The Experts below are selected from a list of 258 Experts worldwide ranked by ideXlab platform

Sivakanth Gopi - One of the best experts on this subject based on the ideXlab platform.

  • lower bounds for constant query affine invariant lccs and ltcs
    ACM Transactions on Computation Theory, 2017
    Co-Authors: Arnab Bhattacharyya, Sivakanth Gopi
    Abstract:

    Affine-invariant codes are codes whose coordinates form a vector space over a finite field and which are invariant under affine transformations of the coordinate space. They form a natural, well-studied class of codes; they include popular codes such as Reed-Muller and Reed-Solomon. A particularly appealing feature of affine-invariant codes is that they seem well suited to admit local correctors and testers. In this work, we give lower bounds on the length of locally correctable and locally testable affine-invariant codes with constant query complexity. We show that if a code C ⊂ ΣKn is an r-query affine invariant locally correctable code (LCC), where K is a finite field and Σ is a finite alphabet, then the number of codewords in C is at most exp(OK,r,vΣv(nr−1)). Also, we show that if C ⊂ ΣKn is an r-query affine invariant locally testable code (LTC), then the number of codewords in C is at most exp(OK,r,vΣv(nr−2)). The dependence on n in these bounds is tight for constant-query LCCs/LTCs, since Guo, Kopparty, and Sudan (ITCS’13) constructed affine-invariant codes via lifting that have the same asymptotic tradeoffs. Note that our result holds for non-linear codes, whereas previously, Ben-Sasson and Sudan (RANDOM’11) assumed linearity to derive similar results. Our analysis uses higher-order Fourier analysis. In particular, we show that the codewords corresponding to an affine-invariant LCC/LTC must be far from each other with respect to Gowers norm of an appropriate order. This then allows us to bound the number of codewords, using known decomposition theorems, which approximate any Bounded Function in terms of a finite number of low-degree non-classical polynomials, up to a small error in the Gowers norm.

  • lower bounds for constant query affine invariant lccs and ltcs
    Conference on Computational Complexity, 2016
    Co-Authors: Arnab Bhattacharyya, Sivakanth Gopi
    Abstract:

    Affine-invariant codes are codes whose coordinates form a vector space over a finite field and which are invariant under affine transformations of the coordinate space. They form a natural, well-studied class of codes; they include popular codes such as Reed-Muller and Reed-Solomon. A particularly appealing feature of affine-invariant codes is that they seem well-suited to admit local correctors and testers. In this work, we give lower bounds on the length of locally correctable and locally testable affine-invariant codes with constant query complexity. We show that if a code C ⊂ ΣKn is an r-query locally correctable code (LCC), where K is a finite field and Σ is a finite alphabet, then the number of codewords in C is at most exp(OK,r,|Σ|(nr-1)). Also, we show that if C ⊂ ΣKn is an r-query locally testable code (LTC), then the number of codewords in C is at most exp(OK,r,|Σ|(nr-2)). The dependence on n in these bounds is tight for constant-query LCCs/LTCs, since Guo, Kopparty and Sudan (ITCS'13) construct affine-invariant codes via lifting that have the same asymptotic tradeoffs. Note that our result holds for non-linear codes, whereas previously, Ben-Sasson and Sudan (RANDOM'11) assumed linearity to derive similar results. Our analysis uses higher-order Fourier analysis. In particular, we show that the codewords corresponding to an affine-invariant LCC/LTC must be far from each other with respect to Gowers norm of an appropriate order. This then allows us to bound the number of codewords, using known decomposition theorems which approximate any Bounded Function in terms of a finite number of low-degree non-classical polynomials, upto a small error in the Gowers norm.

Li-chen Fu - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear adaptive speed and torque control of induction motors with unknown rotor resistance
    IEEE Transactions on Industrial Electronics, 2001
    Co-Authors: Li-chen Fu, Chin-yu Tsai
    Abstract:

    In this paper, we propose a nonlinear adaptive speed and torque controller of induction motors with unknown rotor resistance. All the system parameters except rotor resistance are assumed to be known, and only the stator currents and rotor speed are assumed to be available. The desired speed and torque should be a smooth Bounded Function. A complete proof of the global stability without singularity is given, and the output error will converge to zero asymptotically. Finally, the simulation and experimental results are given to demonstrate the effectiveness of the proposed controller.

  • Nonlinear adaptive speed and torque servo control of induction motors with unknown rotor resistance
    Proceedings of the 1997 American Control Conference (Cat. No.97CH36041), 1997
    Co-Authors: Li-chen Fu
    Abstract:

    We propose a nonlinear adaptive speed and torque controller of induction motors with unknown rotor resistance. All the system parameters except rotor resistance are assumed to be known and only the stator currents and rotor speed are assumed to be available. The desired speed and torque should be any continuously differentiable Bounded Function. A complete proof of the global stability without singularity is given and the output error will converge to zero asymptotically. Finally, simulation and experimental results are given to demonstrate the effectiveness.

Arnab Bhattacharyya - One of the best experts on this subject based on the ideXlab platform.

  • lower bounds for constant query affine invariant lccs and ltcs
    ACM Transactions on Computation Theory, 2017
    Co-Authors: Arnab Bhattacharyya, Sivakanth Gopi
    Abstract:

    Affine-invariant codes are codes whose coordinates form a vector space over a finite field and which are invariant under affine transformations of the coordinate space. They form a natural, well-studied class of codes; they include popular codes such as Reed-Muller and Reed-Solomon. A particularly appealing feature of affine-invariant codes is that they seem well suited to admit local correctors and testers. In this work, we give lower bounds on the length of locally correctable and locally testable affine-invariant codes with constant query complexity. We show that if a code C ⊂ ΣKn is an r-query affine invariant locally correctable code (LCC), where K is a finite field and Σ is a finite alphabet, then the number of codewords in C is at most exp(OK,r,vΣv(nr−1)). Also, we show that if C ⊂ ΣKn is an r-query affine invariant locally testable code (LTC), then the number of codewords in C is at most exp(OK,r,vΣv(nr−2)). The dependence on n in these bounds is tight for constant-query LCCs/LTCs, since Guo, Kopparty, and Sudan (ITCS’13) constructed affine-invariant codes via lifting that have the same asymptotic tradeoffs. Note that our result holds for non-linear codes, whereas previously, Ben-Sasson and Sudan (RANDOM’11) assumed linearity to derive similar results. Our analysis uses higher-order Fourier analysis. In particular, we show that the codewords corresponding to an affine-invariant LCC/LTC must be far from each other with respect to Gowers norm of an appropriate order. This then allows us to bound the number of codewords, using known decomposition theorems, which approximate any Bounded Function in terms of a finite number of low-degree non-classical polynomials, up to a small error in the Gowers norm.

  • lower bounds for constant query affine invariant lccs and ltcs
    Conference on Computational Complexity, 2016
    Co-Authors: Arnab Bhattacharyya, Sivakanth Gopi
    Abstract:

    Affine-invariant codes are codes whose coordinates form a vector space over a finite field and which are invariant under affine transformations of the coordinate space. They form a natural, well-studied class of codes; they include popular codes such as Reed-Muller and Reed-Solomon. A particularly appealing feature of affine-invariant codes is that they seem well-suited to admit local correctors and testers. In this work, we give lower bounds on the length of locally correctable and locally testable affine-invariant codes with constant query complexity. We show that if a code C ⊂ ΣKn is an r-query locally correctable code (LCC), where K is a finite field and Σ is a finite alphabet, then the number of codewords in C is at most exp(OK,r,|Σ|(nr-1)). Also, we show that if C ⊂ ΣKn is an r-query locally testable code (LTC), then the number of codewords in C is at most exp(OK,r,|Σ|(nr-2)). The dependence on n in these bounds is tight for constant-query LCCs/LTCs, since Guo, Kopparty and Sudan (ITCS'13) construct affine-invariant codes via lifting that have the same asymptotic tradeoffs. Note that our result holds for non-linear codes, whereas previously, Ben-Sasson and Sudan (RANDOM'11) assumed linearity to derive similar results. Our analysis uses higher-order Fourier analysis. In particular, we show that the codewords corresponding to an affine-invariant LCC/LTC must be far from each other with respect to Gowers norm of an appropriate order. This then allows us to bound the number of codewords, using known decomposition theorems which approximate any Bounded Function in terms of a finite number of low-degree non-classical polynomials, upto a small error in the Gowers norm.

Chin-yu Tsai - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear adaptive speed and torque control of induction motors with unknown rotor resistance
    IEEE Transactions on Industrial Electronics, 2001
    Co-Authors: Li-chen Fu, Chin-yu Tsai
    Abstract:

    In this paper, we propose a nonlinear adaptive speed and torque controller of induction motors with unknown rotor resistance. All the system parameters except rotor resistance are assumed to be known, and only the stator currents and rotor speed are assumed to be available. The desired speed and torque should be a smooth Bounded Function. A complete proof of the global stability without singularity is given, and the output error will converge to zero asymptotically. Finally, the simulation and experimental results are given to demonstrate the effectiveness of the proposed controller.

Ping Zhang - One of the best experts on this subject based on the ideXlab platform.

  • STRIATED REGULARITY OF 2-D INHOMOGENEOUS INCOMPRESSIBLE NAVIER-STOKES SYSTEM WITH VARIABLE VISCOSITY
    Communications in Mathematical Physics, 2020
    Co-Authors: Marius Paicu, Ping Zhang
    Abstract:

    In this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier-Stokes equations with viscous coefficient depending on the density and with initial density being discontinuous across some smooth interface. Compared with the previous results for the inhomogeneous Navier-Stokes equations with constant viscosity, the main difficulty here lies in the fact that the L 1 in time Lipschitz estimate of the velocity field can not be obtained by energy method (see [11, 20, 21] for instance). Motivated by the key idea of Chemin to solve 2-D vortex patch of ideal fluid ([6, 7]), namely, striated regularity can help to get the L ∞ Boundedness of the double Riesz transform, we derive the a priori L 1 in time Lipschitz estimate of the velocity field under the assumption that the viscous coefficient is close enough to a positive constant in the Bounded Function space. As an application, we shall prove the propagation of H 3 regularity of the interface between fluids with different densities.

  • Global Fujita-Kato solution of 3-D inhomogeneous incompressible Navier-Stokes system
    arXiv: Analysis of PDEs, 2018
    Co-Authors: Ping Zhang
    Abstract:

    In this paper, we shall prove the global existence of weak solutions to 3D inhomogeneous incompressible Navier-Stokes system $({\rm INS})$ with initial density in the Bounded Function space and having a positive lower bound and with initial velocity being sufficiently small in the critical Besov space, $\dot B^{\f12}_{2,1}.$ This result corresponds to the Fujita-Kato solutions of the classical Navier-Stokes system. The same idea can be used to prove the global existence of weak solutions in the \emph{critical Functional framework} to $({\rm INS})$ with one component of the initial velocity being large and can also be applied to provide a lower bound for the lifespan of smooth enough solutions of $({\rm INS}).$