Dynamic recurrent neural network for system identification and control

A dynamic recurrent neural network (DRNN) that can be viewed as a generalisation of the Hopfield neural network is proposed to identify and control a class of control affine systems. In this approach, the identified network is used in the context of the differential geometric control to synthesise a state feedback that cancels the nonlinear terms of the plant yielding a linear plant which can then be controlled using a standard PID controller.

Representing geometrical knowledge

This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

Influence of end-capping on the self-assembly of model amyloid peptide fragments

The influence of charge and aromatic stacking interactions on the self-assembly of a series of four model amyloid peptides has been examined. The four model peptides are based on the KLVFF motif from the amyloid Beta peptide, ABeta(16-20) extended at the N terminus with two Beta-alanine residues. We have studied NH2-BetaABetaAKLVFF-COOH (FF), NH2-BetaABetaAKLVFCOOH (F), CH3CONH-BetaABetaAKLVFF-CONH2 (CapF), and CH3CONH-BetaABetaAKLVFFCONH2 (CapFF). The former two are uncapped (net charge plus 2) and differ by one hydrophobic phenylalanine residue; the latter two are the analogous capped peptides (net charge plus 1). The self-assembly characteristics of these peptides are remarkably different and strongly dependent on concentration. NMR shows a shift from carboxylate to carboxylic acid forms upon increasing concentration. Saturation transfer measurements of solvent molecules indicate selective involvement of phenylalanine residues in driving the self-assembly process of CapFF due presumably to the effect of aromatic stacking interactions. FTIR spectroscopy reveals beta-sheet features for the two peptides containing two phenylalanine residues but not the single phenylalanine residue, pointing again to the driving force for self-assembly. Circular dichroism (CD) in dilute solution reveals the polyproline II conformation, except for F which is disordered. We discuss the relationship of this observation to the significant pH shift observed for this peptide when compared the calculated value. Atomic force microscopy and cryogenic-TEM reveals the formation of twisted fibrils for CapFF, as previously also observed for FF. The influence of salt on the self-assembly of the model beta-sheet forming capped peptide CapFF was investigated by FTIR. Cryo-TEM reveals that the extent of twisting decreases with increased salt concentration, leading to the formation of flat ribbon structures. These results highlight the important role of aggregation-induced pKa shifts in the self-assembly of model beta-sheet peptides.

Tuning the self-assembly of the bioactive dipeptide L-carnosine by incorporation of a bulky aromatic substituent

The dipeptide L-carnosine has a number of important biological properties. Here, we explore the effect of attachment of a bulky hydrophobic aromatic unit, Fmoc [N-(fluorenyl-9-methoxycarbonyl)] on the self-assembly of Fmoc-L-carnosine, i.e., Fmoc-Beta-alanine-histidine (Fmoc-BetaAH). It is shown that Fmoc-BetaAH forms well-defined amyloid fibril containing Beta sheets above a critical aggregation concentration, which is determined from pyrene and ThT fluorescence experiments. Twisted fibrils were imaged by cryogenic transmission electron microscopy. The zinc-binding properties of Fmoc-BetaAH were investigated by FTIR and Raman spectroscopy since the formation of metal ion complexes with the histidine residue in carnosine is well-known, and important to its biological roles. Observed changes in the spectra may reflect differences in the packing of the Fmoc-dipeptides due to electrostatic interactions. Cryo-TEM shows that this leads to changes in the fibril morphology. Hydrogelation is also induced by addition of an appropriate concentration of zinc ions. Our work shows that the Fmoc motif can be employed to drive the self-assembly of carnosine into amyloid fibrils.

Stochastic volatility jump-diffusions for European equity index dynamics

Major research on equity index dynamics has investigated only US indices (usually the S&P 500) and has provided contradictory results. In this paper a clarification and extension of that previous research is given. We find that European equity indices have quite different dynamics from the S&P 500. Each of the European indices considered may be satisfactorily modelled using either an affine model with price and volatility jumps or a GARCH volatility process without jumps. The S&P 500 dynamics are much more difficult to capture in a jump-diffusion framework.

Dynamic input/output linearization using recurrent neural networks

A dynamic recurrent neural network (DRNN) is used to input/output linearize a control affine system in the globally linearizing control (GLC) structure. The network is trained as a part of a closed loop that involves a PI controller, the goal is to use the network, as a dynamic feedback, to cancel the nonlinear terms of the plant. The stability of the configuration is guarantee if the network and the plant are asymptotically stable and the linearizing input is bounded.

Stable linearization using multilayer neural networks

The main limitation of linearization theory that prevents its application in practical problems is the need for an exact knowledge of the plant. This requirement is eliminated and it is shown that a multilayer network can synthesise the state feedback coefficients that linearize a nonlinear control affine plant. The stability of the linearizing closed loop can be guaranteed if the autonomous plant is asymptotically stable and the state feedback is bounded.

Modulating self-assembly of a nanotape-forming peptide amphiphile with an oppositely charged surfactant

A peptide amphiphile (PA) C16-KTTKS, containing a pentapeptide headgroup based on a sequence from procollagen I attached to a hexadecyl lipid chain, self-assembles into extended nanotapes in aqueous solution. The tapes are based on bilayer structures, with a 5.2 nm spacing. Here, we investigate the effect of addition of the oppositely charged anionic surfactant sodium dodecyl sulfate (SDS) via AFM, electron microscopic methods, small-angle X-ray scattering and X-ray diffraction among other methods. We show that addition of SDS leads to a transition from tapes to fibrils, via intermediate states that include twisted ribbons. Addition of SDS is also shown to enhance the development of remarkable lateral ‘‘stripes’’ on the nanostructures, which have a 4 nm periodicity. This is ascribed to counterion condensation. The transition in the nanostructure leads to changes in macroscopic properties, in particular a transition from sol to gel is noted on increasing SDS (with a further reentrant transition to sol on further increase of SDS concentration). Formation of a gel may be useful in applications of this PA in skincare applications and we show that this can be controlled via development of a network of fine stranded fibrils.

Development of orientation during electrospinning of fibres of poly(ε-caprolactone)

We explore the influence of a rotating collector on the internal structure of poly(ε-caprolactone) fibres electrospun from a solution in dichloroethane. We find that above a threshold collector speed, the mean fibre diameter reduces as the speed increases and the fibres are further extended. Small-angle and wide-angle X-ray scattering techniques show a preferred orientation of the lamellar crystals normal to the fibre axis which increases with collector speed to a maximum and then reduces. We have separated out the processes of fibre alignment on the collector and the orientation of crystals within the fibres. There are several stages to this behaviour which correspond to the situations (a) where the collector speed is slower than the fibre spinning rate, (b) the fibre is mechanically extended by the rotating collector and (c) where the deformation leads to fibre fracture. The mechanical deformation leads to a development of preferred orientation with extension which is similar to the prediction of the pseudo-affine deformation model and suggests that the deformation takes place during the spinning process after the crystals have formed.

Structure property relationships in electrically conducting copolymers formed from pyrrole and N-methyl pyrrole

A series of copolymers containing differing proportions of pyrrole and N-methyl pyrrole were prepared electrochemically at various temperatures using acetonitrile as the solvent. The resultant electrical conductivity decreases universally with increasing fraction of N-methyl pyrrole. Films prepared with p-toluene sulfonate as the dopant show a marked variation in structural anisotropy as revealed by X-ray scattering with apparent copolymer content. There is a clear trend between the variation in electrical conductivity and this structural anisotropy. Different patterns of behaviour are observed for films prepared using perchlorate as the dopant and this is attributed to the role of the dopant and final structure in determining the relative reactivities of the pyrrole and N-methyl pyrrole monomers. These observations support the concept that the introduction of methyl substituents into a polypyrrole chain results in a twisted chain conformation. The structure and properties of the resultant copolymer films are particularly sensitive to the preparation conditions.

A wide-angle X-ray study of the development of molecular orientation in crosslinked natural rubber

Molecular orientation parameters have been measured for the non-crystalline component of crosslinked natural rubber samples deformed in uniaxial tension as a function of the extension ratio and of temperature. The orientation parapeters 〈P2(cosα)〉 and 〈P4(cosα)〉 were obtained by an analysis of the anisotropy of the wide-angle X-ray scattering functions. For the measurements made at high temperatures the level of crystallinity detected was negligible and the orientation-strain behaviour could be compared directly with the predictions of molecular models of rubber elasticity. The molecular orientation behaviour with strain was found to be at variance with the estimates of the affine model particularly at low and moderate strains. Extension of the crosslinked rubber at room temperature led to strain-crystallization and measurements of both the molecular orientation of the non-crystalline chains and the degree of crystallinity during extension and relaxation enabled the role of the crystallites in the deformation process to be considered in detail. The intrinsic birefringence of the non-crystalline component was estimated, through the use of the 〈P2(cosα)〉 values obtained from X-ray scattering measurements, to be 0.20±0.02.

Coupling between mesogenic units and polymer backbone in side-chain liquid crystal polymers and elastomers

The levels of alignment of the mesogenic units and of the polymer backbone trajectory for polyacrylate based nematic side-chain liquid crystal polymers and elastomers were evaluated by using wide angle X-ray and small angle neutron scattering procedures. The X-ray scattering measurements show that substantial levels of preferred orientation of the mesogenic units may be introduced through magnetic fields for uncrosslinked polymers and through mechanical extension for liquid crystal elastomers. Small angle neutron scattering measurements show that for highly aligned samples an anisotropic polymer backbone trajectory is observed in which the envelope is slightly extended by ∼ 10% in the direction parallel to the axis of alignment of the mesogenic units. The sense of this coupling differs from that recorded for other uncrosslinked side-chain liquid crystal polymers. Possible mechanisms to account for this anisotropy and its relationship to the properties of liquid crystal elastomers are discussed. The observed deformation behaviour of the liquid crystal elastomer is non-affine and this appears to confirm the dominating influence of the liquid crystal order of the side chains on the mechanical properties of these novel networks.

The determination of molecular orientation in uniaxially compressed PMMA by X-ray scattering

A procedure is presented for obtaining full molecular orientation information from wide angle X-ray scattering patterns of deformed non-crystalline polymers. The method is based on the analysis of experimental and calculated scattering patterns into their spherical harmonics. The results obtained for PMMA are compared with values predicted by the pseudo affine and affine deformation schemes.

Fibrillisation of ring-closed amyloid peptides

Ring-closing olefin metathesis reactions are used to create intramolecularly ring closed peptides or inter-molecularly ring-closed peptide dimers based on a designed amyloid peptide sequence. The uncrosslinked peptide self-assembles into high aspect ratio nanotubes, however ring-closing leads to the formation of fibrillar and twisted/helical ribbon structures.

From ensemble forecasts to predictive distribution functions

The translation of an ensemble of model runs into a probability distribution is a common task in model-based prediction. Common methods for such ensemble interpretations proceed as if verification and ensemble were draws from the same underlying distribution, an assumption not viable for most, if any, real world ensembles. An alternative is to consider an ensemble as merely a source of information rather than the possible scenarios of reality. This approach, which looks for maps between ensembles and probabilistic distributions, is investigated and extended. Common methods are revisited, and an improvement to standard kernel dressing, called ‘affine kernel dressing’ (AKD), is introduced. AKD assumes an affine mapping between ensemble and verification, typically not acting on individual ensemble members but on the entire ensemble as a whole, the parameters of this mapping are determined in parallel with the other dressing parameters, including a weight assigned to the unconditioned (climatological) distribution. These amendments to standard kernel dressing, albeit simple, can improve performance significantly and are shown to be appropriate for both overdispersive and underdispersive ensembles, unlike standard kernel dressing which exacerbates over dispersion. Studies are presented using operational numerical weather predictions for two locations and data from the Lorenz63 system, demonstrating both effectiveness given operational constraints and statistical significance given a large sample.