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- Xiaoqun Wang, Jin-Wu Tsai, Bridget LaMonica, Arnold R. Kriegstein
- Nature neuroscience
- 2011

A hallmark of mammalian brain evolution is cortical expansion, which reflects an increase in the number of cortical neurons established by the progenitor cell subtypes present and the number of their neurogenic divisions. Recent studies have revealed a new class of radial glia-like (oRG) progenitor cells in the human brain, which reside in the outer… (More)

Quasi-Monte Carlo (QMC) methods are successfully used for high-dimensional integrals arising in many applications. To understand this success, the notion of effective dimension has been introduced. In this paper, we analyse certain function classes commonly used in QMC methods for empirical and theoretical investigations and show that the problem of… (More)

Many problems in mathematical finance can be formulated as high-dimensional integrals, where the large number of dimensions arises from small time steps in time discretization and/or a large number of state variables. Quasi-Monte Carlo (QMC) methods have been successfully used for approximating such integrals. To understand this success, this paper focuses… (More)

We study the problem of multivariate integration and the construction of good lattice rules in weighted Korobov spaces with general weights. These spaces are not necessarily tensor products of spaces of univariate functions. Sufficient conditions for tractability and strong tractability of multivariate integration in such weighted function spaces are found.… (More)

Good lattice rules are an important type of quasi-Monte Carlo algorithms. They are known to have good theoretical properties, in the sense that they can achieve an error bound (or optimal error bound) that is independent of the dimension for weighted spaces with suitably decaying weights. To use the theory of weighted function spaces for practical… (More)

Quasi-Monte Carlo (QMC) methods are playing an increasingly important role in the pricing of complex financial derivatives. For models in which the prices of the underlying assets are driven by Brownian motions, the efficiency of QMC methods is known to depend crucially on the method of generating the Brownian motions. This paper focuses on the impact of… (More)

- Yong-Chun Yu, Ronald S. Bultje, Xiaoqun Wang, Song-Hai Shi
- Nature
- 2009

Neurons in the mammalian neocortex are organized into functional columns. Within a column, highly specific synaptic connections are formed to ensure that similar physiological properties are shared by neuron ensembles spanning from the pia to the white matter. Recent studies indicate that synaptic connectivity in the neocortex is sparse and highly specific… (More)

- Xiaoqun Wang, Jin-Wu Tsai, Janice H. Imai, Wei-Nan Lian, Richard B. Vallee, Song-Hai Shi
- Nature
- 2009

Asymmetric divisions of radial glia progenitors produce self-renewing radial glia and differentiating cells simultaneously in the ventricular zone (VZ) of the developing neocortex. Whereas differentiating cells leave the VZ to constitute the future neocortex, renewing radial glia progenitors stay in the VZ for subsequent divisions. The differential… (More)

Dimensionally unbounded problems are frequently encountered in practice, such as in simulations of stochastic processes, in particle and light transport problems and in the problems of mathematical finance. This paper considers quasi-Monte Carlo integration algorithms for weighted classes of functions of infinitely many variables, in which the dependence of… (More)