Discourse priming of homophones in individuals with dominant subcortical lesions, cortical lesions, and Parkinson’s disease

An on-line priming experiment was used to investigate discourse-level processing in four matched groups of subjects: individuals with nonthalamic subcortical lesions (NSL) ( n =10), normal control subjects ( n =10), subjects with Parkinsons disease (PD) ( n =10), and subjects with cortical lesions ( n =10). Subjects listened to paragraphs that ended in lexical ambiguities, and then made speeded lexical decisions on visual letter strings that were: nonwords, matched control words, contextually appropriate associates of the lexical ambiguity, contextually inappropriate associates of the ambiguity, and inferences (representing information which could be drawn from the paragraphs but was not explicitly stated). Targets were presented at an interstimulus interval (ISI) of 0 or 1000ms. NSL and PD subjects demonstrated priming for appropriate and inappropriate associates at the short ISI, similar to control subjects and cortical lesion subjects, but were unable to demonstrate selective priming of the appropriate associate and inference words at the long ISI. These results imply intact automatic lexical processing and a breakdown in discourse-based meaning selection and inference development via attentional/strategic mechanisms.

On learning context-free and context-sensitive languages

The long short-term memory (LSTM) is not the only neural network which learns a context sensitive language. Second-order sequential cascaded networks (SCNs) are able to induce means from a finite fragment of a context-sensitive language for processing strings outside the training set. The dynamical behavior of the SCN is qualitatively distinct from that observed in LSTM networks. Differences in performance and dynamics are discussed.

Entangled subspaces and quantum symmetries

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize its entanglement, so that a first subspace is more entangled than a second, if the Schmidt string of the second majorizes the Schmidt string of the first. The idea is applied to the antisymmetric and symmetric tensor products of a finite-dimensional Hilbert space with itself, and also to the tensor product of an angular momentum j with a spin 1/2. When adapted to the subspaces of states of the nonrelativistic hydrogen atom with definite total angular momentum (orbital plus spin), within the space of bound states with a given total energy, this leads to a complete ordering of those subspaces by their Schmidt strings.