A note on syntactical and semantical functions

We say that a semantical function is correlated with a syntactical function F iff for any structure A and any sentence we have A F A .It is proved that for a syntactical function F there is a semantical function correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function there is a syntactical function F correlated with iff for any finitely axiomatizable class X the class ^–1X is also finitely axiomatizable (i.e. iff is continuous in model class topology).     

A note on the gross configurations of the human auditory cortex

Gross inspection of 30 human brains (60 hemispheres) from patients without hearing impairment revealed the following configurations of gyri: one on left and two on right (14 of 30); two on left and two on right (11 of 30); one on left and one on right (3 of 30); two on left and one on right (1 of 30); and two on left and three on right (1 of 30). The last group has since been extended to include all combinations other than the first four and the proportions of these combinations appear to persist in larger tallies. Thirteen of the 30 brains displayed double gyri on the left while 25 had double gyri on the right. Seventeen of the 30 brains possessed a single gyrus on the left and four specimens had a single gyrus on the right. In general, the left side has a tendency to fewer gyral markings. The average cortical surface area on the left is 1198 mm² compared to 1380 on the right.     

A note on monotonicity of item response functions for ordered polytomous item response theory models

A monotone relationship between a true score (τ) and a latent trait level (θ) has been a key assumption for many psychometric applications. The monotonicity property in dichotomous response models is evident as a result of a transformation via a test characteristic curve. Monotonicity in polytomous models, in contrast, is not immediately obvious because item response functions are determined by a set of response category curves, which are conceivably non-monotonic in θ. The purpose of the present note is to demonstrate strict monotonicity in ordered polytomous item response models. Five models that are widely used in operational assessments are considered for proof: the generalized partial credit model (Muraki, 1992, Applied Psychological Measurement, 16, 159), the nominal model (Bock, 1972, Psychometrika, 37, 29), the partial credit model (Masters, 1982, Psychometrika, 47, 147), the rating scale model (Andrich, 1978, Psychometrika, 43, 561), and the graded response model (Samejima, 1972, A general model for free-response data (Psychometric Monograph no. 18). Psychometric Society, Richmond). The study asserts that the item response functions in these models strictly increase in θ and thus there exists strict monotonicity between τ and θ under certain specified conditions. This conclusion validates the practice of customarily using τ in place of θ in applied settings and provides theoretical grounds for one-to-one transformations between the two scales.     

A note on erotic arousal value of moving and stationary human forms

For subhuman vertebrates there already exists a huge body of information on male and female courtship behaviour and in many instances the impact of movement patterns on the prospective partner has been assessed. However, little information is available on the erotic impact of human movement patterns.In analysing erotic preferences by means of the phallometric method, moving vs. still pictures has been a factor in a variety of studies. Kolá?ský and Madlafousek (1973) compared the erotic responses of normal and sexually deviant males to filmed courtship behaviour, non-erotic activities and stills of the same female. They found that dynamically presented filmed courtship patterns were more arousing for normal heterosexual males than stills on which no particular activity was shown, and that these stills were more arousing than movie pictures of nonerotic activities.In a study of classical conditioning, McConaghy (1970) found he could not condition positive penile responses to geometric figures when using still pictures of nude females as unconditioned stimuli, but that this was possible when using movies. He concluded that the movie pictures had a greater impact on his Ss than the stills and supported this impression with another study in which he compared responses to movies and stills of nude females (McConaghy, 1973). However, the persons on the movies were not identical with those on the stills and the depicted behavioural configurations varied widely. In the following study, results are reported on the erotic value of a relatively simple movement pattern, namely walking towards the viewer and smiling, vs. a still picture of the same person smiling.