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Increasingly sophisticated applications of static analysis place increased burden on the reliability of the analysis techniques. Often, the failure of the analysis technique to detect some information my mean that the time or space complexity of the generated code would be altered. Thus, it is important to precisely characterize the power of static analysis techniques. We follow the approach of Selur et. al. who studied the power of strictness analysis techniques. Their result can be summarized by saying 'strictness analysis is perfect up to variations in constants.' In other words, strictness analysis is as good as it could be, short of actually distinguishing between concrete values. We use this approach to characterize a broad class of analysis techniques based on abstract interpretation including, but not limited to, strictness analysis. For the first-order case, we consider abstract interpretations where the abstract domain for data values is totally ordered. This condition is satisfied by Mycroft's strictness analysis that of Sekar et. al. and Wadler's analysis of list-strictness. For such abstract interpretations, we show that the analysis is complete in the sense that, short of actually distinguishing between concrete values with the same abstraction, it gives the best possible information. We further generalize these results to typed lambda calculus with pairs and higher-order functions. Note that products and function spaces over totally ordered domains are not totally ordered. In fact, the notion of completeness used in the first-order case fails if product domains or function spaces are added. We formulate a weaker notion of completeness based on observability of values. Two values (including pairs and functions) are considered indistinguishable if their observable components are indistinguishable. We show that abstract interpretation of typed lambda calculus programs is complete up to this notion of indistinguishability. We use denotationally
Thrya primarily defines a set of abstract C++ class interfaces needed for the development of abstract numerical atgorithms (ANAs) such as iterative linear solvers, transient solvers all the way up to optimization. At the foundation of these interfaces are abstract C++ classes for vectors, vector spaces, linear operators and multi-vectors. Also included in the Thyra package is C++ code for creating concrete vector, vector space, linear operator, and multi-vector subclasses as well as other utilities to aid in the development of ANAs. Currently, very general and efficient concrete subclass implementations exist for serial and SPMD in-core vectors and multi-vectors. Codemore also currently exists for testing objects and providing composite objects such as product vectors. less
It is generally assumed that abstract concepts are linguistically coded, in line with imaging evidence of greater engagement of the left perisylvian language network for abstract than concrete words (Binder JR, Desai RH, Graves WW, Conant LL. 2009. Where is the semantic system? A critical review and meta-analysis of 120 functional neuroimaging studies. Cerebral Cortex. 19:2767-2796; Wang J, Conder JA, Blitzer DN, Shinkareva SV. 2010. Neural representation of abstract and concrete concepts: A meta-analysis of neuroimaging studies. Hum Brain Map. 31:1459-1468). Recent behavioral work, which used tighter matching of items than previous studies, however, suggests that abstract concepts also entail affective processing to a greater extent than concrete concepts (Kousta S-T, Vigliocco G, Vinson DP, Andrews M, Del Campo E. The representation of abstract words: Why emotion matters. J Exp Psychol Gen. 140:14-34). Here we report a functional magnetic resonance imaging experiment that shows greater engagement of the rostral anterior cingulate cortex, an area associated with emotion processing (e.g., Etkin A, Egner T, Peraza DM, Kandel ER, Hirsch J. 2006. Resolving emotional conflict: A role for the rostral anterior cingulate cortex in modulating activity in the amygdala. Neuron. 52:871), in abstract processing. For abstract words, activation in this area was modulated by the hedonic valence (degree of positive or negative affective association) of our items. A correlation analysis of more than 1,400 English words further showed that abstract words, in general, receive higher ratings for affective associations (both valence and arousal) than concrete words, supporting the view that engagement of emotional processing is generally required for processing abstract words. We argue that these results support embodiment views of semantic representation, according to which, whereas concrete concepts are grounded in our sensory-motor experience, affective experience is crucial in the
A consolidated approach to the study of the mental representation of word meanings has consisted in contrasting different domains of knowledge, broadly reflecting the abstract-concrete dichotomy. More fine-grained semantic distinctions have emerged in neuropsychological and cognitive neuroscience work, reflecting semantic category specificity, but almost exclusively within the concrete domain. Theoretical advances, particularly within the area of embodied cognition, have more recently put forward the idea that distributed neural representations tied to the kinds of experience maintained with the concepts' referents might distinguish conceptual meanings with a high degree of specificity, including those within the abstract domain. Here we report the results of two psycholinguistic rating studies incorporating such theoretical advances with two main objectives: first, to provide empirical evidence of fine-grained distinctions within both the abstract and the concrete semantic domains with respect to relevant psycholinguistic dimensions; second, to develop a carefully controlled linguistic stimulus set that may be used for auditory as well as visual neuroimaging studies focusing on the parametrization of the semantic space beyond the abstract-concrete dichotomy. Ninety-six participants rated a set of 210 sentences across pre-selected concrete (mouth, hand, or leg action-related) and abstract (mental state-, emotion-, mathematics-related) categories, with respect either to different semantic domain-related scales (rating study 1), or to concreteness, familiarity, and context availability (rating study 2). Inferential statistics and correspondence analyses highlighted distinguishing semantic and psycholinguistic traits for each of the pre-selected categories, indicating that a simple abstract-concrete dichotomy is not sufficient to account for the entire semantic variability within either domains.
A consolidated approach to the study of the mental representation of word meanings has consisted in contrasting different domains of knowledge, broadly reflecting the abstract-concrete dichotomy. More fine-grained semantic distinctions have emerged in neuropsychological and cognitive neuroscience work, reflecting semantic category specificity, but almost exclusively within the concrete domain. Theoretical advances, particularly within the area of embodied cognition, have more recently put forward the idea that distributed neural representations tied to the kinds of experience maintained with the concepts' referents might distinguish conceptual meanings with a high degree of specificity, including those within the abstract domain. Here we report the results of two psycholinguistic rating studies incorporating such theoretical advances with two main objectives: first, to provide empirical evidence of fine-grained distinctions within both the abstract and the concrete semantic domains with respect to relevant psycholinguistic dimensions; second, to develop a carefully controlled linguistic stimulus set that may be used for auditory as well as visual neuroimaging studies focusing on the parametrization of the semantic space beyond the abstract-concrete dichotomy. Ninety-six participants rated a set of 210 sentences across pre-selected concrete (mouth, hand, or leg action-related) and abstract (mental state-, emotion-, mathematics-related) categories, with respect either to different semantic domain-related scales (rating study 1), or to concreteness, familiarity, and context availability (rating study 2). Inferential statistics and correspondence analyses highlighted distinguishing semantic and psycholinguistic traits for each of the pre-selected categories, indicating that a simple abstract-concrete dichotomy is not sufficient to account for the entire semantic variability within either domains. PMID:23825625
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