An Efficient Conservative Integrator With a Chain Regularization for the Few-Body Problem

Minesaki, Yukitaka

doi:10.1088/0004-6256/150/4/102

Cited by 4 publications

(1 citation statement)

References 21 publications

(35 reference statements)

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“…The logic of this approach is that the ℓ 2,1 regularization generally improves the accuracy of classifiers in the presence of a large number of uninformative or redundant image measurements (as it is often the case of neuroimaging studies), while the ℓ 2 regularization improves the accuracy of classifiers in the event that all provided image measurements are informative [17, 18]. Our chained-regularization scheme, which uses a sequential dependency approach to identify a pattern to be applied for determining group membership of individuals, is different from chain-regularization [30], a concept used in physics to describe group of objects interacting with each other in a chain.…”

Section: Introductionmentioning

confidence: 99%

Chained regularization for identifying brain patterns specific to HIV infection

et al. 2018

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Human Immunodeficiency Virus (HIV) infection continues to have major adverse public health and clinical consequences despite the effectiveness of combination Antiretroviral Therapy (cART) in reducing HIV viral load and improving immune function. As successfully treated individuals with HIV infection age, their cognition declines faster than reported for normal aging. This phenomenon underlines the importance of improving long-term care, which requires a better understanding of the impact of HIV on the brain. In this paper, automated identification of patients and brain regions affected by HIV infection are modeled as a classification problem, whose solution is determined in two steps within our proposed Chained-Regularization framework. The first step focuses on selecting the HIV pattern (i.e., the most informative constellation of brain region measurements for distinguishing HIV infected subjects from healthy controls) by constraining the search for the optimal parameter setting of the classifier via group sparsity (ℓ-norm). The second step improves classification accuracy by constraining the parameterization with respect to the selected measurements and the Euclidean regularization (ℓ-norm). When applied to the cortical and subcortical structural Magnetic Resonance Images (MRI) measurements of 65 controls and 65 HIV infected individuals, this approach is more accurate in distinguishing the two cohorts than more common models. Finally, the brain regions of the identified HIV pattern concur with the HIV literature that uses traditional group analysis models.

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Section: Introductionmentioning

confidence: 99%

Chained regularization for identifying brain patterns specific to HIV infection

et al. 2018

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n-gon Equilibria of the Discrete -body Problem

Minesaki

2017

ApJ

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We prove that the discrete-time general -body problem (d-G BP) proposed by Minesaki can exactly trace the orbits of elliptic relative equilibrium solutions in the original general -body problem (G BP). These orbits include the orbits of relative equilibrium solutions that have already been discovered. Before this proof, no discrete-time system had been shown to retain the orbits of elliptic relative equilibrium solutions in BP. d-G BP can also precisely reproduce doubly symmetric orbits of the general -body problem, each of which passes near a square equilibrium solution over a long time interval.

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Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

Minesaki

2018

ApJ

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We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

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An Efficient Conservative Integrator With a Chain Regularization for the Few-Body Problem

Cited by 4 publications

References 21 publications

Chained regularization for identifying brain patterns specific to HIV infection

Chained regularization for identifying brain patterns specific to HIV infection

n-gon Equilibria of the Discrete -body Problem

Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

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