The Experts below are selected from a list of 13164 Experts worldwide ranked by ideXlab platform
Brett D Wick - One of the best experts on this subject based on the ideXlab platform.
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a study of the matrix carleson Embedding Theorem with applications to sparse operators
Journal of Mathematical Analysis and Applications, 2016Co-Authors: Kelly Bickel, Brett D WickAbstract:Abstract In this paper, we study the dyadic Carleson Embedding Theorem in the matrix weighted setting. We provide two new proofs of this Theorem, which highlight connections between the matrix Carleson Embedding Theorem and both maximal functions and H 1 -BMO duality. Along the way, we establish boundedness results about maximal functions associated to matrix A 2 weights and duality results concerning H 1 and BMO sequence spaces in the matrix setting. As an application, we then use this Carleson Embedding Theorem to show that if S is a sparse operator, then the operator norm of S on L 2 ( W ) satisfies ‖ S ‖ L 2 ( W ) → L 2 ( W ) ≲ [ W ] A 2 3 2 , for every matrix A 2 weight W.
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a study of the matrix carleson Embedding Theorem with applications to sparse operators
arXiv: Classical Analysis and ODEs, 2015Co-Authors: Kelly Bickel, Brett D WickAbstract:In this paper, we study the dyadic Carleson Embedding Theorem in the matrix weighted setting. We provide two new proofs of this Theorem, which highlight connections between the matrix Carleson Embedding Theorem and both maximal functions and $H^1$-BMO duality. Along the way, we establish boundedness results about new maximal functions associated to matrix $A_2$ weights and duality results concerning $H^1$ and BMO sequence spaces in the matrix setting. As an application, we then use this Carleson Embedding Theorem to show that if $S$ is a sparse operator, then the operator norm of $S$ on $L^2(W)$ satisfies: \[ \| S\|_{L^2(W) \rightarrow L^2(W)} \lesssim [W]_{A_2}^{\frac{3}{2}},\] for every matrix $A_2$ weight $W$.
Saeed Zolfaghari - One of the best experts on this subject based on the ideXlab platform.
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residual analysis and combination of Embedding Theorem and artificial intelligence in chaotic time series forecasting
Applied Artificial Intelligence, 2011Co-Authors: Muhammad Ardalanifarsa, Saeed ZolfaghariAbstract:A combination of Embedding Theorem and artificial intelligence along with residual analysis is used to analyze and forecast chaotic time series. Based on Embedding Theorem, the time series is reconstructed into proper phase space points and fed into a neural network whose weights and biases are improved using genetic algorithms. As the residuals of predicted time series demonstrated chaotic behavior, they are reconstructed as a new chaotic time series. A new neural network is trained to forecast future values of residual time series. The residual analysis is repeated several times. Finally, a neural network is trained to capture the relationship among the predicted value of the original time series, residuals, and the original time series. The method is applied to two chaotic time series, Mackey-Glass and Lorenz, for validation, and it is concluded that the proposed method can forecast the chaotic time series more effectively and accurately than existing methods.
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chaotic time series prediction with residual analysis method using hybrid elman narx neural networks
Neurocomputing, 2010Co-Authors: Muhammad Ardalanifarsa, Saeed ZolfaghariAbstract:Residual analysis using hybrid Elman-NARX neural network along with Embedding Theorem is used to analyze and predict chaotic time series. Using Embedding Theorem, the Embedding parameters are determined and the time series is reconstructed into proper phase space points. The embedded phase space points are fed into an Elman neural network and trained. The residual of predicted time series is analyzed, and it was observed that residuals demonstrate chaotic behaviour. The residuals are considered as a new chaotic time series and reconstructed according to Embedding Theorem. A new Elman neural network is trained to predict the future value of the residual time series. The residual analysis is repeated several times. Finally, a NARX network is used to capture the relationship among the predicted value of original time series and residuals and original time series. The method is applied to Mackey-Glass and Lorenz equations which produce chaotic time series, and to a real life chaotic time series, Sunspot time series, to evaluate the validity of the proposed technique. Numerical experimental results confirm that the proposed method can predict the chaotic time series more effectively and accurately when compared with the existing prediction methods.
Hitoshi Tanaka - One of the best experts on this subject based on the ideXlab platform.
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the n linear Embedding Theorem
Potential Analysis, 2016Co-Authors: Hitoshi TanakaAbstract:Let σ i , i = 1,…, n, denote positive Borel measures on \(\mathbb {R}^{d}\), let \(\mathcal {D}\) denote the usual collection of dyadic cubes in \(\mathbb {R}^{d}\) and let \(K:\,\mathcal {D}\to [0,\infty )\) be a map. In this paper we give a characterization of the n linear Embedding Theorem. That is, we give a characterization of the inequality $$\sum\limits_{Q\in\mathcal{D}} K(Q)\prod\limits_{i=1}^{n}\left|{\int}_{Q}f_{i}\,d{\sigma}_{i}\right| \le C\prod\limits_{i=1}^{n} \|f_{i}\|_{L^{p_{i}}(d{\sigma}_{i})} $$ in terms of the multilinear Sawyer testing conditions and the n weight discrete Wolff potential conditions, when 1 < p i < ∞.
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the n linear Embedding Theorem
arXiv: Classical Analysis and ODEs, 2015Co-Authors: Hitoshi TanakaAbstract:Let $\sigma_i$, $i=1,\ldots,n$, denote positive Borel measures on $\mathbb{R}^d$, let $\mathcal{D}$ denote the usual collection of dyadic cubes in $\mathbb{R}^d$ and let $K:\,\mathcal{D}\to[0,\infty)$ be a~map. In this paper we give a~characterization of the $n$ linear Embedding Theorem. That is, we give a~characterization of the inequality $$ \sum_{Q\in\mathcal{D}} K(Q)\prod_{i=1}^n\left|\int_{Q}f_i\,d\sigma_i\right| \le C \prod_{i=1}^n \|f_i\|_{L^{p_i}(d\sigma_i)} $$ in terms of multilinear Sawyer's checking condition and discrete multinonlinear Wolff's potential, when $1
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The trilinear Embedding Theorem
arXiv: Classical Analysis and ODEs, 2014Co-Authors: Hitoshi TanakaAbstract:Let $\sigma_i$, $i=1,2,3$, denote positive Borel measures on $\mathbb{R}^n$, let $\mathcal{D}$ denote the usual collection of dyadic cubes in $\mathbb{R}^n$ and let $K:\,\mathcal{D}\to[0,\infty)$ be a map. In this paper we give a characterization of the trilinear Embedding Theorem. That is, we give a characterization of the inequality $$ \sum_{Q\in\mathcal{D}} K(Q)\prod_{i=1}^3\left|\int_{Q}f_i\,d\sigma_i\right| \le C \prod_{i=1}^3 \|f_i\|_{L^{p_i}(d\sigma_i)} $$ in terms of discrete Wolff's potential and Sawyer's checking condition, when $1
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the trilinear Embedding Theorem
arXiv: Classical Analysis and ODEs, 2014Co-Authors: Hitoshi TanakaAbstract:Let $\sigma_i$, $i=1,2,3$, denote positive Borel measures on $\mathbb{R}^n$, let $\mathcal{D}$ denote the usual collection of dyadic cubes in $\mathbb{R}^n$ and let $K:\,\mathcal{D}\to[0,\infty)$ be a map. In this paper we give a characterization of the trilinear Embedding Theorem. That is, we give a characterization of the inequality $$ \sum_{Q\in\mathcal{D}} K(Q)\prod_{i=1}^3\left|\int_{Q}f_i\,d\sigma_i\right| \le C \prod_{i=1}^3 \|f_i\|_{L^{p_i}(d\sigma_i)} $$ in terms of discrete Wolff's potential and Sawyer's checking condition, when $1
Kelly Bickel - One of the best experts on this subject based on the ideXlab platform.
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a study of the matrix carleson Embedding Theorem with applications to sparse operators
Journal of Mathematical Analysis and Applications, 2016Co-Authors: Kelly Bickel, Brett D WickAbstract:Abstract In this paper, we study the dyadic Carleson Embedding Theorem in the matrix weighted setting. We provide two new proofs of this Theorem, which highlight connections between the matrix Carleson Embedding Theorem and both maximal functions and H 1 -BMO duality. Along the way, we establish boundedness results about maximal functions associated to matrix A 2 weights and duality results concerning H 1 and BMO sequence spaces in the matrix setting. As an application, we then use this Carleson Embedding Theorem to show that if S is a sparse operator, then the operator norm of S on L 2 ( W ) satisfies ‖ S ‖ L 2 ( W ) → L 2 ( W ) ≲ [ W ] A 2 3 2 , for every matrix A 2 weight W.
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a study of the matrix carleson Embedding Theorem with applications to sparse operators
arXiv: Classical Analysis and ODEs, 2015Co-Authors: Kelly Bickel, Brett D WickAbstract:In this paper, we study the dyadic Carleson Embedding Theorem in the matrix weighted setting. We provide two new proofs of this Theorem, which highlight connections between the matrix Carleson Embedding Theorem and both maximal functions and $H^1$-BMO duality. Along the way, we establish boundedness results about new maximal functions associated to matrix $A_2$ weights and duality results concerning $H^1$ and BMO sequence spaces in the matrix setting. As an application, we then use this Carleson Embedding Theorem to show that if $S$ is a sparse operator, then the operator norm of $S$ on $L^2(W)$ satisfies: \[ \| S\|_{L^2(W) \rightarrow L^2(W)} \lesssim [W]_{A_2}^{\frac{3}{2}},\] for every matrix $A_2$ weight $W$.
Muhammad Ardalanifarsa - One of the best experts on this subject based on the ideXlab platform.
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residual analysis and combination of Embedding Theorem and artificial intelligence in chaotic time series forecasting
Applied Artificial Intelligence, 2011Co-Authors: Muhammad Ardalanifarsa, Saeed ZolfaghariAbstract:A combination of Embedding Theorem and artificial intelligence along with residual analysis is used to analyze and forecast chaotic time series. Based on Embedding Theorem, the time series is reconstructed into proper phase space points and fed into a neural network whose weights and biases are improved using genetic algorithms. As the residuals of predicted time series demonstrated chaotic behavior, they are reconstructed as a new chaotic time series. A new neural network is trained to forecast future values of residual time series. The residual analysis is repeated several times. Finally, a neural network is trained to capture the relationship among the predicted value of the original time series, residuals, and the original time series. The method is applied to two chaotic time series, Mackey-Glass and Lorenz, for validation, and it is concluded that the proposed method can forecast the chaotic time series more effectively and accurately than existing methods.
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chaotic time series prediction with residual analysis method using hybrid elman narx neural networks
Neurocomputing, 2010Co-Authors: Muhammad Ardalanifarsa, Saeed ZolfaghariAbstract:Residual analysis using hybrid Elman-NARX neural network along with Embedding Theorem is used to analyze and predict chaotic time series. Using Embedding Theorem, the Embedding parameters are determined and the time series is reconstructed into proper phase space points. The embedded phase space points are fed into an Elman neural network and trained. The residual of predicted time series is analyzed, and it was observed that residuals demonstrate chaotic behaviour. The residuals are considered as a new chaotic time series and reconstructed according to Embedding Theorem. A new Elman neural network is trained to predict the future value of the residual time series. The residual analysis is repeated several times. Finally, a NARX network is used to capture the relationship among the predicted value of original time series and residuals and original time series. The method is applied to Mackey-Glass and Lorenz equations which produce chaotic time series, and to a real life chaotic time series, Sunspot time series, to evaluate the validity of the proposed technique. Numerical experimental results confirm that the proposed method can predict the chaotic time series more effectively and accurately when compared with the existing prediction methods.