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CPS1972 Livio Corain et al.
setting is the following: if not all 0(ℎ) in (2) are true, it must exist an ordering
[1],[2],…,[C] among and/or such that
2

where “” should be intended as ˮ when there exists at least one univariate
component of τ and for which the strict inequality holds, and at the
2

2
same time, there isn’t any univariate component of τ and for which
the opposite strict inequality holds. When the last condition is not true, “” is
intended as “=”, meaning that the two τ and are tied in the ranking.
2

Note that, within a multivariate setting, we state that two multivariate
2
parameters are tied not only when all univariate τ and are equal but
−
+
also when that 1(ℎ) and 1(ℎ) + are jointly true. For more details on the
ranking methodology within a multivariate setting we refer the reader to
Arboretti et al. (2014).

3. Result
Simulation Study
In order prove the effectiveness of the proposed methodology we
performed a simulation study where cell shape data were obtained by
simulating artificial slices from randomly generated 3D geometric solids within
a virtual volume (see Figure 2). By applying imaging routines for detection and
outline of simulated cell contours (Grisan et al., 2018), we got a set of cell
morphometric indicators (listed in Table 1). Subsequently, we added to those
values some random variation according to three multivariate distributions:
normal, Student’s t with 3 d.f. and an g-and-h right skewed distribution, as
examples of a heavy-tailed and skewed distributions respectively. The
advantage of using this kind of strategy to simulate cell morphometric data
instead of simply directly generate those data is twofold: first, we can naturally
capture the underlying geometrical correlation among size and regularity-
related descriptors; secondly, our virtual cuts induces a level of variability
which simulated the actual laboratory process of brain samples processing and
cutting to obtain the tissue slices. Due to editorial limitations, we cannot
include here results of our simulation study and we refer the interested readers
to the forthcoming extended version of the present short paper.
Application to Comparative Neuroanatomy
We applied the proposed procedure to a comparative neuroanatomy
study aimed at quantifying possible morphometric structural differences in the
brain cytoarchitecture of three sex-related bovine populations, i.e. male,
female and intersex freemartins. The freemartin syndrome is the most
common form of intersexuality in the bovine species, arising from vascular
connections between the placentas of heterosexual twin foetuses (Graïc et al.,
2018). A series of 10 male, 10 female and 8 freemartin adult bovine brain (24

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