Context-free and context-sensitive dynamics in recurrent neural networks

Continuous-valued recurrent neural networks can learn mechanisms for processing context-free languages. The dynamics of such networks is usually based on damped oscillation around fixed points in state space and requires that the dynamical components are arranged in certain ways. It is shown that qualitatively similar dynamics with similar constraints hold for a(n)b(n)c(n), a context-sensitive language. The additional difficulty with a(n)b(n)c(n), compared with the context-free language a(n)b(n), consists of 'counting up' and 'counting down' letters simultaneously. The network solution is to oscillate in two principal dimensions, one for counting up and one for counting down. This study focuses on the dynamics employed by the sequential cascaded network, in contrast to the simple recurrent network, and the use of backpropagation through time. Found solutions generalize well beyond training data, however, learning is not reliable. The contribution of this study lies in demonstrating how the dynamics in recurrent neural networks that process context-free languages can also be employed in processing some context-sensitive languages (traditionally thought of as requiring additional computation resources). This continuity of mechanism between language classes contributes to our understanding of neural networks in modelling language learning and processing.

Circular proteins in plants - Solution structure of a novel macrocyclic trypsin inhibitor from Momordica cochinchinensis

Much interest has been generated by recent reports on the discovery of circular (i.e. head-to-tail cyclized) proteins in plants. Here we report the three-dimensional structure of one of the newest such circular proteins, MCoTI-II, a novel trypsin inhibitor from Momordica cochinchinensis, a member of the Cucurbitaceae plant family. The structure consists of a small beta -sheet, several turns, and a cystine knot arrangement of the three disulfide bonds. Interestingly, the molecular topology is similar to that of the plant cyclotides (Craik, D. J., Daly, N. L., Bond, T., and Waine, C. (1999) J. Mol. Biol, 294, 1327-1336), which derive from the Rubiaceae and Violaceae plant families, have antimicrobial activities, and exemplify the cyclic cystine knot structural motif as part of their circular backbone. The sequence, biological activity, and plant family of MCoTI-II are all different from known cyclotides. However, given the structural similarity, cyclic backbone, and plant origin of MCoTI-II, we propose that MCoTI-II can be classified as a new member of the cyclotide class of proteins. The expansion of the cyclotides to include trypsin inhibitory activity and a new plant family highlights the importance and functional variability of circular proteins and the fact that they are more common than has previously been believed, Insights into the possible roles of backbone cyclization have been gained by a comparison of the structure of MCoTI-II with the homologous acyclic trypsin inhibitors CMTI-I and EETI-II from the Cucurbitaceae plant family.

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A numerical study of flexural buckling of foliated rock slopes

The occurrence of foliated rock masses is common in mining environment. Methods employing continuum approximation in describing the deformation of such rock masses possess a clear advantage over methods where each rock layer and each inter-layer interface (joint) is explicitly modelled. In devising such a continuum model it is imperative that moment (couple) stresses and internal rotations associated with the bending of the rock layers be properly incorporated in the model formulation. Such an approach will lead to a Cosserat-type theory. In the present model, the behaviour of the intact rock layer is assumed to be linearly elastic and the joints are assumed to be elastic-perfectly plastic. Condition of slip at the interfaces are determined by a Mohr-Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformations. The model is incorporated into the finite element program AFENA and validated against an analytical solution of elementary buckling problems of a layered medium under gravity loading. A design chart suitable for assessing the stability of slopes in foliated rock masses against flexural buckling failure has been developed. The design chart is easy to use and provides a quick estimate of critical loading factors for slopes in foliated rock masses. It is shown that the model based on Euler's buckling theory as proposed by Cavers (Rock Mechanics and Rock Engineering 1981; 14:87-104) substantially overestimates the critical heights for a vertical slope and underestimates the same for sub-vertical slopes. Copyright (C) 2001 John Wiley & Sons, Ltd.

The aesthetic turn in international political theory

This essay explores the nature and significance of aesthetic approaches to international political theory. More specifically, it contrasts aesthetic with mimetic forms of representation. The latter, which have dominated the study of international relations, seek to represent politics as realistically and authentically as possible, aiming at capturing world politics as it really is. An aesthetic approach, by contrast, assumes that there is always a gap between a form of representation and what is represented therewith. Rather than ignoring or seeking to narrow this gap, as mimetic approaches do, aesthetic insight recognises that the inevitable difference between the represented and its representation is the very location of politics. The essay, thus, argues for the need to reclaim the political value of the aesthetic; not to replace social science or technological reason, but to broaden our abilities to comprehend and deal with the key dilemmas of world politics. The ensuing model of thought facilitates productive interactions across different faculties, including sensibility, imagination and reason, without any of them annihilating the unique position and insight of the other.

In vivo protein cyclization promoted by a circularly permuted Synechocystis sp PCC6803 DnaB mini-intein

A synthetic Synechocystis sp. PCC6803 DnaB split mini-intein gene was constructed for the in vivo cyclization of recombinant proteins expressed in Escherichia coli. The system was used to cyclize the NH2-terminal domain of E. coli DnaB, the structure of which had been determined previously by NMR spectroscopy. Cyclization was found to proceed efficiently, with little accumulation of precursor, and the product was purified in high yield. The solution structure of cyclic DnaB-N is not significantly different from that of linear DnaB-N and it unfolds reversibly at temperatures similar to14 degreesC higher. Improved hydrogen bonding was observed in the first and last helices, and the length of the last helix was increased, while the 9-amino acid linker used to join the NH2 and COOH termini was found to be highly mobile. The measured thermodynamic stabilization of the structure (DeltaDeltaG approximate to 2 kcal/mol) agrees well with the value estimated from the reduced conformational entropy in the unfolded form. Simple polymer theory can be used to predict likely free energy changes resulting from protein cyclization and how the stabilization depends on the size of the protein and the length of the linker used to connect the termini.

Analytical solution to the zero-inertia problem for surge flow phenomena in nonprismatic channels

Surge flow phenomena. e.g.. as a consequence of a dam failure or a flash flood, represent free boundary problems. ne extending computational domain together with the discontinuities involved renders their numerical solution a cumbersome procedure. This contribution proposes an analytical solution to the problem, It is based on the slightly modified zero-inertia (ZI) differential equations for nonprismatic channels and uses exclusively physical parameters. Employing the concept of a momentum-representative cross section of the moving water body together with a specific relationship for describing the cross sectional geometry leads, after considerable mathematical calculus. to the analytical solution. The hydrodynamic analytical model is free of numerical troubles, easy to run, computationally efficient. and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model compares very favorably with a full hydrodynamic numerical model in respect to published results of surge flow simulations in different types of prismatic channels. In order to extend these considerations to natural rivers, the accuracy of the analytical model in describing an irregular cross section is investigated and tested successfully. A sensitivity and error analysis reveals the important impact of the hydraulic radius on the velocity of the surge, and this underlines the importance of an adequate description of the topography, The new approach is finally applied to simulate a surge propagating down the irregularly shaped Isar Valley in the Bavarian Alps after a hypothetical dam failure. The straightforward and fully stable computation of the flood hydrograph along the Isar Valley clearly reflects the impact of the strongly varying topographic characteristics on the How phenomenon. Apart from treating surge flow phenomena as a whole, the analytical solution also offers a rigorous alternative to both (a) the approximate Whitham solution, for generating initial values, and (b) the rough volume balance techniques used to model the wave tip in numerical surge flow computations.

Production under uncertainty and choice under uncertainty in the emergence of generalized expected utility theory

This paper presents a personal view of the interaction between the analysis of choice under uncertainty and the analysis of production under uncertainty. Interest in the foundations of the theory of choice under uncertainty was stimulated by applications of expected utility theory such as the Sandmo model of production under uncertainty. This interest led to the development of generalized models including rank-dependent expected utility theory. In turn, the development of generalized expected utility models raised the question of whether such models could be used in the analysis of applied problems such as those involving production under uncertainty. Finally, the revival of the state-contingent approach led to the recognition of a fundamental duality between choice problems and production problems.

Conformations of platypus venom C-type natriuretic peptide in aqueous solution and sodium dodecyl sulfate micelles

Nuclear magnetic resonance spectroscopy was used to investigate the conformations of the platypus venom C-type natriuretic peptide A (OvCNPa) in aqueous solutions and in solutions containing sodium dodecyl sulfate (SDS) micelles. The chemically synthesized OvCNPa showed a substantial decrease in flexibility in aqueous solution at 10 degreesC, allowing the observation of medium- and long-range nuclear Overhauser enhancement (NOE) connectivities. Three-dimensional structures calculated using these data showed flexible and reasonably well-defined regions, the locations of which were similar in the two solvents. In aqueous solution, the linear part that spans residues 3-14 was basically an extended conformation while the cyclic portion, defined by residues 23-39, contained a series of beta-turns. The overall shape of the cyclic portion was similar to that observed for an atrial natriuretic peptide (ANP) variant in aqueous solution. OvCNPa adopted a different conformation in SDS micelles wherein the N-terminal region, defined by residues 2-10, was more compact, characterised by turns and a helix, while the cyclic region had turns and an overall shape that was fundamentally different from those structures observed in aqueous solution. The hydrophobic cluster, situated at the centre of the ring of the structure in aqueous solution, was absent in the structure in the presence of SDS micelles. Thus, OvCNPa interacts with SDS micelles and can possibly form ion-channels in cell membranes. (C) 2002 Elsevier Science Ltd. All rights reserved.

Analytical solution for tidal propagation in a coupled semi-confined/phreatic coastal aquifer

An analytical solution is derived for tidal fluctuations in a coupled coastal aquifer system consisting of a semi-confined aquifer, a thin semi-permeable layer and a phreatic aquifer. Based on the solution, we study the interactions (via leakage) between the confined and unconfined aquifers in response to tides. The results show that, under certain conditions, leakage from the confined aquifer can affect considerably the tidal water table fluctuation in the phreatic aquifer and vice versa. Ignoring these effects could lead to errors in estimating aquifer properties based on tidal signals. (C) 2002 Elsevier Science Ltd. All rights reserved.

On the theory of mixing-frequency electron spin-echo envelope modulation spectroscopy

It has recently been stated that the parametrization of the time variables in the one-dimensional (I-D) mixing-frequency electron spin-echo envelope modulation (MIF-ESEEM) experiment is incorrect and hence the wrong frequencies for correlated nuclear transitions are predicted. This paper is a direct response to such a claim, its purpose being to show that the parametrization in land 2-D MIF-ESEEM experiments possesses the same form as that used in other 4-pulse incrementation schemes and predicts the same correlation frequencies. We show that the parametrization represents a shearing transformation of the 2-D time-domain and relate the resulting frequency domain spectrum to the HYSCORE spectrum in terms of a skew-projection. It is emphasized that the parametrization of the time-domain variables may be chosen arbitrarily and affects neither the computation of the correct nuclear frequencies nor the resulting resolution. The usefulness or otherwise of the MIF parameters \gamma\ > 1 is addressed, together with the validity of the original claims of the authors with respect to resolution enhancement in cases of purely homogeneous and inhomogeneous broadening. Numerical simulations are provided to illustrate the main points.

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Texture alignment in simple shear

We illustrate the flow behaviour of fluids with isotropic and anisotropic microstructure (internal length, layering with bending stiffness) by means of numerical simulations of silo discharge and flow alignment in simple shear. The Cosserat theory is used to provide an internal length in the constitutive model through bending stiffness to describe isotropic microstructure and this theory is coupled to a director theory to add specific orientation of grains to describe anisotropic microstructure. The numerical solution is based on an implicit form of the Material Point Method developed by Moresi et al. [1].