special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications International audience In a recent paper we gave a counterexample to a longstanding conjecture concerning the characterization of regular languages of level 2 in the Straubing-Therien concatenation hierarchy of star-free languages. In that paper a new upper bound for the corresponding pseudovariety of monoids was implicitly given. In this paper we show that it is decidable whether a given monoid belongs to the new upper bound. We also prove that this new upper bound is incomparable with the previous upper bound.

Objectives Using prenatally fixed dermatoglyphics features as markers of prenatal sex development is limited due to insufficient knowledge on their sex differences. This study aims to examine more thoroughly sex differences in radioulnar contrasts. Methods Fingerprints of 360 females and 331 males from four samples of different ethnic backgrounds (Czechs, Slovaks, Vietnamese and Lusatian Sorbs) were studied. On both hands, finger ridge counts were recorded, and all possible radioulnar contrasts were computed as a difference between ridge count at a radial position minus ridge count at a respective ulnar position on the hand. Radioulnar contrasts with population‐congruent and numerically large dimorphism were selected and the dimorphism of the selected radioulnar contrasts was then tested using nonparametric analysis of variance. Results Greater dimorphism of radioulnar contrasts occurred on the right hand than on the left hand. Population congruent direction and relatively strong dimorphism (Cohen’s d greater than 0.3) was found in six radioulnar contrasts on the right hand, all of which involved the radial ridge count of the 2nd finger. Of these, the highest average dimorphism was observed for the difference between the radial ridge count of the 2nd finger and the ulnar ridge count of the 4th finger (2r4u contrast), where the average effect size from all four population samples was comparable to a published average effect size of the 2D:4D finger length ratio. Conclusion We propose that 2r4u contrast of ridge counts could serve as a marker of prenatal sexual development targeting a temporally narrow developmental window.

Objectives At present, medical thermal imaging is still considered a mere qualitative tool enabling us to distinguish between but lacking the ability to quantify the physiological and nonphysiological states of the body. Such a capability would, however, facilitate solving the problem of medical quantification, whose presence currently manifests itself within the entire healthcare system. Methods A generally applicable method to enhance captured 3D spatial data carrying temperature-related information is presented; in this context, all equations required for other data fusions are derived. The method can be utilized for high-density point clouds or detailed meshes at a high resolution but is conveniently usable in large objects with sparse points. Results The benefits of the approach are experimentally demonstrated on 3D thermal scans of injured subjects. We obtained diagnostic information inaccessible via traditional methods. Conclusion Using a 3D model and thermal image data fusion allows the quantification of inflammation, facilitating more precise injury and illness diagnostics or monitoring. The technique offers a wide application potential in medicine and multiple technological domains, including electrical and mechanical engineering.

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Relatively slight overall changes in digit ratio in puberty and adolescence themselves are not inconsistent with the use of the 2D:4D ratio as an indirect marker of prenatal sexual differentiation. Nevertheless, individual changes in the ratios varied substantially in this study and differed from the average trends. Future studies should focus on the nature of interindividual developmental differences in the digit and metacarpal ratios.

A variety of models are available for the estimation of parameters of the human growth curve. Several have been widely and successfully used with longitudinal data that are reasonably complete. On the other hand, the modeling of data for a limited number of observation points is problematic and requires the interpolation of the interval between points and often an extrapolation of the growth trajectory beyond the range of empirical limits (prediction). This study tested a new approach for fitting a relatively limited number of longitudinal data using the normal variation of human empirical growth curves. First, functional principal components analysis was done for curve phase and amplitude using complete and dense data sets for a reference sample (Brno Growth Study). Subsequently, artificial curves were generated with a combination of 12 of the principal components and applied for fitting to the newly analyzed data with the Levenberg–Marquardt optimization algorithm. The approach was tested on seven 5-points/year longitudinal data samples of adolescents extracted from the reference sample. The samples differed in their distance from the mean age at peak velocity for the sample and were tested by a permutation leave-one-out approach. The results indicated the potential of this method for growth modeling as a user-friendly application for practical applications in pediatrics, auxology and youth sport.

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