Niche-dependent development of functional neuronal networks from embryonic stem cell-derived neural populations

Background  

The present work was performed to investigate the ability of two different embryonic stem (ES) cell-derived neural precursor populations to generate functional neuronal networks in vitro. The first ES cell-derived neural precursor population was cultivated as free-floating neural aggregates which are known to form a developmental niche comprising different types of neural cells, including neural precursor cells (NPCs), progenitor cells and even further matured cells. This niche provides by itself a variety of different growth factors and extracellular matrix proteins that influence the proliferation and differentiation of neural precursor and progenitor cells. The second population was cultivated adherently in monolayer cultures to control most stringently the extracellular environment. This population comprises highly homogeneous NPCs which are supposed to represent an attractive way to provide well-defined neuronal progeny. However, the ability of these different ES cell-derived immature neural cell populations to generate functional neuronal networks has not been assessed so far.     

Playing with Numbers, with Fermions and Bosons

We construct nonlinear maps which realize the fermionization of bosons and the bosonization of fermions with the view of obtaining states coding naturally integers in standard or in binary basis. Specifically, with reference to spin systems, we derive raising and lowering bosonic operators in terms of standard fermionic operators and vice versa. The crucial role of multiboson operators in the whole construction is emphasized. Dedicated to Giuseppe Castagnoli for his 65th birthday.     

颗粒-颗粒接触力的热力学模型

以颗粒二体接触力模型为基础和出发点的软球离散元模拟是当前颗粒物理和力学领域广泛应用的研究手段.但文献上经常使用的、包括著名的Hertz-Mindlin和Luding在内的力模型并没有完全明确弹性势能或耗散热的计算方法,故从热力学层面看它们还需要完善.考虑到机械能的耗散行为是这类材料的重要物理内容,本文借鉴近年来提出的颗粒固体流体动力学(GSH)思路,提出一种具有明确势能和热功率的接触力建模方法.该理论除明确给出了机械能和热能的计算公式外,还能具体描述能量守恒、热力学平衡态和熵增加等基本原理,解决了传统接触力模型在这些方面的欠缺问题.初步计算显示本文模型的恢复系数可以随碰撞速率的增加而减弱,这比现有的其他模型更符合实验观测.虽然为简单起见这些公式仅局限于二维和忽略颗粒转动运动情况,文中讨论了如何推广到三维含转动情形,以及所涉及的滚动和扭转接触力的热力学处理问题.鉴于是否在Onsager非平衡热力学基础上建模是本文给出的接触力公式有别于当前其他模型的关键所在,文中强调了这里的主要建模对象应该是热力学特征函数和Onsager迁移系数,而接触力是它们的推导结果.这是一个与目前直接针对接触力进行建模的不同思路.文中对颗粒物质特有的、反映样品几何变形与弹应变之间联络的一个非对角迁移系数做了详细介绍,并且认为它与打滑等复杂力学现象关系密切,无论宏观GSH尺度上,还是细观接触力尺度上都不可忽略.     

Stochastic Attractors for Shell Phenomenological Models of Turbulence

Recently, it has been proposed that the Navier–Stokes equations and a relevant linear advection model have the same long-time statistical properties, in particular, they have the same scaling exponents of their structure functions. This assertion has been investigate rigorously in the context of certain nonlinear deterministic phenomenological shell model, the Sabra shell model, of turbulence and its corresponding linear advection counterpart model. This relationship has been established through a “homotopy-like” coefficient λ which bridges continuously between the two systems. That is, for λ=1 one obtains the full nonlinear model, and the corresponding linear advection model is achieved for λ=0. In this paper, we investigate the validity of this assertion for certain stochastic phenomenological shell models of turbulence driven by an additive noise. We prove the continuous dependence of the solutions with respect to the parameter λ. Moreover, we show the existence of a finite-dimensional random attractor for each value of λ and establish the upper semicontinuity property of this random attractors, with respect to the parameter λ. This property is proved by a pathwise argument. Our study aims toward the development of basic results and techniques that may contribute to the understanding of the relation between the long-time statistical properties of the nonlinear and linear models.     

Joint temporal density measurements for two-photon state characterization

We demonstrate a technique for characterizing two-photon quantum states based on joint temporal correlation measurements using time-resolved single-photon detection by femtosecond up-conversion. We measure for the first time the joint temporal density of a two-photon entangled state, showing clearly the time anticorrelation of the coincident-frequency entangled photon pair generated by ultrafast spontaneous parametric down-conversion under extended phase-matching conditions. The new technique enables us to manipulate the frequency entanglement by varying the down-conversion pump bandwidth to produce a nearly unentangled two-photon state that is expected to yield a heralded single-photon state with a purity of 0.88. The time-domain correlation technique complements existing frequency-domain measurement methods for a more complete characterization of photonic entanglement.     

Global bifurcations in a laser with injected signal: Beyond Adler's approximation

We discuss the dynamics in the laser with an injected signal from a perturbative point of view showing how different aspects of the dynamics get their definitive character at different orders in the perturbation scheme. At the lowest order Adler's equation [Proc. IRE 34, 351 (1946)] is recovered. More features emerge at first order including some bifurcations sets and the global reinjection conjectured in Physica D 109, 293 (1997). The type of codimension-2 bifurcations present can only be resolved at second order. We show that of the two averaging approximations proposed [Opt. Commun. 111, 173 (1994); Quantum Semiclassic. Opt. 9, 797 (1997); Quantum Semiclassic. Opt. 8, 805 (1996)] differing in the second order terms, only one is accurate to the order required, hence, solving the apparent contradiction among these results. We also show in numerical studies how a homoclinic orbit of the Sil'nikov type, bifurcates into a homoclinic tangency of a periodic orbit of vanishing amplitude. The local vector field at the transition point contains a Hopf-saddle-node singularity, which becomes degenerate and changes type. The overall global bifurcation is of codimension-3. The parameter governing this transition is theta, the cavity detuning (with respect to the atomic frequency) of the laser. (c) 2001 American Institute of Physics.     

A borel-weil-bott approach to representations of sl q (2, ℂ)

We use a quite concrete and simple realization of sl _q (2, ) involving finite difference operators. We interpret them as derivations (in the noncommutative sense) on a suitable graded algebra, which gives rise to the noncommutative scheme ¹ II ^1* as the counterpart of the standard ¹ = Sl(2, )/B.     

Continuously tunable 1 byte delay in coupled-resonator optical waveguides

A reconfigurable coupled-resonator optical waveguide made of a few directly coupled ring resonators is employed to control the delay of data streams modulated at tens of gigabits per second. A delay of 8 bit lengths (1 optical byte) with a small pulse broadening and 1 dB/bit fractional loss is achieved by using only eight rings. The limiting role of waveguide loss and spurious backreflections is experimentally investigated. The high storage efficiency (1 bit/ring) of the device enables an easy, reliable, hitless, and relatively low-power-consuming management of the delay. A higher storage efficiency is demonstrated to be associated to an unavoidable higher pulse distortion.     

Single-shot extreme ultraviolet laser imaging of nanostructures with wavelength resolution

We have demonstrated near-wavelength resolution microscopy in the extreme ultraviolet. Images of 50 nm diameter nanotubes were obtained with a single ~1 ns duration pulse from a desktop-size 46.9 nm laser. We measured the modulation transfer function of the microscope for three different numerical aperture zone plate objectives, demonstrating that 54 nm half-period structures can be resolved. The combination of near-wavelength spatial resolution and high temporal resolution opens myriad opportunities in imaging, such as the ability to directly investigate dynamics of nanoscale structures.     

Modules Over the Noncommutative Torus and Elliptic Curves

Using the Weil–Brezin–Zak transform of solid state physics, we describe line bundles over elliptic curves in terms of Weyl operators. We then discuss the connection with finitely generated projective modules over the algebra A _θ of the noncommutative torus. We show that such A _θ -modules have a natural interpretation as Moyal deformations of vector bundles over an elliptic curve E _τ , under the condition that the deformation parameter θ and the modular parameter τ satisfy a non-trivial relation.