Comparison of the generic neuronal differentiation and neuron subtype specification functions of mammalian achaete-scute and atonal homologs in cultured neural progenitor cells

In the vertebrate peripheral nervous system, the proneural genes neurogenin 1 and neurogenin 2 (Ngn1 and Ngn2), and Mash1 are required for sensory and autonomic neurogenesis, respectively. In cultures of neural tube-derived, primitive PNS progenitors NGNs promote expression of sensory markers and MASH1 that of autonomic markers. These effects do not simply reflect enhanced neuronal differentiation, suggesting that both bHLH factors also specify neuronal identity like their Drosophila counterparts. At high concentrations of BMP2 or in neural crest stem cells (NCSCs), however, NGNs like MASH1 promote only autonomic marker expression. These data suggest that that the identity specification function of NGNs is more sensitive to context than is that of MASH1. In NCSCs, MASH1 is more sensitive to Notch-mediated inhibition of neurogenesis and cell cycle arrest, than are the NGNs. Thus, the two proneural genes differ in other functional properties besides the neuron subtype identities they can promote. These properties may explain cellular differences between MASH1- and NGN-dependent lineages in the timing of neuronal differentiation and cell cycle exit

A method for solving systems of non-linear differential equations with moving singularities

We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by establishing certain `moving' jump conditions across them. We show how a first integral of the differential equations, if available, can also be used for checking the accuracy of the numerical solution.Comment: 9 pages, 7 eps figures, to appear in Comput. Phys. Co

Solving Langevin equation with the bicolour rooted tree method

Stochastic differential equations, especially the one called Langevin equation, play an important role in many fields of modern science. In this paper, we use the bicolour rooted tree method, which is based on the stochastic Taylor expansion, to get the systematic pattern of the high order algorithm for Langevin equation. We propose a popular test problem, which is related to the energy relaxation in the double well, to test the validity of our algorithm and compare our algorithm with other usually used algorithms in simulations. And we also consider the time-dependent Langevin equation with the Ornstein-Uhlenbeck noise as our second example to demonstrate the versatility of our method

Neural crest stem cells undergo multilineage differentiation in developing peripheral nerves to generate endoneurial fibroblasts in addition to Schwann cells

Neural crest stem cells (NCSCs) persist in peripheral nerves throughout late gestation but their function is unknown. Current models of nerve development only consider the generation of Schwann cells from neural crest, but the presence of NCSCs raises the possibility of multilineage differentiation. We performed Cre-recombinase fate mapping to determine which nerve cells are neural crest derived. Endoneurial fibroblasts, in addition to myelinating and non-myelinating Schwann cells, were neural crest derived, whereas perineurial cells, pericytes and endothelial cells were not. This identified endoneurial fibroblasts as a novel neural crest derivative, and demonstrated that trunk neural crest does give rise to fibroblasts in vivo, consistent with previous studies of trunk NCSCs in culture. The multilineage differentiation of NCSCs into glial and non-glial derivatives in the developing nerve appears to be regulated by neuregulin, notch ligands, and bone morphogenic proteins, as these factors are expressed in the developing nerve, and cause nerve NCSCs to generate Schwann cells and fibroblasts, but not neurons, in culture. Nerve development is thus more complex than was previously thought, involving NCSC self-renewal, lineage commitment and multilineage differentiation

Quantum Control of Interacting Bosons in Periodic Optical Lattice

We study the avoided crossings in the dynamics of quantum controlled excitations for an interacting two-boson system in an optical lattice. Specifically, we perform numerical simulations of quantum control in this system where driving pulses connect the undriven stationary states in a manner characteristic of Stimulated Raman Adiabatic Passage (STIRAP). We demonstrate that the dynamics of such a transition is affected by chaos induced avoided crossings, resulting in a loss in coherence of the final outcome in the adiabatic limit.Comment: Accepted for publication in Physica E. Typo corrections to final versio

ON the CONSERVATION of the VERTICAL ACTION in GALACTIC DISKS

We employ high-resolution N-body simulations of isolated spiral galaxy models, from low-amplitude, multi-armed galaxies to Milky Way-like disks, to estimate the vertical action of ensembles of stars in an axisymmetrical potential. In the multi-armed galaxy the low-amplitude arms represent tiny perturbations of the potential, hence the vertical action for a set of stars is conserved, although after several orbital periods of revolution the conservation degrades significantly. For a Milky Way-like galaxy with vigorous spiral activity and the formation of a bar, our results show that the potential is far from steady, implying that the action is not a constant of motion. Furthermore, because of the presence of high-amplitude arms and the bar, considerable in-plane and vertical heating occurs that forces stars to deviate from near-circular orbits, reducing the degree at which the actions are conserved for individual stars, in agreement with previous results, but also for ensembles of stars. If confirmed, this result has several implications, including the assertion that the thick disk of our Galaxy forms by radial migration of stars, under the assumption of the conservation of the action describing the vertical motion of stars. © 2016. The American Astronomical Society. All rights reserved

Simulation of heat transport in low-dimensional oscillator lattices

The study of heat transport in low-dimensional oscillator lattices presents a formidable challenge. Theoretical efforts have been made trying to reveal the underlying mechanism of diversified heat transport behaviors. In lack of a unified rigorous treatment, approximate theories often may embody controversial predictions. It is therefore of ultimate importance that one can rely on numerical simulations in the investigation of heat transfer processes in low-dimensional lattices. The simulation of heat transport using the non-equilibrium heat bath method and the Green-Kubo method will be introduced. It is found that one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) momentum-conserving nonlinear lattices display power-law divergent, logarithmic divergent and constant thermal conductivities, respectively. Next, a novel diffusion method is also introduced. The heat diffusion theory connects the energy diffusion and heat conduction in a straightforward manner. This enables one to use the diffusion method to investigate the objective of heat transport. In addition, it contains fundamental information about the heat transport process which cannot readily be gathered otherwise.Comment: Article published in: Thermal transport in low dimensions: From statistical physics to nanoscale heat transfer, S. Lepri, ed. Lecture Notes in Physics, vol. 921, pp. 239 - 274, Springer-Verlag, Berlin, Heidelberg, New York (2016

Integrating rotation from angular velocity

Abstract\ud The integration of the rotation from a given angular velocity is often required in practice. The present paper explores how the choice of the parametrization of rotation, when employed in conjuction with different numerical time-integration schemes, effects the accuracy and the computational efficiency. Three rotation parametrizations – the rotational vector, the Argyris tangential vector and the rotational quaternion – are combined with three different numerical time-integration schemes, including classical explicit Runge–Kutta method and the novel midpoint rule proposed here. The key result of the study is the assessment of the integration errors of various parametrization–integration method combinations. In order to assess the errors, we choose a time-dependent function corresponding to a rotational vector, and derive the related exact time-dependent angular velocity. This is then employed in the numerical solution as the data. The resulting numerically integrated approximate rotations are compared with the analytical solution. A novel global solution error norm for discrete solutions given by a set of values at chosen time-points is employed. Several characteristic angular velocity functions, resulting in small, finite and fast oscillating rotations are studied

Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

In this paper an optimisation algorithm based on Differential Dynamic Programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution