Computations of Vector-Valued Siegel Modular Forms

We carry out some computations of vector-valued Siegel modular forms of degree two, weight (k, 2) and level one, and highlight three experimental results: (1) we identify a rational eigenform in a three-dimensional space of cusp forms; (2) we observe that non-cuspidal eigenforms of level one are not always rational; (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. (C) 2013 Elsevier Inc. All rights reserved.

Mental reversal of imagined melodies: A role for the posterior parietal cortex

Two fMRI experiments explored the neural substrates of a musical imagery task that required manipulation of the imagined sounds: temporal reversal of a melody. Musicians were presented with the first few notes of a familiar tune (Experiment 1) or its title (Experiment 2), followed by a string of notes that was either an exact or an inexact reversal. The task was to judge whether the second string was correct or not by mentally reversing all its notes, thus requiring both maintenance and manipulation of the represented string. Both experiments showed considerable activation of the superior parietal lobe (intraparietal sulcus) during the reversal process. Ventrolateral and dorsolateral frontal cortices were also activated, consistent with the memory load required during the task. We also found weaker evidence for some activation of right auditory cortex in both studies, congruent with results from previous simpler music imagery tasks. We interpret these results in the context of other mental transformation tasks, such as mental rotation in the visual domain, which are known to recruit the intraparietal sulcus region, and we propose that this region subserves general computations that require transformations of a sensory input. Mental imagery tasks may thus have both task or modality-specific components as well as components that supersede any specific codes and instead represent amodal mental manipulation.

Multimodal Integration in Statistical Learning: Evidence from the McGurk Illusion

Recent advances in the field of statistical learning have established that learners are able to track regularities of multimodal stimuli, yet it is unknown whether the statistical computations are performed on integrated representations or on separate, unimodal representations. In the present study, we investigated the ability of adults to integrate audio and visual input during statistical learning. We presented learners with a speech stream synchronized with a video of a speaker's face. In the critical condition, the visual (e.g., /gi/) and auditory (e.g., /mi/) signals were occasionally incongruent, which we predicted would produce the McGurk illusion, resulting in the perception of an audiovisual syllable (e.g., /ni/). In this way, we used the McGurk illusion to manipulate the underlying statistical structure of the speech streams, such that perception of these illusory syllables facilitated participants' ability to segment the speech stream. Our results therefore demonstrate that participants can integrate audio and visual input to perceive the McGurk illusion during statistical learning. We interpret our findings as support for modality-interactive accounts of statistical learning.