This article presents an experimental study on the naturally biased association between shape and color. For each basic geometric shape studied, participants were asked to indicate the color perceived as most closely related to it, choosing from the Natural Color System Hue Circle. Results show that the choices of color for each shape were not random, that is, participants systematically established an association between shapes and colors when explicitly asked to choose the color that, in their view, without any presupposition, they saw as the most naturally related to a series of given shapes. The strongest relations were found between the triangle and yellows, and the circle and square with reds. By contrast, the parallelogram was connected particularly infrequently with yellows and the pyramid with reds. Correspondence analysis suggested that two main aspects determine these relationships, namely the "warmth" and degree of "natural lightness" of hues.

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The study analyses the existence of cross-modal associations in the general population between a series of paintings and a series of clips of classical (guitar) music. Because of the complexity of the stimuli, the study differs from previous analyses conducted on the association between visual and auditory stimuli, which predominantly analyzed single tones and colors by means of psychophysical methods and forced choice responses. More recently, the relation between music and shape has been analyzed in terms of music visualization, or relatively to the role played by emotion in the association, and free response paradigms have also been accepted. In our study, in order to investigate what attributes may be responsible for the phenomenon of the association between visual and auditory stimuli, the clip/painting association was tested in two experiments: the first used the semantic differential on a unidimensional rating scale of adjectives; the second employed a specific methodology based on subjective perceptual judgments in first person account. Because of the complexity of the stimuli, it was decided to have the maximum possible uniformity of style, composition and musical color. The results show that multisensory features expressed by adjectives such as “quick,” “agitated,” and “strong,” and their antonyms “slow,” “calm,” and “weak” characterized both the visual and auditory stimuli, and that they may have had a role in the associations. The results also suggest that the main perceptual features responsible for the clip/painting associations were hue, lightness, timbre, and musical tempo. Contrary to what was expected, the musical mode usually related to feelings of happiness (major mode), or to feelings of sadness (minor mode), and spatial orientation (vertical and horizontal) did not play a significant role in the association. The consistency of the associations was shown when evaluated on the whole sample, and after considering the different backgrounds and expertise of the subjects. No substantial difference was found between expert and non-expert subjects. The methods used in the experiment (semantic differential and subjective judgements in first person account) corroborated the interpretation of the results as associations due to patterns of qualitative similarity present in stimuli of different sensory modalities and experienced as such by the subjects. The main result of the study consists in showing the existence of cross-modal associations between highly complex stimuli; furthermore, the second experiment employed a specific methodology based on subjective perceptual judgments.

An accurate normal approximation for the cumulative distribution function of the chi-square distribution with n degrees of freedom is proposed. This considers a linear combination of appropriate fractional powers of chi-square. Numerical results show that the maximum absolute error associated with the new transformation is substantially lower than that found for other power transformations of a chi-square random variable for all the degrees of freedom considered (1 6 n 6 1000).

Purpose To provide national, population-based estimates of the prevalence of overweight and obesity in the Italian population. Methods Prevalence estimates of overweight and obesity were calculated in seven waves (2001–2008) of the cross-sectional Multipurpose Household Survey organized by the Italian National Institute of Statistics which are representative of the general adult Italian population. Sampling weights were used to estimate prevalence figures as well as their standard errors. Mean-difference plot was employed to evaluate changes in the distribution of BMI across sex and age categories. Results Almost half of Italian men and about 1 out of 3 Italian women are overweight or obese. Between 2001 and 2008 the age-standardized prevalence of overweight (obesity) increased of 1.4% (1.9%) in males and of 0.4% (0.5%) in females. Mean-difference plots showed an upward shift for BMI distribution with an increasing skewness. Conclusions Obesity epidemic is one of the major issue in USA and other developed countries. However if for “epidemic” we mean that in Italy obesity is steadily rising then our data give little support to this interpretation. In fact, trends observed between 1983 and 2008 suggest that the rates of changes in the prevalence of overweight and/or obesity are not increasing.