Color Degree Sum Conditions for Rainbow Triangles in Edge-Colored Graphs
Li, Ruonan; Ning, Bo; Zhang, Shenggui
Let G be an edge-colored graph and v a vertex of G. The color degree of v is the number of colors appearing on the edges incident to v. A rainbow triangle in G is one in which all edges have distinct colors. In this paper, we first prove that an edge-colored graph on n vertices contains a rainbow
Coloring geographical threshold graphs
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Percus, Allon [Los Alamos National Laboratory; Muller, Tobias [EINDHOVEN UNIV. OF TECH
2008-01-01
We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.
On dominator colorings in graphs
Indian Academy of Sciences (India)
colors required for a dominator coloring of G is called the dominator .... Theorem 1.3 shows that the complete graph Kn is the only connected graph of order n ... Conversely, if a graph G satisfies condition (i) or (ii), it is easy to see that χd(G) =.
Rabern, Landon
2007-01-01
We improve upper bounds on the chromatic number proven independently in \\cite{reedNote} and \\cite{ingo}. Our main lemma gives a sufficient condition for two paths in graph to be completely joined. Using this, we prove that if a graph has an optimal coloring with more than $\\frac{\\omega}{2}$ singleton color classes, then it satisfies $\\chi \\leq \\frac{\\omega + \\Delta + 1}{2}$. It follows that a graph satisfying $n - \\Delta < \\alpha + \\frac{\\omega - 1}{2}$ must also satisfy $\\chi \\leq \\frac{\\ome...
Acyclicity in edge-colored graphs
DEFF Research Database (Denmark)
Gutin, Gregory; Jones, Mark; Sheng, Bin
2017-01-01
A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type...
Properly colored connectivity of graphs
Li, Xueliang; Qin, Zhongmei
2018-01-01
A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references. Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introduction to proper connection of graphs for new and advanced researchers, a solid book for a graduate level topics course, or as a reference for those interested in expanding and further developing research in the area.
Color evaluation of computer-generated color rainbow holography
International Nuclear Information System (INIS)
Shi, Yile; Wang, Hui; Wu, Qiong
2013-01-01
A color evaluation approach for computer-generated color rainbow holography (CGCRH) is presented. Firstly, the relationship between color quantities of a computer display and a color computer-generated holography (CCGH) colorimetric system is discussed based on color matching theory. An isochromatic transfer relationship of color quantity and amplitude of object light field is proposed. Secondly, the color reproduction mechanism and factors leading to the color difference between the color object and the holographic image that is reconstructed by CGCRH are analyzed in detail. A quantitative color calculation method for the holographic image reconstructed by CGCRH is given. Finally, general color samples are selected as numerical calculation test targets and the color differences between holographic images and test targets are calculated based on our proposed method. (paper)
DEFF Research Database (Denmark)
Jensen, T.R.; Thomassen, Carsten
2000-01-01
If k is a prime power, and G is a graph with n vertices, then a k-coloring of G may be considered as a vector in GF(k)(n). We prove that the subspace of GF(3)(n) spanned by all 3-colorings of a planar triangle-free graph with n vertices has dimension n. In particular, any such graph has at least n...... - 1 nonequivalent 3-colorings, and the addition of any edge or any vertex of degree 3 results in a 3-colorable graph. (C) 2000 John Wiley & Sons, Inc....
Equitable Colorings Of Corona Multiproducts Of Graphs
Directory of Open Access Journals (Sweden)
Furmánczyk Hanna
2017-11-01
Full Text Available A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by =(G. It is known that the problem of computation of =(G is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013 103–120].
Coloring sums of extensions of certain graphs
Directory of Open Access Journals (Sweden)
Johan Kok
2017-12-01
Full Text Available We recall that the minimum number of colors that allow a proper coloring of graph $G$ is called the chromatic number of $G$ and denoted $\\chi(G$. Motivated by the introduction of the concept of the $b$-chromatic sum of a graph the concept of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum are introduced in this paper. The extended graph $G^x$ of a graph $G$ was recently introduced for certain regular graphs. This paper furthers the concepts of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum to extended paths and cycles. Bipartite graphs also receive some attention. The paper concludes with patterned structured graphs. These last said graphs are typically found in chemical and biological structures.
Acyclicity in edge-colored graphs
DEFF Research Database (Denmark)
Gutin, Gregory; Jones, Mark; Sheng, Bin
2017-01-01
A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type i......+1, i=1,2,3,4. The first three types are equivalent to the absence of PC cycles, PC closed trails, and PC closed walks, respectively. While graphs of types 1, 2 and 3 can be recognized in polynomial time, the problem of recognizing graphs of type 4 is, somewhat surprisingly, NP-hard even for 2-edge-colored...... graphs (i.e., when only two colors are used). The same problem with respect to type 5 is polynomial-time solvable for all edge-colored graphs. Using the five types, we investigate the border between intractability and tractability for the problems of finding the maximum number of internally vertex...
Paths and cycles in colored graphs
Li, Xueliang; Zhang, Shenggui; Hurink, Johann L.; Pickl, Stefan; Broersma, Haitze J.; Faigle, U.
2001-01-01
Let G be an (edge-)colored graph. A path (cycle) is called monochromatic if all the edges of it have the same color, and is called heterochromatic if all the edges of it have different colors. In this note, some sufficient conditions for the existence of monochromatic and heterochromatic paths and
Chartrand, Gary; Rosen, Kenneth H
2008-01-01
Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex coloring...
Graph Theory. 2. Vertex Descriptors and Graph Coloring
Directory of Open Access Journals (Sweden)
Lorentz JÄNTSCHI
2002-12-01
Full Text Available This original work presents the construction of a set of ten sequence matrices and their applications for ordering vertices in graphs. For every sequence matrix three ordering criteria are applied: lexicographic ordering, based on strings of numbers, corresponding to every vertex, extracted as rows from sequence matrices; ordering by the sum of path lengths from a given vertex; and ordering by the sum of paths, starting from a given vertex. We also examine a graph that has different orderings for the above criteria. We then proceed to demonstrate that every criterion induced its own partition of graph vertex. We propose the following theoretical result: both LAVS and LVDS criteria generate identical partitioning of vertices in any graph. Finally, a coloring of graph vertices according to introduced ordering criteria was proposed.
PERANCANGAN SISTEM PENJADWALAN PEMBELAJARAN MENGGUNAKAN GRAPH COLORING
Directory of Open Access Journals (Sweden)
Taufik Hidayatulloh
2016-03-01
Full Text Available Abstract - In learning scheduling problem often faced by schools in the new academic year. Sometimes collisions on the schedule was not found when the learning process has begun, so it is necessary to re-schedule on the schedule. And this resulted in the teaching and learning first weeks less to run well. Researchers previously have used various methods to solve the scheduling as Tabu search, Simulated Annealing, Network Flow, Graph Coloring. Graph Coloring (coloring of a graph is the simplest method and the experimental results indicate that the development of methods of scheduling Graph Coloring deliver results that meet an average of 93% across the specified constraints. At the time of split schedules that require extra energy at the start of learning did not experience a collision. With this system is expected to facilitate the allocation of space, teachers, lessons to avoid a collision. Keywords: Information Systems, Scheduling, graph coloring Abstraksi - Dalam masalah penjadwalan pembelajaran sering dihadapi sekolah pada tahun ajaran baru. Terkadang tabrakan pada jadwal itu baru ditemukan ketika proses belajar mengajar telah dimulai, sehingga perlu dilakukan penjadwalan ulang pada jadwal tersebut. Dan hal ini mengakibatkan kegiatan belajar mengajar pada minggu-minggu pertama kurang dapat berjalan dengan baik. Para peneliti sebelumnya telah menggunakan berbagai metode untuk memecahkan penjadwalan seperti Tabu search, Simulated Annealing, Network Flow, Graph Coloring. Graph Coloring (pewarnaan graf merupakan metode yang paling sederhana dan hasil percobaan menunjukkan bahwa pengembangan metode Graph Coloring memberikan hasil penjadwalan yang memenuhi rata-rata 93% seluruh constraints yang ditentukan. Pada saat membagi jadwal memerlukan energi ekstra agar pada saat di mulai pembelajaran tidak mengalami tabrakan. Dengan sistem ini diharapkan dapat mempermudah dalam mengalokasikan ruangan, guru, pelajaran agar tidak mengalami tabrakan. Kata
Distributed graph coloring fundamentals and recent developments
Barenboim, Leonid
2013-01-01
The focus of this monograph is on symmetry breaking problems in the message-passing model of distributed computing. In this model a communication network is represented by a n-vertex graph G = (V,E), whose vertices host autonomous processors. The processors communicate over the edges of G in discrete rounds. The goal is to devise algorithms that use as few rounds as possible.A typical symmetry-breaking problem is the problem of graph coloring. Denote by ? the maximum degree of G. While coloring G with ? + 1 colors is trivial in the centralized setting, the problem becomes much more challenging
Twin edge colorings of certain square graphs and product graphs
Directory of Open Access Journals (Sweden)
R Rajarajachozhan
2016-04-01
Full Text Available A twin edge $k\\!$-coloring of a graph $G$ is a proper edge $k$-coloring of $G$ with the elements of $\\mathbb{Z}_k$ so that the induced vertex $k$-coloring, in which the color of a vertex $v$ in $G$ is the sum in $\\mathbb{Z}_k$ of the colors of the edges incident with $v,$ is a proper vertex $k\\!$-coloring. The minimum $k$ for which $G$ has a twin edge $k\\!$-coloring is called the twin chromatic index of $G.$ Twin chromatic index of the square $P_n^2,$ $n\\ge 4,$ and the square $C_n^2,$ $n\\ge 6,$ are determined. In fact, the twin chromatic index of the square $C_7^2$ is $\\Delta+2,$ where $\\Delta$ is the maximum degree. Twin chromatic index of $C_m\\,\\Box\\,P_n$ is determined, where $\\Box$ denotes the Cartesian product. $C_r$ and $P_r$ are, respectively, the cycle, and the path on $r$ vertices each.
A CLASSIFIER SYSTEM USING SMOOTH GRAPH COLORING
Directory of Open Access Journals (Sweden)
JORGE FLORES CRUZ
2017-01-01
Full Text Available Unsupervised classifiers allow clustering methods with less or no human intervention. Therefore it is desirable to group the set of items with less data processing. This paper proposes an unsupervised classifier system using the model of soft graph coloring. This method was tested with some classic instances in the literature and the results obtained were compared with classifications made with human intervention, yielding as good or better results than supervised classifiers, sometimes providing alternative classifications that considers additional information that humans did not considered.
Whole Genome Phylogenetic Tree Reconstruction using Colored de Bruijn Graphs
Lyman, Cole
2017-01-01
We present kleuren, a novel assembly-free method to reconstruct phylogenetic trees using the Colored de Bruijn Graph. kleuren works by constructing the Colored de Bruijn Graph and then traversing it, finding bubble structures in the graph that provide phylogenetic signal. The bubbles are then aligned and concatenated to form a supermatrix, from which a phylogenetic tree is inferred. We introduce the algorithm that kleuren uses to accomplish this task, and show its performance on reconstructin...
Network evolution driven by dynamics applied to graph coloring
International Nuclear Information System (INIS)
Wu Jian-She; Li Li-Guang; Yu Xin; Jiao Li-Cheng; Wang Xiao-Hua
2013-01-01
An evolutionary network driven by dynamics is studied and applied to the graph coloring problem. From an initial structure, both the topology and the coupling weights evolve according to the dynamics. On the other hand, the dynamics of the network are determined by the topology and the coupling weights, so an interesting structure-dynamics co-evolutionary scheme appears. By providing two evolutionary strategies, a network described by the complement of a graph will evolve into several clusters of nodes according to their dynamics. The nodes in each cluster can be assigned the same color and nodes in different clusters assigned different colors. In this way, a co-evolution phenomenon is applied to the graph coloring problem. The proposed scheme is tested on several benchmark graphs for graph coloring
General Vertex-Distinguishing Total Coloring of Graphs
Directory of Open Access Journals (Sweden)
Chanjuan Liu
2014-01-01
Full Text Available The general vertex-distinguishing total chromatic number of a graph G is the minimum integer k, for which the vertices and edges of G are colored using k colors such that any two vertices have distinct sets of colors of them and their incident edges. In this paper, we figure out the exact value of this chromatic number of some special graphs and propose a conjecture on the upper bound of this chromatic number.
One-sided interval edge-colorings of bipartite graphs
DEFF Research Database (Denmark)
Casselgren, Carl Johan; Toft, Bjarne
2016-01-01
Let G be a bipartite graph with parts X and Y . An X-interval coloring of G is a proper edge coloring of G by integers such that the colors on the edges incident to any vertex in X form an interval. Denote by χ′int(G,X) the minimum k such that G has an X-interval coloring with k colors. In this p...
Perfect 2-colorings of the generalized Petersen graph
Indian Academy of Sciences (India)
It is obvious that GP(n, k) is a 3-regular connected graph. DEFINITION 2.2 ... vertex of color i, the number of its neighbors of color j is equal to aij . ... By the given conditions, we can see that a parameter matrix of a perfect 2-coloring of. GP(n, k) ...
Some results on square-free colorings of graphs
DEFF Research Database (Denmark)
Barat, Janos
2004-01-01
on the vertices or edges of a path. Conversely one can form sequences from a vertex or edge coloring of a graph in different ways. Thus there are several possibilities to generalize the square-free concept to graphs. Following Alon, Grytczuk, Haluszczak, Riordan and Bresar, Klavzar we study several so called...... square-free graph parameters, and answer some questions they posed. The main result is that the class of k-trees has bounded square-free vertex coloring parameter. Thus we can color the vertices of a k-tree using O(c^k) colors if c>6 such that the color sequence on any path is square......-free. It is conjectured that a similar phenomenon holds for planar graphs, so a finite number of colors are enough. We support this conjecture by showing that this number is at most 12 for outerplanar graphs. On the other hand we prove that some outerplanar graphs require at least 7 colors. Using this latter we construct...
Integrated color face graphs for plant accident display
International Nuclear Information System (INIS)
Hara, Fumio
1987-01-01
This paper presents an integrated man-machine interface that uses cartoon-like colored graphs in the form of faces, that, through different facial expressions, display a plant condition. This is done by drawing the face on a CRT by nonlinearly transforming 31 variables and coloring the face. This integrated color graphics technique is applied to display the progess of events in the Three Mile Island nuclear power plant accident. Human visual perceptive characteristics are investigated in relation to the perception of the plant accident process, the naturality in face color change, and the consistency between facial expressions and colors. This paper concludes that colors used in an integrated color face graphs must be completely consistent with emotional feelings perceived from the colors. (author)
Perfect 3-colorings of the cubic graphs of order 10
Directory of Open Access Journals (Sweden)
Mehdi Alaeiyan
2017-10-01
Full Text Available Perfect coloring is a generalization of the notion of completely regular codes, given by Delsarte. A perfect m-coloring of a graph G with m colors is a partition of the vertex set of G into m parts A_1, A_2, ..., A_m such that, for all $ i,j \\in \\lbrace 1, ... , m \\rbrace $, every vertex of A_i is adjacent to the same number of vertices, namely, a_{ij} vertices, of A_j. The matrix $A=(a_{ij}_{i,j\\in \\lbrace 1,... ,m\\rbrace }$, is called the parameter matrix. We study the perfect 3-colorings (also known as the equitable partitions into three parts of the cubic graphs of order 10. In particular, we classify all the realizable parameter matrices of perfect 3-colorings for the cubic graphs of order 10.
Frog: Asynchronous Graph Processing on GPU with Hybrid Coloring Model
Energy Technology Data Exchange (ETDEWEB)
Shi, Xuanhua; Luo, Xuan; Liang, Junling; Zhao, Peng; Di, Sheng; He, Bingsheng; Jin, Hai
2018-01-01
GPUs have been increasingly used to accelerate graph processing for complicated computational problems regarding graph theory. Many parallel graph algorithms adopt the asynchronous computing model to accelerate the iterative convergence. Unfortunately, the consistent asynchronous computing requires locking or atomic operations, leading to significant penalties/overheads when implemented on GPUs. As such, coloring algorithm is adopted to separate the vertices with potential updating conflicts, guaranteeing the consistency/correctness of the parallel processing. Common coloring algorithms, however, may suffer from low parallelism because of a large number of colors generally required for processing a large-scale graph with billions of vertices. We propose a light-weight asynchronous processing framework called Frog with a preprocessing/hybrid coloring model. The fundamental idea is based on Pareto principle (or 80-20 rule) about coloring algorithms as we observed through masses of realworld graph coloring cases. We find that a majority of vertices (about 80%) are colored with only a few colors, such that they can be read and updated in a very high degree of parallelism without violating the sequential consistency. Accordingly, our solution separates the processing of the vertices based on the distribution of colors. In this work, we mainly answer three questions: (1) how to partition the vertices in a sparse graph with maximized parallelism, (2) how to process large-scale graphs that cannot fit into GPU memory, and (3) how to reduce the overhead of data transfers on PCIe while processing each partition. We conduct experiments on real-world data (Amazon, DBLP, YouTube, RoadNet-CA, WikiTalk and Twitter) to evaluate our approach and make comparisons with well-known non-preprocessed (such as Totem, Medusa, MapGraph and Gunrock) and preprocessed (Cusha) approaches, by testing four classical algorithms (BFS, PageRank, SSSP and CC). On all the tested applications and
Two-colorable graph states with maximal Schmidt measure
International Nuclear Information System (INIS)
Severini, Simone
2006-01-01
The Schmidt measure was introduced by Eisert and Briegel for quantifying the degree of entanglement of multipartite quantum systems [J. Eisert, H.-J. Briegel, Phys. Rev. A 64 (2001) 22306]. For two-colorable graph states, the Schmidt measure is related to the spectrum of the associated graph. We observe that almost all two-colorable graph states have maximal Schmidt measure and we construct specific examples. By making appeal to a result of Ehrenfeucht et al. [A. Ehrenfeucht, T. Harju, G. Rozenberg, Discrete Math. 278 (2004) 45], we point out that the graph operations called local complementation and switching form a transitive group acting on the set of all graph states of a given dimension
Coloring graphs from lists with bounded size of their union
Czech Academy of Sciences Publication Activity Database
Král´, D.; Sgall, Jiří
2005-01-01
Roč. 49, č. 3 (2005), s. 177-186 ISSN 0364-9024 R&D Projects: GA ČR(CZ) GA201/01/1195; GA MŠk(CZ) LN00A056 Institutional research plan: CEZ:AV0Z10190503 Keywords : graph coloring * list coloring Subject RIV: BA - General Mathematics Impact factor: 0.319, year: 2005
Voice-Centric LTE Femtocells and Improper Graph Colorings
DEFF Research Database (Denmark)
Garcia, Luis Guilherme Uzeda; Pedersen, Klaus; Mogensen, Preben
2012-01-01
. The investigation revolves around the sensible definition of the underlying graph, i.e. the network model, rather than focusing on the coloring algorithms and their properties. Ultimately, we posit that improper online graph-coloring suffices and is actually preferable. In short, settling for less......This paper addresses carrier-based inter-cell interference coordination (CB-ICIC) among LTE femtocells operating on a single carrier. CB-ICIC is in many ways linked to the widely investigated dynamic channel assignment problem, which is often studied in the context of graph coloring......-than-optimal configurations avoids uncontrolled service interruptions. Such disruptions tend to raise understandable concerns when it comes to fully autonomous selection of operational CCs. Our results dispel such concerns by showing that conservative methods can achieve most of the benefits of unrestricted off-line coloring...
Color normalization of histology slides using graph regularized sparse NMF
Sha, Lingdao; Schonfeld, Dan; Sethi, Amit
2017-03-01
Computer based automatic medical image processing and quantification are becoming popular in digital pathology. However, preparation of histology slides can vary widely due to differences in staining equipment, procedures and reagents, which can reduce the accuracy of algorithms that analyze their color and texture information. To re- duce the unwanted color variations, various supervised and unsupervised color normalization methods have been proposed. Compared with supervised color normalization methods, unsupervised color normalization methods have advantages of time and cost efficient and universal applicability. Most of the unsupervised color normaliza- tion methods for histology are based on stain separation. Based on the fact that stain concentration cannot be negative and different parts of the tissue absorb different stains, nonnegative matrix factorization (NMF), and particular its sparse version (SNMF), are good candidates for stain separation. However, most of the existing unsupervised color normalization method like PCA, ICA, NMF and SNMF fail to consider important information about sparse manifolds that its pixels occupy, which could potentially result in loss of texture information during color normalization. Manifold learning methods like Graph Laplacian have proven to be very effective in interpreting high-dimensional data. In this paper, we propose a novel unsupervised stain separation method called graph regularized sparse nonnegative matrix factorization (GSNMF). By considering the sparse prior of stain concentration together with manifold information from high-dimensional image data, our method shows better performance in stain color deconvolution than existing unsupervised color deconvolution methods, especially in keeping connected texture information. To utilized the texture information, we construct a nearest neighbor graph between pixels within a spatial area of an image based on their distances using heat kernal in lαβ space. The
On square-free edge colorings of graphs
DEFF Research Database (Denmark)
Barat, Janos; Varju, P.P.
2008-01-01
An edge coloring of a graph is called square-free, if the sequence of colors on certain walks is not a square, that is not of the form x(1,)...,x(m), x(1),...,x(m), for any m epsilon N. Recently, various classes of walks have been suggested to be considered in the above definition. We construct...... graphs, for which the minimum number of colors needed for a square-free coloring is different if the considered set of walks vary, solving a problem posed by Bre ar and Klav2ar. We also prove the following: if an edge coloring of G is not square-free (even in the most general sense), then the length...
Coloring triangle-free graphs with fixed size
DEFF Research Database (Denmark)
Thomassen, Carsten; Gimbel, John
2000-01-01
Combining recent results on colorings and Ramsey theory, we show that if G is a triangle-free graph with e edges then the chromatic number of G is at most cel(1/3)(log e)(-2/3) for some constant c. In a previous paper, we found an upper bound on the chromatic number of a triangle-free graph of ge...
Spanning trees with many or few colors in edge-colored graphs
Broersma, Haitze J.; Li, Xueliang; Li, Xueliang
1997-01-01
Given a graph G = (V,E) and a (not necessarily proper) edge-coloring of G, we consider the complexity of finding a spanning tree of G with as many different colors as possible, and of finding one with as few different colors as possible. We show that the first problem is equivalent to finding a
Directed paths with few or many colors in colored directed graphs
Li, X.; Li, Xueliang; Zhang, S.; Broersma, Haitze J.
2000-01-01
Given a graph $D=(V(D),A(D))$ and a coloring of $D$, not necessarily a proper coloring of either the arcs or the vertices of $D$, we consider the complexity of finding a path of $D$ from a given vertex $s$ to another given vertex $t$ with as few different colors as possible, and of finding one with
Multicolored spanning subgraphs in G-colorings of complete graphs
International Nuclear Information System (INIS)
Akbari, S.; Zare, S.
2007-08-01
Let G = {g 1 , ..., g n } be a finite abelian group. Consider the complete graph with the vertex set {g 1 , ..., g n }}. The G-coloring of K n is a proper edge coloring in which the color of edge {g i , g j } is g i + g j , l ≤ i ≤ j ≤ n. We prove that in the G-coloring of the complete graph K n , there exists a multicolored Hamilton path if G is not an elementary abelian 2-group. Furthermore, we show that if n is odd, then the G-coloring of K n can be decomposed into multicolored 2-factors and if l r is the number of elements of order r in G, 3 ≤ r ≤ n. then there are exactly (l r )/2 multicolored r-uniform 2-factors in this decomposition. This provides a generalization of a recent result due to Constantine which states: For any prime number p > 2, there exists a proper edge coloring of K p which is decomposable into multicolored Hamilton cycles. (author)
Equitable Coloring of Graphs. Recent Theoretical Results and New Practical Algorithms
Directory of Open Access Journals (Sweden)
Furmańczyk Hanna
2016-09-01
Full Text Available In many applications in sequencing and scheduling it is desirable to have an underlaying graph as equitably colored as possible. In this paper we survey recent theoretical results concerning conditions for equitable colorability of some graphs and recent theoretical results concerning the complexity of equitable coloring problem. Next, since the general coloring problem is strongly NP-hard, we report on practical experiments with some efficient polynomial-time algorithms for approximate equitable coloring of general graphs.
A HYBRID ALGORITHM FOR THE ROBUST GRAPH COLORING PROBLEM
Directory of Open Access Journals (Sweden)
Román Anselmo Mora Gutiérrez
2016-08-01
Full Text Available A hybridalgorithm which combines mathematical programming techniques (Kruskal’s algorithm and the strategy of maintaining arc consistency to solve constraint satisfaction problem “CSP” and heuristic methods (musical composition method and DSATUR to resolve the robust graph coloring problem (RGCP is proposed in this paper. Experimental result shows that this algorithm is better than the other algorithms presented on the literature.
Rainbow vacua of colored higher-spin (A)dS_3 gravity
International Nuclear Information System (INIS)
Gwak, Seungho; Joung, Euihun; Mkrtchyan, Karapet; Rey, Soo-Jong
2016-01-01
We study the color-decoration of higher-spin (anti)-de Sitter gravity in three dimensions. We show that the rainbow vacua, which we found recently for the colored gravity theory, also pertain in the colored higher-spin theory. The color singlet spin-two plays the role of first fundamental form (metric). The difference is that when spontaneous breaking of color symmetry takes place, the Goldstone modes of massless spin-two combine with all other spins and become the maximal-depth partially massless fields of the highest spin in the theory, forming a Regge trajectory.
A DNA Computing Model for the Graph Vertex Coloring Problem Based on a Probe Graph
Directory of Open Access Journals (Sweden)
Jin Xu
2018-02-01
Full Text Available The biggest bottleneck in DNA computing is exponential explosion, in which the DNA molecules used as data in information processing grow exponentially with an increase of problem size. To overcome this bottleneck and improve the processing speed, we propose a DNA computing model to solve the graph vertex coloring problem. The main points of the model are as follows: ① The exponential explosion problem is solved by dividing subgraphs, reducing the vertex colors without losing the solutions, and ordering the vertices in subgraphs; and ② the bio-operation times are reduced considerably by a designed parallel polymerase chain reaction (PCR technology that dramatically improves the processing speed. In this article, a 3-colorable graph with 61 vertices is used to illustrate the capability of the DNA computing model. The experiment showed that not only are all the solutions of the graph found, but also more than 99% of false solutions are deleted when the initial solution space is constructed. The powerful computational capability of the model was based on specific reactions among the large number of nanoscale oligonucleotide strands. All these tiny strands are operated by DNA self-assembly and parallel PCR. After thousands of accurate PCR operations, the solutions were found by recognizing, splicing, and assembling. We also prove that the searching capability of this model is up to O(359. By means of an exhaustive search, it would take more than 896 000 years for an electronic computer (5 × 1014 s−1 to achieve this enormous task. This searching capability is the largest among both the electronic and non-electronic computers that have been developed since the DNA computing model was proposed by Adleman’s research group in 2002 (with a searching capability of O(220. Keywords: DNA computing, Graph vertex coloring problem, Polymerase chain reaction
Three-coloring graphs with no induced seven-vertex path II : using a triangle
Chudnovsky, Maria; Maceli, Peter; Zhong, Mingxian
2015-01-01
In this paper, we give a polynomial time algorithm which determines if a given graph containing a triangle and no induced seven-vertex path is 3-colorable, and gives an explicit coloring if one exists. In previous work, we gave a polynomial time algorithm for three-coloring triangle-free graphs with no induced seven-vertex path. Combined, our work shows that three-coloring a graph with no induced seven-vertex path can be done in polynomial time.
Multiscale weighted colored graphs for protein flexibility and rigidity analysis
Bramer, David; Wei, Guo-Wei
2018-02-01
Protein structural fluctuation, measured by Debye-Waller factors or B-factors, is known to correlate to protein flexibility and function. A variety of methods has been developed for protein Debye-Waller factor prediction and related applications to domain separation, docking pose ranking, entropy calculation, hinge detection, stability analysis, etc. Nevertheless, none of the current methodologies are able to deliver an accuracy of 0.7 in terms of the Pearson correlation coefficients averaged over a large set of proteins. In this work, we introduce a paradigm-shifting geometric graph model, multiscale weighted colored graph (MWCG), to provide a new generation of computational algorithms to significantly change the current status of protein structural fluctuation analysis. Our MWCG model divides a protein graph into multiple subgraphs based on interaction types between graph nodes and represents the protein rigidity by generalized centralities of subgraphs. MWCGs not only predict the B-factors of protein residues but also accurately analyze the flexibility of all atoms in a protein. The MWCG model is validated over a number of protein test sets and compared with many standard methods. An extensive numerical study indicates that the proposed MWCG offers an accuracy of over 0.8 and thus provides perhaps the first reliable method for estimating protein flexibility and B-factors. It also simultaneously predicts all-atom flexibility in a molecule.
In search of the rainbow: Colored inks in surgical pathology
Directory of Open Access Journals (Sweden)
Chandralekha Tampi
2012-01-01
Full Text Available Introduction: Although surgical pathologists are aware of the multiple advantages that coloured inks contribute to surgical pathology practice, these coloured inks are not available in India and importing them is not a viable proposition. A systematic search for locally available coloring agents was done, and resulted in identifying specific shades within a popular set of children′s hobby colors of a particular brand. They retain their bright distinct colors on paraffin blocks and sections. These paints are available all over India, and are cheap, safe, and easy to use. Coloring gross specimen excision margins with different colors, adds precision to margin examination. It allows three-dimensional microscopic reconstruction of the tumor vis-a-vis its various neighboring anatomic structures. It allows postoperative comparison of tissue planes predicted by preoperative imaging. It maintains orientation of grossed and dissected specimens, enabling the pathologist to re-visit the grossed specimen, if required, and confidently allows further sampling if necessary. Aim: A systematic search for indigenous coloring agents was carried out, which included the dyes used in the histopathology laboratory, gelatin, commercially available paints, including acrylic paints and inks. Results: The study identified specific shades within a brand of acrylic colors that are easily available and simple to use, with good results on microscopic examination. Conclusion: Colored inks lend precision to margin examination. A set of easily procurable colors are available in our country, which are easy to use, with distinct bright colors, safe, and reliable.
MATHEMATICA APPLICATION FOR GRAPH COLORING AT THE INTERSECTION OF JALAN PANGERAN ANTASARI JAKARTA
Directory of Open Access Journals (Sweden)
Suwarno Suwarno
2017-12-01
Full Text Available This research examines about graph coloring using Welch-Powell algorithm. This research begins by trying to understand about graph coloring and its algorithm. The case study was conducted at the intersection of Pangeran Antasari Street. In the formation of graph obtained 12 vertices as traffic flow and 16 edges as traffic path. The results of this study obtained 4 chromatic numbers which describes 4 stages of traffic light arrangement. This paper also explains the application of Mathematica software in graph coloring.
The number of k-colorings of a graph on a fixed surface
DEFF Research Database (Denmark)
Thomassen, Carsten
2006-01-01
We prove that, for every fixed surface S, there exists a largest positive constant c such that every 5-colorable graph with n vertices on S has at least c center dot 2(n) distinct 5-colorings. This is best possible in the sense that, for each sufficiently large natural number n, there is a graph ...
On interval and cyclic interval edge colorings of (3,5)-biregular graphs
DEFF Research Database (Denmark)
Casselgren, Carl Johan; Petrosyan, Petros; Toft, Bjarne
2017-01-01
A proper edge coloring f of a graph G with colors 1,2,3,…,t is called an interval coloring if the colors on the edges incident to every vertex of G form an interval of integers. The coloring f is cyclic interval if for every vertex v of G, the colors on the edges incident to v either form an inte...
The number of colorings of planar graphs with no separating triangles
DEFF Research Database (Denmark)
Thomassen, Carsten
2017-01-01
A classical result of Birkhoff and Lewis implies that every planar graph with . n vertices has at least . 152n-1 distinct 5-vertex-colorings. Equality holds for planar triangulations with . n-4 separating triangles. We show that, if a planar graph has no separating triangle, then it has at least ...
Human Colors-The Rainbow Garden of Pathology: What Gives Normal and Pathologic Tissues Their Color?
Piña-Oviedo, Sergio; Ortiz-Hidalgo, Carlos; Ayala, Alberto G
2017-03-01
- Colors are important to all living organisms because they are crucial for camouflage and protection, metabolism, sexual behavior, and communication. Human organs obviously have color, but the underlying biologic processes that dictate the specific colors of organs and tissues are not completely understood. A literature search on the determinants of color in human organs yielded scant information. - To address 2 specific questions: (1) why do human organs have color, and (2) what gives normal and pathologic tissues their distinctive colors? - Endogenous colors are the result of complex biochemical reactions that produce biologic pigments: red-brown cytochromes and porphyrins (blood, liver, spleen, kidneys, striated muscle), brown-black melanins (skin, appendages, brain nuclei), dark-brown lipochromes (aging organs), and colors that result from tissue structure (tendons, aponeurosis, muscles). Yellow-orange carotenes that deposit in lipid-rich tissues are only produced by plants and are acquired from the diet. However, there is lack of information about the cause of color in other organs, such as the gray and white matter, neuroendocrine organs, and white tissues (epithelia, soft tissues). Neoplastic tissues usually retain the color of their nonneoplastic counterpart. - Most available information on the function of pigments comes from studies in plants, microorganisms, cephalopods, and vertebrates, not humans. Biologic pigments have antioxidant and cytoprotective properties and should be considered as potential future therapies for disease and cancer. We discuss the bioproducts that may be responsible for organ coloration and invite pathologists and pathology residents to look at a "routine grossing day" with a different perspective.
Generating QCD amplitudes in the color-flow basis with MadGraph
International Nuclear Information System (INIS)
Hagiwara, Kaoru; Takaesu, Yoshitaro
2011-01-01
We propose to make use of the off-shell recursive relations with the color-flow decomposition in the calculation of QCD amplitudes on MadGraph. We introduce colored quarks and their interactions with nine gluons in the color-flow basis plus an Abelian gluon on MadGraph, such that it generates helicity amplitudes in the color-flow basis with off-shell recursive formulae for multi-gluon sub-amplitudes. We demonstrate calculations of up to 5-jet processes such as gg→5g, u anti u→5g and uu→uuggg. Although our demonstration is limited, it paves the way to evaluate amplitudes with more quark lines and gluons with MadGraph. (orig.)
Perfect 2-colorings of the generalized Petersen graph
Indian Academy of Sciences (India)
There are no perfect 2-colorings of GP(n, 2) with the matrix A3. Proof. Suppose, contrary to our claim, there is a perfect 2-coloring of GP(n, 2) with the matrix A3. By Lemma 3.4, there are 2 vertices ai and bi, for some 0 ≤ i ≤ n−1, such that they are the same color. By symmetry, without loss of generality, we can assume T (a0) ...
Spectrum Graph Coloring and Applications to Wi-Fi Channel Assignment
Directory of Open Access Journals (Sweden)
David Orden
2018-03-01
Full Text Available We introduce and explore a family of vertex-coloring problems, which, surprisingly enough, have not been considered before despite stemming from the problem of Wi-Fi channel assignment. Given a spectrum of colors, endowed with a matrix of interferences between each pair of colors, the Threshold Spectrum Coloring problem fixes the number of colors available and aims to minimize the interference threshold, i.e., the maximum of the interferences at the vertices. Conversely, the Chromatic Spectrum Coloring problem fixes a threshold and aims to minimize the number of colors for which respecting that threshold is possible. As the main theoretical results, we prove tight upper bounds for the solutions to each problem. Since both problems turn out to be NP-hard, we complete the scene with experimental results. We propose a DSATUR-based heuristic and study its performance to minimize the maximum vertex interference in Wi-Fi channel assignment, both for randomly-generated graphs and for a real-world scenario. Further, for all these graphs, we experimentally check the goodness of the theoretical bounds.
Sabbah, Shai; Zhu, Changhai; Hornsby, Mark A. W.; Kamermans, Maarten; Hawryshyn, Craig W.
2013-01-01
Color vision is most beneficial when the visual system is color constant and can correct the excitations of photoreceptors for differences in environmental irradiance. A phenomenon related to color constancy is color induction, where the color of an object shifts away from the color of its
Deciding the On-line Chromatic Number of a Graph with Pre-coloring is PSPACE-complete
DEFF Research Database (Denmark)
Kudahl, Christian
2015-01-01
In an on-line coloring, the vertices of a graph are revealed one by one. An algorithm assigns a color to each vertex after it is revealed. When a vertex is revealed, it is also revealed which of the previous vertices it is adjacent to. The on-line chromatic number of a graph, G, is the smallest...... number of colors an algorithm will need when on-line-coloring G. The algorithm may know G, but not the order in which the vertices are revealed. The problem of determining if the on-line chromatic number of a graph is less than or equal to k, given a pre-coloring, is shown to be PSPACE-complete....
Directory of Open Access Journals (Sweden)
Yonggu Kim
2017-10-01
Full Text Available This research determines the optimal investment timing using real options valuation to support decision-making for economic sustainability assessment. This paper illustrates an option pricing model using the Black-Scholes model applied to a case project to understand the model performance. Applicability of the project to the model requires two Monte Carlo simulations to satisfy a Markov process and a Wiener process. The position of project developers is not only the seller of products, but it is also the buyer of raw materials. Real options valuation can be influenced by the volatility of cash outflow, as well as the volatility of cash inflow. This study suggests two-color rainbow options valuation to overcome this issue, which is demonstrated for a steel plant project. The asymmetric results of the case study show that cash outflow (put option influences the value of the steel plant project more than cash inflow (call option does of which the discussion of the results is referred to a sensitivity analysis. The real options valuation method proposed in this study contributes to the literature on applying the new model, taking into consideration that investors maximize project profitability for economic sustainable development.
The End of the Rainbow? Color Schemes for Improved Data Graphics
Light, Adam; Bartlein, Patrick J.
2004-10-01
Modern computer displays and printers enable the widespread use of color in scientific communication, but the expertise for designing effective graphics has not kept pace with the technology for producing them. Historically, even the most prestigious publications have tolerated high defect rates in figures and illustrations, and technological advances that make creating and reproducing graphics easier do not appear to have decreased the frequency of errors. Flawed graphics consequently beget more flawed graphics as authors emulate published examples. Color has the potential to enhance communication, but design mistakes can result in color figures that are less effective than gray scale displays of the same data. Empirical research on human subjects can build a fundamental understanding of visual perception and scientific methods can be used to evaluate existing designs, but creating effective data graphics is a design task and not fundamentally a scientific pursuit. Like writing well, creating good data graphics requires a combination of formal knowledge and artistic sensibility tempered by experience: a combination of ``substance, statistics, and design''.
Directory of Open Access Journals (Sweden)
Tellini Silvia Mara
2015-12-01
Full Text Available By sharing the experiences of women and the black community of her time, represented as a journey towards womanhood on stage, Afro- American playwright Ntozake Shange deconstructs the patriarchal structure of language, by pushing the boundaries of genres as she assembles prose, poetry and stage performance in a “choreopoem” capable of empowering and liberating the trajectories of the represented black women. The present study explores the semiotic and linguistic deconstructions of the patriarchal ideology in for colored girls who have considered suicide/ when the rainbow is enuf, aiming at a discussion of the author’s experimentalism with language outside instituted discursive paradigms regarding women. Considering that the concept of the liberation of the individual is strongly historicized in the play, the characters of the seven ladies are focalized as being tightly related to the feminist movement in North America in the seventies. Furthermore, the implications of ideological impositions and limited roles for women in society are analyzed.
Study of Chromatic parameters of Line, Total, Middle graphs and Graph operators of Bipartite graph
Nagarathinam, R.; Parvathi, N.
2018-04-01
Chromatic parameters have been explored on the basis of graph coloring process in which a couple of adjacent nodes receives different colors. But the Grundy and b-coloring executes maximum colors under certain restrictions. In this paper, Chromatic, b-chromatic and Grundy number of some graph operators of bipartite graph has been investigat
完全图的点可区别强全染色算法%Strong Vertex-distinguishing Total Coloring Algorithm of Complete Graph
Institute of Scientific and Technical Information of China (English)
赵焕平; 刘平; 李敬文
2012-01-01
According to the definition of strong vertex-distinguishing total coloring, this paper combines with the symmetry of complete graph, proposes a new strong vertex-distinguishing total coloring algorithm. The algorithm divides the filled colors into two parts: overcolor and propercolor. At the premise of getting the coloring number and the coloring frequency, it uses colored at first to enhance its convergence. Experimental results show that this algorithm has a lower time complexity.%根据图的点可区别全染色的定义,结合完全图的对称性,提出一种新的点可区别强全染色算法.该算法将需要填充的颜色分为超色数和正常色数2个部分,在得到染色数量和染色次数的前提下,对超色数进行染色以增强算法收敛性.实验结果表明,该算法具有较低的时间复杂度.
Aparanji, Santosh; Balaswamy, V.; Arun, S.; Supradeepa, V. R.
2018-02-01
In this work, we report and analyse the surprising observation of a rainbow of visible colors, spanning 390nm to 620nm, in silica-based, Near Infrared, continuous-wave, cascaded Raman fiber lasers. The cascaded Raman laser is pumped at 1117nm at around 200W and at full power we obtain 100 W at 1480nm. With increasing pump power at 1117nm, the fiber constituting the Raman laser glows in various hues along its length. From spectroscopic analysis of the emitted visible light, it was identified to be harmonic and sum-frequency components of various locally propagating wavelength components. In addition to third harmonic components, surprisingly, even 2nd harmonic components were observed. Despite being a continuous-wave laser, we expect the phase-matching occurring between the core-propagating NIR light with the cladding-propagating visible wavelengths and the intensity fluctuations characteristic of Raman lasers to have played a major role in generation of visible light. In addition, this surprising generation of visible light provides us a powerful non-contact method to deduce the spectrum of light propagating in the fiber. Using static images of the fiber captured by a standard visible camera such as a DSLR, we demonstrate novel, image-processing based techniques to deduce the wavelength component propagating in the fiber at any given spatial location. This provides a powerful diagnostic tool for both length and power resolved spectral analysis in Raman fiber lasers. This helps accurate prediction of the optimal length of fiber required for complete and efficient conversion to a given Stokes wavelength.
Buick, Tony
2010-01-01
The world is full of color, from the blue ocean and the yellow daffodils and sunflowers in green carpeted meadows to the majestic purple mountains in the distance and brightly hued coral reefs off the edges of tropical coasts. But what is color, exactly? Why do we see things in different colors? Do we all see the same colors? Like the surface of our planet, the sky above us offers us an endless palette of color, a visual feast for the eyes. Besides atmospheric phenomena such as sunsets and rainbows, there are the many varied worlds of the Solar System, which we can spy through our telescopes, with their subtle colorings of beige and blue and green. Faraway star systems have suns that come in shades ranging from red and yellow to blue and white. Scientists even often use "false colors" to enhance the features of images they take of structures, such as the rings of Saturn and Jupiter’s clouds. This book, with its clear explanations of what makes the sky such a colorful place and in its great wealth of picture...
Rainbow paths with prescribed ends
DEFF Research Database (Denmark)
Alishahi, Meysam; Taherkhani, Ali; Thomassen, Carsten
2011-01-01
vertices. We also prove that every connected graph with atleast one edge has a proper k-coloring (for some k) such that every vertex of color i has a neighbor of color i + 1 (mod k). C-5 shows that k may have to be greater than the chromatic number. However, if the graph is connected, infinite and locally...... finite, and has finite chromatic number, then the k-coloring exists for every k >= chi(G). In fact, the k-coloring can be chosen such that every vertex is a starting vertex of an infinite path such that the color increases by 1 (mod k) along each edge. The method is based on the circular chromatic number...... chi(c)(G). In particular, we verify the above conjecture for all connected graphs whose circular chromatic number equals the chromatic number....
Koerts, Filip; Bürger, Mathias; van der Schaft, Abraham; De Persis, Claudio
2017-01-01
In this paper, we study parameter-independent stability in qualitatively heterogeneous passive networked systems containing damped and undamped nodes. Given the graph topology and a set of damped nodes, we ask if output consensus is achieved for all system parameter values. For given parameter
Relating 2-Rainbow Domination To Roman Domination
Directory of Open Access Journals (Sweden)
Alvarado José D.
2017-11-01
Full Text Available For a graph G, let R(G and yr2(G denote the Roman domination number of G and the 2-rainbow domination number of G, respectively. It is known that yr2(G ≤ R(G ≤ 3/2yr2(G. Fujita and Furuya [Difference between 2-rainbow domination and Roman domination in graphs, Discrete Appl. Math. 161 (2013 806-812] present some kind of characterization of the graphs G for which R(G − yr2(G = k for some integer k. Unfortunately, their result does not lead to an algorithm that allows to recognize these graphs efficiently. We show that for every fixed non-negative integer k, the recognition of the connected K4-free graphs G with yR(G − yr2(G = k is NP-hard, which implies that there is most likely no good characterization of these graphs. We characterize the graphs G such that yr2(H = yR(H for every induced subgraph H of G, and collect several properties of the graphs G with R(G = 3/2yr2(G.
Modeling Software Evolution using Algebraic Graph Rewriting
Ciraci, Selim; van den Broek, Pim
We show how evolution requests can be formalized using algebraic graph rewriting. In particular, we present a way to convert the UML class diagrams to colored graphs. Since changes in software may effect the relation between the methods of classes, our colored graph representation also employs the
A faithful functor among algebras and graphs
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vigo Aguiar, Jesús (Coordinador)
2016-01-01
The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertex-colored graphs, we describe here a pair of graphs that enable us to find a faithful functor between finite-dimensional algebras over finite fields and these graphs.
Endriss, U.; Grandi, U.
Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference
Rainbow Particle Imaging Velocimetry
Xiong, Jinhui
2017-04-27
Despite significant recent progress, dense, time-resolved imaging of complex, non-stationary 3D flow velocities remains an elusive goal. This work tackles this problem by extending an established 2D method, Particle Imaging Velocimetry, to three dimensions by encoding depth into color. The encoding is achieved by illuminating the flow volume with a continuum of light planes (a “rainbow”), such that each depth corresponds to a specific wavelength of light. A diffractive component in the camera optics ensures that all planes are in focus simultaneously. With this setup, a single color camera is sufficient to track 3D trajectories of particles by combining 2D spatial and 1D color information. For reconstruction, this thesis derives an image formation model for recovering stationary 3D particle positions. 3D velocity estimation is achieved with a variant of 3D optical flow that accounts for both physical constraints as well as the rainbow image formation model. The proposed method is evaluated by both simulations and an experimental prototype setup.
Zhang, L.-C.; Patone, M.
2017-01-01
We synthesise the existing theory of graph sampling. We propose a formal definition of sampling in finite graphs, and provide a classification of potential graph parameters. We develop a general approach of Horvitz–Thompson estimation to T-stage snowball sampling, and present various reformulations of some common network sampling methods in the literature in terms of the outlined graph sampling theory.
Total dominator chromatic number of a graph
Directory of Open Access Journals (Sweden)
Adel P. Kazemi
2015-06-01
Full Text Available Given a graph $G$, the total dominator coloring problem seeks a proper coloring of $G$ with the additional property that every vertex in the graph is adjacent to all vertices of a color class. We seek to minimize the number of color classes. We initiate to study this problem on several classes of graphs, as well as finding general bounds and characterizations. We also compare the total dominator chromatic number of a graph with the chromatic number and the total domination number of it.
Voloshin, Vitaly I
2002-01-01
The theory of graph coloring has existed for more than 150 years. Historically, graph coloring involved finding the minimum number of colors to be assigned to the vertices so that adjacent vertices would have different colors. From this modest beginning, the theory has become central in discrete mathematics with many contemporary generalizations and applications. Generalization of graph coloring-type problems to mixed hypergraphs brings many new dimensions to the theory of colorings. A main feature of this book is that in the case of hypergraphs, there exist problems on both the minimum and th
Brouwer, A.E.; Haemers, W.H.; Brouwer, A.E.; Haemers, W.H.
2012-01-01
This chapter presents some simple results on graph spectra.We assume the reader is familiar with elementary linear algebra and graph theory. Throughout, J will denote the all-1 matrix, and 1 is the all-1 vector.
A new characterization of trivially perfect graphs
Directory of Open Access Journals (Sweden)
Christian Rubio Montiel
2015-03-01
Full Text Available A graph $G$ is \\emph{trivially perfect} if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number $\\alpha(G$ equals the number of (maximal cliques $m(G$. We characterize the trivially perfect graphs in terms of vertex-coloring and we extend some definitions to infinite graphs.
Energy Technology Data Exchange (ETDEWEB)
Awad, Adel; Ali, Ahmed Farag [Center for Theoretical Physics, Zewail City of Science and Technology, Giza, 12588 (Egypt); Majumder, Barun, E-mail: aawad@zewailcity.edu.eg, E-mail: ahmed.ali@fsc.bu.edu.eg, E-mail: barunbasanta@iitgn.ac.in [Indian Institute of Technology Gandhinagar, Ahmedabad, Gujarat 382424 (India)
2013-10-01
In this work, we study FRW cosmologies in the context of gravity rainbow. We discuss the general conditions for having a nonsingular FRW cosmology in gravity rainbow. We propose that gravity rainbow functions can be fixed using two known modified dispersion relation (MDR), which have been proposed in literature. The first MDR was introduced by Amelino-Camelia, et el. in [9] and the second was introduced by Magueijo and Smolin in [24]. Studying these FRW-like cosmologies, after fixing the gravity rainbow functions, leads to nonsingular solutions which can be expressed in exact forms.
Realizable Triples in Dominator Colorings
National Research Council Canada - National Science Library
Fletcher, Douglas M
2007-01-01
Given a graph G and its vertex set V(G), the chromatic number, Chi(G), represents the minimum number of colors required to color the vertices of G so that no two adjacent vertices have the same color...
Transforming White Light into Rainbows: Segmentation Strategies for Successful School Tax Elections
Senden, J. Bradford; Lifto, Don E.
2009-01-01
In the late 1600s, British physicist Sir Isaac Newton first demonstrated refraction and dispersion in a triangular prism. He discovered that a prism could decompose white light into a spectrum. Hold a prism up to the light at the correct angle and white light magically splits into vivid colors of the rainbow! So what do prisms and rainbows have to…
Bollobás, Béla
1998-01-01
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...
DEFF Research Database (Denmark)
Vestergaard, Preben Dahl; Hartnell, Bert L.
2006-01-01
There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done, the gr...
National Aeronautics and Space Administration — Inspired by the light scattering and focusing properties of distributed optical assemblies in Nature, such as rainbows and aerosols, and by recent laboratory...
Planar graphs theory and algorithms
Nishizeki, T
1988-01-01
Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.
Graphs with Eulerian unit spheres
Knill, Oliver
2015-01-01
d-spheres in graph theory are inductively defined as graphs for which all unit spheres S(x) are (d-1)-spheres and that the removal of one vertex renders the graph contractible. Eulerian d-spheres are geometric d-spheres which are d+1 colorable. We prove here that G is an Eulerian sphere if and only if the degrees of all the (d-2)-dimensional sub-simplices in G are even. This generalizes a Kempe-Heawood result for d=2 and is work related to the conjecture that all d-spheres have chromatic numb...
On 4-critical t-perfect graphs
Benchetrit, Yohann
2016-01-01
It is an open question whether the chromatic number of $t$-perfect graphs is bounded by a constant. The largest known value for this parameter is 4, and the only example of a 4-critical $t$-perfect graph, due to Laurent and Seymour, is the complement of the line graph of the prism $\\Pi$ (a graph is 4-critical if it has chromatic number 4 and all its proper induced subgraphs are 3-colorable). In this paper, we show a new example of a 4-critical $t$-perfect graph: the complement of the line gra...
Yau, Donald
2016-01-01
The subject of this book is the theory of operads and colored operads, sometimes called symmetric multicategories. A (colored) operad is an abstract object which encodes operations with multiple inputs and one output and relations between such operations. The theory originated in the early 1970s in homotopy theory and quickly became very important in algebraic topology, algebra, algebraic geometry, and even theoretical physics (string theory). Topics covered include basic graph theory, basic category theory, colored operads, and algebras over colored operads. Free colored operads are discussed in complete detail and in full generality. The intended audience of this book includes students and researchers in mathematics and other sciences where operads and colored operads are used. The prerequisite for this book is minimal. Every major concept is thoroughly motivated. There are many graphical illustrations and about 150 exercises. This book can be used in a graduate course and for independent study.
Fabrication of digital rainbow holograms and 3-D imaging using SEM based e-beam lithography.
Firsov, An; Firsov, A; Loechel, B; Erko, A; Svintsov, A; Zaitsev, S
2014-11-17
Here we present an approach for creating full-color digital rainbow holograms based on mixing three basic colors. Much like in a color TV with three luminescent points per single screen pixel, each color pixel of initial image is presented by three (R, G, B) distinct diffractive gratings in a hologram structure. Change of either duty cycle or area of the gratings are used to provide proper R, G, B intensities. Special algorithms allow one to design rather complicated 3D images (that might even be replacing each other with hologram rotation). The software developed ("RainBow") provides stability of colorization of rotated image by means of equalizing of angular blur from gratings responsible for R, G, B basic colors. The approach based on R, G, B color synthesis allows one to fabricate gray-tone rainbow hologram containing white color what is hardly possible in traditional dot-matrix technology. Budgetary electron beam lithography based on SEM column was used to fabricate practical examples of digital rainbow hologram. The results of fabrication of large rainbow holograms from design to imprinting are presented. Advantages of the EBL in comparison to traditional optical (dot-matrix) technology is considered.
The Return of Rainbow Diet Pills
Cohen, Pieter A.; Goday, Alberto; Swann, John P.
2012-01-01
The US Food and Drug Administration (FDA) has recently warned consumers about the risks of weight loss supplements adulterated with multiple pharmaceutical agents. Some of these supplements combine potent anorectics, such as amphetamines derivatives, with benzodiazepines, beta-blockers, and other medications to suppress the anorectics’ adverse effects. These weight loss supplements represent the most recent generation of rainbow diet pills, named for their bright and varied colors, which date back more than 70 years. Beginning in the 1940s, several US pharmaceutical firms aggressively promoted rainbow pills to physicians and patients. By the 1960s the pills had caused dozens of deaths before the FDA began removing them from the US market. We used a variety of original resources to trace these deadly pills from their origins in the United States to their popularity in Spain and Brazil to their reintroduction to the United States as weight loss dietary supplements. PMID:22813089
Efficient Algorithmic Frameworks via Structural Graph Theory
2016-10-28
constant. For example, they measured that, on large samples of the entire network, the Amazon graph has average degree 17.7, the Facebook graph has average...department heads’ opinions of departments, and generally lack transparency and well-defined measures . On the other hand, the National Research Council (the...Efficient and practical resource block allocation for LTE -based D2D network via graph coloring. Wireless Networks 20(4): 611-624 (2014) 50. Hossein
On the local edge antimagicness of m-splitting graphs
Albirri, E. R.; Dafik; Slamin; Agustin, I. H.; Alfarisi, R.
2018-04-01
Let G be a connected and simple graph. A split graph is a graph derived by adding new vertex v‧ in every vertex v‧ such that v‧ adjacent to v in graph G. An m-splitting graph is a graph which has m v‧-vertices, denoted by mSpl(G). A local edge antimagic coloring in G = (V, E) graph is a bijection f:V (G)\\to \\{1,2,3,\\ldots,|V(G)|\\} in which for any two adjacent edges e 1 and e 2 satisfies w({e}1)\
DEFF Research Database (Denmark)
Seiller, Thomas
2016-01-01
Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should...... be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define...... "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite...
Trudeau, Richard J
1994-01-01
Preface1. Pure Mathematics Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. Graphs Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics The Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar Graphs Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions; Kuratowski's Theorem; Determining Whether a Graph is Planar or
Institute of Scientific and Technical Information of China (English)
杨芳; 王治文; 陈祥恩; 马春燕
2013-01-01
首先,给出了完全图Kp和星Sq的合成的点可区别正常边色数的一个上界:当p≥2,q≥4时,上界是pq+1.再利用正多边形的对称性以及组合分析的方法来构造染色,分别得到了当p=2,q≥4;p≥3,q=4;p是偶数且p≥4,q=5;pq是奇数且p≥3,q≥5时,完全图Kp和星Sq的合成的点可区别正常边色数.%Firstly,we gave an upper bound for the vertex-distinguishing proper edge chromatic number of composition of complete graph Kp and star Sq,which is pq + 1 for p ≥ 2,q ≥ 4.Then by constructing coloring in terms of the symmetry of regular polygons and the methods of combinatorial analysis,we obtained respectively vertex-distinguishing proper edge chromatic numbers for composition of complete graph Kp and star Sq when p=2,q≥4;p≥3,q=4;pisevenandp≥4,q=5;pqisoddandp≥3,q≥5.
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
Diestel, Reinhard
2017-01-01
This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...
Every plane graph of maximum degree 8 has an edge-face 9-colouring.
R.J. Kang (Ross); J.-S. Sereni; M. Stehlík
2011-01-01
textabstractAn edge-face coloring of a plane graph with edge set $E$ and face set $F$ is a coloring of the elements of $E\\cup F$ such that adjacent or incident elements receive different colors. Borodin proved that every plane graph of maximum degree $\\Delta \\ge 10$ can be edge-face colored with
Gould, Ronald
2012-01-01
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S
Chartrand, Gary; Zhang, Ping
2010-01-01
Gary Chartrand has influenced the world of Graph Theory for almost half a century. He has supervised more than a score of Ph.D. dissertations and written several books on the subject. The most widely known of these texts, Graphs and Digraphs, … has much to recommend it, with clear exposition, and numerous challenging examples [that] make it an ideal textbook for the advanced undergraduate or beginning graduate course. The authors have updated their notation to reflect the current practice in this still-growing area of study. By the authors' estimation, the 5th edition is approximately 50% longer than the 4th edition. … the legendary Frank Harary, author of the second graph theory text ever produced, is one of the figures profiled. His book was the standard in the discipline for several decades. Chartrand, Lesniak and Zhang have produced a worthy successor.-John T. Saccoman, MAA Reviews, June 2012 (This book is in the MAA's basic library list.)As with the earlier editions, the current text emphasizes clear...
Selmke, Markus; Selmke, Sarah
2018-04-01
We describe a three-dimensional (3D) rainbow demonstration experiment. Its key idea is to convey a particular aspect of the natural phenomenon, namely, the origin of the perceived rainbow being multiple individual glints from within a rainshower. Raindrops in this demonstration are represented by acrylic spheres arranged on pillars within a cubic volume. Defocused imaging with a camera or the eye reveals a mosaic rainbow (segment) when viewed and illuminated in the appropriate fashion.
The chromatic polynomial and list colorings
DEFF Research Database (Denmark)
Thomassen, Carsten
2009-01-01
We prove that, if a graph has a list of k available colors at every vertex, then the number of list-colorings is at least the chromatic polynomial evaluated at k when k is sufficiently large compared to the number of vertices of the graph.......We prove that, if a graph has a list of k available colors at every vertex, then the number of list-colorings is at least the chromatic polynomial evaluated at k when k is sufficiently large compared to the number of vertices of the graph....
Approximate Computing Techniques for Iterative Graph Algorithms
Energy Technology Data Exchange (ETDEWEB)
Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh; Kalyanaraman, Anantharaman; Chavarria Miranda, Daniel G.; Krishnamoorthy, Sriram
2017-12-18
Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with low impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.
The b-chromatic number of power graphs
Directory of Open Access Journals (Sweden)
Brice Effantin
2003-06-01
Full Text Available The b-chromatic number of a graph G is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i, with 1 ≤ i≤ k, has at least one representant x i adjacent to a vertex of every color j, 1 ≤ j ≠ i ≤ k. In this paper, we discuss the b-chromatic number of some power graphs. We give the exact value of the b-chromatic number of power paths and power complete binary trees, and we bound the b-chromatic number of power cycles.
On Complexity of Flooding Games on Graphs with Interval Representations
Fukui, Hiroyuki; Otachi, Yota; Uehara, Ryuhei; Uno, Takeaki; Uno, Yushi
2012-01-01
The flooding games, which are called Flood-It, Mad Virus, or HoneyBee, are a kind of coloring games and they have been becoming popular online. In these games, each player colors one specified cell in his/her turn, and all connected neighbor cells of the same color are also colored by the color. This flooding or coloring spreads on the same color cells. It is natural to consider these new coloring games on more general boards, or general graphs. Recently, computational complexities of the var...
Graphs of groups on surfaces interactions and models
White, AT
2001-01-01
The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English
Graph visualization (Invited talk)
Wijk, van J.J.; Kreveld, van M.J.; Speckmann, B.
2012-01-01
Black and white node link diagrams are the classic method to depict graphs, but these often fall short to give insight in large graphs or when attributes of nodes and edges play an important role. Graph visualization aims obtaining insight in such graphs using interactive graphical representations.
The chromatic number of a graph of girth 5 on a fixed surface
DEFF Research Database (Denmark)
Thomassen, Carsten
2003-01-01
We prove a color extension result implying that, for every fixed surface S, there are only finitely many 4-color-critical graphs of girth 5 on S. The result is best possible in the sense that there are infinitely many 4-color-critical graphs of girth 4 on S, except when S is the sphere, As a cons......, As a consequence, the chromatic number of graphs of girth 5 on S can be found in polynomial time....
All aboard the Rainbow Warrior
International Nuclear Information System (INIS)
Walker, I.
1980-01-01
An account is given of the attempt by Rainbow Warrior to intercept Pacific Swan at Cherbourg Harbour, to protest against the transport of spent nuclear fuel from England to France for reprocessing. (U.K.)
Conway, Lorraine
This packet of student materials contains a variety of worksheet activities dealing with science graphs and science word games. These reproducible materials deal with: (1) bar graphs; (2) line graphs; (3) circle graphs; (4) pictographs; (5) histograms; (6) artgraphs; (7) designing your own graphs; (8) medical prefixes; (9) color prefixes; (10)…
Pragmatic Graph Rewriting Modifications
Rodgers, Peter; Vidal, Natalia
1999-01-01
We present new pragmatic constructs for easing programming in visual graph rewriting programming languages. The first is a modification to the rewriting process for nodes the host graph, where nodes specified as 'Once Only' in the LHS of a rewrite match at most once with a corresponding node in the host graph. This reduces the previously common use of tags to indicate the progress of matching in the graph. The second modification controls the application of LHS graphs, where those specified a...
Integer Flows and Circuit Covers of Graphs and Signed Graphs
Cheng, Jian
The work in Chapter 2 is motivated by Tutte and Jaeger's pioneering work on converting modulo flows into integer-valued flows for ordinary graphs. For a signed graphs (G, sigma), we first prove that for each k ∈ {2, 3}, if (G, sigma) is (k - 1)-edge-connected and contains an even number of negative edges when k = 2, then every modulo k-flow of (G, sigma) can be converted into an integer-valued ( k + 1)-ow with a larger or the same support. We also prove that if (G, sigma) is odd-(2p+1)-edge-connected, then (G, sigma) admits a modulo circular (2 + 1/ p)-flows if and only if it admits an integer-valued circular (2 + 1/p)-flows, which improves all previous result by Xu and Zhang (DM2005), Schubert and Steffen (EJC2015), and Zhu (JCTB2015). Shortest circuit cover conjecture is one of the major open problems in graph theory. It states that every bridgeless graph G contains a set of circuits F such that each edge is contained in at least one member of F and the length of F is at most 7/5∥E(G)∥. This concept was recently generalized to signed graphs by Macajova et al. (JGT2015). In Chapter 3, we improve their upper bound from 11∥E( G)∥ to 14/3 ∥E(G)∥, and if G is 2-edgeconnected and has even negativeness, then it can be further reduced to 11/3 ∥E(G)∥. Tutte's 3-flow conjecture has been studied by many graph theorists in the last several decades. As a new approach to this conjecture, DeVos and Thomassen considered the vectors as ow values and found that there is a close relation between vector S1-flows and integer 3-NZFs. Motivated by their observation, in Chapter 4, we prove that if a graph G admits a vector S1-flow with rank at most two, then G admits an integer 3-NZF. The concept of even factors is highly related to the famous Four Color Theorem. We conclude this dissertation in Chapter 5 with an improvement of a recent result by Chen and Fan (JCTB2016) on the upperbound of even factors. We show that if a graph G contains an even factor, then it
Bapat, Ravindra B
2014-01-01
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...
A first generation integrated physical and genetic map of the rainbow trout genome
The rainbow trout physical map was previously constructed from DNA fingerprinting of 192,096 BAC clones using the 4-color high-information content fingerprinting (HICF) method. The clones were assembled into physical map contigs using the finger-printing contig (FPC) program. The map is composed of ...
Adaptive Graph Convolutional Neural Networks
Li, Ruoyu; Wang, Sheng; Zhu, Feiyun; Huang, Junzhou
2018-01-01
Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for eac...
3-biplacement of bipartite graphs
Directory of Open Access Journals (Sweden)
Lech Adamus
2008-01-01
Full Text Available Let \\(G=(L,R;E\\ be a bipartite graph with color classes \\(L\\ and \\(R\\ and edge set \\(E\\. A set of two bijections \\(\\{\\varphi_1 , \\varphi_2\\}\\, \\(\\varphi_1 , \\varphi_2 :L \\cup R \\to L \\cup R\\, is said to be a \\(3\\-biplacement of \\(G\\ if \\(\\varphi_1(L= \\varphi_2(L = L\\ and \\(E \\cap \\varphi_1^*(E=\\emptyset\\, \\(E \\cap \\varphi_2^*(E=\\emptyset\\, \\(\\varphi_1^*(E \\cap \\varphi_2^*(E=\\emptyset\\, where \\(\\varphi_1^*\\, \\(\\varphi_2^*\\ are the maps defined on \\(E\\, induced by \\(\\varphi_1\\, \\(\\varphi_2\\, respectively. We prove that if \\(|L| = p\\, \\(|R| = q\\, \\(3 \\leq p \\leq q\\, then every graph \\(G=(L,R;E\\ of size at most \\(p\\ has a \\(3\\-biplacement.
Directory of Open Access Journals (Sweden)
C. Dalfo
2015-10-01
Full Text Available We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors.
A short list color proof of Grotzsch's theorem
DEFF Research Database (Denmark)
Thomassen, Carsten
2000-01-01
We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable.......We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable....
On the Lucky labeling of Graphs
Ahadi, Arash; Dehghan, Ali; Mollaahmadi, Esmael
2010-01-01
Suppose the vertices of a graph $G$ were labeled arbitrarily by positive integers, and let $Sum(v)$ denote the sum of labels over all neighbors of vertex $v$. A labeling is lucky if the function $Sum$ is a proper coloring of $G$, that is, if we have $Sum(u) \
Soetevent, A.R.
2010-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial
Graphing Inequalities, Connecting Meaning
Switzer, J. Matt
2014-01-01
Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…
Directory of Open Access Journals (Sweden)
Amine Labriji
2017-07-01
Full Text Available The topic of identifying the similarity of graphs was considered as highly recommended research field in the Web semantic, artificial intelligence, the shape recognition and information research. One of the fundamental problems of graph databases is finding similar graphs to a graph query. Existing approaches dealing with this problem are usually based on the nodes and arcs of the two graphs, regardless of parental semantic links. For instance, a common connection is not identified as being part of the similarity of two graphs in cases like two graphs without common concepts, the measure of similarity based on the union of two graphs, or the one based on the notion of maximum common sub-graph (SCM, or the distance of edition of graphs. This leads to an inadequate situation in the context of information research. To overcome this problem, we suggest a new measure of similarity between graphs, based on the similarity measure of Wu and Palmer. We have shown that this new measure satisfies the properties of a measure of similarities and we applied this new measure on examples. The results show that our measure provides a run time with a gain of time compared to existing approaches. In addition, we compared the relevance of the similarity values obtained, it appears that this new graphs measure is advantageous and offers a contribution to solving the problem mentioned above.
van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime
2016-01-01
This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,
Fuzzy Graph Language Recognizability
Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros
2012-01-01
Part 5: Fuzzy Logic; International audience; Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.
Brouwer, A.E.; Haemers, W.H.
2012-01-01
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association
Upper bound for the span of pencil graph
Parvathi, N.; Vimala Rani, A.
2018-04-01
An L(2,1)-Coloring or Radio Coloring or λ coloring of a graph is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x) ‑ f(y)| ≥ 2 if d(x,y) = 1 and |f(x) ‑ f(y)| ≥ 1 if d(x,y)=2, where d(x,y) denotes the distance between x and y in G. The L(2,1)-coloring number or span number λ(G) of G is the smallest number k such that G has an L(2,1)-coloring with max{f(v) : v ∈ V(G)} = k. [2]The minimum number of colors used in L(2,1)-coloring is called the radio number rn(G) of G (Positive integer). Griggs and yeh conjectured that λ(G) ≤ Δ2 for any simple graph with maximum degree Δ>2. In this article, we consider some special graphs like, n-sunlet graph, pencil graph families and derive its upper bound of (G) and rn(G).
Energy Technology Data Exchange (ETDEWEB)
Garattini, Remo [Universita degli Studi di Bergamo, Department of Engineering and Applied Sciences, Dalmine, Bergamo (Italy); I.N.F.N.-sezione di Milano, Milan (Italy); Mandanici, Gianluca [Universita degli Studi di Bergamo, Department of Engineering and Applied Sciences, Dalmine, Bergamo (Italy)
2017-01-15
In recent years, a growing interest in the equilibrium of compact astrophysical objects like white dwarf and neutron stars has been manifested. In particular, various modifications due to Planck-scale energy effects have been considered. In this paper we analyze the modification induced by gravity's rainbow on the equilibrium configurations described by the Tolman-Oppenheimer-Volkoff (TOV) equation. Our purpose is to explore the possibility that the rainbow Planck-scale deformation of space-time could support the existence of different compact stars. (orig.)
Hell, Pavol
2004-01-01
This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics.Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level an
Simplicial complexes of graphs
Jonsson, Jakob
2008-01-01
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
Introduction to quantum graphs
Berkolaiko, Gregory
2012-01-01
A "quantum graph" is a graph considered as a one-dimensional complex and equipped with a differential operator ("Hamiltonian"). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., "meso-" or "nano-scale") system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on qu...
Rainbow Particle Imaging Velocimetry
Xiong, Jinhui
2017-01-01
dimensions by encoding depth into color. The encoding is achieved by illuminating the flow volume with a continuum of light planes (a “rainbow”), such that each depth corresponds to a specific wavelength of light. A diffractive component in the camera optics
Graphing trillions of triangles.
Burkhardt, Paul
2017-07-01
The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.
Hierarchical graphs for rule-based modeling of biochemical systems
Directory of Open Access Journals (Sweden)
Hu Bin
2011-02-01
Full Text Available Abstract Background In rule-based modeling, graphs are used to represent molecules: a colored vertex represents a component of a molecule, a vertex attribute represents the internal state of a component, and an edge represents a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions. A rule that specifies addition (removal of an edge represents a class of association (dissociation reactions, and a rule that specifies a change of a vertex attribute represents a class of reactions that affect the internal state of a molecular component. A set of rules comprises an executable model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system. Results For purposes of model annotation, we propose the use of hierarchical graphs to represent structural relationships among components and subcomponents of molecules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR complex. We also show that computational methods developed for regular graphs can be applied to hierarchical graphs. In particular, we describe a generalization of Nauty, a graph isomorphism and canonical labeling algorithm. The generalized version of the Nauty procedure, which we call HNauty, can be used to assign canonical labels to hierarchical graphs or more generally to graphs with multiple edge types. The difference between the Nauty and HNauty procedures is minor, but for completeness, we provide an explanation of the entire HNauty algorithm. Conclusions Hierarchical graphs provide more intuitive formal representations of proteins and other structured molecules with multiple functional components than do the regular graphs of current languages for
Chartrand, Gary
1984-01-01
Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap
Adriaan R. Soetevent
2010-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial discontinuities in firm-level demand may occur. I show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs. I conjecture that this non-existence result holds...
Pim Heijnen; Adriaan Soetevent
2014-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. We derive an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. These graph models of price competition may lead to spatial discontinuities in firm-level demand. We show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs and conjecture that this non-existence result holds more general...
Directory of Open Access Journals (Sweden)
Aleks Kissinger
2014-03-01
Full Text Available String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes", on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.
Gelfand, I M; Shnol, E E
1969-01-01
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu
Creating more effective graphs
Robbins, Naomi B
2012-01-01
A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr
Energy Technology Data Exchange (ETDEWEB)
Lothian, Joshua [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sullivan, Blair D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Baker, Matthew B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Schrock, Jonathan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Poole, Stephen W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2013-10-01
The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of different application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.
DEFF Research Database (Denmark)
Mansutti, Alessio; Miculan, Marino; Peressotti, Marco
2017-01-01
We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly...... also problems which are “mixed” instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give...
Directory of Open Access Journals (Sweden)
Alberto Apostolico
2009-08-01
Full Text Available The Web Graph is a large-scale graph that does not fit in main memory, so that lossless compression methods have been proposed for it. This paper introduces a compression scheme that combines efficient storage with fast retrieval for the information in a node. The scheme exploits the properties of the Web Graph without assuming an ordering of the URLs, so that it may be applied to more general graphs. Tests on some datasets of use achieve space savings of about 10% over existing methods.
Vaidya spacetime in massive gravity's rainbow
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Yaghoub Heydarzade
2017-11-01
Full Text Available In this paper, we will analyze the energy dependent deformation of massive gravity using the formalism of massive gravity's rainbow. So, we will use the Vainshtein mechanism and the dRGT mechanism for the energy dependent massive gravity, and thus analyze a ghost free theory of massive gravity's rainbow. We study the energy dependence of a time-dependent geometry, by analyzing the radiating Vaidya solution in this theory of massive gravity's rainbow. The energy dependent deformation of this Vaidya metric will be performed using suitable rainbow functions.
Cliques, coloring, and satisfiability
Johnson, David S
1996-01-01
The purpose of a DIMACS Challenge is to encourage and coordinate research in the experimental analysis of algorithms. The First DIMACS Challenge encouraged experimental work in the area of network flow and matchings. The Second DIMACS Challenge, on which this volume is based, took place in conjunction with the DIMACS Special Year on Combinatorial Optimization. Addressed here are three difficult combinatorial optimization problems: finding cliques in a graph, coloring the vertices of a graph, and solving instances of the satisfiability problem. These problems were chosen both for their practical interest and because of their theoretical intractability.
Chinese Postman Problem on edge-colored multigraphs
DEFF Research Database (Denmark)
Gutin, Gregory; Jones, Mark; Sheng, Bin
2017-01-01
It is well-known that the Chinese Postman Problem on undirected and directed graphs is polynomial-time solvable. We extend this result to edge-colored multigraphs. Our result is in sharp contrast to the Chinese Postman Problem on mixed graphs, i.e., graphs with directed and undirected edges, for ...
Graph Theory. 1. Fragmentation of Structural Graphs
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Lorentz JÄNTSCHI
2002-12-01
Full Text Available The investigation of structural graphs has many fields of applications in engineering, especially in applied sciences like as applied chemistry and physics, computer sciences and automation, electronics and telecommunication. The main subject of the paper is to express fragmentation criteria in graph using a new method of investigation: terminal paths. Using terminal paths are defined most of the fragmentation criteria that are in use in molecular topology, but the fields of applications are more generally than that, as I mentioned before. Graphical examples of fragmentation are given for every fragmentation criteria. Note that all fragmentation is made with a computer program that implements a routine for every criterion.[1] A web routine for tracing all terminal paths in graph can be found at the address: http://vl.academicdirect.ro/molecular_topology/tpaths/ [1] M. V. Diudea, I. Gutman, L. Jäntschi, Molecular Topology, Nova Science, Commack, New York, 2001, 2002.
Skin Segmentation Based on Graph Cuts
Institute of Scientific and Technical Information of China (English)
HU Zhilan; WANG Guijin; LIN Xinggang; YAN Hong
2009-01-01
Skin segmentation is widely used in many computer vision tasks to improve automated visualiza-tion. This paper presents a graph cuts algorithm to segment arbitrary skin regions from images. The detected face is used to determine the foreground skin seeds and the background non-skin seeds with the color probability distributions for the foreground represented by a single Gaussian model and for the background by a Gaussian mixture model. The probability distribution of the image is used for noise suppression to alle-viate the influence of the background regions having skin-like colors. Finally, the skin is segmented by graph cuts, with the regional parameter y optimally selected to adapt to different images. Tests of the algorithm on many real wodd photographs show that the scheme accurately segments skin regions and is robust against illumination variations, individual skin variations, and cluttered backgrounds.
A graph rewriting programming language for graph drawing
Rodgers, Peter
1998-01-01
This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computationally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools are all text based. Recent developments in graph rewriting systems have produced computationally com...
de Mol, M.J.; Rensink, Arend; Hunt, James J.
This paper introduces an approach for adding graph transformation-based functionality to existing JAVA programs. The approach relies on a set of annotations to identify the intended graph structure, as well as on user methods to manipulate that structure, within the user’s own JAVA class
Cohen, A.M.; Beineke, L.W.; Wilson, R.J.; Cameron, P.J.
2004-01-01
In this chapter we investigate the classification of distance-transitive graphs: these are graphs whose automorphism groups are transitive on each of the sets of pairs of vertices at distance i, for i = 0, 1,.... We provide an introduction into the field. By use of the classification of finite
Joyner, W David
2017-01-01
This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards ad...
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
DEFF Research Database (Denmark)
Husfeldt, Thore
2015-01-01
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...
Packing Degenerate Graphs Greedily
Czech Academy of Sciences Publication Activity Database
Allen, P.; Böttcher, J.; Hladký, J.; Piguet, Diana
2017-01-01
Roč. 61, August (2017), s. 45-51 ISSN 1571-0653 R&D Projects: GA ČR GJ16-07822Y Institutional support: RVO:67985807 Keywords : tree packing conjecture * graph packing * graph processes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics
Generalized connectivity of graphs
Li, Xueliang
2016-01-01
Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Autoregressive Moving Average Graph Filtering
Isufi, Elvin; Loukas, Andreas; Simonetto, Andrea; Leus, Geert
2016-01-01
One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation. The design phi...
Farming of Freshwater Rainbow Trout in Denmark
DEFF Research Database (Denmark)
Jokumsen, Alfred; Svendsen, Lars Moeslund
Textbook on Farming of Freshwater Rainbow Trout in Denmark. Danish edition with the title: Opdræt af regnbueørred i Danmark......Textbook on Farming of Freshwater Rainbow Trout in Denmark. Danish edition with the title: Opdræt af regnbueørred i Danmark...
Perspective on rainbow-ladder truncation
International Nuclear Information System (INIS)
Eichmann, G.; Alkofer, R.; Krassnigg, A.; Cloeet, I. C.; Roberts, C. D.
2008-01-01
Prima facie the systematic implementation of corrections to the rainbow-ladder truncation of QCD's Dyson-Schwinger equations will uniformly reduce in magnitude those calculated mass-dimensioned results for pseudoscalar and vector meson properties that are not tightly constrained by symmetries. The aim and interpretation of studies employing rainbow-ladder truncation are reconsidered in this light
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar
2017-03-06
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar; Leus, Geert
2017-01-01
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Bollobas, Bela
2004-01-01
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A
Parallel algorithms for finding cliques in a graph
International Nuclear Information System (INIS)
Szabo, S
2011-01-01
A clique is a subgraph in a graph that is complete in the sense that each two of its nodes are connected by an edge. Finding cliques in a given graph is an important procedure in discrete mathematical modeling. The paper will show how concepts such as splitting partitions, quasi coloring, node and edge dominance are related to clique search problems. In particular we will discuss the connection with parallel clique search algorithms. These concepts also suggest practical guide lines to inspect a given graph before starting a large scale search.
A short list color proof of Grötzsch's theorem
DEFF Research Database (Denmark)
Thomassen, Carsten
2003-01-01
We give a short proof of the result that every planar graph of girth 5 is 3-choosable and hence also of Grotzsch's theorem saying that every planar triangle-free graph is 3-colorable.......We give a short proof of the result that every planar graph of girth 5 is 3-choosable and hence also of Grotzsch's theorem saying that every planar triangle-free graph is 3-colorable....
Directory of Open Access Journals (Sweden)
Haynes Teresa W.
2014-08-01
Full Text Available A path π = (v1, v2, . . . , vk+1 in a graph G = (V,E is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi ≥ deg(vi+1, where deg(vi denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds
Tailored Random Graph Ensembles
International Nuclear Information System (INIS)
Roberts, E S; Annibale, A; Coolen, A C C
2013-01-01
Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.
Alspach, BR
1985-01-01
This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.
Wilson, Robin J
1985-01-01
Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. This book provides a comprehensive introduction to the subject.
Hyperbolicity in median graphs
Indian Academy of Sciences (India)
mic problems in hyperbolic spaces and hyperbolic graphs have been .... that in general the main obstacle is that we do not know the location of ...... [25] Jonckheere E and Lohsoonthorn P, A hyperbolic geometry approach to multipath routing,.
Uniform Single Valued Neutrosophic Graphs
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S. Broumi
2017-09-01
Full Text Available In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.
Collective Rationality in Graph Aggregation
Endriss, U.; Grandi, U.; Schaub, T.; Friedrich, G.; O'Sullivan, B.
2014-01-01
Suppose a number of agents each provide us with a directed graph over a common set of vertices. Graph aggregation is the problem of computing a single “collective” graph that best represents the information inherent in this profile of individual graphs. We consider this aggregation problem from the
International Nuclear Information System (INIS)
Barra, F.; Gaspard, P.
2001-01-01
We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator that generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms that decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs that converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system that undergoes a diffusion process before it escapes
Snell, Joel
2017-01-01
There are numerous aspects to being non-Caucasian that may not be known by Whites. Persons of color suggest folks who are African, South Americans, Native Americans, Biracial, Asians and others. The question is what do these individuals feel relative to their color and facial characteristics. Eugene Robinson suggest that the future favorable color…
Storying Ubuntu as a rainbow nation
Directory of Open Access Journals (Sweden)
Wonke Buqa
2015-06-01
Full Text Available South Africa is often referred to as the �Rainbow Nation�. This term was coined by Desmond Tutu during the advent of democracy in the country. Tutu stated: �They tried to make us one colour: purple. We say we are the rainbow people! We are the new people of the new South Africa!� This article seeks to answer the question as to whether the Rainbow Nation is a true reflection of Ubuntu in South Africa or whether it is just idealism.
Efficient graph-cut tattoo segmentation
Kim, Joonsoo; Parra, Albert; Li, He; Delp, Edward J.
2015-03-01
Law enforcement is interested in exploiting tattoos as an information source to identify, track and prevent gang-related crimes. Many tattoo image retrieval systems have been described. In a retrieval system tattoo segmentation is an important step for retrieval accuracy since segmentation removes background information in a tattoo image. Existing segmentation methods do not extract the tattoo very well when the background includes textures and color similar to skin tones. In this paper we describe a tattoo segmentation approach by determining skin pixels in regions near the tattoo. In these regions graph-cut segmentation using a skin color model and a visual saliency map is used to find skin pixels. After segmentation we determine which set of skin pixels are connected with each other that form a closed contour including a tattoo. The regions surrounded by the closed contours are considered tattoo regions. Our method segments tattoos well when the background includes textures and color similar to skin.
Proxy Graph: Visual Quality Metrics of Big Graph Sampling.
Nguyen, Quan Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra
2017-06-01
Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.
Fractional graph theory a rational approach to the theory of graphs
Scheinerman, Edward R
2013-01-01
A unified treatment of the most important results in the study of fractional graph concepts, this volume explores the various ways in which integer-valued concepts can be modified to derive nonintegral values. It begins with the general fractional theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics. Subjects include fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, and fractional isomorphism. The final chapter examines additional topics such as fractional domination, fractional intersection numbers
On some covering graphs of a graph
Directory of Open Access Journals (Sweden)
Shariefuddin Pirzada
2016-10-01
Full Text Available For a graph $G$ with vertex set $V(G=\\{v_1, v_2, \\dots, v_n\\}$, let $S$ be the covering set of $G$ having the maximum degree over all the minimum covering sets of $G$. Let $N_S[v]=\\{u\\in S : uv \\in E(G \\}\\cup \\{v\\}$ be the closed neighbourhood of the vertex $v$ with respect to $S.$ We define a square matrix $A_S(G= (a_{ij},$ by $a_{ij}=1,$ if $\\left |N_S[v_i]\\cap N_S[v_j] \\right| \\geq 1, i\
News from Online: A Spectrum of Color
Sweeney Judd, Carolyn
1999-06-01
Thomas Chasteen's site ( http://www.shsu.edu/~chm_tgc/sounds/sound.html) shows how to separate colors using a tuneable monochromator. This graphic comes from his monochromator animation ( http://www.shsu.edu/~chemistry/monochromator/mono.gif). Science Media's site ( http://www.scimedia.com/index.html#scimedia) includes spectroscopy tutorials by Brian Tissue. This graphic can be found at http://www.scimedia.com/chem-ed/light/graphics/em-rad.gif (©1998 B. M. Tissue, www.scimedia.com). All the colors in the rainbow! Now that is a good place to start. Go to About Rainbows ( http://www.unidata.ucar.edu/staff/blynds/rnbw.html), a tutorial from astronomer Beverly Lynds, working with the University Corporation for Atmospheric Research. The tutorial begins with a historical perspective, complete with a sketch by René Descartes in 1637. The bibliography makes this tutorial a good starting point for color exploration. About Rainbows brings you questions to explorefor example, "What happens when you look at a rainbow through dark glasses?" Try the links to these other sites. Project SkyMath: Making Mathematical Connections ( http://www.unidata.ucar.edu/staff/blynds/Skymath.html) is especially for the middle school student. Reproducible masters of these teaching modules can be printed in English and Spanish. From Project SkyMath, you can go to Blue-Skies, a user-friendly graphical interface from The Weather Underground at the University of Michigan ( http://groundhog.sprl.umich.edu/BS.html). And speaking of blue skies, look at a great site, Why is the Sky Blue at http://acept.la.asu.edu/PiN/act/sky/sky.shtml. This is a super site from the Arizona Collaborative for Excellence in the Preparation of Teachers, by the Department of Physics and Astronomy at Arizona State University. If you go to Patterns in Nature: Light and Optics at http://acept.la.asu.edu/PiN/act/activities.shtml, plan to spend some time, for it is wonderful. Another link from the About Rainbows tutorial goes to
Fundamentals of algebraic graph transformation
Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele
2006-01-01
Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...
The STAPL Parallel Graph Library
Harshvardhan,
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.
Strong oriented chromatic number of planar graphs without short cycles
Directory of Open Access Journals (Sweden)
Mickaël Montassier
2008-01-01
Full Text Available Let M be an additive abelian group. A strong oriented coloringof an oriented graph G is a mapping φ from V(G to M such that (1 φ(u ≠ φ(v whenever uv is an arc in G and (2 φ(v - φ(u ≠ -(φ(t - φ(z whenever uv and zt are two arcs in G. We say that G has a M-strong-oriented coloring. The strong oriented chromatic number of an oriented graph, denoted by χ s (G, is the minimal order of a group M, such that G has M-strong-oriented coloring. This notion was introduced by Nešetřil and Raspaud. In this paper, we pose the following problem: Let i ≥ 4 be an integer. Let G be an oriented planar graph without cycles of lengths 4 to i. Which is the strong oriented chromatic number of G ? Our aim is to determine the impact of triangles on the strong oriented coloring. We give some hints of answers to this problem by proving that: (1 the strong oriented chromatic number of any oriented planar graph without cycles of lengths 4 to 12 is at most 7, and (2 the strong oriented chromatic number of any oriented planar graph without cycles of length 4 or 6 is at most 19.
White, AT
1985-01-01
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.
Ribes, Luis
2017-01-01
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open quest...
Subdominant pseudoultrametric on graphs
Energy Technology Data Exchange (ETDEWEB)
Dovgoshei, A A; Petrov, E A [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)
2013-08-31
Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.
Quantitative graph theory mathematical foundations and applications
Dehmer, Matthias
2014-01-01
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat
Cheung, King Sing
2014-01-01
Petri nets are a formal and theoretically rich model for the modelling and analysis of systems. A subclass of Petri nets, augmented marked graphs possess a structure that is especially desirable for the modelling and analysis of systems with concurrent processes and shared resources.This monograph consists of three parts: Part I provides the conceptual background for readers who have no prior knowledge on Petri nets; Part II elaborates the theory of augmented marked graphs; finally, Part III discusses the application to system integration. The book is suitable as a first self-contained volume
Dayal, Amit; Brock, David
2018-01-01
Prashant Chandrasekar, a lead developer for the Social Interactome project, has tasked the team with creating a graph representation of the data collected from the social networks involved in that project. The data is currently stored in a MySQL database. The client requested that the graph database be Cayley, but after a literature review, Neo4j was chosen. The reasons for this shift will be explained in the design section. Secondarily, the team was tasked with coming up with three scena...
Stevanovic, Dragan
2015-01-01
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-01-01
Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most
Using Graph and Vertex Entropy to Compare Empirical Graphs with Theoretical Graph Models
Directory of Open Access Journals (Sweden)
Tomasz Kajdanowicz
2016-09-01
Full Text Available Over the years, several theoretical graph generation models have been proposed. Among the most prominent are: the Erdős–Renyi random graph model, Watts–Strogatz small world model, Albert–Barabási preferential attachment model, Price citation model, and many more. Often, researchers working with real-world data are interested in understanding the generative phenomena underlying their empirical graphs. They want to know which of the theoretical graph generation models would most probably generate a particular empirical graph. In other words, they expect some similarity assessment between the empirical graph and graphs artificially created from theoretical graph generation models. Usually, in order to assess the similarity of two graphs, centrality measure distributions are compared. For a theoretical graph model this means comparing the empirical graph to a single realization of a theoretical graph model, where the realization is generated from the given model using an arbitrary set of parameters. The similarity between centrality measure distributions can be measured using standard statistical tests, e.g., the Kolmogorov–Smirnov test of distances between cumulative distributions. However, this approach is both error-prone and leads to incorrect conclusions, as we show in our experiments. Therefore, we propose a new method for graph comparison and type classification by comparing the entropies of centrality measure distributions (degree centrality, betweenness centrality, closeness centrality. We demonstrate that our approach can help assign the empirical graph to the most similar theoretical model using a simple unsupervised learning method.
Handbook of graph grammars and computing by graph transformation
Engels, G; Kreowski, H J; Rozenberg, G
1999-01-01
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran
Topics in graph theory graphs and their Cartesian product
Imrich, Wilfried; Rall, Douglas F
2008-01-01
From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.
Colored Tensor Models - a Review
Directory of Open Access Journals (Sweden)
Razvan Gurau
2012-04-01
Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.
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Bisseling, R.H.; Byrka, J.; Cerav-Erbas, S.; Gvozdenovic, N.; Lorenz, M.; Pendavingh, R.A.; Reeves, C.; Röger, M.; Verhoeven, A.; Berg, van den J.B.; Bhulai, S.; Hulshof, J.; Koole, G.; Quant, C.; Williams, J.F.
2006-01-01
Splitting a large software system into smaller and more manageable units has become an important problem for many organizations. The basic structure of a software system is given by a directed graph with vertices representing the programs of the system and arcs representing calls from one program to
Budhiraja, A.S.; Mukherjee, D.; Wu, R.
2017-01-01
We consider a variation of the supermarket model in which the servers can communicate with their neighbors and where the neighborhood relationships are described in terms of a suitable graph. Tasks with unit-exponential service time distributions arrive at each vertex as independent Poisson
DEFF Research Database (Denmark)
Kucharik, Marcel; Hofacker, Ivo; Stadler, Peter
2014-01-01
of the folding free energy landscape, however, can provide the relevant information. Results We introduce the basin hopping graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect...
The STAPL Parallel Graph Library
Harshvardhan,; Fidel, Adam; Amato, Nancy M.; Rauchwerger, Lawrence
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable
Energy Technology Data Exchange (ETDEWEB)
Winlaw, Manda [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); De Sterck, Hans [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoffrey [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-26
In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.
Groupies in multitype random graphs
Shang, Yilun
2016-01-01
A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erd?s-R?nyi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.
Groupies in multitype random graphs.
Shang, Yilun
2016-01-01
A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erdős-Rényi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.
Temporal Representation in Semantic Graphs
Energy Technology Data Exchange (ETDEWEB)
Levandoski, J J; Abdulla, G M
2007-08-07
A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.
Quantum walks on quotient graphs
International Nuclear Information System (INIS)
Krovi, Hari; Brun, Todd A.
2007-01-01
A discrete-time quantum walk on a graph Γ is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup
A generalization of total graphs
Indian Academy of Sciences (India)
M Afkhami
2018-04-12
Apr 12, 2018 ... product of any lower triangular matrix with the transpose of any element of U belongs to U. The ... total graph of R, which is denoted by T( (R)), is a simple graph with all elements of R as vertices, and ...... [9] Badawi A, On dot-product graph of a commutative ring, Communications in Algebra 43 (2015). 43–50.
Graph transformation tool contest 2008
Rensink, Arend; van Gorp, Pieter
This special section is the outcome of the graph transformation tool contest organised during the Graph-Based Tools (GraBaTs) 2008 workshop, which took place as a satellite event of the International Conference on Graph Transformation (ICGT) 2008. The contest involved two parts: three “off-line case
Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Luo, Xiangfeng
2015-12-01
Graph mining has been a popular research area because of its numerous application scenarios. Many unstructured and structured data can be represented as graphs, such as, documents, chemical molecular structures, and images. However, an issue in relation to current research on graphs is that they cannot adequately discover the topics hidden in graph-structured data which can be beneficial for both the unsupervised learning and supervised learning of the graphs. Although topic models have proved to be very successful in discovering latent topics, the standard topic models cannot be directly applied to graph-structured data due to the "bag-of-word" assumption. In this paper, an innovative graph topic model (GTM) is proposed to address this issue, which uses Bernoulli distributions to model the edges between nodes in a graph. It can, therefore, make the edges in a graph contribute to latent topic discovery and further improve the accuracy of the supervised and unsupervised learning of graphs. The experimental results on two different types of graph datasets show that the proposed GTM outperforms the latent Dirichlet allocation on classification by using the unveiled topics of these two models to represent graphs.
Pate, Monica; Raclariu, Ana-Maria; Strominger, Andrew
2017-01-01
A transient color flux across null infinity in classical Yang-Mills theory is considered. It is shown that a pair of test `quarks' initially in a color singlet generically acquire net color as a result of the flux. A nonlinear formula is derived for the relative color rotation of the quarks. For weak color flux the formula linearizes to the Fourier transform of the soft gluon theorem. This color memory effect is the Yang-Mills analog of the gravitational memory effect.
Algorithms for Planar Graphs and Graphs in Metric Spaces
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
structural properties that can be exploited. For instance, a road network or a wire layout on a microchip is typically (near-)planar and distances in the network are often defined w.r.t. the Euclidean or the rectilinear metric. Specialized algorithms that take advantage of such properties are often orders...... of magnitude faster than the corresponding algorithms for general graphs. The first and main part of this thesis focuses on the development of efficient planar graph algorithms. The most important contributions include a faster single-source shortest path algorithm, a distance oracle with subquadratic...... for geometric graphs and graphs embedded in metric spaces. Roughly speaking, the stretch factor is a real value expressing how well a (geo-)metric graph approximates the underlying complete graph w.r.t. distances. We give improved algorithms for computing the stretch factor of a given graph and for augmenting...
Harary, Frank
2015-01-01
Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc
Spectral fluctuations of quantum graphs
International Nuclear Information System (INIS)
Pluhař, Z.; Weidenmüller, H. A.
2014-01-01
We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry
Dynamic Representations of Sparse Graphs
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Fagerberg, Rolf
1999-01-01
We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....
Domination criticality in product graphs
Directory of Open Access Journals (Sweden)
M.R. Chithra
2015-07-01
Full Text Available A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G with connected domination number, γc(G=2,3 and characterize such graphs. Also, we characterize the k−γ-vertex (edge critical graphs and k−γc-vertex (edge critical graphs for k=2,3 where γ denotes the domination number of G. We also discuss the vertex criticality in grids.
Graph Creation, Visualisation and Transformation
Directory of Open Access Journals (Sweden)
Maribel Fernández
2010-03-01
Full Text Available We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting.
Nonsingular universe in massive gravity's rainbow
Hendi, S. H.; Momennia, M.; Eslam Panah, B.; Panahiyan, S.
2017-06-01
One of the fundamental open questions in cosmology is whether we can regard the universe evolution without singularity like a Big Bang or a Big Rip. This challenging subject stimulates one to regard a nonsingular universe in the far past with an arbitrarily large vacuum energy. Considering the high energy regime in the cosmic history, it is believed that Einstein gravity should be corrected to an effective energy dependent theory which could be acquired by gravity's rainbow. On the other hand, employing massive gravity provided us with solutions to some of the long standing fundamental problems of cosmology such as cosmological constant problem and self acceleration of the universe. Considering these aspects of gravity's rainbow and massive gravity, in this paper, we initiate studying FRW cosmology in the massive gravity's rainbow formalism. At first, we show that although massive gravity modifies the FRW cosmology, but it does not itself remove the big bang singularity. Then, we generalize the massive gravity to the case of energy dependent spacetime and find that massive gravity's rainbow can remove the early universe singularity. We bring together all the essential conditions for having a nonsingular universe and the effects of both gravity's rainbow and massive gravity generalizations on such criteria are determined.
Analysis of the Perfect Table Fuzzy Rainbow Tradeoff
Directory of Open Access Journals (Sweden)
Byoung-Il Kim
2014-01-01
Full Text Available Cryptanalytic time memory tradeoff algorithms are tools for inverting one-way functions, and they are used in practice to recover passwords that restrict access to digital documents. This work provides an accurate complexity analysis of the perfect table fuzzy rainbow tradeoff algorithm. Based on the analysis results, we show that the lesser known fuzzy rainbow tradeoff performs better than the original rainbow tradeoff, which is widely believed to be the best tradeoff algorithm. The fuzzy rainbow tradeoff can attain higher online efficiency than the rainbow tradeoff and do so at a lower precomputation cost.
Graph Sampling for Covariance Estimation
Chepuri, Sundeep Prabhakar
2017-04-25
In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non-parametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.
Hendrix, William; Jenkins, John; Padmanabhan, Kanchana; Chakraborty, Arpan
2014-01-01
Practical Graph Mining with R presents a "do-it-yourself" approach to extracting interesting patterns from graph data. It covers many basic and advanced techniques for the identification of anomalous or frequently recurring patterns in a graph, the discovery of groups or clusters of nodes that share common patterns of attributes and relationships, the extraction of patterns that distinguish one category of graphs from another, and the use of those patterns to predict the category of new graphs. Hands-On Application of Graph Data Mining Each chapter in the book focuses on a graph mining task, such as link analysis, cluster analysis, and classification. Through applications using real data sets, the book demonstrates how computational techniques can help solve real-world problems. The applications covered include network intrusion detection, tumor cell diagnostics, face recognition, predictive toxicology, mining metabolic and protein-protein interaction networks, and community detection in social networks. De...
Canonical Labelling of Site Graphs
Directory of Open Access Journals (Sweden)
Nicolas Oury
2013-06-01
Full Text Available We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an extension of Hopcroft's partition refinement algorithm. All run in quadratic worst case time individually. However, one of the edge enumeration algorithms runs in sub-quadratic time for graphs with "many" automorphisms, and the partition refinement algorithm runs in sub-quadratic time for graphs with "few" bisimulation equivalences. This suite of algorithms was chosen based on the expectation that graphs fall in one of those two categories. If that is the case, a combined algorithm runs in sub-quadratic worst case time. Whether this expectation is reasonable remains an interesting open problem.
Several classes of graphs and their r-dynamic chromatic numbers
Dafik; Meganingtyas, D. E. W.; Dwidja Purnomo, K.; Dicky Tarmidzi, M.; Hesti Agustin, Ika
2017-06-01
Let G be a simple, connected and undirected graph. Let r, k be natural numbers. By a proper k-coloring of a graph G, we mean a map c : V (G) → S, where |S| = k, such that any two adjacent vertices receive different colors. An r-dynamic k-coloring is a proper k-coloring c of G such that |c(N(v))| ≥ min{r, d(v)} for each vertex v in V (G), where N(v) is the neighborhood of v and c(S) = {c(v) : v ∈ S} for a vertex subset S. The r-dynamic chromatic number, written as χ r (G), is the minimum k such that G has an r-dynamic k-coloring. By simple observation it is easy to see that χ r (G) ≤ χ r+1(G), however χ r+1(G) - χ r (G) does not always show a small difference for any r. Thus, finding an exact value of χ r (G) is significantly useful. In this paper, we will study some of them especially when G are prism graph, three-cyclical ladder graph, joint graph and circulant graph.
Learning heat diffusion graphs
Thanou, Dorina; Dong, Xiaowen; Kressner, Daniel; Frossard, Pascal
2016-01-01
Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or pre-determined sensing arrangements, like in road transportation networks for example. In general though, the data structure is not readily available and becomes pretty difficult to define. In particular, the global smoothness assumptions, that most of the...
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Understanding Charts and Graphs.
1987-07-28
Farenheit degrees, which have no Onaturalo zero ); finally, ratio scales have numbers that are ordered so that the magnitudes of differences are important and...system. They have to do with the very nature of how marks serve as meaningful symbols. In the ideal case, a chart or graph will be absolutely unambiguous...and these laws comprise this principle (see Stevens, 1974). Absolute discriminability: A minimal magnitude of a mark is necessary for it to be detected
Thermodynamic phase transition of a black hole in rainbow gravity
Directory of Open Access Journals (Sweden)
Zhong-Wen Feng
2017-09-01
Full Text Available In this letter, using the rainbow functions that were proposed by Magueijo and Smolin, we investigate the thermodynamics and the phase transition of rainbow Schwarzschild black hole. First, we calculate the rainbow gravity corrected Hawking temperature. From this modification, we then derive the local temperature, free energy, and other thermodynamic quantities in an isothermal cavity. Finally, we analyze the critical behavior, thermodynamic stability, and phase transition of the rainbow Schwarzschild black hole. The results show that the rainbow gravity can stop the Hawking radiation in the final stages of black holes' evolution and lead to the remnants of black holes. Furthermore, one can observe that the rainbow Schwarzschild black hole has one first-order phase transition, two second-order phase transitions, and three Hawking–Page-type phase transitions in the framework of rainbow gravity theory.
Graphs cospectral with a friendship graph or its complement
Directory of Open Access Journals (Sweden)
Alireza Abdollahi
2013-12-01
Full Text Available Let $n$ be any positive integer and let $F_n$ be the friendship (or Dutch windmill graph with $2n+1$ vertices and $3n$ edges. Here we study graphs with the same adjacency spectrum as the $F_n$. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let $G$ be a graph cospectral with $F_n$. Here we prove that if $G$ has no cycle of length $4$ or $5$, then $Gcong F_n$. Moreover if $G$ is connected and planar then $Gcong F_n$.All but one of connected components of $G$ are isomorphic to $K_2$.The complement $overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues, that is, if $overline{F_n}$ is cospectral with a graph $H$, then $Hcong overline{F_n}$.
Global rainbow refractometry for droplet temperature measurement
International Nuclear Information System (INIS)
Pascal Lemaitre; Emmanuel Porcheron; Amandine Nuboer; Philippe Brun; Pierre Cornet; Jeanne Malet; Jacques Vendel; Laurent Bouilloux; Gerard Grehan
2005-01-01
Full text of publication follows: In order to establish an accurate database to characterize the heat and mass transfers between a spray and the atmosphere with thermal-hydraulic conditions representative of a hypothetical nuclear reactor accident in the containment enclosure of a pressurized water reactor (PWR), the French Institut de Radioprotection et de Surete Nucleaire (IRSN) has developed the TOSQAN experimental facility. This experiment is highly instrumented with non-intrusive diagnostics allowing to measure droplet size and velocity and gas concentrations [1]. The aim of this work is to present the Global Rainbow Thermometry (GRT), which is an advanced non-intrusive optical diagnostic, developed to measure the mean temperature of a set of falling droplets, in a measurement volume of 1 cm 3 . The final paper will be divided in three parts. In the first one, we will explain the principle of the rainbow formation and how droplet temperature can be deduced from the rainbow analysis [2]. This part will be illustrated with the theoretical background on the rainbow and numerical simulations of the global rainbow. The second part will be devoted to present the global rainbow experimental set-up we have developed on optical table, its experimental qualification and finally its implementation on the TOSQAN facility [3]. Finally, we will present the temperature measurements achieved in TOSQAN for thermal-hydraulic conditions representative of a hypothetical nuclear reactor accident. These measurements are useful to characterize the heat and mass transfers between the spraying droplets and the air-steam mixture composing the atmosphere. This analysis will be exposed in a two companion papers. References: [1] E. Porcheron, P. Brun, P. Cornet, J. Malet, J. Vendel. Optical diagnostics applied for single and multi-phase flow characterization in the TOSQAN facility dedicated for thermal hydraulic containment studies. NURETH-10 Seoul, Korea, October 5-9, 2003. [2] P
Global rainbow refractometry for droplet temperature measurement
Energy Technology Data Exchange (ETDEWEB)
Pascal Lemaitre; Emmanuel Porcheron; Amandine Nuboer; Philippe Brun; Pierre Cornet; Jeanne Malet; Jacques Vendel; Laurent Bouilloux [Institut de Radioprotection et de Surete Nucleaire DSU/SERAC, BP 68, 91192 Gif-sur-Yvette Cedex (France); Gerard Grehan [UMR 6614 CORIA, Laboratoire d' Electromagnetisme et Systemes Particulaires Site Universitaire du Madrillet, Avenue de l' universite BP 12, 76 801 Saint Etienne du Rouvray Cedex, (France)
2005-07-01
Full text of publication follows: In order to establish an accurate database to characterize the heat and mass transfers between a spray and the atmosphere with thermal-hydraulic conditions representative of a hypothetical nuclear reactor accident in the containment enclosure of a pressurized water reactor (PWR), the French Institut de Radioprotection et de Surete Nucleaire (IRSN) has developed the TOSQAN experimental facility. This experiment is highly instrumented with non-intrusive diagnostics allowing to measure droplet size and velocity and gas concentrations [1]. The aim of this work is to present the Global Rainbow Thermometry (GRT), which is an advanced non-intrusive optical diagnostic, developed to measure the mean temperature of a set of falling droplets, in a measurement volume of 1 cm{sup 3}. The final paper will be divided in three parts. In the first one, we will explain the principle of the rainbow formation and how droplet temperature can be deduced from the rainbow analysis [2]. This part will be illustrated with the theoretical background on the rainbow and numerical simulations of the global rainbow. The second part will be devoted to present the global rainbow experimental set-up we have developed on optical table, its experimental qualification and finally its implementation on the TOSQAN facility [3]. Finally, we will present the temperature measurements achieved in TOSQAN for thermal-hydraulic conditions representative of a hypothetical nuclear reactor accident. These measurements are useful to characterize the heat and mass transfers between the spraying droplets and the air-steam mixture composing the atmosphere. This analysis will be exposed in a two companion papers. References: [1] E. Porcheron, P. Brun, P. Cornet, J. Malet, J. Vendel. Optical diagnostics applied for single and multi-phase flow characterization in the TOSQAN facility dedicated for thermal hydraulic containment studies. NURETH-10 Seoul, Korea, October 5-9, 2003. [2] P
Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs
DEFF Research Database (Denmark)
Bensmail, Julien; Renault, Gabriel
2016-01-01
An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪⋯∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently co...
X-Graphs: Language and Algorithms for Heterogeneous Graph Streams
2017-09-01
are widely used by academia and industry. 15. SUBJECT TERMS Data Analytics, Graph Analytics, High-Performance Computing 16. SECURITY CLASSIFICATION...form the core of the DeepDive Knowledge Construction System. 2 INTRODUCTION The goal of the X-Graphs project was to develop computational techniques...memory multicore machine. Ringo is based on Snap.py and SNAP, and uses Python . Ringo now allows the integration of Delite DSL Framework Graph
Studies on the metabolism of astaxanthin in the rainbow trout (Salmo gairdneri)
International Nuclear Information System (INIS)
Al-Khalifah, A.S.
1986-01-01
Racemic astaxanthin was fed to rainbow trout (Salmo gairdneri) for 2, 4, and 6 weeks. The fish showed a bright pink coloration of the skin and flesh; the highest amount of astaxanthin was found in the skin of fish fed the test diet for six weeks. Lutein, 3-epilutein, and zeaxanthin were also detected in the flesh and skin; it was concluded that astaxanthin was converted to zeaxanthin in the skin. The mean vitamin A content of the liver was determined; the ratio of vitamin A 1 :vitamin A 2 was approximately 1:3. Retinol and 3,4-dehydroretinol were extracted from the intestine of rainbow trout low in vitamin A, after force feeding with astaxanthin using a feeding tube. Antibiotic-treated fish had no marked difference in vitamin A content compared with a control group that received no antibiotic. This proves that astaxanthin was converted to vitamin A in fish depleted of vitamin A, that microorganisms were not involved in the conversion, and that conversion occurred in the intestine. An in vitro study using 3 H 3S, 3S'-astaxanthin incubated with duodenal and ileal segments of the intestine provided HLPC and radioisotope data, which showed that rainbow trout were able to bioconvert astaxanthin to vitamin A
Heuristics for the Robust Coloring Problem
Directory of Open Access Journals (Sweden)
Miguel Ángel Gutiérrez Andrade
2011-03-01
Full Text Available Let $G$ and $\\bar{G}$ be complementary graphs. Given a penalty function defined on the edges of $G$, we will say that the rigidity of a $k$-coloring of $G$ is the sum of the penalties of the edges of G joining vertices of the same color. Based on the previous definition, the Robust Coloring Problem (RCP is stated as the search of the minimum rigidity $k$-coloring. In this work a comparison of heuristics based on simulated annealing, GRASP and scatter search is presented. These are the best results for the RCP that have been obtained.
Endomorphisms of graph algebras
DEFF Research Database (Denmark)
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D...... that the restriction to the diagonal MASA of an automorphism which globally preserves both D_E and the core AF-subalgebra eventually commutes with the corresponding one-sided shift. Secondly, we exhibit several properties of proper endomorphisms, investigate invertibility of localized endomorphisms both on C...
Yap, Hian-Poh
1996-01-01
This book provides an up-to-date and rapid introduction to an important and currently active topic in graph theory. The author leads the reader to the forefront of research in this area. Complete and easily readable proofs of all the main theorems, together with numerous examples, exercises and open problems are given. The book is suitable for use as a textbook or as seminar material for advanced undergraduate and graduate students. The references are comprehensive and so it will also be useful for researchers as a handbook.
Graph Algorithm Animation with Grrr
Rodgers, Peter; Vidal, Natalia
2000-01-01
We discuss geometric positioning, highlighting of visited nodes and user defined highlighting that form the algorithm animation facilities in the Grrr graph rewriting programming language. The main purpose of animation was initially for the debugging and profiling of Grrr code, but recently it has been extended for the purpose of teaching algorithms to undergraduate students. The animation is restricted to graph based algorithms such as graph drawing, list manipulation or more traditional gra...
Optimization Problems on Threshold Graphs
Directory of Open Access Journals (Sweden)
Elena Nechita
2010-06-01
Full Text Available During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predeterminate properties, as well as combinations of such decompositions. In this paper we characterize threshold graphs using the weakly decomposition, determine: density and stability number, Wiener index and Wiener polynomial for threshold graphs.
Eulerian Graphs and Related Topics
Fleischner, Herbert
1990-01-01
The two volumes comprising Part 1 of this work embrace the theme of Eulerian trails and covering walks. They should appeal both to researchers and students, as they contain enough material for an undergraduate or graduate graph theory course which emphasizes Eulerian graphs, and thus can be read by any mathematician not yet familiar with graph theory. But they are also of interest to researchers in graph theory because they contain many recent results, some of which are only partial solutions to more general problems. A number of conjectures have been included as well. Various problems (such a
Rainbows: Mie computations and the Airy approximation.
Wang, R T; van de Hulst, H C
1991-01-01
Efficient and accurate computation of the scattered intensity pattern by the Mie formulas is now feasible for size parameters up to x = 50,000 at least, which in visual light means spherical drops with diameters up to 6 mm. We present a method for evaluating the Mie coefficients from the ratios between Riccati-Bessel and Neumann functions of successive order. We probe the applicability of the Airy approximation, which we generalize to rainbows of arbitrary p (number of internal reflections = p - 1), by comparing the Mie and Airy intensity patterns. Millimeter size water drops show a match in all details, including the position and intensity of the supernumerary maxima and the polarization. A fairly good match is still seen for drops of 0.1 mm. A small spread in sizes helps to smooth out irrelevant detail. The dark band between the rainbows is used to test more subtle features. We conclude that this band contains not only externally reflected light (p = 0) but also a sizable contribution f rom the p = 6 and p = 7 rainbows, which shift rapidly with wavelength. The higher the refractive index, the closer both theories agree on the first primary rainbow (p = 2) peak for drop diameters as small as 0.02 mm. This may be useful in supporting experimental work.
Molecular characterization of rainbow trout, Oncorhynchus mykiss ...
Indian Academy of Sciences (India)
Molecular Genetics Laboratory, Directorate of Coldwater Fisheries Research, Bhimtal 263 ... Mir J. I., Ali S., Patiyal R. S. and Singh A. K. 2015 Molecular characterization of rainbow trout, ..... 5 × 106 MCMC repeats for final sampling of data. .... enhancing aquaculture productivity in the coldwater regions. ... simulation study.
Bath vaccination of rainbow trout against yersiniosis
DEFF Research Database (Denmark)
Raida, Martin Kristian; Buchmann, Kurt
2007-01-01
disease (ERM), was investigated at 5, 15 and 25° C. Rainbow trout fry were kept at controlled temperatures for two month before they were immersed in a commercial Yersinia ruckeri O1 bacterin for 10 minutes. Control groups were sham vaccinated using pure water. Fish were challenged with Yersinia ruckeri O...
Molecular characterization of rainbow trout, Oncorhynchus mykiss
Indian Academy of Sciences (India)
Home; Journals; Journal of Genetics; Volume 94; Online resources. Molecular characterization of rainbow trout, Oncorhynchus mykiss (Walbaum, 1792) stocks in India. Ashoktaru Barat Prabhati K. Sahoo Rohit Kumar Javaid I. Mir Shahnawaz Ali Rabindar S. Patiyal Atul K. Singh. Volume 94 Online resources 2015 pp e13- ...
Energy Technology Data Exchange (ETDEWEB)
Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?
Directory of Open Access Journals (Sweden)
Mehmet Fatih Öçal
2017-01-01
Full Text Available Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students’ learning during graphing functions. However, the display of graphs of functions that students sketched by hand may be relatively different when compared to the correct forms sketched using graphing software. The possible misleading effects of this situation brought a discussion of a misconception (asymptote misconception on graphing functions. The purpose of this study is two- fold. First of all, this study investigated whether using graphing software (GeoGebra in this case helps students to determine and resolve this misconception in calculus classrooms. Second, the reasons for this misconception are sought. The multiple case study was utilized in this study. University students in two calculus classrooms who received instructions with (35 students or without GeoGebra assisted instructions (32 students were compared according to whether they fell into this misconception on graphing basic functions (1/x, lnx, ex. In addition, students were interviewed to reveal the reasons behind this misconception. Data were analyzed by means of descriptive and content analysis methods. The findings indicated that those who received GeoGebra assisted instruction were better in resolving it. In addition, the reasons behind this misconception were found to be teacher-based, exam-based and some other factors.
A simple proof of orientability in colored group field theory.
Caravelli, Francesco
2012-01-01
Group field theory is an emerging field at the boundary between Quantum Gravity, Statistical Mechanics and Quantum Field Theory and provides a path integral for the gluing of n-simplices. Colored group field theory has been introduced in order to improve the renormalizability of the theory and associates colors to the faces of the simplices. The theory of crystallizations is instead a field at the boundary between graph theory and combinatorial topology and deals with n-simplices as colored graphs. Several techniques have been introduced in order to study the topology of the pseudo-manifold associated to the colored graph. Although of the similarity between colored group field theory and the theory of crystallizations, the connection between the two fields has never been made explicit. In this short note we use results from the theory of crystallizations to prove that color in group field theories guarantees orientability of the piecewise linear pseudo-manifolds associated to each graph generated perturbatively. Colored group field theories generate orientable pseudo-manifolds. The origin of orientability is the presence of two interaction vertices in the action of colored group field theories. In order to obtain the result, we made the connection between the theory of crystallizations and colored group field theory.
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
Said Broumi; Mohamed Talea; Assia Bakali; Florentin Smarandache
2016-01-01
In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.
Mulligan, Jeffrey B.
2017-01-01
A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. The difficulty addressed here is the fact that, because of metamerism, we cannot know with certainty the spectrum that produced a particular color solely on the basis of sensory data. Knowledge of the spectrum is not required to compute additive mixture of colors, but is critical for subtractive (multiplicative) mixture. Therefore, we cannot predict with certainty the multiplicative interactions between colors based solely on sensory data. There are two potential applications of a color algebra: first, to aid modeling phenomena of human visual perception, such as color constancy and transparency; and, second, to provide better models of the interactions of lights and surfaces for computer graphics rendering.
National Aeronautics and Space Administration — Satellite-derived Ocean Color Data sets from historical and currently operational NASA and International Satellite missions including the NASA Coastal Zone Color...
Şahin, Ebru
1998-01-01
Ankara : Bilkent University, Department of Interior Architecture and Environmental Design and Institute of Fine Arts, 1998. Thesis (Ph.D) -- Bilkent University, 1998 Includes bibliographical refences. In this study, visual aspects of color and neurophysiological processes involved in the phenomenon, language of color and color models were explained in addition to the discussion of different ideas, orientations and previous works behind the subject of matter. Available color ...
On an edge partition and root graphs of some classes of line graphs
Directory of Open Access Journals (Sweden)
K Pravas
2017-04-01
Full Text Available The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line graph of a graph $G$ into the edge sets of the Gallai and anti-Gallai graphs of $G$. Based on this, an optimal algorithm to find the root graph of a line graph is obtained. Moreover, root graphs of diameter-maximal, distance-hereditary, Ptolemaic and chordal graphs are also discussed.
Phase rainbow refractometry for accurate droplet variation characterization.
Wu, Yingchun; Promvongsa, Jantarat; Saengkaew, Sawitree; Wu, Xuecheng; Chen, Jia; Gréhan, Gérard
2016-10-15
We developed a one-dimensional phase rainbow refractometer for the accurate trans-dimensional measurements of droplet size on the micrometer scale as well as the tiny droplet diameter variations at the nanoscale. The dependence of the phase shift of the rainbow ripple structures on the droplet variations is revealed. The phase-shifting rainbow image is recorded by a telecentric one-dimensional rainbow imaging system. Experiments on the evaporating monodispersed droplet stream show that the phase rainbow refractometer can measure the tiny droplet diameter changes down to tens of nanometers. This one-dimensional phase rainbow refractometer is capable of measuring the droplet refractive index and diameter, as well as variations.
The planar cubic Cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Groupies in random bipartite graphs
Yilun Shang
2010-01-01
A vertex $v$ of a graph $G$ is called a groupie if its degree is notless than the average of the degrees of its neighbors. In thispaper we study the influence of bipartition $(B_1,B_2)$ on groupiesin random bipartite graphs $G(B_1,B_2,p)$ with both fixed $p$ and$p$ tending to zero.
Nested Dynamic Condition Response Graphs
DEFF Research Database (Denmark)
Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs
2012-01-01
We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner...
Bell inequalities for graph states
International Nuclear Information System (INIS)
Toth, G.; Hyllus, P.; Briegel, H.J.; Guehne, O.
2005-01-01
Full text: In the last years graph states have attracted an increasing interest in the field of quantum information theory. Graph states form a family of multi-qubit states which comprises many popular states such as the GHZ states and the cluster states. They also play an important role in applications. For instance, measurement based quantum computation uses graph states as resources. From a theoretical point of view, it is remarkable that graph states allow for a simple description in terms of stabilizing operators. In this contribution, we investigate the non-local properties of graph states. We derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positively of the partial transpose or the geometric measure of entanglement. (author)
Graph Sampling for Covariance Estimation
Chepuri, Sundeep Prabhakar; Leus, Geert
2017-01-01
specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non
Network reconstruction via graph blending
Estrada, Rolando
2016-05-01
Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.
A cluster algorithm for graphs
S. van Dongen
2000-01-01
textabstractA cluster algorithm for graphs called the emph{Markov Cluster algorithm (MCL~algorithm) is introduced. The algorithm provides basically an interface to an algebraic process defined on stochastic matrices, called the MCL~process. The graphs may be both weighted (with nonnegative weight)
Quantum chaos on discrete graphs
International Nuclear Information System (INIS)
Smilansky, Uzy
2007-01-01
Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of ζ functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)
RJSplot: Interactive Graphs with R.
Barrios, David; Prieto, Carlos
2018-03-01
Data visualization techniques provide new methods for the generation of interactive graphs. These graphs allow a better exploration and interpretation of data but their creation requires advanced knowledge of graphical libraries. Recent packages have enabled the integration of interactive graphs in R. However, R provides limited graphical packages that allow the generation of interactive graphs for computational biology applications. The present project has joined the analytical power of R with the interactive graphical features of JavaScript in a new R package (RJSplot). It enables the easy generation of interactive graphs in R, provides new visualization capabilities, and contributes to the advance of computational biology analytical methods. At present, 16 interactive graphics are available in RJSplot, such as the genome viewer, Manhattan plots, 3D plots, heatmaps, dendrograms, networks, and so on. The RJSplot package is freely available online at http://rjsplot.net. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
On the local vertex antimagic total coloring of some families tree
Febriani Putri, Desi; Dafik; Hesti Agustin, Ika; Alfarisi, Ridho
2018-04-01
Let G(V, E) be a graph of vertex set V and edge set E. Local vertex antimagic total coloring developed from local edge and local vertex antimagic coloring of graph. Local vertex antimagic total coloring is defined f:V(G)\\cup E(G)\\to \\{1,2,3,\\ldots,|V(G)|+|E(G)|\\} if for any two adjacent vertices v 1 and v 2, w({v}1)\
On characterizing terrain visibility graphs
Directory of Open Access Journals (Sweden)
William Evans
2015-06-01
Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.
Color Categories and Color Appearance
Webster, Michael A.; Kay, Paul
2012-01-01
We examined categorical effects in color appearance in two tasks, which in part differed in the extent to which color naming was explicitly required for the response. In one, we measured the effects of color differences on perceptual grouping for hues that spanned the blue-green boundary, to test whether chromatic differences across the boundary…
Color Terms and Color Concepts
Davidoff, Jules
2006-01-01
In their lead articles, both Kowalski and Zimiles (2006) and O'Hanlon and Roberson (2006) declare a general relation between color term knowledge and the ability to conceptually represent color. Kowalski and Zimiles, in particular, argue for a priority for the conceptual representation in color term acquisition. The complexities of the interaction…
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-11-12
Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most existing algorithms for graph embedding only rely on the topology information and fail to use the copious information in nodes as well as edges. As a result, their performance for many tasks may not be satisfactory. In this thesis, we proposed a novel and general framework for graph embedding with rich text information (GERI) through constructing a heterogeneous network, in which we integrate node and edge content information with graph topology. Specially, we designed a novel biased random walk to explore the constructed heterogeneous network with the notion of flexible neighborhood. Our sampling strategy can compromise between BFS and DFS local search on heterogeneous graph. To further improve our algorithm, we proposed semi-supervised GERI (SGERI), which learns graph embedding in an discriminative manner through heterogeneous network with label information. The efficacy of our method is demonstrated by extensive comparison experiments with 9 baselines over multi-label and multi-class classification on various datasets including Citeseer, Cora, DBLP and Wiki. It shows that GERI improves the Micro-F1 and Macro-F1 of node classification up to 10%, and SGERI improves GERI by 5% in Wiki.
CORECLUSTER: A Degeneracy Based Graph Clustering Framework
Giatsidis , Christos; Malliaros , Fragkiskos; Thilikos , Dimitrios M. ,; Vazirgiannis , Michalis
2014-01-01
International audience; Graph clustering or community detection constitutes an important task forinvestigating the internal structure of graphs, with a plethora of applications in several domains. Traditional tools for graph clustering, such asspectral methods, typically suffer from high time and space complexity. In thisarticle, we present \\textsc{CoreCluster}, an efficient graph clusteringframework based on the concept of graph degeneracy, that can be used along withany known graph clusteri...
Wrolstad, Ronald E.; Smith, Daniel E.
Color, flavor, and texture are the three principal quality attributes that determine food acceptance, and color has a far greater influence on our judgment than most of us appreciate. We use color to determine if a banana is at our preferred ripeness level, and a discolored meat product can warn us that the product may be spoiled. The marketing departments of our food corporations know that, for their customers, the color must be "right." The University of California Davis scorecard for wine quality designates four points out of 20, or 20% of the total score, for color and appearance (1). Food scientists who establish quality control specifications for their product are very aware of the importance of color and appearance. While subjective visual assessment and use of visual color standards are still used in the food industry, instrumental color measurements are extensively employed. Objective measurement of color is desirable for both research and industrial applications, and the ruggedness, stability, and ease of use of today's color measurement instruments have resulted in their widespread adoption.
Color categories and color appearance
Webster, Michael A.; Kay, Paul
2011-01-01
We examined categorical effects in color appearance in two tasks, which in part differed in the extent to which color naming was explicitly required for the response. In one, we measured the effects of color differences on perceptual grouping for hues that spanned the blue–green boundary, to test whether chromatic differences across the boundary were perceptually exaggerated. This task did not require overt judgments of the perceived colors, and the tendency to group showed only a weak and inconsistent categorical bias. In a second case, we analyzed results from two prior studies of hue scaling of chromatic stimuli (De Valois, De Valois, Switkes, & Mahon, 1997; Malkoc, Kay, & Webster, 2005), to test whether color appearance changed more rapidly around the blue–green boundary. In this task observers directly judge the perceived color of the stimuli and these judgments tended to show much stronger categorical effects. The differences between these tasks could arise either because different signals mediate color grouping and color appearance, or because linguistic categories might differentially intrude on the response to color and/or on the perception of color. Our results suggest that the interaction between language and color processing may be highly dependent on the specific task and cognitive demands and strategies of the observer, and also highlight pronounced individual differences in the tendency to exhibit categorical responses. PMID:22176751
Processing of Color Words Activates Color Representations
Richter, Tobias; Zwaan, Rolf A.
2009-01-01
Two experiments were conducted to investigate whether color representations are routinely activated when color words are processed. Congruency effects of colors and color words were observed in both directions. Lexical decisions on color words were faster when preceding colors matched the color named by the word. Color-discrimination responses…
Hierarchy of modular graph identities
International Nuclear Information System (INIS)
D’Hoker, Eric; Kaidi, Justin
2016-01-01
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.
Semantic graphs and associative memories
Pomi, Andrés; Mizraji, Eduardo
2004-12-01
Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.
Hierarchy of modular graph identities
Energy Technology Data Exchange (ETDEWEB)
D’Hoker, Eric; Kaidi, Justin [Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy,University of California,Los Angeles, CA 90095 (United States)
2016-11-09
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.
On the r-dynamic chromatic number of the corronation by complete graph
Indah Kristiana, Arika; Imam Utoyo, M.; Dafik
2018-04-01
In this paper we will study the r-dynamic chromatic number of the coronation by complete graph. A proper k-coloring of graph G such that the neighbors of any vertex v receive at least min{r, d(v)} different colors. The r-dynamic chromatic number, χ r (G) is the minimum k such that graph G has an r-dynamic k-coloring. We will obtain lower bound of the r-dynamic chromatic number of {χ }r({K}nȯ H), and {χ }r(Hȯ {K}m) We also study the exact value of the r-dynamic chromatic number of {χ }r({K}nȯ {S}m),{χ }r({K}nȯ {F}m),{χ }r({S}nȯ {K}m),{χ }r({F}nȯ {K}m) and {χ }r({K}nȯ {K}m) for m, n > 3.
Developing and evaluating Quilts for the depiction of large layered graphs.
Bae, Juhee; Watson, Ben
2011-12-01
Traditional layered graph depictions such as flow charts are in wide use. Yet as graphs grow more complex, these depictions can become difficult to understand. Quilts are matrix-based depictions for layered graphs designed to address this problem. In this research, we first improve Quilts by developing three design alternatives, and then compare the best of these alternatives to better-known node-link and matrix depictions. A primary weakness in Quilts is their depiction of skip links, links that do not simply connect to a succeeding layer. Therefore in our first study, we compare Quilts using color-only, text-only, and mixed (color and text) skip link depictions, finding that path finding with the color-only depiction is significantly slower and less accurate, and that in certain cases, the mixed depiction offers an advantage over the text-only depiction. In our second study, we compare Quilts using the mixed depiction to node-link diagrams and centered matrices. Overall results show that users can find paths through graphs significantly faster with Quilts (46.6 secs) than with node-link (58.3 secs) or matrix (71.2 secs) diagrams. This speed advantage is still greater in large graphs (e.g. in 200 node graphs, 55.4 secs vs. 71.1 secs for node-link and 84.2 secs for matrix depictions). © 2011 IEEE
Acoustic rainbow trapping by coiling up space
Ni, Xu
2014-11-13
We numerically realize the acoustic rainbow trapping effect by tapping an air waveguide with space-coiling metamaterials. Due to the high refractive-index of the space-coiling metamaterials, our device is more compact compared to the reported trapped-rainbow devices. A numerical model utilizing effective parameters is also calculated, whose results are consistent well with the direct numerical simulation of space-coiling structure. Moreover, such device with the capability of dropping different frequency components of a broadband incident temporal acoustic signal into different channels can function as an acoustic wavelength division de-multiplexer. These results may have potential applications in acoustic device design such as an acoustic filter and an artificial cochlea.
Acoustic rainbow trapping by coiling up space
Ni, Xu; Wu, Ying; Chen, Ze-Guo; Zheng, Li-Yang; Xu, Ye-Long; Nayar, Priyanka; Liu, Xiao-Ping; Lu, Ming-Hui; Chen, Yan-Feng
2014-01-01
We numerically realize the acoustic rainbow trapping effect by tapping an air waveguide with space-coiling metamaterials. Due to the high refractive-index of the space-coiling metamaterials, our device is more compact compared to the reported trapped-rainbow devices. A numerical model utilizing effective parameters is also calculated, whose results are consistent well with the direct numerical simulation of space-coiling structure. Moreover, such device with the capability of dropping different frequency components of a broadband incident temporal acoustic signal into different channels can function as an acoustic wavelength division de-multiplexer. These results may have potential applications in acoustic device design such as an acoustic filter and an artificial cochlea.
XML Graphs in Program Analysis
DEFF Research Database (Denmark)
Møller, Anders; Schwartzbach, Michael I.
2011-01-01
of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey the use of XML graphs for program analysis with four very different languages: XACT (XML in Java), Java Servlets (Web application programming), XSugar......XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...
International Nuclear Information System (INIS)
Hasson, Raymond.
1976-06-01
After a short introduction explaining the reasons why color metallography was adopted, the various operations involved in this technique are described in turn and illustrated by colored photomicrographs. The sample preparation (cutting, covering) and surface preparation (trimming, polishing, finishing) are described briefly. The operations specific to color metallography are then detailed: revelation of the structure of polished surfaces, dye impregnation techniques, optical systems used in macrography, in micrography, different light sources used in microscopy, photographic methods [fr
A first generation BAC-based physical map of the rainbow trout genome
Directory of Open Access Journals (Sweden)
Thorgaard Gary H
2009-10-01
Full Text Available Abstract Background Rainbow trout (Oncorhynchus mykiss are the most-widely cultivated cold freshwater fish in the world and an important model species for many research areas. Coupling great interest in this species as a research model with the need for genetic improvement of aquaculture production efficiency traits justifies the continued development of genomics research resources. Many quantitative trait loci (QTL have been identified for production and life-history traits in rainbow trout. A bacterial artificial chromosome (BAC physical map is needed to facilitate fine mapping of QTL and the selection of positional candidate genes for incorporation in marker-assisted selection (MAS for improving rainbow trout aquaculture production. This resource will also facilitate efforts to obtain and assemble a whole-genome reference sequence for this species. Results The physical map was constructed from DNA fingerprinting of 192,096 BAC clones using the 4-color high-information content fingerprinting (HICF method. The clones were assembled into physical map contigs using the finger-printing contig (FPC program. The map is composed of 4,173 contigs and 9,379 singletons. The total number of unique fingerprinting fragments (consensus bands in contigs is 1,185,157, which corresponds to an estimated physical length of 2.0 Gb. The map assembly was validated by 1 comparison with probe hybridization results and agarose gel fingerprinting contigs; and 2 anchoring large contigs to the microsatellite-based genetic linkage map. Conclusion The production and validation of the first BAC physical map of the rainbow trout genome is described in this paper. We are currently integrating this map with the NCCCWA genetic map using more than 200 microsatellites isolated from BAC end sequences and by identifying BACs that harbor more than 300 previously mapped markers. The availability of an integrated physical and genetic map will enable detailed comparative genome
Modeling human color categorization: Color discrimination and color memory
Heskes, T.; van den Broek, Egon; Lucas, P.; Hendriks, Maria A.; Vuurpijl, L.G.; Puts, M.J.H.; Wiegerinck, W.
2003-01-01
Color matching in Content-Based Image Retrieval is done using a color space and measuring distances between colors. Such an approach yields non-intuitive results for the user. We introduce color categories (or focal colors), determine that they are valid, and use them in two experiments. The experiments conducted prove the difference between color categorization by the cognitive processes color discrimination and color memory. In addition, they yield a Color Look-Up Table, which can improve c...
Directory of Open Access Journals (Sweden)
Dominique Lafon
2011-05-01
Full Text Available The goal of this article is to present specific capabilities and limitations of the use of color digital images in a characterization process. The whole process is investigated, from the acquisition of digital color images to the analysis of the information relevant to various applications in the field of material characterization. A digital color image can be considered as a matrix of pixels with values expressed in a vector-space (commonly 3 dimensional space whose specificity, compared to grey-scale images, is to ensure a coding and a representation of the output image (visualisation printing that fits the human visual reality. In a characterization process, it is interesting to regard color image attnbutes as a set of visual aspect measurements on a material surface. Color measurement systems (spectrocolorimeters, colorimeters and radiometers and cameras use the same type of light detectors: most of them use Charge Coupled Devices sensors. The difference between the two types of color data acquisition systems is that color measurement systems provide a global information of the observed surface (average aspect of the surface: the color texture is not taken into account. Thus, it seems interesting to use imaging systems as measuring instruments for the quantitative characterization of the color texture.
Thermodynamics and luminosities of rainbow black holes
Energy Technology Data Exchange (ETDEWEB)
Mu, Benrong [Physics Teaching and Research section, College of Medical Technology, Chengdu University of Traditional Chinese Medicine, No. 1166 Liutai Avenue, Chengdu (China); Wang, Peng; Yang, Haitang, E-mail: mubenrong@uestc.edu.cn, E-mail: pengw@scu.edu.cn, E-mail: hyanga@scu.edu.cn [Center for Theoretical Physics, College of Physical Science and Technology, Sichuan University, No. 24 South Section 1 Yihuan Road, Chengdu (China)
2015-11-01
Doubly special relativity (DSR) is an effective model for encoding quantum gravity in flat spacetime. As result of the nonlinearity of the Lorentz transformation, the energy-momentum dispersion relation is modified. One simple way to import DSR to curved spacetime is ''Gravity's rainbow'', where the spacetime background felt by a test particle would depend on its energy. Focusing on the ''Amelino-Camelia dispersion relation'' which is E{sup 2} = m{sup 2}+p{sup 2}[1−η(E/m{sub p}){sup n}] with n > 0, we investigate the thermodynamical properties of a Schwarzschild black hole and a static uncharged black string for all possible values of η and n in the framework of rainbow gravity. It shows that there are non-vanishing minimum masses for these two black holes in the cases with η < 0 and n ≥ 2. Considering effects of rainbow gravity on both the Hawking temperature and radius of the event horizon, we use the geometric optics approximation to compute luminosities of a 2D black hole, a Schwarzschild one and a static uncharged black string. It is found that the luminosities can be significantly suppressed or boosted depending on the values of η and n.
Szabó, György; Fáth, Gábor
2007-07-01
Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by non-mean-field-type social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Graph anomalies in cyber communications
Energy Technology Data Exchange (ETDEWEB)
Vander Wiel, Scott A [Los Alamos National Laboratory; Storlie, Curtis B [Los Alamos National Laboratory; Sandine, Gary [Los Alamos National Laboratory; Hagberg, Aric A [Los Alamos National Laboratory; Fisk, Michael [Los Alamos National Laboratory
2011-01-11
Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail.
Open Graphs and Computational Reasoning
Directory of Open Access Journals (Sweden)
Lucas Dixon
2010-06-01
Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.
Woeginger, G.J.
1998-01-01
In this short note we argue that the toughness of split graphs can be computed in polynomial time. This solves an open problem from a recent paper by Kratsch et al. (Discrete Math. 150 (1996) 231–245).
Generating random networks and graphs
Coolen, Ton; Roberts, Ekaterina
2017-01-01
This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...
An Interview with Alex Sanchez, Author of "Rainbow Boys."
Emert, Toby
2002-01-01
Presents an interview with Alex Sanchez. Notes that his book "Rainbow Boys" has been called the "best gay youth book of the year." Notes that "Rainbow Boys" chronicles the lives of three high school seniors who struggle to manage their issues about sexual identity and coming out to themselves, to each other, and to the world. (SG)
2004-01-01
[figure removed for brevity, see original site] Released 7 May 2004 This daytime visible color image was collected on May 30, 2002 during the Southern Fall season in Atlantis Chaos. The THEMIS VIS camera is capable of capturing color images of the martian surface using its five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from the use of multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation. Image information: VIS instrument. Latitude -34.5, Longitude 183.6 East (176.4 West). 38 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D
Graph theory and its applications
Gross, Jonathan L
2006-01-01
Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
Graphs with branchwidth at most three
Bodlaender, H.L.; Thilikos, D.M.
1997-01-01
In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three, if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph
A Modal-Logic Based Graph Abstraction
Bauer, J.; Boneva, I.B.; Kurban, M.E.; Rensink, Arend; Ehrig, H; Heckel, R.; Rozenberg, G.; Taentzer, G.
2008-01-01
Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract
Graphs whose complement and square are isomorphic
DEFF Research Database (Denmark)
Pedersen, Anders Sune
2014-01-01
We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-compl...
Building Scalable Knowledge Graphs for Earth Science
Ramachandran, Rahul; Maskey, Manil; Gatlin, Patrick; Zhang, Jia; Duan, Xiaoyi; Miller, J. J.; Bugbee, Kaylin; Christopher, Sundar; Freitag, Brian
2017-01-01
Knowledge Graphs link key entities in a specific domain with other entities via relationships. From these relationships, researchers can query knowledge graphs for probabilistic recommendations to infer new knowledge. Scientific papers are an untapped resource which knowledge graphs could leverage to accelerate research discovery. Goal: Develop an end-to-end (semi) automated methodology for constructing Knowledge Graphs for Earth Science.
Port-Hamiltonian Systems on Open Graphs
Schaft, A.J. van der; Maschke, B.M.
2010-01-01
In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
Skew-adjacency matrices of graphs
Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.
2012-01-01
The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic
Chromatic polynomials of random graphs
International Nuclear Information System (INIS)
Van Bussel, Frank; Fliegner, Denny; Timme, Marc; Ehrlich, Christoph; Stolzenberg, Sebastian
2010-01-01
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.
Commuting graphs of matrix algebras
International Nuclear Information System (INIS)
Akbari, S.; Bidkhori, H.; Mohammadian, A.
2006-08-01
The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all non- central elements of R and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this paper we investigate some graph theoretic properties of Γ(M n (F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GL n (F) and SL n (F). We show that Γ(M n (F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GL n (F)) and Γ(SL n (F)). Also we show that for two fields E and F and integers m, n ≥> 2, if Γ(M m (E)) ≅ Γ(M n (F)), then m = n and vertical bar E vertical bar = vertical bar F vertical bar. (author)
Rainbows in nature: recent advances in observation and theory
International Nuclear Information System (INIS)
Haußmann, Alexander
2016-01-01
This topical review presents an overview of the common and less common observations of rainbows in natural rainfall, and the theoretical concepts that have been developed for their explanation. Mainly throughout the last 20 years, many new and intriguing effects have been photographed or documented for the first time, such as higher-order (tertiary, quaternary, etc) and twinned rainbows, as well as rainbows generated by nearby artificial light sources. In order to provide a sound explanation, the inclusion of natural non-spherical (i.e. oblate) raindrop shapes as well as natural broad polydisperse raindrop distributions into the classical rainbow theory (Lorenz–Mie and Debye scattering) is outlined. Thus, the article provides a condensed up-to-date synopsis complementing classical textbooks and earlier reviews on the physics of rainbows. It is intended to serve both active sky observers as well as physics teachers who want to keep up with current developments in the field. (review)
Graph Quasicontinuous Functions and Densely Continuous Forms
Directory of Open Access Journals (Sweden)
Lubica Hola
2017-07-01
Full Text Available Let $X, Y$ be topological spaces. A function $f: X \\to Y$ is said to be graph quasicontinuous if there is a quasicontinuous function $g: X \\to Y$ with the graph of $g$ contained in the closure of the graph of $f$. There is a close relation between the notions of graph quasicontinuous functions and minimal usco maps as well as the notions of graph quasicontinuous functions and densely continuous forms. Every function with values in a compact Hausdorff space is graph quasicontinuous; more generally every locally compact function is graph quasicontinuous.
International Nuclear Information System (INIS)
Harari, H.
1985-01-01
If leptons are composite and if they contain colored preons, one expects the existence of heavy color-octet fermions with quantum numbers similar to those of ordinary leptons. Such a ''colored lepton'' should decay into a gluon and a lepton, yielding a unique experimental signature. Charged ''colored leptons'' probably have masses of the order of the compositeness scale Λ > or approx. 1 TeV. They may be copiously produced at future multi-TeV e + e - , ep and hadron colliders. ''Colored neutrinos'' may have both Dirac and Majorana masses. They could be much lighter than Λ, possibly as light as 100 GeV or less. In such a case they should be readily produced at the CERN anti pp collider, yielding spectacular monojet and dijet events. They may also be produced at LEP and HERA. (orig.)
... Color Blindness? Who Is at Risk for Color Blindness? Color Blindness Causes Color Blindness Diagnosis and Treatment How Color Blindness Is Tested What Is Color Blindness? Leer en Español: ¿Qué es el daltonismo? Written ...
On the Adjacent Strong Equitable Edge Coloring of Pn ∨ Pn, Pn ∨ Cn and Cn ∨ Cn
Liu Jun; Zhao Chuan Cheng; Yao Shu Xia; Guo Ren Zhi; Yue Qiu Ju
2016-01-01
A proper edge coloring of graph G is called equitable adjacent strong edge coloring if colored sets from every two adjacent vertices incident edge are different,and the number of edges in any two color classes differ by at most one,which the required minimum number of colors is called the adjacent strong equitable edge chromatic number. In this paper, we discuss the adjacent strong equitable edge coloring of join-graphs about Pn ∨ Pn, Pn ∨ Cn and Cn ∨ Cn.
Interactive Graph Layout of a Million Nodes
Peng Mi; Maoyuan Sun; Moeti Masiane; Yong Cao; Chris North
2016-01-01
Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph to...
Khovanov homology of graph-links
Energy Technology Data Exchange (ETDEWEB)
Nikonov, Igor M [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2012-08-31
Graph-links arise as the intersection graphs of turning chord diagrams of links. Speaking informally, graph-links provide a combinatorial description of links up to mutations. Many link invariants can be reformulated in the language of graph-links. Khovanov homology, a well-known and useful knot invariant, is defined for graph-links in this paper (in the case of the ground field of characteristic two). Bibliography: 14 titles.
Beyond the Rainbow: Retrieval Practice Leads to Better Spelling than Does Rainbow Writing
Jones, Angela C.; Wardlow, Liane; Pan, Steven C.; Zepeda, Cristina; Heyman, Gail D.; Dunlosky, John; Rickard, Timothy C.
2016-01-01
In three experiments, we compared the effectiveness of rainbow writing and retrieval practice, two common methods of spelling instruction. In experiment 1 (n = 14), second graders completed 2 days of spelling practice, followed by spelling tests 1 day and 5 weeks later. A repeated measures analysis of variance demonstrated that spelling accuracy…
PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION
Directory of Open Access Journals (Sweden)
W. Dorner
2016-06-01
Full Text Available After the success of GNSS (Global Navigational Satellite Systems and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS – Real Time Locating Services (e.g. WIFI and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites, but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.
Shan, Xiao; Xiahou, Chengkui; Connor, J N L
2018-01-03
In earlier research, we have demonstrated that broad "hidden" rainbows can occur in the product differential cross sections (DCSs) of state-to-state chemical reactions. Here we ask the question: can pronounced and localized rainbows, rather than broad hidden ones, occur in reactive DCSs? Further motivation comes from recent measurements by H. Pan and K. Liu, J. Phys. Chem. A, 2016, 120, 6712, of a "bulge" in a reactive DCS, which they conjecture is a rainbow. Our theoretical approach uses a "weak" version of Heisenberg's scattering matrix program (wHSMP) introduced by X. Shan and J. N. L. Connor, Phys. Chem. Chem. Phys., 2011, 13, 8392. This wHSMP uses four general physical principles for chemical reactions to suggest simple parameterized forms for the S matrix; it does not employ a potential energy surface. We use a parameterization in which the modulus of the S matrix is a smooth-step function of the total angular momentum quantum number, J, and (importantly) its phase is a cubic polynomial in J. We demonstrate for a Legendre partial wave series (PWS) the existence of pronounced rainbows, supernumerary rainbows, and other interference effects, in reactive DCSs. We find that reactive rainbows can be more complicated in their structure than the familiar rainbows of elastic scattering. We also analyse the angular scattering using Nearside-Farside (NF) PWS theory and NF PWS Local Angular Momentum (LAM) theory, including resummations of the PWS. In addition, we apply full and NF asymptotic (semiclassical) rainbow theories to the PWS - in particular, the uniform Airy and transitional Airy approximations for the farside scattering. This lets us prove that structure in the DCSs are indeed rainbows, supernumerary rainbows as well as other interference effects.
DEFF Research Database (Denmark)
Hansen, Heinz J.M.; Olsen, Allan Gylling; Rosenkilde, Per
1993-01-01
Zoofysiologi, Osmoregulation, Lipid metabolism, Ecotoxicology, Rainbow trout, Oncorhynchus mykiss.......Zoofysiologi, Osmoregulation, Lipid metabolism, Ecotoxicology, Rainbow trout, Oncorhynchus mykiss....
STRUCTURAL ANNOTATION OF EM IMAGES BY GRAPH CUT
Energy Technology Data Exchange (ETDEWEB)
Chang, Hang; Auer, Manfred; Parvin, Bahram
2009-05-08
Biological images have the potential to reveal complex signatures that may not be amenable to morphological modeling in terms of shape, location, texture, and color. An effective analytical method is to characterize the composition of a specimen based on user-defined patterns of texture and contrast formation. However, such a simple requirement demands an improved model for stability and robustness. Here, an interactive computational model is introduced for learning patterns of interest by example. The learned patterns bound an active contour model in which the traditional gradient descent optimization is replaced by the more efficient optimization of the graph cut methods. First, the energy function is defined according to the curve evolution. Next, a graph is constructed with weighted edges on the energy function and is optimized with the graph cut algorithm. As a result, the method combines the advantages of the level set method and graph cut algorithm, i.e.,"topological" invariance and computational efficiency. The technique is extended to the multi-phase segmentation problem; the method is validated on synthetic images and then applied to specimens imaged by transmission electron microscopy(TEM).
Color inference in visual communication: the meaning of colors in recycling.
Schloss, Karen B; Lessard, Laurent; Walmsley, Charlotte S; Foley, Kathleen
2018-01-01
People interpret abstract meanings from colors, which makes color a useful perceptual feature for visual communication. This process is complicated, however, because there is seldom a one-to-one correspondence between colors and meanings. One color can be associated with many different concepts (one-to-many mapping) and many colors can be associated with the same concept (many-to-one mapping). We propose that to interpret color-coding systems, people perform assignment inference to determine how colors map onto concepts. We studied assignment inference in the domain of recycling. Participants saw images of colored but unlabeled bins and were asked to indicate which bins they would use to discard different kinds of recyclables and trash. In Experiment 1, we tested two hypotheses for how people perform assignment inference. The local assignment hypothesis predicts that people simply match objects with their most strongly associated color. The global assignment hypothesis predicts that people also account for the association strengths between all other objects and colors within the scope of the color-coding system. Participants discarded objects in bins that optimized the color-object associations of the entire set, which is consistent with the global assignment hypothesis. This sometimes resulted in discarding objects in bins whose colors were weakly associated with the object, even when there was a stronger associated option available. In Experiment 2, we tested different methods for encoding color-coding systems and found that people were better at assignment inference when color sets simultaneously maximized the association strength between assigned color-object parings while minimizing associations between unassigned pairings. Our study provides an approach for designing intuitive color-coding systems that facilitate communication through visual media such as graphs, maps, signs, and artifacts.
Eigenfunction statistics on quantum graphs
International Nuclear Information System (INIS)
Gnutzmann, S.; Keating, J.P.; Piotet, F.
2010-01-01
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.
Directory of Open Access Journals (Sweden)
Andreas P. Braun
2016-04-01
Full Text Available Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5 by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.
Degree-based graph construction
International Nuclear Information System (INIS)
Kim, Hyunju; Toroczkai, Zoltan; Erdos, Peter L; Miklos, Istvan; Szekely, Laszlo A
2009-01-01
Degree-based graph construction is a ubiquitous problem in network modelling (Newman et al 2006 The Structure and Dynamics of Networks (Princeton Studies in Complexity) (Princeton, NJ: Princeton University Press), Boccaletti et al 2006 Phys. Rep. 424 175), ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive construction and sampling questions with aspects that are still open today. Here we give necessary and sufficient conditions for a sequence of nonnegative integers to be realized as a simple graph's degree sequence, such that a given (but otherwise arbitrary) set of connections from an arbitrarily given node is avoided. We then use this result to present a swap-free algorithm that builds all simple graphs realizing a given degree sequence. In a wider context, we show that our result provides a greedy construction method to build all the f-factor subgraphs (Tutte 1952 Can. J. Math. 4 314) embedded within K n setmn S k , where K n is the complete graph and S k is a star graph centred on one of the nodes. (fast track communication)
Hierarchical organisation of causal graphs
International Nuclear Information System (INIS)
Dziopa, P.
1993-01-01
This paper deals with the design of a supervision system using a hierarchy of models formed by graphs, in which the variables are the nodes and the causal relations between the variables of the arcs. To obtain a representation of the variables evolutions which contains only the relevant features of their real evolutions, the causal relations are completed with qualitative transfer functions (QTFs) which produce roughly the behaviour of the classical transfer functions. Major improvements have been made in the building of the hierarchical organization. First, the basic variables of the uppermost level and the causal relations between them are chosen. The next graph is built by adding intermediary variables to the upper graph. When the undermost graph has been built, the transfer functions parameters corresponding to its causal relations are identified. The second task consists in the upwelling of the information from the undermost graph to the uppermost one. A fusion procedure of the causal relations has been designed to compute the QFTs relevant for each level. This procedure aims to reduce the number of parameters needed to represent an evolution at a high level of abstraction. These techniques have been applied to the hierarchical modelling of nuclear process. (authors). 8 refs., 12 figs
Pulu, Tupou L.; And Others
This first grade workbook is designed for children in bilingual Inupiat-English programs in the Alaskan villages of Ambler, Kiana, Kobuk, Noorvik, Selawik, and Shungnak. Each page has a captioned black-and-white drawing to be colored. (CFM)
Rius Tormo, Palmira
2010-01-01
Póster presentado en el IX Congreso Nacional del Color, Alicante, 29-30 junio, 1-2 julio 2010. La exposición que se propone tiene como núcleo principal el color y muestra las posibilidades expresivas que aporta a los diferentes materiales. Las 7 obras presentadas buscan la armonía estética y la fuerza simbólica.
Reversed rainbow with a nonlocal metamaterial
Energy Technology Data Exchange (ETDEWEB)
Morgado, Tiago A., E-mail: tiago.morgado@co.it.pt; Marcos, João S.; Silveirinha, Mário G., E-mail: mario.silveirinha@co.it.pt [Department of Electrical Engineering, Instituto de Telecomunicações, University of Coimbra, 3030 Coimbra (Portugal); Costa, João T. [CST AG, Bad Nauheimer Strasse 19, 64289 Darmstadt (Germany); Costa, Jorge R. [Instituto de Telecomunicações and Instituto Universitário de Lisboa (ISCTE-IUL), 1649-026 Lisboa (Portugal); Fernandes, Carlos A. [Instituto de Telecomunicações, and Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa (Portugal)
2014-12-29
One of the intriguing potentials of metamaterials is the possibility to realize a nonlocal electromagnetic reaction, such that the effective medium response at a given point is fundamentally entangled with the macroscopic field distribution at long distances. Here, it is experimentally and numerically verified that a microwave nonlocal metamaterial formed by crossed metallic wires enables a low-loss broadband anomalous material response such that the refractive index decreases with frequency. Notably, it is shown that an electromagnetic beam refracted by our metamaterial prism creates a reversed microwave rainbow.
Revisiting the round bottom flask rainbow experiment
Selmke, Markus; Selmke, Sarah
2018-01-01
A popular demonstration experiment in optics uses a round-bottom flask filled with water to project a circular rainbow on a screen with a hole through which the flask is illuminated. We show how the vessel's wall shifts the first- and second-order bows towards each other and consequently reduces the width of Alexander's dark band. We address the challenge this introduces in observing Alexander's dark band, and explain the importance of a sufficient distance between the flask and the screen. The wall-effect also introduces a splitting of the bows that can easily be misinterpreted.
Graph modeling systems and methods
Neergaard, Mike
2015-10-13
An apparatus and a method for vulnerability and reliability modeling are provided. The method generally includes constructing a graph model of a physical network using a computer, the graph model including a plurality of terminating vertices to represent nodes in the physical network, a plurality of edges to represent transmission paths in the physical network, and a non-terminating vertex to represent a non-nodal vulnerability along a transmission path in the physical network. The method additionally includes evaluating the vulnerability and reliability of the physical network using the constructed graph model, wherein the vulnerability and reliability evaluation includes a determination of whether each terminating and non-terminating vertex represents a critical point of failure. The method can be utilized to evaluate wide variety of networks, including power grid infrastructures, communication network topologies, and fluid distribution systems.
Feder, Tomá s; Motwani, Rajeev
2009-01-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Feder, Tomás
2009-06-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Negation switching invariant signed graphs
Directory of Open Access Journals (Sweden)
Deepa Sinha
2014-04-01
Full Text Available A signed graph (or, $sigraph$ in short is a graph G in which each edge x carries a value $\\sigma(x \\in \\{-, +\\}$ called its sign. Given a sigraph S, the negation $\\eta(S$ of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs $S_{1}$ and $S_{2}$ on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus' or `-' (`minus' to vertices of $S_{1}$ such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains $S_{2}$. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and $\\eta (S$ are signed isomorphic.
International Nuclear Information System (INIS)
Rosmanis, Ansis
2011-01-01
I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.
NONSINGULAR UNIVERSES IN GAUSS–BONNET GRAVITY’S RAINBOW
International Nuclear Information System (INIS)
Hendi, Seyed Hossein; Momennia, Mehrab; Panah, Behzad Eslam; Faizal, Mir
2016-01-01
In this paper, we study the rainbow deformation of Friedmann-Robertson-Walker (FRW) cosmology in both Einstein gravity and Gauss–Bonnet (GB) gravity. We demonstrate that the singularity in FRW cosmology can be removed because of the rainbow deformation of the FRW metric. We obtain the general constraints required for FRW cosmology to be free of singularities. We observe that the inclusion of GB gravity can significantly change the constraints required to obtain nonsingular universes. We use rainbow functions motivated by the hard spectra of gamma-ray bursts to deform FRW cosmology and explicitly demonstrate that such a deformation removes the singularity in FRW cosmology.
NONSINGULAR UNIVERSES IN GAUSS–BONNET GRAVITY’S RAINBOW
Energy Technology Data Exchange (ETDEWEB)
Hendi, Seyed Hossein; Momennia, Mehrab; Panah, Behzad Eslam [Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz 71454 (Iran, Islamic Republic of); Faizal, Mir [Department of Physics and Astronomy, University of Lethbridge, Lethbridge, AB T1K 3M4 (Canada)
2016-08-20
In this paper, we study the rainbow deformation of Friedmann-Robertson-Walker (FRW) cosmology in both Einstein gravity and Gauss–Bonnet (GB) gravity. We demonstrate that the singularity in FRW cosmology can be removed because of the rainbow deformation of the FRW metric. We obtain the general constraints required for FRW cosmology to be free of singularities. We observe that the inclusion of GB gravity can significantly change the constraints required to obtain nonsingular universes. We use rainbow functions motivated by the hard spectra of gamma-ray bursts to deform FRW cosmology and explicitly demonstrate that such a deformation removes the singularity in FRW cosmology.
On Graph Rewriting, Reduction and Evaluation
DEFF Research Database (Denmark)
Zerny, Ian
2010-01-01
We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter-derive a t......We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter...
The fascinating world of graph theory
Benjamin, Arthur; Zhang, Ping
2015-01-01
Graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducin
Graph-based modelling in engineering
Rysiński, Jacek
2017-01-01
This book presents versatile, modern and creative applications of graph theory in mechanical engineering, robotics and computer networks. Topics related to mechanical engineering include e.g. machine and mechanism science, mechatronics, robotics, gearing and transmissions, design theory and production processes. The graphs treated are simple graphs, weighted and mixed graphs, bond graphs, Petri nets, logical trees etc. The authors represent several countries in Europe and America, and their contributions show how different, elegant, useful and fruitful the utilization of graphs in modelling of engineering systems can be. .
XML Graphs in Program Analysis
DEFF Research Database (Denmark)
Møller, Anders; Schwartzbach, Michael Ignatieff
2007-01-01
XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...... of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey four very different applications: XML in Java, Java Servlets and JSP, transformations between XML and non-XML data, and XSLT....
Graph topologies on closed multifunctions
Directory of Open Access Journals (Sweden)
Giuseppe Di Maio
2003-10-01
Full Text Available In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.
Cyclic graphs and Apery's theorem
International Nuclear Information System (INIS)
Sorokin, V N
2002-01-01
This is a survey of results about the behaviour of Hermite-Pade approximants for graphs of Markov functions, and a survey of interpolation problems leading to Apery's result about the irrationality of the value ζ(3) of the Riemann zeta function. The first example is given of a cyclic graph for which the Hermite-Pade problem leads to Apery's theorem. Explicit formulae for solutions are obtained, namely, Rodrigues' formulae and integral representations. The asymptotic behaviour of the approximants is studied, and recurrence formulae are found
Interacting particle systems on graphs
Sood, Vishal
In this dissertation, the dynamics of socially or biologically interacting populations are investigated. The individual members of the population are treated as particles that interact via links on a social or biological network represented as a graph. The effect of the structure of the graph on the properties of the interacting particle system is studied using statistical physics techniques. In the first chapter, the central concepts of graph theory and social and biological networks are presented. Next, interacting particle systems that are drawn from physics, mathematics and biology are discussed in the second chapter. In the third chapter, the random walk on a graph is studied. The mean time for a random walk to traverse between two arbitrary sites of a random graph is evaluated. Using an effective medium approximation it is found that the mean first-passage time between pairs of sites, as well as all moments of this first-passage time, are insensitive to the density of links in the graph. The inverse of the mean-first passage time varies non-monotonically with the density of links near the percolation transition of the random graph. Much of the behavior can be understood by simple heuristic arguments. Evolutionary dynamics, by which mutants overspread an otherwise uniform population on heterogeneous graphs, are studied in the fourth chapter. Such a process underlies' epidemic propagation, emergence of fads, social cooperation or invasion of an ecological niche by a new species. The first part of this chapter is devoted to neutral dynamics, in which the mutant genotype does not have a selective advantage over the resident genotype. The time to extinction of one of the two genotypes is derived. In the second part of this chapter, selective advantage or fitness is introduced such that the mutant genotype has a higher birth rate or a lower death rate. This selective advantage leads to a dynamical competition in which selection dominates for large populations
Decomposing a planar graph of girth 5 into an independent set and a forest
DEFF Research Database (Denmark)
Kawarabayashi, Ken-ichi; Thomassen, Carsten
2009-01-01
We use a list-color technique to extend the result of Borodin and Glebov that the vertex set of every planar graph of girth at least 5 can be partitioned into an independent set and a set which induces a forest. We apply this extension to also extend Grötzsch's theorem that every planar triangle-...
Multiple graph regularized protein domain ranking
Wang, Jim Jing-Yan
2012-11-19
Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.
Multiple graph regularized protein domain ranking
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
2012-01-01
Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.
Multiple graph regularized protein domain ranking.
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
2012-11-19
Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.
Multiple graph regularized protein domain ranking
Directory of Open Access Journals (Sweden)
Wang Jim
2012-11-01
Full Text Available Abstract Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.
Utilization of dietary urea in rainbow trout.
Kaushik, S J; Dabrowski, K R; Dabrowska, H; Olah, E; Luquet, P
1983-01-01
Experiments were conducted to examine the potential utilization of dietary urea by rainbow trout. A control diet and two diets supplemented with 1 and 3% of urea were fed to fish. Postprandial levels of urea and ammonia in blood plasma, and postprandial excretion of these metabolites were followed during 24 h. Apparent digestibility of urea in rainbow trout was very high (greater than 98%). Maximum values of urea levels in plasma were reached 6 h (32.3 +/- 10.2 micrograms/ml) after a meal in the control fish and respectively 6 h (83.4 +/- 18.4 micrograms/ml) and 8 h (250.3 +/- 96.1 micrograms/ml) after a meal in trout fed 1 and 3% urea diets. Peaks of urea excretion rates appeared 7-9 h after meal, coinciding with the highest circulating urea concentration. Total daily urea excretion amounted to 5.53, 10.43 and 33.80 mg urea N/100 mg N intake in trout fed the control, 1 and 3% urea diets, respectively. It is concluded that the dietary urea is readily absorbed in the digestive tract of trout but is totally excreted thus leading to no beneficial effect on nitrogen balance. This excretion of urea also takes place passively without any increase in energy demands.
... present from birth) color vision problems: Achromatopsia -- complete color blindness , seeing only shades of gray Deuteranopia -- difficulty telling ... Vision test - color; Ishihara color vision test Images Color blindness tests References Bowling B. Hereditary fundus dystrophies. In: ...
Modeling human color categorization: Color discrimination and color memory
Heskes, T.; van den Broek, Egon; Lucas, P.; Hendriks, Maria A.; Vuurpijl, L.G.; Puts, M.J.H.; Wiegerinck, W.
2003-01-01
Color matching in Content-Based Image Retrieval is done using a color space and measuring distances between colors. Such an approach yields non-intuitive results for the user. We introduce color categories (or focal colors), determine that they are valid, and use them in two experiments. The
Constructing Knowledge Graphs of Depression
Huang, Zhisheng; Yang, Jie; van Harmelen, Frank; Hu, Qing
2017-01-01
Knowledge Graphs have been shown to be useful tools for integrating multiple medical knowledge sources, and to support such tasks as medical decision making, literature retrieval, determining healthcare quality indicators, co-morbodity analysis and many others. A large number of medical knowledge
Partitioning graphs into connected parts
Hof, van 't P.; Paulusma, D.; Woeginger, G.J.; Frid, A.; Morozov, A.S.; Rybalchenko, A.; Wagner, K.W.
2009-01-01
The 2-DISJOINT CONNECTED SUBGRAPHS problem asks if a given graph has two vertex-disjoint connected subgraphs containing pre-specified sets of vertices. We show that this problem is NP-complete even if one of the sets has cardinality 2. The LONGEST PATH CONTRACTIBILITY problem asks for the largest
Isoperimetric inequalities for minimal graphs
International Nuclear Information System (INIS)
Pacelli Bessa, G.; Montenegro, J.F.
2007-09-01
Based on Markvorsen and Palmer's work on mean time exit and isoperimetric inequalities we establish slightly better isoperimetric inequalities and mean time exit estimates for minimal graphs in N x R. We also prove isoperimetric inequalities for submanifolds of Hadamard spaces with tamed second fundamental form. (author)
Ancestral Genres of Mathematical Graphs
Gerofsky, Susan
2011-01-01
Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…
Humidity Graphs for All Seasons.
Esmael, F.
1982-01-01
In a previous article in this journal (Vol. 17, p358, 1979), a wet-bulb depression table was recommended for two simple experiments to determine relative humidity. However, the use of a graph is suggested because it gives the relative humidity directly from the wet and dry bulb readings. (JN)
Contracting a planar graph efficiently
DEFF Research Database (Denmark)
Holm, Jacob; Italiano, Giuseppe F.; Karczmarz, Adam
2017-01-01
the data structure, we can achieve optimal running times for decremental bridge detection, 2-edge connectivity, maximal 3-edge connected components, and the problem of finding a unique perfect matching for a static planar graph. Furthermore, we improve the running times of algorithms for several planar...
Graph Model Based Indoor Tracking
DEFF Research Database (Denmark)
Jensen, Christian Søndergaard; Lu, Hua; Yang, Bin
2009-01-01
The tracking of the locations of moving objects in large indoor spaces is important, as it enables a range of applications related to, e.g., security and indoor navigation and guidance. This paper presents a graph model based approach to indoor tracking that offers a uniform data management...
A graph with fractional revival
Bernard, Pierre-Antoine; Chan, Ada; Loranger, Érika; Tamon, Christino; Vinet, Luc
2018-02-01
An example of a graph that admits balanced fractional revival between antipodes is presented. It is obtained by establishing the correspondence between the quantum walk on a hypercube where the opposite vertices across the diagonals of each face are connected and, the coherent transport of single excitations in the extension of the Krawtchouk spin chain with next-to-nearest neighbour interactions.
Fixation Time for Evolutionary Graphs
Nie, Pu-Yan; Zhang, Pei-Ai
Evolutionary graph theory (EGT) is recently proposed by Lieberman et al. in 2005. EGT is successful for explaining biological evolution and some social phenomena. It is extremely important to consider the time of fixation for EGT in many practical problems, including evolutionary theory and the evolution of cooperation. This study characterizes the time to asymptotically reach fixation.
Mathematical Minute: Rotating a Function Graph
Bravo, Daniel; Fera, Joseph
2013-01-01
Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.
Towards a theory of geometric graphs
Pach, Janos
2004-01-01
The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been su...
Bounds on Gromov hyperbolicity constant in graphs
Indian Academy of Sciences (India)
Infinite graphs; Cartesian product graphs; independence number; domin- ation number; geodesics ... the secure transmission of information through the internet (see [15, 16]). In particular, ..... In particular, δ(G) is an integer multiple of 1/4.
Summary: beyond fault trees to fault graphs
International Nuclear Information System (INIS)
Alesso, H.P.; Prassinos, P.; Smith, C.F.
1984-09-01
Fault Graphs are the natural evolutionary step over a traditional fault-tree model. A Fault Graph is a failure-oriented directed graph with logic connectives that allows cycles. We intentionally construct the Fault Graph to trace the piping and instrumentation drawing (P and ID) of the system, but with logical AND and OR conditions added. Then we evaluate the Fault Graph with computer codes based on graph-theoretic methods. Fault Graph computer codes are based on graph concepts, such as path set (a set of nodes traveled on a path from one node to another) and reachability (the complete set of all possible paths between any two nodes). These codes are used to find the cut-sets (any minimal set of component failures that will fail the system) and to evaluate the system reliability
Torsional rigidity, isospectrality and quantum graphs
International Nuclear Information System (INIS)
Colladay, Don; McDonald, Patrick; Kaganovskiy, Leon
2017-01-01
We study torsional rigidity for graph and quantum graph analogs of well-known pairs of isospectral non-isometric planar domains. We prove that such isospectral pairs are distinguished by torsional rigidity. (paper)
International Nuclear Information System (INIS)
Wilczek, F.
1997-01-01
The asymptotic freedom of QCD suggests that at high density - where one forms a Fermi surface at very high momenta - weak coupling methods apply. These methods suggest that chiral symmetry is restored and that an instability toward color triplet condensation (color superconductivity) sets in. Here I attempt, using variational methods, to estimate these effects more precisely. Highlights include demonstration of a negative pressure in the uniform density chiral broken phase for any non-zero condensation, which we take as evidence for the philosophy of the MIT bag model; and demonstration that the color gap is substantial - several tens of MeV - even at modest densities. Since the superconductivity is in a pseudoscalar channel, parity is spontaneously broken
Energy Technology Data Exchange (ETDEWEB)
Wilczek, F. [Institute for Advanced Study, Princeton, NJ (United States)
1997-09-22
The asymptotic freedom of QCD suggests that at high density - where one forms a Fermi surface at very high momenta - weak coupling methods apply. These methods suggest that chiral symmetry is restored and that an instability toward color triplet condensation (color superconductivity) sets in. Here I attempt, using variational methods, to estimate these effects more precisely. Highlights include demonstration of a negative pressure in the uniform density chiral broken phase for any non-zero condensation, which we take as evidence for the philosophy of the MIT bag model; and demonstration that the color gap is substantial - several tens of MeV - even at modest densities. Since the superconductivity is in a pseudoscalar channel, parity is spontaneously broken.
Rainbows in channeling of charged particles in crystals and nanotubes
Nešković, Nebojša; Ćosić, Marko
2017-01-01
This book discusses the effects, modeling, latest results, and nanotechnology applications of rainbows that appear during channeling of charged particles in crystals and nanotubes. The authors begin with a brief review of the optical and particle rainbow effects followed by a detailed description of crystal rainbows, which appear in ion channeling in crystals, and their modeling using catastrophe theory. The effects of spatial and angular focusing of channeled ions are described, with special attention given to the applications of the former effect to subatomic microscopy. The results of a thorough study of the recent high-resolution channeling experiments performed with protons of energies between 2.0 and 0.7 MeV and a 55 nm thick silicon crystal are also provided. This study opens up the potential for accurate analysis of very thin crystals. Also presented are recent results related to rainbows occurring in proton transmission through carbon nanotubes, and a detailed quantum consideration of the transmissio...
Charged dilatonic black holes in gravity's rainbow
Energy Technology Data Exchange (ETDEWEB)
Hendi, S.H. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Faizal, Mir [University of Waterloo, Department of Physics and Astronomy, Waterloo, ON (Canada); Panah, B.E. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Panahiyan, S. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Shahid Beheshti University, Physics Department, Tehran (Iran, Islamic Republic of)
2016-05-15
In this paper, we present charged dilatonic black holes in gravity's rainbow. We study the geometric and thermodynamic properties of black hole solutions. We also investigate the effects of rainbow functions on different thermodynamic quantities for these charged black holes in dilatonic gravity's rainbow. Then we demonstrate that the first law of thermodynamics is valid for these solutions. After that, we investigate thermal stability of the solutions using the canonical ensemble and analyze the effects of different rainbow functions on the thermal stability. In addition, we present some arguments regarding the bound and phase transition points in context of geometrical thermodynamics. We also study the phase transition in extended phase space in which the cosmological constant is treated as the thermodynamic pressure. Finally, we use another approach to calculate and demonstrate that the obtained critical points in extended phase space represent a second order phase transition for these black holes. (orig.)
Rainbow Trout Distribution, Pacific Northwest (updated March, 2006)
Pacific States Marine Fisheries Commission — This dataset is a record of fish distribution and activity for RAINBOW TROUT contained in the StreamNet database. This feature class was created based on linear...
A Practical Approach to Rainbow Trout (Oncorhynchus mykiss) Seed Production
, Orhan Çakır
2002-01-01
Rainbow trout (Oncorhynchus mykiss) grows faster and has great disease resistance. Therefore this species has been preferred to culture for years. Fry production, feeding and management of broodstock are explained practically in order to increase profitability.
Bond graph modeling of centrifugal compression systems
Uddin, Nur; Gravdahl, Jan Tommy
2015-01-01
A novel approach to model unsteady fluid dynamics in a compressor network by using a bond graph is presented. The model is intended in particular for compressor control system development. First, we develop a bond graph model of a single compression system. Bond graph modeling offers a different perspective to previous work by modeling the compression system based on energy flow instead of fluid dynamics. Analyzing the bond graph model explains the energy flow during compressor surge. Two pri...
A Graph Calculus for Predicate Logic
Directory of Open Access Journals (Sweden)
Paulo A. S. Veloso
2013-03-01
Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation.
Sphere and dot product representations of graphs
R.J. Kang (Ross); T. Müller (Tobias)
2012-01-01
textabstractA graph $G$ is a $k$-sphere graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such that $ij\\in E(G)$ if and only if the distance between $v_i$ and $v_j$ is at most $1$. A graph $G$ is a $k$-dot product graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such
Deep Learning with Dynamic Computation Graphs
Looks, Moshe; Herreshoff, Marcello; Hutchins, DeLesley; Norvig, Peter
2017-01-01
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different shape and size for every input, such networks do not directly support batched training or inference. They are also difficult to implement in popular deep learning libraries, which are based on static data-flow graphs. We introduce a technique called dynami...
Constructs for Programming with Graph Rewrites
Rodgers, Peter
2000-01-01
Graph rewriting is becoming increasingly popular as a method for programming with graph based data structures. We present several modifications to a basic serial graph rewriting paradigm and discuss how they improve coding programs in the Grrr graph rewriting programming language. The constructs we present are once only nodes, attractor nodes and single match rewrites. We illustrate the operation of the constructs by example. The advantages of adding these new rewrite modifiers is to reduce t...
Effects of cooking methods on electrophoretic patterns of rainbow trout
Directory of Open Access Journals (Sweden)
Yasemen Yanar
2011-07-01
Full Text Available The aim of this study was to determine the effects of different cooking methods on the electrophoretic patterns of rainbow trout (Oncorhynchus mykiss fillets using sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE. Raw rainbow trout were deep-fried, microwaved, grilled, and baked and then monitored for changes in the electrophoretic pattern. All cooking methods resulted in significant moisture loss when compared to the raw sample (P
How can rainbow gravity affect on gravitational force?
Sefiedgar, A. S.
2015-01-01
According to Verlinde's recent proposal, the gravity is originally an entropic force. In this work, we obtain the corrections to the entropy-area law of black holes within rainbow gravity. The corrected entropy-area law leads to the modifications of the number of bits $N$. Inspired by Verlinde's argument on the entropic force, and using the modified number of bits, we can investigate the effects of rainbow gravity on the modified Newtonian dynamics, Newton's law of gravitation, and Einstein's...
On the sizes of expander graphs and minimum distances of graph codes
DEFF Research Database (Denmark)
Høholdt, Tom; Justesen, Jørn
2014-01-01
We give lower bounds for the minimum distances of graph codes based on expander graphs. The bounds depend only on the second eigenvalue of the graph and the parameters of the component codes. We also give an upper bound on the size of a degree regular graph with given second eigenvalue....
McMillen, Sue; McMillen, Beth
2010-01-01
Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy. Even students who are able to "create" bar graphs may struggle to correctly "interpret" them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information…
The groupies of random multipartite graphs
Portmann, Marius; Wang, Hongyun
2012-01-01
If a vertex $v$ in a graph $G$ has degree larger than the average of the degrees of its neighbors, we call it a groupie in $G$. In the current work, we study the behavior of groupie in random multipartite graphs with the link probability between sets of nodes fixed. Our results extend the previous ones on random (bipartite) graphs.
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo
2009-01-01
In this report we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java
An intersection graph of straight lines
DEFF Research Database (Denmark)
Thomassen, Carsten
2002-01-01
G. Ehrlich, S. Even, and R.E. Tarjan conjectured that the graph obtained from a complete 3 partite graph K4,4,4 by deleting the edges of four disjoint triangles is not the intersection graph of straight line segments in the plane. We show that it is....
Girth 5 graphs from relative difference sets
DEFF Research Database (Denmark)
Jørgensen, Leif Kjær
2005-01-01
We consider the problem of construction of graphs with given degree $k$ and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed ...
Cycles in weighted graphs and related topics
Zhang, Shenggui
2002-01-01
This thesis contains results on paths andcycles in graphs andon a more or less relatedtopic, the vulnerability of graphs. In the first part of the thesis, Chapters 2 through 5, we concentrate on paths andcycles in weightedgraphs. A number of sufficient conditions are presentedfor graphs to contain
Graph Transformation Semantics for a QVT Language
Rensink, Arend; Nederpel, Ronald; Bruni, Roberto; Varró, Dániel
It has been claimed by many in the graph transformation community that model transformation, as understood in the context of Model Driven Architecture, can be seen as an application of graph transformation. In this paper we substantiate this claim by giving a graph transformation-based semantics to
Girth 5 graphs from relative difference sets
DEFF Research Database (Denmark)
Jørgensen, Leif Kjær
We consider the problem of construction of graphs with given degree and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by G...
Improper colouring of (random) unit disk graphs
Kang, R.J.; Müller, T.; Sereni, J.S.
2008-01-01
For any graph G, the k-improper chromatic number ¿k(G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree k. We investigate ¿k for unit disk graphs and random unit disk graphs to generalise results of McDiarmid and Reed
Alliances and Bisection Width for Planar Graphs
DEFF Research Database (Denmark)
Olsen, Martin; Revsbæk, Morten
2013-01-01
An alliance in a graph is a set of vertices (allies) such that each vertex in the alliance has at least as many allies (counting the vertex itself) as non-allies in its neighborhood of the graph. We show that any planar graph with minimum degree at least 4 can be split into two alliances in polyn...
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo; Lee, D.; Lopes, A.; Poetzsch-Heffter, A.
2009-01-01
In this work we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java syntax
RATGRAPH: Computer Graphing of Rational Functions.
Minch, Bradley A.
1987-01-01
Presents an easy-to-use Applesoft BASIC program that graphs rational functions and any asymptotes that the functions might have. Discusses the nature of rational functions, graphing them manually, employing a computer to graph rational functions, and describes how the program works. (TW)
A new cluster algorithm for graphs
S. van Dongen
1998-01-01
textabstractA new cluster algorithm for graphs called the emph{Markov Cluster algorithm ($MCL$ algorithm) is introduced. The graphs may be both weighted (with nonnegative weight) and directed. Let~$G$~be such a graph. The $MCL$ algorithm simulates flow in $G$ by first identifying $G$ in a
Well-covered graphs and factors
DEFF Research Database (Denmark)
Randerath, Bert; Vestergaard, Preben D.
2006-01-01
A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. Every well-covered graph G without isolated vertices has a perf...
47 CFR 80.761 - Conversion graphs.
2010-10-01
... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units is... 47 Telecommunication 5 2010-10-01 2010-10-01 false Conversion graphs. 80.761 Section 80.761...
Energy Technology Data Exchange (ETDEWEB)
Wang, W.; Zhang, X. [College of Chemistry and Chemical Engineering, Ocean University of China, Qingdao (China); Wang, J. [College of Chemistry and Chemical Engineering, Ocean University of China, Qingdao (China); State Key Laboratory for Corrosion and Protection, Shenyang (China)
2009-10-15
The crevice corrosion occurrence probability of stainless steel (SS) AISI 316 was increased under ennoblement condition due to chemically added H{sub 2}O{sub 2} into seawater. The H{sub 2}O{sub 2} was used to simulate the important factor causing ennoblement in natural marine biofilm. Morphology of the crevice corrosion was observed using an incident-light source microscopy. Some interesting ''rainbow'' fringes were observed around micro-crevices. The mechanism was discussed from the ions diffusion and potential distribution during the crevice formation. This result shows that under ennoblement condition the colored fringe is a distinct characteristic of the morphology of localized corrosion for stainless steel. (Abstract Copyright [2009], Wiley Periodicals, Inc.)
Rainbow Particle Imaging Velocimetry for Dense 3D Fluid Velocity Imaging
Xiong, Jinhui
2017-04-11
Despite significant recent progress, dense, time-resolved imaging of complex, non-stationary 3D flow velocities remains an elusive goal. In this work we tackle this problem by extending an established 2D method, Particle Imaging Velocimetry, to three dimensions by encoding depth into color. The encoding is achieved by illuminating the flow volume with a continuum of light planes (a “rainbow”), such that each depth corresponds to a specific wavelength of light. A diffractive component in the camera optics ensures that all planes are in focus simultaneously. For reconstruction, we derive an image formation model for recovering stationary 3D particle positions. 3D velocity estimation is achieved with a variant of 3D optical flow that accounts for both physical constraints as well as the rainbow image formation model. We evaluate our method with both simulations and an experimental prototype setup.
Virulence of Flavobacterium columnare genomovars in rainbow trout Oncorhynchus mykiss.
Evenhuis, Jason P; LaFrentz, Benjamin R
2016-08-09
Flavobacterium columnare is the causative agent of columnaris disease and is responsible for significant economic losses in aquaculture. F. columnare is a Gram-negative bacterium, and 5 genetic types or genomovars have been described based on restriction fragment length polymorphism of the 16S rRNA gene. Previous research has suggested that genomovar II isolates are more virulent than genomovar I isolates to multiple species of fish, including rainbow trout Oncorhynchus mykiss. In addition, improved genotyping methods have shown that some isolates previously classified as genomovar I, and used in challenge experiments, were in fact genomovar III. Our objective was to confirm previous results with respect to genomovar II virulence, and to determine the susceptibility of rainbow trout to other genomovars. The virulence of 8 genomovar I, 4 genomovar II, 3 genomovar II-B, and 5 genomovar III isolates originating from various sources was determined through 3 independent challenges in rainbow trout using an immersion challenge model. Mean cumulative percent mortality (CPM) of ~49% for genomovar I isolates, ~1% for genomovar II, ~5% for the II-B isolates, and ~7% for the III isolates was observed. The inability of genomovar II isolates to produce mortalities in rainbow trout was unanticipated based on previous studies, but may be due to a number of factors including rainbow trout source and water chemistry. The source of fish and/or the presence of sub-optimal environment may influence the susceptibility of rainbow trout to different F. columnare genomovars.
Johnson, Heidi S. S.; Maki, Jennifer A.
2009-01-01
This article reports a study conducted by members of the WellU Academic Integration Subcommittee of The College of St. Scholastica's College's Healthy Campus Initiative plan whose purpose was to determine whether changing color in the classroom could have a measurable effect on students. One simple improvement a school can make in a classroom is…
International Nuclear Information System (INIS)
Jennings, B.K.; Miller, G.A.
1993-01-01
The anomously large transmission of nucleons through a nucleus following a hard collision is explored. This effect, known as color transparency, is believed to be a prediction of QCD. The necessary conditions for its occurrence and the effects that must be included a realistic calculation are discussed
International Nuclear Information System (INIS)
Miller, G.A.
1993-01-01
Imagine shooting a beam of protons of high momentum P through an atomic nucleus. Usually the nuclear interactions prevent the particles from emerging with momentum ∼P. Further, the angular distribution of elastically scattered protons is close to the optical diffraction pattern produced by a black disk. Thus the nucleus acts as a black disk and is not transparent. However, certain high momentum transfer reactions in which a proton is knocked out of the nucleus may be completely different. Suppose that the high momentum transfer process leads to the formation of a small-size color singlet wavepacket that is ejected from the nucleus. The effects of gluons emitted by color singlet systems of closely separated quarks and gluons tend to cancel. Thus the wavepacket-nuclear interactions are suppressed, the nucleus becomes transparant and one says that color transparency CT occurs. The observation of CT also requires that the wavepacket not expand very much while it moves through the nucleus. Simple quantum mechanical formulations can assess this expansion. The creation of a small-sized wavepacket is expected in asymptotic perturbative effects. The author reviews the few experimental attempts to observe color transparency in nuclear (e,e'p) and (p,pp) reactions and interpret the data and their implications
International Nuclear Information System (INIS)
Pire, B.; Ralston, J.P.
1991-01-01
This paper reviews the physics of color transparency and the unexpected energy dependence of recent measurements of high-energy fixed-angle elastic scattering in nuclear targets. The authors point out advantages of using transparency as a tool, introducing two concepts - spin and flavor flow filtering - that may be studied with nuclear targets. The special case of electroproduction is also considered
Diazo Printing of ERTS Color Composites
Mcmurtry, G. J.; Petersen, G. W. (Principal Investigator); Kowalik, W. S.
1975-01-01
The author has identified the following significant results. ERTS-1 color composites were made with the help of a Diazo developer and printer. Five single channel, density standards were established, using typical ERTS images, in order to determine exposure time. These standards were used to develop a graph from which the exposure time for any transparency can be estimated. Exposure times varied from 3 to 30 minutes, and clear colored polyester sheets from two manufactures were used with slightly different, but equally successful, results.
On a conjecture concerning helly circle graphs
Directory of Open Access Journals (Sweden)
Durán Guillermo
2003-01-01
Full Text Available We say that G is an e-circle graph if there is a bijection between its vertices and straight lines on the cartesian plane such that two vertices are adjacent in G if and only if the corresponding lines intersect inside the circle of radius one. This definition suggests a method for deciding whether a given graph G is an e-circle graph, by constructing a convenient system S of equations and inequations which represents the structure of G, in such a way that G is an e-circle graph if and only if S has a solution. In fact, e-circle graphs are exactly the circle graphs (intersection graphs of chords in a circle, and thus this method provides an analytic way for recognizing circle graphs. A graph G is a Helly circle graph if G is a circle graph and there exists a model of G by chords such that every three pairwise intersecting chords intersect at the same point. A conjecture by Durán (2000 states that G is a Helly circle graph if and only if G is a circle graph and contains no induced diamonds (a diamond is a graph formed by four vertices and five edges. Many unsuccessful efforts - mainly based on combinatorial and geometrical approaches - have been done in order to validate this conjecture. In this work, we utilize the ideas behind the definition of e-circle graphs and restate this conjecture in terms of an equivalence between two systems of equations and inequations, providing a new, analytic tool to deal with it.
Approximation and hardness results for the maximum edge q-coloring problem
DEFF Research Database (Denmark)
Adamaszek, Anna Maria; Popa, Alexandru
2016-01-01
We consider the problem of coloring edges of a graph subject to the following constraints: for every vertex v, all the edges incident with v have to be colored with at most q colors. The goal is to find a coloring satisfying the above constraints and using the maximum number of colors. Notice...... ϵ>0 and any q≥2 assuming the unique games conjecture (UGC), or 1+−ϵ for any ϵ>0 and any q≥3 (≈1.19 for q=2) assuming P≠NP. These results hold even when the considered graphs are bipartite. On the algorithmic side, we restrict to the case q=2, since this is the most important in practice and we show...... a 5/3-approximation algorithm for graphs which have a perfect matching....
Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes
Directory of Open Access Journals (Sweden)
Katona Gyula Y.
2014-11-01
Full Text Available The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs.
Subsampling for graph power spectrum estimation
Chepuri, Sundeep Prabhakar; Leus, Geert
2016-01-01
In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.
Subsampling for graph power spectrum estimation
Chepuri, Sundeep Prabhakar
2016-10-06
In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.
Proving relations between modular graph functions
International Nuclear Information System (INIS)
Basu, Anirban
2016-01-01
We consider modular graph functions that arise in the low energy expansion of the four graviton amplitude in type II string theory. The vertices of these graphs are the positions of insertions of vertex operators on the toroidal worldsheet, while the links are the scalar Green functions connecting the vertices. Graphs with four and five links satisfy several non-trivial relations, which have been proved recently. We prove these relations by using elementary properties of Green functions and the details of the graphs. We also prove a relation between modular graph functions with six links. (paper)
Immunity to VHS virus in rainbow trout
DEFF Research Database (Denmark)
Lorenzen, Niels; Olesen, Niels Jørgen; Koch, C.
1999-01-01
Viral hemorrhagic septicemia virus (VHSV) is the rhabdovirus that causes most disease problems in farmed rainbow trout in Europe. Survivors of infection are usually immune to reinfection but as with other fish viruses, development of a modern recombinant vaccine has been complicated by the limited...... knowledge of the immune mechanisms and antigens involved in induction of immunity. Neutralizing and protective monoclonal antibodies recognize the envelope glycoprotein (G protein) which is the only viral protein known to be present on the surface of the virus particle. Immunoblotting analyses...... with monoclonal antibodies as well as with sera from immunized trout have indicated that protein conformation plays an important role in neutralization epitopes. The virus neutralizing activity often found in sera from convalescent trout is highly dependent on a poorly defined complementing activity in normal...
Xiong, B.; Oude Elberink, S.; Vosselman, G.
2014-07-01
In the task of 3D building model reconstruction from point clouds we face the problem of recovering a roof topology graph in the presence of noise, small roof faces and low point densities. Errors in roof topology graphs will seriously affect the final modelling results. The aim of this research is to automatically correct these errors. We define the graph correction as a graph-to-graph problem, similar to the spelling correction problem (also called the string-to-string problem). The graph correction is more complex than string correction, as the graphs are 2D while strings are only 1D. We design a strategy based on a dictionary of graph edit operations to automatically identify and correct the errors in the input graph. For each type of error the graph edit dictionary stores a representative erroneous subgraph as well as the corrected version. As an erroneous roof topology graph may contain several errors, a heuristic search is applied to find the optimum sequence of graph edits to correct the errors one by one. The graph edit dictionary can be expanded to include entries needed to cope with errors that were previously not encountered. Experiments show that the dictionary with only fifteen entries already properly corrects one quarter of erroneous graphs in about 4500 buildings, and even half of the erroneous graphs in one test area, achieving as high as a 95% acceptance rate of the reconstructed models.
Report on the Audit ot the Acquisition of the Tacit Rainbow Anti-Radiation Missile System
1991-06-24
This is our final report on the audit of the Tacit Rainbow Anti-Radiation Missile System (Tacit Rainbow) for your information and use. We performed... the audit from March through December 1990. The audit objective was to evaluate the acquisition management of the air-launched Tacit Rainbow system to...contains no recommendations because DoD took action to cancel the Tacit Rainbow system in FY 1992. We are bringing the issues identified during the audit to
Homosexual Identity in Alex Sanchez's 'Rainbow Trilogy'
Directory of Open Access Journals (Sweden)
Nanda Vidyastria
2017-03-01
Full Text Available This research aims at describing 1 stages of homosexual identity development in three main characters in the Rainbow Trilogy using Cass model, 2 factors influencing the development of homosexual identity using D Augellis theory, and 3 forms of victimization towards homosexuals experienced by the main characters using theories of D Augelli and Rivers. Queer studies was applied to describe and analyze the data in forms of words, phrases, sentences, statements, dialogues as well as monologues in the Rainbow Trilogy, recording thoughts and actions by the characters in accordance with the research focus. As a result, the research finds out that the three novels describe clearly all stages of Cass model of homosexual identity development in Jason and Kyle, including their identity confusions, comparisons, acceptances, tolerances, prides and syntheses. In Nelson, only one stage that can be identified as Nelson is described as one whose sexual identity has been formed. The research also reveals how factors of personal subjectivity and action, interactive intimacy and sociohistorical connection are connected to each others and also influencing the homosexual identity developments of the main characters. Besides, the research also shows that various kinds of victimization occur to Jason, Kyle and Nelson. Normative victimizations made to feel different are experienced by Nelson and Kyle. Family stressor and prejudices in connection to AIDS are experienced by the three characters. Victimization of direct attacks in forms of verbal and physical abuses are experienced by Kyle and Nelson. Lastly, the research finds out that Nelson is the only character experiencing sexual abuse. It occurs in form of undesired comments oriented to a sexual violence.
Significance evaluation in factor graphs
DEFF Research Database (Denmark)
Madsen, Tobias; Hobolth, Asger; Jensen, Jens Ledet
2017-01-01
in genomics and the multiple-testing issues accompanying them, accurate significance evaluation is of great importance. We here address the problem of evaluating statistical significance of observations from factor graph models. Results Two novel numerical approximations for evaluation of statistical...... significance are presented. First a method using importance sampling. Second a saddlepoint approximation based method. We develop algorithms to efficiently compute the approximations and compare them to naive sampling and the normal approximation. The individual merits of the methods are analysed both from....... Conclusions The applicability of saddlepoint approximation and importance sampling is demonstrated on known models in the factor graph framework. Using the two methods we can substantially improve computational cost without compromising accuracy. This contribution allows analyses of large datasets...
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
Flux networks in metabolic graphs
International Nuclear Information System (INIS)
Warren, P B; Queiros, S M Duarte; Jones, J L
2009-01-01
A metabolic model can be represented as a bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualization of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for other organisms
On the centrality of some graphs
Directory of Open Access Journals (Sweden)
Vecdi Aytac
2017-10-01
Full Text Available A central issue in the analysis of complex networks is the assessment of their stability and vulnerability. A variety of measures have been proposed in the literature to quantify the stability of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. Different measures for graph vulnerability have been introduced so far to study different aspects of the graph behavior after removal of vertices or links such as connectivity, toughness, scattering number, binding number, residual closeness and integrity. In this paper, we consider betweenness centrality of a graph. Betweenness centrality of a vertex of a graph is portion of the shortest paths all pairs of vertices passing through a given vertex. In this paper, we obtain exact values for betweenness centrality for some wheel related graphs namely gear, helm, sunflower and friendship graphs.
Quantum walk on a chimera graph
Xu, Shu; Sun, Xiangxiang; Wu, Jizhou; Zhang, Wei-Wei; Arshed, Nigum; Sanders, Barry C.
2018-05-01
We analyse a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum walk features such as localization that starkly distinguishes classical from quantum behaviour. Motivated by technological thrusts, we study continuous-time quantum walk on enhanced variants of the chimera graph and on diminished chimera graph with a random removal of vertices. We explain the quantum walk by constructing a generating set for a suitable subgroup of graph isomorphisms and corresponding symmetry operators that commute with the quantum walk Hamiltonian; the Hamiltonian and these symmetry operators provide a complete set of labels for the spectrum and the stationary states. Our quantum walk characterization of the chimera graph and its variants yields valuable insights into graphs used for designing quantum-annealers.
Fibonacci number of the tadpole graph
Directory of Open Access Journals (Sweden)
Joe DeMaio
2014-10-01
Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.
Software for Graph Analysis and Visualization
Directory of Open Access Journals (Sweden)
M. I. Kolomeychenko
2014-01-01
Full Text Available This paper describes the software for graph storage, analysis and visualization. The article presents a comparative analysis of existing software for analysis and visualization of graphs, describes the overall architecture of application and basic principles of construction and operation of the main modules. Furthermore, a description of the developed graph storage oriented to storage and processing of large-scale graphs is presented. The developed algorithm for finding communities and implemented algorithms of autolayouts of graphs are the main functionality of the product. The main advantage of the developed software is high speed processing of large size networks (up to millions of nodes and links. Moreover, the proposed graph storage architecture is unique and has no analogues. The developed approaches and algorithms are optimized for operating with big graphs and have high productivity.
Parallel External Memory Graph Algorithms
DEFF Research Database (Denmark)
Arge, Lars Allan; Goodrich, Michael T.; Sitchinava, Nodari
2010-01-01
In this paper, we study parallel I/O efficient graph algorithms in the Parallel External Memory (PEM) model, one o f the private-cache chip multiprocessor (CMP) models. We study the fundamental problem of list ranking which leads to efficient solutions to problems on trees, such as computing lowest...... an optimal speedup of Â¿(P) in parallel I/O complexity and parallel computation time, compared to the single-processor external memory counterparts....
Submanifolds weakly associated with graphs
Indian Academy of Sciences (India)
A CARRIAZO, L M FERN ´ANDEZ and A RODRÍGUEZ-HIDALGO. Department of Geometry and Topology, ..... by means of trees (connected graphs without cycles) and forests (disjoint unions of trees, see [6]) given in [3], by extending it to weak ... CR-submanifold. In this case, every tree is a K2. Finally, Theorem 3.8 of [3] can ...
Topological structure of dictionary graphs
International Nuclear Information System (INIS)
Fuks, Henryk; Krzeminski, Mark
2009-01-01
We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers-that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 10 3 and 10 4 . A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.
Quantum information processing with graph states
International Nuclear Information System (INIS)
Schlingemann, Dirk-Michael
2005-04-01
Graph states are multiparticle states which are associated with graphs. Each vertex of the graph corresponds to a single system or particle. The links describe quantum correlations (entanglement) between pairs of connected particles. Graph states were initiated independently by two research groups: On the one hand, graph states were introduced by Briegel and Raussendorf as a resource for a new model of one-way quantum computing, where algorithms are implemented by a sequence of measurements at single particles. On the other hand, graph states were developed by the author of this thesis and ReinhardWerner in Braunschweig, as a tool to build quantum error correcting codes, called graph codes. The connection between the two approaches was fully realized in close cooperation of both research groups. This habilitation thesis provides a survey of the theory of graph codes, focussing mainly, but not exclusively on the author's own research work. We present the theoretical and mathematical background for the analysis of graph codes. The concept of one-way quantum computing for general graph states is discussed. We explicitly show how to realize the encoding and decoding device of a graph code on a one-way quantum computer. This kind of implementation is to be seen as a mathematical description of a quantum memory device. In addition to that, we investigate interaction processes, which enable the creation of graph states on very large systems. Particular graph states can be created, for instance, by an Ising type interaction between next neighbor particles which sits at the points of an infinitely extended cubic lattice. Based on the theory of quantum cellular automata, we give a constructive characterization of general interactions which create a translationally invariant graph state. (orig.)
Degree Associated Edge Reconstruction Number of Graphs with Regular Pruned Graph
Directory of Open Access Journals (Sweden)
P. Anusha Devi
2015-10-01
Full Text Available An ecard of a graph $G$ is a subgraph formed by deleting an edge. A da-ecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph $G,~dern(G,$ is the minimum number of da-ecards that uniquely determines $G.$ The adversary degree associated edge reconstruction number of a graph $G, adern(G,$ is the minimum number $k$ such that every collection of $k$ da-ecards of $G$ uniquely determines $G.$ The maximal subgraph without end vertices of a graph $G$ which is not a tree is the pruned graph of $G.$ It is shown that $dern$ of complete multipartite graphs and some connected graphs with regular pruned graph is $1$ or $2.$ We also determine $dern$ and $adern$ of corona product of standard graphs.
The Full Ward-Takahashi Identity for Colored Tensor Models
Pérez-Sánchez, Carlos I.
2018-03-01
Colored tensor models (CTM) is a random geometrical approach to quantum gravity. We scrutinize the structure of the connected correlation functions of general CTM-interactions and organize them by boundaries of Feynman graphs. For rank- D interactions including, but not restricted to, all melonic φ^4 -vertices—to wit, solely those quartic vertices that can lead to dominant spherical contributions in the large- N expansion—the aforementioned boundary graphs are shown to be precisely all (possibly disconnected) vertex-bipartite regularly edge- D-colored graphs. The concept of CTM-compatible boundary-graph automorphism is introduced and an auxiliary graph calculus is developed. With the aid of these constructs, certain U (∞)-invariance of the path integral measure is fully exploited in order to derive a strong Ward-Takahashi Identity for CTMs with a symmetry-breaking kinetic term. For the rank-3 φ^4 -theory, we get the exact integral-like equation for the 2-point function. Similarly, exact equations for higher multipoint functions can be readily obtained departing from this full Ward-Takahashi identity. Our results hold for some Group Field Theories as well. Altogether, our non-perturbative approach trades some graph theoretical methods for analytical ones. We believe that these tools can be extended to tensorial SYK-models.
Full Text Available ... One Use Facts About Colored Contacts and Halloween Safety Colored Contact Lens Facts Over-the-Counter Costume ... use of colored contact lenses , from the U.S. Food and Drug Administration (FDA). Are the colored lenses ...
Thermodynamics of charged dilatonic BTZ black holes in rainbow gravity
Dehghani, M.
2018-02-01
In this paper, the charged three-dimensional Einstein's theory coupled to a dilatonic field has been considered in the rainbow gravity. The dilatonic potential has been written as the linear combination of two Liouville-type potentials. Four new classes of charged dilatonic rainbow black hole solutions, as the exact solution to the coupled field equations of the energy dependent space time, have been obtained. Two of them are correspond to the Coulomb's electric field and the others are consequences of a modified Coulomb's law. Total charge and mass as well as the entropy, temperature and electric potential of the new charged black holes have been calculated in the presence of rainbow functions. Although the thermodynamic quantities are affected by the rainbow functions, it has been found that the first law of black hole thermodynamics is still valid for all of the new black hole solutions. At the final stage, making use of the canonical ensemble method and regarding the black hole heat capacity, the thermal stability or phase transition of the new rainbow black hole solutions have been analyzed.
Thermodynamics of charged dilatonic BTZ black holes in rainbow gravity
Directory of Open Access Journals (Sweden)
M. Dehghani
2018-02-01
Full Text Available In this paper, the charged three-dimensional Einstein's theory coupled to a dilatonic field has been considered in the rainbow gravity. The dilatonic potential has been written as the linear combination of two Liouville-type potentials. Four new classes of charged dilatonic rainbow black hole solutions, as the exact solution to the coupled field equations of the energy dependent space time, have been obtained. Two of them are correspond to the Coulomb's electric field and the others are consequences of a modified Coulomb's law. Total charge and mass as well as the entropy, temperature and electric potential of the new charged black holes have been calculated in the presence of rainbow functions. Although the thermodynamic quantities are affected by the rainbow functions, it has been found that the first law of black hole thermodynamics is still valid for all of the new black hole solutions. At the final stage, making use of the canonical ensemble method and regarding the black hole heat capacity, the thermal stability or phase transition of the new rainbow black hole solutions have been analyzed.
Replica methods for loopy sparse random graphs
International Nuclear Information System (INIS)
Coolen, ACC
2016-01-01
I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement. (paper)
Chemical Graph Transformation with Stereo-Information
DEFF Research Database (Denmark)
Andersen, Jakob Lykke; Flamm, Christoph; Merkle, Daniel
2017-01-01
Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms and their neighbo......Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms...... and their neighbours in space. Stereoisomers of chemical compounds thus cannot be distinguished, even though their chemical activity may differ substantially. In this contribution we propose an extended chemical graph transformation system with attributes that encode information about local geometry. The modelling...... of graph transformation, but we here propose a framework that also allows for partially specified stereoinformation. While there are several stereochemical configurations to be considered, we focus here on the tetrahedral molecular shape, and suggest general principles for how to treat all other chemically...
Reconstructing Topological Graphs and Continua
Gartside, Paul; Pitz, Max F.; Suabedissen, Rolf
2015-01-01
The deck of a topological space $X$ is the set $\\mathcal{D}(X)=\\{[X \\setminus \\{x\\}] \\colon x \\in X\\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever $\\mathcal{D}(X)=\\mathcal{D}(Y)$ then $X$ is homeomorphic to $Y$. It is shown that all metrizable compact connected spaces are reconstructible. It follows that all finite graphs, when viewed as a 1-dimensional cell-complex, are reconstructible in the topological sense, and more genera...
Decomposing a graph into bistars
DEFF Research Database (Denmark)
Thomassen, Carsten
2013-01-01
Bárat and the present author conjectured that, for each tree T, there exists a natural number kT such that the following holds: If G is a kT-edge-connected graph such that |E(T)| divides |E(G)|, then G has a T-decomposition, that is, a decomposition of the edge set into trees each of which...... is isomorphic to T. The conjecture has been verified for infinitely many paths and for each star. In this paper we verify the conjecture for an infinite family of trees that are neither paths nor stars, namely all the bistars S(k,k+1)....
3D Rainbow Particle Tracking Velocimetry
Aguirre-Pablo, Andres A.; Xiong, Jinhui; Idoughi, Ramzi; Aljedaani, Abdulrahman B.; Dun, Xiong; Fu, Qiang; Thoroddsen, Sigurdur T.; Heidrich, Wolfgang
2017-11-01
A single color camera is used to reconstruct a 3D-3C velocity flow field. The camera is used to record the 2D (X,Y) position and colored scattered light intensity (Z) from white polyethylene tracer particles in a flow. The main advantage of using a color camera is the capability of combining different intensity levels for each color channel to obtain more depth levels. The illumination system consists of an LCD projector placed perpendicularly to the camera. Different intensity colored level gradients are projected onto the particles to encode the depth position (Z) information of each particle, benefiting from the possibility of varying the color profiles and projected frequencies up to 60 Hz. Chromatic aberrations and distortions are estimated and corrected using a 3D laser engraved calibration target. The camera-projector system characterization is presented considering size and depth position of the particles. The use of these components reduces dramatically the cost and complexity of traditional 3D-PTV systems.
Linear game non-contextuality and Bell inequalities—a graph-theoretic approach
International Nuclear Information System (INIS)
Rosicka, M; Ramanathan, R; Gnaciński, P; Horodecki, M; Horodecki, K; Horodecki, P; Severini, S
2016-01-01
We study the classical and quantum values of a class of one- and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR (XOR-d) games we study are a subclass of the well-known linear games. We introduce a ‘constraint graph’ associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the graph-theoretic characterization to relate the task of finding equivalent games to the notion of signed graphs and switching equivalence from graph theory. We relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, which is known to be MaxSNP hard, and connect the computation of the classical value of XOR-d games to the identification of specific cycles in the graph. We construct an orthogonality graph of the game from the constraint graph and study its Lovász theta number as a general upper bound on the quantum value even in the case of single-party contextual XOR-d games. XOR-d games possess appealing properties for use in device-independent applications such as randomness of the local correlated outcomes in the optimal quantum strategy. We study the possibility of obtaining quantum algebraic violation of these games, and show that no finite XOR-d game possesses the property of pseudo-telepathy leaving the frequently used chained Bell inequalities as the natural candidates for such applications. We also show this lack of pseudo-telepathy for multi-party XOR-type inequalities involving two-body correlation functions. (paper)
Linear game non-contextuality and Bell inequalities—a graph-theoretic approach
Rosicka, M.; Ramanathan, R.; Gnaciński, P.; Horodecki, K.; Horodecki, M.; Horodecki, P.; Severini, S.
2016-04-01
We study the classical and quantum values of a class of one- and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR (XOR-d) games we study are a subclass of the well-known linear games. We introduce a ‘constraint graph’ associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the graph-theoretic characterization to relate the task of finding equivalent games to the notion of signed graphs and switching equivalence from graph theory. We relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, which is known to be MaxSNP hard, and connect the computation of the classical value of XOR-d games to the identification of specific cycles in the graph. We construct an orthogonality graph of the game from the constraint graph and study its Lovász theta number as a general upper bound on the quantum value even in the case of single-party contextual XOR-d games. XOR-d games possess appealing properties for use in device-independent applications such as randomness of the local correlated outcomes in the optimal quantum strategy. We study the possibility of obtaining quantum algebraic violation of these games, and show that no finite XOR-d game possesses the property of pseudo-telepathy leaving the frequently used chained Bell inequalities as the natural candidates for such applications. We also show this lack of pseudo-telepathy for multi-party XOR-type inequalities involving two-body correlation functions.
Do focal colors look particularly "colorful"?
Witzel, Christoph; Franklin, Anna
2014-04-01
If the most typical red, yellow, green, and blue were particularly colorful (i.e., saturated), they would "jump out to the eye." This would explain why even fundamentally different languages have distinct color terms for these focal colors, and why unique hues play a prominent role in subjective color appearance. In this study, the subjective saturation of 10 colors around each of these focal colors was measured through a pairwise matching task. Results show that subjective saturation changes systematically across hues in a way that is strongly correlated to the visual gamut, and exponentially related to sensitivity but not to focal colors.
Automatic color preference correction for color reproduction
Tsukada, Masato; Funayama, Chisato; Tajima, Johji
2000-12-01
The reproduction of natural objects in color images has attracted a great deal of attention. Reproduction more pleasing colors of natural objects is one of the methods available to improve image quality. We developed an automatic color correction method to maintain preferred color reproduction for three significant categories: facial skin color, green grass and blue sky. In this method, a representative color in an object area to be corrected is automatically extracted from an input image, and a set of color correction parameters is selected depending on the representative color. The improvement in image quality for reproductions of natural image was more than 93 percent in subjective experiments. These results show the usefulness of our automatic color correction method for the reproduction of preferred colors.
On path hypercompositions in graphs and automata
Directory of Open Access Journals (Sweden)
Massouros Christos G.
2016-01-01
Full Text Available The paths in graphs define hypercompositions in the set of their vertices and therefore it is feasible to associate hypercompositional structures to each graph. Similarly, the strings of letters from their alphabet, define hypercompositions in the automata, which in turn define the associated hypergroups to the automata. The study of the associated hypercompositional structures gives results in both, graphs and automata theory.
Attack Graph Construction for Security Events Analysis
Directory of Open Access Journals (Sweden)
Andrey Alexeevich Chechulin
2014-09-01
Full Text Available The paper is devoted to investigation of the attack graphs construction and analysis task for a network security evaluation and real-time security event processing. Main object of this research is the attack modeling process. The paper contains the description of attack graphs building, modifying and analysis technique as well as overview of implemented prototype for network security analysis based on attack graph approach.
Steiner Distance in Graphs--A Survey
Mao, Yaping
2017-01-01
For a connected graph $G$ of order at least $2$ and $S\\subseteq V(G)$, the \\emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. In this paper, we summarize the known results on the Steiner distance parameters, including Steiner distance, Steiner diameter, Steiner center, Steiner median, Steiner interval, Steiner distance hereditary graph, Steiner distance stable graph, average Steiner distance, and Steiner ...
Density conditions for triangles in multipartite graphs
DEFF Research Database (Denmark)
Bondy, Adrian; Shen, Jin; Thomassé, Stephan
2006-01-01
subgraphs in G. We investigate in particular the case where G is a complete multipartite graph. We prove that a finite tripartite graph with all edge densities greater than the golden ratio has a triangle and that this bound is best possible. Also we show that an infinite-partite graph with finite parts has...... a triangle, provided that the edge density between any two parts is greater than 1/2....
ColorMoves: Optimizing Color's Potential for Exploration and Communication of Data
Samsel, F.
2017-12-01
Color is the most powerful perceptual channel available for exposing and communicating data. Most visualizations are rendered in one of a handful of common colormaps - the rainbow, cool-warm, heat map and viridis. These maps meet the basic criteria for encoding data - perceptual uniformity and reasonable discriminatory power. However, as the size and complexity of data grows, our need to optimize the potential of color grows. The ability to expose greater detail and differentiate between multiple variables becomes ever more important. To meet this need we have created ColorMoves, an interactive colormap construction tool that enables scientists to quickly and easily align a concentration contrast with the data ranges of interest. Perceptual research tells us that luminance is the strongest contrast and thus provides the highest degree of perceptual discrimination. However, the most commonly used colormaps contain a limited range of luminance contrast. ColorMoves enables interactive constructing colormaps enabling one to distribute the luminance where is it most needed. The interactive interface enables optimal placement of the color scales. The ability to watch the changes on ones data, in real time makes precision adjustment quick and easy. By enabling more precise placement and multiple ranges of luminance one can construct colomaps containing greater discriminatory power. By selecting from the wide range of color scale hues scientists can create colormaps intuitive to their subject. ColorMoves is comprised of four main components: a set of 40 color scales; a histogram of the data distribution; a viewing area showing the colormap on your data; and the controls section. The 40 color scales span the spectrum of hues, saturation levels and value distributions. The histogram of the data distribution enables placement of the color scales in precise locations. The viewing area show is the impact of changes on the data in real time. The controls section enables export
Decomposing a planar graph into an independent set and a 3-degenerate graph
DEFF Research Database (Denmark)
Thomassen, Carsten
2001-01-01
We prove the conjecture made by O. V. Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and a set inducing a 3-degenerate graph. (C) 2001 Academic Press....
Thermal fluctuations of dilaton black holes in gravity's rainbow
Dehghani, M.
2018-06-01
In this work, thermodynamics and phase transition of some new dilaton black hole solutions have been explored in the presence of the rainbow functions. By introducing an energy dependent space time, the dilaton potential has been obtained as the linear combination of two Liouville-type potentials and three new classes of black hole solutions have been constructed. The conserved and thermodynamic quantities of the new dilaton black holes have been calculated in the energy dependent space times. It has been shown that, even if some of the thermodynamic quantities are affected by the rainbow functions, the thermodynamical first law still remains valid. Also, the impacts of rainbow functions on the stability or phase transition of the new black hole solutions have been investigated. Finally, the quantum gravitational effects on the thermodynamics and phase transition of the solutions have been studied through consideration of the thermal fluctuations.
Composition measurements of binary mixture droplets by rainbow refractometry.
Wilms, J; Weigand, B
2007-04-10
So far, refractive index measurements by rainbow refractometry have been used to determine the temperature of single droplets and ensembles of droplets. Rainbow refractometry is, for the first time, to the best of our knowledge, applied to measure composition histories of evaporating, binary mixture droplets. An evaluation method is presented that makes use of Airy theory and the simultaneous size measurement by Mie scattering imaging. The method further includes an empirical correction function for a certain diameter and refractive index range. The measurement uncertainty was investigated by numerical simulations with Lorenz-Mie theory. For the experiments, an optical levitation setup was used allowing for long measurement periods. Temperature measurements of single-component droplets at different temperature levels are shown to demonstrate the accuracy of rainbow refractometry. Measurements of size and composition histories of binary mixture droplets are presented for two different mixtures. Experimental results show good agreement with numerical results using a rapid-mixing model.
Composition measurements of binary mixture droplets by rainbow refractometry
International Nuclear Information System (INIS)
Wilms, J.; Weigand, B.
2007-01-01
So far, refractive index measurements by rainbow refractometry have been used to determine the temperature of single droplets and ensembles of droplets. Rainbow refractometry is, for the first time, to the best of our knowledge, applied to measure composition histories of evaporating, binary mixture droplets. An evaluation method is presented that makes use of Airy theory and the simultaneous size measurement by Mie scattering imaging. The method further includes an empirical correction function for a certain diameter and refractive index range. The measurement uncertainty was investigated by numerical simulations with Lorenz-Mie theory. For the experiments, an optical levitation setup was used allowing for long measurement periods. Temperature measurements of single-component droplets at different temperature levels are shown to demonstrate the accuracy of rainbow refractometry. Measurements of size and composition histories of binary mixture droplets are presented for two different mixtures. Experimental results show good agreement with numerical results using a rapid-mixing model
Remnants of black rings from gravity’s rainbow
Energy Technology Data Exchange (ETDEWEB)
Ali, Ahmed Farag [Center for Fundamental Physics, Zewail City of Science and Technology,6th of October City, Giza 12588 (Egypt); Department of Physics, Faculty of Science, Benha University,Benha 13518 (Egypt); Faizal, Mir [Department of Physics and Astronomy, University of Waterloo,Waterloo, Ontario, N2L 3G1 (Canada); Khalil, Mohammed M. [Department of Electrical Engineering, Alexandria University,El-Horreya Rd., Alexandria 12544 (Egypt)
2014-12-29
In this paper, we investigate a spinning black ring and a charged black ring in the context of gravity’s rainbow. By incorporating rainbow functions proposed by Amelino-Camelia, et al. in http://dx.doi.org/10.1142/S0217751X97000566 http://dx.doi.org/10.12942/lrr-2013-5 in the metric of the black rings, a considerable modification happens to their thermodynamical properties. We calculate corrections to the temperature, entropy and heat capacity of the black rings. These calculations demonstrate that the behavior of Hawking radiation changes considerably near the Planck scale in gravity’s rainbow, where it is shown that black rings do not evaporate completely and a remnant is left as the black rings evaporate down to Planck scale.
Graph algorithms in the titan toolkit.
Energy Technology Data Exchange (ETDEWEB)
McLendon, William Clarence, III; Wylie, Brian Neil
2009-10-01
Graph algorithms are a key component in a wide variety of intelligence analysis activities. The Graph-Based Informatics for Non-Proliferation and Counter-Terrorism project addresses the critical need of making these graph algorithms accessible to Sandia analysts in a manner that is both intuitive and effective. Specifically we describe the design and implementation of an open source toolkit for doing graph analysis, informatics, and visualization that provides Sandia with novel analysis capability for non-proliferation and counter-terrorism.
Xu, Kexiang; Trinajstić, Nenad
2015-01-01
This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921—2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number o...
Mechatronic modeling and simulation using bond graphs
Das, Shuvra
2009-01-01
Introduction to Mechatronics and System ModelingWhat Is Mechatronics?What Is a System and Why Model Systems?Mathematical Modeling Techniques Used in PracticeSoftwareBond Graphs: What Are They?Engineering SystemsPortsGeneralized VariablesBond GraphsBasic Components in SystemsA Brief Note about Bond Graph Power DirectionsSummary of Bond Direction RulesDrawing Bond Graphs for Simple Systems: Electrical and MechanicalSimplification Rules for Junction StructureDrawing Bond Graphs for Electrical SystemsDrawing Bond Graphs for Mechanical SystemsCausalityDrawing Bond Graphs for Hydraulic and Electronic Components and SystemsSome Basic Properties and Concepts for FluidsBond Graph Model of Hydraulic SystemsElectronic SystemsDeriving System Equations from Bond GraphsSystem VariablesDeriving System EquationsTackling Differential CausalityAlgebraic LoopsSolution of Model Equations and Their InterpretationZeroth Order SystemsFirst Order SystemsSecond Order SystemTransfer Functions and Frequency ResponsesNumerical Solution ...
An algebraic approach to graph codes
DEFF Research Database (Denmark)
Pinero, Fernando
This thesis consists of six chapters. The first chapter, contains a short introduction to coding theory in which we explain the coding theory concepts we use. In the second chapter, we present the required theory for evaluation codes and also give an example of some fundamental codes in coding...... theory as evaluation codes. Chapter three consists of the introduction to graph based codes, such as Tanner codes and graph codes. In Chapter four, we compute the dimension of some graph based codes with a result combining graph based codes and subfield subcodes. Moreover, some codes in chapter four...
Interactive Graph Layout of a Million Nodes
Directory of Open Access Journals (Sweden)
Peng Mi
2016-12-01
Full Text Available Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph topology. This algorithm can interactively layout graphs with millions of nodes, and support real-time interaction to explore alternative graph layouts. Users can directly manipulate the layout of vertices in a force-directed fashion. The complexity of traditional repulsive force computation is reduced by approximating calculations based on the hierarchical structure of multi-level clustered graphs. We evaluate the algorithm performance, and demonstrate human-in-the-loop layout in two sensemaking case studies. Moreover, we summarize lessons learned for designing interactive large graph layout algorithms on the GPU.
Text-Filled Stacked Area Graphs
DEFF Research Database (Denmark)
Kraus, Martin
2011-01-01
-filled stacked area graphs; i.e., graphs that feature stacked areas that are filled with small-typed text. Since these graphs allow for computing the text layout automatically, it is possible to include large amounts of textual detail with very little effort. We discuss the most important challenges and some...... solutions for the design of text-filled stacked area graphs with the help of an exemplary visualization of the genres, publication years, and titles of a database of several thousand PC games....
Reconstructing Nearly Simple Polytopes from their Graph
Doolittle, Joseph
2017-01-01
We present a partial description of which polytopes are reconstructible from their graphs. This is an extension of work by Blind and Mani (1987) and Kalai (1988), which showed that simple polytopes can be reconstructed from their graphs. In particular, we introduce a notion of $h$-nearly simple and prove that 1-nearly simple and 2-nearly simple polytopes are reconstructible from their graphs. We also give an example of a 3-nearly simple polytope which is not reconstructible from its graph. Fu...
A Reduction of the Graph Reconstruction Conjecture
Directory of Open Access Journals (Sweden)
Monikandan S.
2014-08-01
Full Text Available A graph is said to be reconstructible if it is determined up to isomor- phism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all non-geodetic and non-interval-regular blocks G with diam(G = 2 or diam(Ḡ = diam(G = 3 are reconstructible
VT Digital Line Graph Miscellaneous Transmission Lines
Vermont Center for Geographic Information — (Link to Metadata) This datalayer is comprised of Miscellaineous Transmission Lines. Digital line graph (DLG) data are digital representations of cartographic...
Development and usage of a false color display technique for presenting Seasat-A scatterometer data
Jackson, C. B.
1980-01-01
A computer generated false color program which creates digital multicolor graphics to display geophysical surface parameters measured by the Seasat-A satellite scatterometer (SASS) is described. The data is incrementally scaled over the range of acceptable values and each increment and its data points are assigned a color. The advantage of the false color display is that it visually infers cool or weak data versus hot or intense data by using the rainbow of colors. For example, with wind speeds, levels of yellow and red could be used to imply high winds while green and blue could imply calmer air. The SASS data is sorted into geographic regions and the final false color images are projected onto various world maps with superimposed land/water boundaries.
Derefeldt, Gunilla A. M.; Menu, Jean-Pierre; Swartling, Tiina
1995-04-01
This report surveys cognitive aspects of color in terms of behavioral, neuropsychological, and neurophysiological data. Color is usually defined as psychophysical color or as perceived color. Behavioral data on categorical color perception, absolute judgement of colors, color coding, visual search, and visual awareness refer to the more cognitive aspects of color. These are of major importance in visual synthesis and spatial organization, as already shown by the Gestalt psychologists. Neuropsychological and neurophysiological findings provide evidence for an interrelation between cognitive color and spatial organization. Color also enhances planning strategies, as has been shown by studies on color and eye movements. Memory colors and the color- language connections in the brain also belong among the cognitive aspects of color.
Majdinasab, Marjan; Hosseini, Seyed Mohammad Hashem; Sepidname, Marziyeh; Negahdarifar, Manizheh; Li, Peiwu
2018-05-01
Alginate is a non-toxic, renewable, and linear copolymer obtained from the brown algae Laminaria digitata that can be easily shaped into beads. Its good gel forming properties have made it useful for entrapping food and pharmaceutical ingredients. In this study, alginate beads were used in a novel application as a colorimetric sensor in food intelligent packaging. Colorimetric sensor was developed through entrapping red cabbage extract as a pH indicator in alginate beads. The pH indicator beads were used in rainbow trout packaging for monitoring fillets spoilage. Color change of beads during fish storage was measured using the CIELab method. The alginate bead colorimetric sensor is validated by measuring total volatile basic nitrogen (TVB-N) levels and microbial populations in fish samples. Moreover, peroxide value (PV) and thiobarbituric acid reactive substances (TBARS) were evaluated during storage. Results indicated that increasing the bacterial population during storage and production of proteolytic enzymes resulted in protein degradation, accumulation of volatile amine compounds, increase in the pH and finally color change of alginate beads. The values of TVB-N, pH, PV and TBARS increased with time of storage. The results of TVB-N and microbial growth were in accordance with color change of beads and CIELab data. Therefore, the proposed system enjoys a high sensitivity to pH variations and is capable of monitoring the spoilage of fish or other protein-rich products through its wide range of color changes. The alginate beads containing the red cabbage extract can, thus, be used as a low-cost colorimetric sensor for intelligent packaging applications.
Racialism and Representation in the Rainbow Nation
Directory of Open Access Journals (Sweden)
Fileve T. Palmer
2016-11-01
Full Text Available Despite a commitment to non-racialism in the South African Constitution and anthropology’s steadfast position that race is a social construction, race is still a highly valued ideology with real-life implications for citizens. In South Africa, racialism particularly affects heterogeneous, multigenerational, multiethnic creole people known as “Coloureds.” The larger category of Coloured is often essentialized based on its intermediary status between Black and White and its relationship to South Africa’s “mother city” (Cape Town, where the majority of Coloured people live. Through research on Coloured identity in KwaZulu-Natal, South Africa, I show how the nuances of personal and collective histories, spatial constraints, and education affect the identities of youth and elders differently from their Cape counterparts. By incorporating a photo-voice methodology, which I called Photo Ethnography Project (PEP, participants produced their own visual materials and challenged essentialized versions of themselves (specifically and South Africa (in general. Through three public displays of photography and narratives, youth in three communities answered the question of what it means to be Coloured in today’s rainbow nation.
Matthen, Mohan
1999-01-01
What is color? What is color vision? Most philosophers answer by reference to humans: to human color qualia, or to the environmental properties or "quality spaces" perceived by humans. It is argued, with reference to empirical findings concerning comparative color vision and the evolution of color vision, that all such attempts are mistaken. An adequate definition of color vision must eschew reference to its outputs in the human cognition and refer only to inputs: color vision consists in...
Rainbow refractometry on particles with radial refractive index gradients
Energy Technology Data Exchange (ETDEWEB)
Saengkaew, Sawitree [CNRS/Universite et INSA de Rouen, UMR 6614/CORIA, BP12, 76 800, Saint Etienne du Rouvray CEDEX (France); Chulalongkorn University, Center of Excellence in Particle Technology, Faculty of Engineering, Bangkok (Thailand); Charinpanitkul, Tawatchai; Vanisri, Hathaichanok; Tanthapanichakoon, Wiwut [Chulalongkorn University, Center of Excellence in Particle Technology, Faculty of Engineering, Bangkok (Thailand); Biscos, Yves; Garcia, Nicolas; Lavergne, Gerard [ONERA/DMAE, Toulouse (France); Mees, Loic; Gouesbet, Gerard; Grehan, Gerard [CNRS/Universite et INSA de Rouen, UMR 6614/CORIA, BP12, 76 800, Saint Etienne du Rouvray CEDEX (France)
2007-10-15
The rainbow refractrometry, under its different configurations (classical and global), is an attractive technique to extract information from droplets in evaporation such as diameter and temperature. Recently a new processing strategy has been developed which increases dramatically the size and refractive index measurements accuracy for homogeneous droplets. Nevertheless, for mono component as well as for multicomponent droplets, the presence of temperature and/or of concentration gradients induce the presence of a gradient of refractive index which affects the interpretation of the recorded signals. In this publication, the effect of radial gradient on rainbow measurements with a high accuracy never reached previously is quantified. (orig.)
Immunity to rhabdoviruses in rainbow trout: the antibody response
DEFF Research Database (Denmark)
Lorenzen, Niels; Lapatra, S.E.
1999-01-01
to their occasional detrimental effect on rainbow trout farming. Research efforts have been focused on understanding the mechanisms involved in protective immunity. Several specific and nonspecific cellular and humoral parameters are believed to be involved, but only the antibody response has been characterised......, have demonstrated that rainbow trout can produce specific and highly functional antibodies that are able to neutralise virus pathogenicity in vitro as well as in vivo. The apparently more restricted antibody response to IHNV and VHSV antigens in fish compared to mammals could possibly be explained...... aspects of antibody response and antibody reactivity with IHNV and VHSV antigens....
Vertebral column deformities in farmed rainbow trout ( Oncorhynchus mykiss )
DEFF Research Database (Denmark)
Madsen, Lone; Dalsgaard, Inger
1999-01-01
Farmed rainbow trout (Oncorhynchus mykiss) were fed diets with either different levels of vitamin C, or diets enriched with glucan or chitin, from feeding start and 6 months onwards. At an average weight of 100 g, the trout were X-rayed to determine the deformity level. The investigations showed...... of deformities (4.8%). In all groups examined, the deformities were spread over the whole vertebral column. The deformities in the group fed the low vitamin C diet were more severe than those found in the other groups. An outbreak of the disease rainbow trout fry syndrome (RTFS) caused by the bacterium...
Three-dimensional dilatonic gravity's rainbow: Exact solutions
International Nuclear Information System (INIS)
Hossein Hendi, Seyed; Eslam Panah, Behzad; Panahiyan, Shahram
2016-01-01
Deep relations of dark energy scenario and string theory results into dilaton gravity, on the one hand, and the connection between quantum gravity and gravity's rainbow, on the other hand, motivate us to consider three-dimensional dilatonic black hole solutions in gravity's rainbow. We obtain two classes of the solutions, which are polynomial and logarithmic forms. We also calculate conserved and thermodynamic quantities, and examine the first law of thermodynamics for both classes. In addition, we study thermal stability and show that one of the classes is thermally stable while the other one is unstable.
On cyclic orthogonal double covers of circulant graphs by special infinite graphs
Directory of Open Access Journals (Sweden)
R. El-Shanawany
2017-12-01
Full Text Available In this article, a technique to construct cyclic orthogonal double covers (CODCs of regular circulant graphs by certain infinite graph classes such as complete bipartite and tripartite graphs and disjoint union of butterfly and K1,2n−10 is introduced.
The complexity of the matching-cut problem for planar graphs and other graph classes
Bonsma, P.S.
2009-01-01
The Matching-Cut problem is the problem to decide whether a graph has an edge cut that is also a matching. Previously this problem was studied under the name of the Decomposable Graph Recognition problem, and proved to be -complete when restricted to graphs with maximum degree four. In this paper it
Bieryla, Allyson; Diaz Merced, Wanda; Davis, Daniel
2018-06-01
In astronomy, the relationship between color and temperature is an important concept. This concept can be demonstrated in a laboratory or seen at telescope when observing stars. A blind/visually-impaired (B/VI) person would not be able to engage in the same observational demonstrations that are typically done to explain this concept. We’ve developed a tool for B/VI students to participate in these types of observational activities. Using an arduino compatible micro controller with and RGB light sensor, we are able to convert filtered light into sound. The device will produce different timbres for different wavelengths of light, which can then be used to distinguish the temperature of an object. The device is handheld, easy to program and inexpensive to reproduce (< $50). It is also fitted to mount on a telescope for observing. The design schematic and code will be open source and available for download.
Probability on graphs random processes on graphs and lattices
Grimmett, Geoffrey
2018-01-01
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Enabling Graph Appliance for Genome Assembly
Energy Technology Data Exchange (ETDEWEB)
Singh, Rina [ORNL; Graves, Jeffrey A [ORNL; Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Shankar, Mallikarjun [ORNL
2015-01-01
In recent years, there has been a huge growth in the amount of genomic data available as reads generated from various genome sequencers. The number of reads generated can be huge, ranging from hundreds to billions of nucleotide, each varying in size. Assembling such large amounts of data is one of the challenging computational problems for both biomedical and data scientists. Most of the genome assemblers developed have used de Bruijn graph techniques. A de Bruijn graph represents a collection of read sequences by billions of vertices and edges, which require large amounts of memory and computational power to store and process. This is the major drawback to de Bruijn graph assembly. Massively parallel, multi-threaded, shared memory systems can be leveraged to overcome some of these issues. The objective of our research is to investigate the feasibility and scalability issues of de Bruijn graph assembly on Cray s Urika-GD system; Urika-GD is a high performance graph appliance with a large shared memory and massively multithreaded custom processor designed for executing SPARQL queries over large-scale RDF data sets. However, to the best of our knowledge, there is no research on representing a de Bruijn graph as an RDF graph or finding Eulerian paths in RDF graphs using SPARQL for potential genome discovery. In this paper, we address the issues involved in representing a de Bruin graphs as RDF graphs and propose an iterative querying approach for finding Eulerian paths in large RDF graphs. We evaluate the performance of our implementation on real world ebola genome datasets and illustrate how genome assembly can be accomplished with Urika-GD using iterative SPARQL queries.
Using color management in color document processing
Nehab, Smadar
1995-04-01
Color Management Systems have been used for several years in Desktop Publishing (DTP) environments. While this development hasn't matured yet, we are already experiencing the next generation of the color imaging revolution-Device Independent Color for the small office/home office (SOHO) environment. Though there are still open technical issues with device independent color matching, they are not the focal point of this paper. This paper discusses two new and crucial aspects in using color management in color document processing: the management of color objects and their associated color rendering methods; a proposal for a precedence order and handshaking protocol among the various software components involved in color document processing. As color peripherals become affordable to the SOHO market, color management also becomes a prerequisite for common document authoring applications such as word processors. The first color management solutions were oriented towards DTP environments whose requirements were largely different. For example, DTP documents are image-centric, as opposed to SOHO documents that are text and charts centric. To achieve optimal reproduction on low-cost SOHO peripherals, it is critical that different color rendering methods are used for the different document object types. The first challenge in using color management of color document processing is the association of rendering methods with object types. As a result of an evolutionary process, color matching solutions are now available as application software, as driver embedded software and as operating system extensions. Consequently, document processing faces a new challenge, the correct selection of the color matching solution while avoiding duplicate color corrections.
Guts of surfaces and the colored Jones polynomial
Futer, David; Purcell, Jessica
2013-01-01
This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement. We show that certain coefficients of the polynomial measure how far this surface is from being a fiber for the knot; in particular, the surface is a fiber if and only if a particular coefficient vanishes. We also relate hyperbolic volume to colored Jones polynomials. Our method is to generalize the checkerboard decompositions of alternating knots. Under mild diagrammatic hypotheses, we show that these surfaces are essential, and obtain an ideal polyhedral decomposition of their complement. We use normal surface theory to relate the pieces of the JSJ decomposition of the complement to the combinatorics of certain surface spines (state graphs). Since state graphs have p...
Guided color consistency optimization for image mosaicking
Xie, Renping; Xia, Menghan; Yao, Jian; Li, Li
2018-01-01
This paper studies the problem of color consistency correction for sequential images with diverse color characteristics. Existing algorithms try to adjust all images to minimize color differences among images under a unified energy framework, however, the results are prone to presenting a consistent but unnatural appearance when the color difference between images is large and diverse. In our approach, this problem is addressed effectively by providing a guided initial solution for the global consistency optimization, which avoids converging to a meaningless integrated solution. First of all, to obtain the reliable intensity correspondences in overlapping regions between image pairs, we creatively propose the histogram extreme point matching algorithm which is robust to image geometrical misalignment to some extents. In the absence of the extra reference information, the guided initial solution is learned from the major tone of the original images by searching some image subset as the reference, whose color characteristics will be transferred to the others via the paths of graph analysis. Thus, the final results via global adjustment will take on a consistent color similar to the appearance of the reference image subset. Several groups of convincing experiments on both the synthetic dataset and the challenging real ones sufficiently demonstrate that the proposed approach can achieve as good or even better results compared with the state-of-the-art approaches.
Modeling human color categorization
van den Broek, Egon; Schouten, Th.E.; Kisters, P.M.F.
A unique color space segmentation method is introduced. It is founded on features of human cognition, where 11 color categories are used in processing color. In two experiments, human subjects were asked to categorize color stimuli into these 11 color categories, which resulted in markers for a
Isospectral graphs with identical nodal counts
International Nuclear Information System (INIS)
Oren, Idan; Band, Ram
2012-01-01
According to a recent conjecture, isospectral objects have different nodal count sequences (Gnutzmann et al 2005 J. Phys. A: Math. Gen. 38 8921–33). We study generalized Laplacians on discrete graphs, and use them to construct the first non-trivial counterexamples to this conjecture. In addition, these examples demonstrate a surprising connection between isospectral discrete and quantum graphs. (paper)
Compression-based inference on graph data
Bloem, P.; van den Bosch, A.; Heskes, T.; van Leeuwen, D.
2013-01-01
We investigate the use of compression-based learning on graph data. General purpose compressors operate on bitstrings or other sequential representations. A single graph can be represented sequentially in many ways, which may in uence the performance of sequential compressors. Using Normalized
On minimum degree conditions for supereulerian graphs
Broersma, Haitze J.; Xiong, L.
1999-01-01
A graph is called supereulerian if it has a spanning closed trail. Let $G$ be a 2-edge-connected graph of order $n$ such that each minimal edge cut $E \\subseteq E (G)$ with $|E| \\le 3$ satisfies the property that each component of $G-E$ has order at least $(n-2)/5$. We prove that either $G$ is
On the exterior structure of graphs
International Nuclear Information System (INIS)
Kastler, Daniel
2004-01-01
After a detailed ab initio description of the exterior structure of graphs as handled by Connes and Kreimer in their work on renormalization (illustrated by the example of the φ 3 model in six dimensions) we spell out in detail their study of the Lie algebra of infinitesimal characters and of the group of characters of the Hopf algebra of Feynman graphs
The Minimum Distance of Graph Codes
DEFF Research Database (Denmark)
Høholdt, Tom; Justesen, Jørn
2011-01-01
We study codes constructed from graphs where the code symbols are associated with the edges and the symbols connected to a given vertex are restricted to be codewords in a component code. In particular we treat such codes from bipartite expander graphs coming from Euclidean planes and other...... geometries. We give results on the minimum distances of the codes....
Domination versus disjunctive domination in graphs | Henning ...
African Journals Online (AJOL)
Domination versus disjunctive domination in graphs. Michael A Henning, Sinclair A Marcon. Abstract. A dominating set in a graph G is a set S of vertices of G such that every vertex not in S is adjacent to a vertex of S. The domination number of G is the minimum cardinality of a dominating set of G. For a positive integer b, ...
Eigenvalues and expansion of bipartite graphs
DEFF Research Database (Denmark)
Høholdt, Tom; Janwa, Heeralal
2012-01-01
We prove lower bounds on the largest and second largest eigenvalue of the adjacency matrix of bipartite graphs and give necessary and sufficient conditions for equality. We give several examples of classes that are optimal with respect to the bouns. We prove that BIBD-graphs are characterized by ...
Indian Academy of Sciences (India)
1National Centre for Advanced Research in Discrete Mathematics ... 3Department of Computer Science, Ball State University, Muncie, IN, USA .... The corona of two disjoint graphs G1 and G2 is defined to be the graph G = G1 ◦ G2,.
Trajectories entropy in dynamical graphs with memory
Directory of Open Access Journals (Sweden)
Francesco eCaravelli
2016-04-01
Full Text Available In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.
Graphs, Ideal Flow, and the Transportation Network
Teknomo, Kardi
2016-01-01
This lecture discusses the mathematical relationship between network structure and network utilization of transportation network. Network structure means the graph itself. Network utilization represent the aggregation of trajectories of agents in using the network graph. I show the similarity and relationship between the structural pattern of the network and network utilization.
Supplantation of Mental Operations on Graphs
Vogel, Markus; Girwidz, Raimund; Engel, Joachim
2007-01-01
Research findings show the difficulties younger students have in working with graphs. Higher mental operations are necessary for a skilled interpretation of abstract representations. We suggest connecting a concrete representation of the modeled problem with the related graph. The idea is to illustrate essential mental operations externally. This…
Some remarks on definability of process graphs
Grabmayer, C.A.; Klop, J.W.; Luttik, B.; Baier, C.; Hermanns, H.
2006-01-01
We propose the notions of "density" and "connectivity" of infinite process graphs and investigate them in the context of the wellknown process algebras BPA and BPP. For a process graph G, the density function in a state s maps a natural number n to the number of states of G with distance less or
On revealing graph cycles via boundary measurements
International Nuclear Information System (INIS)
Belishev, M I; Wada, N
2009-01-01
This paper deals with boundary value inverse problems on a metric graph, the structure of the graph being assumed unknown. The question under consideration is how to detect from the dynamical and/or spectral inverse data whether the graph contains cycles (is not a tree). For any graph Ω, the dynamical as well as spectral boundary inverse data determine the so-called wave diameter d w : H -1 (Ω) → R defined on functionals supported in the graph. The known fact is that if Ω is a tree then d w ≥ 0 holds and, in this case, the inverse data determine Ω up to isometry. A graph Ω is said to be coordinate if the functions {dist Ω (., γ)} γin∂Ω constitute a coordinate system on Ω. For such graphs, we propose a procedure, which reveals the presence/absence of cycles. The hypothesis is that Ω contains cycles if and only if d w takes negative values. We do not justify this hypothesis in the general case but reduce it to a certain special class of graphs (suns)
Declarative Process Mining for DCR Graphs
DEFF Research Database (Denmark)
Debois, Søren; Hildebrandt, Thomas T.; Laursen, Paw Høvsgaard
2017-01-01
We investigate process mining for the declarative Dynamic Condition Response (DCR) graphs process modelling language. We contribute (a) a process mining algorithm for DCR graphs, (b) a proposal for a set of metrics quantifying output model quality, and (c) a preliminary example-based comparison...
A Graph Library Extension of SVG
DEFF Research Database (Denmark)
Nørmark, Kurt
2007-01-01
be aggregated as a single node, and an entire graph can be embedded in a single node. In addition, a number of different graph animations are described. The starting point of the SVG extension is a library that provides an exact of mirror of SVG 1.1 in the functional programming language Scheme. Each element...
From concatenated codes to graph codes
DEFF Research Database (Denmark)
Justesen, Jørn; Høholdt, Tom
2004-01-01
We consider codes based on simple bipartite expander graphs. These codes may be seen as the first step leading from product type concatenated codes to more complex graph codes. We emphasize constructions of specific codes of realistic lengths, and study the details of decoding by message passing...
Graph coarsening and clustering on the GPU
Fagginger Auer, B.O.; Bisseling, R.H.
2013-01-01
Agglomerative clustering is an effective greedy way to quickly generate graph clusterings of high modularity in a small amount of time. In an effort to use the power offered by multi-core CPU and GPU hardware to solve the clustering problem, we introduce a fine-grained sharedmemory parallel graph
Pixels to Graphs by Associative Embedding
Newell, Alejandro; Deng, Jia
2017-01-01
network such that it takes in an input image and produces a full graph. This is done end-to-end in a single stage with the use of associative embeddings. The network learns to simultaneously identify all of the elements that make up a graph and piece them
Isomorphisms and traversability of directed path graphs
Broersma, Haitze J.; Li, Xueliang; Li, X.
1998-01-01
The concept of a line digraph is generalized to that of a directed path graph. The directed path graph $\\forw P_k(D)$ of a digraph $D$ is obtained by representing the directed paths on $k$ vertices of $D$ by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in $D$
Perfect secure domination in graphs
Directory of Open Access Journals (Sweden)
S.V. Divya Rashmi
2017-07-01
Full Text Available Let $G=(V,E$ be a graph. A subset $S$ of $V$ is a dominating set of $G$ if every vertex in $Vsetminus S$ is adjacent to a vertex in $S.$ A dominating set $S$ is called a secure dominating set if for each $vin Vsetminus S$ there exists $uin S$ such that $v$ is adjacent to $u$ and $S_1=(Ssetminus{u}cup {v}$ is a dominating set. If further the vertex $uin S$ is unique, then $S$ is called a perfect secure dominating set. The minimum cardinality of a perfect secure dominating set of $G$ is called the perfect secure domination number of $G$ and is denoted by $gamma_{ps}(G.$ In this paper we initiate a study of this parameter and present several basic results.
Graph Mining Meets the Semantic Web
Energy Technology Data Exchange (ETDEWEB)
Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Lim, Seung-Hwan [ORNL
2015-01-01
The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today, data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. We address that need through implementation of three popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, and PageRank). We implement these algorithms as SPARQL queries, wrapped within Python scripts. We evaluate the performance of our implementation on 6 real world data sets and show graph mining algorithms (that have a linear-algebra formulation) can indeed be unleashed on data represented as RDF graphs using the SPARQL query interface.
On the nullity number of graphs
Directory of Open Access Journals (Sweden)
Mustapha Aouchiche
2017-10-01
Full Text Available The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 (2007 60--67] that $\\eta \\le n - D$, where $\\eta$, n and D denote the nullity number, the order and the diameter of a connected graph, respectively. We first give a necessary condition on the extremal graphs corresponding to that bound, and then we strengthen the bound itself using the maximum clique number. In addition, we prove bounds on the nullity using the number of pendant neighbors in a graph. One of those bounds is an improvement of a known bound involving the domination number.
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2011-01-01
in a third syntactic theory. The structure of the store-based abstract machine corresponding to this third syntactic theory oincides with that of Turner's original reduction machine. The three syntactic theories presented here The three syntactic heories presented here therefore have the following......We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this syntactic theory as a reduction semantics, which we refocus into the first storeless abstract machine...... for combinatory graph reduction, which we refunctionalize into the first storeless natural semantics for combinatory graph reduction.We then factor out the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand, resulting in a second syntactic theory, this one...
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2013-01-01
, as a store-based reduction semantics of combinatory term graphs. We then refocus this store-based reduction semantics into a store-based abstract machine. The architecture of this store-based abstract machine coincides with that of Turner's original reduction machine. The three syntactic theories presented......We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this rst syntactic theory as a storeless reduction semantics of combinatory terms. We then factor out...... the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand . The factored terms can be interpreted as term graphs in the sense of Barendregt et al. We express this second syntactic theory, which we prove equivalent to the rst, as a storeless reduction semantics...
Algorithms and Data Structures for Graphs
DEFF Research Database (Denmark)
Rotenberg, Eva
are planar graphs, which are those that can be drawn on a piece of paper without any pair of edges crossing. For planar graphs where each edge can only be traversed in one direction, a fundamental question is whether there is a route from vertex A to vertex B in the graph. We show how such a graph can...... of the form: "Is there an edge such that all paths between A and B go via that edge?" and which can quickly be updated when edges are inserted or deleted. We further show how to represent a planar graph such that we can quickly update our representation when an edge is deleted, and such that questions...
OPEX: Optimized Eccentricity Computation in Graphs
Energy Technology Data Exchange (ETDEWEB)
Henderson, Keith [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2011-11-14
Real-world graphs have many properties of interest, but often these properties are expensive to compute. We focus on eccentricity, radius and diameter in this work. These properties are useful measures of the global connectivity patterns in a graph. Unfortunately, computing eccentricity for all nodes is O(n2) for a graph with n nodes. We present OPEX, a novel combination of optimizations which improves computation time of these properties by orders of magnitude in real-world experiments on graphs of many different sizes. We run OPEX on graphs with up to millions of links. OPEX gives either exact results or bounded approximations, unlike its competitors which give probabilistic approximations or sacrifice node-level information (eccentricity) to compute graphlevel information (diameter).
On The Roman Domination Stable Graphs
Directory of Open Access Journals (Sweden)
Hajian Majid
2017-11-01
Full Text Available A Roman dominating function (or just RDF on a graph G = (V,E is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u = 0 is adjacent to at least one vertex v for which f(v = 2. The weight of an RDF f is the value f(V (G = Pu2V (G f(u. The Roman domination number of a graph G, denoted by R(G, is the minimum weight of a Roman dominating function on G. A graph G is Roman domination stable if the Roman domination number of G remains unchanged under removal of any vertex. In this paper we present upper bounds for the Roman domination number in the class of Roman domination stable graphs, improving bounds posed in [V. Samodivkin, Roman domination in graphs: the class RUV R, Discrete Math. Algorithms Appl. 8 (2016 1650049].
Pristine transfinite graphs and permissive electrical networks
Zemanian, Armen H
2001-01-01
A transfinite graph or electrical network of the first rank is obtained conceptually by connecting conventionally infinite graphs and networks together at their infinite extremities. This process can be repeated to obtain a hierarchy of transfiniteness whose ranks increase through the countable ordinals. This idea, which is of recent origin, has enriched the theories of graphs and networks with radically new constructs and research problems. The book provides a more accessible introduction to the subject that, though sacrificing some generality, captures the essential ideas of transfiniteness for graphs and networks. Thus, for example, some results concerning discrete potentials and random walks on transfinite networks can now be presented more concisely. Conversely, the simplifications enable the development of many new results that were previously unavailable. Topics and features: *A simplified exposition provides an introduction to transfiniteness for graphs and networks.*Various results for conventional g...
A model of language inflection graphs
Fukś, Henryk; Farzad, Babak; Cao, Yi
2014-01-01
Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to the abundance of inflectional forms. We construct the simplest form of inflection graphs, namely a bipartite graph in which one group of vertices corresponds to dictionary headwords and the other group to inflected forms encountered in a given text. We, then, study projection of this graph on the set of headwords. The projection decomposes into a large number of connected components, to be called word groups. Distribution of sizes of word group exhibits some remarkable properties, resembling cluster distribution in a lattice percolation near the critical point. We propose a simple model which produces graphs of this type, reproducing the desired component distribution and other topological features.
Disease management research using event graphs.
Allore, H G; Schruben, L W
2000-08-01
Event Graphs, conditional representations of stochastic relationships between discrete events, simulate disease dynamics. In this paper, we demonstrate how Event Graphs, at an appropriate abstraction level, also extend and organize scientific knowledge about diseases. They can identify promising treatment strategies and directions for further research and provide enough detail for testing combinations of new medicines and interventions. Event Graphs can be enriched to incorporate and validate data and test new theories to reflect an expanding dynamic scientific knowledge base and establish performance criteria for the economic viability of new treatments. To illustrate, an Event Graph is developed for mastitis, a costly dairy cattle disease, for which extensive scientific literature exists. With only a modest amount of imagination, the methodology presented here can be seen to apply modeling to any disease, human, plant, or animal. The Event Graph simulation presented here is currently being used in research and in a new veterinary epidemiology course. Copyright 2000 Academic Press.
Pixels to Graphs by Associative Embedding
Newell, Alejandro
2017-06-22
Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional neural network such that it takes in an input image and produces a full graph. This is done end-to-end in a single stage with the use of associative embeddings. The network learns to simultaneously identify all of the elements that make up a graph and piece them together. We benchmark on the Visual Genome dataset, and report a Recall@50 of 9.7% compared to the prior state-of-the-art at 3.4%, a nearly threefold improvement on the challenging task of scene graph generation.
Inferring ontology graph structures using OWL reasoning
Rodriguez-Garcia, Miguel Angel
2018-01-05
Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies\\' semantic content remains a challenge.We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies\\' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph .Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.
Inferring ontology graph structures using OWL reasoning.
Rodríguez-García, Miguel Ángel; Hoehndorf, Robert
2018-01-05
Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies' semantic content remains a challenge. We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph . Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.
NITRO MUSK ADDUCTS OF RAINBOW TROUT ...
Rainbow trout and other fish species can serve as 'sentinel' species for the assessment of ecological status and the presence of certain environmental contaminants. As such they act as bioindicators of exposure. Here we present seminal data regarding dose-response and toxicokinetics of trout hemoglobin adduct formation from exposure to nitro musks that are frequently used as fragrance ingredients in formulations of personal care products. Hemoglobin adducts serve as biomarkers of exposure of the sentinel species as we have shown in previous studies of hemoglobin adducts formed in trout and environmental carp exposed to musk xylene (MX) and musk ketone (MK). Gas chromatography-electron capture negative ion chemical ionization-mass spectrometry (GC-NICI-MS) employing selected ion monitoring is used to measure 4-amino-MX (4-AMX), 2-amino-MX (2-AMX), and 2-amino-MK (2-AMK) released by alkaline hydrolysis from the sulfinamide adducts of hemoglobin. Dose-response and toxicokinetics were investigated using this sensitive method for analysis of these metabolites. In the dose-response investigation, the concentrations of 4-AMX and 2-2AMX are observed to pass through a maximum at 0.10 mg/g. In the case of 2-AMK, the adduct concentration is almost the same at dosages in the range of 0.030 to 0.10 mg/g. For toxicokinetics, the concentration of the metabolites in the Hb reaches a maximum in the 3-day sample after administration of MX or MK. Further elimination of the metabo
Embedding Color Watermarks in Color Images
Directory of Open Access Journals (Sweden)
Wu Tung-Lin
2003-01-01
Full Text Available Robust watermarking with oblivious detection is essential to practical copyright protection of digital images. Effective exploitation of the characteristics of human visual perception to color stimuli helps to develop the watermarking scheme that fills the requirement. In this paper, an oblivious watermarking scheme that embeds color watermarks in color images is proposed. Through color gamut analysis and quantizer design, color watermarks are embedded by modifying quantization indices of color pixels without resulting in perceivable distortion. Only a small amount of information including the specification of color gamut, quantizer stepsize, and color tables is required to extract the watermark. Experimental results show that the proposed watermarking scheme is computationally simple and quite robust in face of various attacks such as cropping, low-pass filtering, white-noise addition, scaling, and JPEG compression with high compression ratios.
Teaching the Absorption of Light Colours Using an Artificial Rainbow
Yurumezoglu, Kemal; Isik, Hakan; Arikan, Gizem; Kabay, Gozde
2015-01-01
This paper presents an experimental activity based on the absorption of light colours by pigments. The activity is constructed using a stepwise design and offers an opportunity for students and teachers to compare and generalize the interactions between light and pigment colours. The light colours composing an artificial rainbow produced in the…
Estrogenic response of bisphenol A in rainbow trout (Oncorhynchus mykiss)
DEFF Research Database (Denmark)
Lindholst, Christian; Pedersen, Knud Ladegaard; Pedersen, Søren Nørby
2000-01-01
Bisphenol A (BPA) previously shown to possess xenoestrogenic activities was administered to rainbow trout (Oncorhynchus mykiss) through a continuos flow system. The estrogenic response expressed as the induction of vitellogenin (VTG) synthesis was measured during 12 days of exposure, using a direct...
Rainbow-shift mechanism behind discrete optical-potential ambiguities
International Nuclear Information System (INIS)
Brandan, M.E.; McVoy, K.W.
1991-01-01
Some years ago, Drisko et al. suggested that the discrete ambiguity often encountered for elastic scattering optical potentials could be understood as being due to the interior or small-l S-matrix elements for two ''equivalent'' potentials differing in phase by 2π, l-by-l. We point out that the absence of this phase change for peripheral partial waves is equally essential, and suggest that a deeper understanding of the ambiguity may be achieved by viewing it as a consequence of a farside interference between interior and peripheral partial waves. It is this interference which produces the broad ''Airy maxima'' of a nuclear rainbow, and we show that a Drisko-type phase-shift increment δ l →(δ l +π) for low-l phases relative to the high-l ones is exactly what is needed to shift a farside rainbow pattern by one Airy maximum, thus providing an equivalent ''rainbow-shift'' interpretation of the discrete ambiguity. The physical importance of both interpretations lies in the fact that the existence of discrete ambiguities (as well as of nuclear rainbows) is explicit evidence for low-l transparency in nucleus-nucleus collisions. The essential role played by low partial waves explains why peripheral reactions have generally not proven helpful in resolving this ambiguity
Toxicokinetics of perfluorooctane sulfonate in rainbow trout (Oncorhynchus mykiss)
Rainbow trout (Oncorhynchus mykiss) confined to respirometer-metabolism chambers were dosed with perfluorooctane sulfonate (PFOS) by intra-arterial injection and sampled to obtain concentration time-course data for plasma, and either urine or expired water. The data were then an...
Gyori, Ervin; Lovasz, Laszlo
2006-01-01
This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes survey articles reviewing classical theorems, as well as new, state-of-the-art results. Also presented are cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc. The open problems and the latest results in the papers are sure to inspire further research.
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