Mathematical modeling of the malignancy of cancer using graph evolution

Cataloged from PDF version of article.We report a novel computational method based on graph evolution process to model the malignancy of brain cancer called glioma. In this work, we analyze the phases that a graph passes through during its evolution and demonstrate strong relation between the malignancy of cancer and the phase of its graph. From the photomicrographs of tissues, which are diagnosed as normal, low-grade cancerous and high-grade cancerous, we construct cell-graphs based on the locations of cells; we probabilistically generate an edge between every pair of cells depending on the Euclidean distance between them. For a cell-graph, we extract connectivity information including the properties of its connected components in order to analyze the phase of the cell-graph. Working with brain tissue samples surgically removed from 12 patients, we demonstrate that cell-graphs generated for different tissue types evolve differently and that they exhibit different phase properties, which distinguish a tissue type from another. (C) 2007 Elsevier Inc. All rights reserved

Efficient successor retrieval operations for aggregate query processing on clustered road networks

Cataloged from PDF version of article.Get-Successors (GS) which retrieves all successors of a junction is a kernel operation used to facilitate aggregate computations in road network queries. Efficient implementation of the GS operation is crucial since the disk access cost of this operation constitutes a considerable portion of the total query processing cost. Firstly, we propose a new successor retrieval operation Get-Unevaluated-Successors (GUS), which retrieves only the unevaluated successors of a given junction. The GUS operation is an efficient implementation of the GS operation, where the candidate successors to be retrieved are pruned according to the properties and state of the algorithm. Secondly, we propose a hypergraph-based model for clustering successively retrieved junctions by the GUS operations to the same pages. The proposed model utilizes query logs to correctly capture the disk access cost of GUS operations. The proposed GUS operation and associated clustering model are evaluated for two different instances of GUS operations which typically arise in Dijkstra's single source shortest path algorithm and incremental network expansion framework. Our simulation results show that the proposed successor retrieval operation together with the proposed clustering hypergraph model is quite effective in reducing the number of disk accesses in query processing. (C) 2010 Published by Elsevier Inc

A result on generalized derivations on right ideals of prime rings

Let R be a prime ring of characteristic other than 2 and let I be a nonzero right ideal of R. Also let U be the right Utumi quotient ring of R and let C be the center of U. If G is a generalized derivation of R such that [[G(x), x], G(x)] = 0 for all x ∈ I, then R is commutative or there exist a, b ∈ U such that G(x) = ax + xb for all x ∈ R and one of the following assertions is true: (1) (a - λ)I = (0) = (b + λ)I for some λ ∈ C, (2) (a - λ)I = (0) for some λ ∈ C and b ∈ C.Нехай R — просте кiльце, характеристика якого не дорiвнює 2, а I — ненульовий правий iдеал R. Нехай U — праве фактор-кiльце Утумi кiльця R, а C — центр U. Якщо G є узагальненим диференцiюванням R таким, що [[G(x),x],G(x)]=0 для всiх x∈I, то R є комутативним або iснують a,b∈U такi, що G(x)=ax+xb для всiх x∈R i виконується одне з наступних тверджень: (1)(a−λ)I=(0)=(b+A)Iдля деякогоλ∈C, (2)(a−λ)I=(0)для деякогоλ∈Cіb∈C

Local object patterns for representation and classification of colon tissue images

Cataloged from PDF version of article.This paper presents a new approach for the effective representation and classification of images of histopathological colon tissues stained with hematoxylin and eosin. In this approach, we propose to decompose a tissue image into its histological components and introduce a set of new texture descriptors, which we call local object patterns, on these components to model their composition within a tissue. We define these descriptors using the idea of local binary patterns, which quantify a pixel by constructing a binary string based on relative intensities of its neighbors. However, as opposed to pixel-level local binary patterns, we define our local object pattern descriptors at the component level to quantify a component. To this end, we specify neighborhoods with different locality ranges and encode spatial arrangements of the components within the specified local neighborhoods by generating strings. We then extract our texture descriptors from these strings to characterize histological components and construct the bag-of-words representation of an image from the characterized components. Working on microscopic images of colon tissues, our experiments reveal that the use of these component-level texture descriptors results in higher classification accuracies than the previous textural approaches. © 2013 IEEE

Graph run-length matrices for histopathological image segmentation

Cataloged from PDF version of article.The histopathological examination of tissue specimens is essential for cancer diagnosis and grading. However, this examination is subject to a considerable amount of observer variability as it mainly relies on visual interpretation of pathologists. To alleviate this problem, it is very important to develop computational quantitative tools, for which image segmentation constitutes the core step. In this paper, we introduce an effective and robust algorithm for the segmentation of histopathological tissue images. This algorithm incorporates the background knowledge of the tissue organization into segmentation. For this purpose, it quantifies spatial relations of cytological tissue components by constructing a graph and uses this graph to define new texture features for image segmentation. This new texture definition makes use of the idea of gray-level run-length matrices. However, it considers the runs of cytological components on a graph to form a matrix, instead of considering the runs of pixel intensities. Working with colon tissue images, our experiments demonstrate that the texture features extracted from "graph run-length matrices" lead to high segmentation accuracies, also providing a reasonable number of segmented regions. Compared with four other segmentation algorithms, the results show that the proposed algorithm is more effective in histopathological image segmentatio

A color and shape based algorithm for segmentation of white blood cells in peripheral blood and bone marrow images

Cataloged from PDF version of article.Computer-based imaging systems are becoming important tools for quantitative assessment of peripheral blood and bone marrow samples to help experts diagnose blood disorders such as acute leukemia. These systems generally initiate a segmentation stage where white blood cells are separated from the background and other nonsalient objects. As the success of such imaging systems mainly depends on the accuracy of this stage, studies attach great importance for developing accurate segmentation algorithms. Although previous studies give promising results for segmentation of sparsely distributed normal white blood cells, only a few of them focus on segmenting touching and overlapping cell clusters, which is usually the case when leukemic cells are present. In this article, we present a new algorithm for segmentation of both normal and leukemic cells in peripheral blood and bone marrow images. In this algorithm, we propose to model color and shape characteristics of white blood cells by defining two transformations and introduce an efficient use of these transformations in a marker-controlled watershed algorithm. Particularly, these domain specific characteristics are used to identify markers and define the marking function of the watershed algorithm as well as to eliminate false white blood cells in a postprocessing step. Working on 650 white blood cells in peripheral blood and bone marrow images, our experiments reveal that the proposed algorithm improves the segmentation performance compared with its counterparts, leading to high accuracies for both sparsely distributed normal white blood cells and dense leukemic cell clusters. (C) 2014 International Society for Advancement of Cytometr

A link-based storage scheme for efficient aggregate query processing on clustered road networks

Cataloged from PDF version of article.The need to have efficient storage schemes for spatial networks is apparent when the volume of query processing in some road networks (e.g., the navigation systems) is considered. Specifically, under the assumption that the road network is stored in a central server, the adjacent data elements in the network must be clustered on the disk in such a way that the number of disk page accesses is kept minimal during the processing of network queries. In this work, we introduce the link-based storage scheme for clustered road networks and compare it with the previously proposed junction-based storage scheme. in order to investigate the performance of aggregate network queries in clustered road networks, we extend our recently proposed clustering hypergraph model from junction-based storage to link-based storage. We propose techniques for additional storage savings in bidirectional networks that make the link-based storage scheme even more preferable in terms of the storage efficiency. We evaluate the performance of our link-based storage scheme against the junction-based storage scheme both theoretically and empirically. The results of the experiments conducted on a wide range of road network datasets show that the link-based storage scheme is preferable in terms of both storage and query processing efficiency. (C) 2009 Elsevier B.V. All rights reserved