The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

P Gunter - One of the best experts on this subject based on the ideXlab platform.

  • orientational photorefractive effect in nematic liquid crystal with externally applied fields
    Journal of Applied Physics, 2000
    Co-Authors: Guoquan Zhang, G Montemezzani, P Gunter
    Abstract:

    Light-induced space-charge fields and the related orientational photorefractive effects in nematic liquid crystal cells are studied both theoretically and experimentally. Analytical solutions for the refractive index change distribution are obtained under the single-elastic-Constant Approximation with various configurations of externally applied electric and magnetic fields and of the nematic liquid crystal director. The effects of the rigid boundary condition are investigated in detail. The grating spacing for which the refractive index change is maximized depends on the strength of external electric and magnetic fields. The responses of parallel cells differ from those of homeotropic cells, both upon the dependencies on the grating spacing and on the external fields. Under the same conditions, the orientational photorefractive effects are stronger in parallel cells than in homeotropic ones. It is also shown that the investigated effects will be greatly enhanced near the Freedericksz transition. Experime...

  • orientational photorefractive effect in nematic liquid crystal with externally applied fields
    Journal of Applied Physics, 2000
    Co-Authors: Guoquan Zhang, G Montemezzani, P Gunter
    Abstract:

    Light-induced space-charge fields and the related orientational photorefractive effects in nematic liquid crystal cells are studied both theoretically and experimentally. Analytical solutions for the refractive index change distribution are obtained under the single-elastic-Constant Approximation with various configurations of externally applied electric and magnetic fields and of the nematic liquid crystal director. The effects of the rigid boundary condition are investigated in detail. The grating spacing for which the refractive index change is maximized depends on the strength of external electric and magnetic fields. The responses of parallel cells differ from those of homeotropic cells, both upon the dependencies on the grating spacing and on the external fields. Under the same conditions, the orientational photorefractive effects are stronger in parallel cells than in homeotropic ones. It is also shown that the investigated effects will be greatly enhanced near the Freedericksz transition. Experimental verifications of the photorefractive response in parallel aligned cells confirm the necessity to consider the boundary conditions explicitly.

Oded Regev - One of the best experts on this subject based on the ideXlab platform.

  • The complexity of the covering radius problem
    computational complexity, 2005
    Co-Authors: Venkatesan Guruswami, Daniele Micciancio, Oded Regev
    Abstract:

    We initiate the study of the computational complexity of the covering radius problem for lattices, and Approximation versions of the problem for both lattices and linear codes. We also investigate the computational complexity of the shortest linearly independent vectors problem, and its relation to the covering radius problem for lattices. For the covering radius on n -dimensional lattices, we show that the problem can be approximated within any Constant factor γ( n ) > 1 in random exponential time 2^ O ( n ). We also prove that suitably defined gap versions of the problem lie in AM for λ( n ) = 2, in coAM for $$ \gamma (n) = {\sqrt {n/\log n} }, $$ and in NP ∩ coNP for $$ \gamma (n) = {\sqrt n }. $$ For the covering radius on n -dimensional linear codes, we show that the problem can be solved in deterministic polynomial time for Approximation factor $$ \gamma (n) = \log n, $$ but cannot be solved in polynomial time for some $$ \gamma (n) = \Omega (\log \log n) $$ unless NP can be simulated in deterministic $$ n^{{O(\log \log \log n)}} $$ time. Moreover, we prove that the problem is NP-hard for any Constant Approximation factor, it is Π_2-hard for some Constant Approximation factor, and that it is unlikely to be Π_2-hard for Approximation factors larger than 2 (by giving an AM protocol for the appropriate gap problem). This is a natural hardness of Approximation result in the polynomial hierarchy. For the shortest independent vectors problem, we give a coAM protocol achieving Approximation factor $$ \gamma (n) = {\sqrt {n/\log n} }, $$ solving an open problem of Blömer and Seifert (STOC’99), and prove that the problem is also in coNP for $$ \gamma (n) = {\sqrt n }. $$ Both results are obtained by giving a gap-preserving nondeterministic polynomial time reduction to the closest vector problem.

  • The complexity of the covering radius problem on lattices and codes
    Proceedings. 19th IEEE Annual Conference on Computational Complexity 2004., 2004
    Co-Authors: Venkatesan Guruswami, Daniele Micciancio, Oded Regev
    Abstract:

    We initiate the study of the computational complexity of the covering radius problem for point lattices, and Approximation versions of the problem for both lattices and linear codes. We also investigate the computational complexity of the shortest linearly independent vectors problem, and its relation to the covering radius problem for lattices. For the covering radius on n-dimensional lattices, we show that the problem can be approximated within any Constant factor /spl gamma/(n) > 1 in random exponential time 2/sup O(n)/, it is in AM for /spl gamma/(n) = 2, in coAM for /spl gamma/(n) = /spl radic/(n log n), and in NP /spl cap/ coNP for /spl gamma/(n) = /spl radic/n. For the covering radius on n-dimensional linear codes, we show that the problem can be solved in deterministic polynomial time for Approximation factor /spl gamma/(n) = log n, but cannot be solved in polynomial time for some /spl gamma/(n) = /spl Omega/(log log n) unless NP can be simulated in deterministic n/sup O(log log log n)/ time. Moreover, we prove that the problem is NP-hard for every Constant Approximation factor, it is /spl Pi//sub 2/-hard for some Constant Approximation factor, and it is in AM for Approximation factor 2. So, it is unlikely to be /spl Pi//sub 2/-hard for Approximation factors larger than 2. This is a natural hardness of Approximation result in the polynomial hierarchy. For the shortest independent vectors problem, we give a coAM protocol achieving Approximation factor /spl gamma/(n) = /spl radic/(n/log n), solving an open problem of Blomer and Seifert (1999), and prove that the problem is also in coNP for /spl gamma/(n) = /spl radic/n. Both results are obtained by giving a gap-preserving nondeterministic polynomial time reduction to the closest vector problem.

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

  • orientational photorefractive effect in nematic liquid crystal with externally applied fields
    Journal of Applied Physics, 2000
    Co-Authors: Guoquan Zhang, G Montemezzani, P Gunter
    Abstract:

    Light-induced space-charge fields and the related orientational photorefractive effects in nematic liquid crystal cells are studied both theoretically and experimentally. Analytical solutions for the refractive index change distribution are obtained under the single-elastic-Constant Approximation with various configurations of externally applied electric and magnetic fields and of the nematic liquid crystal director. The effects of the rigid boundary condition are investigated in detail. The grating spacing for which the refractive index change is maximized depends on the strength of external electric and magnetic fields. The responses of parallel cells differ from those of homeotropic cells, both upon the dependencies on the grating spacing and on the external fields. Under the same conditions, the orientational photorefractive effects are stronger in parallel cells than in homeotropic ones. It is also shown that the investigated effects will be greatly enhanced near the Freedericksz transition. Experime...

  • orientational photorefractive effect in nematic liquid crystal with externally applied fields
    Journal of Applied Physics, 2000
    Co-Authors: Guoquan Zhang, G Montemezzani, P Gunter
    Abstract:

    Light-induced space-charge fields and the related orientational photorefractive effects in nematic liquid crystal cells are studied both theoretically and experimentally. Analytical solutions for the refractive index change distribution are obtained under the single-elastic-Constant Approximation with various configurations of externally applied electric and magnetic fields and of the nematic liquid crystal director. The effects of the rigid boundary condition are investigated in detail. The grating spacing for which the refractive index change is maximized depends on the strength of external electric and magnetic fields. The responses of parallel cells differ from those of homeotropic cells, both upon the dependencies on the grating spacing and on the external fields. Under the same conditions, the orientational photorefractive effects are stronger in parallel cells than in homeotropic ones. It is also shown that the investigated effects will be greatly enhanced near the Freedericksz transition. Experimental verifications of the photorefractive response in parallel aligned cells confirm the necessity to consider the boundary conditions explicitly.

Venkatesan Guruswami - One of the best experts on this subject based on the ideXlab platform.

  • The complexity of the covering radius problem
    computational complexity, 2005
    Co-Authors: Venkatesan Guruswami, Daniele Micciancio, Oded Regev
    Abstract:

    We initiate the study of the computational complexity of the covering radius problem for lattices, and Approximation versions of the problem for both lattices and linear codes. We also investigate the computational complexity of the shortest linearly independent vectors problem, and its relation to the covering radius problem for lattices. For the covering radius on n -dimensional lattices, we show that the problem can be approximated within any Constant factor γ( n ) > 1 in random exponential time 2^ O ( n ). We also prove that suitably defined gap versions of the problem lie in AM for λ( n ) = 2, in coAM for $$ \gamma (n) = {\sqrt {n/\log n} }, $$ and in NP ∩ coNP for $$ \gamma (n) = {\sqrt n }. $$ For the covering radius on n -dimensional linear codes, we show that the problem can be solved in deterministic polynomial time for Approximation factor $$ \gamma (n) = \log n, $$ but cannot be solved in polynomial time for some $$ \gamma (n) = \Omega (\log \log n) $$ unless NP can be simulated in deterministic $$ n^{{O(\log \log \log n)}} $$ time. Moreover, we prove that the problem is NP-hard for any Constant Approximation factor, it is Π_2-hard for some Constant Approximation factor, and that it is unlikely to be Π_2-hard for Approximation factors larger than 2 (by giving an AM protocol for the appropriate gap problem). This is a natural hardness of Approximation result in the polynomial hierarchy. For the shortest independent vectors problem, we give a coAM protocol achieving Approximation factor $$ \gamma (n) = {\sqrt {n/\log n} }, $$ solving an open problem of Blömer and Seifert (STOC’99), and prove that the problem is also in coNP for $$ \gamma (n) = {\sqrt n }. $$ Both results are obtained by giving a gap-preserving nondeterministic polynomial time reduction to the closest vector problem.

  • The complexity of the covering radius problem on lattices and codes
    Proceedings. 19th IEEE Annual Conference on Computational Complexity 2004., 2004
    Co-Authors: Venkatesan Guruswami, Daniele Micciancio, Oded Regev
    Abstract:

    We initiate the study of the computational complexity of the covering radius problem for point lattices, and Approximation versions of the problem for both lattices and linear codes. We also investigate the computational complexity of the shortest linearly independent vectors problem, and its relation to the covering radius problem for lattices. For the covering radius on n-dimensional lattices, we show that the problem can be approximated within any Constant factor /spl gamma/(n) > 1 in random exponential time 2/sup O(n)/, it is in AM for /spl gamma/(n) = 2, in coAM for /spl gamma/(n) = /spl radic/(n log n), and in NP /spl cap/ coNP for /spl gamma/(n) = /spl radic/n. For the covering radius on n-dimensional linear codes, we show that the problem can be solved in deterministic polynomial time for Approximation factor /spl gamma/(n) = log n, but cannot be solved in polynomial time for some /spl gamma/(n) = /spl Omega/(log log n) unless NP can be simulated in deterministic n/sup O(log log log n)/ time. Moreover, we prove that the problem is NP-hard for every Constant Approximation factor, it is /spl Pi//sub 2/-hard for some Constant Approximation factor, and it is in AM for Approximation factor 2. So, it is unlikely to be /spl Pi//sub 2/-hard for Approximation factors larger than 2. This is a natural hardness of Approximation result in the polynomial hierarchy. For the shortest independent vectors problem, we give a coAM protocol achieving Approximation factor /spl gamma/(n) = /spl radic/(n/log n), solving an open problem of Blomer and Seifert (1999), and prove that the problem is also in coNP for /spl gamma/(n) = /spl radic/n. Both results are obtained by giving a gap-preserving nondeterministic polynomial time reduction to the closest vector problem.

G Montemezzani - One of the best experts on this subject based on the ideXlab platform.

  • orientational photorefractive effect in nematic liquid crystal with externally applied fields
    Journal of Applied Physics, 2000
    Co-Authors: Guoquan Zhang, G Montemezzani, P Gunter
    Abstract:

    Light-induced space-charge fields and the related orientational photorefractive effects in nematic liquid crystal cells are studied both theoretically and experimentally. Analytical solutions for the refractive index change distribution are obtained under the single-elastic-Constant Approximation with various configurations of externally applied electric and magnetic fields and of the nematic liquid crystal director. The effects of the rigid boundary condition are investigated in detail. The grating spacing for which the refractive index change is maximized depends on the strength of external electric and magnetic fields. The responses of parallel cells differ from those of homeotropic cells, both upon the dependencies on the grating spacing and on the external fields. Under the same conditions, the orientational photorefractive effects are stronger in parallel cells than in homeotropic ones. It is also shown that the investigated effects will be greatly enhanced near the Freedericksz transition. Experime...

  • orientational photorefractive effect in nematic liquid crystal with externally applied fields
    Journal of Applied Physics, 2000
    Co-Authors: Guoquan Zhang, G Montemezzani, P Gunter
    Abstract:

    Light-induced space-charge fields and the related orientational photorefractive effects in nematic liquid crystal cells are studied both theoretically and experimentally. Analytical solutions for the refractive index change distribution are obtained under the single-elastic-Constant Approximation with various configurations of externally applied electric and magnetic fields and of the nematic liquid crystal director. The effects of the rigid boundary condition are investigated in detail. The grating spacing for which the refractive index change is maximized depends on the strength of external electric and magnetic fields. The responses of parallel cells differ from those of homeotropic cells, both upon the dependencies on the grating spacing and on the external fields. Under the same conditions, the orientational photorefractive effects are stronger in parallel cells than in homeotropic ones. It is also shown that the investigated effects will be greatly enhanced near the Freedericksz transition. Experimental verifications of the photorefractive response in parallel aligned cells confirm the necessity to consider the boundary conditions explicitly.