monsoon ◽  
Random Component ◽  
Maximum Entropy Spectral Analysis ◽  
Early Late

Maximum Entropy Spectral Analysis of the time series for the onset dates of the southwest monsoon over Kerala (India) revealed several periodicities significant at a 2a a priori level. some at a 3 C a  priori level However these contributed only 40-50% to the total variance thus indicating 50-60% as purely random component. Also many of the significant periodicities observed were in the QBO region (T = 2-3 years) which. due to their variable periodicities and amplitudes, are almost equivalent to a random component. Hence predictions were possible only with a  limit exceeding 5 days which are probably not very useful for any planning purposes agricultural or otherwise. No relationship was found between onset dates of established monsoon rainfall and the 50 hPa mean monthly equatorial zonal wind for the months of March, April, May or June. However there is a possibility that a relationship may exist between westerly (easterly) winds in May and early (late) onset of the first monsoon (or pre-monsoon ?) rainfall in Kerala. Meager or otherwise.    

scholarly journals Analysis in the frequency domain of multicomponent oscillatory modes of the human electroencephalogram extracted with multivariate empirical mode decomposition

2020 ◽  
Author(s):  
Eduardo Arrufat-Pié ◽  
Mario Estévez-Báez ◽  
José Mario Estévez-Carreras ◽  
Calixto Machado Curbelo ◽  
Gerry Leisman ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
Empirical Mode Decomposition ◽  
A Priori ◽  
Quantitative Eeg ◽  
Frequency Resolution ◽  
Intrinsic Mode Functions ◽  
Multivariate Empirical Mode Decomposition ◽  
Healthy Humans ◽  
Mode Decomposition ◽  
Mixing Problem

AbstractConsidering the properties of the empirical mode decomposition to extract from a signal its natural oscillatory components known as intrinsic mode functions (IMFs), the spectral analysis of these IMFs could provide a novel alternative for the quantitative EEG analysis without a priori establish more or less arbitrary band limits. This approach has begun to be used in the last years for studies of EEG records of patients included in database repositories or including a low number of individuals or of limited EEG leads, but a detailed study in healthy humans has not yet been reported. Therefore, in this study the aims were to explore and describe the main spectral indices of the IMFs of the EEG in healthy humans using a method based on the FFT and another on the Hilbert-Huang transform (HHT). The EEG of 34 healthy volunteers was recorded and decomposed using a recently developed multivariate empirical mode decomposition algorithm. Extracted IMFs were submitted to spectral analysis with, and the results were compared with an ANOVA test. The first six decomposed IMFs from the EEG showed frequency values in the range of the classical bands of the EEG (1.5 to 56 Hz). Both methods showed in general similar results for mean weighted frequencies and estimations of power spectral density, although the HHT is recommended because of its better frequency resolution. It was shown the presence of the mode-mixing problem producing a slight overlapping of spectral frequencies mainly between the IMF3 and IMF4 modes.

scholarly journals Modeling and Optimization of RFID Networks Planning Problem

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Hongshan Kong ◽  
Bin Yu
Keyword(s):  
Mathematical Model ◽  
Global Convergence ◽  
Differential Evolution ◽  
Local Convergence ◽  
Evolutionary Strategies ◽  
Planning Problem ◽  
Modeling And Optimization ◽  
Rfid Networks ◽  
Simulation Results

Aimed at solving the RFID networks planning problem, a mathematical model considering tag coverage and reader interference is presented. The DEEPSO algorithm that adds differential evolution and evolutionary strategies to the standard PSO is introduced to the optimization of RFID Networks Planning, which can improve the global convergence ability and particle diversity and can avoid falling into local convergence. According to the simulation results, compared with RFID networks planning by standard PSO, RFID networks planning by DEEPSO is superior.

scholarly journals A Filter Algorithm with Inexact Line Search

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Meiling Liu ◽  
Xueqian Li ◽  
Qinmin Wu
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Local Convergence ◽  
Numerical Experiments ◽  
Line Search ◽  
Second Order ◽  
Lagrangian Function ◽  
Order Correction ◽  
Inexact Line Search ◽  
Mild Conditions

A filter algorithm with inexact line search is proposed for solving nonlinear programming problems. The filter is constructed by employing the norm of the gradient of the Lagrangian function to the infeasibility measure. Transition to superlinear local convergence is showed for the proposed filter algorithm without second-order correction. Under mild conditions, the global convergence can also be derived. Numerical experiments show the efficiency of the algorithm.

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