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Algorithmic Efficiency

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Kostas Orginos – One of the best experts on this subject based on the ideXlab platform.

  • the mobius domain wall fermion algorithm
    Computer Physics Communications, 2017
    Co-Authors: Richard C Brower, H Neff, Kostas Orginos
    Abstract:

    Abstract We present a review of the properties of generalized domain wall Fermions, based on a (real) Mobius transformation on the Wilson overlap kernel, discussing their Algorithmic Efficiency, the degree of explicit chiral violations measured by the residual mass ( m r e s ) and the Ward–Takahashi identities. The Mobius class interpolates between Shamir’s domain wall operator and Borici’s domain wall implementation of Neuberger’s overlap operator without increasing the number of Dirac applications per conjugate gradient iteration. A new scaling parameter ( α ) reduces chiral violations at finite fifth dimension ( L s ) but yields exactly the same overlap action in the limit L s → ∞ . Through the use of 4d Red/Black preconditioning and optimal tuning for the scaling α ( L s ) , we show that chiral symmetry violations are typically reduced by an order of magnitude at fixed L s . We argue that the residual mass for a tuned Mobius algorithm with α = O ( 1 ∕ L s γ ) for γ 1 will eventually fall asymptotically as m r e s = O ( 1 ∕ L s 1 + γ ) in the case of a 5D Hamiltonian with out a spectral gap.

  • the m obius domain wall fermion algorithm
    arXiv: High Energy Physics – Lattice, 2012
    Co-Authors: Richard C Brower, H Neff, Kostas Orginos
    Abstract:

    We present a review of the properties of generalized domain wall Fermions, based on a (real) Mobius transformation on the Wilson overlap kernel, discussing their Algorithmic Efficiency, the degree of explicit chiral violations measured by the residual mass ($m_{res}$) and the Ward-Takahashi identities. The Mobius class interpolates between Shamir’s domain wall operator and Borici’s domain wall implementation of Neuberger’s overlap operator without increasing the number of Dirac applications per conjugate gradient iteration. A new scaling parameter ($\alpha$) reduces chiral violations at finite fifth dimension ($L_s$) but yields exactly the same overlap action in the limit $L_s \rightarrow \infty$. Through the use of 4d Red/Black preconditioning and optimal tuning for the scaling $\alpha(L_s)$, we show that chiral symmetry violations are typically reduced by an order of magnitude at fixed $L_s$. At large $L_s$ we argue that the observed scaling for $m_{res} = O(1/L_s)$ for Shamir is replaced by $m_{res} = O(1/L_s^2)$ for the properly tuned Mobius algorithm with $\alpha = O(L_s)$

Ellen Kuhl – One of the best experts on this subject based on the ideXlab platform.

  • growing skin a computational model for skin expansion in reconstructive surgery
    Journal of The Mechanics and Physics of Solids, 2011
    Co-Authors: Adrian Buganza Tepole, Jonathan Wong, Arun K. Gosain, Ellen Kuhl
    Abstract:

    The goal of this manuscript is to establish a novel computational model for stretch-induced skin growth during tissue expansion. Tissue expansion is a common surgical procedure to grow extra skin for reconstructing birth defects, burn injuries, or cancerous breasts. To model skin growth within the framework of nonlinear continuum mechanics, we adopt the multiplicative decomposition of the deformation gradient into an elastic and a growth part. Within this concept, we characterize growth as an irreversible, stretch-driven, transversely isotropic process parameterized in terms of a single scalar-valued growth multiplier, the in-plane area growth. To discretize its evolution in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum Algorithmic Efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To demonstrate the characteristic features of skin growth, we simulate the process of gradual tissue expander inflation. To visualize growth-induced residual stresses, we simulate a subsequent tissue expander deflation. In particular, we compare the spatio-temporal evolution of area growth, elastic strains, and residual stresses for four commonly available tissue expander geometries. We believe that predictive computational modeling can open new avenues in reconstructive surgery to rationalize and standardize clinical process parameters such as expander geometry, expander size, expander placement, and inflation timing.

  • Stretching skin: The physiological limit and beyond☆
    International Journal of Non-linear Mechanics, 2011
    Co-Authors: Adrian Buganza Tepole, Arun K. Gosain, Ellen Kuhl
    Abstract:

    Abstract The goal of this paper is to establish a novel computational model for skin to characterize its constitutive behavior when stretched within and beyond its physiological limits. Within the physiological regime, skin displays a reversible, highly non-linear, stretch locking, and anisotropic behavior. We model these characteristics using a transversely isotropic chain network model composed of eight wormlike chains. Beyond the physiological limit, skin undergoes an irreversible area growth triggered through mechanical stretch. We model skin growth as a transversely isotropic process characterized through a single internal variable, the scalar-valued growth multiplier. To discretize the evolution of growth in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum Algorithmic Efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To illustrate the characteristic features of skin growth, we first compare the two simple model problems of displacement- and force-driven growth. Then, we model the process of stretch-induced skin growth during tissue expansion. In particular, we compare the spatio-temporal evolution of stress, strain, and area gain for four commonly available tissue expander geometries. We believe that the proposed model has the potential to open new avenues in reconstructive surgery and rationalize critical process parameters in tissue expansion, such as expander geometry, expander size, expander placement, and inflation timing.

Robert Cutler – One of the best experts on this subject based on the ideXlab platform.

  • efficient egg drop contests how middle school girls think about Algorithmic Efficiency
    International Computing Education Research Workshop, 2013
    Co-Authors: Michelle Friend, Robert Cutler
    Abstract:

    In this basic interpretative qualitative study, middle school girls with no formal experience in Algorithmic reasoning, abstraction, or algebra were interviewed individually in order to help understand and explain how they think about Algorithmic Efficiency. A contextually relevant problem (determining the maximum height an “egg-drop contraption” could be dropped without breaking) was described to the students who were then asked 1) to come up with the most efficient solution they could to the problem while describing their thinking for the interviewer; and 2) to determine, from a choice of three solutions proposed by the interviewer, which is the most efficient. Students were found to have varying degrees of success in solving the problem or picking the most efficient solution. The most successful recognized the salient features of the problem and used them to generate possible solutions. The least successful were unable to understand the abstractions inherent in the problem. Students recognized that the most efficient of three proposed solutions may depend on the instance of the problem (where the contraption actually failed). They also understood that there was a “best” solution in general, and chose the solution that had the best worst-case scenario. Compared to college students studied previously using similar Algorithmic reasoning problems, middle school girls appeared to perform similarly. They were able to demonstrate sophisticated computational thinking skills while suffering from some of the same Algorithmic thinking limitations as older students.

  • ICER – Efficient egg drop contests: how middle school girls think about Algorithmic Efficiency
    Proceedings of the ninth annual international ACM conference on International computing education research – ICER '13, 2013
    Co-Authors: Michelle Friend, Robert Cutler
    Abstract:

    In this basic interpretative qualitative study, middle school girls with no formal experience in Algorithmic reasoning, abstraction, or algebra were interviewed individually in order to help understand and explain how they think about Algorithmic Efficiency. A contextually relevant problem (determining the maximum height an “egg-drop contraption” could be dropped without breaking) was described to the students who were then asked 1) to come up with the most efficient solution they could to the problem while describing their thinking for the interviewer; and 2) to determine, from a choice of three solutions proposed by the interviewer, which is the most efficient. Students were found to have varying degrees of success in solving the problem or picking the most efficient solution. The most successful recognized the salient features of the problem and used them to generate possible solutions. The least successful were unable to understand the abstractions inherent in the problem. Students recognized that the most efficient of three proposed solutions may depend on the instance of the problem (where the contraption actually failed). They also understood that there was a “best” solution in general, and chose the solution that had the best worst-case scenario. Compared to college students studied previously using similar Algorithmic reasoning problems, middle school girls appeared to perform similarly. They were able to demonstrate sophisticated computational thinking skills while suffering from some of the same Algorithmic thinking limitations as older students.

Richard C Brower – One of the best experts on this subject based on the ideXlab platform.

  • the mobius domain wall fermion algorithm
    Computer Physics Communications, 2017
    Co-Authors: Richard C Brower, H Neff, Kostas Orginos
    Abstract:

    Abstract We present a review of the properties of generalized domain wall Fermions, based on a (real) Mobius transformation on the Wilson overlap kernel, discussing their Algorithmic Efficiency, the degree of explicit chiral violations measured by the residual mass ( m r e s ) and the Ward–Takahashi identities. The Mobius class interpolates between Shamir’s domain wall operator and Borici’s domain wall implementation of Neuberger’s overlap operator without increasing the number of Dirac applications per conjugate gradient iteration. A new scaling parameter ( α ) reduces chiral violations at finite fifth dimension ( L s ) but yields exactly the same overlap action in the limit L s → ∞ . Through the use of 4d Red/Black preconditioning and optimal tuning for the scaling α ( L s ) , we show that chiral symmetry violations are typically reduced by an order of magnitude at fixed L s . We argue that the residual mass for a tuned Mobius algorithm with α = O ( 1 ∕ L s γ ) for γ 1 will eventually fall asymptotically as m r e s = O ( 1 ∕ L s 1 + γ ) in the case of a 5D Hamiltonian with out a spectral gap.

  • the m obius domain wall fermion algorithm
    arXiv: High Energy Physics – Lattice, 2012
    Co-Authors: Richard C Brower, H Neff, Kostas Orginos
    Abstract:

    We present a review of the properties of generalized domain wall Fermions, based on a (real) Mobius transformation on the Wilson overlap kernel, discussing their Algorithmic Efficiency, the degree of explicit chiral violations measured by the residual mass ($m_{res}$) and the Ward-Takahashi identities. The Mobius class interpolates between Shamir’s domain wall operator and Borici’s domain wall implementation of Neuberger’s overlap operator without increasing the number of Dirac applications per conjugate gradient iteration. A new scaling parameter ($\alpha$) reduces chiral violations at finite fifth dimension ($L_s$) but yields exactly the same overlap action in the limit $L_s \rightarrow \infty$. Through the use of 4d Red/Black preconditioning and optimal tuning for the scaling $\alpha(L_s)$, we show that chiral symmetry violations are typically reduced by an order of magnitude at fixed $L_s$. At large $L_s$ we argue that the observed scaling for $m_{res} = O(1/L_s)$ for Shamir is replaced by $m_{res} = O(1/L_s^2)$ for the properly tuned Mobius algorithm with $\alpha = O(L_s)$

He Zhao – One of the best experts on this subject based on the ideXlab platform.

  • The application of a markov chain model of Algorithmic Efficiency in termination time of TV shows
    2008 3rd IEEE Conference on Industrial Electronics and Applications, 2008
    Co-Authors: Lixia Du, Jiying Li, He Zhao
    Abstract:

    This paper presents a Markov method of Algorithmic Efficiency. A production process can be in either a good or a bad state. The true state is unknown and can only be inferred from observations. If the state is good during one period it may deteriorate and become bad during the next period. Two actions are available: continue or replace (for a fixed cost). The objective is to maximize the expected discounted value of the total future profits. We prove that ldquodominance in expectationrdquo (the expected profit is larger in the good state than in the bad state) suffices for the optimal policy to be of a control limit (CLT) type: continue if and only if the good state probability exceeds the CLT. This condition is weaker than ldquostochastic dominancerdquo, which has been prevailing. We also show that the “expected profit function” is convex, strictly increasing.