The Berkeley Center for Structural Biology at the Advanced Light Source

The Berkeley Center for Structural Biology (BCSB) operates and develops a suite of protein crystallography beamlines at the Advanced Light Source (ALS) located at Lawrence Berkeley National Laboratory (LBNL). Although the ALS was conceived as a low-energy (1.9-GeV), third-generation synchrotron source of vacuum ultraviolet (VUV) and soft X-ray radiation, it was realized during the development of the facility in the mid-1990s that a multipole wiggler coupled with brightness-preserving optics would result in a beamline whose performance in the energy range of 5 to 15 keV would be sufficient for most protein crystallographic experiments. Later, the hard X-ray capabilities of the ALS were expanded by the addition of three superconducting bending magnets, resulting in additional protein crystallography facilities at the ALS [1 A.A. MacDowell, J Synchrotron Radiation 11(6), 447–55 (2004).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]].     

A Large Deviations Principle Related to the Strong Arc-Sine Law

We show a large deviations principle for the family of random variables when t+, where B=(B _u ,u0) is a standard linear Brownian motion.     

Nanotextured multicrystalline Al‐BSF solar cells reaching 18% conversion efficiency using industrially viable solar cell processes

We report recent achievements in adapting industrially used solar cell processes on nanotextured surfaces. Nanostructures were etched into c‐Si surfaces by dry exothermic plasma‐less reaction of F species with Si in atmospheric pressure conditions and then modified using a short post‐etching process. Nanotextured multicrystalline wafers are used to prepare Al‐BSF solar cells using industrially feasible solar cell proc‐ essing steps. In comparison to the reference acidic textured solar cells, the nanostructured cells showed gain in short circuit current (J_sc) of up to 0.8 mA/cm² and absolute gain in conversion efficiency of up to 0.3%. The best nanotextured solar cell was independently certified to reach the conversion efficiency of 18.0%. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Relational Control Structures

In this paper, we outline the use of relational control structures (Regel-Relative) to describe continuous-time linear systems and show how well known time-invariance from control theory can be defined by these algebraic structures. Furthermore, such important system properties as controllability and reachability are introduced to arbitrary (nonlinear, non-smooth, discontinuous) dynamical systems.     

Opportunity to learn problem solving in Dutch primary school mathematics textbooks

In the Netherlands, mathematics textbooks are a decisive influence on the enacted curriculum. About a decade ago, Dutch primary school mathematics textbooks provided hardly any opportunities to learn problem solving. In this study we investigated whether this provision has changed. In order to do so, we carried out a textbook analysis in which we established to what degree current textbooks provide non-routine problem-solving tasks for which students do not immediately have a particular solution strategy at their disposal. We also analyzed to what degree textbooks provide ‘gray-area’ tasks, which are not really non-routine problems, but are also not straightforwardly solvable. In addition, we inventoried other ways in which present textbooks facilitate the opportunity to learn problem solving. Finally, we researched how inclusive these textbooks are with respect to offering opportunities to learn problem solving for students with varying mathematical abilities. The results of our study show that the opportunities that the currently most widely used Dutch textbooks offer to learn problem solving are very limited, and these opportunities are mainly offered in materials meant for more able students. In this regard, Dutch mainstream textbooks have not changed compared to the situation a decade ago. A textbook that is the Dutch edition of a Singapore mathematics textbook stands out in offering the highest number of problem-solving tasks, and in offering these in the materials meant for all students. However, in the ways this textbook facilitates the opportunity to learn problem solving, sometimes a tension occurs concerning the creative character of genuine problem solving.     

Improving the approximation of the probability density function of random nonautonomous logistic‐type differential equations

In this paper, we address the problem of approximating the probability density function of the following random logistic differential equation: P^′(t,ω)=A(t,ω)(1?P(t,ω))P(t,ω), t∈[t₀,T], P(t₀,ω)=P₀(ω), where ω is any outcome in the sample space Ω. In the recent contribution [Cortés, JC, et al. Commun Nonlinear Sci Numer Simulat 2019; 72: 121–138], the authors imposed conditions on the diffusion coefficient A(t) and on the initial condition P₀ to approximate the density function f₁(p,t) of P(t): A(t) is expressed as a Karhunen–Loève expansion with absolutely continuous random coefficients that have certain growth and are independent of the absolutely continuous random variable P₀, and the density of P₀, , is Lipschitz on (0,1). In this article, we tackle the problem in a different manner, by using probability tools that allow the hypotheses to be less restrictive. We only suppose that A(t) is expanded on L²([t₀,T]×Ω), so that we include other expansions such as random power series. We only require absolute continuity for P₀, so that A(t) may be discrete or singular, due to a modified version of the random variable transformation technique. For , only almost everywhere continuity and boundedness on (0,1) are needed. We construct an approximating sequence of density functions in terms of expectations that tends to f₁(p,t) pointwise. Numerical examples illustrate our theoretical results.     

High-gain Tm-doped fluoride fiber amplifier

A diode-pumped Tm-doped fiber-optic amplifier that has a small-signal gain of >30 dB at 1870 nm is reported. Output pulses of up to 3-W peak power at a 1-60-kHz repetition rate can be generated by amplification of 20-40-ns laser diode pulses of up to 2-mW launched peak power. The output signal quality, i.e., the ratio of the output pulse energy and the total amplified spontaneous emission (ASE) output energy between two pulses, depends on the relative propagation direction of pump and signal and can be dramatically increased by choice of the correct propagation scheme. In the optimum pump geometry the pulse energy can be raised to as much as 20 times the ASE energy. This is the first report to the author's knowledge of fiber-optic amplification of short diode laser pulses near 1.9 microm with high repetition rates in Tm-doped fibers.     

Beta Variables as Times Spent in [0, {infty}[ by Certain Perturbed Brownian Motions

The paper shows that the times spent in [0, +) by certain processesY which are defined by perturbations of Brownian motion involvingreflection at maxima and minima are beta distributed. This resultrelies heavily on Ray–Knight theorems for such perturbedBrownian motions.     

Unstable attractors induce perpetual synchronization and desynchronization

Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which unstable attractors arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send pulses alternately, resulting in a periodic dynamics of the network. Under the influence of arbitrarily weak noise, this synchronization is followed by a desynchronization of clusters, a phenomenon induced by attractors that are unstable. Perpetual synchronization and desynchronization lead to a switching among attractors. This is explained by the geometrical fact, that these unstable attractors are surrounded by basins of attraction of other attractors, whereas the full measure of their own basin is located remote from the attractor. Unstable attractors do not only exist in these systems, but moreover dominate the dynamics for large networks and a wide range of parameters.     

On realistic terrains

We study worst-case complexities of visibility and distance structures on terrains under realistic assumptions on edge length ratios and the angles of the triangles, and a more general low-density assumption. We show that the visibility map of a point for a realistic terrain with n triangles has complexity . We also prove that the shortest path between two points p and q on a realistic terrain passes through triangles, and that the bisector of p and q has complexity . We use these results to show that the shortest path map for any point on a realistic terrain has complexity , and that the Voronoi diagram for any set of m points on a realistic terrain has complexity and . Our results immediately imply more efficient algorithms for computing the various structures on realistic terrains.