Discontinuities are common in the pricing and hedging of complex financial derivatives. Quasi-Monte Carlo (QMC) methods for high-dimensional finance problems with discontinuities can be inefficient ...because of the lack of good smoothness and high dimensionality. Interestingly, path simulation method (PSM) may affect both factors, implying its significance in QMC methods. What defines a “good” PSM for problems with discontinuities? The ability to align the discontinuities with the coordinate axes is a desirable property for a PSM. We show that for an arbitrary PSM, there exists a class of options with discontinuous payoff functions such that the transformed functions have only axis-parallel discontinuities, for which good QMC performance can be expected. In this sense, any PSM can be “good” in QMC methods for a specific class of problems. We analyze the structure of discontinuities for digital options using the new approach and show the superiority and the uniqueness (up to a permutation) of the standard construction. We develop a two-step procedure for pricing and hedging derivatives with discontinuous payoff functions. The first step is to design a good PSM that has the ability to align the discontinuities with the coordinate axes and the second step is to further exploit this nice property to remove the discontinuities completely. We prove that the new estimate is unbiased and has smaller variance. Numerical experiments demonstrate that the two-step procedure is very effective in QMC methods for pricing options and estimating Greeks, leading to a dramatic variance reduction. Both the path simulation step and the smoothing step are crucial and beneficial for QMC methods, with the contribution from each step varying depending on the severity of discontinuity.
Modeling the processes of neuronal progenitor proliferation and differentiation to produce mature cortical neuron subtypes is essential for the study of human brain development and the search for ...potential cell therapies. We demonstrated a novel paradigm for the generation of vascularized organoids (vOrganoids) consisting of typical human cortical cell types and a vascular structure for over 200 days as a vascularized and functional brain organoid model. The observation of spontaneous excitatory postsynaptic currents (sEPSCs), spontaneous inhibitory postsynaptic currents (sIPSCs), and bidirectional electrical transmission indicated the presence of chemical and electrical synapses in vOrganoids. More importantly, single-cell RNA-sequencing analysis illustrated that vOrganoids exhibited robust neurogenesis and that cells of vOrganoids differentially expressed genes (DEGs) related to blood vessel morphogenesis. The transplantation of vOrganoids into the mouse S1 cortex resulted in the construction of functional human-mouse blood vessels in the grafts that promoted cell survival in the grafts. This vOrganoid culture method could not only serve as a model to study human cortical development and explore brain disease pathology but also provide potential prospects for new cell therapies for nervous system disorders and injury.
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 subventricular zone. Expansion of the subventricular zone and appearance of oRG cells may have been essential evolutionary steps leading from lissencephalic to gyrencephalic neocortex. Here we show that oRG-like progenitor cells are present in the mouse embryonic neocortex. They arise from asymmetric divisions of radial glia and undergo self-renewing asymmetric divisions to generate neurons. Moreover, mouse oRG cells undergo mitotic somal translocation whereby centrosome movement into the basal process during interphase precedes nuclear translocation. Our finding of oRG cells in the developing rodent brain fills a gap in our understanding of neocortical expansion.
Detected scattered photons can cause cupping and streak artifacts, significantly degrading the quality of CT images. For fast and accurate estimation of scatter intensities resulting from photon ...interactions with a phantom, we first transform the path probability of photons interacting with the phantom into a high-dimensional integral. Secondly, we develope a new efficient algorithm called gQMCFFD, which combines graphics processing unit(GPU)-based quasi-Monte Carlo (QMC) with forced fixed detection to approximate this integral. QMC uses low discrepancy sequences for simulation and is deterministic versions of Monte Carlo. Numerical experiments show that the results are in excellent agreement and the efficiency improvement factors are 4 ∼ 46 times in all simulations by gQMCFFD with comparison to GPU-based Monte Carlo methods. And by combining gQMCFFD with sparse matrix method, the simulation time is reduced to 2 seconds in a single projection angle and the relative difference is 3.53%.
The cellular complexity of human brain development has been intensively investigated, although a regional characterization of the entire human cerebral cortex based on single-cell transcriptome ...analysis has not been reported. Here, we performed RNA-seq on over 4,000 individual cells from 22 brain regions of human mid-gestation embryos. We identified 29 cell sub-clusters, which showed different proportions in each region and the pons showed especially high percentage of astrocytes. Embryonic neurons were not as diverse as adult neurons, although they possessed important features of their destinies in adults. Neuron development was unsynchronized in the cerebral cortex, as dorsal regions appeared to be more mature than ventral regions at this stage. Region-specific genes were comprehensively identified in each neuronal sub-cluster, and a large proportion of these genes were neural disease related. Our results present a systematic landscape of the regionalized gene expression and neuron maturation of the human cerebral cortex.
Abstract
Spin-orbit coupled honeycomb magnets with the Kitaev interaction have received a lot of attention due to their potential of hosting exotic quantum states including quantum spin liquids. Thus ...far, the most studied Kitaev systems are 4
d
/5
d
-based honeycomb magnets. Recent theoretical studies predicted that 3
d
-based honeycomb magnets, including Na
2
Co
2
TeO
6
(NCTO), could also be a potential Kitaev system. Here, we have used a combination of heat capacity, magnetization, electron spin resonance measurements alongside inelastic neutron scattering (INS) to study NCTO’s quantum magnetism, and we have found a field-induced spin disordered state in an applied magnetic field range of 7.5 T <
B
(⊥
b
-axis) < 10.5 T. The INS spectra were also simulated to tentatively extract the exchange interactions. As a 3
d
-magnet with a field-induced disordered state on an effective spin-1/2 honeycomb lattice, NCTO expands the Kitaev model to 3
d
compounds, promoting further interests on the spin-orbital effect in quantum magnets.
Genetic variation confers susceptibility to neurodevelopmental disorders by affecting the development of specific cell types. Changes in cortical and striatal γ-aminobutyric acid–expressing ...(GABAergic) neurons are common in autism and schizophrenia. In this study, we used single-cell RNA sequencing to characterize the emergence of cell diversity in the human ganglionic eminences, the transitory structures of the human fetal brain where striatal and cortical GABAergic neurons are generated. We identified regional and temporal diversity among progenitor cells underlying the generation of a variety of projection neurons and interneurons. We found that these cells are specified within the human ganglionic eminences by transcriptional programs similar to those previously identified in rodents. Our findings reveal an evolutionarily conserved regulatory logic controlling the specification, migration, and differentiation of GABAergic neurons in the human telencephalon.
The hippocampus is an important part of the limbic system in the human brain that has essential roles in spatial navigation and the consolidation of information from short-term memory to long-term ...memory
. Here we use single-cell RNA sequencing and assay for transposase-accessible chromatin using sequencing (ATAC-seq) analysis to illustrate the cell types, cell linage, molecular features and transcriptional regulation of the developing human hippocampus. Using the transcriptomes of 30,416 cells from the human hippocampus at gestational weeks 16-27, we identify 47 cell subtypes and their developmental trajectories. We also identify the migrating paths and cell lineages of PAX6
and HOPX
hippocampal progenitors, and regional markers of CA1, CA3 and dentate gyrus neurons. Multiomic data have uncovered transcriptional regulatory networks of the dentate gyrus marker PROX1. We also illustrate spatially specific gene expression in the developing human prefrontal cortex and hippocampus. The molecular features of the human hippocampus at gestational weeks 16-20 are similar to those of the mouse at postnatal days 0-5 and reveal gene expression differences between the two species. Transient expression of the primate-specific gene NBPF1 leads to a marked increase in PROX1
cells in the mouse hippocampus. These data provides a blueprint for understanding human hippocampal development and a tool for investigating related diseases.
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