A characteristic particle method for traffic flow simulations on highway networks

A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method "particleclaw", which solves scalar one dimensional hyperbolic conservations laws exactly, except for a small error right around shocks. The method is generalized to nonlinear network flows, where particle approximations on the edges are suitably coupled together at the network nodes. It is demonstrated in numerical examples that the resulting particle method can approximate traffic jams accurately, while only devoting a few degrees of freedom to each edge of the network.Comment: 15 pages, 5 figures. Accepted to the proceedings of the Sixth International Workshop Meshfree Methods for PDE 201

A rarefaction-tracking method for hyperbolic conservation laws

We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two neighboring particles, an interpolation is defined by an analytical similarity solution of the conservation law. An interaction of particles represents a collision of characteristics. The resulting shock is resolved by merging particles so that the total area under the function is conserved. The method is variation diminishing, nevertheless, it has no numerical dissipation away from shocks. Although shocks are not explicitly tracked, they can be located accurately. We present numerical examples, and outline specific applications and extensions of the approach.Comment: 21 pages, 7 figures. Similarity 2008 conference proceeding

Integrative analysis identifies key molecular signatures underlying neurodevelopmental deficits in fragile X syndrome

BACKGROUND: Fragile X syndrome (FXS) is a neurodevelopmental disorder caused by epigenetic silencing of FMR1 and loss of FMRP expression. Efforts to understand the molecular underpinnings of the disease have been largely performed in rodent or nonisogenic settings. A detailed examination of the impact of FMRP loss on cellular processes and neuronal properties in the context of isogenic human neurons remains lacking. METHODS: Using CRISPR (clustered regularly interspaced short palindromic repeats)/Cas9 to introduce indels in exon 3 of FMR1, we generated an isogenic human pluripotent stem cell model of FXS that shows complete loss of FMRP expression. We generated neuronal cultures and performed genome-wide transcriptome and proteome profiling followed by functional validation of key dysregulated processes. We further analyzed neurodevelopmental and neuronal properties, including neurite length and neuronal activity, using multielectrode arrays and patch clamp electrophysiology. RESULTS: We showed that the transcriptome and proteome profiles of isogenic FMRP-deficient neurons demonstrate perturbations in synaptic transmission, neuron differentiation, cell proliferation and ion transmembrane transporter activity pathways, and autism spectrum disorder-associated gene sets. We uncovered key deficits in FMRP-deficient cells demonstrating abnormal neural rosette formation and neural progenitor cell proliferation. We further showed that FMRP-deficient neurons exhibit a number of additional phenotypic abnormalities, including neurite outgrowth and branching deficits and impaired electrophysiological network activity. These FMRP-deficient related impairments have also been validated in additional FXS patient-derived human-induced pluripotent stem cell neural cells. CONCLUSIONS: Using isogenic human pluripotent stem cells as a model to investigate the pathophysiology of FXS in human neurons, we reveal key neural abnormalities arising from the loss of FMRP.Peer reviewe

The Optical Rotation of Spirits of Turpentine.

n/