In this issue of the Journal, Ghosh et al. (1) describe the application of two visual assessments to predict breast cancer risk—lobular involution, a histological observation, and mammographic breast density (MBD), a radiological assessment. Previously, this group has demonstrated that more extensive lobular involution was inversely related to both MBD (2) and breast cancer risk (3) in a cohort...

Given a mixing shift of finite type X , we consider which subshifts of finite type Y ⊂ X can be realized as the fixed point shift of an inert involution of X . We establish a condition on the periodic points of X and Y that is necessary for Y to be the fixed point shift of an inert involution of X . We show that this condition is sufficient to realize Y as the fixed point shift of an involution...

In 2000, Babson and Steingrímsson generalized the notion of permutation patterns to the so-called vincular patterns, and they showed that many Mahonian statistics can be expressed as sums of vincular pattern occurrence statistics. STAT is one of such Mahonian statistics discoverd by them. In 2016, Kitaev and the third author introduced a words analogue of STAT and proved a joint equidistributio...

Proper selection of material in manufacturing firms is a vital role of designer depending upon the different era of application. The material selection problem is very complex and challenging task today. Erroneous cull of material frequently leads to astronomically immense cost involution, and finally drives towards unfortunate component or product breakdown. Thus, the designer necessitates dis...

Morphogenetic cell movements mould the shape of the developing organism. These movements have been extensively studied during Drosophila embryonic development. In particular live imaging analyses have revealed the complexities underlying the comparatively simple processes of germband extension, retraction and dorsal closure. I am applying live imaging techniques to an apparently complex morphog...

Morphogenetic cell movements mould the shape of the developing organism. These movements have been extensively studied during Drosophila embryonic development. In particular live imaging analyses have revealed the complexities underlying the comparatively simple processes of germband extension, retraction and dorsal closure. I am applying live imaging techniques to an apparently complex morphog...

Let $X$ be a finitistic space with the mod $2$ cohomology of product projective and $4$-sphere. Assume that admits free involution. In this paper we study algebra quotient by action involution derive some consequences regarding existence $\mathbb{Z}\_2$-equivariant maps between such an $n$-sphere.

In this paper we show how there is associated an integrable Hamiltonian system to a certain set of algebraic-geometric data. Roughly speaking these data consist of a family of algebraic curves, parametrized by an aane algebraic variety B, a subalgebra C of O(B) and a polynomial '(x; y) in two variables. The phase space is constructed geometrically from the family of curves and has a natural pro...

In the present paper it is proved that a variety of associative PI-superalgebras with graded involution finite basic rank over field characteristic zero minimal fixed *-graded exponent if, and only generated by subalgebra an upper block triangular matrix algebra equipped suitable elementary ?2-grading involution.