It has been proved that sphericity testing for digraphs is an NP-complete problem. Here, we investigate sphericity of 3connected single source digraphs. We provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. Our algorithm tests whether a 3-connected single source digraph with n vertices is spherical in O(n) time.

Sphericity of erythrocytes can be estimated from analysis of FSC signal distribution in flow cytometry. Previously, Pearson's coefficient of dissymmetry (PCD) and spherical index (SphI) were applied to determine erythrocyte sphericity from the FSC histogram. The aim of the present study is to illustrate the application of kurtosis as an indicator of erythrocyte sphericity in flow cytometry in a...

BACKGROUND The left ventricular (LV) sphericity is a factor associated with ventricular dysfunction, but it is not well-characterized in the experimental infarction model in rats. OBJECTIVE To analyze the association between the sphericity index (SI), the ventricular function and the infarcted area in an experimental rat model. METHODS Six months after the infarction (AMI, n=33) or simulate...

it has been proved that sphericity testing for digraphs is an np-complete problem. here, we investigate sphericity of 3-connected single source digraphs. we provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $o(n)$ time.

Sphericity and roundness have been employed in sedimentological and geomorphological studies to represent the gross shape of a gravel particle. The original complex definitions of gravel sphericity and roundness led to the use of visual charts or simplified parameters. Although the accurate derivation of sphericity requires the surface area of a gravel particle, manual measurement of the area i...

Unit disk graphs are the intersection graphs of unit diameter closed disks in the plane. This paper reduces SATISFIABILITY to the problem of recognizing unit disk graphs. Equivalently, it shows that determining if a graph has sphericity 2 or less, even if the graph is planar or is known to have sphericity at most 3, is NP-hard. We show how this reduction can be extended to 3 dimensions, thereby...

It has been proved that sphericity testing for digraphs is an NP-complete problem. Here, we investigate sphericity of 3-connected single source digraphs. We provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. Our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $O(n)$ time.

BACKGROUND The objective was the investigation of a possible predictive quantitative impact of initial tumor sphericity, measured by 3D sonography, on response to pre-operative chemotherapy. PATIENTS AND METHODS This 3D ultrasound study was conducted on 41 consecutive primary breast cancer patients who received pre-operative epirubicin and paclitaxel chemotherapy; the tumors were measured by ...

BACKGROUND Left ventricular remodeling (LVR) after AMI characterizes a factor of poor prognosis. There is little information in the literature on the LVR analyzed with three-dimensional echocardiography (3D ECHO). OBJECTIVE To analyze, with 3D ECHO, the geometric and volumetric modifications of the left ventricle (VE) six months after AMI in patients subjected to percutaneous primary treatmen...

BACKGROUND  Different influences of left ventricular (LV) remodeling on anterior and posterior mitral leaflet (AML and PML) tethering in ischemic mitral regurgitation (MR) has not been fully investigated. We hypothesized that progressive outward displacement of papillary muscles, including posterior vector, may cause greater tethering to PML compared to AML. METHODS AND RESULTS  In 79 patient...