This presentation discusses three operations research projects. Project I involves sustainable ecosystem planning for the Loess Plateau region of China using discrete stochastic dynamic programming and evolutionary game theory. The model represents multi-subsystems and their dynamic interactions using equations and parameters. Project II researches locational-marginal-price based distribution power networks. Project III develops an optimization approach for parametric tuning of power system stabilizers based on trajectory sensitivity analysis.
The remote sensing working group has investigated methodology for atmospheric remotesensing retrievals, which are mathematical and computational procedures for inferring the state of the atmosphere from remote sensing observations. Satellite data with fine spatial and temporal
resolution present opportunities to combine information across satellite pixels using spatiotemporal statistical modeling. We present examples of this approach at the process level of a hierarchical model, with a nonlinear radiative transfer model incorporated into the likelihood. In
this framework, we assess the impact of various statistical properties on the relative performance of a multi-pixel retrieval strategy versus an operational one-at-a-time approach. The prospect of adopting the approach is illustrated in the context of estimating atmospheric carbon dioxide concentration with data from NASA's Orbiting Carbon Observatory-2 (OCO-2).
Information-theoretic clustering with applicationsFrank Nielsen
Information-theoretic clustering with applications
Abstract: Clustering is a fundamental and key primitive to discover structural groups of homogeneous data in data sets, called clusters. The most famous clustering technique is the celebrated k-means clustering that seeks to minimize the sum of intra-cluster variances. k-Means is NP-hard as soon as the dimension and the number of clusters are both greater than 1. In the first part of the talk, we first present a generic dynamic programming method to compute the optimal clustering of n scalar elements into k pairwise disjoint intervals. This case includes 1D Euclidean k-means but also other kinds of clustering algorithms like the k-medoids, the k-medians, the k-centers, etc.
We extend the method to incorporate cluster size constraints and show how to choose the appropriate number of clusters using model selection. We then illustrate and refine the method on two case studies: 1D Bregman clustering and univariate statistical mixture learning maximizing the complete likelihood. In the second part of the talk, we introduce a generalization of k-means to cluster sets of histograms that has become an important ingredient of modern information processing due to the success of the bag-of-word modelling paradigm.
Clustering histograms can be performed using the celebrated k-means centroid-based algorithm. We consider the Jeffreys divergence that symmetrizes the Kullback-Leibler divergence, and investigate the computation of Jeffreys centroids. We prove that the Jeffreys centroid can be expressed analytically using the Lambert W function for positive histograms. We then show how to obtain a fast guaranteed approximation when dealing with frequency histograms and conclude with some remarks on the k-means histogram clustering.
References: - Optimal interval clustering: Application to Bregman clustering and statistical mixture learning IEEE ISIT 2014 (recent result poster) http://arxiv.org/abs/1403.2485
- Jeffreys Centroids: A Closed-Form Expression for Positive Histograms and a Guaranteed Tight Approximation for Frequency Histograms.
IEEE Signal Process. Lett. 20(7): 657-660 (2013) http://arxiv.org/abs/1303.7286
http://www.i.kyoto-u.ac.jp/informatics-seminar/
This document provides an outline and overview of key concepts for estimating curves and surfaces from data using basis functions and penalized least squares regression. It discusses representing a curve or surface using basis functions, fitting the coefficients using ordinary least squares, and adding a penalty term to the least squares objective function to produce a smoothed estimate. The smoothing parameter λ controls the tradeoff between fit to the data and smoothness of the estimate. Cross-validation can be used to choose λ.
Bandit-based RMHC is a new algorithm that combines random mutation hill climbing (RMHC) with an upper confidence bound (UCB) selection method. It outperforms standard RMHC on benchmark problems like Royal Road and OneMax, finding better solutions using fewer fitness evaluations. It is particularly effective for noisy problems, sometimes using an order of magnitude fewer evaluations than RMHC. The algorithm shows promise for efficiently tuning game parameters to generate new game variants.
The issues about maneuvering target track prediction were discussed in this paper. Firstly, using Kalman filter which based on current statistical model describes the state of maneuvering target motion, thereby analyzing time range of the target maneuvering occurred. Then, predict the target trajectory in real time by the improved gray prediction model. Finally, residual test and posterior variance test model accuracy, model accuracy is accurate.
Optimal interval clustering: Application to Bregman clustering and statistica...Frank Nielsen
This document summarizes an academic paper on optimal interval clustering and its applications to Bregman clustering and statistical mixture learning. It begins by introducing hard clustering and center-based clustering approaches. It then describes how k-means clustering is NP-hard in higher dimensions but polynomial-time in 1D using dynamic programming. The document outlines an optimal interval clustering algorithm using dynamic programming with runtime O(n2kT1(n)) or O(n2T1(n)) using a lookup table. It discusses how this can be applied to 1D Bregman clustering and learning statistical mixtures, providing experimental results on Gaussian mixture models. Finally, it considers perspectives on hierarchical clustering, dynamic clustering maintenance, and streaming approximations.
Binary Vector Reconstruction via Discreteness-Aware Approximate Message PassingRyo Hayakawa
The document proposes a Discreteness-Aware Approximate Message Passing (DAMP) algorithm for reconstructing discrete-valued vectors from underdetermined linear measurements. DAMP extends existing AMP algorithms to handle discrete variables by incorporating probability distributions of the elements. The algorithm is analyzed using state evolution to derive conditions for perfect reconstruction. A Bayes optimal version of DAMP is also developed by minimizing mean squared error. Simulation results demonstrate improved reconstruction performance compared to conventional methods.
The remote sensing working group has investigated methodology for atmospheric remotesensing retrievals, which are mathematical and computational procedures for inferring the state of the atmosphere from remote sensing observations. Satellite data with fine spatial and temporal
resolution present opportunities to combine information across satellite pixels using spatiotemporal statistical modeling. We present examples of this approach at the process level of a hierarchical model, with a nonlinear radiative transfer model incorporated into the likelihood. In
this framework, we assess the impact of various statistical properties on the relative performance of a multi-pixel retrieval strategy versus an operational one-at-a-time approach. The prospect of adopting the approach is illustrated in the context of estimating atmospheric carbon dioxide concentration with data from NASA's Orbiting Carbon Observatory-2 (OCO-2).
Information-theoretic clustering with applicationsFrank Nielsen
Information-theoretic clustering with applications
Abstract: Clustering is a fundamental and key primitive to discover structural groups of homogeneous data in data sets, called clusters. The most famous clustering technique is the celebrated k-means clustering that seeks to minimize the sum of intra-cluster variances. k-Means is NP-hard as soon as the dimension and the number of clusters are both greater than 1. In the first part of the talk, we first present a generic dynamic programming method to compute the optimal clustering of n scalar elements into k pairwise disjoint intervals. This case includes 1D Euclidean k-means but also other kinds of clustering algorithms like the k-medoids, the k-medians, the k-centers, etc.
We extend the method to incorporate cluster size constraints and show how to choose the appropriate number of clusters using model selection. We then illustrate and refine the method on two case studies: 1D Bregman clustering and univariate statistical mixture learning maximizing the complete likelihood. In the second part of the talk, we introduce a generalization of k-means to cluster sets of histograms that has become an important ingredient of modern information processing due to the success of the bag-of-word modelling paradigm.
Clustering histograms can be performed using the celebrated k-means centroid-based algorithm. We consider the Jeffreys divergence that symmetrizes the Kullback-Leibler divergence, and investigate the computation of Jeffreys centroids. We prove that the Jeffreys centroid can be expressed analytically using the Lambert W function for positive histograms. We then show how to obtain a fast guaranteed approximation when dealing with frequency histograms and conclude with some remarks on the k-means histogram clustering.
References: - Optimal interval clustering: Application to Bregman clustering and statistical mixture learning IEEE ISIT 2014 (recent result poster) http://arxiv.org/abs/1403.2485
- Jeffreys Centroids: A Closed-Form Expression for Positive Histograms and a Guaranteed Tight Approximation for Frequency Histograms.
IEEE Signal Process. Lett. 20(7): 657-660 (2013) http://arxiv.org/abs/1303.7286
http://www.i.kyoto-u.ac.jp/informatics-seminar/
This document provides an outline and overview of key concepts for estimating curves and surfaces from data using basis functions and penalized least squares regression. It discusses representing a curve or surface using basis functions, fitting the coefficients using ordinary least squares, and adding a penalty term to the least squares objective function to produce a smoothed estimate. The smoothing parameter λ controls the tradeoff between fit to the data and smoothness of the estimate. Cross-validation can be used to choose λ.
Bandit-based RMHC is a new algorithm that combines random mutation hill climbing (RMHC) with an upper confidence bound (UCB) selection method. It outperforms standard RMHC on benchmark problems like Royal Road and OneMax, finding better solutions using fewer fitness evaluations. It is particularly effective for noisy problems, sometimes using an order of magnitude fewer evaluations than RMHC. The algorithm shows promise for efficiently tuning game parameters to generate new game variants.
The issues about maneuvering target track prediction were discussed in this paper. Firstly, using Kalman filter which based on current statistical model describes the state of maneuvering target motion, thereby analyzing time range of the target maneuvering occurred. Then, predict the target trajectory in real time by the improved gray prediction model. Finally, residual test and posterior variance test model accuracy, model accuracy is accurate.
Optimal interval clustering: Application to Bregman clustering and statistica...Frank Nielsen
This document summarizes an academic paper on optimal interval clustering and its applications to Bregman clustering and statistical mixture learning. It begins by introducing hard clustering and center-based clustering approaches. It then describes how k-means clustering is NP-hard in higher dimensions but polynomial-time in 1D using dynamic programming. The document outlines an optimal interval clustering algorithm using dynamic programming with runtime O(n2kT1(n)) or O(n2T1(n)) using a lookup table. It discusses how this can be applied to 1D Bregman clustering and learning statistical mixtures, providing experimental results on Gaussian mixture models. Finally, it considers perspectives on hierarchical clustering, dynamic clustering maintenance, and streaming approximations.
Binary Vector Reconstruction via Discreteness-Aware Approximate Message PassingRyo Hayakawa
The document proposes a Discreteness-Aware Approximate Message Passing (DAMP) algorithm for reconstructing discrete-valued vectors from underdetermined linear measurements. DAMP extends existing AMP algorithms to handle discrete variables by incorporating probability distributions of the elements. The algorithm is analyzed using state evolution to derive conditions for perfect reconstruction. A Bayes optimal version of DAMP is also developed by minimizing mean squared error. Simulation results demonstrate improved reconstruction performance compared to conventional methods.
The document discusses error analysis for quasi-Monte Carlo methods used for numerical integration. It introduces the concepts of reproducing kernel Hilbert spaces and mean square discrepancy to analyze integration error. Specifically, it shows that the mean square discrepancy of randomized low-discrepancy point sets can be computed in O(n) operations, whereas the standard discrepancy requires O(n^2) operations, making randomized quasi-Monte Carlo methods more efficient for high-dimensional integration problems.
Visualizing, Modeling and Forecasting of Functional Time Serieshanshang
The document discusses visualization and forecasting of functional time series data. It introduces visualization methods like rainbow plots, functional bagplots, and functional highest density region boxplots which can detect outliers. It also covers modeling and forecasting functional time series, as well as seasonal univariate time series using a functional approach. Several outlier detection techniques for functional data are compared, including those based on functional depth, integrated squared error, and robust Mahalanobis distance.
The melting of the West Antarctic ice sheet (WAIS) is likely to cause a significant rise in sea levels. Studying the present state of WAIS and predicting its future behavior involves the use of computer models of ice sheet dynamics as well as observational data. I will outline general statistical challenges posed by these scientific questions and data sets.
This discussion is based on joint work with Yawen Guan (Penn State/SAMSI), Won Chang (U. of Cincinnati), Patrick Applegate, David Pollard (Penn State)
This document provides a summary of spatial data modeling and analysis techniques. It begins with an outline of the topics to be covered, including additive statistical models for spatial data, spatial covariance functions, the multivariate normal distribution, kriging for prediction and uncertainty, and the likelihood function for parameter estimation. It then introduces the key concepts and equations for modeling spatial processes as Gaussian random fields with specified covariance functions. Examples are given of commonly used covariance functions and the types of random surfaces they generate. Kriging is described as a best linear unbiased prediction technique that uses a spatial covariance function and observations to make predictions at unknown locations. The document concludes with examples of parameter estimation via maximum likelihood and using the fitted model to make predictions and conditional simulations
Our techniques provide fast wavelet tree construction in practice based on recent theoretical work. Experiments on real datasets show our methods using the PEXT and PSHUFB CPU instructions outperform previous approaches. For wavelet trees, our methods are 1.9x faster than naive construction on average and competitive with state-of-the-art. For wavelet matrices, we achieve speedups of 1.1-1.9x over the state-of-the-art. This work provides the first practical implementation of the fastest known wavelet tree construction algorithms.
Spatio-Spectral Multichannel Reconstruction from few Low-Resolution Multispec...Amine Hadj-Youcef
This presentation deals with the reconstruction of a 3-D spatio-spectral object observed by a multispectral imaging system, where the original object is blurred with a spectral-variant PSF (Point Spread Function) and integrated over few broad spectral bands. In order to tackle this ill-posed problem, we propose a linear forward model that accounts for direct (or auto) channels and between (or cross) channels degradation, by modeling the imaging system response and the spectral distribution of the object with a piecewise linear function. Reconstruction based on regularization method is proposed, by enforcing spatial and spectral smoothness of the object. We test our approach on simulated data of the Mid-InfraRed Instrument (MIRI) Imager of the James Webb Space Telescope (JWST). Results on simulated multispectral data show a significant improvement over the conventional multichannel method.
Fast Identification of Heavy Hitters by Cached and Packed Group TestingRakuten Group, Inc.
The document summarizes a research paper on efficiently identifying heavy hitters in data streams using cached and packed group testing techniques. The paper proposes using packed bidirectional counter arrays to implement the operations of combinatorial group testing (CGT) in constant time. This improves the time complexity of CGT for updating frequencies and querying heavy hitters from O(log(n)) to O(1), eliminating dependency on the size of the data universe n. Experimental results show the proposed method achieves competitive precision, update throughput, and query throughput compared to existing CGT and hierarchical count-min sketch approaches.
We combined: low-rank tensor techniques and FFT to compute kriging, estimate variance, compute conditional covariance. We are able to solve 3D problems with very high resolution
1. Approximate message passing (AMP) is an algorithm that can be used for compressed sensing problems to recover a sparse signal x from linear measurements y=Ax+v in near-linear time.
2. Distributed AMP extends the AMP algorithm to distributed settings where multiple nodes take independent measurements yk=Akx+vk of the same signal x.
3. The distributed AMP algorithm involves nodes running AMP independently on their local measurements and aggregating information through message passing updates to estimate the signal x in a distributed manner.
1. The document discusses various algorithms and methods for solving optimization problems involving sparse signal recovery from underdetermined linear systems.
2. Key algorithms mentioned include iterative shrinkage-thresholding algorithms like FISTA, proximal splitting methods like ADMM, and regularization-based methods involving sparse-promoting penalties like l1-norm and sum of absolute values.
3. Applications discussed include compressed sensing, sparse signal recovery from MIMO systems, and discrete signal reconstruction problems.
A Hough Transform Based On a Map-Reduce AlgorithmIJERA Editor
This paper presents a method that proposes the composition of the Map-Reduce algorithm and the Hough
Transform method to research particular features of shape in the Big Data of images. We introduce the first
formal translation of the Hough Transform method into the Map-Reduce pattern. The Hough transform is
applied to one image or to several images in parallel. The context of the application of this method concerns Big
Data that requires Map-Reduce functions to improve the processing time and the need of object detection in
noisy pictures with the Hough Transform method.
MVPA with SpaceNet: sparse structured priorsElvis DOHMATOB
The GraphNet (aka S-Lasso), as well as other “sparsity + structure” priors like TV (Total-Variation), TV-L1, etc., are not easily applicable to brain data because of technical problems
relating to the selection of the regularization parameters. Also, in
their own right, such models lead to challenging high-dimensional optimization problems. In this manuscript, we present some heuristics for speeding up the overall optimization process: (a) Early-stopping, whereby one halts the optimization process when the test score (performance on leftout data) for the internal cross-validation for model-selection stops improving, and (b) univariate feature-screening, whereby irrelevant (non-predictive) voxels are detected and eliminated before the optimization problem is entered, thus reducing the size of the problem. Empirical results with GraphNet on real MRI (Magnetic Resonance Imaging) datasets indicate that these heuristics are a win-win strategy, as they add speed without sacrificing the quality of the predictions. We expect the proposed heuristics to work on other models like TV-L1, etc.
The document discusses discrete signal reconstruction using Discreteness-Aware Approximate Message Passing (DAMP). DAMP is an algorithm that can reconstruct discrete signals from compressed measurements by taking the discreteness of the signal into account. It is shown to outperform other methods like AMP and soft thresholding in terms of achieving lower mean square error and higher recovery rates, especially for signals with higher cardinality. The theoretical behavior of DAMP is also analyzed and shown to match empirical results.
- The document discusses methods for determining when to stop sampling in Monte Carlo integration to achieve a desired error tolerance.
- For independent and identically distributed (IID) sampling, the central limit theorem can be used to determine the necessary sample size based on the variance of the integrand.
- Quasi-Monte Carlo sampling can achieve faster convergence rates by using low-discrepancy point sets that more uniformly sample the domain. The error can be analyzed in the frequency domain based on the decay of the true Fourier coefficients.
- Bayesian cubature methods model the integrand as a Gaussian process, allowing inference of hyperparameters from sample points to improve integration accuracy.
In this talk we consider the question of how to use QMC with an empirical dataset, such as a set of points generated by MCMC. Using ideas from partitioning for parallel computing, we apply recursive bisection to reorder the points, and then interleave the bits of the QMC coordinates to select the appropriate point from the dataset. Numerical tests show that in the case of known distributions this is almost as effective as applying QMC directly to the original distribution. The same recursive bisection can also be used to thin the dataset, by recursively bisecting down to many small subsets of points, and then randomly selecting one point from each subset. This makes it possible to reduce the size of the dataset greatly without significantly increasing the overall error. Co-author: Fei Xie
The document discusses measuring sample quality using kernels. It introduces the kernel Stein discrepancy (KSD) as a new quality measure for comparing samples approximating a target distribution. The KSD is based on Stein's method and uses reproducing kernels. It can detect when a sample sequence is converging to the target distribution or not. Computing the KSD reduces to pairwise evaluations of kernel functions and is feasible. The KSD converges to zero if and only if the sample sequence converges to the target distribution for certain choices of kernels like the inverse multiquadric kernel with parameter between -1 and 0.
Double-grid 2D solver for Boussinesq Equation (BEq) ... DraftEmanuele Cordano
This is a draft presentation with the first application of the BEq model ... now it is published on http://onlinelibrary.wiley.com/doi/10.1002/wrcr.20072/abstract
The document discusses learning graphical models from data. It describes two main tasks: inference, which is computing answers to queries about a probability distribution described by a Bayesian network, and learning, which is estimating a model from data. It provides examples of learning for completely observed models, including maximum likelihood estimation for the parameters of a conditional Gaussian model. It also discusses supervised versus unsupervised learning of hidden Markov models, and techniques for dealing with small training sets like adding pseudocounts to estimates.
GPU acceleration of a non-hydrostatic ocean model with a multigrid Poisson/He...Takateru Yamagishi
To meet the demand for fast and detailed calculations in numerical ocean simulations, we implemented a non-hydrostatic ocean model on a graphics processing unit (GPU). We improved the model’s Poisson/Helmholtz solver by optimizing the memory access, using instruction-level parallelism, and applying a mixed precision calculation to the preconditioning of the Poisson/Helmholtz solver. The GPU-implemented model was 4.7 times faster than a comparable central processing unit execution. The output errors due to this implementation will not significantly influence oceanic studies.
The document discusses several algorithms for solving shortest path problems on graphs:
1. The Floyd-Warshall algorithm finds shortest paths between all pairs of vertices in a graph and runs in O(V3) time.
2. Bellman-Ford solves the single-source shortest paths problem for graphs with negative edge weights.
3. Dijkstra's algorithm solves the single-source shortest paths problem faster than Bellman-Ford for graphs with non-negative edge weights.
The document discusses three fundamental algorithms paradigms: recursion, divide-and-conquer, and dynamic programming. Recursion uses method calls to break down problems into simpler subproblems. Divide-and-conquer divides problems into independent subproblems, solves each, and combines solutions. Dynamic programming breaks problems into overlapping subproblems and builds up solutions, storing results of subproblems to avoid recomputing them. Examples like mergesort and calculating Fibonacci numbers are provided to illustrate the approaches.
The document discusses error analysis for quasi-Monte Carlo methods used for numerical integration. It introduces the concepts of reproducing kernel Hilbert spaces and mean square discrepancy to analyze integration error. Specifically, it shows that the mean square discrepancy of randomized low-discrepancy point sets can be computed in O(n) operations, whereas the standard discrepancy requires O(n^2) operations, making randomized quasi-Monte Carlo methods more efficient for high-dimensional integration problems.
Visualizing, Modeling and Forecasting of Functional Time Serieshanshang
The document discusses visualization and forecasting of functional time series data. It introduces visualization methods like rainbow plots, functional bagplots, and functional highest density region boxplots which can detect outliers. It also covers modeling and forecasting functional time series, as well as seasonal univariate time series using a functional approach. Several outlier detection techniques for functional data are compared, including those based on functional depth, integrated squared error, and robust Mahalanobis distance.
The melting of the West Antarctic ice sheet (WAIS) is likely to cause a significant rise in sea levels. Studying the present state of WAIS and predicting its future behavior involves the use of computer models of ice sheet dynamics as well as observational data. I will outline general statistical challenges posed by these scientific questions and data sets.
This discussion is based on joint work with Yawen Guan (Penn State/SAMSI), Won Chang (U. of Cincinnati), Patrick Applegate, David Pollard (Penn State)
This document provides a summary of spatial data modeling and analysis techniques. It begins with an outline of the topics to be covered, including additive statistical models for spatial data, spatial covariance functions, the multivariate normal distribution, kriging for prediction and uncertainty, and the likelihood function for parameter estimation. It then introduces the key concepts and equations for modeling spatial processes as Gaussian random fields with specified covariance functions. Examples are given of commonly used covariance functions and the types of random surfaces they generate. Kriging is described as a best linear unbiased prediction technique that uses a spatial covariance function and observations to make predictions at unknown locations. The document concludes with examples of parameter estimation via maximum likelihood and using the fitted model to make predictions and conditional simulations
Our techniques provide fast wavelet tree construction in practice based on recent theoretical work. Experiments on real datasets show our methods using the PEXT and PSHUFB CPU instructions outperform previous approaches. For wavelet trees, our methods are 1.9x faster than naive construction on average and competitive with state-of-the-art. For wavelet matrices, we achieve speedups of 1.1-1.9x over the state-of-the-art. This work provides the first practical implementation of the fastest known wavelet tree construction algorithms.
Spatio-Spectral Multichannel Reconstruction from few Low-Resolution Multispec...Amine Hadj-Youcef
This presentation deals with the reconstruction of a 3-D spatio-spectral object observed by a multispectral imaging system, where the original object is blurred with a spectral-variant PSF (Point Spread Function) and integrated over few broad spectral bands. In order to tackle this ill-posed problem, we propose a linear forward model that accounts for direct (or auto) channels and between (or cross) channels degradation, by modeling the imaging system response and the spectral distribution of the object with a piecewise linear function. Reconstruction based on regularization method is proposed, by enforcing spatial and spectral smoothness of the object. We test our approach on simulated data of the Mid-InfraRed Instrument (MIRI) Imager of the James Webb Space Telescope (JWST). Results on simulated multispectral data show a significant improvement over the conventional multichannel method.
Fast Identification of Heavy Hitters by Cached and Packed Group TestingRakuten Group, Inc.
The document summarizes a research paper on efficiently identifying heavy hitters in data streams using cached and packed group testing techniques. The paper proposes using packed bidirectional counter arrays to implement the operations of combinatorial group testing (CGT) in constant time. This improves the time complexity of CGT for updating frequencies and querying heavy hitters from O(log(n)) to O(1), eliminating dependency on the size of the data universe n. Experimental results show the proposed method achieves competitive precision, update throughput, and query throughput compared to existing CGT and hierarchical count-min sketch approaches.
We combined: low-rank tensor techniques and FFT to compute kriging, estimate variance, compute conditional covariance. We are able to solve 3D problems with very high resolution
1. Approximate message passing (AMP) is an algorithm that can be used for compressed sensing problems to recover a sparse signal x from linear measurements y=Ax+v in near-linear time.
2. Distributed AMP extends the AMP algorithm to distributed settings where multiple nodes take independent measurements yk=Akx+vk of the same signal x.
3. The distributed AMP algorithm involves nodes running AMP independently on their local measurements and aggregating information through message passing updates to estimate the signal x in a distributed manner.
1. The document discusses various algorithms and methods for solving optimization problems involving sparse signal recovery from underdetermined linear systems.
2. Key algorithms mentioned include iterative shrinkage-thresholding algorithms like FISTA, proximal splitting methods like ADMM, and regularization-based methods involving sparse-promoting penalties like l1-norm and sum of absolute values.
3. Applications discussed include compressed sensing, sparse signal recovery from MIMO systems, and discrete signal reconstruction problems.
A Hough Transform Based On a Map-Reduce AlgorithmIJERA Editor
This paper presents a method that proposes the composition of the Map-Reduce algorithm and the Hough
Transform method to research particular features of shape in the Big Data of images. We introduce the first
formal translation of the Hough Transform method into the Map-Reduce pattern. The Hough transform is
applied to one image or to several images in parallel. The context of the application of this method concerns Big
Data that requires Map-Reduce functions to improve the processing time and the need of object detection in
noisy pictures with the Hough Transform method.
MVPA with SpaceNet: sparse structured priorsElvis DOHMATOB
The GraphNet (aka S-Lasso), as well as other “sparsity + structure” priors like TV (Total-Variation), TV-L1, etc., are not easily applicable to brain data because of technical problems
relating to the selection of the regularization parameters. Also, in
their own right, such models lead to challenging high-dimensional optimization problems. In this manuscript, we present some heuristics for speeding up the overall optimization process: (a) Early-stopping, whereby one halts the optimization process when the test score (performance on leftout data) for the internal cross-validation for model-selection stops improving, and (b) univariate feature-screening, whereby irrelevant (non-predictive) voxels are detected and eliminated before the optimization problem is entered, thus reducing the size of the problem. Empirical results with GraphNet on real MRI (Magnetic Resonance Imaging) datasets indicate that these heuristics are a win-win strategy, as they add speed without sacrificing the quality of the predictions. We expect the proposed heuristics to work on other models like TV-L1, etc.
The document discusses discrete signal reconstruction using Discreteness-Aware Approximate Message Passing (DAMP). DAMP is an algorithm that can reconstruct discrete signals from compressed measurements by taking the discreteness of the signal into account. It is shown to outperform other methods like AMP and soft thresholding in terms of achieving lower mean square error and higher recovery rates, especially for signals with higher cardinality. The theoretical behavior of DAMP is also analyzed and shown to match empirical results.
- The document discusses methods for determining when to stop sampling in Monte Carlo integration to achieve a desired error tolerance.
- For independent and identically distributed (IID) sampling, the central limit theorem can be used to determine the necessary sample size based on the variance of the integrand.
- Quasi-Monte Carlo sampling can achieve faster convergence rates by using low-discrepancy point sets that more uniformly sample the domain. The error can be analyzed in the frequency domain based on the decay of the true Fourier coefficients.
- Bayesian cubature methods model the integrand as a Gaussian process, allowing inference of hyperparameters from sample points to improve integration accuracy.
In this talk we consider the question of how to use QMC with an empirical dataset, such as a set of points generated by MCMC. Using ideas from partitioning for parallel computing, we apply recursive bisection to reorder the points, and then interleave the bits of the QMC coordinates to select the appropriate point from the dataset. Numerical tests show that in the case of known distributions this is almost as effective as applying QMC directly to the original distribution. The same recursive bisection can also be used to thin the dataset, by recursively bisecting down to many small subsets of points, and then randomly selecting one point from each subset. This makes it possible to reduce the size of the dataset greatly without significantly increasing the overall error. Co-author: Fei Xie
The document discusses measuring sample quality using kernels. It introduces the kernel Stein discrepancy (KSD) as a new quality measure for comparing samples approximating a target distribution. The KSD is based on Stein's method and uses reproducing kernels. It can detect when a sample sequence is converging to the target distribution or not. Computing the KSD reduces to pairwise evaluations of kernel functions and is feasible. The KSD converges to zero if and only if the sample sequence converges to the target distribution for certain choices of kernels like the inverse multiquadric kernel with parameter between -1 and 0.
Double-grid 2D solver for Boussinesq Equation (BEq) ... DraftEmanuele Cordano
This is a draft presentation with the first application of the BEq model ... now it is published on http://onlinelibrary.wiley.com/doi/10.1002/wrcr.20072/abstract
The document discusses learning graphical models from data. It describes two main tasks: inference, which is computing answers to queries about a probability distribution described by a Bayesian network, and learning, which is estimating a model from data. It provides examples of learning for completely observed models, including maximum likelihood estimation for the parameters of a conditional Gaussian model. It also discusses supervised versus unsupervised learning of hidden Markov models, and techniques for dealing with small training sets like adding pseudocounts to estimates.
GPU acceleration of a non-hydrostatic ocean model with a multigrid Poisson/He...Takateru Yamagishi
To meet the demand for fast and detailed calculations in numerical ocean simulations, we implemented a non-hydrostatic ocean model on a graphics processing unit (GPU). We improved the model’s Poisson/Helmholtz solver by optimizing the memory access, using instruction-level parallelism, and applying a mixed precision calculation to the preconditioning of the Poisson/Helmholtz solver. The GPU-implemented model was 4.7 times faster than a comparable central processing unit execution. The output errors due to this implementation will not significantly influence oceanic studies.
The document discusses several algorithms for solving shortest path problems on graphs:
1. The Floyd-Warshall algorithm finds shortest paths between all pairs of vertices in a graph and runs in O(V3) time.
2. Bellman-Ford solves the single-source shortest paths problem for graphs with negative edge weights.
3. Dijkstra's algorithm solves the single-source shortest paths problem faster than Bellman-Ford for graphs with non-negative edge weights.
The document discusses three fundamental algorithms paradigms: recursion, divide-and-conquer, and dynamic programming. Recursion uses method calls to break down problems into simpler subproblems. Divide-and-conquer divides problems into independent subproblems, solves each, and combines solutions. Dynamic programming breaks problems into overlapping subproblems and builds up solutions, storing results of subproblems to avoid recomputing them. Examples like mergesort and calculating Fibonacci numbers are provided to illustrate the approaches.
This document presents a new algorithm for detecting dust storms using MODIS thermal infrared data. The algorithm uses brightness temperature differences (BTD) between bands 8.6, 11, and 12, which are normalized to account for the effect of land surface temperature on BTD. Results show the normalized BTD can successfully separate airborne dust from clouds and different surface types, including bright deserts, during both day and night.
The document presents a methodology for prototyping an albedo algorithm for GOES-R using MODIS data. It uses an optimization approach that incorporates atmospheric radiative transfer modeling and land surface BRDF modeling to estimate surface albedo, spectral reflectance, and aerosol optical depth from MODIS TOA reflectance observations. The estimates were validated against ground measurements and other satellite products, showing good agreement within F&PS requirements for albedo accuracy and reflectance precision. Future work will include additional validations and improving diurnal albedo estimation using geostationary data.
Stochastic Integer Programming. An Algorithmic PerspectiveSSA KPI
This document outlines challenges and algorithms for solving stochastic integer programs (SIPs). It discusses two-stage SIPs, where discrete decisions are made in two stages with uncertainties between stages. The key challenges are evaluating the cost of recourse decisions and optimizing over non-convex, discontinuous objective functions. For problems with simple integer recourse, where uncertainties affect right-hand sides, the document presents structural results and algorithms to address the challenges. It also discusses approaches for general mixed-integer recourse problems using approximations and the sample average approximation method.
This chapter discusses database design and management. It describes relational and object-oriented database models. For relational databases, entities are represented as tables related by primary and foreign keys. Object databases represent data as objects with attributes and relationships. Hybrid systems store objects in relational databases. The chapter also covers distributed databases which partition data across multiple physical locations for performance and availability.
WE1.L10 - USE OF NASA DATA IN THE JOINT CENTER FOR SATELLITE DATA ASSIMILATIONgrssieee
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*** For the video of this presentation please see http://lanyrd.com/2013/sotm/scpktb/
*** Full schedule available at http://wiki.openstreetmap.org/wiki/State_Of_The_Map_2013
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On prognozisys of manufacturing double basemsejjournal
In this paper we introduce a modification of recently introduced analytical approach to model mass- and
heat transport. The approach gives us possibility to model the transport in multilayer structures with account
nonlinearity of the process and time-varing coefficients and without matching the solutions at the
interfaces of the multilayer structures. As an example of using of the approach we consider technological
process to manufacture more compact double base heterobipolar transistor. The technological approach
based on manufacturing a heterostructure with required configuration, doping of required areas of this heterostructure
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The Analytical Nature of the Greens Function in the Vicinity of a Simple Poleijtsrd
It is known that the Green function of a boundary value problem is a meromorphic function of a spectral parameter. When the boundary conditions contain integro differential terms, then the meromorphism of the Greens function of such a problem can also be proved. In this case, it is possible to write out the structure of the residue at the singular points of the Greens function of the boundary value problem with integro differential perturbations. An analysis of the structure of the residue allows us to state that the corresponding functions of the original operator are sufficiently smooth functions. Surprisingly, the adjoint operator can have non smooth eigenfunctions. The degree of non smoothness of the eigenfunction of the adjoint operator to an operator with integro differential boundary conditions is clarified. It is indicated that even those conjugations to multipoint boundary value problems have non smooth eigenfunctions. Ghulam Hazrat Aimal Rasa "The Analytical Nature of the Green's Function in the Vicinity of a Simple Pole" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-6 , October 2020, URL: https://www.ijtsrd.com/papers/ijtsrd33696.pdf Paper Url: https://www.ijtsrd.com/mathemetics/applied-mathamatics/33696/the-analytical-nature-of-the-greens-function-in-the-vicinity-of-a-simple-pole/ghulam-hazrat-aimal-rasa
Field Induced Josephson Junction (FIJJ) is defined as the physical system made by placement of ferromagnetic strip directly or indirectly [insulator layer in-between] on the top of superconducting strip [3, 4, 7]. The analysis conducted in extended Ginzburg-Landau, Bogoliubov-de Gennes and RCSJ [11] models essentially points that the system is in most case a weak-link Josephson junction [2] and sometimes has features of tunneling Josephson junction [1]. Generalization of Field Induced Josephson junctions leads to the case of network of robust coupled field induced Josephson junctions [4] that interact in inductive way. Also the scheme of superconducting Random Access Memory (RAM) for Rapid Single Flux [8, 9] quantum (RSFQ) computer is drawn [6, 10] using the concept of tunneling Josephson junction [1] and Field Induced Josephson junction [3, 4].
The given presentation is also available by YouTube (https://www.youtube.com/watch?v=uIqXqiwDsSM).
Literature
[1]. B.D.Josephson, Possible new effects in superconductive tunnelling, PL, Vol.1, No. 251, 1962
[2]. K.Likharev, Josephson junctions Superconducting weak links, RMP, Vol. 51, No. 101, 1979
[3]. K.Pomorski and P.Prokopow, Possible existence of field induced Josephson junctions, PSS B, Vol.249, No.9, 2012
[4]. K.Pomorski, PhD thesis: Physical description of unconventional Josephson junction, Jagiellonian University, 2015
[4]. K.Pomorski, H.Akaike, A.Fujimaki, Towards robust coupled field induced Josephson junctions, arxiv:1607.05013, 2016
[6]. K.Pomorski, H.Akaike, A.Fujimaki, Relaxation method in description of RAM memory cell in RSFQ computer, Procedings of Applied Conference 2016 (in progress)
[7]. J.Gelhausen and M.Eschrig, Theory of a weak-link superconductor-ferromagnet Josephson structure, PRB, Vol.94, 2016
[8]. K.K. Likharev, Rapid Single Flux Quantum Logic (http://pavel.physics.sunysb.edu/RSFQ/Research/WhatIs/rsfqre2m.html)
[9]. Proceedings of Applied Superconductivity Confence 2016, plenary talk by N.Yoshikawa, Low-energy high-performance computing based on superconducting technology (http://ieeecsc.org/pages/plenary-series-applied-superconductivity-conference-2016-asc-2016#Plenary7)
[10]. A.Y.Herr and Q.P.Herr, Josephson magnetic random access memory system and method, International patent nr:8 270 209 B2, 2012
[11]. J.A.Blackburn, M.Cirillo, N.Gronbech-Jensen, A survey of classical and quantum interpretations of experiments on Josephson junctions at very low temperatures, arXiv:1602.05316v1, 2016
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Boston university; operations research presentation; 2013
1. OPERATIONS RESEARCH PRESENTATION
OPERATIONS RESEARCH
PRESENTATIONPRESENTATION
Al i Y ZhAlvin Yuan Zhang
Center of Information and System Engineering
Boston University
b t @b dyzboston@bu.edu
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
2. OPERATIONS RESEARCH PRESENTATION
OUTLINE
1 Project I: Sustainable Ecosystem (SE) Planning Based on Discrete
Stochastic Dynamic Programming (DSDP) and Evolutionary Game
Theory (EGT)
Project II: Research on the Locational‐Marginal‐Price (LMP) Based
Distribution Power Network
2
Project III: Optimization Approach to Parametric Tuning of Power
System Stabilizer (PSS) Based on Trajectory Sensitivity (TS) Analysis
3
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
3. OPERATIONS RESEARCH PRESENTATION
Project I: SE Planning Based on DSDP and EGT
Introduction
Why investigating SE Planning?
Ecosystems have been faced with server threats under the impacts of climate and humankind together
Different patterns of resource utilization could directly influenced ecosystem heath
Sustainability is an important target of developing nature ecosystem, i.e., SE
Difficulties
Ecosystems are usually influenced by many factors which are difficult to define and quantify
Research related to ecosystem is rather difficult due to its complex structures and metabolic processes
Direction: To represent multi‐subsystems and their dynamic interactions in an analytical form using a
reasonable number of equations and parameters!reasonable number of equations and parameters!
Drawbacks of Previous Work
Fundamental weakness is that they use strictly deterministic and quantitative approaches to describe systems
that are full of uncertainty and only qualitatively understoodthat are full of uncertainty and only qualitatively understood
Mainly focus on economically developed and densely populated areas, but neglected regions with adverse
weather conditions, such as Loess Plateau
Merely focused on analysis of overall resource planning among multi‐subsystems, but ignore impacts of dynamic
relationship among them, namely evolutionary game relations
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
Motivation: To explore some feasible applications of decision theory/method into SE planning, with a
specific area of ecological resource planning, such as water resource planning problem!
p g , y y g
4. OPERATIONS RESEARCH PRESENTATION
Project I: SE Planning Based on DSDP and EGT
Brief Overview of Loess Plateau
Extensive region (530,000 km2 ‐ larger than Spain and almost as large as France)
Extreme loss of soil fertility and reduction in arability
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
Natural and human factors threat the sustainability of Loess Plateau, especially the
shortage of water resource
5. OPERATIONS RESEARCH PRESENTATION
Project I: SE Planning Based on DSDP and EGT
Simplified DSDP Model for SE Planning
Definition 1: Resource and User
Define the total kinds of concerned resource as m,
Definition 2: Time Horizon
Define time horizon as k=1 2 N which represent,
which is utilized by n user subsystems (or known as
users). These users can be regarded as residents,
companies, governments, agriculture firms, etc.
Define time horizon as k=1, 2, …, N, which represent
the period when each user begin to utilize the
resource.
Definition 3: State Variable
Define state variable at time k as follows:
11 12 1( ) ( ) ( )x k x k x k
Definition 4: Decision Variable
Define decision variable at time k as follows:
( ) ( ) ( )u k u k u k
11 12 1
21 22 2
1 2
( ) ( ) ( )
( ) ( ) ( )
, 1,...,
( ) ( ) ( )
n
n
k
m m mn
x k x k x k
x k x k x k
k N
x k x k x k
X
11 12 1
21 22 2
1 2
( ) ( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( )
n
n
k k k
m m mn
u k u k u k
u k u k u k
u k u k u k
U U X
where xij(k) denotes as the case of whether the i‐th
resource is used by the j‐th user. If xij(k)=1, the i‐th
resource is assigned to the j‐th user; otherwise not.
1 2( ) ( ) ( )m m mn
where uij(k) denotes as the amount of resource that
the j‐th user decide to use from the i‐th one.
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
6. OPERATIONS RESEARCH PRESENTATION
Project I: SE Planning Based on DSDP and EGT
Simplified DSDP Model for SE Planning
111u
Define reward function at time interval [k, k+1] as
Definition 6: Reward Function
1
2
2
21u
12u
22u
u
ijC
ijS
[ , ]
follows
V
11 12 1
21 22 2
( ) ( ) ( )
( ) ( ) ( )
n
n
k
r k r k r k
r k r k r k
2
3
13u
23u
where rij (k) can be express as
V
1 2( ) ( ) ( )
k
m m mnr k r k r k
Definition 5: Transition Probability Matrix
Define state variable at time as follows:
h S d t th d f th j th th t
( ), ( ) 0
( )
0, ( ) 0
ij ij ij ij
ij
ij
S C u k x k
r k
x k
1| 1
11 12 1
21 22 2
( | , )
( ) ( ) ( )
( ) ( ) ( )
k k k k k
l
l
p k p k p k
p k p k p k
X XP P X X U
where Sij denote the reward of the j‐th user that
utilized the i‐th resource=; denote the cost Cij of the
j‐th user that utilized per‐unit amount of the i‐th
resource. Assume Sij =S~|j and Cij =Ci|~ .
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
1 2( ) ( ) ( )l l llu k u k p k
7. OPERATIONS RESEARCH PRESENTATION
Project I: SE Planning Based on DSDP and EGT
Simplified DSDP Model for SE Planning
Mathematically speaking, there are 2mxn kinds of
Remark 1
Based on Remark 2, P(Xk+1|Xk,Uk)=P(Xk+1|Xk, Uk),
Remark 3
y p g,
possible selection of Xk. However, it is obviously
that we can’t select every element of Xk as zero,
which means there is no resource is assigned to any
user. Assume that each resource will be assigned to
arbitrary user; and each use can get at least one
, ( k+1| k, k) ( k+1| k, k),
which is a stochastic matrix that can’t be easily
derived from analytical modeling. Referring C. C. Lin
et al*, we will use the statistic data of water
resource bulletin** to determine PXk+1|Xk. Using the
maximum likehood estimator, PXk+1|Xk could be
kind of resources. Thus, each row and each column
of Xk will have at least an integer 1 for any k=1,2, …,
N .
Moreover, a stationary Markov chain is used to
h bl h h d
Xk 1|Xk
estimated as the observation data as follows:
h h b f f h
ˆ ( ) , 1,...,ij
ij
i
N
p k k N
N
generate the state variable Xk, which is assumed to
take on a finite number of values
(1) (2) ( ) ( )
{ , ,..., ,..., }i l
k k k k k kX X X X X X
where Nij is the number of occurrences of the
transition from Xk
(i) to Xk
(j) at time k, and Ni is the
total number of times that has occurred at time k.
Remark 2
For any xij(k)=0, uij=0; xij(k)=1, 0<uij≤max(uij). Then,
Uk is dependent of Xk with a similar matrix structure.
W ill hi f i h f ll i di i
* C. C. Lin, et al, “A stochastic control strategy for hybrid electric vehicles,”
Proceedings of the American Control Conference, vol. 5, pp. 4710–4715, 2004.
** http://www.sxmwr.gov.cn/gb-zxfw-news-3-dfnj-28873
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
We will use this fact in the following discussions.
8. OPERATIONS RESEARCH PRESENTATION
Project I: SE Planning Based on DSDP and EGT
Simplified DSDP Model for SE Planning
DSDP model (Using DP Algorithm)
X( )k kJ
X X X(1) (2) (3)
0 0 1 0 0 1 0 1 0
, ,
1 1 0 1 1 1 1 0 1k k k
X X
U U
X X
U U
P X
X
1| 1 1
1 1
1 1
max ( ) ( , ) ( )
max ( ) ( ) ( )
k k
k k
k k
m n
ij k k
i j
m n
ij ij k k
r k i j g
r k p k J
X X X(4) (5) (6)
0 1 1 0 1 1 0 1 0
, ,
1 0 0 1 0 1 1 1 1k k k
X X X(7) (8) (9)
0 1 1 0 1 1 1 0 0
, ,
1 1 0 1 1 1 0 1 1k k k
U U
X X1 1k k
k k
j j
i j
Water Resource Planning based on the
Proposed DSDP Model
f d d i 2
X X X(10) (11) (12)
1 0 1 1 0 1 1 1 0
, ,
0 1 0 0 1 1 0 0 1k k k
X X X(13) (14) (15)
1 1 1 1 1 0 1 1 1
, ,
0 0 1 0 1 1 0 1 0k k k
surface water and ground water, i.e., m=2
Users subsystems can be classified as three
parts: agricultural firms, industrial usage and
daily usage, i.e., n=3
0 0 1 0 1 1 0 1 0
X X X(16) (17) (18)
1 1 1 1 0 0 1 0 1
, ,
0 1 1 1 1 1 1 1 0k k k
X X X(19) (20) (21)
1 0 1 1 1 0 1 1 1
, ,
1 1 1 1 0 1 1 0 0k k k
As indicated in 2011 Water Data Bulletin,
| |
3
3 4 1 ,
5j iS C
1 1 1 1 0 1 1 0 0k k k
X X X
X
(22) (23) (24)
(25)
1 1 1 1 1 0 1 1 1
, , ,
1 0 1 1 1 1 1 1 0
1 1 1
k k k
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
X(25)
1 1 1k
We list all the 25 possible cases of Xk as follows:
9. OPERATIONS RESEARCH PRESENTATION
Project I: SE Planning Based on DSDP and EGT
Simplified DSDP Model for SE Planning
Transition probability matrix PXk+1|Xk as
k=9
*Optimal results of water planning of L.P.
0.8
0.2
0.4
0.6
1|kk+XXP
10
15
20
25
0
5
10
15
20
0
( )iI
( )j
kXI
5
25
( )i
kXI
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
* Yuan Zhang. “Sustainable Ecosystem Planning Based on Discrete Stochastic Dynamic Programming and Evolutionary Game Theory”,
arXiv:1305.1990v2 [math.OC], May 2013.
10. OPERATIONS RESEARCH PRESENTATION
Project I: SE Planning Based on DSDP and EGT
Evolutionary Game Analysis of Water Resource Planning of L. P.
*Optimal results of water planning of L.P.
(cont…)
Evolutionary game theory as a supplemen‐
tation of the proposed SDP model
Two participants to do game playing in group A and B
Each payoff equals to 1 or 0, and u, v, (u>1, v>1 )
denote as the payoff of A and B, under cooperation
case, respectively
Two strategies in the decision games namely CTwo strategies in the decision games, namely, C
(sustainable usage), D (unsustainable usage)
p as the ratio of participant who choose strategy C
among group A; q as the ratio of choosing strategy D
among group B.a o g g oup
(p,q) can represent the evolutionary dynamics of the
system, which can satisfies** :
/ (1 )( 1)
/ (1 )( 1)
dp dt p p uq
dq dt q q vp
*
/ (1 )( 1)dq dt q q vp
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
* Yuan Zhang. “Sustainable Ecosystem Planning Based on Discrete Stochastic Dynamic Programming and Evolutionary Game Theory”,
arXiv:1305.1990v2 [math.OC], May 2013.
** D. Friedman, “Evolutionary games in economics,” Econometrica, vol. 6, no. 3, pp.637–660, 1991.
11. OPERATIONS RESEARCH PRESENTATION
Project I: SE Planning Based on DSDP and EGT
Evolutionary Game Analysis of Water Resource Planning of L. P.
*Evolutionary game theory as a supplementation of the proposed SDP model (Cont…)
Two ESS points: Q1=(0,0) & Q4=(1,1)
Three unstable points: Q2=(0 1) Q3=(1 0) Q5=(1/v 1/u)Three unstable points: Q2 (0,1), Q3 (1,0), Q5 (1/v, 1/u)
4(1,1)Q2(0,1)Q
5Q
Increasing v & u
1(0, 0)Q 3(1, 0)Q
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
* Yuan Zhang. “Sustainable Ecosystem Planning Based on Discrete Stochastic Dynamic Programming and Evolutionary Game Theory”,
arXiv:1305.1990v2 [math.OC], May 2013.
12. OPERATIONS RESEARCH PRESENTATION
Project I: SE Planning Based on DSDP and EGT
Conclusion
Conclusion
SE planning of the Loess Plateau area has been analyzed based on DSDP model and EGT
The concept of SE planning is introduced with specifications in ecological resource planning
Transition probability matrix is calculated in a statistic sense so as to derive the DSDP model
Although the approach is applied to the water resource planning of Loess Plateau as an example, the
methodology of using DSDP and EGT is applicable to other complex systems
Further reading: Yuan Zhang ‐‐ http://arxiv.org/abs/1305.1990
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
13. OPERATIONS RESEARCH PRESENTATION
Project II: Research on LMP-Based Distribution Power Network
Background Introduction
Necessity of investigating LMP in distribution network
Integration of smart grid in the electricity networks allows for the expansion of the real time marginal cost g f g y p g
based pricing to the distribution network
Due to increasing demands of energy generation and consumption, standard network structures will not be
sufficient to provide state‐of‐the‐art security of supply under increasing cost pressure
Power losses in the middle and cascading failures on customer side usually take place in distribution network g y p
with most of loads or electronics connected
Transaction of utilization and provision of real and reactive power by participants requires the improvement
of pricing in distribution network
Overall goal of LMP‐based distribution network
Propose a redesigned market that could embrace the distribution level and extend the clearing prices accounting
for the marginal costs that occur in this level, i.e., LMP
Consider effects of power consumers/ producers on LMP, when connected at the low voltage level ff f p / p , g
Direction: Investigate distribution level LMP that are incorporating marginal costs of real and reactive power,
transformer loss of life, and voltage control limits
Possibility: Propose certain novel optimization approach for distribution market clearing problem.
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
14. OPERATIONS RESEARCH PRESENTATION
Project II: Research on LMP-Based Distribution Power Network
Distribution network market clearing problem
2 2
2 2 2 2
0 ( ) ( )
sin(arccos( ))
( ) ( ) ( ) ( )
i i i
i i i
i i i i i
g g g
b b b
d d d
b b b
e e e e e
P Q C
Q P A
C P Q C P
Objective function & constraints* Power
Constraints of
generator,
d b d
, ,
, ,
,min i i i
i
b m b m
b m b m
g d dP
b g b b b
b i i
f f
f f
P c u P
tM
2 2 2 2
( ) ( ) ( ) ( ) ,
0,
0,
0,
i i i i i
i
e e e e e
b b b b b i
i
e
b i i
i i
C P Q C P e
if e is standalone
P if e is associated withd
if e is associated withg
distributed
loads and
electronic
devices
Cost of real power production of
the slack bus minus real power
consumption
Cost of transformer loss of life
,
, (1)
2 2
, (1)
2
1
b m
M
M
P
b
P
b
V
P
C C Q
c V
,
,
i i i
i i i
g e d
b b b b
i i i
g e d
b b b b
P P P P b
Q Q Q Q b
Overall
real and
reactive
balance at
Cost of real power procured at substation
Opportunity cost compensation generator
of reactive power at the substation
Cost of required voltage increase at the
2
, , , ,
. .
cos( ) sin( ), ( , )b m b b m b m b m b m b m b m b m
st
P V G VV G A A VV B A A b m
,
,
,
2
1500 1500
exp ,
383 273b m
b m
f b mH
f
H A
f
i i i
each bus
Transformer
Cost of required voltage increase at the
substation for voltage control
, , , ,
2
, , , ,
,
,
cos( ) sin( ), ( , )
,
,
b m b b m b m b m b m b m b m b m
b m b m n b m b m b m b m b m b m
b b m
m
b b m
Q V B VV B A A VV G A A m n
P P b
Q Q b
, , , ,
2
1, 2, , 3, , ,
2 2
, , ,
,
, ( , )
b m b m b m b m
H A
f f f b m f b m b m
b m b m b m
k k S k S f
S P Q b m
V V V b
loss of life
l l d f l
Real /Reactive power flow
on any line and its injections
at any bus
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
m ,
0
b b bV V V b
A
Voltage limitation & default
angle value for slack bus
at any bus
* E. Ntakou, M. C. Caramanis, “Price Discovery in Dynamic Power Markets with Low-Voltage Distriution-Network Participants,” Manuscript , Mar. 2013.
15. OPERATIONS RESEARCH PRESENTATION
Project II: Research on LMP-Based Distribution Power Network
Distribution network market clearing problem
Objective function & constraints (cont…)
Nonlinear objective function under constraint of a non‐convex setj
Using KKT condition to obtain the dual variable , which denotes as LMP of real and reactive power at each
bus in the distribution network
,P Q
b b
M t QP Q
,
, ,
, , (, (1) , (1)1)
2 2
, (1)
2 1m n Mm n M
m n m
M
n M
f b b m
b b
f bP P
b b
P V
b m
f mf b b
M t Q
c V
C
P Q V V
P P PQ P P
, , , (, (1) , (1)1)
2 1m n Mm n M Mf b b mf bQ P P V
M t Q
c V
P Q V V
, ,
2 2
, (1)
2 1
m n m n M
b b b b
b m
f mf b b
c V
CQ Q QQ Q Q
h d t i l l ffi i t f l/ ti
, (1) , (1) , (1) , (1)M M M Mb b b bP Q P Q
where denote as marginal loss coefficients of real/reactive power;
, ( ) , ( ) , ( ) , ( )
, , ,M M M Mb b b b
b b b bP P Q Q
denote as marginal cost of transformer loss of life; denote as marginal, ,
,m n m nf f
b bP Q
,m m
b b
V V
Q P
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
cost of voltage control that increases voltage at each bus as well as meets constraints in the problem.
16. OPERATIONS RESEARCH PRESENTATION
Project II: Research on LMP-Based Distribution Power Network
Distribution network market clearing problem
Objective function & constraints (cont…)
Using Matlab to do power flow calculation and then solve the aformentioned LMP in distribution networkUsing Matlab to do power flow calculation and then solve the aformentioned LMP in distribution network
Analyzing LMP based on some numerical results obtained from a give distribution level network
Related considerations of LMP in distribution network
Uniqueness of the solution: Radial power network (YES, unique); Meshed power network (NO, may be multiple…)Uniqueness of the solution: Radial power network (YES, unique); Meshed power network (NO, may be multiple…)
Multi‐period consideration: Evolution of LMP varied with Time & Space
Simplification approach: Linearization…
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
17. OPERATIONS RESEARCH PRESENTATION
Project II: Research on LMP-Based Distribution Power Network
Convex Relaxation: An Interesting Idea for Solving Market Clearing Problem
Conexify*
L. W. Gan, et al., proposed a convex relaxation method for optimal power flow in tree networks**
opt
x
( )f x
This form can then be transformed
into Second‐Order‐Cone constraint
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
* Oral communication with Prof. M. C. Caramanis.
** L. W. Gan, N. Li, U. Topcu, S. Low, “On the exactness of convex relaxation for optimal power flow in tree networks,” IEEE 51st Conference on Decision and Control, Dec.
2012 Caramanis.
18. OPERATIONS RESEARCH PRESENTATION
Project II: Research on LMP-Based Distribution Power Network
Reference
M. C. Caramanis, et al., “Provision of Regulation Service Reserves by Flexible Distributed Loads,” IEEE 51st Annual
Conference on Decision and Control, Dec. 2012.
M T Wishart et al “Smart demand‐sided management of LV distribution networks using multi‐objectiveM. T. Wishart, et al, Smart demand sided management of LV distribution networks using multi objective
decision making,” Manuscript for IEEE PES Transactions on Smart Grid.
M. C. Caramanis, “It is time for power market reform to allow for retail customer participation and distribution
network marginal pricing ” IEEE Smart Grid Mar 2012network marginal pricing, IEEE Smart Grid, Mar. 2012.
S. M. M. Agah, H. A. Abyaneh, “Distribution transformer loss‐of‐life reduction by increasing penetration of
distributed generation,” IEEE Transaction on Power Delivery, Apr. 2011.
M. C. Caramanis, R. E. Bohn and F. C. Schweppe, “Optimal spot pricing: price and theory,” IEEE Transactions on
PAS, vol. 101, 1982.
C. Y. Lee, H. C. Chang, H. C. Chen, “A method for estimating transformer temperatures and elapsed lives
considering operation loads”, WSEAS Transactions On Systems, Issue 11, vol. 7, pp.1349‐1358, Nov. 2008.considering operation loads , WSEAS Transactions On Systems, Issue 11, vol. 7, pp.1349 1358, Nov. 2008.
M. Thomson, D. G. Infield, “Network power flow analysis for a high penetration of distributed generation,” IEEE
Transactions and Power Systems, vol. 22, no. 3, pp. 1157‐1162, Aug. 2007.
E Nt k M C C i “P i Di i D i P M k t ith L V lt Di t i ti N t k
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
E. Ntakou, M. C. Caramanis, “Price Discovery in Dynamic Power Markets with Low‐Voltage Distriution‐Network
Participants,” Manuscript for IEEE Conference on decision and Control, Mar. 2013.
19. OPERATIONS RESEARCH PRESENTATION
Project III: Optimization Approach to Parametric Tuning of PS Based on TS
Research Background of Optimal PSS Parametric Tuning
Why Introducing PSS?
Grid interconnection of P.S. lead to oscillation that inhibits its long‐term stability
PSS is introduced as a feedback controller to decrease oscillations, and increase the reliability
Optimal PSS parametric tuning is crucial to P.S., and become a focal point of much on‐going research
Drawbacks of Previous Work
Merely focused on local equilibrium point/orbit, i.e., small disturbance ‐based
P.S. is essentially a hard (nonlinear and nonsmooth) dynamic system undergoing large disturbance (LD)
Traditional PSS optimization methods fail to obtain globally optimal parameter setTraditional PSS optimization methods fail to obtain globally optimal parameter set
Motivation: A LD‐based Optimal PSS parameter tuning approach should be explored!
DifficultiesDifficulties
Discontinuous change of P.S. structural dynamics under LD
Hybrid Power System (HPS): A mix of continuous‐time, discrete‐time and discrete‐event dynamics
TS analysis can focus around transient flow trajectory
Direction: Exploring from LD based optimization approach to evaluate TS under constraints of HPS model!
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
Direction: Exploring from LD‐based optimization approach to evaluate TS under constraints of HPS model!
20. OPERATIONS RESEARCH PRESENTATION
Project III: Optimization Approach to Parametric Tuning of PS Based on TS
Modeling of PSS and HPS
Major parameter set of PSS
1 2 3 4( , , , , )sK T T T Tl
TS information will be obtained from
Is iV ω
Definition 1: Switching Event
Switching event SE(i)
is defined as any event that
d l h h f l bcan directly trigger the change of algebraic states y
at the i‐th period, which can then form a switching
event set ASE, with its index set denoted as ISE.
Definition 2: Reset Event
Reset event RE(j)
is defined as any event that can
directly trigger the change of discrete states z at the
j‐th period which can then form a reset event set
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
j th period, which can then form a reset event set
ARE, with its index set denoted as IRE.
21. OPERATIONS RESEARCH PRESENTATION
Project III: Optimization Approach to Parametric Tuning of PS Based on TS
Modeling of PSS and HPS (Cont…)
* Compact HPS model of parameter‐dependent differential‐algebraic‐discrete (DAD)
[ , , ] n m p
c
x x z l ( , )x f x y
: n l p m n
f
: n l p m m
g
: ( )j n l p m l
h
(0)
( ) ( )
( ) ( )
( , )
( , ), ;
( , ), ; SE
i i
SE
Ai i
SE
SE A
i I
SE A
0 g x y
g x y
0
g x y
* Ian A. Hiskens and M. A. Pai. “Trajectory Sensitivity Analysis of Hybrid Systems” IEEE Trans. Power Sys. 47 (2), 2000. NOT GENERAL!
p
l
Incorporating parameters λ into the state x
( ) ( )
( )
( , ), ;
, ;
RE
RE
j j
RE A
j
RE A
RE A j I
RE A j I
z h x y
z 0
Ian A. Hiskens and M. A. Pai. Trajectory Sensitivity Analysis of Hybrid Systems IEEE Trans. Power Sys. 47 (2), 2000. NOT GENERAL!
Mapping SE(i)
and RE(j)
into two triggering hypersurfaces H(i)(x,y) and S(j)(x,y)
( )x f x y ( ) ( )t tx xy
(0)
( ) ( )
( ) ( )
( , )
( , )
( , ), ( , ) 0;
{1,2}
( ) ( ) 0;
i i
i i
H
i
H
x f x y
0 g x y
g x y x y
0
g x y x y
( ) ( , )ot t xx xy
( ) ( , )ot t yy xy
0 0( ) ( , )o ot t xx x xy
Trajectory
Flow
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
( ) ( )
( )
( , ), ( , ) 0;
, ( , ) 0; RE
j
A
H
S j I
g x y x y
z 0 x y
0( , ( , )) ( , )o o o ot y0 g x x g x yy
0l
Initial
Condition
22. OPERATIONS RESEARCH PRESENTATION
Project III: Optimization Approach to Parametric Tuning of PS Based on TS
Optimal PSS Parametric Tuning Based on TS
n l p m+ + +
2
min ( , )
f
K t
f iJ t dt x
Objective Function TS Analysis for HPS
1 1( ( ), ( ))J Jt tx y
p
x
y 0 0( , )x y
0Dx
1( )Jt+
Dx
t
2 2( ( ), ( ))J Jt tx y
2( )Jt+
Dx
0
1
(0)
( ) ( )
. . ( , )
( , )
( ) ( ) 0;
f it
i
i i
s t
H
x f x y
0 g x y
g x y x y
l
0 0t
(1)
( , ) 0H =x y
1Jt
1Jt
1Jt 2Jt
2Jt
(2)
( , ) 0H =x y
2Jt
(1)
SE (2)
SE
( ) ( )
( ) ( )
( )
( , ), ( , ) 0;
{1,2}
( , ), ( , ) 0;
, ( , ) 0;
( )
RE
i i
j
A
H
i
H
S j I
t
g x y x y
0
g x y x y
z 0 x y
TS (red parts)
0
0
( )
( )
, {1,2,..., }
o
o
i i i
t
t
i K
x x
y y
l l l
0
0
0
0
( )
)) (
( )
(
tt
t t
x
x
x
y
x x
y x
TS dynamics equations
1 2 1 2{ , , , }, { , , }k i si i iK T T l l l l l
K is the number of generators
Gradient information can be obtained as
TS dynamics equations
0 0
0 0
0
(1 ) (1 )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
d d t t t t
t t t t
x x y x
x x y x
x / x f x f y
0 g x g y
( ) ( ) ( ) ( )d d / f f
1 2[ , ]J Jt t t
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
1
( , ) 2 ( )
f
o
t
i
K
f i
t i
J t t
x ll
0 0
0 0
0
(2 ) (2 )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
d d t t t t
t t t t
x x y x
x x y x
x / x f x f y
0 g x g y
2[ , ]J ft t t
23. OPERATIONS RESEARCH PRESENTATION
Project III: Optimization Approach to Parametric Tuning of PS Based on TS
Optimal PSS Parametric Tuning Based on TS
TS Analysis for HPS (Cont…)
Refer Ian A. Hiskens et al, jump conditions for
th iti it ft th t t i i t
1 1( ( ), ( ))J Jt tx y
n l p m+ + +
x
y 0 0( , )x y
2 2( ( ), ( ))J Jt tx y
the sensitivity after the event triggering tJ1:
0 0 0
0 0 1
1 1 1
(1 ) 1 (1 )
1
( ) ( ) ( )
( ) [ ( ) ]|
J
J J J
J t
t t t
t
x x x
x y x x
x x f f
y g g x
0 0t
(1)
( , ) 0H =x y
0Dx
1Jt
1Jt
1Jt
1( )Jt+
Dx
t
2Jt
2Jt
(2)
( , ) 0H =x y
2Jt
2( )Jt+
Dx
(1)
SE (2)
SE
Updating the jump condition for the sensitivity
after the event triggering tJ2:
0 0 02 2 2( ) ( ) ( )J J Jt t t
x x xx x f f SE SE0 0 0
0 0 2
(2 ) 1 (2 )
2( ) [ ( ) ]|
J
J t
t
x y x xy g g x
Optimum searching using Conjugate Gradient Method (CGM)p g g j g ( )
1
1 1 1
, 0
( )
k k k k k
k k k kJ
d
d dl
l l
l
Powell‐Fletcher‐Reeves Rule
( ) ( ) ( )
[0 1] [0 1]
kk k m k k k kJ J s s J
d dll l l
Armijo Rule
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
1 1
1
( ) ( ) ( )
, 1,..., 1
( ) ( )
k k k
k
k k
J J J
k n
J J
l l l
l l
l l l
l l
[0,1], [0,1]
24. OPERATIONS RESEARCH PRESENTATION
Project III: Optimization Approach to Parametric Tuning of PS Based on TS
Application to IEEE Standard Test System
IEEE three‐machine‐nine‐bus standard test system
2G 3G
7 8 9
1
2
5
4
6
3
1G
1
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION
* Yuan Zhang. “Optimization Approach to Parametric Tuning of Power System Stabilizer Based on Trajectory Sensitivity Analysis”, arXiv:1305.0978v2 [cs.SY] , May 2013
25. OPERATIONS RESEARCH PRESENTATION
Project III: Optimization Approach to Parametric Tuning of PS Based on TS
Conclusion
Conclusion
Optimal PSS parametric tuning method is studied from the viewpoint of TS, both theoretically and numerically
Discontinuity is a major obstacle to analyze the constraints of this optimization problem
Gradient information of the objective function is obtained from TS of state variables w.r.t. PSS parameters
Objective function considers the transient features under large disturbances, which indicates that the proposed
method can effectively damp the spontaneous oscillation caused by large disturbance
Further reading: Yuan Zhang ‐‐ http://arxiv.org/abs/1305.0978
Yuan Zhang Boston University yzboston@bu.edu OPERATIONS RESEARCH PRESENTATION