OBJECTIVE Wnt signalling is critical for normal intestinal development and homeostasis. Wnt dysregulation occurs in almost all human and murine intestinal tumours and an optimal but not excessive level of Wnt activation is considered favourable for tumourigenesis. The authors assessed effects of pan-intestinal Wnt activation on tissue homeostasis, taking… (More)
We study the singular part of the partition monoid P n ; that is, the ideal P n \ S n , where S n is the symmetric group. Our main results are presentations in terms of generators and relations, and we also show that P n \ S n is idempotent generated, and that its rank and idempotent-rank are both equal to n+1 2 = 1 2 n(n + 1). One of our presentations uses… (More)
The dual symmetric inverse monoid I * n is the inverse monoid of all isomorphisms between quotients of an n-set. We give a monoid presentation of I * n and, along the way, establish criteria for a monoid to be inverse when it is generated by completely regular elements.
BACKGROUND AND STUDY AIMS During colorectal endoscopic submucosal dissection (ESD), the feature of a muscle layer being pulled toward a neoplastic tumor is sometimes detected. We call this feature the muscle-retracting sign (MR sign). The aim of this study was to evaluate whether the MR sign is associated with particular types of neoplastic lesions and… (More)
The variant of a semigroup S with respect to an element a ∈ S, denoted S a , is the semigroup with underlying set S and operation defined by x y = xay for x, y ∈ S. In this article, we study variants T a X of the full transformation semigroup T X on a finite set X. We explore the structure of T a X as well as its subsemigroups Reg(T a X) (consisting of all… (More)