Integration of a generalized H\'enon-Heiles Hamiltonian

The generalized H\'enon-Heiles Hamiltonian $H=1/2(P_X^2+P_Y^2+c_1X^2+c_2Y^2)+aXY^2-bX^3/3$ with an additional nonpolynomial term $\mu Y^{-2}$ is known to be Liouville integrable for three sets of values of $(b/a,c_1,c_2)$. It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton-Jacobi equations, we succeed here, in the two other cases, to integrate the equations of motion with hyperelliptic functions.Comment: LaTex 2e. To appear, Journal of Mathematical Physic

Completeness of the cubic and quartic H\'enon-Heiles Hamiltonians

The quartic H\'enon-Heiles Hamiltonian $H = (P_1^2+P_2^2)/2+(\Omega_1 Q_1^2+\Omega_2 Q_2^2)/2 +C Q_1^4+ B Q_1^2 Q_2^2 + A Q_2^4 +(1/2)(\alpha/Q_1^2+\beta/Q_2^2) - \gamma Q_1$ passes the Painlev\'e test for only four sets of values of the constants. Only one of these, identical to the traveling wave reduction of the Manakov system, has been explicitly integrated (Wojciechowski, 1985), while the three others are not yet integrated in the generic case $(\alpha,\beta,\gamma)\not=(0,0,0)$. We integrate them by building a birational transformation to two fourth order first degree equations in the classification (Cosgrove, 2000) of such polynomial equations which possess the Painlev\'e property. This transformation involves the stationary reduction of various partial differential equations (PDEs). The result is the same as for the three cubic H\'enon-Heiles Hamiltonians, namely, in all four quartic cases, a general solution which is meromorphic and hyperelliptic with genus two. As a consequence, no additional autonomous term can be added to either the cubic or the quartic Hamiltonians without destroying the Painlev\'e integrability (completeness property).Comment: 10 pages, To appear, Theor.Math.Phys. Gallipoli, 34 June--3 July 200

Float zone experiments in space

The molten zone/freezing crystal interface system and all the mechanisms were examined. If Marangoni convection produces oscillatory flows in the float zone of semiconductor materials, such as silicon, then it is unlikely that superior quality crystals can be grown in space using this process. The major goals were: (1) to determine the conditions for the onset of Marangoni flows in molten tin, a model system for low Prandtl number molten semiconductor materials; (2) to determine whether the flows can be suppressed by a thin oxide layer; and (3) based on experimental and mathematical analysis, to predict whether oscillatory flows will occur in the float zone silicon geometry in space, and if so, could it be suppressed by thin oxide or nitride films. Techniques were developed to analyze molten tin surfaces in a UHV system in a disk float zone geometry to minimize buoyancy flows. The critical Marangoni number for onset of oscillatory flows was determined to be greater than 4300 on atomically clean molten tin surfaces

On reductions of some KdV-type systems and their link to the quartic He'non-Heiles Hamiltonian

A few 2+1-dimensional equations belonging to the KP and modified KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.Comment: 12 pages, 3 figures, NATO ARW, 15-19 september 2002, Elb

Asymmetries in tongue-palate contact during speech

Research has shown that speech articulation tends to be asymmetrical in the transverse plane of the vocal tract. A recent meta-study of previously published electropalatograms revealed that 83% of these images show asymmetrical tongue-palate contact [1]. The present study investigated articulation asymmetry on the basis of a large number of electropalatograms acquired in a sentence-reading task at the Centre for Speech Technology Research, Edinburgh University (Mocha: Multichannel Articulatory Database). The vast majority (97.5%) of these palatograms showed some degree of left-right asymmetry, with greater contact on the left-hand side being the more common finding. Asymmetry was not strongly determined by voice or place of articulation. However, it was highly dependent on manner, with fricatives and the lateral approximant showing the greatest degree of asymmetry. Characterisation of articulation asymmetry could improve our understanding of the speech-production process and its relationship with both neural organisation and the anatomy of the organs of speech

Texture Segmentation: An Objective Comparison between Traditional and Deep-Learning Methodologies

This paper compares a series of traditional and deep learning methodologies for the segmentation of textures. Six well-known texture composites first published by Randen and Hus{\o}y were used to compare traditional segmentation techniques (co-occurrence, filtering, local binary patterns, watershed, multiresolution sub-band filtering) against a deep-learning approach based on the U-Net architecture. For the latter, the effects of depth of the network, number of epochs and different optimisation algorithms were investigated. Overall, the best results were provided by the deep-learning approach. However, the best results were distributed within the parameters, and many configurations provided results well below the traditional techniques

Transfer from implicit to explicit phonological abilities in first and second language learners

Children's abilities to process the phonological structure of words are important predictors of their literacy development. In the current study, we examined the interrelatedness between implicit (i.e., speech decoding) and explicit (i.e., phonological awareness) phonological abilities, and especially the role therein of lexical specificity (i.e., the ability to learn to recognize spoken words based on only minimal acoustic-phonetic differences). We tested 75 Dutch monolingual and 64 Turkish–Dutch bilingual kindergartners. SEM analyses showed that speech decoding predicted lexical specificity, which in turn predicted rhyme awareness in the first language learners but phoneme awareness in the second language learners. Moreover, in the latter group there was an impact of the second language: Dutch speech decoding and lexical specificity predicted Turkish phonological awareness, which in turn predicted Dutch phonological awareness. We conclude that language-specific phonological characteristics underlie different patterns of transfer from implicit to explicit phonological abilities in first and second language learners

Lexical specificity training effects in second language learners

Children who start formal education in a second language may experience slower vocabulary growth in that language and subsequently experience disadvantages in literacy acquisition. The current study asked whether lexical specificity training can stimulate bilingual children's phonological awareness, which is considered to be a precursor to literacy. Therefore, Dutch monolingual and Turkish-Dutch bilingual children were taught new Dutch words with only minimal acoustic-phonetic differences. As a result of this training, the monolingual and the bilingual children improved on phoneme blending, which can be seen as an early aspect of phonological awareness. During training, the bilingual children caught up with the monolingual children on words with phonological overlap between their first language Turkish and their second language Dutch. It is concluded that learning minimal pair words fosters phoneme awareness, in both first and second language preliterate children, and that for second language learners phonological overlap between the two languages positively affects training outcomes, likely due to linguistic transfe

Boundary theories of critical matchgate tensor networks

Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states whose site-averaged ground state properties match the translation-invariant critical Ising model. In this work, we substantially sharpen this relationship by deriving disordered local Hamiltonians generalizing the critical Ising model whose ground and low-energy excited states are accurately represented by the matchgate ansatz without any averaging. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model based on layers of the hyperbolic lattice, breaking the conformal symmetries of the critical Ising model in a controlled manner. We provide a direct identification of correlation functions of ground and low-energy excited states between the disordered and translation-invariant models and give numerical evidence that the former approaches the latter in the large bond dimension limit. This establishes tensor networks on regular hyperbolic tilings as an effective tool for the study of conformal field theories. Furthermore, our numerical probes of the bulk parameters corresponding to boundary excited states constitute a first step towards a tensor network bulk-boundary dictionary between regular hyperbolic geometries and critical boundary states