The Experts below are selected from a list of 192 Experts worldwide ranked by ideXlab platform
Sridhar Krishnan - One of the best experts on this subject based on the ideXlab platform.
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Group sparse structure and elastic-net regularization for compressive sensing of pulse-type physiological signals
Biomedical Signal Processing and Control, 2020Co-Authors: Jeevan K. Pant, Sridhar KrishnanAbstract:Abstract Objective Group Gini (Gr. Gini) and average-group Gini (AvgGr. Gini) indexes are introduced for the evaluation of group-sparsity of rhythmic pulse-type physiological signals, and a new method for the reconstruction of physiological pulse-type rhythmic signals for compressive sensing (CS) applications is proposed. Methods Gr. Gini and AvgGr. Gini indexes are developed by generalizing the conventional Gini index, for the evaluation of sparsity of signals with grouped nonzero components. The signal reconstruction CS method is based on applying generalized Elastic-Net regularized least-squares. The elastic-net function is generalized by including nonconvex lp-Pseudonorm, so that its minimization results in enhanced group-sparse structure on the first-order difference (FoD) and second-order difference (SoD) of the signal. It operates by taking advantage of the pre-existing group-sparse structure on the FoD and SoD components of the original signal. This method is effective for reconstructing signals with pulse-type structures by encouraging the grouping of significant signal components. Results Simulation results demonstrate that the Gr. Gini and AvgGr. Gini indexes can effectively evaluate group sparse-structure. The proposed CS method can offer improvement in signal-to-noise ratio (SNR), structural similarity index measure, Gr. Gini index, and AvgGr. Gini index. It is found to offer improvement of Gr.Gini index, AvgGr.Gini index, and SNR by 0.4 % , 0.4 % , and 5.29 dB respectively, for electrocardiogram (ECG) signals and by 5.89 % , 5.89 % , 16 dB, respectively, for foot-gait signals. Conclusion The proposed CS method is effective for enhancing reconstruction performance of pulse-type physiological signals. Significance It can be useful for the development of healthcare system for remote and long-term telemonitoring of pulse-type physiological signals.
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Sparse Signal Reconstruction Using Multi-Sequential Lp Optimization
2018 IEEE International Symposium on Circuits and Systems (ISCAS), 2018Co-Authors: Jeevan K. Pant, Sridhar KrishnanAbstract:An improved nonconvex optimization based algorithm for the reconstruction of sparse signals for compressive sensing is proposed. The algorithm is based on minimizing nonconvex Lp Pseudonorm by using two multiple sequences of sub-optimizations. If the two iterates in between any two sub-optimizations happen to be very similar, one of the iterates is merged with the other. The merged iterate is then set to another randomly chosen vector that is orthogonal to the iterate obtained after merging. The multiple sequences of sub-optimizations can be implemented to run simultaneously in two cores of a multicore computer. Simulation results are presented which indicate that the proposed algorithm can offer improvement in the percentage of perfect signal reconstructions by upto 7% and reduction in the CPU time required to run the algorithm by upto 11%, relative to the competing algorithms.
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ISCAS - Sparse Signal Reconstruction Using Multi-Sequential Lp Optimization
2018 IEEE International Symposium on Circuits and Systems (ISCAS), 2018Co-Authors: Jeevan K. Pant, Sridhar KrishnanAbstract:An improved nonconvex optimization based algorithm for the reconstruction of sparse signals for compressive sensing is proposed. The algorithm is based on minimizing nonconvex Lp Pseudonorm by using two multiple sequences of sub-optimizations. If the two iterates in between any two sub-optimizations happen to be very similar, one of the iterates is merged with the other. The merged iterate is then set to another randomly chosen vector that is orthogonal to the iterate obtained after merging. The multiple sequences of sub-optimizations can be implemented to run simultaneously in two cores of a multicore computer. Simulation results are presented which indicate that the proposed algorithm can offer improvement in the percentage of perfect signal reconstructions by upto 7% and reduction in the CPU time required to run the algorithm by upto 11%, relative to the competing algorithms.
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EMBC - Compressive sensing of foot-gait signals by enhancing group block-sparse structure on the first-order difference
Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and, 2016Co-Authors: Jeevan K. Pant, Sridhar KrishnanAbstract:A new technique for improving the signal reconstruction performance for compressive sensing of gait signals is proposed. The algorithm is based on the minimization of a pseudo-norm which promotes group-block-sparse structure on the first-order difference of the signal. Signal blocks in foot gait signals occur as groups, and the locations of the group are estimated based on the regularization promoting block-sparse structure. The group locations are used for minimizing the Pseudonorm for promoting group-block-sparse structure. Simulation results demonstrate that the proposed technique yields upto 0.76dB improvement in the reconstruction performance for foot-gait signals relative to the algorithms promoting block-sparse structure.
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Compressive sensing of foot-gait signals by enhancing group block-sparse structure on the first-order difference
2016 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2016Co-Authors: Jeevan K. Pant, Sridhar KrishnanAbstract:A new technique for improving the signal reconstruction performance for compressive sensing of gait signals is proposed. The algorithm is based on the minimization of a pseudo-norm which promotes group-block-sparse structure on the first-order difference of the signal. Signal blocks in foot gait signals occur as groups, and the locations of the group are estimated based on the regularization promoting block-sparse structure. The group locations are used for minimizing the Pseudonorm for promoting group-block-sparse structure. Simulation results demonstrate that the proposed technique yields upto 0.76dB improvement in the reconstruction performance for foot-gait signals relative to the algorithms promoting block-sparse structure.
Jeevan K. Pant - One of the best experts on this subject based on the ideXlab platform.
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Compressive sensing using lp optimization
2020Co-Authors: Jeevan K. PantAbstract:Three problems in compressive sensing, namely, recovery of sparse signals from noise-free measurements, recovery of sparse signals from noisy measurements, and recovery of so called block-sparse signals from noisy measurements, are investigated. In Chapter 2, the reconstruction of sparse signals from noise-free measurements is investigated and three algorithms are developed. The first and second algorithms minimize the approximate L0 and Lp Pseudonorms, respectively, in the null space of the measurement matrix using a sequential quasi-Newton algorithm. An efficient line search based on Banach's fixed-point theorem is developed and applied in the second algorithm. The third algorithm minimizes the approximate Lp Pseudonorm in the null space by using a sequential conjugate-gradient (CG) algorithm. Simulation results are presented which demonstrate that the proposed algorithms yield improved signal reconstruction performance relative to that of the iterative reweighted (IR), smoothed L0 (SL0), and L1-minimization based algorithms. They also require a reduced amount of computations relative to the IR and L1-minimization based algorithms. The Lp-minimization based algorithms require less computation than the SL0 algorithm. In Chapter 3, the reconstruction of sparse signals and images from noisy measurements is investigated. First, two algorithms for the reconstruction of signals are developed by minimizing an Lp-Pseudonorm regularized squared error as the objective function using the sequential optimization procedure developed in Chapter 2. The first algorithm minimizes the objective function by taking steps along descent directions that are computed in the null space of the measurement matrix and its complement space. The second algorithm minimizes the objective function in the time domain by using a CG algorithm. Second, the well known total variation (TV) norm has been extended to a nonconvex version called the TVp Pseudonorm and an algorithm for the reconstruction of images is developed that involves minimizing a TVp-Pseudonorm regularized squared error using a sequential Fletcher-Reeves' CG algorithm. Simulation results are presented which demonstrate that the first two algorithms yield improved signal reconstruction performance relative to the IR, SL0, and L1-minimization based algorithms and require a reduced amount of computation relative to the IR and L1-minimization based algorithms. The TVp-minimization based algorithm yields improved image reconstruction performance and a reduced amount of computation relative to Romberg's algorithm. In Chapter 4, the reconstruction of so-called block-sparse signals is investigated. The L2/1 norm is extended to a nonconvex version, called the L2/p Pseudonorm, and an algorithm based on the minimization of an L2/p-Pseudonorm regularized squared error is developed. The minimization is carried out using a sequential Fletcher-Reeves' CG algorithm and the line search described in Chapter 2. A reweighting technique for the reduction of amount of computation and a method…
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Group sparse structure and elastic-net regularization for compressive sensing of pulse-type physiological signals
Biomedical Signal Processing and Control, 2020Co-Authors: Jeevan K. Pant, Sridhar KrishnanAbstract:Abstract Objective Group Gini (Gr. Gini) and average-group Gini (AvgGr. Gini) indexes are introduced for the evaluation of group-sparsity of rhythmic pulse-type physiological signals, and a new method for the reconstruction of physiological pulse-type rhythmic signals for compressive sensing (CS) applications is proposed. Methods Gr. Gini and AvgGr. Gini indexes are developed by generalizing the conventional Gini index, for the evaluation of sparsity of signals with grouped nonzero components. The signal reconstruction CS method is based on applying generalized Elastic-Net regularized least-squares. The elastic-net function is generalized by including nonconvex lp-Pseudonorm, so that its minimization results in enhanced group-sparse structure on the first-order difference (FoD) and second-order difference (SoD) of the signal. It operates by taking advantage of the pre-existing group-sparse structure on the FoD and SoD components of the original signal. This method is effective for reconstructing signals with pulse-type structures by encouraging the grouping of significant signal components. Results Simulation results demonstrate that the Gr. Gini and AvgGr. Gini indexes can effectively evaluate group sparse-structure. The proposed CS method can offer improvement in signal-to-noise ratio (SNR), structural similarity index measure, Gr. Gini index, and AvgGr. Gini index. It is found to offer improvement of Gr.Gini index, AvgGr.Gini index, and SNR by 0.4 % , 0.4 % , and 5.29 dB respectively, for electrocardiogram (ECG) signals and by 5.89 % , 5.89 % , 16 dB, respectively, for foot-gait signals. Conclusion The proposed CS method is effective for enhancing reconstruction performance of pulse-type physiological signals. Significance It can be useful for the development of healthcare system for remote and long-term telemonitoring of pulse-type physiological signals.
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Sparse Signal Reconstruction Using Multi-Sequential Lp Optimization
2018 IEEE International Symposium on Circuits and Systems (ISCAS), 2018Co-Authors: Jeevan K. Pant, Sridhar KrishnanAbstract:An improved nonconvex optimization based algorithm for the reconstruction of sparse signals for compressive sensing is proposed. The algorithm is based on minimizing nonconvex Lp Pseudonorm by using two multiple sequences of sub-optimizations. If the two iterates in between any two sub-optimizations happen to be very similar, one of the iterates is merged with the other. The merged iterate is then set to another randomly chosen vector that is orthogonal to the iterate obtained after merging. The multiple sequences of sub-optimizations can be implemented to run simultaneously in two cores of a multicore computer. Simulation results are presented which indicate that the proposed algorithm can offer improvement in the percentage of perfect signal reconstructions by upto 7% and reduction in the CPU time required to run the algorithm by upto 11%, relative to the competing algorithms.
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ISCAS - Sparse Signal Reconstruction Using Multi-Sequential Lp Optimization
2018 IEEE International Symposium on Circuits and Systems (ISCAS), 2018Co-Authors: Jeevan K. Pant, Sridhar KrishnanAbstract:An improved nonconvex optimization based algorithm for the reconstruction of sparse signals for compressive sensing is proposed. The algorithm is based on minimizing nonconvex Lp Pseudonorm by using two multiple sequences of sub-optimizations. If the two iterates in between any two sub-optimizations happen to be very similar, one of the iterates is merged with the other. The merged iterate is then set to another randomly chosen vector that is orthogonal to the iterate obtained after merging. The multiple sequences of sub-optimizations can be implemented to run simultaneously in two cores of a multicore computer. Simulation results are presented which indicate that the proposed algorithm can offer improvement in the percentage of perfect signal reconstructions by upto 7% and reduction in the CPU time required to run the algorithm by upto 11%, relative to the competing algorithms.
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EMBC - Compressive sensing of foot-gait signals by enhancing group block-sparse structure on the first-order difference
Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and, 2016Co-Authors: Jeevan K. Pant, Sridhar KrishnanAbstract:A new technique for improving the signal reconstruction performance for compressive sensing of gait signals is proposed. The algorithm is based on the minimization of a pseudo-norm which promotes group-block-sparse structure on the first-order difference of the signal. Signal blocks in foot gait signals occur as groups, and the locations of the group are estimated based on the regularization promoting block-sparse structure. The group locations are used for minimizing the Pseudonorm for promoting group-block-sparse structure. Simulation results demonstrate that the proposed technique yields upto 0.76dB improvement in the reconstruction performance for foot-gait signals relative to the algorithms promoting block-sparse structure.
Nikos Paragios - One of the best experts on this subject based on the ideXlab platform.
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Compressed-sensing-based content-driven hierarchical reconstruction: Theory and application to C-arm cone-beam tomography
Medical Physics, 2015Co-Authors: Hélène Langet, Cyril Riddell, Aymeric Reshef, Yves Trousset, Arthur Tenenhaus, Elisabeth Lahalle, Gilles Fleury, Nikos ParagiosAbstract:Purpose: This paper addresses the reconstruction of x-ray cone-beam computed tomography (CBCT) for interventional C-arm systems. Subsampling of CBCT is a significant issue with C-arms due to their slow rotation and to the low frame rate of their flat panel x-ray detectors. The aim of this work is to propose a novel method able to handle the subsampling artifacts generally observed with analytical reconstruction, through a content-driven hierarchical reconstruction based on compressed sensing. Methods: The central idea is to proceed with a hierarchical method where the most salient features (high intensities or gradients) are reconstructed first to reduce the artifacts these features induce. These artifacts are addressed first because their presence contaminates less salient features. Several hierarchical schemes aiming at streak artifacts reduction are introduced for C-arm CBCT: the empirical orthogonal matching pursuit approach with the ℓ0 Pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the ℓ1-norm constraint of compressed sensing, for reconstructing sparse vessels over a nonsparse background; homotopy with total variation (TV); and a novel empirical extension to nonlinear diffusion (NLD). Such principles are implemented with penalized iterative filtered backprojection algorithms. For soft-tissue imaging, the authors compare the use of TV and NLD filters as sparsity constraints, both optimized with the alternating direction method of multipliers, using a threshold for TV and a nonlinear weighting for NLD. Results: The authors show on simulated data that their approach provides fast convergence to good approximations of the solution of the TV-constrained minimization problem introduced by the compressed sensing theory. Using C-arm CBCT clinical data, the authors show that both TV and NLD can deliver improved image quality by reducing streaks. Conclusions: A flexible compressed-sensing-based algorithmic approach is proposed that is able to accommodate for a wide range of constraints. It is successfully applied to C-arm CBCT images that may not be so well approximated by piecewise constant functions.
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Compressed‐sensing‐based content‐driven hierarchical reconstruction: Theory and application to C‐arm cone‐beam tomography
Medical Physics, 2015Co-Authors: Hélène Langet, Cyril Riddell, Aymeric Reshef, Yves Trousset, Arthur Tenenhaus, Elisabeth Lahalle, Gilles Fleury, Nikos ParagiosAbstract:Purpose: This paper addresses the reconstruction of x-ray cone-beam computed tomography (CBCT) for interventional C-arm systems. Subsampling of CBCT is a significant issue with C-arms due to their slow rotation and to the low frame rate of their flat panel x-ray detectors. The aim of this work is to propose a novel method able to handle the subsampling artifacts generally observed with analytical reconstruction, through a content-driven hierarchical reconstruction based on compressed sensing. Methods: The central idea is to proceed with a hierarchical method where the most salient features (high intensities or gradients) are reconstructed first to reduce the artifacts these features induce. These artifacts are addressed first because their presence contaminates less salient features. Several hierarchical schemes aiming at streak artifacts reduction are introduced for C-arm CBCT: the empirical orthogonal matching pursuit approach with the l0 Pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the l1-norm constraint of compressed sensing, for reconstructing sparse vessels over a nonsparse background; homotopy with total variation (TV); and a novel empirical extension to nonlinear diffusion (NLD). Such principles are implemented with penalized iterative filtered backprojection algorithms. For soft-tissue imaging, the authors compare the use of TV and NLD filters as sparsity constraints, both optimized with the alternating direction method of multipliers, using a threshold for TV and a nonlinear weighting for NLD. Results: The authors show on simulated data that their approach provides fast convergence to good approximations of the solution of the TV-constrained minimization problem introduced by the compressed sensing theory. Using C-arm CBCT clinical data, the authors show that both TV and NLD can deliver improved image quality by reducing streaks. Conclusions: A flexible compressed-sensing-based algorithmic approach is proposed that is able to accommodate for a wide range of constraints. It is successfully applied to C-arm CBCT images that may not be so well approximated by piecewise constant functions.
Hélène Langet - One of the best experts on this subject based on the ideXlab platform.
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Compressed-sensing-based content-driven hierarchical reconstruction: Theory and application to C-arm cone-beam tomography
Medical Physics, 2015Co-Authors: Hélène Langet, Cyril Riddell, Aymeric Reshef, Yves Trousset, Arthur Tenenhaus, Elisabeth Lahalle, Gilles Fleury, Nikos ParagiosAbstract:Purpose: This paper addresses the reconstruction of x-ray cone-beam computed tomography (CBCT) for interventional C-arm systems. Subsampling of CBCT is a significant issue with C-arms due to their slow rotation and to the low frame rate of their flat panel x-ray detectors. The aim of this work is to propose a novel method able to handle the subsampling artifacts generally observed with analytical reconstruction, through a content-driven hierarchical reconstruction based on compressed sensing. Methods: The central idea is to proceed with a hierarchical method where the most salient features (high intensities or gradients) are reconstructed first to reduce the artifacts these features induce. These artifacts are addressed first because their presence contaminates less salient features. Several hierarchical schemes aiming at streak artifacts reduction are introduced for C-arm CBCT: the empirical orthogonal matching pursuit approach with the ℓ0 Pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the ℓ1-norm constraint of compressed sensing, for reconstructing sparse vessels over a nonsparse background; homotopy with total variation (TV); and a novel empirical extension to nonlinear diffusion (NLD). Such principles are implemented with penalized iterative filtered backprojection algorithms. For soft-tissue imaging, the authors compare the use of TV and NLD filters as sparsity constraints, both optimized with the alternating direction method of multipliers, using a threshold for TV and a nonlinear weighting for NLD. Results: The authors show on simulated data that their approach provides fast convergence to good approximations of the solution of the TV-constrained minimization problem introduced by the compressed sensing theory. Using C-arm CBCT clinical data, the authors show that both TV and NLD can deliver improved image quality by reducing streaks. Conclusions: A flexible compressed-sensing-based algorithmic approach is proposed that is able to accommodate for a wide range of constraints. It is successfully applied to C-arm CBCT images that may not be so well approximated by piecewise constant functions.
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Compressed‐sensing‐based content‐driven hierarchical reconstruction: Theory and application to C‐arm cone‐beam tomography
Medical Physics, 2015Co-Authors: Hélène Langet, Cyril Riddell, Aymeric Reshef, Yves Trousset, Arthur Tenenhaus, Elisabeth Lahalle, Gilles Fleury, Nikos ParagiosAbstract:Purpose: This paper addresses the reconstruction of x-ray cone-beam computed tomography (CBCT) for interventional C-arm systems. Subsampling of CBCT is a significant issue with C-arms due to their slow rotation and to the low frame rate of their flat panel x-ray detectors. The aim of this work is to propose a novel method able to handle the subsampling artifacts generally observed with analytical reconstruction, through a content-driven hierarchical reconstruction based on compressed sensing. Methods: The central idea is to proceed with a hierarchical method where the most salient features (high intensities or gradients) are reconstructed first to reduce the artifacts these features induce. These artifacts are addressed first because their presence contaminates less salient features. Several hierarchical schemes aiming at streak artifacts reduction are introduced for C-arm CBCT: the empirical orthogonal matching pursuit approach with the l0 Pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the l1-norm constraint of compressed sensing, for reconstructing sparse vessels over a nonsparse background; homotopy with total variation (TV); and a novel empirical extension to nonlinear diffusion (NLD). Such principles are implemented with penalized iterative filtered backprojection algorithms. For soft-tissue imaging, the authors compare the use of TV and NLD filters as sparsity constraints, both optimized with the alternating direction method of multipliers, using a threshold for TV and a nonlinear weighting for NLD. Results: The authors show on simulated data that their approach provides fast convergence to good approximations of the solution of the TV-constrained minimization problem introduced by the compressed sensing theory. Using C-arm CBCT clinical data, the authors show that both TV and NLD can deliver improved image quality by reducing streaks. Conclusions: A flexible compressed-sensing-based algorithmic approach is proposed that is able to accommodate for a wide range of constraints. It is successfully applied to C-arm CBCT images that may not be so well approximated by piecewise constant functions.
Boris Kruglikov - One of the best experts on this subject based on the ideXlab platform.
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vanishing of the entropy Pseudonorm for certain integrable systems
Electronic Research Announcements of The American Mathematical Society, 2006Co-Authors: Vladimir S Matveev, Boris KruglikovAbstract:We introduce the notion of entropy Pseudonorm for an action of R and prove that it vanishes for the group actions associated with a big class of integrable Hamiltonian systems. 1. Entropy Pseudonorm Let W be a smooth manifold and Φ : (R, +) → Diff(W ) a smooth action on it. Assume there exists a compact Φ-invariant exhaustion of W . Define the following function on R (where htop is the topological entropy): ρΦ(v) = htop(Φ(v)), v ∈ R. This function is a Pseudonorm on R (ρΦ(v) is well-defined because with our hypothesis the entropy hd of [Bo] does not depend on the distance function d, homogeneity is standard and the triangle inequality follows from the Hu formula [H]). We call ρΦ the entropy Pseudonorm. We will investigate it in the case of the Poisson action corresponding to an integrable Hamiltonian system on a symplectic manifold (W , ω). Namely, let (W , ω) possess pair-wise Poisson commuting functions I1, I2, . . . , In, which are functionally independent almost everywhere. Denote by φi the time τ shift along the Hamiltonian vector field of the function Ii. The maps φi commute and therefore generate the Poisson action of the group (R, +), Φ(τ1, . . . , τn) def = φ1 1 ◦ · · · ◦ φn n : W 2n → W , with the corresponding momentum map Ψ = (I1, . . . , In) : W 2n → R, see [A]. The entropy Pseudonorm ρΦ vanishes in the following important cases: − Williamson-Vey-Eliasson-Ito non-degenerate singularities [E, I]; − Taimanov non-degeneracy condition [T]. In the first case vanishing of topological entropy of the Hamiltonian flow was proved in [P2], in the second case in [T]. Since there is nothing special about the Hamiltonian in these situations, it can be changed to any of the integrals and ρΦ ≡ 0 follows. Also in [P1, BP]) vanishing of htop was proven for the cases: − Systems integrable with periodic integrals; − Collectively integrable systems (the definition is in [GS]). It is not difficult to see that in both cases the entropy Pseudonorm ρΦ vanishes as well. Note that Liouville integrability does not imply vanishing of topological entropy, see [BT] (more examples in [Bu]). For these examples the entropy Pseudonorm is degenerate, but it is possible to construct integrable examples [K] such that ρΦ is a norm. In the present paper we prove vanishing of the entropy Pseudonorm for another class of integrable systems. These systems were recently actively studied in mathematical physics in the
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deformation of big pseudoholomorphic disks and application to the hanh Pseudonorm
Comptes Rendus Mathematique, 2004Co-Authors: Boris KruglikovAbstract:Dette er forfatternes aksepterte versjon. This is the author’s final accepted manuscript.
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deformation of big pseudoholomorphic disks and application to the hanh Pseudonorm
arXiv: Complex Variables, 2003Co-Authors: Boris KruglikovAbstract:We simplify proof of the theorem that close to any pseudoholomorphic disk there passes a pseudoholomorphic disk of arbitrary close size with any pre-described sufficiently close direction. We apply these results to the Kobayashi and Hanh pseudodistances. It is shown they coincide in dimensions higher than four. The result is new even in the complex case.
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existence of close pseudoholomorphic disks for almost complex manifolds and an applications to kobayashi royden Pseudonorm
arXiv: Complex Variables, 2000Co-Authors: Boris KruglikovAbstract:In this paper we extend the notion of the Kobayashi-Royden Pseudonorm for almost complex manifolds. Its basic properties known from the complex analysis are preserved in the nonintegrable case as well. The main theorem on coincidence of the pseudodistance induced by this Pseudonorm with the Kobayashi pseudodistance for the almost complex manifold is equivalent to the possibility of deforming slightly a pseudoholomorphic disk in an almost complex manifold. We also describe the result in terms of h-principle and consider a geometric application for moduli spaces of pseudoholomorphic curves.
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existence of close pseudoholomorphic disks for almost complex manifolds and an application to the kobayashi royden Pseudonorm
Functional Analysis and Its Applications, 1999Co-Authors: Boris KruglikovAbstract:Dette er forfatternes aksepterte versjon. This is the author’s final accepted manuscript.
