Browsing by Author "Hsieh, Wen-Yuan"

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Convex Quadratic Equation
(2020-09-01)
Lin, Li-Gang
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Liang, Yew-Wen
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Hsieh, Wen-Yuan
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電控工程研究所
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Institute of Electrical and Control Engineering
Two main results (A) and (B) are presented in algebraic closed forms. (A) Regarding the convex quadratic equation, an analytical equivalent solvability condition and parameterization of all solutions are formulated, for the first time in the literature and in a unified framework. The philosophy is based on the matrix algebra, while facilitated by a novel equivalence/coordinate transformation (with respect to the much more challenging case of rank-deficient Hessian matrix). In addition, the parameter-solution bijection is verified. From the perspective via (A), a major application is re-examined that accounts for the other main result (B), which deals with both the infinite and finite-time horizon nonlinear optimal control. By virtue of (A), the underlying convex quadratic equations associated with the Hamilton-Jacobi equation, Hamilton-Jacobi inequality, and Hamilton-Jacobi-Bellman equation are explicitly solved, respectively. Therefore, the long quest for the constituent of the optimal controller, gradient of the associated value function, can be captured in each solution set. Moving forward, a preliminary to exactly locate the optimality using the state-dependent (resp., differential) Riccati equation scheme is prepared for the remaining symmetry condition.
DYNAMIC MAPPING OF AMPHETAMINE RESPONSE IN THE RAT BRAIN USING BOLD AND IRON TECHNIQUES
(2007-06-01)
Shih, Yen-Yu
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Chen, You-Yin
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Hsieh, Wen-Yuan
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Huang, Ying-Yuan
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Chang, Chen
Conventional blood oxygenation level dependent (BOLD) functional magnetic resonance imaging (fMRI) has been wildly used in neuroscience studies. Even though the BOLD method offers the functional information, the low signal-to-noise ratio could not provide an activated brain area accurately and the signal could not be easily inspected from the complicated neuronal interactions. In this regard, the present study aims to use an ultra-small super-paramagnetic iron oxide (USPIO) nanoparticle coated with covalently bound bifunctional poly(ethylene glycol) polymers to enhance the brain functional responses by the IRON (increased relaxation with iron oxide nanoparticles) technique. The R1 and R2 of this USPIO were 53.6 mMsec-1 and 359.8mMsec-1, respectively, and both were higher than most of the commercial products under 0.47 T nuclear magnetic resonance measurement. In this study, the time activity curves in responsive brain areas were evaluated following USPIO injection (3 mg of Fe/kg). The amphetamine (2 mg/kg) was used as a functional stimulator to reveal the changes of relative cerebral blood volume in different brain areas. All imaging experiments were performed by Bruker Biospec BMT 47/40 4.7 T MRI system. The results show that, compared to the BOLD signals; significant event related responses were observed in striatum, insular cortex, nucleus accumbens, somatosensory cortices, and lateral thalamus using the IRON technique. Furthermore, the usability of this USPIO in detecting rCBV responses was confirmed by comparing with previous researches.