Green's relations, regularity and abundancy for semigroups of quasi-onto transformations

Let V be an infinite-dimensional vector space and for every infinite cardinal n such that n≤dimV, let AE(V,n) denote the semigroup of all linear transformations of V whose defect is less than n. In 2009, Mendes-Gonçalves and Sullivan studied the ideal structure of AE(V,n). Here, we consider a similarly-defined semigroup AE(X,q) of transformations defined on an infinite set X. Quite surprisingly, the results obtained for sets differ substantially from the results obtained in the linear setting.

An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.

Three-dimensional technology facilitates surgical performance of novice laparoscopy surgeons: a quantitative assessment on a porcine kidney model

Objective To determine whether the use of 3-dimensional (3D) imaging translates into a better surgical performance of naïve urologic laparoscopic surgeons during pyeloplasty (PY) and partial nephrectomy (PN) procedures. Materials and Methods Eighteen surgeons without any previous laparoscopic experience were randomly assigned to perform PY and PN in a porcine model using initially 2-dimensional (2D) and 3D laparoscopy. A surgical performance score was rated by an "expert" tutor through a modified 5-item global rating scale contemplating operative field view, bimanual dexterity, efficiency, tissue handling, and autonomy. Overall surgical time, complications, subjective perception of participating surgeons, and inconveniences related to the 3D vision were recorded. Results No difference in terms if operative time was found between 2D or 3D laparoscopy for both the PY (P =.51) and the PN (P =.28) procedures. A better rate in terms of surgical performance score was noted by the tutors when the study participants were using 3D vs 2D, for both PY (3.6 [0.8] vs 3.0 [0.4]; P =.034) and PN (3.6 [0.51] vs 3.15 [0.63]; P =.001). No complications occurred in any of the procedures. Most (77.2%) of the participating na??ve laparoscopic surgeons had the perception that 3D laparoscopy was overall easier than 2D. Headache (18.1%), nausea (18.1%), and visual disturbance (18.1%) were the most common issues reported by the surgeons during 3D procedures. Conclusion Despite the absence of translation in a shorter operative time, the use of 3D technology seems to facilitate the surgical performance of naive surgeons during laparoscopic kidney procedures on a porcine model.

Behavior-based price discrimination in a multi-dimensional preferences market

NIPE WP 04/ 2016

Topological abstraction of higher-dimensional automata

Higher-dimensional automata constitute a very expressive model for concurrent systems. In this paper, we discuss ``topological abstraction" of higher-dimensional automata, i.e., the replacement of HDAs by smaller ones that can be considered equivalent from the point of view of both computer science and topology. By definition, topological abstraction preserves the homotopy type, the trace category, and the homology graph of an HDA. We establish conditions under which cube collapses yield topological abstractions of HDAs.