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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)
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)
Tillering in rice (Oryza sativa L.) is an important agronomic trait for grain production, and also a model system for the study of branching in monocotyledonous plants. Rice tiller is a specialized grain-bearing branch that is formed on the unelongated basal internode and grows independently of the mother stem (culm) by means of its own adventitious roots.(More)
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)
The Halton sequence is a well-known multi-dimensional low discrepancy sequence. In this paper, we propose a new method for randomizing the Halton sequence: we randomize the start point of each component of the sequence. This method combines the potential accuracy advantage of Halton sequence in multi-dimensional integration with the practical error(More)
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)
Multivariate integration of high dimension s occurs in many applications. In many such applications, for example in finance, integrands can often be approximated by sums of functions of just a few variables. In this situation the superposition (or effective) dimension is small, and we can model the problem with finite-order weights, where the weights(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)