Elemental mapping and quantitative analysis of Cu, Zn, and Fe in rat brain sections by laser ablation ICP-MS

This report details the application of laser ablation quadrupole ICP-MS for the (multi)elemental mapping of 100-μm-thick sections of rat brain. The laser spot size used was 60 μm, and the laser scan speed was 120 μm s⁻¹. The analysis was relatively rapid, allowing mapping of a whole brain thin section (≈1 cm²) in about 2 h. Furthermore, the method was amenable to multi-element data collection including the physiologically important elements P and S and afforded sub μg g⁻¹ detection limits for the important trace elements Cu and Zn. Calibrations were performed with pressed pellets of biological certified reference materials, and the elemental distributions and concentrations of Cu, Zn, and Fe were determined in whole rat brain sections. The distributions and concentration ranges for these elements were consistent with previous studies and demonstrate the utility of this technique for rapid mapping of brain thin sections.     

Compact chip-scale filter based on curved waveguide Bragg gratings

We propose a method for miniaturization of filters based on curved waveguide Bragg gratings, so that long structures can be packed into a small area on a chip. This eliminates the stitching errors introduced in the fabrication process, which compromise the performance of long Bragg gratings. Our approach relies on cascading curved waveguide Bragg gratings with the same radius of curvature. An analytical model for the analysis of these devices was developed, and a filter based on this model was designed and fabricated in a silicon on insulator platform. The filter had a total length of 920μm, occupied an area of 190μm×114μm, and exhibited a stop band of 1.7nm at 1.55μm and an extinction ratio larger than 23dB.     

Passivation of aluminum with alkyl phosphonic acids for biochip applications

Self-assembly of decylphosphonic acid (DPA) and octadecylphosphonic acid (ODPA) was studied on aluminum films using XPS, ToF-SIMS and surface wettability. Modified aluminum films were tested for passivation against silanization and subsequent oligonucleotide attachment. Passivation ratios of at least 450:1 compared to unprotected aluminum were obtained, as quantified by attachment of radio-labeled oligos.     

A forest building process on simple graphs

Consider the following process on a simple graph without isolated vertices: order the edges randomly and keep an edge if and only if it contains a vertex which is not contained in some preceding edge. The resulting set of edges forms a spanning forest of the graph.The probability of obtaining $k$ components in this process for complete bipartite graphs is determined as well as a formula for the expected number of components in any graph. A generic recurrence and some additional basic properties are discussed.     

Univalence as a principle of logic

It is sometimes convenient or useful in mathematics to treat isomorphic structures as the same. The recently proposed Univalence Axiom for the foundations of mathematics elevates this idea to a foundational principle in the setting of homotopy type theory. It provides a simple and precise way in which isomorphic structures can be identified. We explore the motivations and consequences, both mathematical and philosophical, of making such a new logical postulate.     

Irreducible Apollonian Configurations and Packings

An Apollonian configuration of circles is a collection of circles in the plane with disjoint interiors such that the complement of the interiors of the circles consists of curvilinear triangles. One well-studied method of forming an Apollonian configuration is to start with three mutually tangent circles and fill a curvilinear triangle with a new circle, then repeat with each newly created curvilinear triangle. More generally, we can start with three mutually tangent circles and a rule (or rules) for how to fill a curvilinear triangle with circles.     

Tiling Polygons with Lattice Triangles

Given a simple polygon with rational coordinates having one vertex at the origin and an adjacent vertex on the x-axis, we look at the problem of the location of the vertices for a tiling of the polygon using lattice triangles (i.e., triangles which are congruent to a triangle with the coordinates of the vertices being integer). We show that the coordinates of the vertices in any tiling are rationals with the possible denominators odd numbers dependent on the cotangents of the angles in the triangles.     

NSLS‐II: A proposed new synchrotron at Brookhaven National Laboratory

A workshop on high-resolution X-ray emission spectroscopy was held in conjunction with the joint NSLS/CFN 2006 Users' Meeting. With the availability of high-brightness X-ray sources, and the development of improved optics and detectors for high-resolution (millivolt to volt) X-ray detection, X-ray emission spectroscopy (XES) has become one of the more rapidly growing areas of condensed matter synchrotron science. Most of the applications to date have focused on using XES for problems in condensed matter physics. The goal of this workshop was to illustrate the potential of XES for addressing important questions in chemistry and biology.     

Option pricing when asset returns jump interruptedly

This paper proposes an extension of Merton's jump‐diffusion model to reflect the time inhomogeneity caused by changes of market states. The benefit is that it simultaneously captures two salient features in asset returns: heavy tailness and volatility clustering. On the basis of an empirical analysis where jumps are found to happen much more frequently in risky periods than in normal periods, we assume that the Poisson process for driving jumps is governed by a two‐state on‐off Markov chain. This makes jumps happen interruptedly and helps to generate different dynamics under these two states. We provide a full analysis for the proposed model and derive the recursive formulas for the conditional state probabilities of the underlying Markov chain. These analytical results lead to an algorithm that can be implemented to determine the prices of European options under normal and risky states. Numerical examples are given to demonstrate how time inhomogeneity influences return distributions, option prices, and volatility smiles. The contrasting patterns seen in different states indicate the insufficiency of using time‐homogeneous models and justify the use of the proposed model. Copyright © 2012 John Wiley & Sons, Ltd.