Relative order defines a topology for recurrent networks

This paper uses techniques from control theory in the analysis of trained recurrent neural networks. Differential geometry is used as a framework, which allows the concept of relative order to be applied to neural networks. Any system possessing finite relative order has a left-inverse. Any recurrent network with finite relative order also has an inverse, which is shown to be a recurrent network.

Stable reduced-order models for discrete-time systems

The Routh-stability method is employed to reduce the order of discrete-time system transfer functions. It is shown that the Routh approximant is well suited to reduce both the denominator and the numerator polynomials, although alternative methods, such as PadÃ�Â(c)-Markov approximation, are also used to fit the model numerator coefficients.

A new approach to reduced-order modelling

An error polynomial is defined, the coefficients of which indicate the difference at any instant between a system and a model of lower order approximating the system. It is shown how Markov parameters and time series proportionals of the model can be matched with those of the system by setting error polynomial coefficients to zero. Also discussed is the way in which the error between system and model can be considered as being a filtered form of an error input function specified by means of model parameter selection.

Structural characterisation of bisintercalation in higher-order DNA at a junction-like quadruplex

We report the single-crystal X-ray structure for the complex of the bisacridine bis-(9-aminooctyl(2-(dimethylaminoethyl)acridine-4-carboxamide)) with the oligonucleotide d(CGTACG)2 to a resolution of 2.4 Å. Solution studies with closed circular DNA show this compound to be a bisintercalating threading agent, but so far we have no crystallographic or NMR structural data conforming to the model of contiguous intercalation within the same duplex. Here, with the hexameric duplex d(CGTACG), the DNA is observed to undergo a terminal cytosine base exchange to yield an unusual guanine quadruplex intercalation site through which the bisacridine threads its octamethylene linker to fuse two DNA duplexes. The 4-carboxamide side-chains form anchoring hydrogen-bonding interactions with guanine O6 atoms on each side of the quadruplex. This higher-order DNA structure provides insight into an unexpected property of bisintercalating threading agents, and suggests the idea of targeting such compounds specifically at four-way DNA junctions.