The numerical solution of linear ordinary differential equations by feedforward neural networks

It is demonstrated, through theory and examples, how it is possible to construct directly and noniteratively a feedforward neural network to approximate arbitrary linear ordinary differential equations. The method, using the hard limit transfer function, is linear in storage and processing time, and the L₂ norm of the network approximation error decreases quadratically with the increasing number of hidden layer neurons. The construction requires imposing certain constraints on the values of the input, bias, and output weights, and the attribution of certain roles to each of these parameters.

All results presented used the hard limit transfer function. However, the noniterative approach should also be applicable to the use of hyperbolic tangents, sigmoids, and radial basis functions.     

Self-Immolative Activation of β-Galactosidase-Responsive Probes for In Vivo MR Imaging in Mouse Models

Our lab has developed a new series of self-immolative MR agents for the rapid detection of enzyme activity in mouse models expressing β-galactosidase (β-gal). We investigated two molecular architectures to create agents that detect β-gal activity by modulating the coordination of water to Gd^III. The first is an intermolecular approach, wherein we designed several structural isomers to maximize coordination of endogenous carbonate ions. The second involves an intramolecular mechanism for q modulation. We incorporated a pendant coordinating carboxylate ligand with a 2, 4, 6, or 8 carbon linker to saturate ligand coordination to the Gd^III ion. This renders the agent ineffective. We show that one agent in particular (6-C pendant carboxylate) is an extremely effective MR reporter for the detection of enzyme activity in a mouse model expressing β-gal.     

Neuropeptide delivery to the brain: a von Willebrand factor signal peptide to direct neuropeptide secretion

Background  

Multiple neuropeptides, sometimes with opposing functions, can be produced from one precursor gene. To study the roles of the different neuropeptides encoded by one large precursor we developed a method to overexpress minigenes and establish local secretion.     

Optimization of Pulsed-DEER Measurements for Gd-Based Labels: Choice of Operational Frequencies, Pulse Durations and Positions, and Temperature

In this work, the experimental conditions and parameters necessary to optimize the long-distance (≥60 Å) double electron–electron resonance (DEER) measurements of biomacromolecules labeled with Gd(III) tags are analyzed. The specific parameters discussed are the temperature, microwave band, the separation between the pumping and observation frequencies, pulse train repetition rate, pulse durations and pulse positioning in the electron paramagnetic resonance spectrum. It was found that: (1) in optimized DEER measurements, the observation pulses have to be applied at the maximum of the electron paramagnetic resonance spectrum; (2) the optimal temperature range for K_a-band measurements is 14–17 K, while in W-band the optimal temperatures are between 6 and 9 K; (iv) W-band is preferable to K_a-band for DEER measurements. Recent achievements and the conditions necessary for short-distance measurements (<15 Å) are also briefly discussed.     

Vacuum moulding of a superplastic in two dimensions

A mathematical model is proposed for the process of vacuum superplasticforming. The model exploits the fact that in most industrialapplications the sheet aspect ratio (thickness/sheet width)is small. After an initial consideration of some of the moregeneral properties and the literature of superplastic materials,the elastic/plastic deformation of an internally-inflated thin-walledcylinder is examined. Plates of arbitrary geometry are thenconsidered. A quasisteady model in which the sheet moves througha sequence of steady states is developed. Some simplified closed-formsolutions are examined, but for general cases a system of nonlinearpartial differential equations must be solved numerically. Anefficient and accurate semi-explicit numerical scheme is proposedand a simplified stability analysis is presented; the methodis then used to compute properties of superplastic vacuum mouldedsheets in a number of practically motivated cases.     

Synthesis and electrochemical characterization of a transition-metal-modified ligand-receptor pair

The energetics of weak interactions (van der Waals forces, hydrogen bonding) are difficult to quantify in biological ligand-receptor pairs. Insight into the biochemical role these forces play is critical to an understanding of signal transduction events and the drug discovery process. Ruthenium pentaammine and iron tetracyano complexes modified with either biotin or desthiobiotin have been synthesized and characterized. These modified biological ligands bind to the protein avidin in a manner similar to that of native biotin. Experiments using redox mediators show that the avidin-bound complexes are electrochemically accessible.