229 research outputs found

    Isospectral domains with mixed boundary conditions

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    We construct a series of examples of planar isospectral domains with mixed Dirichlet-Neumann boundary conditions. This is a modification of a classical problem proposed by M. Kac.Comment: 9 figures. Statement of Theorem 5.1 correcte

    High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows

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    We relate high-energy limits of Laplace-type and Dirac-type operators to frame flows on the corresponding manifolds, and show that the ergodicity of frame flows implies quantum ergodicity in an appropriate sense for those operators. Observables for the corresponding quantum systems are matrix-valued pseudodifferential operators and therefore the system remains non-commutative in the high-energy limit. We discuss to what extent the space of stationary high-energy states behaves classically.Comment: 26 pages, latex2

    Eigenvectors of the discrete Laplacian on regular graphs - a statistical approach

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    In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical observations, suggesting that the eigenvectors follow a Gaussian distribution. Following this assumption, we reconstruct some properties of the nodal structure which were observed in numerical simulations, but were not explained so far. We also show that some statistical properties of the nodal pattern cannot be described in terms of a percolation model, as opposed to the suggested correspondence for eigenvectors of 2 dimensional manifolds.Comment: 28 pages, 11 figure

    Comparing phoneme frequency, age of acquisition, and loss in aphasia:Implications for phonological universals

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    Phonological complexity may be central to the nature of human language. It may shape the distribution of phonemes and phoneme sequences within languages, but also determine age of acquisition and susceptibility to loss in aphasia. We evaluated this claim using frequency statistics derived from a corpus of phonologically transcribed Italian words (phonitalia, available at phonitalia,org), rankings of phoneme age of acquisition (AoA) and rate of phoneme errors in patients with apraxia of speech (AoS) as an indication of articulatory complexity. These measures were related to cross-linguistically derived markedness rankings. We found strong correspondences. AoA, however, was predicted by both apraxic errors and frequency, suggesting independent contributions of these variables. Our results support the reality of universal principles of complexity. In addition they suggest that these complexity principles have articulatory underpinnings since they modulate the production of patients with AoS, but not the production of patients with more central phonological difficulties

    Tropological space : the imaginary space of figuration

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    The paper is devoted to the concept of tropological space, introduced by Michel Foucault in 1966 and alluded to in Hayden White’s tropics of discourse (1973, 1978, 2000), but never described in any detail in literary semantics or linguistic stylistics. The author presents her theory of a triple functional subdivision of stylistic figures and, consequently, of tropes (micro-, macro- and mega (meta)-level of description) and relates it to a gradually expanding tropological space of particular figures, their chains and groupings within a text. The author postulates that tropological space, the imaginary space created through figuration, is a sub-space of the Wittgensteinian logical space as well as a sub-space of textual / discursive space. Although the discussion refers mostly to literary texts, tropology – a branch of stylistics / poetics / rhetoric makes generalizations valid for the study of all kinds of texts / discourses. Figuration is assumed here to be an inherent feature of conceptual and linguistic expression. Finally, the author raises a methodological query as to the ontological status of tropological space, opting for the approach which treats it as a peculiar kind of semantic space rather than a mere metaphoric term. The discussion is based mostly on the Anglo-American studies on figuration (K. Burke, H. White, P. de Man, J. Hillis Miller, G. Hartman) that are rooted in the neo-classical rhetoric and writings of G. Vico. This line of thinking draws its philosophical inspiration from the European hermeneutics of P. Ricoeur, the Foucaultian theory of discourses and the Derridean deconstructionist ideas on the operation of language. The author brings additionally into consideration the conception of artistic space propagated by the Russian semiotic tradition and V. N. Toporov (1983/2003) in particular

    Grasping Kinematics from the Perspective of the Individual Digits: A Modelling Study

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    Grasping is a prototype of human motor coordination. Nevertheless, it is not known what determines the typical movement patterns of grasping. One way to approach this issue is by building models. We developed a model based on the movements of the individual digits. In our model the following objectives were taken into account for each digit: move smoothly to the preselected goal position on the object without hitting other surfaces, arrive at about the same time as the other digit and never move too far from the other digit. These objectives were implemented by regarding the tips of the digits as point masses with a spring between them, each attracted to its goal position and repelled from objects' surfaces. Their movements were damped. Using a single set of parameters, our model can reproduce a wider variety of experimental findings than any previous model of grasping. Apart from reproducing known effects (even the angles under which digits approach trapezoidal objects' surfaces, which no other model can explain), our model predicted that the increase in maximum grip aperture with object size should be greater for blocks than for cylinders. A survey of the literature shows that this is indeed how humans behave. The model can also adequately predict how single digit pointing movements are made. This supports the idea that grasping kinematics follow from the movements of the individual digits

    Natural Variation in Arabidopsis Cvi-0 Accession Reveals an Important Role of MPK12 in Guard Cell CO2 Signaling

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    Plant gas exchange is regulated by guard cells that form stomatal pores. Stomatal adjustments are crucial for plant survival; they regulate uptake of CO2 for photosynthesis, loss of water, and entrance of air pollutants such as ozone. We mapped ozone hypersensitivity, more open stomata, and stomatal CO2-insensitivity phenotypes of the Arabidopsis thaliana accession Cvi-0 to a single amino acid substitution in MITOGEN-ACTIVATED PROTEIN (MAP) KINASE 12 (MPK12). In parallel, we showed that stomatal CO2-insensitivity phenotypes of a mutant cis (CO2-insensitive) were caused by a deletion of MPK12. Lack of MPK12 impaired bicarbonate-induced activation of S-type anion channels. We demonstrated that MPK12 interacted with the protein kinase HIGH LEAF TEMPERATURE 1 (HT1)-a central node in guard cell CO2 signaling-and that MPK12 functions as an inhibitor of HT1. These data provide a new function for plant MPKs as protein kinase inhibitors and suggest a mechanism through which guard cell CO2 signaling controls plant water management.</p

    When Ears Drive Hands: The Influence of Contact Sound on Reaching to Grasp

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    Background Most research on the roles of auditory information and its interaction with vision has focused on perceptual performance. Little is known on the effects of sound cues on visually-guided hand movements. Methodology/Principal Findings We recorded the sound produced by the fingers upon contact as participants grasped stimulus objects which were covered with different materials. Then, in a further session the pre-recorded contact sounds were delivered to participants via headphones before or following the initiation of reach-to-grasp movements towards the stimulus objects. Reach-to-grasp movement kinematics were measured under the following conditions: (i) congruent, in which the presented contact sound and the contact sound elicited by the to-be-grasped stimulus corresponded; (ii) incongruent, in which the presented contact sound was different to that generated by the stimulus upon contact; (iii) control, in which a synthetic sound, not associated with a real event, was presented. Facilitation effects were found for congruent trials; interference effects were found for incongruent trials. In a second experiment, the upper and the lower parts of the stimulus were covered with different materials. The presented sound was always congruent with the material covering either the upper or the lower half of the stimulus. Participants consistently placed their fingers on the half of the stimulus that corresponded to the presented contact sound. Conclusions/Significance Altogether these findings offer a substantial contribution to the current debate about the type of object representations elicited by auditory stimuli and on the multisensory nature of the sensorimotor transformations underlying action
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