Critical behavior in a cross-situational lexicon learning scenario

The associationist account for early word learning is based on the co-occurrence between referents and words. Here we introduce a noisy cross-situational learning scenario in which the referent of the uttered word is eliminated from the context with probability gamma, thus modeling the noise produced by out-of-context words. We examine the performance of a simple associative learning algorithm and find a critical value of the noise parameter gamma(c) above which learning is impossible. We use finite-size scaling to show that the sharpness of the transition persists across a region of order tau(-1/2) about gamma(c), where tau is the number of learning trials, as well as to obtain the learning error (scaling function) in the critical region. In addition, we show that the distribution of durations of periods when the learning error is zero is a power law with exponent -3/2 at the critical point. Copyright (C) EPLA, 2012

CONTEXT TREE SELECTION AND LINGUISTIC RHYTHM RETRIEVAL FROM WRITTEN TEXTS

The starting point of this article is the question "How to retrieve fingerprints of rhythm in written texts?" We address this problem in the case of Brazilian and European Portuguese. These two dialects of Modern Portuguese share the same lexicon and most of the sentences they produce are superficially identical. Yet they are conjectured, on linguistic grounds, to implement different rhythms. We show that this linguistic question can be formulated as a problem of model selection in the class of variable length Markov chains. To carry on this approach, we compare texts from European and Brazilian Portuguese. These texts are previously encoded according to some basic rhythmic features of the sentences which can be automatically retrieved. This is an entirely new approach from the linguistic point of view. Our statistical contribution is the introduction of the smallest maximizer criterion which is a constant free procedure for model selection. As a by-product, this provides a solution for the problem of optimal choice of the penalty constant when using the BIC to select a variable length Markov chain. Besides proving the consistency of the smallest maximizer criterion when the sample size diverges, we also make a simulation study comparing our approach with both the standard BIC selection and the Peres-Shields order estimation. Applied to the linguistic sample constituted for our case study, the smallest maximizer criterion assigns different context-tree models to the two dialects of Portuguese. The features of the selected models are compatible with current conjectures discussed in the linguistic literature.

Breast imaging: is the sonographic descriptor of orientation valid for magnetic resonance imaging?

Purpose: To evaluate if the Breast Imaging Reporting and Data System (BI-RADS) ultrasound descriptor of orientation can be used in magnetic resonance imaging (MRI). Materials and Methods: We conducted a retrospective study to evaluate breast mass lesions identified by MRI from 2008 to 2010 who had ultrasound (US) and histopathologic confirmation. Lesions were measured in the craniocaudal (CC), anteroposterior (AP), and transverse (T) axes and classified as having a nonparallel orientation, longest axis perpendicular to Cooper's ligaments, or in a parallel orientation when the longest axis is parallel to Cooper's ligaments. The MR image data were correlated with the US orientation according to BI-RADS and histopathological diagnosis. Results: We evaluated 71 lesions in 64 patients. On MRI, 27 lesions (38.0%) were nonparallel (8 benign and 19 malignant), and 44 lesions (62.0%) were parallel (33 benign and 11 malignant). There was significant agreement between the lesion orientation on US and MRI (kappa value = 0.901). The positive predictive values (PPV) for parallel orientation malignancy on MR and US imaging were 70.4% and 73.1%, respectively. Conclusion: A descriptor of orientation for breast lesions can be used on MRI with PPV for malignant lesions similar to US. J. Magn. Reson. Imaging 2012; 36:13831388. (C) 2012 Wiley Periodicals, Inc.