This project is to develop an automated breast density segmentation system. Breast density has been shown to be a key indicator of breast cancer risk. Currently the primary computational system for analyzing breast density is a semiautomated segmentation system that requires a radiologist to set thresholds for the segmentation algorithm. This results in reader variability, which reduces the val...

In the present work we deal with set-valued equilibrium problems for which we provide sufficient conditions for the existence of a solution. The conditions that we consider are imposed not on the whole domain, but rather on a self segment-dense subset of it, a special type of dense subset. As an application, we obtain a generalized Debreu-Gale-Nikaido type theorem, with a considerable weakned W...

In 1998, S. Romaguera [13] introduced the notion of cofinally Čech-complete spaces equivalent to spaces which we later called ultracomplete spaces. We define the subset of points of a space X at which X is not locally compact and call it an nlc set. In 1999, Garćıa-Máynez and S. Romaguera [6] proved that every cofinally Čech-complete space has a bounded nlc set. In 2001, D. Buhagiar [1] proved ...

Let (G, τ ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If (G, τ ) has the A(iii)-property, then its completion (Ĝ, τ̂ ) is an order-complete locally solid lattice group. (2) If G is order-complete and τ has the Fatou property, then the order intervals of G are τ -complete. (3) If (G, τ ) has the Fatou property, then G is order-dense in Ĝ and...

We propose a class of locally Lipschitz functions with piecewise structure for use as Lyapunov hybrid dynamical systems. Subject to some regularity the dynamics, we show that inequalities can be checked only on dense set and thus avoid checking them at points nondifferentiability function. Connections other classes or regular are also discussed, applications systems included.

A frame $L$ is called {it coz-dense} if $Sigma_{coz(alpha)}=emptyset$ implies $alpha=mathbf 0$. Let $mathcal RL$ be the ring of real-valued continuous functions on a coz-dense and completely regular frame $L$. We present a description of the socle of the ring $mathcal RL$ based on minimal ideals of $mathcal RL$ and zero sets in pointfree topology. We show that socle of $mathcal RL$ is an essent...

It has been established by Inoue that a complex locally C*-algebra with a dense ideal posesses a bounded approximate identity which belonges to that ideal. It has been shown by Fritzsche that if a unital complex locally C*-algebra has an unbounded element then it also has a dense one-sided ideal. In the present paper we obtain analogues of the aforementioned results of Inoue and Fritzsche for r...

A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such groups are called locally precompact. Within the class of locally precompact groups, the authors classify those groups with the following topological properties: (a) Dieudonné completeness; (b) local realcompactness; (c) r...

BACKGROUND The most time consuming and limiting step in three dimensional (3D) cine displacement encoding with stimulated echoes (DENSE) MR image analysis is the demarcation of the left ventricle (LV) from its surrounding anatomical structures. The aim of this study is to implement a semi-automated segmentation algorithm for 3D cine DENSE CMR using a guide point model approach. METHODS A 3D m...