A characterization and an application of weight-regular partitions of graphs

A natural generalization of a regular (or equitable) partition of a graph, which makes sense also for non-regular graphs, is the so-called weight-regular partition, which gives to each vertex $u\in V$ a weight that equals the corresponding entry $\nu_u$ of the Perron eigenvector $\mathbf{\nu}$. This paper contains three main results related to weight-regular partitions of a graph. The first is a characterization of weight-regular partitions in terms of double stochastic matrices. Inspired by a characterization of regular graphs by Hoffman, we also provide a new characterization of weight-regularity by using a Hoffman-like polynomial. As a corollary, we obtain Hoffman's result for regular graphs. In addition, we show an application of weight-regular partitions to study graphs that attain equality in the classical Hoffman's lower bound for the chromatic number of a graph, and we show that weight-regularity provides a condition under which Hoffman's bound can be improved

An application of Hoffman graphs for spectral characterizations of graphs

In this paper, we present the first application of Hoffman graphs for spectral characterizations of graphs. In particular, we show that the $2$-clique extension of the $(t+1)\times(t+1)$-grid is determined by its spectrum when $t$ is large enough. This result will help to show that the Grassmann graph $J_2(2D,D)$ is determined by its intersection numbers as a distance regular graph, if $D$ is large enough

VOLAR V-Y ADVANCEMENT FLAPS IN RECONSTRUCTING FINGERTIP INJURIES

Fingertip injuries with exposed bones and joints require immediate or early closure for the preservation of function and avoidance of complications. The ideal procedure should maintain the length of the finger and cover the defect with non-tender, well-padded skin with normal sensation. The aim of this study was to evaluate the role of the different types of volar V-Y advancement flaps in reconstructing and resurfacing injuries of the fingertips at different levels and angles. Thirty patients (N=30) sustaining fingertip injuries of variable etiology and lost components, type III & IV according to Allen’s classification were divided into two groups (n=15) according to the extent of tissue loss.V-Y Volar flap has been used for patients of group I; Neurovascular V-Y Advancement Flap for patients of group II. All subjective complaints (tenderness, cold intolerance and incomplete extension) were resolved within six months of follow up. With respect to the complications there were no statistically significant difference in except for light touch examination. The simple V-Y volar advancement flap, with apex at DIP, and the neurovascular V-Y advancement flap, with the apex at PIP can be used in Allen III and IV types of fingertip injuries. The choice of either flap depends on the direction of injury. The former is better reserved for the dorsally-directed tissue loss. The latter is preferably used in either the volarly-slanting tissue loss or the perpendicular(guillotine) fingertip amputation

Some Spectral and Quasi-Spectral Characterizations of Distance-Regular Graphs

In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using the preintersection numbers we give some new spectral and quasi-spectral characterizations of distance-regularity, in particular for graphs with large girth or large odd-girth

Spectral Bounds for the Connectivity of Regular Graphs with Given Order

The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to connectivity attributes such as the vertex- and edge-connectivity, isoperimetric number, and characteristic path length. In this paper, we present two upper bounds for the second-largest eigenvalues of regular graphs and multigraphs of a given order which guarantee a desired vertex- or edge-connectivity. The given bounds are in terms of the order and degree of the graphs, and hold with equality for infinite families of graphs. These results answer a question of Mohar.Comment: 24 page

Some spectral and quasi-spectral characterizations of distance-regular graphs

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using the preintersection numbers we give some new spectral and quasi-spectral characterizations of distance-regularity, in particular for graphs with large girth or large odd-girth. (C) 2016 Published by Elsevier Inc.Peer ReviewedPostprint (author's final draft

Simulating 129-Xe Hyperpolarization

Hyperpolarized 129-Xe is an important resource in many fields of medical physics and MRI research. The physics of the efficient production of hyperpolarized 129-Xe is therefore equally worth investigation. The main process of hyperpolarizing 129-Xe is Spin Exchange Optical Pumping (SEOP) and is dependent on several physical factors that can be difficult to constantly change in a lab setting. Physical modelling of 129-Xe hyperpolarization allows for the more efficient testing of hyperpolarization physics in a wide array of experimental setups to better determine the optimal values for hyperpolarization. This research project attempted to create a working model for 129-Xe hyperpolarization using MATLAB and Simulink with the physical modelling Simscape library, finding varying levels of success when compared to experimentally determined values

Throughput Maximization in Cloud Radio Access Networks using Network Coding

This paper is interested in maximizing the total throughput of cloud radio access networks (CRANs) in which multiple radio remote heads (RRHs) are connected to a central computing unit known as the cloud. The transmit frame of each RRH consists of multiple radio resources blocks (RRBs), and the cloud is responsible for synchronizing these RRBS and scheduling them to users. Unlike previous works that consider allocating each RRB to only a single user at each time instance, this paper proposes to mix the flows of multiple users in each RRB using instantly decodable network coding (IDNC). The proposed scheme is thus designed to jointly schedule the users to different RRBs, choose the encoded file sent in each of them, and the rate at which each of them is transmitted. Hence, the paper maximizes the throughput which is defined as the number of correctly received bits. To jointly fulfill this objective, we design a graph in which each vertex represents a possible user-RRB association, encoded file, and transmission rate. By appropriately choosing the weights of vertices, the scheduling problem is shown to be equivalent to a maximum weight clique problem over the newly introduced graph. Simulation results illustrate the significant gains of the proposed scheme compared to classical coding and uncoded solutions.Comment: 7 pages, 7 figure

CUSTOMER CHURN ANALYSIS USING BINARY LOGISTIC REGRESSION MODEL

These days, the fundamental target of all organizations is to accomplish a reasonable gainfulness. Organizations are looking to decide the elements, which has direct impact on their benefit and attempt to investigate them so as to pick up favorable circumstances on their rivals. With this solid aggressive market, holding customers turns into the fundamental objective of telecom mobile service providers opposed to drawing in new customers, since the expense of holding a customer is viewed as low contrasted with the expense of pulling in another customer as referenced before by numerous researchers. Thus, Customer Churn Analytics is one of the significant elements that organizations should concentrate on to help their goal of accomplishing a reasonable benefit. In Telecommunication area, the business aims to serve customers, and analyzing customer churn will give the executives a thought regarding the probability of a customer to leave the organization. The primary goal of this paper is to highlight the main factors that affect customer churn and then analyze them by using the Binary Logistic Regression Model. A case study in Kuwait telecommunication section was taken as an application for such algorithm. A non-probability sampling technique is used (Snowball) to select a sample of 120 customer and analyze them by using the statistical software SPSS and MINITAB, results shows that the Customers’ Gender, Marital Status, Monthly Bill as well as the Service Quality have significant effects on Customer Churn