A biohybrid dynamic random access memory

We report that GABA(A) receptors in a patch-clamped biological cell form a short-term memory circuit when integrated with a scanning-probe microfluidic device. Laminar patterns of receptor activators (agonists) provided by the microfluidic device define and periodically update the data input which is read and stored by the receptors as state distributions (based on intrinsic multistate kinetics). The memory is discharged over time and lasts for seconds to minutes depending on the input function. The function of the memory can be represented by an equivalent electronic circuit with striking similarity in function to a dynamic random access memory (DRAM) used in electronic computers. Multiplexed biohybrid memories may form the basis of large-scale integrated biocomputational/sensor devices with the curious ability to use chemical signals including odorants, neurotransmitters, chemical and biological warfare agents, and many more as input signals.     

A concise total synthesis of DL-histrionicotoxin

The synthesis of (+/-)-histrionicotoxin has been achieved in just nine steps using a two-directional synthesis strategy. Key reactions include a two-directional cross-metathesis, a tandem oxime formation/Michael addition/1,4-prototopic shift/[3 + 2]-cycloaddition cascade, a selective Z,Z-bisenyne formation, and a one-pot N-O and bischloroacetylene reduction.     

Characterisation of spatial and temporal changes in pH gradients in microfluidic channels using optically trapped fluorescent sensors

This paper demonstrates the use of micron sized beads, modified with fluorescent dyes, as non-invasive sensors to probe the local changes in pH, within a microfluidic channel. To achieve this, amine modified polystyrene spheres (either 3 microm or 6 microm in diameter) were functionalised with the pH sensitive fluorochrome SNARF-1 to produce point sensors. The modified beads were trapped at defined positions close to a pair of integrated planar gold microelectrodes within the channel, using optical tweezers. Both transient and steady-state electrochemical potentials were applied to the microelectrode pair in order to generate changes in the local pH, associated with electrolysis. The functionalised beads indicated the pH changes in the channel, measured as a change in the fluorescence signal, generated by the immobilised pH sensitive dye. Responses were measured with temporal resolutions of between 1 and 200 ms, whilst the spatial resolution of the pH gradients was limited by the size of the beads to 3 microm.     

Barry Edward Johnson 1937-2002

Barry Johnson made major contributions to the theory of Banachalgebras, by stimulating research on automatic continuity andcohomology in these algebras. His research on the continuousHochschild cohomology of Banach and operator algebras led tomajor developments in these areas, and to a recognition of ‘amenability’as more than simply a group-theoretic idea, but also one thatis widely applicable in modern analysis.     

Some Exact Results for a Two-Dimensional System of Particles

The Laughlin variational wave function of a quantum liquid used in studying the fractional quantum Hall effect may be interpreted as a two-dimensional system of particles interacting via a logarithmic interaction, with a centripetal force proportional to the square of the distance from the origin. We present exact calculations of the partition function, radial distribution function, and particle density for systems of up to six particles. Received April 25, 1994; revised August 5, 1994; accepted for publication August 30, 1994     

Biased Random Walks, Lyapunov Functions, and Stochastic Analysis of Best Fit Bin Packing

We study the average case performance of the Best Fit algorithm for on-line bin packing under the distributionU{j, k}, in which the item sizes are uniformly distributed in the discrete range {1/k, 2/k,…,j/k}. Our main result is that, in the casej = k − 2, the expected waste for an infinite stream of items remains bounded. This settles an open problem posed by Coffmanet al.[[4]]. It is also the first result which involves a detailed analysis of the infinite multidimensional Markov chain underlying the algorithm.     

Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts

Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called Number Worlds that was designed to support the exploration of elementary number theory concepts by making the essential relationships and patterns more accessible to learners. Based on our research with pre-service elementary school teachers, we show how both the visual representations embedded in the microworld, and the possibilities afforded for experimentation affect learners' understanding and appreciation of basic concepts in elementary number theory. We also discuss the aesthetic and affective dimensions of the research participants' engagement with the learning environment. This revised version was published online in July 2006 with corrections to the Cover Date.     

Re-evaluating the performance of the nonlinear prediction error for the detection of deterministic dynamics

The nonlinear prediction error in combination with appropriately generated surrogate data is widely used as a discriminating statistic for weak nonlinearity. In this paper two of the most widely used formulations of this particular measure are evaluated using data from exemplary nonlinear and linear systems. It is found that both methods, contrary to expectation and accepted utility, give rise to substantial false positive and false negative detection rates in purely linear and nonlinear systems respectively. These findings suggest that the nonlinear prediction error should be used with considerable caution. The implications of these findings for the search for nonlinearity in the human electroencephalogram are briefly discussed.     

SOME CENTRALITY RESULTS NEW AND OLD

We prove a number of results on betweenness and closeness centrality and centralization. In particular, we prove the much used normalization expression for closeness centrality first given by Freeman (1979) Freeman, L. C. 1979. Centrality in social networks conceptual clarification. Social Networks, 1: 215–239. [Crossref], [Web of Science ®] , [Google Scholar], correcting an error in the justification given in his paper. We explore the relationship between betweenness and the cutting number and use these results to prove and correct some centrality and centralization formulae first proposed by Borgatti and Everett (1997) Borgatti, S. P. and Everett, M. G. 1997. Network analysis of 2-mode data. Social Networks, 19: 243–269. [Crossref], [Web of Science ®] , [Google Scholar].