Total and average distance are not only interesting invariants of graphs in their own right but are also used for studying properties or classifying graphical systems that depend on the number of edges traversed. Recent examples include studies of computer networks [3] and the use of graphical invariants to partially classify the structure of molecules [1]. There have been a number of conjectur...

We prove several best-possible lower bounds in terms of the order and the average degree for the independence number of graphs which are connected and/or satisfy some odd girth condition. Our main result is the extension of a lower bound for the independence number of triangle-free graphs of maximum degree at most 3 due to Heckman and Thomas [A New Proof of the Independence Ratio of Triangle-Fr...

Eccentricity detection is a crucial issue for highspeed rotating machinery, which concerns the stability and safety of the machinery. Conventional techniques in industry for eccentricity detection are mainly based on measuring certain physical indicators, which are costly and hard to deploy. In this paper, we propose RED, a non-intrusive, low-cost, and realtime RFID-based eccentricity detection...

Subjects made saccades to point and spatially-extended targets located at a randomly-selected eccentricity (3.8-4.2 deg) under conditions designed to promote best possible accuracy based only on the visual information present in a single trial. Saccadic errors to point targets were small. The average difference between mean saccade size and target eccentricity was about 1% of eccentricity. Prec...

In this paper, we show that the spectral radius ratio for node degree could be used to analyze the variation of node degree during the evolution of complex networks. We focus on three commonly studied models of complex networks: random networks, scale-free networks and small-world networks. The spectral radius ratio for node degree is defined as the ratio of the principal (largest) eigenvalue o...

Each breast cancer has its unique spatial shape, but the clinical importance and the underlying mechanism for the three-dimensional tumor shapes are mostly unknown. We collected the data on the three-dimensional tumor size and tumor volume data of invasive breast cancers from 2,250 patients who underwent surgery between Jan 2000 and Jul 2007. The degree of tumor eccentricity was estimated by us...

PURPOSE To evaluate the degree of metamorphopsia in 42 patients before and 6 months after vitrectomy for idiopathic unilateral macular hole. METHODS Semicircular test and reference stimuli of variable diameters were applied in a binocular test that measured interocular size disparity in patients with unilateral macular hole. The test was applied 1 day before surgery and repeated after 6 month...

This paper presents a new and precise mo del for different kinds of eccentric rotor of rotating machines based on polar signals concepts. Eccentricity faults in each static, dynamic and mixed cases cause that the non-uniform air-gap of machine be established. The applied model using polar signals for eccentric rotors have removed the usage approximations in two recent decays. Eccentricity coeff...