| 1. |
- Dzougoutov, Anna, et al.
(author)
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Adaptive Monte Carlo Algorithms for Stopped Diffusion
- 2005. - 44
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In: Multiscale Methods in Science and Engineering. - Berlin : Springer-Verlag. - 9783540264446 ; , s. 59-88
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Book chapter (other academic/artistic)abstract
- We present adaptive algorithms for weak approximation of stopped diffusion using the Monte Carlo Euler method. The goal is to compute an expected value of a given function g depending on the solution X of an Itô stochastic differential equation and on the first exit time τ from a given domain.The main steps in the extension to stopped diffusion processes are to use a conditional probability to estimate the first exit time error and introduce difference quotients to approximate the initial data of the dual solutions.
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| 2. |
- Jeon, Iksoo, et al.
(author)
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Neuronal Properties, In Vivo Effects, and Pathology of a Huntington's Disease Patient-Derived Induced Pluripotent Stem Cells
- 2012
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In: Stem Cells. - : Oxford University Press (OUP). - 1549-4918 .- 1066-5099. ; 30:9, s. 2054-2062
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Journal article (peer-reviewed)abstract
- Induced pluripotent stem cells (iPSCs) generated from somatic cells of patients can be used to model different human diseases. They may also serve as sources of transplantable cells that can be used in novel cell therapies. Here, we analyzed neuronal properties of an iPSC line derived from a patient with a juvenile form of Huntington's disease (HD) carrying 72 CAG repeats (HD-iPSC). Although its initial neural inducing activity was lower than that of human embryonic stem cells, we found that HD-iPSC can give rise to GABAergic striatal neurons, the neuronal cell type that is most susceptible to degeneration in HD. We then transplanted HD-iPSC-derived neural precursors into a rat model of HD with a unilateral excitotoxic striatal lesion and observed a significant behavioral recovery in the grafted rats. Interestingly, during our in vitro culture and when the grafts were examined at 12 weeks after transplantation, no aggregate formation was detected. However, when the culture was treated with a proteasome inhibitor (MG132) or when the cells engrafted into neonatal brains were analyzed at 33 weeks, there were clear signs of HD pathology. Taken together, these results indicate that, although HD-iPSC carrying 72 CAG repeats can form GABAergic neurons and give rise to functional effects in vivo, without showing an overt HD phenotype, it is highly susceptible to proteasome inhibition and develops HD pathology at later stages of transplantation. These unique features of HD-iPSC will serve as useful tools to study HD pathology and develop novel therapeutics. Stem Cells 2012; 30: 20542062
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| 3. |
- Kim, Se-Hoon, et al.
(author)
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Nanophase oxalate precursors of thermoelectric CoSb3 by controlled coprecipitation predicted by thermodynamic modeling
- 2016
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In: Advanced Powder Technology. - : Elsevier. - 0921-8831 .- 1568-5527. ; 27:2, s. 773-778
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Journal article (peer-reviewed)abstract
- The precursors for the formation of thermoelectric skutterudite CoSb3 nanoparticles are predicted by thermodynamic modeling of the complex chemical species. Based on the results, equimolar mixture of CoC2O4 center dot 2H(2)O and Sb(C2O4) OH are successively co-precipitated under controlled conditions of pH = 2.7 and concentration of reactants. The as synthesized powder was decomposed at 350 degrees C to remove the organic molecules and further reduced to CoSb3 phase by heating at 530 degrees C under hydrogen flow. The obtained powder was consolidated by spark plasma sintering (SPS). CoSb3 prepared by controlled chemical co-precipitation has p-type behavior with a positive sign of the Seebeck coefficient. TE transport properties were measured, which revealed that the Seebeck coefficient increased 2.5 times with increasing the temperature and it is lower than the ball milled CoSb3. Thermal conductivity of sintered CoSb3 at 773 K starts from 0.06 W/cm K at room temperature and decreases to 0.04 W/cm K at 700 K, which is lower than the bulk counterpart. The ZT of coprecipitated CoSb3 and SPS consolidated at 773 K shows 2 times higher than the ball milled one. (C) 2016 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
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| 4. |
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| 5. |
- Moon, Kyoung-Sook, et al.
(author)
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An Adaptive Algorithm for Ordinary, Stochastic and Partial Differential Equations
- 2005
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In: Recent Advances in Adaptive Computation. - Providence : American Mathematical Society. - 0821836625 ; , s. 325-343
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Book chapter (other academic/artistic)abstract
- The theory of a posteriori error estimates suitable for adaptive refinement is well established. This work focuses on the fundamental, but less studied, issue of convergence rates of adaptive algorithms. In particular, this work describes a simple and general adaptive algorithm applied to ordinary, stochastic and partial differential equations with proven convergence rates. The presentation has three parts: The error approximations used to build error indicators for the adaptive algorithm are based on error expansions with computable leading order terms. It is explained how to measure optimal convergence rates for approximation of functionals of the solution, and why convergence of the error density is always useful and subtle in the case of stochastic and partial differential equations. The adaptive algorithm, performing successive mesh refinements, either reduces the maximal error indicator by a factor or stops with the error asymptotically bounded by the prescribed accuracy requirement. Furthermore, the algorithm stops using the optimal number of degrees of freedom, up to a problem independent factor.
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| 6. |
- Moon, Kyoung-Sook, et al.
(author)
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Convergence rates for adaptive weak approximation of stochastic differential equations
- 2005
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In: Stochastic Analysis and Applications. - : Informa UK Limited. - 0736-2994 .- 1532-9356. ; 23:3, s. 511-558
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Journal article (peer-reviewed)abstract
- Convergence rates of adaptive algorithms for weak approximations of Ito stochastic differential equations are proved for the Monte Carlo Euler method. Two algorithms based either oil optimal stochastic time steps or optimal deterministic time steps are studied. The analysis of their computational complexity combines the error expansions with a posteriori leading order term introduced in Szepessy et al. [Szepessy, A.. R. Tempone, and G. Zouraris. 2001. Comm. Pare Appl. Math. 54:1169-1214] and ail extension of the convergence results for adaptive algorithms approximating deterministic ordinary differential equations, derived in Moon et al. [Moon, K.-S., A. Szepessy, R. Tempone, and G. Zouraris. 2003. Numer. Malh. 93:99-129]. The main step in the extension is the proof of the almost sure convergence of the error density. Both adaptive alogrithms are proven to stop with asymptotically optimal number of steps up to a problem independent factor defined in the algorithm. Numerical examples illustrate the behavior of the adaptive algorithms, motivating when stochastic and deterministic adaptive time steps are more efficient than constant time steps and when adaptive stochastic steps are more efficient than adaptive deterministic steps.
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| 7. |
- Moon, Kyoung-Sook, et al.
(author)
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Convergence rates for an adaptive dual weighted residual finite element algorithm
- 2006
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In: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 46:2, s. 367-407
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Journal article (peer-reviewed)abstract
- Basic convergence rates are established for an adaptive algorithm based on the dual weighted residual error representation, [GRAPHICS] applied to isoparametric d-linear quadrilateral finite element approximation of functionals of multi scale solutions to second order elliptic partial differential equations in bounded domains of R-d. In contrast to the usual aim to derive an a posteriori error estimate, this work derives, as the mesh size tends to zero, a uniformly convergent error expansion for the error density, with computable leading order term. It is shown that the optimal adaptive isotropic mesh uses a number of elements proportional to the d/2 power of the Ld/d+2 quasi-norm of the error density; the same error for approximation with a uniform mesh requires a number of elements proportional to the d/2 power of the larger L-1 norm of the same error density. A point is that this measure recognizes different convergence rates for multi scale problems, although the convergence order may be the same. The main result is a proof that the adaptive algorithm based on successive subdivisions of elements reduces the maximal error indicator with a factor or stops with the error asymptotically bounded by the tolerance using the optimal number of elements, up to a problem independent factor. An important step is to prove uniform convergence of the expansion for the error density, which is based on localized averages of second order difference quotients of the primal and dual finite element solutions. The averages are used since the difference quotients themselves do not converge pointwise for adapted meshes. The proof uses weak convergence techniques with a symmetrizer for the second order difference quotients and a splitting of the error into a dominating contribution, from elements with no hanging nodes or edges on the initial mesh, and a remaining asymptotically negligible part. Numerical experiments for an elasticity problem with a crack and different variants of the averages show that the algorithm is useful in practice also for relatively large tolerances, much larger than the small tolerances needed to theoretically guarantee that the algorithm works well.
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