Generalized Ramsey numbers through adiabatic quantum optimization
NASA Astrophysics Data System (ADS)
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-09-01
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers r( G, H), the emergent order is characterized by graphs G and H. In this paper we: (i) present a quantum algorithm for computing generalized Ramsey numbers by reformulating the computation as a combinatorial optimization problem which is solved using adiabatic quantum optimization; and (ii) determine the Ramsey numbers r({{T}}m,{{T}}n) for trees of order m,n = 6,7,8, most of which were previously unknown.
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-01
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.
On Ramsey (P3, P6)-minimal graphs
NASA Astrophysics Data System (ADS)
Rahmadani, Desi; Baskoro, Edy Tri; Assiyatun, Hilda
2016-02-01
Finding all Ramsey (G, H)-minimal graphs for a certain pair of graphs G and H is an interesting and difficult problem. Even though, it is just for small graphs G and H. In this paper, we determine some Ramsey (P3, P6)-minimal graphs of small order. We also characterize all such Ramsey minimal graphs of order 6 by using their degree sequences. We prove that Ramsey (P3, P6)-minimal graphs have diameter at least two. We construct an infinite class of trees [6] which provides Ramsey (P3, P6)-minimal graphs.
On Ramsey (3K2, K3) - minimal graphs
NASA Astrophysics Data System (ADS)
Wijaya, Kristiana; Baskoro, Edy Tri; Assiyatun, Hilda; Suprijanto, Djoko
2016-02-01
The Ramsey graph theory has many interesting applications, such as in the fields of communications, information retrieval, and decision making. One of growing topics in Ramsey theory is Ramsey minimal graph. For any given graphs G and H, find graphs F such that any red-blue coloring of all edges of F contains either a red copy of G or a blue copy of H. If this condition is not satisfied by the graph F - e, then we call the graph F as a Ramsey (G, H) - minimal. In this paper, we derive the properties of (3K2, K3) - minimal graphs. We, then, characterize all Ramsey (3K2, K3) - minimal graphs.
Computing the isoperimetric number of a graph
Golovach, P.A.
1995-01-01
Let G be a finite graph. Denote by {partial_derivative}X, where X {contained_in} VG, the set of edges of the graph G with one end in X and the other end in the set VG{backslash}X. The ratio i(G) = min {vert_bar}{vert_bar}X{vert_bar}/{vert_bar}X{vert_bar}, where the minimum is over all nonempty subsets X of the set VG such that {vert_bar}X{vert_bar} {le} {vert_bar} VG {vert_bar}/2, is called the isoperimetric number of the graph G. It is easy to see that the isoperimetric number may be used as a {open_quotes}measure of connectivity{close_quotes} of the graph. The problem of determining the isoperimetric number is clearly linked with graph partition problems, which often arise in various applications. The isoperimetric number is also important for studying Riemann surfaces. These and other applications of the isoperimetric number justify the analysis of graphs of this kind. The properties of the isoperimetric number are presented in more detail elsewhere. It is shown elsewhere that the computation of the isoperimetric number is an NP-hard problem for graphs with multiple edges. We will show that the decision problem {open_quotes}given the graph G and two integers s and t decide if i(G) {le} s/t{close_quotes} is NP-complete even for simple graphs with vertex degrees not exceeding 3. Note that the isoperimetric number of a tree can be computed by a known polynomial-time algorithm.
Recognition of Graphs with Convex Quadratic Stability Number
NASA Astrophysics Data System (ADS)
Pacheco, Maria F.; Cardoso, Domingos M.
2009-09-01
A stable set of a graph is a set of mutually non-adjacent vertices. The determination of a maximum size stable set, which is called maximum stable set, and the determination of its size, which is called stability number, are central combinatorial optimization problems. However, given a nonnegative integer k, to determine if a graph G has a stable set of size k is NP-complete. In this paper we deal with graphs for which the stability number can be determined by solving a convex quadratic programming problem. Such graphs were introduced in [13] and are called graphs with convex-QP stability number. A few algorithmic techniques for the recognition of this type of graphs in particular families are presented.
Colour Mathematics: With Graphs and Numbers
ERIC Educational Resources Information Center
LoPresto, Michael C.
2009-01-01
The different combinations involved in additive and subtractive colour mixing can often be difficult for students to remember. Using transmission graphs for filters of the primary colours and a numerical scheme to write out the relationships are good exercises in analytical thinking that can help students recall the combinations rather than just…
Colour mathematics: with graphs and numbers
NASA Astrophysics Data System (ADS)
Lo Presto, Michael C.
2009-07-01
The different combinations involved in additive and subtractive colour mixing can often be difficult for students to remember. Using transmission graphs for filters of the primary colours and a numerical scheme to write out the relationships are good exercises in analytical thinking that can help students recall the combinations rather than just attempting to memorize them.
The rainbow connection number of some subdivided roof graphs
NASA Astrophysics Data System (ADS)
Susanti, Bety Hayat; Salman, A. N. M.; Simanjuntak, Rinovia
2016-02-01
Let G be an edge-colored graph where adjacent edges may have the same color. A path in G is called rainbow if its edges have distinct colors. A graph G is rainbow connected if any two distinct vertices in G are connected by a rainbow path. The smallest number of colors that are needed in order to make G rainbow connected is called the rainbow connection number of G, denoted by rc(G). In this paper, we determine the rainbow connection number of some subdivided roof graphs.
The (strong) rainbow connection number of stellar graphs
NASA Astrophysics Data System (ADS)
Shulhany, M. A.; Salman, A. N. M.
2016-02-01
Let G = (V,E) be a simple, connected, and finite graph. A function c from E to {1, 2, …, k} is said rainbow k-coloring of G, if for any pair of vertices u and v in V, there exists au - vpath whose edges have different colors. The rainbow connection number of G, denoted by rc(G), is the smallest positive integer k such that Ghas a rainbow k-coloring. Furthermore, such the function c is said strong rainbow k-coloring, if for any pair of vertices u and v in V, there exists a rainbow u-v path with its length is equal to distance betweenu and v. The smallest positive integer k such that G has a strong rainbow k-coloring is defined as the strong rainbow connection number, denoted by src(G).In this paper, we introduce a new class of graphs, namely stellar graphs. A stellar graph on 2mn+1 vertices, denoted by Stm,n, is the corona product of a trivial graph and mcopies ladder graph on 2n vertices (K1⊙m.Ln). We determine the (strong) rainbow connection number of stellar graphs.
Locating-chromatic number for a graph of two components
NASA Astrophysics Data System (ADS)
Welyyanti, Des; Simanjuntak, Rinovia; Uttunggadewa, Saladin; Baskoro, Edy Tri
2016-02-01
The study of locating-chromatic number of a graph initiated by Chartrand et al. [5] is only limited for connected graphs. In 2014, Welyyanti et al. extended this notion so that the locating-chromatic number can also be applied to disconnected graphs. Let c be a k-coloring of a disconnected graph H(V, E) and ∏ = {C1,C2, …, Ck} be the partition of V (H) induced by c, where Ci is the set of all vertices receiving color i. The color code c∏(v) of a vertex v ∈ H is the ordered k-tuple (d(v,C1), d(v,C2), …, d(v,Ck)), where d(v,Ci) = min{d(v, x)|x ∈ Ci} and d(v,Ci) < ∞ for all i ∈ [1, k]. If all vertices of H have distinct color codes, then c is called a locating-coloring of H. The locating-chromatic number of H, denoted by χ'L(H ) , is the smallest k such that H admits a locating-coloring with k colors, otherwise we say that χ'L(H )=∞ . In this paper, we determine locating-chromatic number of a graph with two components where each component has the locating-chromatic number 3.
Computing the Edge-Neighbour-Scattering Number of Graphs
NASA Astrophysics Data System (ADS)
Wei, Zongtian; Qi, Nannan; Yue, Xiaokui
2013-11-01
A set of edges X is subverted from a graph G by removing the closed neighbourhood N[X] from G. We denote the survival subgraph by G=X. An edge-subversion strategy X is called an edge-cut strategy of G if G=X is disconnected, a single vertex, or empty. The edge-neighbour-scattering number of a graph G is defined as ENS(G) = max{ω(G/X)-|X| : X is an edge-cut strategy of G}, where w(G=X) is the number of components of G=X. This parameter can be used to measure the vulnerability of networks when some edges are failed, especially spy networks and virus-infected networks. In this paper, we prove that the problem of computing the edge-neighbour-scattering number of a graph is NP-complete and give some upper and lower bounds for this parameter.
On the Crossing Numbers of Cartesian Products of Stars and Graphs on Five Vertices
NASA Astrophysics Data System (ADS)
Klešč, Marián
There are known crossing numbers of Cartesian products of stars with all graphs of order at most four. In this paper we are dealing with the Cartesian products of stars with graphs on five vertices. We give the exact values of crossing numbers for some of these graphs and we summarise all known results concerning crossing numbers of these graphs. In addition, we give the crossing number of the join product of star and the cycle C 5 with one additional edge.
Kupavskii, A B; Raigorodskii, A M
2013-10-31
We investigate in detail some properties of distance graphs constructed on the integer lattice. Such graphs find wide applications in problems of combinatorial geometry, in particular, such graphs were employed to answer Borsuk's question in the negative and to obtain exponential estimates for the chromatic number of the space. This work is devoted to the study of the number of cliques and the chromatic number of such graphs under certain conditions. Constructions of sequences of distance graphs are given, in which the graphs have unit length edges and contain a large number of triangles that lie on a sphere of radius 1/√3 (which is the minimum possible). At the same time, the chromatic numbers of the graphs depend exponentially on their dimension. The results of this work strengthen and generalize some of the results obtained in a series of papers devoted to related issues. Bibliography: 29 titles.
Mitra, Tapan; Sorger, Gerhard
2013-09-01
Studying a one-sector economy populated by finitely many heterogeneous households that are subject to no-borrowing constraints, we confirm a conjecture by Frank P. Ramsey according to which, in the long run, society would be divided into the set of patient households who own the entire capital stock and impatient ones without any physical wealth. More specifically, we prove (i) that there exists a unique steady state equilibrium that is globally asymptotically stable and (ii) that along every equilibrium the most patient household owns the entire capital of the economy after some finite time. Furthermore, we prove that despite the presence of the no-borrowing constraints all equilibria are efficient. Our results are derived for the continuous-time formulation of the model that was originally used by Ramsey, and they stand in stark contrast to results that - over the last three decades - have been found in the discrete-time version of the model. PMID:24926104
Graph of Total Number of Oligos Within Windows of a Sequence
1995-11-28
SEQWIN is user-friendly software which graphs the total number of oligos present in a sequence. The sequence is scanned one window at a time; windows can be overlapping. Each bar on the graph represents a single window down the sequence. The user specifies the sequence of interest and a list of oligos as program input. If the sequence is known, locations of specific structure or sequences can be specified and compared with the bars onmore » a graph. The window size, amount of overlap of the windows, number of windows to be considered, and the starting position of the first window used can be adjusted at the user's discretion.« less
Distance graphs having large chromatic numbers and containing no cliques or cycles of a given size
Demekhin, Evgenii E; Raigorodskii, Andrei M; Rubanov, Oleg I
2013-04-30
It is established that there exist sequences of distance graphs G{sub n} subset of R{sup n}, with chromatic numbers which grow exponentially, but, at the same time, without cliques or cycles of a given size. Bibliography: 42 titles.
ERIC Educational Resources Information Center
Earnest, Darrell
2015-01-01
This article reports on students' problem-solving approaches across three representations--number lines, coordinate planes, and function graphs--the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a "hierarchical representational…
ERIC Educational Resources Information Center
Earnest, Darrell Steven
2012-01-01
This dissertation explores fifth and eighth grade students' interpretations of three kinds of mathematical representations: number lines, the Cartesian plane, and graphs of linear functions. Two studies were conducted. In Study 1, I administered the paper-and-pencil Linear Representations Assessment (LRA) to examine students'…
NASA Technical Reports Server (NTRS)
Butler, Ricky W.; Sjogren, Jon A.
1998-01-01
This paper documents the NASA Langley PVS graph theory library. The library provides fundamental definitions for graphs, subgraphs, walks, paths, subgraphs generated by walks, trees, cycles, degree, separating sets, and four notions of connectedness. Theorems provided include Ramsey's and Menger's and the equivalence of all four notions of connectedness.
A Miniaturisation of Ramsey's Theorem
NASA Astrophysics Data System (ADS)
de Smet, Michiel; Weiermann, Andreas
We approximate the strength of the infinite Ramsey Theorem by iterating a finitary version. This density principle, in the style of Paris, together with PA will give rise to a first-order theory which achieves a lot of the strength of ACA0 and the original infinitary version. To prove our result, we use a generalisation of the results by Bigorajska and Kotlarski about partitioning α-large sets.
Large Deviation Function for the Number of Eigenvalues of Sparse Random Graphs Inside an Interval.
Metz, Fernando L; Pérez Castillo, Isaac
2016-09-01
We present a general method to obtain the exact rate function Ψ_{[a,b]}(k) controlling the large deviation probability Prob[I_{N}[a,b]=kN]≍e^{-NΨ_{[a,b]}(k)} that an N×N sparse random matrix has I_{N}[a,b]=kN eigenvalues inside the interval [a,b]. The method is applied to study the eigenvalue statistics in two distinct examples: (i) the shifted index number of eigenvalues for an ensemble of Erdös-Rényi graphs and (ii) the number of eigenvalues within a bounded region of the spectrum for the Anderson model on regular random graphs. A salient feature of the rate function in both cases is that, unlike rotationally invariant random matrices, it is asymmetric with respect to its minimum. The asymmetric character depends on the disorder in a way that is compatible with the distinct eigenvalue statistics corresponding to localized and delocalized eigenstates. The results also show that the level compressibility κ_{2}/κ_{1} for the Anderson model on a regular graph satisfies 0<κ_{2}/κ_{1}<1 in the bulk regime, in contrast with the behavior found in Gaussian random matrices. Our theoretical findings are thoroughly compared to numerical diagonalization in both cases, showing a reasonable good agreement. PMID:27636476
Large Deviation Function for the Number of Eigenvalues of Sparse Random Graphs Inside an Interval
NASA Astrophysics Data System (ADS)
Metz, Fernando L.; Pérez Castillo, Isaac
2016-09-01
We present a general method to obtain the exact rate function Ψ[a ,b ](k ) controlling the large deviation probability Prob[IN[a ,b ]=k N ]≍e-N Ψ[a ,b ](k ) that an N ×N sparse random matrix has IN[a ,b ]=k N eigenvalues inside the interval [a ,b ]. The method is applied to study the eigenvalue statistics in two distinct examples: (i) the shifted index number of eigenvalues for an ensemble of Erdös-Rényi graphs and (ii) the number of eigenvalues within a bounded region of the spectrum for the Anderson model on regular random graphs. A salient feature of the rate function in both cases is that, unlike rotationally invariant random matrices, it is asymmetric with respect to its minimum. The asymmetric character depends on the disorder in a way that is compatible with the distinct eigenvalue statistics corresponding to localized and delocalized eigenstates. The results also show that the level compressibility κ2/κ1 for the Anderson model on a regular graph satisfies 0 <κ2/κ1<1 in the bulk regime, in contrast with the behavior found in Gaussian random matrices. Our theoretical findings are thoroughly compared to numerical diagonalization in both cases, showing a reasonable good agreement.
Graph Embedding Techniques for Bounding Condition Numbers of Incomplete Factor Preconditioning
NASA Technical Reports Server (NTRS)
Guattery, Stephen
1997-01-01
We extend graph embedding techniques for bounding the spectral condition number of preconditioned systems involving symmetric, irreducibly diagonally dominant M-matrices to systems where the preconditioner is not diagonally dominant. In particular, this allows us to bound the spectral condition number when the preconditioner is based on an incomplete factorization. We provide a review of previous techniques, describe our extension, and give examples both of a bound for a model problem, and of ways in which our techniques give intuitive way of looking at incomplete factor preconditioners.
Oblakov, Konstantin I; Oblakova, Tat'yana A
2012-10-31
The paper is devoted to the characteristic of a graph that is the minimal (over all embeddings of the graph into a space of given dimension) number of points that belong to the same hyperplane. Upper and lower estimates for this number are given that linearly depend on the dimension of the space. For trees a more precise upper estimate is obtained, which asymptotically coincides with the lower one for large dimension of the space. Bibliography: 9 titles.
ERIC Educational Resources Information Center
Lane, David M.; Sandor, Aniko
2009-01-01
Statistical graphs are commonly used in scientific publications. Unfortunately, graphs in psychology journals rarely portray distributional information beyond central tendency, and few graphs portray inferential statistics. Moreover, those that do portray inferential information generally do not portray it in a way that is useful for interpreting…
The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces
NASA Astrophysics Data System (ADS)
Alekseevskii, A. V.; Natanzon, S. M.
2008-08-01
We extend the definition of Hurwitz numbers to the case of seamed surfaces, which arise in new models of mathematical physics, and prove that they form a system of correlators for a Klein topological field theory in the sense defined in [1]. We find the corresponding Cardy-Frobenius algebras, which yield a method for calculating the Hurwitz numbers. As a by-product, we prove that the vector space generated by the bipartite graphs with n edges possesses a natural binary operation that makes this space into a non-commutative Frobenius algebra isomorphic to the algebra of intertwining operators for a representation of the symmetric group S_n on the space generated by the set of all partitions of a set of n elements.
A Novel Graph-based Algorithm to Infer Recurrent Copy Number Variations in Cancer
Chi, Chen; Ajwad, Rasif; Kuang, Qin; Hu, Pingzhao
2016-01-01
Many cancers have been linked to copy number variations (CNVs) in the genomic DNA. Although there are existing methods to analyze CNVs from individual samples, cancer-causing genes are more frequently discovered in regions where CNVs are common among tumor samples, also known as recurrent CNVs. Integrating multiple samples and locating recurrent CNV regions remain a challenge, both computationally and conceptually. We propose a new graph-based algorithm for identifying recurrent CNVs using the maximal clique detection technique. The algorithm has an optimal solution, which means all maximal cliques can be identified, and guarantees that the identified CNV regions are the most frequent and that the minimal regions have been delineated among tumor samples. The algorithm has successfully been applied to analyze a large cohort of breast cancer samples and identified some breast cancer-associated genes and pathways. PMID:27773988
More than numbers: the power of graphs in meta-analysis.
Bax, Leon; Ikeda, Noriaki; Fukui, Naohito; Yaju, Yukari; Tsuruta, Harukazu; Moons, Karel G M
2009-01-15
In meta-analysis, the assessment of graphs is widely used in an attempt to identify or rule out heterogeneity and publication bias. A variety of graphs are available for this purpose. To date, however, there has been no comparative evaluation of the performance of these graphs. With the objective of assessing the reproducibility and validity of graph ratings, the authors simulated 100 meta-analyses from 4 scenarios that covered situations with and without heterogeneity and publication bias. From each meta-analysis, the authors produced 11 types of graphs (box plot, weighted box plot, standardized residual histogram, normal quantile plot, forest plot, 3 kinds of funnel plots, trim-and-fill plot, Galbraith plot, and L'Abbé plot), and 3 reviewers assessed the resulting 1,100 plots. The intraclass correlation coefficients (ICCs) for reproducibility of the graph ratings ranged from poor (ICC = 0.34) to high (ICC = 0.91). Ratings of the forest plot and the standardized residual histogram were best associated with parameter heterogeneity. Association between graph ratings and publication bias (censorship of studies) was poor. Meta-analysts should be selective in the graphs they choose for the exploration of their data. PMID:19064649
More than numbers: the power of graphs in meta-analysis.
Bax, Leon; Ikeda, Noriaki; Fukui, Naohito; Yaju, Yukari; Tsuruta, Harukazu; Moons, Karel G M
2009-01-15
In meta-analysis, the assessment of graphs is widely used in an attempt to identify or rule out heterogeneity and publication bias. A variety of graphs are available for this purpose. To date, however, there has been no comparative evaluation of the performance of these graphs. With the objective of assessing the reproducibility and validity of graph ratings, the authors simulated 100 meta-analyses from 4 scenarios that covered situations with and without heterogeneity and publication bias. From each meta-analysis, the authors produced 11 types of graphs (box plot, weighted box plot, standardized residual histogram, normal quantile plot, forest plot, 3 kinds of funnel plots, trim-and-fill plot, Galbraith plot, and L'Abbé plot), and 3 reviewers assessed the resulting 1,100 plots. The intraclass correlation coefficients (ICCs) for reproducibility of the graph ratings ranged from poor (ICC = 0.34) to high (ICC = 0.91). Ratings of the forest plot and the standardized residual histogram were best associated with parameter heterogeneity. Association between graph ratings and publication bias (censorship of studies) was poor. Meta-analysts should be selective in the graphs they choose for the exploration of their data.
Anderson, Eric C; Ng, Thomas C
2016-02-01
We develop a computational framework for addressing pedigree inference problems using small numbers (80-400) of single nucleotide polymorphisms (SNPs). Our approach relaxes the assumptions, which are commonly made, that sampling is complete with respect to the pedigree and that there is no genotyping error. It relies on representing the inferred pedigree as a factor graph and invoking the Sum-Product algorithm to compute and store quantities that allow the joint probability of the data to be rapidly computed under a large class of rearrangements of the pedigree structure. This allows efficient MCMC sampling over the space of pedigrees, and, hence, Bayesian inference of pedigree structure. In this paper we restrict ourselves to inference of pedigrees without loops using SNPs assumed to be unlinked. We present the methodology in general for multigenerational inference, and we illustrate the method by applying it to the inference of full sibling groups in a large sample (n=1157) of Chinook salmon typed at 95 SNPs. The results show that our method provides a better point estimate and estimate of uncertainty than the currently best-available maximum-likelihood sibling reconstruction method. Extensions of this work to more complex scenarios are briefly discussed. PMID:26450523
NASA Astrophysics Data System (ADS)
Pavlov, Yu L.; Khvorostyanskaya, E. V.
2016-03-01
A model of a configuration graph on N vertices is considered in which the degrees of the vertices are distributed identically and independently according to the law \\mathbf P\\{ξ=k\\}=k-τ-(k+1)-τ, k=1,2,\\dots, τ>0, and the number of edges is no greater than n. Limit theorems for the number of vertices of a particular degree and for the maximum vertex degree as N,n\\to∞ are established. Bibliography: 18 titles.
Conditional ramsey spectroscopy with synchronized atoms.
Xu, Minghui; Holland, M J
2015-03-13
We investigate Ramsey spectroscopy performed on a synchronized ensemble of two-level atoms. The synchronization is induced by the collective coupling of the atoms to a heavily damped mode of an optical cavity. We show that, in principle, with this synchronized system it is possible to observe Ramsey fringes indefinitely, even in the presence of spontaneous emission and other sources of individual-atom dephasing. This could have important consequences for atomic clocks and a wide range of precision metrology applications. PMID:25815931
Haroche-Ramsey experiment as a generalized measurement
NASA Astrophysics Data System (ADS)
de Muynck, W. M.; Hendrikx, A. J.
2001-04-01
A number of atomic beam experiments, related to the Ramsey experiment and a recent experiment by Brune et al. [Phys. Rev. Lett. 77, 4887 (1996)], are studied with respect to the question of complementarity. Three different procedures for obtaining information on the state of the incoming atom are compared. Positive operator-valued measures (POVMs) are explicitly calculated. It is demonstrated that, in principle, it is possible to choose the experimental arrangement so as to admit an interpretation as a joint nonideal measurement yielding interference and ``which-way'' information. Comparison of the different measurements gives insight into the question of which information is provided by a (generalized) quantum mechanical measurement. For this purpose the subspaces of Hilbert-Schmidt space, spanned by the operators of the POVM, are determined for different measurement arrangements and different values of the parameters.
NASA Technical Reports Server (NTRS)
Schatten, K. H.; Scherrer, P. H.; Svalgaard, L.; Wilcox, J. M.
1978-01-01
On physical grounds it is suggested that the sun's polar field strength near a solar minimum is closely related to the following cycle's solar activity. Four methods of estimating the sun's polar magnetic field strength near solar minimum are employed to provide an estimate of cycle 21's yearly mean sunspot number at solar maximum of 140 plus or minus 20. This estimate is considered to be a first order attempt to predict the cycle's activity using one parameter of physical importance.
Graphs, matrices, and the GraphBLAS: Seven good reasons
Kepner, Jeremy; Bader, David; Buluç, Aydın; Gilbert, John; Mattson, Timothy; Meyerhenke, Henning
2015-01-01
The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istcbigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implementmore » a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.« less
Graphs, matrices, and the GraphBLAS: Seven good reasons
Kepner, Jeremy; Bader, David; Buluç, Aydın; Gilbert, John; Mattson, Timothy; Meyerhenke, Henning
2015-01-01
The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istcbigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.
A Semantic Graph Query Language
Kaplan, I L
2006-10-16
Semantic graphs can be used to organize large amounts of information from a number of sources into one unified structure. A semantic query language provides a foundation for extracting information from the semantic graph. The graph query language described here provides a simple, powerful method for querying semantic graphs.
A Robust Ramsey Interferometer for Atomic Timekeeping in Dynamic Environments
NASA Astrophysics Data System (ADS)
Kotru, Krish; Brown, Justin; Butts, David; Choy, Jennifer; Galfond, Marissa; Johnson, David M.; Kinast, Joseph; Timmons, Brian; Stoner, Richard
2014-05-01
We present a laser-based approach to atomic timekeeping, in which atomic phase information is extracted using modified Raman pulses in a Ramsey sequence. We overcome systematic effects associated with differential AC Stark shifts by employing atom optics derived from Raman adiabatic rapid passage (ARP). ARP drives coherent transfer between two hyperfine ground states by sweeping the frequency difference of two optical fields and maintaining a large single-photon detuning. Compared to resonant, pulsed Raman transitions, ARP atom optics afford a >150x reduction in sensitivity to differential AC Stark shifts in a Ramsey interferometer. We also demonstrate that ARP preserves fringe contrast in Ramsey interferometers for cloud displacements reaching the 1/e2 intensity radius of the laser beam. ARP can thus be expected to improve the robustness of clock interferometers operating in dynamic environments. Copyright ©2014 by The Charles Stark Draper Laboratory, Inc. All rights reserved.
Ramsey patterns for multiquantum transitions in fountain experiments
McColm, D. |
1996-12-01
Ramsey patterns for radio-frequency multiquantum transitions among Zeeman levels of the ground state of thallium, cesium, and francium have been calculated. The narrowing of these patterns observed earlier by Gould is predicted to occur only when both static electric and magnetic fields are present. {copyright} {ital 1996 The American Physical Society.}
2007-06-12
GraphLib is a support library used by other tools to create, manipulate, store, and export graphs. It provides a simple interface to specifS arbitrary directed and undirected graphs by adding nodes and edges. Each node and edge can be associated with a set of attributes describing size, color, and shape. Once created, graphs can be manipulated using a set of graph analysis algorithms, including merge, prune, and path coloring operations. GraphLib also has the abilitymore » to export graphs into various open formats such as DOT and GML.« less
Ramsey interferometry with a two-level generalized Tonks-Girardeau gas
Mousavi, S. V.; Campo, A. del; Lizuain, I.; Muga, J. G.
2007-09-15
We propose a solvable generalization of the Tonks-Girardeau model that describes a coherent one-dimensional (1D) gas of cold two-level bosons which interact with two external fields in a Ramsey interferometer. They also interact among themselves by idealized, infinitely strong contact potentials, with interchange of momentum and internal state. We study the corresponding Ramsey fringes and the quantum projection noise which, essentially unaffected by the interactions, remains that for ideal bosons. The dual system of this gas, an ideal gas of two-level fermions coupled by the interaction with the separated fields, produces the same fringes and noise fluctuations. The cases of time-separated and spatially separated fields are studied. For spatially separated fields the fringes may be broadened slightly by increasing the number of particles, but only for large particle numbers far from present experiments with Tonks-Girardeau gases. The uncertainty in the determination of the atomic transition frequency diminishes, essentially with the inverse root of the particle number. The difficulties to implement the model experimentally and possible shortcomings of strongly interacting 1D gases for frequency standards and atomic clocks are discussed.
Hyper-Ramsey spectroscopy of optical clock transitions
Yudin, V. I.; Taichenachev, A. V.; Oates, C. W.; Barber, Z. W.; Lemke, N. D.; Ludlow, A. D.; Sterr, U.; Lisdat, Ch.; Riehle, F.
2010-07-15
We present nonstandard optical Ramsey schemes that use pulses individually tailored in duration, phase, and frequency to cancel spurious frequency shifts related to the excitation itself. In particular, the field shifts and their uncertainties can be radically suppressed (by two to four orders of magnitude) in comparison with the usual Ramsey method (using two equal pulses) as well as with single-pulse Rabi spectroscopy. Atom interferometers and optical clocks based on two-photon transitions, heavily forbidden transitions, or magnetically induced spectroscopy could significantly benefit from this method. In the latter case, these frequency shifts can be suppressed considerably below a fractional level of 10{sup -17}. Moreover, our approach opens the door for high-precision optical clocks based on direct frequency comb spectroscopy.
Generalized hyper-Ramsey resonance with separated oscillating fields
NASA Astrophysics Data System (ADS)
Zanon-Willette, T.; Yudin, V. I.; Taichenachev, A. V.
2015-08-01
An exact generalization of the Ramsey transition probability is derived to improve ultrahigh precision measurement and quantum state engineering when a particle is subjected to independently-tailored separated oscillating fields. The phase shift accumulated at the end of the interrogation scheme and associated with the particle wave function is offering a very high-level control of quantum states throughout various laser parameters conditions. The generalized hyper-Ramsey resonance based on independent manipulation of interaction time, field amplitude, phase, and frequency detuning is presented to increase performances in the next generation of atomic, molecular, and nuclear clocks, to upgrade high-resolution frequency measurement in Penning trap mass spectrometry and for a better control of light-induced frequency shifts in matter-wave interferometer or quantum information processing.
A Fast Ramsey-Bordé Interferometer with Cold Lithium
NASA Astrophysics Data System (ADS)
Copenhaver, Eric; Cassella, Kayleigh; Mueller, Holger
2016-05-01
We demonstrate light-pulse interferometry with bosonic lithium in both Mach-Zehnder and Ramsey-Bordé geometries. We capture 12 million Li-7 atoms at 200 μK and build a fast interferometer with (~ 100 ns) stimulated Raman pulses and short interrogation times (tens to hundreds of microseconds). We achieve approximately 20 % of the maximum fringe contrast, which is limited to 25 % by non-interfering atomic trajectories. The contrast decays at a rate consistent with the limit set by thermal expansion out of the Raman beam. The signal in a Ramsey-Bordé interferometer scales inversely with mass and highlights the advantage of interferometry with light atoms like lithium. This allows for a measurement of the fine structure constant with shorter interrogation times than interferometers based on heavier atoms. Additionally, fast interferometers may have applications in the detection of high frequency signals resulting from exotic physics.
Ramsey-type spectroscopy in the XUV spectral region
Pirri, A.; Sali, E.; Cavalieri, S.; Corsi, C.; Bellini, M.; Eramo, R.
2010-02-02
We report an experimental and theoretical investigation of Ramsey-type spectroscopy with high-order harmonic generation applied to autoionizing states of Krypton. The ionization yield, detected by an ion-mass spectrometer, shows the characteristic quantum interference pattern. The behaviour of the fringe contrast was interpreted on the basis of a simple analytic model, which reproduces the experimental data without any free parameter.
Ramsey resonance of coherent population trapping in slow rubidium beam
NASA Astrophysics Data System (ADS)
Sokolov, I. M.
2016-03-01
We calculate the coherent population trapping (CPT) resonance in slow beam of rubidium 87 atoms caused by of their interaction with bichromatic electromagnetic field in two separated spatial domains. In the case of monovelocity beam we study the properties of the CPT resonance depending on type of working transitions, velocity of the atomic beam, intensity and polarization of electromagnetic fields, and space separation in Ramsey scheme.
A Robust Ramsey Interferometer for Atomic Timekeeping in Dynamic Environments
NASA Astrophysics Data System (ADS)
Kotru, Krish; Brown, Justin; Butts, David; Choy, Jennifer; Galfond, Marissa; Johnson, David M.; Kinast, Joseph; Timmons, Brian; Stoner, Richard
2014-05-01
We present a laser-based approach to atomic timekeeping, in which atomic phase information is extracted using modified Raman pulses in a Ramsey sequence. We overcome systematic effects associated with differential AC Stark shifts and variations in laser beam intensity by employing atom optics derived from Raman adiabatic rapid passage (ARP). This technique drives coherent transfer between two hyperfine ground states by sweeping the frequency difference of two optical fields and maintaining a large single-photon detuning. Compared to a Raman-pulse Ramsey interferometer, we show a >150x reduction in sensitivity to differential AC Stark shifts. We also demonstrate that ARP preserves fringe contrast in Ramsey interferometers for cloud displacements reaching the 1/e2 intensity radius of the laser beam. Deviations of the phase in response to changes in duration, rate, and range of the ARP frequency sweep are bounded to <7 mrad, implying a per-shot fractional frequency uncertainty of 1e-11 for an interrogation time of 10 ms. These characteristics are expected to improve the robustness of clock interferometers operating in dynamic environments. Copyright ©2014 by The Charles Stark Draper Laboratory, Inc. All rights reserved.
NASA Astrophysics Data System (ADS)
Kim, Jongkwang; Wilhelm, Thomas
2008-04-01
Many papers published in recent years show that real-world graphs G(n,m) ( n nodes, m edges) are more or less “complex” in the sense that different topological features deviate from random graphs. Here we narrow the definition of graph complexity and argue that a complex graph contains many different subgraphs. We present different measures that quantify this complexity, for instance C1e, the relative number of non-isomorphic one-edge-deleted subgraphs (i.e. DECK size). However, because these different subgraph measures are computationally demanding, we also study simpler complexity measures focussing on slightly different aspects of graph complexity. We consider heuristically defined “product measures”, the products of two quantities which are zero in the extreme cases of a path and clique, and “entropy measures” quantifying the diversity of different topological features. The previously defined network/graph complexity measures Medium Articulation and Offdiagonal complexity ( OdC) belong to these two classes. We study OdC measures in some detail and compare it with our new measures. For all measures, the most complex graph G has a medium number of edges, between the edge numbers of the minimum and the maximum connected graph n-1
Robustness of random graphs based on graph spectra
NASA Astrophysics Data System (ADS)
Wu, Jun; Barahona, Mauricio; Tan, Yue-jin; Deng, Hong-zhong
2012-12-01
It has been recently proposed that the robustness of complex networks can be efficiently characterized through the natural connectivity, a spectral property of the graph which corresponds to the average Estrada index. The natural connectivity corresponds to an average eigenvalue calculated from the graph spectrum and can also be interpreted as the Helmholtz free energy of the network. In this article, we explore the use of this index to characterize the robustness of Erdős-Rényi (ER) random graphs, random regular graphs, and regular ring lattices. We show both analytically and numerically that the natural connectivity of ER random graphs increases linearly with the average degree. It is also shown that ER random graphs are more robust than the corresponding random regular graphs with the same number of vertices and edges. However, the relative robustness of ER random graphs and regular ring lattices depends on the average degree and graph size: there is a critical graph size above which regular ring lattices are more robust than random graphs. We use our analytical results to derive this critical graph size as a function of the average degree.
Graph ensemble boosting for imbalanced noisy graph stream classification.
Pan, Shirui; Wu, Jia; Zhu, Xingquan; Zhang, Chengqi
2015-05-01
Many applications involve stream data with structural dependency, graph representations, and continuously increasing volumes. For these applications, it is very common that their class distributions are imbalanced with minority (or positive) samples being only a small portion of the population, which imposes significant challenges for learning models to accurately identify minority samples. This problem is further complicated with the presence of noise, because they are similar to minority samples and any treatment for the class imbalance may falsely focus on the noise and result in deterioration of accuracy. In this paper, we propose a classification model to tackle imbalanced graph streams with noise. Our method, graph ensemble boosting, employs an ensemble-based framework to partition graph stream into chunks each containing a number of noisy graphs with imbalanced class distributions. For each individual chunk, we propose a boosting algorithm to combine discriminative subgraph pattern selection and model learning as a unified framework for graph classification. To tackle concept drifting in graph streams, an instance level weighting mechanism is used to dynamically adjust the instance weight, through which the boosting framework can emphasize on difficult graph samples. The classifiers built from different graph chunks form an ensemble for graph stream classification. Experiments on real-life imbalanced graph streams demonstrate clear benefits of our boosting design for handling imbalanced noisy graph stream.
Simmons, G.J.
1988-01-01
We define a class of geometrical constructions in the plane in which each (unextended) line lies on (precisely) k points, and every point is an endpoint of (precisely) one line. We will refer to any construction satisfying these conditions as a campaign graph, or as a k-campaign graph if the value of k isn't clear from the context. A k-campaign graph, G, is said to be critical if no subgraph of G is also a k-campaign graph. 11 figs.
Simmons, G.J.
1991-01-01
In spite of the old adage that No finite sequence of symbols is random,'' there are many instances in which it is desirable to quantify how random'' a finite sequence is. Pseudorandom number generators and cryptographic key generators typically expand a short, randomly chosen, seed sequence into a much longer sequence which should appear random to anyone ignorant of the seed. Unique initiating signals chosen to minimize the likelihood of an accidental initiation of an important action should be random'' to lessen the chance of their natural occurrence, etc. Consequently, numerous tests for the randomness of finite sequences have been proposed. John Milnor argued that if a binary sequence is random then the fraction of 1's, r{sub 1}, should be very nearly 1/2 in it and in all of what he called its derivatives. Since every sequence has a unique derivative this defines a natural family of digraphs, G{sub n}, on 2{sup n} vertices in which vertices are labeled with n-bit binary sequences and an edge is directed from the vertex labeled with the sequence A to the vertex labeled with the sequence B if B is the derivative of A. Each component of G{sub n} is eventually cyclic. This paper is concerned with a special case in which the sequences in a cycle are all cyclic shifts of a single sequence -- hence the name of Ezekiel graphs. Surprising, there are Ezekiel graphs for which r{sub 1} is as close to 1/2 as is numerically possible, i.e., that satisfy Milnor's test for randomness as closely as it can be satisfied, even though the sequence of sequences are about as far from random as is conceivable. In this paper the existence and properties of Ezekiel sequences are investigated from an algebraic standpoint.
Ultrafast double-pulse parametric amplification for precision Ramsey metrology.
Kandula, D Z; Renault, A; Gohle, Ch; Wolf, A L; Witte, S; Hogervorst, W; Ubachs, W; Eikema, K S E
2008-05-12
We demonstrate phase stable, mJ-level parametric amplification of pulse pairs originating from a Ti:Sapphire frequency comb laser. The amplifier-induced phase shift between the pulses has been determined interferometrically with an accuracy of approximately 10 mrad. Typical phase shifts are on the order of 50-200 mrad, depending on the operating conditions. The measured phase-relation can be as stable as 20 mrad rms (1/300(th) of an optical cycle). This makes the system suitable for Ramsey spectroscopy at short wavelengths by employing harmonic upconversion of the double-pulses in nonlinear media.
Lockheed Solar Observatory and the Discovery of Moreton-Ramsey Waves
NASA Astrophysics Data System (ADS)
Tarbell, Theodore D.
2014-06-01
Moreton Waves are high-speed disturbances seen traveling away from large solar flares in H-alpha movies of the solar chromosphere. They were discovered by the observer Harry Ramsey in the late 1950s, and then published and publicized by the director Gail Moreton, both of the Lockheed Solar Observatory in the Hollywood Hills of Southern California. These efforts established the scientific reputation and secured continuing funding of the observatory, whose present-day successor is the Lockheed Martin Solar and Astrophysics Lab in Palo Alto. Moreton waves are rare, and there was limited interest in them until the EIT instrument on SOHO began seeing large numbers of similar waves in the corona in the late 1990s. The exact relation between the two observations is still a research topic today. This talk will describe some of the history of the observatory and the discovery and early interpretation of the waves.
ERIC Educational Resources Information Center
Connery, Keely Flynn
2007-01-01
Graphing predictions is especially important in classes where relationships between variables need to be explored and derived. In this article, the author describes how his students sketch the graphs of their predictions before they begin their investigations on two laboratory activities: Distance Versus Time Cart Race Lab and Resistance; and…
Free Nano-Object Ramsey Interferometry for Large Quantum Superpositions
NASA Astrophysics Data System (ADS)
Wan, C.; Scala, M.; Morley, G. W.; Rahman, ATM. A.; Ulbricht, H.; Bateman, J.; Barker, P. F.; Bose, S.; Kim, M. S.
2016-09-01
We propose an interferometric scheme based on an untrapped nano-object subjected to gravity. The motion of the center of mass (c.m.) of the free object is coupled to its internal spin system magnetically, and a free flight scheme is developed based on coherent spin control. The wave packet of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during our scheme. We find a remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling), and also a dynamical decoupling nature of the scheme itself. Together they secure a high visibility of the resulting Ramsey fringes. The mass independence of our scheme makes it viable for a nano-object selected from an ensemble with a high mass variability. Given these advantages, a quantum superposition with a 100 nm spatial separation for a massive object of 1 09 amu is achievable experimentally, providing a route to test postulated modifications of quantum theory such as continuous spontaneous localization.
Sanfilippo, Antonio P.
2005-12-27
Graph theory is a branch of discrete combinatorial mathematics that studies the properties of graphs. The theory was pioneered by the Swiss mathematician Leonhard Euler in the 18th century, commenced its formal development during the second half of the 19th century, and has witnessed substantial growth during the last seventy years, with applications in areas as diverse as engineering, computer science, physics, sociology, chemistry and biology. Graph theory has also had a strong impact in computational linguistics by providing the foundations for the theory of features structures that has emerged as one of the most widely used frameworks for the representation of grammar formalisms.
Fault-tolerant Hahn-Ramsey interferometry with pulse sequences of alternating detuning
NASA Astrophysics Data System (ADS)
Vitanov, Nikolay V.; Gloger, Timm F.; Kaufmann, Peter; Kaufmann, Delia; Collath, Thomas; Tanveer Baig, M.; Johanning, Michael; Wunderlich, Christof
2015-03-01
A scheme for efficient correction of driving-field frequency drifts in Ramsey interferometry is proposed. The two off-resonant π /2 pulses of duration T used in the traditional Ramsey setup are supplemented with an additional pulse of duration 2 T (approximate π pulse), which is applied midway between the Ramsey pulses and has a detuning of opposite sign to theirs. This scheme, which resembles a Hahn's spin-echo pulse embedded into the Ramsey setup, corrects small-to-moderate random errors in the detuning of the driving field. This allows the observation of Ramsey fringes of high contrast even with a noisy driving field or in inhomogeneously broadened atomic ensembles. The contrast is further improved by replacing the refocusing 2 T pulse by a composite π pulse. We demonstrate the validity of the concept by comparing experimental results from usual Ramsey measurements with Hahn-Ramsey measurements. These experimental results are obtained from microwave-optical double-resonance spectroscopy on 171Yb+ ions in a segmented linear Paul trap. In the same way, we verify qualitatively the predicted advantage from using a composite π pulse for refocusing.
Commuting projections on graphs
Vassilevski, Panayot S.; Zikatanov, Ludmil T.
2013-02-19
For a given (connected) graph, we consider vector spaces of (discrete) functions defined on its vertices and its edges. These two spaces are related by a discrete gradient operator, Grad and its adjoint, ₋Div, referred to as (negative) discrete divergence. We also consider a coarse graph obtained by aggregation of vertices of the original one. Then a coarse vertex space is identified with the subspace of piecewise constant functions over the aggregates. We consider the ℓ_{2}-projection Q_{H} onto the space of these piecewise constants. In the present paper, our main result is the construction of a projection π _{H} from the original edge-space onto a properly constructed coarse edge-space associated with the edges of the coarse graph. The projections π _{H} and Q_{H} commute with the discrete divergence operator, i.e., we have div π _{H} = Q_{H} div. The respective pair of coarse edge-space and coarse vertexspace offer the potential to construct two-level, and by recursion, multilevel methods for the mixed formulation of the graph Laplacian which utilizes the discrete divergence operator. The performance of one two-level method with overlapping Schwarz smoothing and correction based on the constructed coarse spaces for solving such mixed graph Laplacian systems is illustrated on a number of graph examples.
RAMSEYS DRAFT WILDERNESS STUDY AREA AND ADDITION, VIRGINIA.
Lesure, Frank G.; Mory, Peter C.
1984-01-01
Mineral-resource surveys of the Ramseys Draft Wilderness Study Area and adjoining roadless area addition in George Washington National Forest in the western valley and ridge province, Augusta and Highland Counties, Virginia, were done. The surveys outlined three small areas containing anomalous amounts of copper, lead, and zinc related to stratabound red-bed copper mineralization, but these occurrences are not large and are not considered as having mineral-resource potential. The area contains abundant sandstone suitable for construction materials and shale suitable for making brick, tile, and other low-grade ceramic products, but these commodities occur in abundance outside the wilderness study area. Structural conditions are probably favorable for the accumulation of natural gas, but exploratory drilling has not been done sufficiently near the area to evaluate the gas potential.
NASA Astrophysics Data System (ADS)
Beeken, Paul
2014-11-01
Graphing is an essential skill that forms the foundation of any physical science.1 Understanding the relationships between measurements ultimately determines which modeling equations are successful in predicting observations.2 Over the years, science and math teachers have approached teaching this skill with a variety of techniques. For secondary school instruction, the job of graphing skills falls heavily on physics teachers. By virtue of the nature of the topics we cover, it is our mission to develop this skill to the fine art that it is.
Evaluation of Graph Pattern Matching Workloads in Graph Analysis Systems
Hong, Seokyong; Sukumar, Sreenivas Rangan; Vatsavai, Raju
2016-01-01
Graph analysis has emerged as a powerful method for data scientists to represent, integrate, query, and explore heterogeneous data sources. As a result, graph data management and mining became a popular area of research, and led to the development of plethora of systems in recent years. Unfortunately, the number of emerging graph analysis systems and the wide range of applications, coupled with a lack of apples-to-apples comparisons, make it difficult to understand the trade-offs between different systems and the graph operations for which they are designed. A fair comparison of these systems is a challenging task for the following reasons: multiple data models, non-standardized serialization formats, various query interfaces to users, and diverse environments they operate in. To address these key challenges, in this paper we present a new benchmark suite by extending the Lehigh University Benchmark (LUBM) to cover the most common capabilities of various graph analysis systems. We provide the design process of the benchmark, which generalizes the workflow for data scientists to conduct the desired graph analysis on different graph analysis systems. Equipped with this extended benchmark suite, we present performance comparison for nine subgraph pattern retrieval operations over six graph analysis systems, namely NetworkX, Neo4j, Jena, Titan, GraphX, and uRiKA. Through the proposed benchmark suite, this study reveals both quantitative and qualitative findings in (1) implications in loading data into each system; (2) challenges in describing graph patterns for each query interface; and (3) different sensitivity of each system to query selectivity. We envision that this study will pave the road for: (i) data scientists to select the suitable graph analysis systems, and (ii) data management system designers to advance graph analysis systems.
Coloring geographical threshold graphs
Bradonjic, Milan; Percus, Allon; Muller, Tobias
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.
ERIC Educational Resources Information Center
Beeken, Paul
2014-01-01
Graphing is an essential skill that forms the foundation of any physical science. Understanding the relationships between measurements ultimately determines which modeling equations are successful in predicting observations. Over the years, science and math teachers have approached teaching this skill with a variety of techniques. For secondary…
Theory of Ramsey spectroscopy and anomalous segregation in ultracold rubidium
NASA Astrophysics Data System (ADS)
Bradley, A. S.; Gardiner, C. W.
2002-10-01
The recent anomalous segregation experiment (Lewandowski H J, Harber D M, Whitaker D L and Cornell E A 2002 Phys. Rev. Lett. 88 070403) shows dramatic, rapid internal state segregation for two hyperfine levels of 87Rb. We simulate an effective one-dimensional model of the system for experimental parameters and find reasonable agreement with the data. The Ramsey frequency is found to be insensitive to the decoherence of the superposition, and is only equivalent to the interaction energy shift for a pure superposition. A quantum Boltzmann equation describing collisions is derived using quantum kinetic theory, taking into account the different scattering lengths of the internal states. As spin-wave experiments are likely to be attempted at lower temperatures we examine the effect of degeneracy on decoherence by considering the recent experiment, where degeneracy is around 10%. We also find that the segregation effect is only possible when transport terms are included in the equations of motion, and that the interactions only directly alter the momentum distributions of the states. The segregation or spin-wave effect is thus entirely due to coherent atomic motion as foreseen by Lewandowski et al.
Raberto, Marco; Rapallo, Fabio; Scalas, Enrico
2011-01-01
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs. PMID:21887245
Boosting for multi-graph classification.
Wu, Jia; Pan, Shirui; Zhu, Xingquan; Cai, Zhihua
2015-03-01
In this paper, we formulate a novel graph-based learning problem, multi-graph classification (MGC), which aims to learn a classifier from a set of labeled bags each containing a number of graphs inside the bag. A bag is labeled positive, if at least one graph in the bag is positive, and negative otherwise. Such a multi-graph representation can be used for many real-world applications, such as webpage classification, where a webpage can be regarded as a bag with texts and images inside the webpage being represented as graphs. This problem is a generalization of multi-instance learning (MIL) but with vital differences, mainly because instances in MIL share a common feature space whereas no feature is available to represent graphs in a multi-graph bag. To solve the problem, we propose a boosting based multi-graph classification framework (bMGC). Given a set of labeled multi-graph bags, bMGC employs dynamic weight adjustment at both bag- and graph-levels to select one subgraph in each iteration as a weak classifier. In each iteration, bag and graph weights are adjusted such that an incorrectly classified bag will receive a higher weight because its predicted bag label conflicts to the genuine label, whereas an incorrectly classified graph will receive a lower weight value if the graph is in a positive bag (or a higher weight if the graph is in a negative bag). Accordingly, bMGC is able to differentiate graphs in positive and negative bags to derive effective classifiers to form a boosting model for MGC. Experiments and comparisons on real-world multi-graph learning tasks demonstrate the algorithm performance.
Yang, Jing; Yun, Peter; Tian, Yuan; Tan, Bozhong; Gu, Sihong
2014-03-07
A scheme for a Ramsey-coherent population trapping (CPT) atomic clock that eliminates the acousto-optic modulator (AOM) is proposed and experimentally studied. Driven by a periodically microwave modulated current, the vertical-cavity surface-emitting laser emits a continuous beam that switches between monochromatic and multichromatic modes. Ramsey-CPT interference has been studied with this mode-switching beam. In eliminating the AOM, which is used to generate pulsed laser in conventional Ramsey-CPT atomic clock, the physics package of the proposed scheme is virtually the same as that of a conventional compact CPT atomic clock, although the resource budget for the electronics will slightly increase as a microwave switch should be added. By evaluating and comparing experimentally recorded signals from the two Ramsey-CPT schemes, the short-term frequency stability of the proposed scheme was found to be 46% better than the scheme with AOM. The experimental results suggest that the implementation of a compact Ramsey-CPT atomic clock promises better frequency stability.
Understanding Graphs & Charts.
ERIC Educational Resources Information Center
Cleary, John J.; Gravely, Mary Liles
Developed by educators from the Emily Griffith Opportunity School, this teacher's guide was developed for a 4-hour workshop to teach employees how to read the charts and graphs they need in the workplace. The unit covers four types of graphs: pictographs, bar graphs, line graphs, and circle graphs. The guide is divided into four sections: reading…
Winlaw, Manda; De Sterck, Hans; Sanders, Geoffrey
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.
Optical Ramsey spectroscopy in a rotating frame: Sagnac effect in a matter-wave interferometer
Riehle, F.; Kisters, T.; Witte, A.; Helmcke, J. ); Borde, C.J. Laboratoire de Physique des Lasers, Universite Paris, Villetaneuse, France )
1991-07-08
A calcium atomic beam excited in an optical Ramsey geometry was rotated about an axis perpendicular to the plane defined by the laser beams and the atomic beam. A frequency shift of the Ramsey fringes of several kHz has been measured which is proportional to the rotation frequency of the apparatus and to the distance between the laser beams. The results can be interpreted in three equivalent ways as the Sagnac effect in a calcium-atomic-beam interferometer: in the rotating frame of the laser beams either along straight paths or along the curved trajectories of the atoms, or in the inertial atomic frame.
Hierarchical structure of the logical Internet graph
NASA Astrophysics Data System (ADS)
Ge, Zihui; Figueiredo, Daniel R.; Jaiswal, Sharad; Gao, Lixin
2001-07-01
The study of the Internet topology has recently received much attention from the research community. In particular, the observation that the network graph has interesting properties, such as power laws, that might be explored in a myriad of ways. Most of the work in characterizing the Internet graph is based on the physical network graph, i.e., the connectivity graph. In this paper we investigate how logical relationships between nodes of the AS graph can be used to gain insight to its structure. We characterize the logical graph using various metrics and identify the presence of power laws in the number of customers that a provider has. Using these logical relationships we define a structural model of the AS graph. The model highlights the hierarchical nature of logical relationships and the preferential connection to larger providers. We also investigate the consistency of this model over time and observe interesting properties of the hierarchical structure.
The Feynman Identity for Planar Graphs
NASA Astrophysics Data System (ADS)
da Costa, G. A. T. F.
2016-08-01
The Feynman identity (FI) of a planar graph relates the Euler polynomial of the graph to an infinite product over the equivalence classes of closed nonperiodic signed cycles in the graph. The main objectives of this paper are to compute the number of equivalence classes of nonperiodic cycles of given length and sign in a planar graph and to interpret the data encoded by the FI in the context of free Lie superalgebras. This solves in the case of planar graphs a problem first raised by Sherman and sets the FI as the denominator identity of a free Lie superalgebra generated from a graph. Other results are obtained. For instance, in connection with zeta functions of graphs.
Learning Financial Reports From Mixed Symbolic-Spatial Graphs
ERIC Educational Resources Information Center
Tanlamai, Uthai; Soongswang, Oranuj
2011-01-01
Mixed visuals of numbers and graphs are available in various financial reports that demonstrate the financial status and risks of a firm. GWN (graphs with numbers) and TWG (table of numbers with graphs) were used as two alternative visuals derived from the actual data of two large public companies, one from food manufacturing industry (food) and…
Lost Innocent and Sacrificial Delegate: The JonBenet Ramsey Murder.
ERIC Educational Resources Information Center
Conrad, Joann
1999-01-01
Analyzes murder case of 6-year-old JonBenet Ramsey as emblematic of American cultural fascination with images of the innocence of children and the perfect family, and of a change in cultural self-awareness as these images prove illusionary. Considers the role of mass media in marketing a cultural fascination with sexualized images of children and…
ERIC Educational Resources Information Center
Lawes, Jonathan F.
2013-01-01
Graphing polar curves typically involves a combination of three traditional techniques, all of which can be time-consuming and tedious. However, an alternative method--graphing the polar function on a rectangular plane--simplifies graphing, increases student understanding of the polar coordinate system, and reinforces graphing techniques learned…
ERIC Educational Resources Information Center
Nibbelink, William
1982-01-01
An instructional sequence for teaching graphing that has been extensively field tested in kindergarten through grade six is detailed. The material begins with point graphs, employs a movable y-axis to begin with minimal clutter, and has graphs constructed before reading graphs is required. (MP)
Smalter, Aaron; Huan, Jun Luke; Jia, Yi; Lushington, Gerald
2010-01-01
Graph data mining is an active research area. Graphs are general modeling tools to organize information from heterogeneous sources and have been applied in many scientific, engineering, and business fields. With the fast accumulation of graph data, building highly accurate predictive models for graph data emerges as a new challenge that has not been fully explored in the data mining community. In this paper, we demonstrate a novel technique called graph pattern diffusion (GPD) kernel. Our idea is to leverage existing frequent pattern discovery methods and to explore the application of kernel classifier (e.g., support vector machine) in building highly accurate graph classification. In our method, we first identify all frequent patterns from a graph database. We then map subgraphs to graphs in the graph database and use a process we call "pattern diffusion" to label nodes in the graphs. Finally, we designed a graph alignment algorithm to compute the inner product of two graphs. We have tested our algorithm using a number of chemical structure data. The experimental results demonstrate that our method is significantly better than competing methods such as those kernel functions based on paths, cycles, and subgraphs.
A notion of graph likelihood and an infinite monkey theorem
NASA Astrophysics Data System (ADS)
Banerji, Christopher R. S.; Mansour, Toufik; Severini, Simone
2014-01-01
We play with a graph-theoretic analogue of the folklore infinite monkey theorem. We define a notion of graph likelihood as the probability that a given graph is constructed by a monkey in a number of time steps equal to the number of vertices. We present an algorithm to compute this graph invariant and closed formulas for some infinite classes. We have to leave the computational complexity of the likelihood as an open problem.
Fast generation of sparse random kernel graphs
Hagberg, Aric; Lemons, Nathan; Du, Wen -Bo
2015-09-10
The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in time at most ο(n(logn)²). As an example, we show how to generate samples of power-law degree distribution graphs with tunable assortativity.
Fast generation of sparse random kernel graphs
Hagberg, Aric; Lemons, Nathan; Du, Wen -Bo
2015-09-10
The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in timemore » at most ο(n(logn)²). As an example, we show how to generate samples of power-law degree distribution graphs with tunable assortativity.« less
XV-3 in Ames Reseach Center 40x80ft wind tunnel with K. Edenborough and B. Ramsey, engineers
NASA Technical Reports Server (NTRS)
1966-01-01
XV-3 in Ames Reseach Center 40x80ft wind tunnel with K. Edenborough and B. Ramsey, engineers Published in The History of the XV-15 Tilt Rotor Research Aircraft (from Concept to Flight NASA SP-2000-4517)
Subvoxel accurate graph search using non-Euclidean graph space.
Abràmoff, Michael D; Wu, Xiaodong; Lee, Kyungmoo; Tang, Li
2014-01-01
Graph search is attractive for the quantitative analysis of volumetric medical images, and especially for layered tissues, because it allows globally optimal solutions in low-order polynomial time. However, because nodes of graphs typically encode evenly distributed voxels of the volume with arcs connecting orthogonally sampled voxels in Euclidean space, segmentation cannot achieve greater precision than a single unit, i.e. the distance between two adjoining nodes, and partial volume effects are ignored. We generalize the graph to non-Euclidean space by allowing non-equidistant spacing between nodes, so that subvoxel accurate segmentation is achievable. Because the number of nodes and edges in the graph remains the same, running time and memory use are similar, while all the advantages of graph search, including global optimality and computational efficiency, are retained. A deformation field calculated from the volume data adaptively changes regional node density so that node density varies with the inverse of the expected cost. We validated our approach using optical coherence tomography (OCT) images of the retina and 3-D MR of the arterial wall, and achieved statistically significant increased accuracy. Our approach allows improved accuracy in volume data acquired with the same hardware, and also, preserved accuracy with lower resolution, more cost-effective, image acquisition equipment. The method is not limited to any specific imaging modality and readily extensible to higher dimensions.
Composite pulses in Hyper-Ramsey spectroscopy for the next generation of atomic clocks
NASA Astrophysics Data System (ADS)
Zanon-Willette, T.; Minissale, M.; Yudin, V. I.; Taichenachev, A. V.
2016-06-01
The next generation of atomic frequency standards based on an ensemble of neutral atoms or a single-ion will provide very stringent tests in metrology, applied and fundamental physics requiring a new step in very precise control of external systematic corrections. In the proceedings of the 8th Symposium on Frequency Standards and Metrology, we present a generalization of the recent Hyper-Ramsey spectroscopy with separated oscillating fields using composites pulses in order to suppress field frequency shifts induced by the interrogation laser itself. Sequences of laser pulses including specific selection of phases, frequency detunings and durations are elaborated to generate spectroscopic signals with a strong reduction of the light-shift perturbation by off resonant states. New optical clocks based on weakly allowed or completely forbidden transitions in atoms, ions, molecules and nuclei will benefit from these generalized Ramsey schemes to reach relative accuracies well below the 10-18 level.
Accessing Rydberg-dressed interactions using many-body Ramsey dynamics
NASA Astrophysics Data System (ADS)
Mukherjee, Rick; Killian, Thomas; Hazzard, Kaden
2016-05-01
We demonstrate that Ramsey spectroscopy can be used to observe Rydberg-dressed interactions in a many-body system. Our scheme operates comfortably within experimentally measured lifetimes, and accesses a regime where quantum superpositions are crucial. We build a spin-1/2 from one level that is Rydberg-dressed and another that is not. These levels may be hyperfine or long-lived electronic states. An Ising spin model governs the Ramsey dynamics, for which we derive an exact solution. Due to the structure of Rydberg interactions, the dynamics differs significantly from that in other spin systems. As one example, spin echo can increase the rate at which coherence decays. The results are relevant for the current ongoing experiments, including those at Rice University.
Fibonacci Identities, Matrices, and Graphs
ERIC Educational Resources Information Center
Huang, Danrun
2005-01-01
General strategies used to help discover, prove, and generalize identities for Fibonacci numbers are described along with some properties about the determinants of square matrices. A matrix proof for identity (2) that has received immense attention from many branches of mathematics, like linear algebra, dynamical systems, graph theory and others…
Dimer-monomer model on the Towers of Hanoi graphs
NASA Astrophysics Data System (ADS)
Chen, Hanlin; Wu, Renfang; Huang, Guihua; Deng, Hanyuan
2015-07-01
The number of dimer-monomers (matchings) of a graph G is an important graph parameter in statistical physics. Following recent research, we study the asymptotic behavior of the number of dimer-monomers m(G) on the Towers of Hanoi graphs and another variation of the Sierpiński graphs which is similar to the Towers of Hanoi graphs, and derive the recursion relations for the numbers of dimer-monomers. Upper and lower bounds for the entropy per site, defined as μG = limv(G)→∞(lnm(G)/v(G)), where v(G) is the number of vertices in a graph G, on these Sierpiński graphs are derived in terms of the numbers at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of the entropy can be evaluated with more than a hundred significant figures accuracy.
Loops in Reeb Graphs of 2-Manifolds
Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V
2004-12-16
Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.
Loops in Reeb Graphs of 2-Manifolds
Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V
2003-02-11
Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.
Historical overview of Ramsey spectroscopy and its relevance on Time and Frequency Metrology
NASA Astrophysics Data System (ADS)
Amaral, M. M.; Tarelho, L. V. G.; de Souza, M. A.; Baratto, A. C.; Garcia, G. A.; Muller, S. T.; De Martin, J., Jr.; Rodriguez, A. S.; Bebeachibuli, A.; Magalhães, D. V.
2016-07-01
A brief overview of the historical evolution of the method of successive oscillatory fields developed by Norman Ramsey, and some different implementations of the decurrent methodology are presented. We use time and frequency standards, from Cs atomic beams to optical standards, as examples. The scientific progress and the technological implementation achieved through a partnership between USP-SC and INMETRO are shown on the characterization of each time and frequency standard.
Abele, H.; Jenke, T.; Leeb, H.; Schmiedmayer, J.
2010-03-15
We propose to apply Ramsey's method of separated oscillating fields to the spectroscopy of the quantum states in the gravity potential above a horizontal mirror. This method allows a precise measurement of quantum mechanical phaseshifts of a Schroedinger wave packet bouncing off a hard surface in the gravitational field of the Earth. Measurements with ultracold neutrons will offer a sensitivity to Newton's law or hypothetical short-ranged interactions, which is about 21 orders of magnitude below the energy scale of electromagnetism.
Study of field shifts of Ramsey resonances on ultracold atoms and ions
Tabatchikova, K. S.; Taichenachev, A. V.; Dmitriev, A. K.; Yudin, V. I.
2015-02-15
The effect of the finite laser radiation line width and spontaneous relaxation of levels on the efficiency of the suppression of the field shift of the central resonance for the generalized Ramsey scheme with pulses of different lengths and with a phase jump in the second pulse has been considered. The optimal parameters of the scheme corresponding to the minimum frequency shift and maximum amplitude of the resonance have been determined.
Graphing Inequalities, Connecting Meaning
ERIC Educational Resources Information Center
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…
NASA Technical Reports Server (NTRS)
Kantak, Anil V.
1987-01-01
Plotter routine for IBM PC (AKPLOT) designed for engineers and scientists who use graphs as integral parts of their documentation. Allows user to generate graph and edit its appearance on cathode-ray tube. Graph may undergo many interactive alterations before finally dumped from screen to be plotted by printer. Written in BASIC.
ERIC Educational Resources Information Center
Reading Teacher, 2012
2012-01-01
The "Toolbox" column features content adapted from ReadWriteThink.org lesson plans and provides practical tools for classroom teachers. This issue's column features a lesson plan adapted from "Graphing Plot and Character in a Novel" by Lisa Storm Fink and "Bio-graph: Graphing Life Events" by Susan Spangler. Students retell biographic events…
NASA Astrophysics Data System (ADS)
Pluhař, Z.; Weidenmüller, H. A.
2014-04-01
For time-reversal invariant graphs we prove the Bohigas-Giannoni-Schmit conjecture in its most general form: For graphs that are mixing in the classical limit, all spectral correlation functions coincide with those of the Gaussian orthogonal ensemble of random matrices. For open graphs, we derive the analogous identities for all S-matrix correlation functions.
ERIC Educational Resources Information Center
Yoder, Sharon K.
This book discusses four kinds of graphs that are taught in mathematics at the middle school level: pictographs, bar graphs, line graphs, and circle graphs. The chapters on each of these types of graphs contain information such as starting, scaling, drawing, labeling, and finishing the graphs using "LogoWriter." The final chapter of the book…
Detecting alternative graph clusterings.
Mandala, Supreet; Kumara, Soundar; Yao, Tao
2012-07-01
The problem of graph clustering or community detection has enjoyed a lot of attention in complex networks literature. A quality function, modularity, quantifies the strength of clustering and on maximization yields sensible partitions. However, in most real world networks, there are an exponentially large number of near-optimal partitions with some being very different from each other. Therefore, picking an optimal clustering among the alternatives does not provide complete information about network topology. To tackle this problem, we propose a graph perturbation scheme which can be used to identify an ensemble of near-optimal and diverse clusterings. We establish analytical properties of modularity function under the perturbation which ensures diversity. Our approach is algorithm independent and therefore can leverage any of the existing modularity maximizing algorithms. We numerically show that our methodology can systematically identify very different partitions on several existing data sets. The knowledge of diverse partitions sheds more light into the topological organization and helps gain a more complete understanding of the underlying complex network.
Wong, Pak C.; Mackey, Patrick S.; Perrine, Kenneth A.; Foote, Harlan P.; Thomas, James J.
2008-12-23
Methods for visualizing a graph by automatically drawing elements of the graph as labels are disclosed. In one embodiment, the method comprises receiving node information and edge information from an input device and/or communication interface, constructing a graph layout based at least in part on that information, wherein the edges are automatically drawn as labels, and displaying the graph on a display device according to the graph layout. In some embodiments, the nodes are automatically drawn as labels instead of, or in addition to, the label-edges.
Searching for nodes in random graphs.
Lancaster, David
2011-11-01
We consider the problem of searching for a node on a labeled random graph according to a greedy algorithm that selects a route to the desired node using metric information on the graph. Motivated by peer-to-peer networks two types of random graph are proposed with properties particularly amenable to this kind of algorithm. We derive equations for the probability that the search is successful and also study the number of hops required, finding both numerical and analytic evidence of a transition as the number of links is varied.
On the Kirchhoff Index of Graphs
NASA Astrophysics Data System (ADS)
Das, Kinkar C.
2013-09-01
Let G be a connected graph of order n with Laplacian eigenvalues μ1 ≥ μ2 ≥ ... ≥ μn-1 > mn = 0. The Kirchhoff index of G is defined as [xxx] In this paper. we give lower and upper bounds on Kf of graphs in terms on n, number of edges, maximum degree, and number of spanning trees. Moreover, we present lower and upper bounds on the Nordhaus-Gaddum-type result for the Kirchhoff index.
Enabling Graph Appliance for Genome Assembly
Singh, Rina; Graves, Jeffrey A; Lee, Sangkeun; Sukumar, Sreenivas R; Shankar, Mallikarjun
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.
Vortices and superfields on a graph
Kan, Nahomi; Kobayashi, Koichiro; Shiraishi, Kiyoshi
2009-08-15
We extend the dimensional deconstruction by utilizing the knowledge of graph theory. In the dimensional deconstruction, one uses the moose diagram to exhibit the structure of the 'theory space'. We generalize the moose diagram to a general graph with oriented edges. In the present paper, we consider only the U(1) gauge symmetry. We also introduce supersymmetry into our model by use of superfields. We suppose that vector superfields reside at the vertices and chiral superfields at the edges of a given graph. Then we can consider multivector, multi-Higgs models. In our model, [U(1)]{sup p} (where p is the number of vertices) is broken to a single U(1). Therefore, for specific graphs, we get vortexlike classical solutions in our model. We show some examples of the graphs admitting the vortex solutions of simple structure as the Bogomolnyi solution.
Vortices and superfields on a graph
NASA Astrophysics Data System (ADS)
Kan, Nahomi; Kobayashi, Koichiro; Shiraishi, Kiyoshi
2009-08-01
We extend the dimensional deconstruction by utilizing the knowledge of graph theory. In the dimensional deconstruction, one uses the moose diagram to exhibit the structure of the “theory space.” We generalize the moose diagram to a general graph with oriented edges. In the present paper, we consider only the U(1) gauge symmetry. We also introduce supersymmetry into our model by use of superfields. We suppose that vector superfields reside at the vertices and chiral superfields at the edges of a given graph. Then we can consider multivector, multi-Higgs models. In our model, [U(1)]p (where p is the number of vertices) is broken to a single U(1). Therefore, for specific graphs, we get vortexlike classical solutions in our model. We show some examples of the graphs admitting the vortex solutions of simple structure as the Bogomolnyi solution.
NASA Technical Reports Server (NTRS)
Lieberman, R. N.
1972-01-01
Given a directed graph, a natural topology is defined and relationships between standard topological properties and graph theoretical concepts are studied. In particular, the properties of connectivity and separatedness are investigated. A metric is introduced which is shown to be related to separatedness. The topological notions of continuity and homeomorphism. A class of maps is studied which preserve both graph and topological properties. Applications involving strong maps and contractions are also presented.
Sato, K; Nakamura, S; Koseki, T; Yamauchi, F; Baba, M; Mikami, M; Kobayashi, R; Fujikawa, T; Nagaoka, S
1991-08-01
The authors report a 56-year-old woman with Ramsey Hunt syndrome with multiple cranial nerve paralysis and acute respiratory failure. Five days before admission, she experienced right otalgia and right facial pain and consulted an otolaryngologist of our hospital, who diagnosed the illness as acute parotitis and laryngopharyngitis. One day before admission, she experienced mild dyspnea and general fatigue and came to our hospital emergency room. A chest X-ray film revealed no abnormalities but some blisters were observed around her right ear. The next day, her dyspnea became more severe and she was admitted. A chest X-ray film on admission revealed right lower lobe consolidation, and neurological examination disclosed multiple cranial nerve paralysis, i.e., paralysis of the right fifth, seventh, eighth, ninth, tenth, eleventh, twelfth and left tenth cranial nerve. The serum titer of anti-herpes zoster antibody was elevated to 1,024, and the patient was diagnosed as having Ramsey Hunt syndrome with multiple cranial nerve paralysis. Arterial blood gas analysis revealed hypoxemia with hypercapnea, which was considered to be due to aspiration pneumonia and central airway obstruction caused by vocal cord paralysis. Mechanical ventilation was soon instituted and several antibiotics and acyclovir were administered intravenously, with marked effects. Three months after admission, the patient was discharged with no sequelae except mild hoarseness. Patients with herpes zoster oticus, facial nerve paralysis and auditory symptoms are diagnosed as having Ramsey Hunt syndrome. This case was complicated by lower cranial nerve paralysis and acute respiratory failure, which is very rare.(ABSTRACT TRUNCATED AT 250 WORDS)
Lothian, Josh; Powers, Sarah S; Sullivan, Blair D; Baker, Matthew B; Schrock, Jonathan; Poole, Stephen W
2013-12-01
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 dierent 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.
2007-05-22
MpiGraph consists of an MPI application called mpiGraph written in C to measure message bandwidth and an associated crunch_mpiGraph script written in Perl to process the application output into an HTMO report. The mpiGraph application is designed to inspect the health and scalability of a high-performance interconnect while under heavy load. This is useful to detect hardware and software problems in a system, such as slow nodes, links, switches, or contention in switch routing. Itmore » is also useful to characterize how interconnect performance changes with different settings or how one interconnect type compares to another.« less
Jotkowitz, A
2008-10-01
Due to the worldwide shortage of organs for transplantation, there has been an increased use of organs obtained after circulatory death alone. A protocol for this procedure has recently been approved by a major transplant consortium. This development raises serious moral and ethical concerns. Two renowned theologians of the previous generation, Paul Ramsey and Moshe Feinstein, wrote extensively on the ethical issues relating to transplantation, and their work has much relevance to current moral dilemmas. Their writings relating to definition of death, organ transplantation and the care of the terminally ill are briefly presented, and their potential application to the moral problem of organ donation after circulatory death is discussed.
Raman-Ramsey multizone spectroscopy in a pure rubidium vapor cell
Failache, H.; Lenci, L.; Lezama, A.
2010-02-15
In view of application to a miniaturized spectroscopy system, we consider an optical setup that splits a laser beam into several parallel narrow light sheets allowing an effective beam expansion and consequently longer atom-light interaction times. We analyze the multizone coherent population trapping (MZCPT) spectroscopy of alkali-metal-vapor atoms, without buffer gas, in the presence of a split light beam. We show that the MZCPT signal is largely insensitive to intensity broadening. Experimentally observed spectra are in qualitative agreement with the predictions of a simplified model that describes each spectrum as an integral over the atomic velocity distribution of Ramsey multizone spectra.
On the effective size of a non-Weyl graph
NASA Astrophysics Data System (ADS)
Lipovský, Jiřˇí
2016-09-01
We show how to find the coefficient of the leading term of the resonance asymptotics using the method of pseudo-orbit expansion for quantum graphs which do not obey Weyl asymptotics. For a non-Weyl graph we develop a method to reduce the number of edges of a corresponding directed graph. Through this method we prove bounds on the above coefficient depending on the structure of the graph, for graphs with the same lengths of internal edges. We explicitly find the positions of the resolvent resonances.
Topological structure of dictionary graphs
NASA Astrophysics Data System (ADS)
Fukś, Henryk; Krzemiński, Mark
2009-09-01
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 103 and 104. 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.
On the Adjacent Eccentric Distance Sum Index of Graphs
Qu, Hui; Cao, Shujuan
2015-01-01
For a given graph G, ε(v) and deg(v) denote the eccentricity and the degree of the vertex v in G, respectively. The adjacent eccentric distance sum index of a graph G is defined as ξsv(G)=∑v∈V(G)ε(v)D(v)deg(v), where D(v)=∑u∈V(G)d(u,v) is the sum of all distances from the vertex v. In this paper we derive some bounds for the adjacent eccentric distance sum index in terms of some graph parameters, such as independence number, covering number, vertex connectivity, chromatic number, diameter and some other graph topological indices. PMID:26091095
ERIC Educational Resources Information Center
Lind, Joy; Narayan, Darren
2009-01-01
We present the topic of graph connectivity along with a famous theorem of Menger in the real-world setting of the national computer network infrastructure of "National LambdaRail". We include a set of exercises where students reinforce their understanding of graph connectivity by analysing the "National LambdaRail" network. Finally, we give…
ERIC Educational Resources Information Center
Shen, Ji
2009-01-01
In the Walking Out Graphs Lesson described here, students experience several types of representations used to describe motion, including words, sentences, equations, graphs, data tables, and actions. The most important theme of this lesson is that students have to understand the consistency among these representations and form the habit of…
ERIC Educational Resources Information Center
Petrosino, Anthony
2012-01-01
This article responds to arguments by Skidmore and Thompson (this issue of "Educational Researcher") that a graph published more than 10 years ago was erroneously reproduced and "gratuitously damaged" perceptions of the quality of education research. After describing the purpose of the original graph, the author counters assertions that the graph…
ERIC Educational Resources Information Center
Johnson, Millie
1997-01-01
Graphs from media sources and questions developed from them can be used in the middle school mathematics classroom. Graphs depict storage temperature on a milk carton; air pressure measurements on a package of shock absorbers; sleep-wake patterns of an infant; a dog's breathing patterns; and the angle, velocity, and radius of a leaning bicyclist…
ERIC Educational Resources Information Center
Doto, Julianne; Golbeck, Susan
2007-01-01
Collecting data and analyzing the results of experiments is difficult for children. The authors found a surprising way to help their third graders make graphs and draw conclusions from their data: digital photographs. The pictures bridged the gap between an abstract graph and the plants it represented. With the support of the photos, students…
ERIC Educational Resources Information Center
Hirsch, Christian R.
1975-01-01
Using a set of worksheets, students will discover and apply Euler's formula regarding connected planar graphs and play and analyze the game of Sprouts. One sheet leads to the discovery of Euler's formula; another concerns traversability of a graph; another gives an example and a game involving these ideas. (Author/KM)
Using Specialized Graph Paper.
ERIC Educational Resources Information Center
James, C.
1988-01-01
Discusses the use of logarithm and reciprocal graphs in the college physics classroom. Provides examples, such as electrical conductivity, reliability function in the Weibull model, and the Clausius-Clapeyron equation for latent heat of vaporation. Shows graphs with weighting of points. (YP)
NASA Astrophysics Data System (ADS)
Newman, M. E. J.; Martin, Travis
2014-11-01
Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdős and Rényi, in particular, as well as the so-called configuration model, have served as the starting point for numerous calculations. In this paper we describe another large class of random graph models, which we call equitable random graphs and which are flexible enough to represent networks with diverse degree distributions and many nontrivial types of structure, including community structure, bipartite structure, degree correlations, stratification, and others, yet are exactly solvable for a wide range of properties in the limit of large graph size, including percolation properties, complete spectral density, and the behavior of homogeneous dynamical systems, such as coupled oscillators or epidemic models.
Object Discovery: Soft Attributed Graph Mining.
Zhang, Quanshi; Song, Xuan; Shao, Xiaowei; Zhao, Huijing; Shibasaki, Ryosuke
2016-03-01
We categorize this research in terms of its contribution to both graph theory and computer vision. From the theoretical perspective, this study can be considered as the first attempt to formulate the idea of mining maximal frequent subgraphs in the challenging domain of messy visual data, and as a conceptual extension to the unsupervised learning of graph matching. We define a soft attributed pattern (SAP) to represent the common subgraph pattern among a set of attributed relational graphs (ARGs), considering both their structure and attributes. Regarding the differences between ARGs with fuzzy attributes and conventional labeled graphs, we propose a new mining strategy that directly extracts the SAP with the maximal graph size without applying node enumeration. Given an initial graph template and a number of ARGs, we develop an unsupervised method to modify the graph template into the maximal-size SAP. From a practical perspective, this research develops a general platform for learning the category model (i.e., the SAP) from cluttered visual data (i.e., the ARGs) without labeling "what is where," thereby opening the possibility for a series of applications in the era of big visual data. Experiments demonstrate the superior performance of the proposed method on RGB/RGB-D images and videos.
Object Discovery: Soft Attributed Graph Mining.
Zhang, Quanshi; Song, Xuan; Shao, Xiaowei; Zhao, Huijing; Shibasaki, Ryosuke
2016-03-01
We categorize this research in terms of its contribution to both graph theory and computer vision. From the theoretical perspective, this study can be considered as the first attempt to formulate the idea of mining maximal frequent subgraphs in the challenging domain of messy visual data, and as a conceptual extension to the unsupervised learning of graph matching. We define a soft attributed pattern (SAP) to represent the common subgraph pattern among a set of attributed relational graphs (ARGs), considering both their structure and attributes. Regarding the differences between ARGs with fuzzy attributes and conventional labeled graphs, we propose a new mining strategy that directly extracts the SAP with the maximal graph size without applying node enumeration. Given an initial graph template and a number of ARGs, we develop an unsupervised method to modify the graph template into the maximal-size SAP. From a practical perspective, this research develops a general platform for learning the category model (i.e., the SAP) from cluttered visual data (i.e., the ARGs) without labeling "what is where," thereby opening the possibility for a series of applications in the era of big visual data. Experiments demonstrate the superior performance of the proposed method on RGB/RGB-D images and videos. PMID:27046496
On the Spectral Gap of a Quantum Graph
NASA Astrophysics Data System (ADS)
Kennedy, James B.; Kurasov, Pavel; Malenová, Gabriela; Mugnolo, Delio
2016-09-01
We consider the problem of finding universal bounds of "isoperimetric" or "isodiametric" type on the spectral gap of the Laplacian on a metric graph with natural boundary conditions at the vertices, in terms of various analytical and combinatorial properties of the graph: its total length, diameter, number of vertices and number of edges. We investigate which combinations of parameters are necessary to obtain non-trivial upper and lower bounds and obtain a number of sharp estimates in terms of these parameters. We also show that, in contrast to the Laplacian matrix on a combinatorial graph, no bound depending only on the diameter is possible. As a special case of our results on metric graphs, we deduce estimates for the normalised Laplacian matrix on combinatorial graphs which, surprisingly, are sometimes sharper than the ones obtained by purely combinatorial methods in the graph theoretical literature.
Reaction route graphs. III. Non-minimal kinetic mechanisms.
Fishtik, Ilie; Callaghan, Caitlin A; Datta, Ravindra
2005-02-24
The concept of reaction route (RR) graphs introduced recently by us for kinetic mechanisms that produce minimal graphs is extended to the problem of non-minimal kinetic mechanisms for the case of a single overall reaction (OR). A RR graph is said to be minimal if all of the stoichiometric numbers in all direct RRs of the mechanism are equal to +/-1 and non-minimal if at least one stoichiometric number in a direct RR is non-unity, e.g., equal to +/-2. For a given mechanism, four unique topological characteristics of RR graphs are defined and enumerated, namely, direct full routes (FRs), empty routes (ERs), intermediate nodes (INs), and terminal nodes (TNs). These are further utilized to construct the RR graphs. One algorithm involves viewing each IN as a central node in a RR sub-graph. As a result, the construction and enumeration of RR graphs are reduced to the problem of balancing the peripheral nodes in the RR sub-graphs according to the list of FRs, ERs, INs, and TNs. An alternate method involves using an independent set of RRs to draw the RR graph while satisfying the INs and TNs. Three examples are presented to illustrate the application of non-minimal RR graph theory.
NASA Astrophysics Data System (ADS)
Burioni, Raffaella; Chibbaro, Sergio; Vergni, Davide; Vulpiani, Angelo
2012-11-01
We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e., on the time evolution of the reaction product M(t). At variance with pure diffusive processes, characterized by the spectral dimension ds, the important quantity for reaction spreading is found to be the connectivity dimension dl. Numerical data, in agreement with analytical estimates based on the features of n independent random walkers on the graph, show that M(t)˜tdl. In the case of Erdös-Renyi random graphs, the reaction product is characterized by an exponential growth M(t)˜eαt with α proportional to ln
Rashmanlou, Hossein; Samanta, Sovan; Pal, Madhumangal; Borzooei, R A
2016-01-01
The main purpose of this paper is to introduce the notion of vague h-morphism on vague graphs and regular vague graphs. The action of vague h-morphism on vague strong regular graphs are studied. Some elegant results on weak and co weak isomorphism are derived. Also, [Formula: see text]-complement of highly irregular vague graphs are defined. PMID:27536517
Ramsey-like measurement of the decoherence rate between Zeeman sublevels
NASA Astrophysics Data System (ADS)
Shuker, M.; Firstenberg, O.; Sagi, Y.; Ben-Kish, A.; Davidson, N.; Ron, A.
2008-12-01
Two-photon processes that involve different sublevels of the ground state of an atom, are highly sensitive to depopulation and decoherence within the ground state. For example, the spectral width of electromagnetically induced transparency resonances in a Λ -type system, are strongly affected by the ground-state depopulation and decoherence rates. We present a direct measurement of decay rates between hyperfine and Zeeman sublevels in the ground state of Rb87 vapor. Similar to the relaxation-in-the-dark technique, pumping lasers are used to prealign the atomic vapor in a well-defined quantum state. The free propagation of the atomic state is monitored using a Ramsey-like method. Coherence times in the range 1-10ms were measured for room temperature atomic vapor. In the range of the experimental parameters used in this study, the dominant process inducing Zeeman decoherence is the spin-exchange collisions between rubidium atoms.
NASA Astrophysics Data System (ADS)
Yoshida, Ichiro; Hayashi, Nobuhito; Fujita, Kazuki; Taniguchi, Shuya; Hoshina, Yoshitaka; Mitsunaga, Masaharu
2013-02-01
We have simultaneously studied electromagnetically induced transparency (EIT) and Raman Ramsey fringes (RRF) in sodium vapor, in the same theoretical framework and the same experimental scheme. RRF spectra and EIT spectra can be simply distinguished by whether the gate timing of the detection is set at the beginning (RRF) or at the end (EIT) of the excitation pulses. The EIT spectral peaks exhibited pronounced ac Stark shifts linearly depending upon the pumping power (8.8 kHz/mW), while in the RRF spectra such shifts were almost negligible (0.19 kHz/mW), provided that the pulse separation is sufficiently large. This fact promotes RRF as a strong candidate for next-generation compact atomic clocks. Transient spectra in between RRF and EIT have also been investigated by changing the gate timing within the excitation pulse, and the transition time from RRF to EIT was found to be of the order of a few microseconds.
Forster, Jean; Poupart, John; Rhodes, Kristine; Peterson-Hickey, Melanie; Lamont, Genelle; D'Silva, Joanne; Erickson, Darin
2016-01-01
In 2013, it was estimated that the prevalence of cigarette smoking among American Indians was 36.5%, the highest of all racial/ethnic groups in the continental United States (1). Among American Indians, considerable cultural and geographic variation in cigarette smoking exists. Smoking prevalence among American Indians is lowest in the Southwest and highest in the Upper Midwest/Northern Plains (2). Little information is available about tobacco use among urban American Indians, who might not have ever lived on a reservation or be enrolled in or affiliated with a tribe. In Minnesota, a significant proportion of American Indians reside in urban areas. Among Minnesota's residents who identify as American Indian alone or in combination with another race, 30% live in Hennepin County and Ramsey County, which encompass Minneapolis and St. Paul, respectively (collectively known as the Twin Cities). The predominant tribes (Ojibwe [Chippewa] and Dakota/Lakota/Nakota [Sioux]) traditionally have used locally grown tobacco (Nicotiana rustica), red willow, and other plants for religious ceremonies, although nonceremonial tobacco is often substituted for traditional plants. To assess prevalence of cigarette smoking among this population, it is important to distinguish ceremonial tobacco use (smoked or used in other ways) from nonceremonial tobacco use. To obtain estimates of cigarette smoking prevalence among American Indians in Hennepin and Ramsey counties, the American Indian Adult Tobacco Survey was administered to 964 American Indian residents in 2011, using respondent-driven sampling. Among all participants, 59% were current smokers, 19% were former smokers, and 22% had never smoked. Approximately 40% of employed participants reported that someone smoked in their workplace area during the preceding week. High prevalences of cigarette smoking and secondhand smoke exposure among urban American Indians in Minnesota underscores the need for a comprehensive and culturally
Clique graphs and overlapping communities
NASA Astrophysics Data System (ADS)
Evans, T. S.
2010-12-01
It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of communities or clusters is used to illustrate how a clique graph may be exploited. In particular a benchmark network is shown where clique graphs find the overlapping communities accurately while vertex partition methods fail.
On the rainbow coloring for some graph operations
NASA Astrophysics Data System (ADS)
Dafik, Agustin, Ika Hesti; Fajariyato, Anang; Alfarisi, Ridho
2016-02-01
Let G = (V, E) be a nontrivial, finite, simple and undirected connected graph on which is defined a coloring f : E(G) → {1,2, …, k}, k ∈ N. The adjacent edges may be colored the same colors. A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph G is rainbow connected if there exists a rainbow u - v path for every two vertices u and v of G. The rainbow connection number of a graph G, denoted by rc(G), is the smallest number of k colors required to edge color the graph such that the graph is rainbow connected. In this paper, we determine the exact values of rainbow connection number of some special graph operations, namely cartesian product, tensor product, composition of two special graphs and also amalgamation of special graphs. The result shows that all exact values of rc(G) attain a lower bound of the rainbow connectivity, namely diam(G).
Quasiperiodic graphs at the onset of chaos.
Luque, B; Cordero-Gracia, M; Gómez, M; Robledo, A
2013-12-01
We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers.
Key-Node-Separated Graph Clustering and Layouts for Human Relationship Graph Visualization.
Itoh, Takayuki; Klein, Karsten
2015-01-01
Many graph-drawing methods apply node-clustering techniques based on the density of edges to find tightly connected subgraphs and then hierarchically visualize the clustered graphs. However, users may want to focus on important nodes and their connections to groups of other nodes for some applications. For this purpose, it is effective to separately visualize the key nodes detected based on adjacency and attributes of the nodes. This article presents a graph visualization technique for attribute-embedded graphs that applies a graph-clustering algorithm that accounts for the combination of connections and attributes. The graph clustering step divides the nodes according to the commonality of connected nodes and similarity of feature value vectors. It then calculates the distances between arbitrary pairs of clusters according to the number of connecting edges and the similarity of feature value vectors and finally places the clusters based on the distances. Consequently, the technique separates important nodes that have connections to multiple large clusters and improves the visibility of such nodes' connections. To test this technique, this article presents examples with human relationship graph datasets, including a coauthorship and Twitter communication network dataset.
Two linear time, low overhead algorithms for graph layout
2008-01-10
The software comprises two algorithms designed to perform a 2D layout of a graph structure in time linear with respect to the vertices and edges in the graph, whereas most other layout algorithms have a running time that is quadratic with respect to the number of vertices or greater. Although these layout algorithms run in a fraction of the time as their competitors, they provide competitive results when applied to most real-world graphs. These algorithmsmore » also have a low constant running time and small memory footprint, making them useful for small to large graphs.« less
Quasiperiodic Graphs: Structural Design, Scaling and Entropic Properties
NASA Astrophysics Data System (ADS)
Luque, B.; Ballesteros, F. J.; Núñez, A. M.; Robledo, A.
2013-04-01
A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. Finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy.
A Graph Search Heuristic for Shortest Distance Paths
Chow, E
2005-03-24
This paper presents a heuristic for guiding A* search for finding the shortest distance path between two vertices in a connected, undirected, and explicitly stored graph. The heuristic requires a small amount of data to be stored at each vertex. The heuristic has application to quickly detecting relationships between two vertices in a large information or knowledge network. We compare the performance of this heuristic with breadth-first search on graphs with various topological properties. The results show that one or more orders of magnitude improvement in the number of vertices expanded is possible for large graphs, including Poisson random graphs.
Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.
Shang, Yilun
2015-01-01
Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices. PMID:25822506
Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.
Shang, Yilun
2015-01-01
Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.
Optimized Graph Search Using Multi-Level Graph Clustering
NASA Astrophysics Data System (ADS)
Kala, Rahul; Shukla, Anupam; Tiwari, Ritu
Graphs find a variety of use in numerous domains especially because of their capability to model common problems. The social networking graphs that are used for social networking analysis, a feature given by various social networking sites are an example of this. Graphs can also be visualized in the search engines to carry search operations and provide results. Various searching algorithms have been developed for searching in graphs. In this paper we propose that the entire network graph be clustered. The larger graphs are clustered to make smaller graphs. These smaller graphs can again be clustered to further reduce the size of graph. The search is performed on the smallest graph to identify the general path, which may be further build up to actual nodes by working on the individual clusters involved. Since many searches are carried out on the same graph, clustering may be done once and the data may be used for multiple searches over the time. If the graph changes considerably, only then we may re-cluster the graph.
A Theory of Graphs for Reading Comprehension and Writing Communication.
ERIC Educational Resources Information Center
Fry, Edward
Graphs are increasingly being used in written communication and writers expect readers to understand them. One definition of graphs--information transmitted by position of point, line or area on a two dimensional surface--excludes displays composed chiefly of numbers or words such as tables or outlines. However, it does include time lines, flow…
K-theory of locally finite graph C∗-algebras
NASA Astrophysics Data System (ADS)
Iyudu, Natalia
2013-09-01
We calculate the K-theory of the Cuntz-Krieger algebra OE associated with an infinite, locally finite graph, via the Bass-Hashimoto operator. The formulae we get express the Grothendieck group and the Whitehead group in purely graph theoretic terms. We consider the category of finite (black-and-white, bi-directed) subgraphs with certain graph homomorphisms and construct a continuous functor to abelian groups. In this category K0 is an inductive limit of K-groups of finite graphs, which were calculated in Cornelissen et al. (2008) [3]. In the case of an infinite graph with the finite Betti number we obtain the formula for the Grothendieck group K0(OE)=Z, where β(E) is the first Betti number and γ(E) is the valency number of the graph E. We note that in the infinite case the torsion part of K0, which is present in the case of a finite graph, vanishes. The Whitehead group depends only on the first Betti number: K1(OE)=Z. These allow us to provide a counterexample to the fact, which holds for finite graphs, that K1(OE) is the torsion free part of K0(OE).
Subdominant pseudoultrametric on graphs
Dovgoshei, A A; Petrov, E A
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.
Chen, J.; Safro, I.
2011-01-01
Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.
Graphing Calculator Mini Course
NASA Technical Reports Server (NTRS)
Karnawat, Sunil R.
1996-01-01
The "Graphing Calculator Mini Course" project provided a mathematically-intensive technologically-based summer enrichment workshop for teachers of American Indian students on the Turtle Mountain Indian Reservation. Eleven such teachers participated in the six-day workshop in summer of 1996 and three Sunday workshops in the academic year. The project aimed to improve science and mathematics education on the reservation by showing teachers effective ways to use high-end graphing calculators as teaching and learning tools in science and mathematics courses at all levels. In particular, the workshop concentrated on applying TI-82's user-friendly features to understand the various mathematical and scientific concepts.
Light effects in the atomic-motion-induced Ramsey narrowing of dark resonances in wall-coated cells
Breschi, E.; Schori, C.; Di Domenico, G.; Mileti, G.; Kazakov, G.; Litvinov, A.; Matisov, B.
2010-12-15
We report on light shift and broadening in the atomic-motion-induced Ramsey narrowing of dark resonances prepared in alkali-metal vapors contained in wall-coated cells without buffer gas. The atomic-motion-induced Ramsey narrowing is due to the free motion of the polarized atomic spins in and out of the optical interaction region before spin relaxation. As a consequence of this effect, we observe a narrowing of the dark resonance linewidth as well as a reduction of the ground states' light shift when the volume of the interaction region decreases at constant optical intensity. The results can be intuitively interpreted as a dilution of the intensity effect similar to a pulsed interrogation due to the atomic motion. Finally the influence of this effect on the performance of compact atomic clocks is discussed.
Labeled Graph Kernel for Behavior Analysis.
Zhao, Ruiqi; Martinez, Aleix M
2016-08-01
Automatic behavior analysis from video is a major topic in many areas of research, including computer vision, multimedia, robotics, biology, cognitive science, social psychology, psychiatry, and linguistics. Two major problems are of interest when analyzing behavior. First, we wish to automatically categorize observed behaviors into a discrete set of classes (i.e., classification). For example, to determine word production from video sequences in sign language. Second, we wish to understand the relevance of each behavioral feature in achieving this classification (i.e., decoding). For instance, to know which behavior variables are used to discriminate between the words apple and onion in American Sign Language (ASL). The present paper proposes to model behavior using a labeled graph, where the nodes define behavioral features and the edges are labels specifying their order (e.g., before, overlaps, start). In this approach, classification reduces to a simple labeled graph matching. Unfortunately, the complexity of labeled graph matching grows exponentially with the number of categories we wish to represent. Here, we derive a graph kernel to quickly and accurately compute this graph similarity. This approach is very general and can be plugged into any kernel-based classifier. Specifically, we derive a Labeled Graph Support Vector Machine (LGSVM) and a Labeled Graph Logistic Regressor (LGLR) that can be readily employed to discriminate between many actions (e.g., sign language concepts). The derived approach can be readily used for decoding too, yielding invaluable information for the understanding of a problem (e.g., to know how to teach a sign language). The derived algorithms allow us to achieve higher accuracy results than those of state-of-the-art algorithms in a fraction of the time. We show experimental results on a variety of problems and datasets, including multimodal data.
Graph for locked rotor current
NASA Technical Reports Server (NTRS)
Peck, R. R.
1972-01-01
Graph determines effect of stalled motor on a distribution system and eliminates hand calculation of amperage in emergencies. Graph is useful to any manufacturer, contractor, or maintenance department involved in electrical technology.
Graphing techniques for materials laboratory using Excel
NASA Technical Reports Server (NTRS)
Kundu, Nikhil K.
1994-01-01
Engineering technology curricula stress hands on training and laboratory practices in most of the technical courses. Laboratory reports should include analytical as well as graphical evaluation of experimental data. Experience shows that many students neither have the mathematical background nor the expertise for graphing. This paper briefly describes the procedure and data obtained from a number of experiments such as spring rate, stress concentration, endurance limit, and column buckling for a variety of materials. Then with a brief introduction to Microsoft Excel the author explains the techniques used for linear regression and logarithmic graphing.
Single-qubit gates by graph scattering
NASA Astrophysics Data System (ADS)
Underwood, Michael S.; Blumer, Benjamin A.; Feder, David L.
2012-02-01
Continuous-time quantum walkers with tightly peaked momenta can simulate quantum computations by scattering off finite graphs. We enumerate all single-qubit gates that can be enacted by scattering off a single graph on up to n=9 vertices at certain momentum values, and provide numerical evidence that the number of such gates grows exponentially with n. The single-qubit rotations are about axes distributed roughly uniformly on the Bloch sphere, and rotations by both rational and irrational multiples of π are found.
2013-02-19
This library is used in several LLNL projects, including STAT (the Stack Trace Analysis Tool for scalable debugging) and some modules in P^nMPI (a tool MPI tool infrastructure). It can also be used standalone for creating and manipulationg graphs, but its API is primarily tuned to support these other projects
ERIC Educational Resources Information Center
Pitts Bannister, Vanessa R.; Jamar, Idorenyin; Mutegi, Jomo W.
2007-01-01
In this article, the learning progress of one fifth-grade student is examined with regard to the development of her graph interpretation skills as she participated in the Junior Science Institute (JSI), a two-week, science intensive summer camp in which participants engaged in microbiology research and application. By showcasing the student's…
ERIC Educational Resources Information Center
Krueger, Tom
2010-01-01
In this article, the author shares one effective lesson idea on straight line graphs that he applied in his lower ability Y9 class. The author wanted something interesting for his class to do, something that was fun and engaging with direct feedback, and something that worked because someone else had tried it before. In a word, the author admits…
ERIC Educational Resources Information Center
Sokol, William
In this autoinstructional packet, the student is given an experimental situation which introduces him to the process of graphing. The lesson is presented for secondary school students in chemistry. Algebra I and a Del Mod System program (indicated as SE 018 020) are suggested prerequisites for the use of this program. Behavioral objectives are…
ERIC Educational Resources Information Center
Cooper, Carol
1975-01-01
Teachers of an integrated elementary classroom used cookie-sharing time as a learning experience for students. Responsible for dividing varying amounts of cookies daily, the students learned to translate their experiences to graphs of differing sophistication and analyses. Further interpretation and application were done by individual students…
NASA Astrophysics Data System (ADS)
Schrader, Robert
This is an extended version of the talk given at the Nato Advanced Research Workshop: New Challenges in Complex System Physics, May 20-24, 2013 in Samarkand (Uzbekistan). We report on results on three topics in joint work with V. Kostrykin (Mainz, Germany) and J. Potthoff (Mannheim, Germany): Propagation of waves on graphs,
Simmons, G.J.
1985-01-01
Given a graph G and an ordering phi of the vertices, V(G), we define a parsimonious proper coloring (PPC) of V(G) under phi to be a proper coloring of V(G) in the order phi, where a new color is introduced only when a vertex cannot be properly colored in its order with any of the colors already used.
ERIC Educational Resources Information Center
Rose, Kenneth
1974-01-01
Two new types of graph paper are described; focus-focus conic paper and focus-directrix paper. Both types make it easier to draw families of conics. Suggestions for further work are given as is a method for establishing a connection with other ways of looking at the conic sections. (LS)
Temporal Representation in Semantic Graphs
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
Krovi, Hari; Brun, Todd A.
2007-06-15
A discrete-time quantum walk on a graph {gamma} 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.
Random graphs with arbitrary degree distributions and their applications
NASA Astrophysics Data System (ADS)
Newman, M. E. J.; Strogatz, S. H.; Watts, D. J.
2001-08-01
Recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in the past. In this paper we develop in detail the theory of random graphs with arbitrary degree distributions. In addition to simple undirected, unipartite graphs, we examine the properties of directed and bipartite graphs. Among other results, we derive exact expressions for the position of the phase transition at which a giant component first forms, the mean component size, the size of the giant component if there is one, the mean number of vertices a certain distance away from a randomly chosen vertex, and the average vertex-vertex distance within a graph. We apply our theory to some real-world graphs, including the world-wide web and collaboration graphs of scientists and Fortune 1000 company directors. We demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.
Learning a Nonnegative Sparse Graph for Linear Regression.
Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung
2015-09-01
Previous graph-based semisupervised learning (G-SSL) methods have the following drawbacks: 1) they usually predefine the graph structure and then use it to perform label prediction, which cannot guarantee an overall optimum and 2) they only focus on the label prediction or the graph structure construction but are not competent in handling new samples. To this end, a novel nonnegative sparse graph (NNSG) learning method was first proposed. Then, both the label prediction and projection learning were integrated into linear regression. Finally, the linear regression and graph structure learning were unified within the same framework to overcome these two drawbacks. Therefore, a novel method, named learning a NNSG for linear regression was presented, in which the linear regression and graph learning were simultaneously performed to guarantee an overall optimum. In the learning process, the label information can be accurately propagated via the graph structure so that the linear regression can learn a discriminative projection to better fit sample labels and accurately classify new samples. An effective algorithm was designed to solve the corresponding optimization problem with fast convergence. Furthermore, NNSG provides a unified perceptiveness for a number of graph-based learning methods and linear regression methods. The experimental results showed that NNSG can obtain very high classification accuracy and greatly outperforms conventional G-SSL methods, especially some conventional graph construction methods.
Scale-invariant geometric random graphs.
Xie, Zheng; Rogers, Tim
2016-03-01
We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to influence zones that depend on node position in space and time, mimicking the heterogeneity and increased specialization found in growing networks. Through calculations and numerical simulations we explore the consequences of scale invariance for geometric random graphs generated this way. Our analysis reveals a dichotomy between scale-free and Poisson distributions of in- and out-degree, the existence of a random number of hub nodes, high clustering, and unusual percolation behavior. These properties are similar to those of empirically observed web graphs. PMID:27078369
Mining and Indexing Graph Databases
ERIC Educational Resources Information Center
Yuan, Dayu
2013-01-01
Graphs are widely used to model structures and relationships of objects in various scientific and commercial fields. Chemical molecules, proteins, malware system-call dependencies and three-dimensional mechanical parts are all modeled as graphs. In this dissertation, we propose to mine and index those graph data to enable fast and scalable search.…
Recursive Feature Extraction in Graphs
2014-08-14
ReFeX extracts recursive topological features from graph data. The input is a graph as a csv file and the output is a csv file containing feature values for each node in the graph. The features are based on topological counts in the neighborhoods of each nodes, as well as recursive summaries of neighbors' features.
Editing graphs for maximum effect
Murphy, P.W.; Rhiner, R.W.
1991-01-08
The paper contains over eighty rules for editing graphs, arranged under nine major headings in a logical sequence for editing all the graphs in a manuscript. It is excerpted from a monograph used at the Lawrence Livermore National Laboratory to train beginning technical editors in editing graphs; a corresponding Hypercard stack is also used in this training. 6 refs., 4 figs.
ERIC Educational Resources Information Center
Skurnick, Ronald; Davi, Charles; Skurnick, Mia
2005-01-01
Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…
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.
Less Is Less: A Systematic Review of Graph Use in Meta-Analyses
ERIC Educational Resources Information Center
Schild, Anne H. E.; Voracek, Martin
2013-01-01
Graphs are an essential part of scientific communication. Complex datasets, of which meta-analyses are textbook examples, benefit the most from visualization. Although a number of graph options for meta-analyses exist, the extent to which these are used was hitherto unclear. A systematic review on graph use in meta-analyses in three disciplines…
Graphs as a Problem-Solving Tool in 1-D Kinematics
ERIC Educational Resources Information Center
Desbien, Dwain M.
2008-01-01
In this age of the microcomputer-based lab (MBL), students are quite accustomed to looking at graphs of position, velocity, and acceleration versus time. A number of textbooks argue convincingly that the slope of the velocity graph gives the acceleration, the area under the velocity graph yields the displacement, and the area under the…
Ramsey interferometry for resonant Auger decay through core-excited states
NASA Astrophysics Data System (ADS)
Chatterjee, Souvik; Nakajima, Takashi
2016-08-01
We theoretically investigate the electron dynamics in Ne atoms involving core-excited states through the Ramsey scheme with a pair of time-delayed x-ray pulses. Irradiation of Ne atoms by the ˜1 femtosecond x-ray pulse simultaneously populates two core-excited states, and an identical but time-delayed x-ray pulse probes the dynamics of the core-excited electron wave packet which is subject to the resonant Auger decay. The energy-integrated total Auger electron yield and energy-resolved Auger electron spectra in the time domain show periodic structures due to the temporal evolution of the wave packet, from which we can obtain the counterpart in the frequency domain through the Fourier transformation. The Auger electron energy spectra in the time as well as frequency domains show the interference patterns between the two Auger electron wave packets released into the continuum from the superposition of two core-excited states at different times. These spectra are important to clarify the individual contribution of the different Auger decay channels upon core excitation by the x-ray pulse.
Spectral fluctuations of quantum graphs
NASA Astrophysics Data System (ADS)
Pluhař, Z.; Weidenmüller, H. A.
2014-10-01
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.
Spectral fluctuations of quantum graphs
Pluhař, Z.; Weidenmüller, H. A.
2014-10-15
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.
Graph characterization via Ihara coefficients.
Ren, Peng; Wilson, Richard C; Hancock, Edwin R
2011-02-01
The novel contributions of this paper are twofold. First, we demonstrate how to characterize unweighted graphs in a permutation-invariant manner using the polynomial coefficients from the Ihara zeta function, i.e., the Ihara coefficients. Second, we generalize the definition of the Ihara coefficients to edge-weighted graphs. For an unweighted graph, the Ihara zeta function is the reciprocal of a quasi characteristic polynomial of the adjacency matrix of the associated oriented line graph. Since the Ihara zeta function has poles that give rise to infinities, the most convenient numerically stable representation is to work with the coefficients of the quasi characteristic polynomial. Moreover, the polynomial coefficients are invariant to vertex order permutations and also convey information concerning the cycle structure of the graph. To generalize the representation to edge-weighted graphs, we make use of the reduced Bartholdi zeta function. We prove that the computation of the Ihara coefficients for unweighted graphs is a special case of our proposed method for unit edge weights. We also present a spectral analysis of the Ihara coefficients and indicate their advantages over other graph spectral methods. We apply the proposed graph characterization method to capturing graph-class structure and clustering graphs. Experimental results reveal that the Ihara coefficients are more effective than methods based on Laplacian spectra.
Regular homotopy for immersions of graphs into surfaces
NASA Astrophysics Data System (ADS)
Permyakov, D. A.
2016-06-01
We study invariants of regular immersions of graphs into surfaces up to regular homotopy. The concept of the winding number is used to introduce a new simple combinatorial invariant of regular homotopy. Bibliography: 20 titles.
ERIC Educational Resources Information Center
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…
A system for routing arbitrary directed graphs on SIMD architectures
NASA Technical Reports Server (NTRS)
Tomboulian, Sherryl
1987-01-01
There are many problems which can be described in terms of directed graphs that contain a large number of vertices where simple computations occur using data from connecting vertices. A method is given for parallelizing such problems on an SIMD machine model that is bit-serial and uses only nearest neighbor connections for communication. Each vertex of the graph will be assigned to a processor in the machine. Algorithms are given that will be used to implement movement of data along the arcs of the graph. This architecture and algorithms define a system that is relatively simple to build and can do graph processing. All arcs can be transversed in parallel in time O(T), where T is empirically proportional to the diameter of the interconnection network times the average degree of the graph. Modifying or adding a new arc takes the same time as parallel traversal.
Thiruvengadam, Muthu; Yang, Chang-Hsien
2009-10-01
Lisianthus [Eustoma grandiflorum (Raf.) Shinn] is a popular cut flower crop throughout the world, and the demand for this plant for cut flowers and potted plants has been increasing worldwide. Recent advances in genetic engineering have enabled the transformation and regeneration of plants to become a powerful tool for improvement of lisianthus. We have established a highly efficient plant regeneration system and Agrobacterium-mediated genetic transformation of E. grandiflorum. The greatest shoot regeneration frequency and number of shoot buds per explant are observed on media supplemented with 6-Benzylaminopurine (BAP) and alpha-Naphthalene acetic acid (NAA). We report an efficient plant regeneration system using leaf explants via organogenesis with high efficiency of transgenic plants (15%) in culture of 11 weeks' duration. Further ectopic expression of two MADS box genes, LMADS1-M from lily (Lilium longiflorum) and OMADS1 from orchid (Oncidium Gower Ramsey), was performed in E. grandiflorum. Conversion of second whorl petals into sepal-like structures and alteration of third whorl stamen formation were observed in the transgenic E. grandiflorum plants ectopically expressing 35S::LMADS1-M. 35S::OMADS1 transgenic E. grandiflorum plants flowered significantly earlier than non-transgenic plants. This is the first report on the ectopic expression of two MADS box genes in E. grandiflorum using a simple and highly efficient gene transfer protocol. Our results reveal the potential for floral modification in E. grandiflorum through genetic transformation. PMID:19639326
Thiruvengadam, Muthu; Yang, Chang-Hsien
2009-10-01
Lisianthus [Eustoma grandiflorum (Raf.) Shinn] is a popular cut flower crop throughout the world, and the demand for this plant for cut flowers and potted plants has been increasing worldwide. Recent advances in genetic engineering have enabled the transformation and regeneration of plants to become a powerful tool for improvement of lisianthus. We have established a highly efficient plant regeneration system and Agrobacterium-mediated genetic transformation of E. grandiflorum. The greatest shoot regeneration frequency and number of shoot buds per explant are observed on media supplemented with 6-Benzylaminopurine (BAP) and alpha-Naphthalene acetic acid (NAA). We report an efficient plant regeneration system using leaf explants via organogenesis with high efficiency of transgenic plants (15%) in culture of 11 weeks' duration. Further ectopic expression of two MADS box genes, LMADS1-M from lily (Lilium longiflorum) and OMADS1 from orchid (Oncidium Gower Ramsey), was performed in E. grandiflorum. Conversion of second whorl petals into sepal-like structures and alteration of third whorl stamen formation were observed in the transgenic E. grandiflorum plants ectopically expressing 35S::LMADS1-M. 35S::OMADS1 transgenic E. grandiflorum plants flowered significantly earlier than non-transgenic plants. This is the first report on the ectopic expression of two MADS box genes in E. grandiflorum using a simple and highly efficient gene transfer protocol. Our results reveal the potential for floral modification in E. grandiflorum through genetic transformation.
Improving Attack Graph Visualization through Data Reduction and Attack Grouping
John Homer; Ashok Varikuti; Xinming Ou; Miles A. McQueen
2008-09-01
Various tools exist to analyze enterprise network systems and to produce attack graphs detailing how attackers might penetrate into the system. These attack graphs, however, are often complex and difficult to comprehend fully, and a human user may find it problematic to reach appropriate configuration decisions. This paper presents methodologies that can 1) automatically identify portions of an attack graph that do not help a user to understand the core security problems and so can be trimmed, and 2) automatically group similar attack steps as virtual nodes in a model of the network topology, to immediately increase the understandability of the data. We believe both methods are important steps toward improving visualization of attack graphs to make them more useful in configuration management for large enterprise networks. We implemented our methods using one of the existing attack-graph toolkits. Initial experimentation shows that the proposed approaches can 1) significantly reduce the complexity of attack graphs by trimming a large portion of the graph that is not needed for a user to understand the security problem, and 2) significantly increase the accessibility and understandability of the data presented in the attack graph by clearly showing, within a generated visualization of the network topology, the number and type of potential attacks to which each host is exposed.
Quantitative analysis of electrically detected Ramsey fringes in P-doped Si
NASA Astrophysics Data System (ADS)
Greenland, P. T.; Matmon, G.; Villis, B. J.; Bowyer, E. T.; Li, Juerong; Murdin, B. N.; van der Meer, A. F. G.; Redlich, B.; Pidgeon, C. R.; Aeppli, G.
2015-10-01
This work describes detection of the laser preparation and subsequent coherent manipulation of the quantum states of orbital levels of donors in doped Si, by measuring the voltage drop across an irradiated Si sample. This electrical signal, which arises from thermal ionization of excited orbital states, and which is detected on a millisecond time scale by a voltmeter, leads to much more sensitive detection than can be had using optical methods, but has not before been quantitatively described from first principles. We present here a unified theory which relates the voltage drop across the sample to the wave function of the excited donors, and compare its predictions to experiments in which pairs of picosecond pulses from the Dutch free-electron laser FELIX are used to resonantly and coherently excite P donors in Si. Although the voltage drop varies on a millisecond time scale we are able to measure Ramsey oscillation of the excitation on a picosecond time scale, thus confirming that the donor wave function, and not just its excited state population, is crucial in determining the electrical signal. We are also able to extract the recombination rate coefficient to the ground state of the donor as well as the photoionization cross section of the excited state and phonon induced thermal ionization rate from the excited state. These quantities, which were previously of limited interest, are here shown to be important in the description of electrical detection, which, in our unoptimized configuration, is sensitive enough to enable us to detect the excitation of ˜107 donors.
Graph Coarsening for Path Finding in Cybersecurity Graphs
Hogan, Emilie A.; Johnson, John R.; Halappanavar, Mahantesh
2013-01-01
n the pass-the-hash attack, hackers repeatedly steal password hashes and move through a computer network with the goal of reaching a computer with high level administrative privileges. In this paper we apply graph coarsening in network graphs for the purpose of detecting hackers using this attack or assessing the risk level of the network's current state. We repeatedly take graph minors, which preserve the existence of paths in the graph, and take powers of the adjacency matrix to count the paths. This allows us to detect the existence of paths as well as find paths that have high risk of being used by adversaries.
NASA Technical Reports Server (NTRS)
Burleigh, Scott C.
2011-01-01
Contact Graph Routing (CGR) is a dynamic routing system that computes routes through a time-varying topology of scheduled communication contacts in a network based on the DTN (Delay-Tolerant Networking) architecture. It is designed to enable dynamic selection of data transmission routes in a space network based on DTN. This dynamic responsiveness in route computation should be significantly more effective and less expensive than static routing, increasing total data return while at the same time reducing mission operations cost and risk. The basic strategy of CGR is to take advantage of the fact that, since flight mission communication operations are planned in detail, the communication routes between any pair of bundle agents in a population of nodes that have all been informed of one another's plans can be inferred from those plans rather than discovered via dialogue (which is impractical over long one-way-light-time space links). Messages that convey this planning information are used to construct contact graphs (time-varying models of network connectivity) from which CGR automatically computes efficient routes for bundles. Automatic route selection increases the flexibility and resilience of the space network, simplifying cross-support and reducing mission management costs. Note that there are no routing tables in Contact Graph Routing. The best route for a bundle destined for a given node may routinely be different from the best route for a different bundle destined for the same node, depending on bundle priority, bundle expiration time, and changes in the current lengths of transmission queues for neighboring nodes; routes must be computed individually for each bundle, from the Bundle Protocol agent's current network connectivity model for the bundle s destination node (the contact graph). Clearly this places a premium on optimizing the implementation of the route computation algorithm. The scalability of CGR to very large networks remains a research topic
Horizontal visibility graphs from integer sequences
NASA Astrophysics Data System (ADS)
Lacasa, Lucas
2016-09-01
The horizontal visibility graph (HVG) is a graph-theoretical representation of a time series and builds a bridge between dynamical systems and graph theory. In recent years this representation has been used to describe and theoretically compare different types of dynamics and has been applied to characterize empirical signals, by extracting topological features from the associated HVGs which have shown to be informative on the class of dynamics. Among some other measures, it has been shown that the degree distribution of these graphs is a very informative feature that encapsulates nontrivial information of the series's generative dynamics. In particular, the HVG associated to a bi-infinite real-valued series of independent and identically distributed random variables is a universal exponential law P(k)=(1/3){(2/3)}k-2, independent of the series marginal distribution. Most of the current applications have however only addressed real-valued time series, as no exact results are known for the topological properties of HVGs associated to integer-valued series. In this paper we explore this latter situation and address univariate time series where each variable can only take a finite number n of consecutive integer values. We are able to construct an explicit formula for the parametric degree distribution {P}n(k), which we prove to converge to the continuous case for large n and deviates otherwise. A few applications are then considered.
Multipartite entanglement in four-qubit graph states
NASA Astrophysics Data System (ADS)
Jafarpour, Mojtaba; Assadi, Leila
2016-03-01
We consider a compendium of the non-trivial four-qubit graphs, derive their corresponding quantum states and classify them into equivalent classes. We use Meyer-Wallach measure and its generalizations to study block-partition and global entanglement in these states. We obtain several entanglement quantities for each graph state, which present a comprehensive characterization of the entanglement properties of the latter. As a result, a number of correlations between the graph structure and multipartite entanglement quantities have also been established.
Reproducibility of graph metrics of human brain structural networks.
Duda, Jeffrey T; Cook, Philip A; Gee, James C
2014-01-01
Recent interest in human brain connectivity has led to the application of graph theoretical analysis to human brain structural networks, in particular white matter connectivity inferred from diffusion imaging and fiber tractography. While these methods have been used to study a variety of patient populations, there has been less examination of the reproducibility of these methods. A number of tractography algorithms exist and many of these are known to be sensitive to user-selected parameters. The methods used to derive a connectivity matrix from fiber tractography output may also influence the resulting graph metrics. Here we examine how these algorithm and parameter choices influence the reproducibility of proposed graph metrics on a publicly available test-retest dataset consisting of 21 healthy adults. The dice coefficient is used to examine topological similarity of constant density subgraphs both within and between subjects. Seven graph metrics are examined here: mean clustering coefficient, characteristic path length, largest connected component size, assortativity, global efficiency, local efficiency, and rich club coefficient. The reproducibility of these network summary measures is examined using the intraclass correlation coefficient (ICC). Graph curves are created by treating the graph metrics as functions of a parameter such as graph density. Functional data analysis techniques are used to examine differences in graph measures that result from the choice of fiber tracking algorithm. The graph metrics consistently showed good levels of reproducibility as measured with ICC, with the exception of some instability at low graph density levels. The global and local efficiency measures were the most robust to the choice of fiber tracking algorithm.
Maunz, Peter Lukas Wilhelm; Sterk, Jonathan David; Lobser, Daniel; Parekh, Ojas D.; Ryan-Anderson, Ciaran
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%.
Graph Visualization for RDF Graphs with SPARQL-EndPoints
Sukumar, Sreenivas R; Bond, Nathaniel
2014-07-11
RDF graphs are hard to visualize as triples. This software module is a web interface that connects to a SPARQL endpoint and retrieves graph data that the user can explore interactively and seamlessly. The software written in python and JavaScript has been tested to work on screens as little as the smart phones to large screens such as EVEREST.
Fracture and Fragmentation of Simplicial Finite Elements Meshes using Graphs
Mota, A; Knap, J; Ortiz, M
2006-10-18
An approach for the topological representation of simplicial finite element meshes as graphs is presented. It is shown that by using a graph, the topological changes induced by fracture reduce to a few, local kernel operations. The performance of the graph representation is demonstrated and analyzed, using as reference the 3D fracture algorithm by Pandolfi and Ortiz [22]. It is shown that the graph representation initializes in O(N{sub E}{sup 1.1}) time and fractures in O(N{sub I}{sup 1.0}) time, while the reference implementation requires O(N{sub E}{sup 2.1}) time to initialize and O(N{sub I}{sup 1.9}) time to fracture, where NE is the number of elements in the mesh and N{sub I} is the number of interfaces to fracture.
Voter model on the two-clique graph
NASA Astrophysics Data System (ADS)
Masuda, Naoki
2014-07-01
I examine the mean consensus time (i.e., exit time) of the voter model in the so-called two-clique graph. The two-clique graph is composed of two cliques interconnected by some links and considered as a toy model of networks with community structure or multilayer networks. I analytically show that, as the number of interclique links per node is varied, the mean consensus time experiences a crossover between a fast consensus regime [i.e., O (N)] and a slow consensus regime [i.e., O (N2)], where N is the number of nodes. The fast regime is consistent with the result for homogeneous well-mixed graphs such as the complete graph. The slow regime appears only when the entire network has O (1) interclique links. The present results suggest that the effect of community structure on the consensus time of the voter model is fairly limited.
Quantization of gauge fields, graph polynomials and graph homology
Kreimer, Dirk; Sars, Matthias; Suijlekom, Walter D. van
2013-09-15
We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials. The transition to the full gauge theory amplitude is obtained by the use of a third, new, graph polynomial, the corolla polynomial. This implies effectively a covariant quantization without ghosts, where all the relevant signs of the ghost sector are incorporated in a double complex furnished by the corolla polynomial–we call it cycle homology–and by graph homology. -- Highlights: •We derive gauge theory Feynman from scalar field theory with 3-valent vertices. •We clarify the role of graph homology and cycle homology. •We use parametric renormalization and the new corolla polynomial.
Graph-Based Dynamic Assignment Of Multiple Processors
NASA Technical Reports Server (NTRS)
Hayes, Paul J.; Andrews, Asa M.
1994-01-01
Algorithm-to-architecture mapping model (ATAMM) is strategy minimizing time needed to periodically execute graphically described, data-driven application algorithm on multiple data processors. Implemented as operating system managing flow of data and dynamically assigns nodes of graph to processors. Predicts throughput versus number of processors available to execute given application algorithm. Includes rules ensuring application algorithm represented by graph executed periodically without deadlock and in shortest possible repetition time. ATAMM proves useful in maximizing effectiveness of parallel computing systems.
Generating functions for modular graphs and Burgers's equation
NASA Astrophysics Data System (ADS)
Artamkin, I. V.
2005-12-01
It is shown that the generating functions of modular graphs satisfy Burgers's equations, which enable one to obtain in a unified way the generating functions for the virtual Euler characteristic and the Poincaré polynomial of the moduli space of punctured curves \\overline M_{g,n} and for the number (with weights 1/\\vert{\\operatorname{Aut} G}\\vert) of modular graphs G of a definite type.
ERIC Educational Resources Information Center
Axtell, M.; Stickles, J.
2010-01-01
The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings--by professional mathematicians "and" undergraduates. The objective is to find algebraic information within the geometry of these graphs. This topic is approachable by anyone with one or two semesters of abstract algebra. This article gives the…
Graphs as Statements of Belief.
ERIC Educational Resources Information Center
Lake, David
2002-01-01
Identifies points where beliefs are important when making decisions about how graphs are drawn. Describes a simple case of the reaction between 'bicarb soda' and orange or lemon juice and discusses how drawing a graph becomes a statement of belief. (KHR)
A Collection of Features for Semantic Graphs
Eliassi-Rad, T; Fodor, I K; Gallagher, B
2007-05-02
Semantic graphs are commonly used to represent data from one or more data sources. Such graphs extend traditional graphs by imposing types on both nodes and links. This type information defines permissible links among specified nodes and can be represented as a graph commonly referred to as an ontology or schema graph. Figure 1 depicts an ontology graph for data from National Association of Securities Dealers. Each node type and link type may also have a list of attributes. To capture the increased complexity of semantic graphs, concepts derived for standard graphs have to be extended. This document explains briefly features commonly used to characterize graphs, and their extensions to semantic graphs. This document is divided into two sections. Section 2 contains the feature descriptions for static graphs. Section 3 extends the features for semantic graphs that vary over time.
Graph Partitioning and Sequencing Software
1995-09-19
Graph partitioning is a fundemental problem in many scientific contexts. CHACO2.0 is a software package designed to partition and sequence graphs. CHACO2.0 allows for recursive application of several methods for finding small edge separators in weighted graphs. These methods include inertial, spectral, Kernighan Lin and multilevel methods in addition to several simpler strategies. Each of these approaches can be used to partition the graph into two, four, or eight pieces at each level of recursion.more » In addition, the Kernighan Lin method can be used to improve partitions generated by any of the other algorithms. CHACO2.0 can also be used to address various graph sequencing problems, with applications to scientific computing, database design, gene sequencing and other problems.« less
Path similarity skeleton graph matching.
Bai, Xiang; Latecki, Longin Jan
2008-07-01
This paper presents a novel framework to for shape recognition based on object silhouettes. The main idea is to match skeleton graphs by comparing the shortest paths between skeleton endpoints. In contrast to typical tree or graph matching methods, we completely ignore the topological graph structure. Our approach is motivated by the fact that visually similar skeleton graphs may have completely different topological structures. The proposed comparison of shortest paths between endpoints of skeleton graphs yields correct matching results in such cases. The skeletons are pruned by contour partitioning with Discrete Curve Evolution, which implies that the endpoints of skeleton branches correspond to visual parts of the objects. The experimental results demonstrate that our method is able to produce correct results in the presence of articulations, stretching, and occlusion.
Hyperspectral Data Classification Using Factor Graphs
NASA Astrophysics Data System (ADS)
Makarau, A.; Müller, R.; Palubinskas, G.; Reinartz, P.
2012-07-01
and comparison of the probabilities leads to classification. Since the factor graphs operate on input data represented on an alphabet (the represented data transferred into multinomial distribution) the number of training samples can be relatively low. Classification assessment on Salinas hyperspectral data benchmark allowed to obtain a competitive accuracy of classification. Employment of training data consisting of 20 randomly selected points for a class allowed to obtain the overall classification accuracy equal to 85.32% and Kappa equal to 0.8358. Representation of input data on a finite domain discards the curse of dimensionality problem allowing to use large hyperspectral data with a moderately high number of bands.
On the Extremal Wiener Polarity Index of Hückel Graphs
Wang, Hongzhuan
2016-01-01
Graphs are used to model chemical compounds and drugs. In the graphs, each vertex represents an atom of molecule and edges between the corresponding vertices are used to represent covalent bounds between atoms. The Wiener polarity index Wp(G) of a graph G is the number of unordered pairs of vertices u, v of G such that the distance between u and v is equal to 3. The trees and unicyclic graphs with perfect matching, of which all vertices have degrees not greater than three, are referred to as the Hückel trees and unicyclic Hückel graphs, respectively. In this paper, we first consider the smallest and the largest Wiener polarity index among all Hückel trees on 2n vertices and characterize the corresponding extremal graphs. Then we obtain an upper and lower bound for the Wiener polarity index of unicyclic Hückel graphs on 2n vertices. PMID:27247613
A Mathematical Analysis of the R-MAT Random Graph Generator
Groer, Christopher S; Sullivan, Blair D; Poole, Stephen W
2011-01-01
The R-MAT graph generator introduced by Chakrabarti, Faloutsos, and Zhan offers a simple, fast method for generating very large directed graphs. These properties have made it a popular choice as a method of generating graphs for objects of study in a variety of disciplines, from social network analysis to high performance computing. We analyze the graphs generated by R-MAT and model the generator in terms of occupancy problems in order to prove results about the degree distributions of these graphs. We prove that the limiting degree distributions can be expressed as a mixture of normal distributions, contradicting the widely held belief that R-MAT degree distributions exhibit the power law or scale free distribution observed in many real world graphs. Additionally, this paper offers an efficient computational technique for computing the exact degree distribution, as well as concise expressions for a number of properties of R-MAT graphs.
Intergroup networks as random threshold graphs
NASA Astrophysics Data System (ADS)
Saha, Sudipta; Ganguly, Niloy; Mukherjee, Animesh; Krueger, Tyll
2014-04-01
Similar-minded people tend to form social groups. Due to pluralistic homophily as well as a sort of heterophily, people also participate in a wide variety of groups. Thus, these groups generally overlap with each other; an overlap between two groups can be characterized by the number of common members. These common members can play a crucial role in the transmission of information between the groups. As a step towards understanding the information dissemination, we perceive the system as a pruned intergroup network and show that it maps to a very basic graph theoretic concept known as a threshold graph. We analyze several structural properties of this network such as degree distribution, largest component size, edge density, and local clustering coefficient. We compare the theoretical predictions with the results obtained from several online social networks (LiveJournal, Flickr, YouTube) and find a good match.
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.
Semantic graphs and associative memories
NASA Astrophysics Data System (ADS)
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.
A Hybrid Graph Representation for Recursive Backtracking Algorithms
NASA Astrophysics Data System (ADS)
Abu-Khzam, Faisal N.; Langston, Michael A.; Mouawad, Amer E.; Nolan, Clinton P.
Many exact algorithms for NP-hard graph problems adopt the old Davis-Putman branch-and-reduce paradigm. The performance of these algorithms often suffers from the increasing number of graph modifications, such as deletions, that reduce the problem instance and have to be "taken back" frequently during the search process. The use of efficient data structures is necessary for fast graph modification modules as well as fast take-back procedures. In this paper, we investigate practical implementation-based aspects of exact algorithms by providing a hybrid graph representation that addresses the take-back challenge and combines the advantage of {O}(1) adjacency-queries in adjacency-matrices with the advantage of efficient neighborhood traversal in adjacency-lists.
Multigraph: Reusable Interactive Data Graphs
NASA Astrophysics Data System (ADS)
Phillips, M. B.
2010-12-01
There are surprisingly few good software tools available for presenting time series data on the internet. The most common practice is to use a desktop program such as Excel or Matlab to save a graph as an image which can be included in a web page like any other image. This disconnects the graph from the data in a way that makes updating a graph with new data a cumbersome manual process, and it limits the user to one particular view of the data. The Multigraph project defines an XML format for describing interactive data graphs, and software tools for creating and rendering those graphs in web pages and other internet connected applications. Viewing a Multigraph graph is extremely simple and intuitive, and requires no instructions; the user can pan and zoom by clicking and dragging, in a familiar "Google Maps" kind of way. Creating a new graph for inclusion in a web page involves writing a simple XML configuration file. Multigraph can read data in a variety of formats, and can display data from a web service, allowing users to "surf" through large data sets, downloading only those the parts of the data that are needed for display. The Multigraph XML format, or "MUGL" for short, provides a concise description of the visual properties of a graph, such as axes, plot styles, data sources, labels, etc, as well as interactivity properties such as how and whether the user can pan or zoom along each axis. Multigraph reads a file in this format, draws the described graph, and allows the user to interact with it. Multigraph software currently includes a Flash application for embedding graphs in web pages, a Flex component for embedding graphs in larger Flex/Flash applications, and a plugin for creating graphs in the WordPress content management system. Plans for the future include a Java version for desktop viewing and editing, a command line version for batch and server side rendering, and possibly Android and iPhone versions. Multigraph is currently in use on several web
NASA Astrophysics Data System (ADS)
Lavaud, Michel
1982-03-01
A large number of physical quantities (thermodynamic and correlation functions, scattering amplitudes, intermolecular potentials, etc. ...) can be expressed as sums of an infinite number of multiple integrals of the following type: Γ ( {x_1 ,. . . , x_n } ) = int {prod {f_L ( {x_{i,} x_j } )dx_{n + 1} . . . dx_{n + k} } } These are called Mayer graphs in statistical mechanics, Feynman graphs in quantum field theory, and multicenter integrals in quantum chemistry. We call them n-graphs here. In a preceding note [ Physics Letters 62A:295 (1977)], we have proposed a new estimation method which provides upper bounds for arbitrary n-graphs. This article is devoted to developing in detail the foundations of this method. As a first application, we prove that all virial coefficients of polar systems are finite. More generally, we show on some examples that our estimation method can give finite upper bounds for n-graphs occurring in the perturbative developments of thermodynamic functions of neutral, polar, and ionized gases and of Green's functions of Euclidean quantum field theories (thus improving Weinberg's theorem), as also in variational approximations of intermolecular potentials. Our estimation method is based on the Hölder inequality which is an improvement over the mean value estimation method, employed by Riddell, Uhlenbeck, and Groeneveld, except for the hard-sphere gas, where both methods coincide. The method is applied so far only to individual graphs and not to thermodynamic functions.
Graph anomalies in cyber communications
Vander Wiel, Scott A; Storlie, Curtis B; Sandine, Gary; Hagberg, Aric A; Fisk, Michael
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.
Constructing Dense Graphs with Unique Hamiltonian Cycles
ERIC Educational Resources Information Center
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…
Yamabe type equations on graphs
NASA Astrophysics Data System (ADS)
Grigor'yan, Alexander; Lin, Yong; Yang, Yunyan
2016-11-01
Let G = (V , E) be a locally finite graph, Ω ⊂ V be a bounded domain, Δ be the usual graph Laplacian, and λ1 (Ω) be the first eigenvalue of -Δ with respect to Dirichlet boundary condition. Using the mountain pass theorem due to Ambrosetti-Rabinowitz, we prove that if α <λ1 (Ω), then for any p > 2, there exists a positive solution to
Graph signatures for visual analytics.
Wong, Pak Chung; Foote, Harlan; Chin, George; Mackey, Patrick; Perrine, Ken
2006-01-01
We present a visual analytics technique to explore graphs using the concept of a data signature. A data signature, in our context, is a multidimensional vector that captures the local topology information surrounding each graph node. Signature vectors extracted from a graph are projected onto a low-dimensional scatterplot through the use of scaling. The resultant scatterplot, which reflects the similarities of the vectors, allows analysts to examine the graph structures and their corresponding real-life interpretations through repeated use of brushing and linking between the two visualizations. The interpretation of the graph structures is based on the outcomes of multiple participatory analysis sessions with intelligence analysts conducted by the authors at the Pacific Northwest National Laboratory. The paper first uses three public domain data sets with either well-known or obvious features to explain the rationale of our design and illustrate its results. More advanced examples are then used in a customized usability study to evaluate the effectiveness and efficiency of our approach. The study results reveal not only the limitations and weaknesses of the traditional approach based solely on graph visualization, but also the advantages and strengths of our signature-guided approach presented in the paper.
Efficient and Scalable Graph Similarity Joins in MapReduce
Chen, Yifan; Zhang, Weiming; Tang, Jiuyang
2014-01-01
Along with the emergence of massive graph-modeled data, it is of great importance to investigate graph similarity joins due to their wide applications for multiple purposes, including data cleaning, and near duplicate detection. This paper considers graph similarity joins with edit distance constraints, which return pairs of graphs such that their edit distances are no larger than a given threshold. Leveraging the MapReduce programming model, we propose MGSJoin, a scalable algorithm following the filtering-verification framework for efficient graph similarity joins. It relies on counting overlapping graph signatures for filtering out nonpromising candidates. With the potential issue of too many key-value pairs in the filtering phase, spectral Bloom filters are introduced to reduce the number of key-value pairs. Furthermore, we integrate the multiway join strategy to boost the verification, where a MapReduce-based method is proposed for GED calculation. The superior efficiency and scalability of the proposed algorithms are demonstrated by extensive experimental results. PMID:25121135
The peculiar phase structure of random graph bisection
Percus, Allon G; Istrate, Gabriel; Goncalves, Bruno T; Sumi, Robert Z
2008-01-01
The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of 'cut' edges with an endpoint in each subset. When considered over sparse random graphs, the phase structure of the graph bisection problem displays certain familiar properties, but also some surprises. It is known that when the mean degree is below the critical value of 2 log 2, the cutsize is zero with high probability. We study how the minimum cutsize increases with mean degree above this critical threshold, finding a new analytical upper bound that improves considerably upon previous bounds. Combined with recent results on expander graphs, our bound suggests the unusual scenario that random graph bisection is replica symmetric up to and beyond the critical threshold, with a replica symmetry breaking transition possibly taking place above the threshold. An intriguing algorithmic consequence is that although the problem is NP-hard, we can find near-optimal cutsizes (whose ratio to the optimal value approaches 1 asymptotically) in polynomial time for typical instances near the phase transition.
Essential self-adjointness of the graph-Laplacian
NASA Astrophysics Data System (ADS)
Jorgensen, Palle E. T.
2008-07-01
We study the operator theory associated with such infinite graphs G as occur in electrical networks, in fractals, in statistical mechanics, and even in internet search engines. Our emphasis is on the determination of spectral data for a natural Laplace operator associated with the graph in question. This operator Δ will depend not only on G but also on a prescribed positive real valued function c defined on the edges in G. In electrical network models, this function c will determine a conductance number for each edge. We show that the corresponding Laplace operator Δ is automatically essential self-adjoint. By this we mean that Δ is defined on the dense subspace D (of all the real valued functions on the set of vertices G0 with finite support) in the Hilbert space l2(G0). The conclusion is that the closure of the operator Δ is self-adjoint in l2(G0), and so, in particular, that it has a unique spectral resolution, determined by a projection valued measure on the Borel subsets of the infinite half-line. We prove that generically our graph Laplace operator Δ =Δc will have continuous spectrum. For a given infinite graph G with conductance function c, we set up a system of finite graphs with periodic boundary conditions such the finite spectra, for an ascending family of finite graphs, will have the Laplace operator for G as its limit.
Khovanov homology of graph-links
Nikonov, Igor M
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.
Chemical Applications of Graph Theory: Part I. Fundamentals and Topological Indices.
ERIC Educational Resources Information Center
Hansen, Peter J.; Jurs, Peter C.
1988-01-01
Explores graph theory and use of topological indices to predict boiling points. Lists three indices: Wiener Number, Randic Branching Index and Molecular Connectivity, and Molecular Identification numbers. Warns of inadequacies with stereochemistry. (ML)
Private Graphs - Access Rights on Graphs for Seamless Navigation
NASA Astrophysics Data System (ADS)
Dorner, W.; Hau, F.; Pagany, R.
2016-06-01
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.
Sharing Teaching Ideas: Graphing Families of Curves Using Transformations of Reference Graphs
ERIC Educational Resources Information Center
Kukla, David
2007-01-01
This article provides for a fast extremely accurate approach to graphing functions that is based on learning function reference graphs and then applying algebraic transformations to these reference graphs.
Decision net, directed graph, and neural net processing of imaging spectrometer data
NASA Technical Reports Server (NTRS)
Casasent, David; Liu, Shiaw-Dong; Yoneyama, Hideyuki; Barnard, Etienne
1989-01-01
A decision-net solution involving a novel hierarchical classifier and a set of multiple directed graphs, as well as a neural-net solution, are respectively presented for large-class problem and mixture problem treatments of imaging spectrometer data. The clustering method for hierarchical classifier design, when used with multiple directed graphs, yields an efficient decision net. New directed-graph rules for reducing local maxima as well as the number of perturbations required, and the new starting-node rules for extending the reachability and reducing the search time of the graphs, are noted to yield superior results, as indicated by an illustrative 500-class imaging spectrometer problem.
Time-varying Reeb Graphs for Continuous Space-Time Data
Edelsbrunner, H; Harer, J; Mascarenhas, A; Pascucci, V; Snoeyink, J
2008-04-22
The Reeb graph is a useful tool in visualizing real-valued data obtained from computational simulations of physical processes. We characterize the evolution of the Reeb graph of a time-varying continuous function defined in three-dimensional space. We show how to maintain the Reeb graph over time and compress the entire sequence of Reeb graphs into a single, partially persistent data structure, and augment this data structure with Betti numbers to describe the topology of level sets and with path seeds to assist in the fast extraction of level sets for visualization.
Searches on star graphs and equivalent oracle problems
Lee, Jaehak; Lee, Hai-Woong; Hillery, Mark
2011-02-15
We examine a search on a graph among a number of different kinds of objects (vertices), one of which we want to find. In a standard graph search, all of the vertices are the same, except for one, the marked vertex, and that is the one we wish to find. We examine the case in which the unmarked vertices can be of different types, so the background against which the search is done is not uniform. We find that the search can still be successful, but the probability of success is lower than in the uniform background case, and that probability decreases with the number of types of unmarked vertices. We also show how the graph searches can be rephrased as equivalent oracle problems.
NASA Astrophysics Data System (ADS)
Braun, Andreas P.; Schäfer-Nameki, Sakura
2016-04-01
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.
Exact Algorithms for Coloring Graphs While Avoiding Monochromatic Cycles
NASA Astrophysics Data System (ADS)
Talla Nobibon, Fabrice; Hurkens, Cor; Leus, Roel; Spieksma, Frits C. R.
We consider the problem of deciding whether a given directed graph can be vertex partitioned into two acyclic subgraphs. Applications of this problem include testing rationality of collective consumption behavior, a subject in micro-economics. We identify classes of directed graphs for which the problem is easy and prove that the existence of a constant factor approximation algorithm is unlikely for an optimization version which maximizes the number of vertices that can be colored using two colors while avoiding monochromatic cycles. We present three exact algorithms, namely an integer-programming algorithm based on cycle identification, a backtracking algorithm, and a branch-and-check algorithm. We compare these three algorithms both on real-life instances and on randomly generated graphs. We find that for the latter set of graphs, every algorithm solves instances of considerable size within few seconds; however, the CPU time of the integer-programming algorithm increases with the number of vertices in the graph while that of the two other procedures does not. For every algorithm, we also study empirically the transition from a high to a low probability of YES answer as function of a parameter of the problem. For real-life instances, the integer-programming algorithm fails to solve the largest instance after one hour while the other two algorithms solve it in about ten minutes.
Hierarchical sequencing of online social graphs
NASA Astrophysics Data System (ADS)
Andjelković, Miroslav; Tadić, Bosiljka; Maletić, Slobodan; Rajković, Milan
2015-10-01
In online communications, patterns of conduct of individual actors and use of emotions in the process can lead to a complex social graph exhibiting multilayered structure and mesoscopic communities. Using simplicial complexes representation of graphs, we investigate in-depth topology of the online social network constructed from MySpace dialogs which exhibits original community structure. A simulation of emotion spreading in this network leads to the identification of two emotion-propagating layers. Three topological measures are introduced, referred to as the structure vectors, which quantify graph's architecture at different dimension levels. Notably, structures emerging through shared links, triangles and tetrahedral faces, frequently occur and range from tree-like to maximal 5-cliques and their respective complexes. On the other hand, the structures which spread only negative or only positive emotion messages appear to have much simpler topology consisting of links and triangles. The node's structure vector represents the number of simplices at each topology level in which the node resides and the total number of such simplices determines what we define as the node's topological dimension. The presented results suggest that the node's topological dimension provides a suitable measure of the social capital which measures the actor's ability to act as a broker in compact communities, the so called Simmelian brokerage. We also generalize the results to a wider class of computer-generated networks. Investigating components of the node's vector over network layers reveals that same nodes develop different socio-emotional relations and that the influential nodes build social capital by combining their connections in different layers.
The Use of Graphs in Specific Situations of the Initial Conditions of Linear Differential Equations
ERIC Educational Resources Information Center
Buendía, Gabriela; Cordero, Francisco
2013-01-01
In this article, we present a discussion on the role of graphs and its significance in the relation between the number of initial conditions and the order of a linear differential equation, which is known as the initial value problem. We propose to make a functional framework for the use of graphs that intends to broaden the explanations of the…
Sequential visibility-graph motifs
NASA Astrophysics Data System (ADS)
Iacovacci, Jacopo; Lacasa, Lucas
2016-04-01
Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network science. In this work we introduce and study the concept of sequential visibility-graph motifs, smaller substructures of n consecutive nodes that appear with characteristic frequencies. We develop a theory to compute in an exact way the motif profiles associated with general classes of deterministic and stochastic dynamics. We find that this simple property is indeed a highly informative and computationally efficient feature capable of distinguishing among different dynamics and robust against noise contamination. We finally confirm that it can be used in practice to perform unsupervised learning, by extracting motif profiles from experimental heart-rate series and being able, accordingly, to disentangle meditative from other relaxation states. Applications of this general theory include the automatic classification and description of physical, biological, and financial time series.
Algebraic connectivity and graph robustness.
Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.
2009-07-01
Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.
The fragment assembly string graph.
Myers, Eugene W
2005-09-01
We present a concept and formalism, the string graph, which represents all that is inferable about a DNA sequence from a collection of shotgun sequencing reads collected from it. We give time and space efficient algorithms for constructing a string graph given the collection of overlaps between the reads and, in particular, present a novel linear expected time algorithm for transitive reduction in this context. The result demonstrates that the decomposition of reads into kmers employed in the de Bruijn graph approach described earlier is not essential, and exposes its close connection to the unitig approach we developed at Celera. This paper is a preliminary piece giving the basic algorithm and results that demonstrate the efficiency and scalability of the method. These ideas are being used to build a next-generation whole genome assembler called BOA (Berkeley Open Assembler) that will easily scale to mammalian genomes.
Graph Analytics for Signature Discovery
Hogan, Emilie A.; Johnson, John R.; Halappanavar, Mahantesh; Lo, Chaomei
2013-06-01
Within large amounts of seemingly unstructured data it can be diffcult to find signatures of events. In our work we transform unstructured data into a graph representation. By doing this we expose underlying structure in the data and can take advantage of existing graph analytics capabilities, as well as develop new capabilities. Currently we focus on applications in cybersecurity and communication domains. Within cybersecurity we aim to find signatures for perpetrators using the pass-the-hash attack, and in communications we look for emails or phone calls going up or down a chain of command. In both of these areas, and in many others, the signature we look for is a path with certain temporal properties. In this paper we discuss our methodology for finding these temporal paths within large graphs.
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.
Rosmanis, Ansis
2011-02-15
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.
Synchronizability of random rectangular graphs
Estrada, Ernesto Chen, Guanrong
2015-08-15
Random rectangular graphs (RRGs) represent a generalization of the random geometric graphs in which the nodes are embedded into hyperrectangles instead of on hypercubes. The synchronizability of RRG model is studied. Both upper and lower bounds of the eigenratio of the network Laplacian matrix are determined analytically. It is proven that as the rectangular network is more elongated, the network becomes harder to synchronize. The synchronization processing behavior of a RRG network of chaotic Lorenz system nodes is numerically investigated, showing complete consistence with the theoretical results.
Midlet Navigation Graphs in JML
NASA Astrophysics Data System (ADS)
Mostowski, Wojciech; Poll, Erik
In the context of the EU project Mobius on Proof Carrying Code for Java programs (midlets) on mobile devices, we present a way to express midlet navigation graphs in JML. Such navigation graphs express certain security policies for a midlet. The resulting JML specifications can be automatically checked with the static checker ESC/Java2. Our work was guided by a realistically sized case study developed as demonstrator in the project. We discuss practical difficulties with creating efficient and meaningful JML specifications for automatic verification with a lightweight verification tool such as ESC/Java2, and the potential use of these specifications for PCC.
NASA Astrophysics Data System (ADS)
Eto, Yujiro; Sekine, Sawako; Hasegawa, Sho; Sadgrove, Mark; Saito, Hiroki; Hirano, Takuya
2013-05-01
Radio-frequency pulses are applied to probe and control the Larmor precession of a spin-2 Bose-Einstein condensate subject to a magnetic field gradient. Using the techniques of Ramsey interferometry and Stern-Gerlach absorption imaging, a helical spin pattern was clearly observed as spatial variations in the atomic density distribution. We experimentally show that the spin echo technique reduces the effects of spatially inhomogeneous and temporally fluctuating spin evolution, and improves the repeatability of the interferometry.
Thermodynamic characterization of networks using graph polynomials
NASA Astrophysics Data System (ADS)
Ye, Cheng; Comin, César H.; Peron, Thomas K. DM.; Silva, Filipi N.; Rodrigues, Francisco A.; Costa, Luciano da F.; Torsello, Andrea; Hancock, Edwin R.
2015-09-01
In this paper, we present a method for characterizing the evolution of time-varying complex networks by adopting a thermodynamic representation of network structure computed from a polynomial (or algebraic) characterization of graph structure. Commencing from a representation of graph structure based on a characteristic polynomial computed from the normalized Laplacian matrix, we show how the polynomial is linked to the Boltzmann partition function of a network. This allows us to compute a number of thermodynamic quantities for the network, including the average energy and entropy. Assuming that the system does not change volume, we can also compute the temperature, defined as the rate of change of entropy with energy. All three thermodynamic variables can be approximated using low-order Taylor series that can be computed using the traces of powers of the Laplacian matrix, avoiding explicit computation of the normalized Laplacian spectrum. These polynomial approximations allow a smoothed representation of the evolution of networks to be constructed in the thermodynamic space spanned by entropy, energy, and temperature. We show how these thermodynamic variables can be computed in terms of simple network characteristics, e.g., the total number of nodes and node degree statistics for nodes connected by edges. We apply the resulting thermodynamic characterization to real-world time-varying networks representing complex systems in the financial and biological domains. The study demonstrates that the method provides an efficient tool for detecting abrupt changes and characterizing different stages in network evolution.
Component evolution in general random intersection graphs
Bradonjic, Milan; Hagberg, Aric; Hengartner, Nick; Percus, Allon G
2010-01-01
We analyze component evolution in general random intersection graphs (RIGs) and give conditions on existence and uniqueness of the giant component. Our techniques generalize the existing methods for analysis on component evolution in RIGs. That is, we analyze survival and extinction properties of a dependent, inhomogeneous Galton-Watson branching process on general RIGs. Our analysis relies on bounding the branching processes and inherits the fundamental concepts from the study on component evolution in Erdos-Renyi graphs. The main challenge becomes from the underlying structure of RIGs, when the number of offsprings follows a binomial distribution with a different number of nodes and different rate at each step during the evolution. RIGs can be interpreted as a model for large randomly formed non-metric data sets. Besides the mathematical analysis on component evolution, which we provide in this work, we perceive RIGs as an important random structure which has already found applications in social networks, epidemic networks, blog readership, or wireless sensor networks.
Graph-Facts: Trends in Alaska Education 1960-1971.
ERIC Educational Resources Information Center
Hagmeier, John
Eleven graphs present information on status and trends in Alaska in terms of number of public high school graduates, statewide enrollment, expenditures per pupil, local assistance, pupil-staff ratio, transportation, rural school enrollment, correspondence study, school lunch programs, average salaries of professional school personnel, and…
Solutions to some congruence equations via suborbital graphs.
Güler, Bahadır Özgür; Kör, Tuncay; Şanlı, Zeynep
2016-01-01
We relate the connection between the sizes of circuits in suborbital graph for the normalizer of [Formula: see text] in PSL(2,[Formula: see text]) and the congruence equations arising from related group action. We give a number theoretic result which says that all prime divisors of [Formula: see text] for any integer u must be congruent to [Formula: see text]. PMID:27563522
Graphs for Early Elementary Social Studies.
ERIC Educational Resources Information Center
Freeland, Kent; Brewer, Samrie
1989-01-01
Describes a lesson plan that instructs third graders to use graphs. Explains learning objectives, motivating students, conducting a class activity that includes graph construction, and concluding and evaluating the lesson. Lists materials needed. (GG)
Standard Distributions: One Graph Fits All
ERIC Educational Resources Information Center
Wagner, Clifford H.
2007-01-01
Standard distributions are ubiquitous but not unique. With suitable scaling, the graph of a standard distribution serves as the graph for every distribution in the family. The standard exponential can easily be taught in elementary statistics courses.
Understanding Conic Sections Using Alternate Graph Paper
ERIC Educational Resources Information Center
Brown, Elizabeth M.; Jones, Elizabeth
2006-01-01
This article describes two alternative coordinate systems and their use in graphing conic sections. This alternative graph paper helps students explore the idea of eccentricity using the definitions of the conic sections.
Graphing and Social Studies: An Interdisciplinary Activity.
ERIC Educational Resources Information Center
Brehm, Julia L.
1996-01-01
Describes a graphing activity that promotes mathematical connections with social studies lessons. Students should be familiar with graphing on the Cartesian coordinate system to play this variation of the game Battleship on maps of various regions of the world. (AIM)
Comparison Graph of Sea Ice Minimum - 2010
This animated graph tracks the retreat of sea ice, measured in millions of square kilometers, averaged from the start of the satellite record in 1979 through 2000 (white). Next, the graph follows t...
Mathematical Minute: Rotating a Function Graph
ERIC Educational Resources Information Center
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.
Dr.L: Distributed Recursive (Graph) Layout
2007-11-19
Dr. L provides two-dimensional visualizations of very large abstract graph structures. it can be used for data mining applications including biology, scientific literature, and social network analysis. Dr. L is a graph layout program that uses a multilevel force-directed algorithm. A graph is input and drawn using a force-directed algorithm based on simulated annealing. The resulting layout is clustered using a single link algorithm. This clustering is used to produce a coarsened graph (fewer nodes)more » which is then re-drawn. this process is repeated until a sufficiently small graph is produced. The smallest graph is drawn and then used as a basis for drawing the original graph by refining the series of coarsened graphs that were produced. The layout engine can be run in serial or in parallel.« less
Spectra of magnetic chain graphs: coupling constant perturbations
NASA Astrophysics Data System (ADS)
Exner, Pavel; Manko, Stepan S.
2015-03-01
We analyze spectral properties of a quantum graph in the form of a ring chain with a δ coupling in the vertices exposed to a homogeneous magnetic field perpendicular to the graph plane. We find the band spectrum in the case when the chain exhibits a translational symmetry and study the discrete spectrum in the gaps resulting from changing a finite number of vertex coupling constants. In particular, we discuss in detail some examples such as perturbations of one or two vertices, weak perturbation asymptotics, and a pair of distant perturbations.
On atom bond connectivity index of some molecular graphs
NASA Astrophysics Data System (ADS)
Mohammed, Mohanad A.; Atan, K. A.; Khalaf, A. M.; Said, M. R. Md.; Hasni, R.
2016-06-01
The atom-bond connectivity (ABC) index is one of the newly most studied degree based molecular structure descriptors, which have chemical applications. For a graph G, the ABC index can be defined as A B C (G )=Σuv ∈E (G )√{dv+du-2 /dv.du } , where du, the degree of the vertex u is the number of edges with u as an end vertex denotes the degree of a vertex u in G. In this paper, we establish the general formulas for the atom bond connectivity index of molecular graphs of alkenes and cycloalkenes.
Corona graphs as a model of small-world networks
NASA Astrophysics Data System (ADS)
Lv, Qian; Yi, Yuhao; Zhang, Zhongzhi
2015-11-01
We introduce recursive corona graphs as a model of small-world networks. We investigate analytically the critical characteristics of the model, including order and size, degree distribution, average path length, clustering coefficient, and the number of spanning trees, as well as Kirchhoff index. Furthermore, we study the spectra for the adjacency matrix and the Laplacian matrix for the model. We obtain explicit results for all the quantities of the recursive corona graphs, which are similar to those observed in real-life networks.
Multiple directed graph large-class multi-spectral processor
NASA Technical Reports Server (NTRS)
Casasent, David; Liu, Shiaw-Dong; Yoneyama, Hideyuki
1988-01-01
Numerical analysis techniques for the interpretation of high-resolution imaging-spectrometer data are described and demonstrated. The method proposed involves the use of (1) a hierarchical classifier with a tree structure generated automatically by a Fisher linear-discriminant-function algorithm and (2) a novel multiple-directed-graph scheme which reduces the local maxima and the number of perturbations required. Results for a 500-class test problem involving simulated imaging-spectrometer data are presented in tables and graphs; 100-percent-correct classification is achieved with an improvement factor of 5.
Microcomputer Unit: Graphing Straight Lines.
ERIC Educational Resources Information Center
Hastings, Ellen H.; Yates, Daniel S.
1983-01-01
The material is designed to help pupils investigate how the value for slope in the equation of a line affects the inclination for the graph of an equation. A program written in BASIC designed to run on an Apple microcomputer is included. Worksheet masters for duplication are provided. (MP)
Situating Graphs as Workplace Knowledge
ERIC Educational Resources Information Center
Noss, Richard; Bakker, Arthur; Hoyles, Celia; Kent, Phillip
2007-01-01
We investigate the use and knowledge of graphs in the context of a large industrial factory. We are particularly interested in the question of "transparency", a question that has been extensively considered in the general literature on tool use and, more recently, by Michael Roth and his colleagues in the context of scientific work. Roth uses the…
Box graphs and singular fibers
NASA Astrophysics Data System (ADS)
Hayashi, Hirotaka; Lawrie, Craig; Morrison, David R.; Schafer-Nameki, Sakura
2014-05-01
We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional = 2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as "flopping" of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E 6, E7 and E 8.
Affect and Graphing Calculator Use
ERIC Educational Resources Information Center
McCulloch, Allison W.
2011-01-01
This article reports on a qualitative study of six high school calculus students designed to build an understanding about the affect associated with graphing calculator use in independent situations. DeBellis and Goldin's (2006) framework for affect as a representational system was used as a lens through which to understand the ways in which…
Ancestral Genres of Mathematical Graphs
ERIC Educational Resources Information Center
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.
ERIC Educational Resources Information Center
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)
Graphs and Enhancing Maple Multiplication.
ERIC Educational Resources Information Center
Cecil, David R.; Wang, Rongdong
2002-01-01
Description of a technique in Maple programming language that automatically prints all paths of any desired length along with the name of each vertex, proceeding in order from the beginning vertex to the ending vertex for a given graph. (Author/MM)
Label-based routing for a family of small-world Farey graphs
Zhai, Yinhu; Wang, Yinhe
2016-01-01
We introduce an informative labelling method for vertices in a family of Farey graphs, and deduce a routing algorithm on all the shortest paths between any two vertices in Farey graphs. The label of a vertex is composed of the precise locating position in graphs and the exact time linking to graphs. All the shortest paths routing between any pair of vertices, which number is exactly the product of two Fibonacci numbers, are determined only by their labels, and the time complexity of the algorithm is O(n). It is the first algorithm to figure out all the shortest paths between any pair of vertices in a kind of deterministic graphs. For Farey networks, the existence of an efficient routing protocol is of interest to design practical communication algorithms in relation to dynamical processes (including synchronization and structural controllability) and also to understand the underlying mechanisms that have shaped their particular structure. PMID:27167605
Label-based routing for a family of small-world Farey graphs
NASA Astrophysics Data System (ADS)
Zhai, Yinhu; Wang, Yinhe
2016-05-01
We introduce an informative labelling method for vertices in a family of Farey graphs, and deduce a routing algorithm on all the shortest paths between any two vertices in Farey graphs. The label of a vertex is composed of the precise locating position in graphs and the exact time linking to graphs. All the shortest paths routing between any pair of vertices, which number is exactly the product of two Fibonacci numbers, are determined only by their labels, and the time complexity of the algorithm is O(n). It is the first algorithm to figure out all the shortest paths between any pair of vertices in a kind of deterministic graphs. For Farey networks, the existence of an efficient routing protocol is of interest to design practical communication algorithms in relation to dynamical processes (including synchronization and structural controllability) and also to understand the underlying mechanisms that have shaped their particular structure.
Label-based routing for a family of small-world Farey graphs.
Zhai, Yinhu; Wang, Yinhe
2016-01-01
We introduce an informative labelling method for vertices in a family of Farey graphs, and deduce a routing algorithm on all the shortest paths between any two vertices in Farey graphs. The label of a vertex is composed of the precise locating position in graphs and the exact time linking to graphs. All the shortest paths routing between any pair of vertices, which number is exactly the product of two Fibonacci numbers, are determined only by their labels, and the time complexity of the algorithm is O(n). It is the first algorithm to figure out all the shortest paths between any pair of vertices in a kind of deterministic graphs. For Farey networks, the existence of an efficient routing protocol is of interest to design practical communication algorithms in relation to dynamical processes (including synchronization and structural controllability) and also to understand the underlying mechanisms that have shaped their particular structure. PMID:27167605
Label-based routing for a family of small-world Farey graphs.
Zhai, Yinhu; Wang, Yinhe
2016-01-01
We introduce an informative labelling method for vertices in a family of Farey graphs, and deduce a routing algorithm on all the shortest paths between any two vertices in Farey graphs. The label of a vertex is composed of the precise locating position in graphs and the exact time linking to graphs. All the shortest paths routing between any pair of vertices, which number is exactly the product of two Fibonacci numbers, are determined only by their labels, and the time complexity of the algorithm is O(n). It is the first algorithm to figure out all the shortest paths between any pair of vertices in a kind of deterministic graphs. For Farey networks, the existence of an efficient routing protocol is of interest to design practical communication algorithms in relation to dynamical processes (including synchronization and structural controllability) and also to understand the underlying mechanisms that have shaped their particular structure.
Control by quantum dynamics on graphs
Godsil, Chris; Severini, Simone
2010-05-15
We address the study of controllability of a closed quantum system whose dynamical Lie algebra is generated by adjacency matrices of graphs. We characterize a large family of graphs that renders a system controllable. The key property is a graph-theoretic feature consisting of a particularly disordered cycle structure. Disregarding efficiency of control functions, but choosing subfamilies of sparse graphs, the results translate into continuous-time quantum walks for universal computation.
Algorithms and architectures for high performance analysis of semantic graphs.
Hendrickson, Bruce Alan
2005-09-01
Semantic graphs offer one promising avenue for intelligence analysis in homeland security. They provide a mechanism for describing a wide variety of relationships between entities of potential interest. The vertices are nouns of various types, e.g. people, organizations, events, etc. Edges in the graph represent different types of relationships between entities, e.g. 'is friends with', 'belongs-to', etc. Semantic graphs offer a number of potential advantages as a knowledge representation system. They allow information of different kinds, and collected in differing ways, to be combined in a seamless manner. A semantic graph is a very compressed representation of some of relationship information. It has been reported that the semantic graph can be two orders of magnitude smaller than the processed intelligence data. This allows for much larger portions of the data universe to be resident in computer memory. Many intelligence queries that are relevant to the terrorist threat are naturally expressed in the language of semantic graphs. One example is the search for 'interesting' relationships between two individuals or between an individual and an event, which can be phrased as a search for short paths in the graph. Another example is the search for an analyst-specified threat pattern, which can be cast as an instance of subgraph isomorphism. It is important to note than many kinds of analysis are not relationship based, so these are not good candidates for semantic graphs. Thus, a semantic graph should always be used in conjunction with traditional knowledge representation and interface methods. Operations that involve looking for chains of relationships (e.g. friend of a friend) are not efficiently executable in a traditional relational database. However, the semantic graph can be thought of as a pre-join of the database, and it is ideally suited for these kinds of operations. Researchers at Sandia National Laboratories are working to facilitate semantic graph
Development of Image Selection Method Using Graph Cuts
NASA Astrophysics Data System (ADS)
Fuse, T.; Harada, R.
2016-06-01
3D models have been widely used by spread of many available free-software. Additionally, enormous images can be easily acquired, and images are utilized for creating the 3D models recently. The creation of 3D models by using huge amount of images, however, takes a lot of time and effort, and then efficiency for 3D measurement are required. In the efficient strategy, the accuracy of the measurement is also required. This paper develops an image selection method based on network design that means surveying network construction. The proposed method uses image connectivity graph. The image connectivity graph consists of nodes and edges. The nodes correspond to images to be used. The edges connected between nodes represent image relationships with costs as accuracies of orientation elements. For the efficiency, the image connectivity graph should be constructed with smaller number of edges. Once the image connectivity graph is built, the image selection problem is regarded as combinatorial optimization problem and the graph cuts technique can be applied. In the process of 3D reconstruction, low quality images and similar images are also extracted and removed. Through the experiments, the significance of the proposed method is confirmed. It implies potential to efficient and accurate 3D measurement.
Next nearest neighbour Ising models on random graphs
NASA Astrophysics Data System (ADS)
Raymond, Jack; Wong, K. Y. Michael
2012-09-01
This paper develops results for the next nearest neighbour Ising model on random graphs. Besides being an essential ingredient in classic models for frustrated systems, second neighbour interactions arise naturally in several applications, such as the colour diversity problem and graphical games. We demonstrate ensembles of random graphs, including regular connectivity graphs, that have a periodic variation of free energy, with either the ratio of nearest to next nearest couplings, or the mean number of nearest neighbours. When the coupling ratio is integer then paramagnetic phases can be found at zero temperature. This is shown to be related to the locked or unlocked nature of the interactions. For anti-ferromagnetic couplings, spin glass phases are demonstrated at low temperature. The interaction structure is formulated as a factor graph, the solution on a tree is developed. The replica symmetric and energetic one-step replica symmetry breaking solution is developed using the cavity method. We calculate within these frameworks the phase diagram and demonstrate the existence of dynamical transitions at zero temperature for cases of anti-ferromagnetic coupling on regular and inhomogeneous random graphs.
Network Models in Class C on Arbitrary Graphs
NASA Astrophysics Data System (ADS)
Cardy, John
2005-08-01
We consider network models of quantum localisation in which a particle with a two-component wave function propagates through the nodes and along the edges of an arbitrary directed graph, subject to a random SU(2) rotation on each edge it traverses. The propagation through each node is specified by an arbitrary but fixed S-matrix. Such networks model localisation problems in class C of the classification of Altland and Zirnbauer [1], and, on suitable graphs, they model the spin quantum Hall transition. We extend the analyses of Gruzberg, Ludwig and Read [5] and of Beamond, Cardy and Chalker [2] to show that, on an arbitrary graph, the mean density of states and the mean conductance may be calculated in terms of observables of a classical history-dependent random walk on the same graph. The transition weights for this process are explicitly related to the elements of the S-matrices. They are correctly normalised but, on graphs with nodes of degree greater than 4, not necessarily non-negative (and therefore interpretable as probabilities) unless a sufficient number of them happen to vanish. Our methods use a supersymmetric path integral formulation of the problem which is completely finite and rigorous.
Ivanciuc, Ovidiu
2013-06-01
Chemical and molecular graphs have fundamental applications in chemoinformatics, quantitative structureproperty relationships (QSPR), quantitative structure-activity relationships (QSAR), virtual screening of chemical libraries, and computational drug design. Chemoinformatics applications of graphs include chemical structure representation and coding, database search and retrieval, and physicochemical property prediction. QSPR, QSAR and virtual screening are based on the structure-property principle, which states that the physicochemical and biological properties of chemical compounds can be predicted from their chemical structure. Such structure-property correlations are usually developed from topological indices and fingerprints computed from the molecular graph and from molecular descriptors computed from the three-dimensional chemical structure. We present here a selection of the most important graph descriptors and topological indices, including molecular matrices, graph spectra, spectral moments, graph polynomials, and vertex topological indices. These graph descriptors are used to define several topological indices based on molecular connectivity, graph distance, reciprocal distance, distance-degree, distance-valency, spectra, polynomials, and information theory concepts. The molecular descriptors and topological indices can be developed with a more general approach, based on molecular graph operators, which define a family of graph indices related by a common formula. Graph descriptors and topological indices for molecules containing heteroatoms and multiple bonds are computed with weighting schemes based on atomic properties, such as the atomic number, covalent radius, or electronegativity. The correlation in QSPR and QSAR models can be improved by optimizing some parameters in the formula of topological indices, as demonstrated for structural descriptors based on atomic connectivity and graph distance. PMID:23701000
Browsing schematics: Query-filtered graphs with context nodes
NASA Technical Reports Server (NTRS)
Ciccarelli, Eugene C.; Nardi, Bonnie A.
1988-01-01
The early results of a research project to create tools for building interfaces to intelligent systems on the NASA Space Station are reported. One such tool is the Schematic Browser which helps users engaged in engineering problem solving find and select schematics from among a large set. Users query for schematics with certain components, and the Schematic Browser presents a graph whose nodes represent the schematics with those components. The query greatly reduces the number of choices presented to the user, filtering the graph to a manageable size. Users can reformulate and refine the query serially until they locate the schematics of interest. To help users maintain orientation as they navigate a large body of data, the graph also includes nodes that are not matches but provide global and local context for the matching nodes. Context nodes include landmarks, ancestors, siblings, children and previous matches.
Single-qubit unitary gates by graph scattering
NASA Astrophysics Data System (ADS)
Blumer, Benjamin A.; Underwood, Michael S.; Feder, David L.
2011-12-01
We consider the effects of plane-wave states scattering off finite graphs as an approach to implementing single-qubit unitary operations within the continuous-time quantum walk framework of universal quantum computation. Four semi-infinite tails are attached at arbitrary points of a given graph, representing the input and output registers of a single qubit. For a range of momentum eigenstates, we enumerate all of the graphs with up to n=9 vertices for which the scattering implements a single-qubit gate. As n increases, the number of new unitary operations increases exponentially, and for n>6 the majority correspond to rotations about axes distributed roughly uniformly across the Bloch sphere. Rotations by both rational and irrational multiples of π are found.
Systematic and Deterministic Graph-Minor Embedding of Cartesian Products of Complete Graphs
NASA Astrophysics Data System (ADS)
Zaribafiyan, Arman; Marchand, Dominic J. J.; Changiz Rezaei, Seyed Saeed
The limited connectivity of current and next-generation quantum annealers motivates the need for efficient graph-minor embedding methods. The overhead of the widely used heuristic techniques is quickly proving to be a significant bottleneck for real-world applications. To alleviate this obstacle, we propose a systematic deterministic embedding method that exploits the structures of both the input graph of the specific combinatorial optimization problem and the quantum annealer. We focus on the specific case of the Cartesian product of two complete graphs, a regular structure that occurs in many problems. We first divide the problem by embedding one of the factors of the Cartesian product in a repeatable unit. The resulting simplified problem consists of placing copies of this unit and connecting them together appropriately. Aside from the obvious speed and efficiency advantages of a systematic deterministic approach, the embeddings produced can be easily scaled for larger processors and show desirable properties with respect to the number of qubits used and the chain length distribution.
Chemical Applications of Graph Theory: Part II. Isomer Enumeration.
ERIC Educational Resources Information Center
Hansen, Peter J.; Jurs, Peter C.
1988-01-01
Discusses the use of graph theory to aid in the depiction of organic molecular structures. Gives a historical perspective of graph theory and explains graph theory terminology with organic examples. Lists applications of graph theory to current research projects. (ML)
ERIC Educational Resources Information Center
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…
So Many Graphs, So Little Time
ERIC Educational Resources Information Center
Wall, Jennifer J.; Benson, Christine C.
2009-01-01
Interpreting graphs found in various content areas is an important skill for students, especially in light of high-stakes testing. In addition, reading and understanding graphs is an important part of numeracy, or numeric literacy, a skill necessary for informed citizenry. This article explores the different categories of graphs, provides…
Collaborative Robotic Instruction: A Graph Teaching Experience
ERIC Educational Resources Information Center
Mitnik, Ruben; Recabarren, Matias; Nussbaum, Miguel; Soto, Alvaro
2009-01-01
Graphing is a key skill in the study of Physics. Drawing and interpreting graphs play a key role in the understanding of science, while the lack of these has proved to be a handicap and a limiting factor in the learning of scientific concepts. It has been observed that despite the amount of previous graph-working experience, students of all ages…
47 CFR 80.761 - Conversion graphs.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 5 2010-10-01 2010-10-01 false Conversion graphs. 80.761 Section 80.761... 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...
47 CFR 80.761 - Conversion graphs.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 5 2011-10-01 2011-10-01 false Conversion graphs. 80.761 Section 80.761... 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...
47 CFR 80.761 - Conversion graphs.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 47 Telecommunication 5 2013-10-01 2013-10-01 false Conversion graphs. 80.761 Section 80.761... 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...
47 CFR 80.761 - Conversion graphs.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 5 2012-10-01 2012-10-01 false Conversion graphs. 80.761 Section 80.761... 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...
47 CFR 80.761 - Conversion graphs.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 47 Telecommunication 5 2014-10-01 2014-10-01 false Conversion graphs. 80.761 Section 80.761... 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...
Kolesov, Roman; Scully, Marlan O.; Kocharovskaya, Olga
2006-11-15
Coherent population trapping (CPT) in a three-level atomic medium pumped by two subsequent short optical pulses is considered under the condition of negligible population decay from the excited optical state. It is shown that the amount of atomic population transferred to the excited state by the combined action of the pulses strongly depends on the phase of the ground-state coherence excited by the first pulse at the arrival time of the second pulse. Oscillatory behavior of optical excitation efficiency on the time delay between the pulses is predicted. It is also shown that saturating optical pulses can produce population inversion in a resonantly pumped quasi-two-level system. A class of solid materials in which the predicted phenomena can be observed at room temperature is found. It includes some rare-earth and transition-metal doped dielectric crystals where Orbach relaxation between ground-state Zeeman states is suppressed: ruby, alexandrite, and several others. On the basis of the theoretical predictions, experimental observation of Ramsey fringes in CPT spectrum of ruby is reported.
NASA Astrophysics Data System (ADS)
Kolesov, Roman; Scully, Marlan O.; Kocharovskaya, Olga
2006-11-01
Coherent population trapping (CPT) in a three-level atomic medium pumped by two subsequent short optical pulses is considered under the condition of negligible population decay from the excited optical state. It is shown that the amount of atomic population transferred to the excited state by the combined action of the pulses strongly depends on the phase of the ground-state coherence excited by the first pulse at the arrival time of the second pulse. Oscillatory behavior of optical excitation efficiency on the time delay between the pulses is predicted. It is also shown that saturating optical pulses can produce population inversion in a resonantly pumped quasi-two-level system. A class of solid materials in which the predicted phenomena can be observed at room temperature is found. It includes some rare-earth and transition-metal doped dielectric crystals where Orbach relaxation between ground-state Zeeman states is suppressed: ruby, alexandrite, and several others. On the basis of the theoretical predictions, experimental observation of Ramsey fringes in CPT spectrum of ruby is reported.
Shi, Le-Song; Liu, Jin-Ping
2016-01-01
1-aminocyclopropane-1-carboxylic acid (ACC) synthase (ACS) is a rate-limiting enzyme in the biosynthesis of ethylene which regulates many aspects of the plant development and responses to biotic and abiotic stresses. In this study, a full-length cDNA of ACC synthase, OnACS2, was cloned from the senescing flower of Oncidium Gower Ramsey by RACE. The full-length cDNA of OnACS2 (GenBank accession no. JQ822087) was 1557 bp in length with an open reading frame (ORF) of 1308 bp encoding for a protein of 435 amino acid residues. The predicted OnACS2 protein had a molecular mass of 49.1 kDa with pI value of 7.51. Phylogenetic analysis indicated its evolutionary relationships with corresponding orthologous sequences in orchids, Hosta ventricosa and monocots. Real-time PCR assay demonstrated that OnACS2 was constitutively expressed in all tested organs with the highest transcript level in the gynandria. Differential expression pattern of OnACS2 gene correlated to the ethylene production and the subsequent occurrence of senescent symptoms in flower suggested that OnACS2 probably played an important role in the initiation of flower senescence. PMID:26631967
Expert and Novice Approaches to Using Graphs: Evidence from Eye-Track Experiments
NASA Astrophysics Data System (ADS)
Wirth, K. R.; Lindgren, J. M.
2015-12-01
Professionals and students in geology use an array of graphs to study the earth, but relatively little detail is known about how users interact with these graphs. Comprehension of graphical information in the earth sciences is further complicated by the common use of non-traditional formats (e.g., inverted axes, logarithmic scales, normalized plots, ternary diagrams). Many educators consider graph-reading skills an important outcome of general education science curricula, so it is critical that we understand both the development of graph-reading skills and the instructional practices that are most efficacious. Eye-tracking instruments provide quantitative information about eye movements and offer important insights into the development of expertise in graph use. We measured the graph reading skills and eye movements of novices (students with a variety of majors and educational attainment) and experts (faculty and staff from a variety of disciplines) while observing traditional and non-traditional graph formats. Individuals in the expert group consistently demonstrated significantly greater accuracy in responding to questions (e.g., retrieval, interpretation, prediction) about graphs. Among novices, only the number of college math and science courses correlated with response accuracy. Interestingly, novices and experts exhibited similar eye-tracks when they first encountered a new graph; they typically scanned through the title, x and y-axes, and data regions in the first 5-15 seconds. However, experts are readily distinguished from novices by a greater number of eye movements (20-35%) between the data and other graph elements (e.g., title, x-axis, y-axis) both during and after the initial orientation phase. We attribute the greater eye movements between the different graph elements an outcome of the generally better-developed self-regulation skills (goal-setting, monitoring, self-evaluation) that likely characterize individuals in our expert group.
Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks
Rudinger, Kenneth; Gamble, John King; Bach, Eric; Friesen, Mark; Joynt, Robert; Coppersmith, S. N.
2013-07-01
Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erences in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.
Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks
Rudinger, Kenneth; Gamble, John King; Bach, Eric; Friesen, Mark; Joynt, Robert; Coppersmith, S. N.
2013-07-01
Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erencesmore » in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.« less
Indexing molecules with chemical graph identifiers.
Gregori-Puigjané, Elisabet; Garriga-Sust, Rut; Mestres, Jordi
2011-09-01
Fast and robust algorithms for indexing molecules have been historically considered strategic tools for the management and storage of large chemical libraries. This work introduces a modified and further extended version of the molecular equivalence number naming adaptation of the Morgan algorithm (J Chem Inf Comput Sci 2001, 41, 181-185) for the generation of a chemical graph identifier (CGI). This new version corrects for the collisions recognized in the original adaptation and includes the ability to deal with graph canonicalization, ensembles (salts), and isomerism (tautomerism, regioisomerism, optical isomerism, and geometrical isomerism) in a flexible manner. Validation of the current CGI implementation was performed on the open NCI database and the drug-like subset of the ZINC database containing 260,071 and 5,348,089 structures, respectively. The results were compared with those obtained with some of the most widely used indexing codes, such as the CACTVS hash code and the new InChIKey. The analyses emphasize the fact that compound management activities, like duplicate analysis of chemical libraries, are sensitive to the exact definition of compound uniqueness and thus still depend, to a minor extent, on the type and flexibility of the molecular index being used.
Indexing molecules with chemical graph identifiers.
Gregori-Puigjané, Elisabet; Garriga-Sust, Rut; Mestres, Jordi
2011-09-01
Fast and robust algorithms for indexing molecules have been historically considered strategic tools for the management and storage of large chemical libraries. This work introduces a modified and further extended version of the molecular equivalence number naming adaptation of the Morgan algorithm (J Chem Inf Comput Sci 2001, 41, 181-185) for the generation of a chemical graph identifier (CGI). This new version corrects for the collisions recognized in the original adaptation and includes the ability to deal with graph canonicalization, ensembles (salts), and isomerism (tautomerism, regioisomerism, optical isomerism, and geometrical isomerism) in a flexible manner. Validation of the current CGI implementation was performed on the open NCI database and the drug-like subset of the ZINC database containing 260,071 and 5,348,089 structures, respectively. The results were compared with those obtained with some of the most widely used indexing codes, such as the CACTVS hash code and the new InChIKey. The analyses emphasize the fact that compound management activities, like duplicate analysis of chemical libraries, are sensitive to the exact definition of compound uniqueness and thus still depend, to a minor extent, on the type and flexibility of the molecular index being used. PMID:21647928
Fast graph operations in quantum computation
NASA Astrophysics Data System (ADS)
Zhao, Liming; Pérez-Delgado, Carlos A.; Fitzsimons, Joseph F.
2016-03-01
The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in the reverse direction to yield a graph data structure, which allows for more efficient manipulation and comparison of graphs than any possible classical structure. We introduce efficient algorithms for many transformation and comparison operations on graphs represented as graph states, and prove that no classical data structure can have similar performance for the full set of operations studied.
Constrained Graph Optimization: Interdiction and Preservation Problems
Schild, Aaron V
2012-07-30
The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.
Generalized graph states based on Hadamard matrices
Cui, Shawn X.; Yu, Nengkun; Zeng, Bei
2015-07-15
Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a stabilizer group or an encoding circuit, both can be directly given by the graph. To generalize graph states, whose stabilizer groups are abelian subgroups of the Pauli group, one approach taken is to study non-abelian stabilizers. In this work, we propose to generalize graph states based on the encoding circuit, which is completely determined by the graph and a Hadamard matrix. We study the entanglement structures of these generalized graph states and show that they are all maximally mixed locally. We also explore the relationship between the equivalence of Hadamard matrices and local equivalence of the corresponding generalized graph states. This leads to a natural generalization of the Pauli (X, Z) pairs, which characterizes the local symmetries of these generalized graph states. Our approach is also naturally generalized to construct graph quantum codes which are beyond stabilizer codes.
Molecular graph convolutions: moving beyond fingerprints.
Kearnes, Steven; McCloskey, Kevin; Berndl, Marc; Pande, Vijay; Riley, Patrick
2016-08-01
Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular graph convolutions, a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph-atoms, bonds, distances, etc.-which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement. PMID:27558503
Fast Approximate Quadratic Programming for Graph Matching
Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E.
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624
Molecular graph convolutions: moving beyond fingerprints.
Kearnes, Steven; McCloskey, Kevin; Berndl, Marc; Pande, Vijay; Riley, Patrick
2016-08-01
Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular graph convolutions, a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph-atoms, bonds, distances, etc.-which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement.
On a programming language for graph algorithms
NASA Technical Reports Server (NTRS)
Rheinboldt, W. C.; Basili, V. R.; Mesztenyi, C. K.
1971-01-01
An algorithmic language, GRAAL, is presented for describing and implementing graph algorithms of the type primarily arising in applications. The language is based on a set algebraic model of graph theory which defines the graph structure in terms of morphisms between certain set algebraic structures over the node set and arc set. GRAAL is modular in the sense that the user specifies which of these mappings are available with any graph. This allows flexibility in the selection of the storage representation for different graph structures. In line with its set theoretic foundation, the language introduces sets as a basic data type and provides for the efficient execution of all set and graph operators. At present, GRAAL is defined as an extension of ALGOL 60 (revised) and its formal description is given as a supplement to the syntactic and semantic definition of ALGOL. Several typical graph algorithms are written in GRAAL to illustrate various features of the language and to show its applicability.
Molecular graph convolutions: moving beyond fingerprints
NASA Astrophysics Data System (ADS)
Kearnes, Steven; McCloskey, Kevin; Berndl, Marc; Pande, Vijay; Riley, Patrick
2016-08-01
Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular "graph convolutions", a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph---atoms, bonds, distances, etc.---which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement.
Subgraph-Based Filterbanks for Graph Signals
NASA Astrophysics Data System (ADS)
Tremblay, Nicolas; Borgnat, Pierre
2016-08-01
We design a critically-sampled compact-support biorthogonal transform for graph signals, via graph filterbanks. Instead of partitioning the nodes in two sets so as to remove one every two nodes in the filterbank downsampling operations, the design is based on a partition of the graph in connected subgraphs. Coarsening is achieved by defining one "supernode" for each subgraph and the edges for this coarsened graph derives from the connectivity between the subgraphs. Unlike the "one every two nodes" downsampling on bipartite graphs, this coarsening operation does not have an exact formulation in the graph Fourier domain. Instead, we rely on the local Fourier bases of each subgraph to define filtering operations. We apply successfully this method to decompose graph signals, and show promising performance on compression and denoising.
Line graphs as social networks
NASA Astrophysics Data System (ADS)
Krawczyk, M. J.; Muchnik, L.; Mańka-Krasoń, A.; Kułakowski, K.
2011-07-01
It was demonstrated recently that the line graphs are clustered and assortative. These topological features are known to characterize some social networks [M.E.J. Newman, Y. Park, Why social networks are different from other types of networks, Phys. Rev. E 68 (2003) 036122]; it was argued that this similarity reveals their cliquey character. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8×10 6 people.
Graph distance for complex networks
NASA Astrophysics Data System (ADS)
Shimada, Yutaka; Hirata, Yoshito; Ikeguchi, Tohru; Aihara, Kazuyuki
2016-10-01
Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in the theory of complex networks. Here, we propose a graph distance between networks based on a Laplacian matrix that reflects the structural and dynamical properties of networked dynamical systems. Our results indicate that the Laplacian-based graph distance effectively quantifies the structural difference between complex networks. We further show that our approach successfully elucidates the temporal properties underlying temporal networks observed in the context of face-to-face human interactions.
Graph distance for complex networks
Shimada, Yutaka; Hirata, Yoshito; Ikeguchi, Tohru; Aihara, Kazuyuki
2016-01-01
Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in the theory of complex networks. Here, we propose a graph distance between networks based on a Laplacian matrix that reflects the structural and dynamical properties of networked dynamical systems. Our results indicate that the Laplacian-based graph distance effectively quantifies the structural difference between complex networks. We further show that our approach successfully elucidates the temporal properties underlying temporal networks observed in the context of face-to-face human interactions. PMID:27725690
Relativity on Rotated Graph Paper
NASA Astrophysics Data System (ADS)
Salgado, Roberto
2011-11-01
We present visual calculations in special relativity using spacetime diagrams drawn on graph paper that has been rotated by 45 degrees. The rotated lines represent lightlike directions in Minkowski spacetime, and the boxes in the grid (called light-clock diamonds) represent ticks of an inertial observer's lightclock. We show that many quantitative results can be read off a spacetime diagram by counting boxes, using a minimal amount of algebra.
Scale-free Graphs for General Aviation Flight Schedules
NASA Technical Reports Server (NTRS)
Alexandov, Natalia M. (Technical Monitor); Kincaid, Rex K.
2003-01-01
In the late 1990s a number of researchers noticed that networks in biology, sociology, and telecommunications exhibited similar characteristics unlike standard random networks. In particular, they found that the cummulative degree distributions of these graphs followed a power law rather than a binomial distribution and that their clustering coefficients tended to a nonzero constant as the number of nodes, n, became large rather than O(1/n). Moreover, these networks shared an important property with traditional random graphs as n becomes large the average shortest path length scales with log n. This latter property has been coined the small-world property. When taken together these three properties small-world, power law, and constant clustering coefficient describe what are now most commonly referred to as scale-free networks. Since 1997 at least six books and over 400 articles have been written about scale-free networks. In this manuscript an overview of the salient characteristics of scale-free networks. Computational experience will be provided for two mechanisms that grow (dynamic) scale-free graphs. Additional computational experience will be given for constructing (static) scale-free graphs via a tabu search optimization approach. Finally, a discussion of potential applications to general aviation networks is given.
Many-core graph analytics using accelerated sparse linear algebra routines
NASA Astrophysics Data System (ADS)
Kozacik, Stephen; Paolini, Aaron L.; Fox, Paul; Kelmelis, Eric
2016-05-01
Graph analytics is a key component in identifying emerging trends and threats in many real-world applications. Largescale graph analytics frameworks provide a convenient and highly-scalable platform for developing algorithms to analyze large datasets. Although conceptually scalable, these techniques exhibit poor performance on modern computational hardware. Another model of graph computation has emerged that promises improved performance and scalability by using abstract linear algebra operations as the basis for graph analysis as laid out by the GraphBLAS standard. By using sparse linear algebra as the basis, existing highly efficient algorithms can be adapted to perform computations on the graph. This approach, however, is often less intuitive to graph analytics experts, who are accustomed to vertex-centric APIs such as Giraph, GraphX, and Tinkerpop. We are developing an implementation of the high-level operations supported by these APIs in terms of linear algebra operations. This implementation is be backed by many-core implementations of the fundamental GraphBLAS operations required, and offers the advantages of both the intuitive programming model of a vertex-centric API and the performance of a sparse linear algebra implementation. This technology can reduce the number of nodes required, as well as the run-time for a graph analysis problem, enabling customers to perform more complex analysis with less hardware at lower cost. All of this can be accomplished without the requirement for the customer to make any changes to their analytics code, thanks to the compatibility with existing graph APIs.
A Weakly Robust PTAS for Minimum Clique Partition in Unit Disk Graphs
NASA Astrophysics Data System (ADS)
Pirwani, Imran A.; Salavatipour, Mohammad R.
We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques. The problem is NP-hard and various constant factor approximations are known, with the best known ratio of 3. Our main result is a weakly robust polynomial time approximation scheme (PTAS) for UDGs expressed with edge-lengths and ɛ> 0 that either (i) computes a clique partition, or (ii) produces a certificate proving that the graph is not a UDG; if the graph is a UDG, then our partition is guaranteed to be within (1 + ɛ) ratio of the optimum; however, if the graph is not a UDG, it either computes a clique partition, or detects that the graph is not a UDG. Noting that recognition of UDG's is NP-hard even with edge lengths, this is a significant weakening of the input model.
Helping Students Make Sense of Graphs: An Experimental Trial of SmartGraphs Software
NASA Astrophysics Data System (ADS)
Zucker, Andrew; Kay, Rachel; Staudt, Carolyn
2014-06-01
Graphs are commonly used in science, mathematics, and social sciences to convey important concepts; yet students at all ages demonstrate difficulties interpreting graphs. This paper reports on an experimental study of free, Web-based software called SmartGraphs that is specifically designed to help students overcome their misconceptions regarding graphs. SmartGraphs allows students to interact with graphs and provides hints and scaffolding to help students, if they need help. SmartGraphs activities can be authored to be useful in teaching and learning a variety of topics that use graphs (such as slope, velocity, half-life, and global warming). A 2-year experimental study in physical science classrooms was conducted with dozens of teachers and thousands of students. In the first year, teachers were randomly assigned to experimental or control conditions. Data show that students of teachers who use SmartGraphs as a supplement to normal instruction make greater gains understanding graphs than control students studying the same content using the same textbooks, but without SmartGraphs. Additionally, teachers believe that the SmartGraphs activities help students meet learning goals in the physical science course, and a great majority reported they would use the activities with students again. In the second year of the study, several specific variations of SmartGraphs were researched to help determine what makes SmartGraphs effective.
Computational Genomics Using Graph Theory
NASA Astrophysics Data System (ADS)
Schlick, Tamar
2005-03-01
With exciting new discoveries concerning RNA's regulatory cellular roles in gene expression, structural and functional problems associated with DNA's venerable cousin have come to the forefront. RNA folding, for example, is analogous to the well-known protein folding problem, and seeks to link RNA's primary sequence with secondary and tertiary structures. As a single-stranded polynucleotide, RNA's secondary structures are defined by a network of hydrogen bonds, which lead to a variety of stems, loops, junctions, bulges, and other motifs. Supersecondary pseudoknot structures can also occur and, together, lead to RNA's complex tertiary interactions stabilized by salt and solvent ions in the natural cellular milieu. Besides folding, challenges in RNA research include identifying locations and functions of RNA genes, discovering RNA's structural repertoire (folding motifs), designing novel RNAs, and developing new antiviral and antibiotic compounds composed of, or targeting, RNAs. In this talk, I will describe some of these new biological findings concerning RNA and present an approach using graph theory (network theory) to represent RNA secondary structures. Because the RNA motif space using graphs is vastly smaller than RNA's sequence space, many problems related to analyzing and discovering new RNAs can be simplified and studied systematically. Some preliminary applications to designing novel RNAs will also be described.Related ReadingH. H. Gan, S. Pasquali, and T. Schlick, ``A Survey of Existing RNAs using Graph Theory with Implications to RNA Analysis and Design,'' Nuc. Acids Res. 31: 2926--2943 (2003). J. Zorn, H. H. Gan, N. Shiffeldrim, and T. Schlick, ``Structural Motifs in Ribosomal RNAs: Implications for RNA Design and Genomics,'' Biopolymers 73: 340--347 (2004). H. H. Gan, D. Fera, J. Zorn, M. Tang, N. Shiffeldrim, U. Laserson, N. Kim, and T. Schlick,``RAG: RNA-As-Graphs Database -- Concepts, Analysis, and Features,'' Bioinformatics 20: 1285--1291 (2004). U
Computing Information Value from RDF Graph Properties
al-Saffar, Sinan; Heileman, Gregory
2010-11-08
Information value has been implicitly utilized and mostly non-subjectively computed in information retrieval (IR) systems. We explicitly define and compute the value of an information piece as a function of two parameters, the first is the potential semantic impact the target information can subjectively have on its recipient's world-knowledge, and the second parameter is trust in the information source. We model these two parameters as properties of RDF graphs. Two graphs are constructed, a target graph representing the semantics of the target body of information and a context graph representing the context of the consumer of that information. We compute information value subjectively as a function of both potential change to the context graph (impact) and the overlap between the two graphs (trust). Graph change is computed as a graph edit distance measuring the dissimilarity between the context graph before and after the learning of the target graph. A particular application of this subjective information valuation is in the construction of a personalized ranking component in Web search engines. Based on our method, we construct a Web re-ranking system that personalizes the information experience for the information-consumer.
Components in time-varying graphs
NASA Astrophysics Data System (ADS)
Nicosia, Vincenzo; Tang, John; Musolesi, Mirco; Russo, Giovanni; Mascolo, Cecilia; Latora, Vito
2012-06-01
Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, today it is possible to produce and analyze social and biological networks with detailed information on the time of occurrence and duration of each link. However, standard graph metrics introduced so far in complex network theory are mainly suited for static graphs, i.e., graphs in which the links do not change over time, or graphs built from time-varying systems by aggregating all the links as if they were concurrent in time. In this paper, we extend the notion of connectedness, and the definitions of node and graph components, to the case of time-varying graphs, which are represented as time-ordered sequences of graphs defined over a fixed set of nodes. We show that the problem of finding strongly connected components in a time-varying graph can be mapped into the problem of discovering the maximal-cliques in an opportunely constructed static graph, which we name the affine graph. It is, therefore, an NP-complete problem. As a practical example, we have performed a temporal component analysis of time-varying graphs constructed from three data sets of human interactions. The results show that taking time into account in the definition of graph components allows to capture important features of real systems. In particular, we observe a large variability in the size of node temporal in- and out-components. This is due to intrinsic fluctuations in the activity patterns of individuals, which cannot be detected by static graph analysis.
Components in time-varying graphs.
Nicosia, Vincenzo; Tang, John; Musolesi, Mirco; Russo, Giovanni; Mascolo, Cecilia; Latora, Vito
2012-06-01
Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, today it is possible to produce and analyze social and biological networks with detailed information on the time of occurrence and duration of each link. However, standard graph metrics introduced so far in complex network theory are mainly suited for static graphs, i.e., graphs in which the links do not change over time, or graphs built from time-varying systems by aggregating all the links as if they were concurrent in time. In this paper, we extend the notion of connectedness, and the definitions of node and graph components, to the case of time-varying graphs, which are represented as time-ordered sequences of graphs defined over a fixed set of nodes. We show that the problem of finding strongly connected components in a time-varying graph can be mapped into the problem of discovering the maximal-cliques in an opportunely constructed static graph, which we name the affine graph. It is, therefore, an NP-complete problem. As a practical example, we have performed a temporal component analysis of time-varying graphs constructed from three data sets of human interactions. The results show that taking time into account in the definition of graph components allows to capture important features of real systems. In particular, we observe a large variability in the size of node temporal in- and out-components. This is due to intrinsic fluctuations in the activity patterns of individuals, which cannot be detected by static graph analysis. PMID:22757508
JavaGenes: Evolving Graphs with Crossover
NASA Technical Reports Server (NTRS)
Globus, Al; Atsatt, Sean; Lawton, John; Wipke, Todd
2000-01-01
Genetic algorithms usually use string or tree representations. We have developed a novel crossover operator for a directed and undirected graph representation, and used this operator to evolve molecules and circuits. Unlike strings or trees, a single point in the representation cannot divide every possible graph into two parts, because graphs may contain cycles. Thus, the crossover operator is non-trivial. A steady-state, tournament selection genetic algorithm code (JavaGenes) was written to implement and test the graph crossover operator. All runs were executed by cycle-scavagging on networked workstations using the Condor batch processing system. The JavaGenes code has evolved pharmaceutical drug molecules and simple digital circuits. Results to date suggest that JavaGenes can evolve moderate sized drug molecules and very small circuits in reasonable time. The algorithm has greater difficulty with somewhat larger circuits, suggesting that directed graphs (circuits) are more difficult to evolve than undirected graphs (molecules), although necessary differences in the crossover operator may also explain the results. In principle, JavaGenes should be able to evolve other graph-representable systems, such as transportation networks, metabolic pathways, and computer networks. However, large graphs evolve significantly slower than smaller graphs, presumably because the space-of-all-graphs explodes combinatorially with graph size. Since the representation strongly affects genetic algorithm performance, adding graphs to the evolutionary programmer's bag-of-tricks should be beneficial. Also, since graph evolution operates directly on the phenotype, the genotype-phenotype translation step, common in genetic algorithm work, is eliminated.
Massive Scale Cyber Traffic Analysis: A Driver for Graph Database Research
Joslyn, Cliff A.; Choudhury, S.; Haglin, David J.; Howe, Bill; Nickless, William K.; Olsen, Bryan K.
2013-06-19
We describe the significance and prominence of network traffic analysis (TA) as a graph- and network-theoretical domain for advancing research in graph database systems. TA involves observing and analyzing the connections between clients, servers, hosts, and actors within IP networks, both at particular times and as extended over times. Towards that end, NetFlow (or more generically, IPFLOW) data are available from routers and servers which summarize coherent groups of IP packets flowing through the network. IPFLOW databases are routinely interrogated statistically and visualized for suspicious patterns. But the ability to cast IPFLOW data as a massive graph and query it interactively, in order to e.g.\\ identify connectivity patterns, is less well advanced, due to a number of factors including scaling, and their hybrid nature combining graph connectivity and quantitative attributes. In this paper, we outline requirements and opportunities for graph-structured IPFLOW analytics based on our experience with real IPFLOW databases. Specifically, we describe real use cases from the security domain, cast them as graph patterns, show how to express them in two graph-oriented query languages SPARQL and Datalog, and use these examples to motivate a new class of "hybrid" graph-relational systems.
On the spectral distribution of distance-k graph of free product graphs
NASA Astrophysics Data System (ADS)
Arizmendi, Octavio; Gaxiola, Tulio
2016-08-01
We calculate the distribution with respect to the vacuum state of the distance-k graph of a d-regular tree. From this result we show that the distance-k graph of a d-regular graphs converges to the distribution of the distance-k graph of a regular tree. Finally, we prove that, properly normalized, the asymptotic distributions of distance-k graphs of the d-fold free product graph, as d tends to infinity, is given by the distribution of Pk(s), where s is a semicirlce random variable and Pk is the kth Chebychev polynomial.
Area law for random graph states
NASA Astrophysics Data System (ADS)
Collins, Benoît; Nechita, Ion; Życzkowski, Karol
2013-08-01
Random pure states of multi-partite quantum systems, associated with arbitrary graphs, are investigated. Each vertex of the graph represents a generic interaction between subsystems, described by a random unitary matrix distributed according to the Haar measure, while each edge of the graph represents a bipartite, maximally entangled state. For any splitting of the graph into two parts we consider the corresponding partition of the quantum system and compute the average entropy of entanglement. First, in the special case where the partition does not cross any vertex of the graph, we show that the area law is satisfied exactly. In the general case, we show that the entropy of entanglement obeys an area law on average, this time with a correction term that depends on the topologies of the graph and of the partition. The results obtained are applied to the problem of distribution of quantum entanglement in a quantum network with prescribed topology.
Replica methods for loopy sparse random graphs
NASA Astrophysics Data System (ADS)
Coolen, ACC
2016-03-01
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. This paper is dedicated to the memory of our colleague and friend Jun-Ichi Inoue, with whom the author has had the great pleasure and privilege of collaborating.
Graph Frequency Analysis of Brain Signals
NASA Astrophysics Data System (ADS)
Huang, Weiyu; Goldsberry, Leah; Wymbs, Nicholas F.; Grafton, Scott T.; Bassett, Danielle S.; Ribeiro, Alejandro
2016-10-01
This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters traditionally defined for signals supported on regular domains such as discrete time and image grids has been recently generalized to irregular graph domains, and defines brain graph frequencies associated with different levels of spatial smoothness across the brain regions. Brain network frequency also enables the decomposition of brain signals into pieces corresponding to smooth or rapid variations. We relate graph frequency with principal component analysis when the networks of interest denote functional connectivity. The methods are utilized to analyze brain networks and signals as subjects master a simple motor skill. We observe that brain signals corresponding to different graph frequencies exhibit different levels of adaptability throughout learning. Further, we notice a strong association between graph spectral properties of brain networks and the level of exposure to tasks performed, and recognize the most contributing and important frequency signatures at different task familiarity.
Image clustering using fuzzy graph theory
NASA Astrophysics Data System (ADS)
Jafarkhani, Hamid; Tarokh, Vahid
1999-12-01
We propose an image clustering algorithm which uses fuzzy graph theory. First, we define a fuzzy graph and the concept of connectivity for a fuzzy graph. Then, based on our definition of connectivity we propose an algorithm which finds connected subgraphs of the original fuzzy graph. Each connected subgraph can be considered as a cluster. As an application of our algorithm, we consider a database of images. We calculate a similarity measure between any paris of images in the database and generate the corresponding fuzzy graph. The, we find the subgraphs of the resulting fuzzy graph using our algorithm. Each subgraph corresponds to a cluster. We apply our image clustering algorithm to the key frames of news programs to find the anchorperson clusters. Simulation results show that our algorithm is successful to find most of anchorperson frames from the database.
Spectral correlations of individual quantum graphs.
Gnutzmann, Sven; Altland, Alexander
2005-11-01
We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the energy-average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric nonlinear -model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner-Dyson random matrix theory. We explore the stability of the universal random matrix behavior with regard to perturbations, and discuss the crossover between different types of symmetries.
Spectral correlations of individual quantum graphs
Gnutzmann, Sven; Altland, Alexander
2005-11-01
We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the energy-average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric nonlinear {sigma}-model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner-Dyson random matrix theory. We explore the stability of the universal random matrix behavior with regard to perturbations, and discuss the crossover between different types of symmetries.
Separability of Generalized Graph Product States
NASA Astrophysics Data System (ADS)
Zhao, Hui; Fan, Jiao
2013-09-01
We construct two classes of generalized graph product states and study the entanglement of these states. It is first presented that the density matrices of complex edge-weighted digraphs associated with the generalized graph product in mn systems are positive partial transformation and separable states. Then we prove that the density matrices of the vertex-weighted digraphs associated with another generalized graph product are entangled states.
Breddin's graph for tectonic regimes
NASA Astrophysics Data System (ADS)
Célérier, Bernard; Séranne, Michel
2001-05-01
A simple graphical method is proposed to infer the tectonic regime from a fault and slip data set. An abacus is overlaid on a plot of the rake versus strike of the data. This yields the horizontal principal stress directions and a constraint on the stress tensor aspect ratio, in a manner similar to Breddin's graph for two-dimensional strain analysis. The main requirement is that one of the principal stress directions is close to the vertical. This method is illustrated on monophase synthetic and natural data, but is also expected to help sort out multiphase data sets.
NASA Astrophysics Data System (ADS)
Gosti, Giorgio; Batchelder, William H.
We address how the structure of a social communication system affects language coordination. The naming game is an abstraction of lexical acquisition dynamics, in which N agents try to find an agreement on the names to give to objects. Most results on naming games are specific to certain communication network topologies. We present two important results that are general to any graph topology: the first proves that under certain topologies the system always converges to a name-object agreement; the second proves that if these conditions are not met the system may end up in a state in which sub-networks with different competing object-name associations coexist.
The alignment-distribution graph
NASA Technical Reports Server (NTRS)
Chatterjee, Siddhartha; Gilbert, John R.; Schreiber, Robert
1993-01-01
Implementing a data-parallel language such as Fortran 90 on a distributed-memory parallel computer requires distributing aggregate data objects (such as arrays) among the memory modules attached to the processors. The mapping of objects to the machine determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. We present a program representation called the alignment-distribution graph that makes these communication requirements explicit. We describe the details of the representation, show how to model communication cost in this framework, and outline several algorithms for determining object mappings that approximately minimize residual communication.
The alignment-distribution graph
NASA Technical Reports Server (NTRS)
Chatterjee, Siddhartha; Gilbert, John R.; Schreiber, Robert
1993-01-01
Implementing a data-parallel language such as Fortran 90 on a distributed-memory parallel computer requires distributing aggregate data objects (such as arrays) among the memory modules attached to the processors. The mapping of objects to the machine determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. We present a program representation called the alignment distribution graph that makes these communication requirements explicit. We describe the details of the representation, show how to model communication cost in this framework, and outline several algorithms for determining object mappings that approximately minimize residual communication.
Givental Graphs and Inversion Symmetry
NASA Astrophysics Data System (ADS)
Dunin-Barkowski, Petr; Shadrin, Sergey; Spitz, Loek
2013-05-01
Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy.
Experimental quantum annealing: case study involving the graph isomorphism problem
Zick, Kenneth M.; Shehab, Omar; French, Matthew
2015-01-01
Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N2 to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers. PMID:26053973
AmbiguityVis: Visualization of Ambiguity in Graph Layouts.
Wang, Yong; Shen, Qiaomu; Archambault, Daniel; Zhou, Zhiguang; Zhu, Min; Yang, Sixiao; Qu, Huamin
2016-01-01
Node-link diagrams provide an intuitive way to explore networks and have inspired a large number of automated graph layout strategies that optimize aesthetic criteria. However, any particular drawing approach cannot fully satisfy all these criteria simultaneously, producing drawings with visual ambiguities that can impede the understanding of network structure. To bring attention to these potentially problematic areas present in the drawing, this paper presents a technique that highlights common types of visual ambiguities: ambiguous spatial relationships between nodes and edges, visual overlap between community structures, and ambiguity in edge bundling and metanodes. Metrics, including newly proposed metrics for abnormal edge lengths, visual overlap in community structures and node/edge aggregation, are proposed to quantify areas of ambiguity in the drawing. These metrics and others are then displayed using a heatmap-based visualization that provides visual feedback to developers of graph drawing and visualization approaches, allowing them to quickly identify misleading areas. The novel metrics and the heatmap-based visualization allow a user to explore ambiguities in graph layouts from multiple perspectives in order to make reasonable graph layout choices. The effectiveness of the technique is demonstrated through case studies and expert reviews.
Graph run-length matrices for histopathological image segmentation.
Tosun, Akif Burak; Gunduz-Demir, Cigdem
2011-03-01
The histopathological examination of tissue specimens is essential for cancer diagnosis and grading. However, this examination is subject to a considerable amount of observer variability as it mainly relies on visual interpretation of pathologists. To alleviate this problem, it is very important to develop computational quantitative tools, for which image segmentation constitutes the core step. In this paper, we introduce an effective and robust algorithm for the segmentation of histopathological tissue images. This algorithm incorporates the background knowledge of the tissue organization into segmentation. For this purpose, it quantifies spatial relations of cytological tissue components by constructing a graph and uses this graph to define new texture features for image segmentation. This new texture definition makes use of the idea of gray-level run-length matrices. However, it considers the runs of cytological components on a graph to form a matrix, instead of considering the runs of pixel intensities. Working with colon tissue images, our experiments demonstrate that the texture features extracted from "graph run-length matrices" lead to high segmentation accuracies, also providing a reasonable number of segmented regions. Compared with four other segmentation algorithms, the results show that the proposed algorithm is more effective in histopathological image segmentation.
Hybrid graphs as a framework for the small-world effect
NASA Astrophysics Data System (ADS)
Lehmann, Katharina A.; Post, Hendrik D.; Kaufmann, Michael
2006-05-01
In this paper we formalize the small-world effect which describes the surprising fact that a hybrid graph composed of a local graph component and a very sparse random graph has a diameter of O(lnn) whereby the diameter of both components alone is much higher. We show that a large family of these hybrid graphs shows this effect and that this generalized family also includes classic small-world models proposed by various authors although not all of them are captured by the small-world definition given by Watts and Strogatz. Furthermore, we give a detailed upper bound of the hybrid’s graph diameter for different choices of the expected number of random edges by applying a new kind of proof pattern that is applicable to a large number of hybrid graphs. The focus in this paper is on presenting a flexible family of hybrid graphs showing the small-world effect that can be tuned closely to real-world systems.
NASA Astrophysics Data System (ADS)
Štefaňák, M.; Skoupý, S.
2016-08-01
Perfect state transfer between two marked vertices of a graph by means of a discrete-time quantum walk is analyzed. We consider the quantum walk search algorithm with two marked vertices, sender and receiver. It is shown by explicit calculation that, for the coined quantum walks on a star graph and a complete graph with self-loops, perfect state transfer between the sender and receiver vertex is achieved for an arbitrary number of vertices N in O (√{N }) steps of the walk. Finally, we show that Szegedy's walk with queries on a complete graph allows for state transfer with unit fidelity in the limit of large N .
Graph algorithms in the titan toolkit.
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.
Evolutionary Games of Multiplayer Cooperation on Graphs.
Peña, Jorge; Wu, Bin; Arranz, Jordi; Traulsen, Arne
2016-08-01
There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering. PMID:27513946
Simple scale interpolator facilitates reading of graphs
NASA Technical Reports Server (NTRS)
Fetterman, D. E., Jr.
1965-01-01
Simple transparent overlay with interpolation scale facilitates accurate, rapid reading of graph coordinate points. This device can be used for enlarging drawings and locating points on perspective drawings.
Evolutionary Games of Multiplayer Cooperation on Graphs.
Peña, Jorge; Wu, Bin; Arranz, Jordi; Traulsen, Arne
2016-08-01
There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering.
Generation of graph-state streams
Ballester, Daniel; Cho, Jaeyoon; Kim, M. S.
2011-01-15
We propose a protocol to generate a stream of mobile qubits in a graph state through a single stationary parent qubit and discuss two types of its physical implementation, namely, the generation of photonic graph states through an atomlike qubit and the generation of flying atoms through a cavity-mode photonic qubit. The generated graph states fall into an important class that can hugely reduce the resource requirement of fault-tolerant linear optics quantum computation, which was previously known to be far from realistic. In regard to the flying atoms, we also propose a heralded generation scheme, which allows for high-fidelity graph states even under the photon loss.
Evolutionary Games of Multiplayer Cooperation on Graphs
Arranz, Jordi; Traulsen, Arne
2016-01-01
There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering. PMID:27513946
Solar System Number-Crunching.
ERIC Educational Resources Information Center
Albrecht, Bob; Firedrake, George
1997-01-01
Defines terrestrial and Jovian planets and provides directions to obtain planetary data from the National Space Science Data Center Web sites. Provides "number-crunching" activities for the terrestrial planets using Texas Instruments TI-83 graphing calculators: computing volumetric mean radius and volume, density, ellipticity, speed, surface…
Guehne, Otfried; Jungnitsch, Bastian; Moroder, Tobias; Weinstein, Yaakov S.
2011-11-15
The characterization of genuine multiparticle entanglement is important for entanglement theory as well as experimental studies related to quantum-information theory. Here, we completely characterize genuine multiparticle entanglement for four-qubit states diagonal in the cluster-state basis. In addition, we give a complete characterization of multiparticle entanglement for all five-qubit graph states mixed with white noise, for states diagonal in the basis corresponding to the five-qubit Y-shaped graph, and for a family of graph states with an arbitrary number of qubits.
Hickling, T L; Hanley, W G
2005-09-29
Semantic graphs are becoming a valuable tool for organizing and discovering information in an increasingly complex analysis environment. This paper investigates the use of graph topology to measure the strength of relationships in a semantic graph. These relationships are comprised of some number of distinct paths, whose length and configuration jointly characterize the strength of association. We explore these characteristics through the use of three distinct algorithms respectively based upon an electrical conductance model, Newman and Girvan's measure of betweenness [5], and cutsets. Algorithmic performance is assessed based upon a collection of partially ordered subgraphs which were constructed according to our subjective beliefs regarding strength of association.
ERIC Educational Resources Information Center
Xi, Xiaoming
2010-01-01
Motivated by cognitive theories of graph comprehension, this study systematically manipulated characteristics of a line graph description task in a speaking test in ways to mitigate the influence of graph familiarity, a potential source of construct-irrelevant variance. It extends Xi (2005), which found that the differences in holistic scores on…
Helping Students Make Sense of Graphs: An Experimental Trial of SmartGraphs Software
ERIC Educational Resources Information Center
Zucker, Andrew; Kay, Rachel; Staudt, Carolyn
2014-01-01
Graphs are commonly used in science, mathematics, and social sciences to convey important concepts; yet students at all ages demonstrate difficulties interpreting graphs. This paper reports on an experimental study of free, Web-based software called SmartGraphs that is specifically designed to help students overcome their misconceptions regarding…
Feature Tracking Using Reeb Graphs
Weber, Gunther H.; Bremer, Peer-Timo; Day, Marcus S.; Bell, John B.; Pascucci, Valerio
2010-08-02
Tracking features and exploring their temporal dynamics can aid scientists in identifying interesting time intervals in a simulation and serve as basis for performing quantitative analyses of temporal phenomena. In this paper, we develop a novel approach for tracking subsets of isosurfaces, such as burning regions in simulated flames, which are defined as areas of high fuel consumption on a temperature isosurface. Tracking such regions as they merge and split over time can provide important insights into the impact of turbulence on the combustion process. However, the convoluted nature of the temperature isosurface and its rapid movement make this analysis particularly challenging. Our approach tracks burning regions by extracting a temperature isovolume from the four-dimensional space-time temperature field. It then obtains isosurfaces for the original simulation time steps and labels individual connected 'burning' regions based on the local fuel consumption value. Based on this information, a boundary surface between burning and non-burning regions is constructed. The Reeb graph of this boundary surface is the tracking graph for burning regions.
Clique percolation in random graphs
NASA Astrophysics Data System (ADS)
Li, Ming; Deng, Youjin; Wang, Bing-Hong
2015-10-01
As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two k cliques means that they share at least l
Graph states of prime-power dimension from generalized CNOT quantum circuit.
Chen, Lin; Zhou, D L
2016-01-01
We construct multipartite graph states whose dimension is the power of a prime number. This is realized by the finite field, as well as the generalized controlled-NOT quantum circuit acting on two qudits. We propose the standard form of graph states up to local unitary transformations and particle permutations. The form greatly simplifies the classification of graph states as we illustrate up to five qudits. We also show that some graph states are multipartite maximally entangled states in the sense that any bipartition of the system produces a bipartite maximally entangled state. We further prove that 4-partite maximally entangled states exist when the dimension is an odd number at least three or a multiple of four. PMID:27272401
Graph states of prime-power dimension from generalized CNOT quantum circuit
Chen, Lin; Zhou, D. L.
2016-01-01
We construct multipartite graph states whose dimension is the power of a prime number. This is realized by the finite field, as well as the generalized controlled-NOT quantum circuit acting on two qudits. We propose the standard form of graph states up to local unitary transformations and particle permutations. The form greatly simplifies the classification of graph states as we illustrate up to five qudits. We also show that some graph states are multipartite maximally entangled states in the sense that any bipartition of the system produces a bipartite maximally entangled state. We further prove that 4-partite maximally entangled states exist when the dimension is an odd number at least three or a multiple of four. PMID:27272401
Graph states of prime-power dimension from generalized CNOT quantum circuit.
Chen, Lin; Zhou, D L
2016-06-07
We construct multipartite graph states whose dimension is the power of a prime number. This is realized by the finite field, as well as the generalized controlled-NOT quantum circuit acting on two qudits. We propose the standard form of graph states up to local unitary transformations and particle permutations. The form greatly simplifies the classification of graph states as we illustrate up to five qudits. We also show that some graph states are multipartite maximally entangled states in the sense that any bipartition of the system produces a bipartite maximally entangled state. We further prove that 4-partite maximally entangled states exist when the dimension is an odd number at least three or a multiple of four.
Spanning trees on graphs and lattices in d dimensions
NASA Astrophysics Data System (ADS)
Shrock, Robert; Wu, F. Y.
2000-06-01
The problem of enumerating spanning trees on graphs and lattices is considered. We obtain bounds on the number of spanning trees NST and establish inequalities relating the numbers of spanning trees of different graphs or lattices. A general formulation is presented for the enumeration of spanning trees on lattices in d≥2 dimensions, and is applied to the hypercubic, body-centred cubic, face-centred cubic and specific planar lattices including the kagomé, diced, 4-8-8 (bathroom-tile), Union Jack and 3-12-12 lattices. This leads to closed-form expressions for NST for these lattices of finite sizes. We prove a theorem concerning the classes of graphs and lattices →∞, where zL is a finite non-zero constant. This includes the bulk limit of lattices in any spatial dimension, and also sections of lattices whose lengths in some dimensions go to infinity while others are finite. We evaluate zL exactly for the lattices we consider, and discuss the dependence of zL on d and the lattice coordination number. We also establish a relation connecting zL to the free energy of the critical Ising model for planar lattices.
A framework for graph-based synthesis, analysis, and visualization of HPC cluster job data.
Mayo, Jackson R.; Kegelmeyer, W. Philip, Jr.; Wong, Matthew H.; Pebay, Philippe Pierre; Gentile, Ann C.; Thompson, David C.; Roe, Diana C.; De Sapio, Vincent; Brandt, James M.
2010-08-01
The monitoring and system analysis of high performance computing (HPC) clusters is of increasing importance to the HPC community. Analysis of HPC job data can be used to characterize system usage and diagnose and examine failure modes and their effects. This analysis is not straightforward, however, due to the complex relationships that exist between jobs. These relationships are based on a number of factors, including shared compute nodes between jobs, proximity of jobs in time, etc. Graph-based techniques represent an approach that is particularly well suited to this problem, and provide an effective technique for discovering important relationships in job queuing and execution data. The efficacy of these techniques is rooted in the use of a semantic graph as a knowledge representation tool. In a semantic graph job data, represented in a combination of numerical and textual forms, can be flexibly processed into edges, with corresponding weights, expressing relationships between jobs, nodes, users, and other relevant entities. This graph-based representation permits formal manipulation by a number of analysis algorithms. This report presents a methodology and software implementation that leverages semantic graph-based techniques for the system-level monitoring and analysis of HPC clusters based on job queuing and execution data. Ontology development and graph synthesis is discussed with respect to the domain of HPC job data. The framework developed automates the synthesis of graphs from a database of job information. It also provides a front end, enabling visualization of the synthesized graphs. Additionally, an analysis engine is incorporated that provides performance analysis, graph-based clustering, and failure prediction capabilities for HPC systems.
Cyber Graph Queries for Geographically Distributed Data Centers
Berry, Jonathan W.; Collins, Michael; Kearns, Aaron; Phillips, Cynthia A.; Saia, Jared
2015-05-01
We present new algorithms for a distributed model for graph computations motivated by limited information sharing we first discussed in [20]. Two or more independent entities have collected large social graphs. They wish to compute the result of running graph algorithms on the entire set of relationships. Because the information is sensitive or economically valuable, they do not wish to simply combine the information in a single location. We consider two models for computing the solution to graph algorithms in this setting: 1) limited-sharing: the two entities can share only a polylogarithmic size subgraph; 2) low-trust: the entities must not reveal any information beyond the query answer, assuming they are all honest but curious. We believe this model captures realistic constraints on cooperating autonomous data centers. We have algorithms in both setting for s - t connectivity in both models. We also give an algorithm in the low-communication model for finding a planted clique. This is an anomaly- detection problem, finding a subgraph that is larger and denser than expected. For both the low- communication algorithms, we exploit structural properties of social networks to prove perfor- mance bounds better than what is possible for general graphs. For s - t connectivity, we use known properties. For planted clique, we propose a new property: bounded number of triangles per node. This property is based upon evidence from the social science literature. We found that classic examples of social networks do not have the bounded-triangles property. This is because many social networks contain elements that are non-human, such as accounts for a business, or other automated accounts. We describe some initial attempts to distinguish human nodes from automated nodes in social networks based only on topological properties.
Teaching Discrete Mathematics with Graphing Calculators.
ERIC Educational Resources Information Center
Masat, Francis E.
Graphing calculator use is often thought of in terms of pre-calculus or continuous topics in mathematics. This paper contains examples and activities that demonstrate useful, interesting, and easy ways to use a graphing calculator with discrete topics. Examples are given for each of the following topics: functions, mathematical induction and…
Student Reasoning about Graphs in Different Contexts
ERIC Educational Resources Information Center
Ivanjek, Lana; Susac, Ana; Planinic, Maja; Andrasevic, Aneta; Milin-Sipus, Zeljka
2016-01-01
This study investigates university students' graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the…
Universal spectral statistics in quantum graphs.
Gnutzmann, Sven; Altland, Alexander
2004-11-01
We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random-matrix theory. The stability of these correlations with regard to nonuniversal corrections is analyzed in terms of the linear operator governing the classical dynamics on the graph.
Graphs and Statistics: A Resource Handbook.
ERIC Educational Resources Information Center
New York State Education Dept., Albany. Bureau of General Education Curriculum Development.
Graphical representation of statistical data is the focus of this resource handbook. Only graphs which present numerical information are discussed. Activities involving the making, interpreting, and use of various types of graphs and tables are included. Sections are also included which discuss statistical terms, normal distribution and…
Using a Microcomputer for Graphing Practice.
ERIC Educational Resources Information Center
Beichner, Robert J.
1986-01-01
Describes a laboratory exercise that introduces physics students to graphing. Presents the program format and sample output of a computer simulation of an experiment which tests the effects of sound intensity on the crawling speed of a snail. Provides students with practice in making exponential or logarithmic graphs. (ML)
Graphing Calculators: The Newest Revolution in Mathematics.
ERIC Educational Resources Information Center
Clutter, Martha
1999-01-01
Asserts that there are numerous advantages to using graphing calculators, including the teaching of higher-level thinking skills and allowing students to draw conclusions about what they are learning. However, mathematics educators face such challenges as teaching students when it is appropriate to use graphing calculators, course-content…
Multi-A Graph Patrolling and Partitioning
NASA Astrophysics Data System (ADS)
Elor, Y.; Bruckstein, A. M.
2012-12-01
We introduce a novel multi agent patrolling algorithm inspired by the behavior of gas filled balloons. Very low capability ant-like agents are considered with the task of patrolling an unknown area modeled as a graph. While executing the proposed algorithm, the agents dynamically partition the graph between them using simple local interactions, every agent assuming the responsibility for patrolling his subgraph. Balanced graph partition is an emergent behavior due to the local interactions between the agents in the swarm. Extensive simulations on various graphs (environments) showed that the average time to reach a balanced partition is linear with the graph size. The simulations yielded a convincing argument for conjecturing that if the graph being patrolled contains a balanced partition, the agents will find it. However, we could not prove this. Nevertheless, we have proved that if a balanced partition is reached, the maximum time lag between two successive visits to any vertex using the proposed strategy is at most twice the optimal so the patrol quality is at least half the optimal. In case of weighted graphs the patrol quality is at least (1)/(2){lmin}/{lmax} of the optimal where lmax (lmin) is the longest (shortest) edge in the graph.
Cognitive Aids for Guiding Graph Comprehension
ERIC Educational Resources Information Center
Mautone, Patricia D.; Mayer, Richard E.
2007-01-01
This study sought to improve students' comprehension of scientific graphs by adapting scaffolding techniques used to aid text comprehension. In 3 experiments involving 121 female and 88 male college students, some students were shown cognitive aids prior to viewing 4 geography graphs whereas others were not; all students were then asked to write a…
Pattern Perception and the Comprehension of Graphs.
ERIC Educational Resources Information Center
Pinker, Steven
Three experiments tested the hypothesis that graphs convey information effectively because they can display global trends as geometric patterns that visual systems encode easily. A novel type of graph was invented in which angles/lengths of line segments joined end-to-end represented variables of rainfall and temperature of a set of months. It was…
Developing Data Graph Comprehension. Third Edition
ERIC Educational Resources Information Center
Curcio, Frances
2010-01-01
Since the dawn of civilization, pictorial representations and symbols have been used to communicate simple statistics. Efficient and effective, they are still used today in the form of pictures and graphs to record and present data. Who can tie their shoes? How many calories are in your favorite food? Make data and graphs relevant and interesting…
A Ring Construction Using Finite Directed Graphs
ERIC Educational Resources Information Center
Bardzell, Michael
2012-01-01
In this paper we discuss an interesting class of noncommutative rings which can be constructed using finite directed graphs. This construction also creates a vector space. These structures provide undergraduate students connections between ring theory and graph theory and, among other things, allow them to see a ring unity element that looks quite…
TI-83 Graphing Calculator Keystroke Guide.
ERIC Educational Resources Information Center
Panik, Cathy
This document presents keystrokes for the Texas Instrument (TI-83) graphing calculator. After presenting some basic TI-83 keystrokes, activities for student practice are listed. This is followed by keystrokes for TI-83 advanced functions such as evaluating function values, finding the zero of a function, finding the intersection of two graphs,…
Supplantation of Mental Operations on Graphs
ERIC Educational Resources Information Center
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…
Graph Mining Meets the Semantic Web
Lee, Sangkeun; Sukumar, Sreenivas R; Lim, Seung-Hwan
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 linear area embedding of planar graphs
NASA Astrophysics Data System (ADS)
Dolev, D.; Trickey, H.
1981-09-01
Planar embedding with minimal area of graphs on an integer grid is one of the major issues in VLSI. Valiant (V) gave an algorithm to construct a planar embedding for trees in linear area; he also proved that there are planar graphs that require quadratic area. An algorithm to embed outerplanar graphs in linear area is given. This algorithm is extended to work for every planar graph that has the following property: for every vertex there exists a path of length less than K to the exterior face, where K is a constant. Finally, finding a minimal embedding area is shown to be NP-complete for forests, and hence more general types of graphs.
Structure and strategy in encoding simplified graphs
NASA Technical Reports Server (NTRS)
Schiano, Diane J.; Tversky, Barbara
1992-01-01
Tversky and Schiano (1989) found a systematic bias toward the 45-deg line in memory for the slopes of identical lines when embedded in graphs, but not in maps, suggesting the use of a cognitive reference frame specifically for encoding meaningful graphs. The present experiments explore this issue further using the linear configurations alone as stimuli. Experiments 1 and 2 demonstrate that perception and immediate memory for the slope of a test line within orthogonal 'axes' are predictable from purely structural considerations. In Experiments 3 and 4, subjects were instructed to use a diagonal-reference strategy in viewing the stimuli, which were described as 'graphs' only in Experiment 3. Results for both studies showed the diagonal bias previously found only for graphs. This pattern provides converging evidence for the diagonal as a cognitive reference frame in encoding linear graphs, and demonstrates that even in highly simplified displays, strategic factors can produce encoding biases not predictable solely from stimulus structure alone.
Hierarchical, 4-connected Small-World Graph
NASA Astrophysics Data System (ADS)
Goncalves, Bruno; Boettcher, Stefan
2008-03-01
A new sequences of graphs are introduced that mimic small-world properties. The graphs are recursively constructed but retain a fixed, regular degree. They consist of a one-dimensional lattice backbone overlayed by a hierarchical sequence of long-distance links in a pattern reminiscent of the tower-of-hanoi sequence. These 4-regular graphs are non-planar, have a diameter growing as 2^√2N^2 (or as [2N]^α with α˜√2N^2/22N^2), and a nontrivial phase transition Tc>0, for the Ising ferromagnet. These results suggest that these graphs are similar to small-world graphs with mean-field-like properties.
Quantum graphs and random-matrix theory
NASA Astrophysics Data System (ADS)
Pluhař, Z.; Weidenmüller, H. A.
2015-07-01
For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas-Giannoni-Schmit (BGS) conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that the generating function for every (P,Q) correlation function for both closed and open graphs coincides with the corresponding expression of random-matrix theory. We show that the classical Perron-Frobenius operator is bistochastic and possesses a single eigenvalue +1. In the quantum case that implies the existence of a zero (or massless) mode of the effective action. That mode causes universal fluctuation properties. Avoiding the saddle-point approximation we show that for graphs that are classically mixing (i.e. for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap) and that do not carry a special class of bound states, the zero mode dominates in the limit of infinite graph size.
NASA Astrophysics Data System (ADS)
Debnath, Lokenath
2010-09-01
This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Königsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real physical systems are included. We also mention some important and modern applications of graph theory or network problems from transportation to telecommunications. Graphs or networks are effectively used as powerful tools in industrial, electrical and civil engineering, communication networks in the planning of business and industry. Graph theory and combinatorics can be used to understand the changes that occur in many large and complex scientific, technical and medical systems. With the advent of fast large computers and the ubiquitous Internet consisting of a very large network of computers, large-scale complex optimization problems can be modelled in terms of graphs or networks and then solved by algorithms available in graph theory. Many large and more complex combinatorial problems dealing with the possible arrangements of situations of various kinds, and computing the number and properties of such arrangements can be formulated in terms of networks. The Knight's tour problem, Hamilton's tour problem, problem of magic squares, the Euler Graeco-Latin squares problem and their modern developments in the twentieth century are also included.
Review on Graph Clustering and Subgraph Similarity Based Analysis of Neurological Disorders
Thomas, Jaya; Seo, Dongmin; Sael, Lee
2016-01-01
How can complex relationships among molecular or clinico-pathological entities of neurological disorders be represented and analyzed? Graphs seem to be the current answer to the question no matter the type of information: molecular data, brain images or neural signals. We review a wide spectrum of graph representation and graph analysis methods and their application in the study of both the genomic level and the phenotypic level of the neurological disorder. We find numerous research works that create, process and analyze graphs formed from one or a few data types to gain an understanding of specific aspects of the neurological disorders. Furthermore, with the increasing number of data of various types becoming available for neurological disorders, we find that integrative analysis approaches that combine several types of data are being recognized as a way to gain a global understanding of the diseases. Although there are still not many integrative analyses of graphs due to the complexity in analysis, multi-layer graph analysis is a promising framework that can incorporate various data types. We describe and discuss the benefits of the multi-layer graph framework for studies of neurological disease. PMID:27258269
Review on Graph Clustering and Subgraph Similarity Based Analysis of Neurological Disorders.
Thomas, Jaya; Seo, Dongmin; Sael, Lee
2016-06-01
How can complex relationships among molecular or clinico-pathological entities of neurological disorders be represented and analyzed? Graphs seem to be the current answer to the question no matter the type of information: molecular data, brain images or neural signals. We review a wide spectrum of graph representation and graph analysis methods and their application in the study of both the genomic level and the phenotypic level of the neurological disorder. We find numerous research works that create, process and analyze graphs formed from one or a few data types to gain an understanding of specific aspects of the neurological disorders. Furthermore, with the increasing number of data of various types becoming available for neurological disorders, we find that integrative analysis approaches that combine several types of data are being recognized as a way to gain a global understanding of the diseases. Although there are still not many integrative analyses of graphs due to the complexity in analysis, multi-layer graph analysis is a promising framework that can incorporate various data types. We describe and discuss the benefits of the multi-layer graph framework for studies of neurological disease.
GraphReduce: Large-Scale Graph Analytics on Accelerator-Based HPC Systems
Sengupta, Dipanjan; Agarwal, Kapil; Song, Shuaiwen; Schwan, Karsten
2015-09-30
Recent work on real-world graph analytics has sought to leverage the massive amount of parallelism offered by GPU devices, but challenges remain due to the inherent irregularity of graph algorithms and limitations in GPU-resident memory for storing large graphs. We present GraphReduce, a highly efficient and scalable GPU-based framework that operates on graphs that exceed the device’s internal memory capacity. GraphReduce adopts a combination of both edge- and vertex-centric implementations of the Gather-Apply-Scatter programming model and operates on multiple asynchronous GPU streams to fully exploit the high degrees of parallelism in GPUs with efficient graph data movement between the host and the device.
GraphReduce: Processing Large-Scale Graphs on Accelerator-Based Systems
Sengupta, Dipanjan; Song, Shuaiwen; Agarwal, Kapil; Schwan, Karsten
2015-11-15
Recent work on real-world graph analytics has sought to leverage the massive amount of parallelism offered by GPU devices, but challenges remain due to the inherent irregularity of graph algorithms and limitations in GPU-resident memory for storing large graphs. We present GraphReduce, a highly efficient and scalable GPU-based framework that operates on graphs that exceed the device’s internal memory capacity. GraphReduce adopts a combination of edge- and vertex-centric implementations of the Gather-Apply-Scatter programming model and operates on multiple asynchronous GPU streams to fully exploit the high degrees of parallelism in GPUs with efficient graph data movement between the host and device.
Balanced Paths in Colored Graphs
NASA Astrophysics Data System (ADS)
Bianco, Alessandro; Faella, Marco; Mogavero, Fabio; Murano, Aniello
We consider finite graphs whose edges are labeled with elements, called colors, taken from a fixed finite alphabet. We study the problem of determining whether there is an infinite path where either (i) all colors occur with the same asymptotic frequency, or (ii) there is a constant which bounds the difference between the occurrences of any two colors for all prefixes of the path. These two notions can be viewed as refinements of the classical notion of fair path, whose simplest form checks whether all colors occur infinitely often. Our notions provide stronger criteria, particularly suitable for scheduling applications based on a coarse-grained model of the jobs involved. We show that both problems are solvable in polynomial time, by reducing them to the feasibility of a linear program.
Relativity on rotated graph paper
NASA Astrophysics Data System (ADS)
Salgado, Roberto B.
2016-05-01
We demonstrate a method for constructing spacetime diagrams for special relativity on graph paper that has been rotated by 45°. The diagonal grid lines represent light-flash worldlines in Minkowski spacetime, and the boxes in the grid (called "clock diamonds") represent units of measurement corresponding to the ticks of an inertial observer's light clock. We show that many quantitative results can be read off a spacetime diagram simply by counting boxes, with very little algebra. In particular, we show that the squared interval between two events is equal to the signed area of the parallelogram on the grid (called the "causal diamond") with opposite vertices corresponding to those events. We use the Doppler effect—without explicit use of the Doppler formula—to motivate the method.
Graph Theoretical Analysis Reveals: Women's Brains Are Better Connected than Men's.
Szalkai, Balázs; Varga, Bálint; Grolmusz, Vince
2015-01-01
Deep graph-theoretic ideas in the context with the graph of the World Wide Web led to the definition of Google's PageRank and the subsequent rise of the most popular search engine to date. Brain graphs, or connectomes, are being widely explored today. We believe that non-trivial graph theoretic concepts, similarly as it happened in the case of the World Wide Web, will lead to discoveries enlightening the structural and also the functional details of the animal and human brains. When scientists examine large networks of tens or hundreds of millions of vertices, only fast algorithms can be applied because of the size constraints. In the case of diffusion MRI-based structural human brain imaging, the effective vertex number of the connectomes, or brain graphs derived from the data is on the scale of several hundred today. That size facilitates applying strict mathematical graph algorithms even for some hard-to-compute (or NP-hard) quantities like vertex cover or balanced minimum cut. In the present work we have examined brain graphs, computed from the data of the Human Connectome Project, recorded from male and female subjects between ages 22 and 35. Significant differences were found between the male and female structural brain graphs: we show that the average female connectome has more edges, is a better expander graph, has larger minimal bisection width, and has more spanning trees than the average male connectome. Since the average female brain weighs less than the brain of males, these properties show that the female brain has better graph theoretical properties, in a sense, than the brain of males. It is known that the female brain has a smaller gray matter/white matter ratio than males, that is, a larger white matter/gray matter ratio than the brain of males; this observation is in line with our findings concerning the number of edges, since the white matter consists of myelinated axons, which, in turn, roughly correspond to the connections in the brain graph
Graph Theoretical Analysis Reveals: Women’s Brains Are Better Connected than Men’s
Szalkai, Balázs; Varga, Bálint; Grolmusz, Vince
2015-01-01
Deep graph-theoretic ideas in the context with the graph of the World Wide Web led to the definition of Google’s PageRank and the subsequent rise of the most popular search engine to date. Brain graphs, or connectomes, are being widely explored today. We believe that non-trivial graph theoretic concepts, similarly as it happened in the case of the World Wide Web, will lead to discoveries enlightening the structural and also the functional details of the animal and human brains. When scientists examine large networks of tens or hundreds of millions of vertices, only fast algorithms can be applied because of the size constraints. In the case of diffusion MRI-based structural human brain imaging, the effective vertex number of the connectomes, or brain graphs derived from the data is on the scale of several hundred today. That size facilitates applying strict mathematical graph algorithms even for some hard-to-compute (or NP-hard) quantities like vertex cover or balanced minimum cut. In the present work we have examined brain graphs, computed from the data of the Human Connectome Project, recorded from male and female subjects between ages 22 and 35. Significant differences were found between the male and female structural brain graphs: we show that the average female connectome has more edges, is a better expander graph, has larger minimal bisection width, and has more spanning trees than the average male connectome. Since the average female brain weighs less than the brain of males, these properties show that the female brain has better graph theoretical properties, in a sense, than the brain of males. It is known that the female brain has a smaller gray matter/white matter ratio than males, that is, a larger white matter/gray matter ratio than the brain of males; this observation is in line with our findings concerning the number of edges, since the white matter consists of myelinated axons, which, in turn, roughly correspond to the connections in the brain graph
Survival time of the susceptible-infected-susceptible infection process on a graph
NASA Astrophysics Data System (ADS)
van de Bovenkamp, Ruud; Van Mieghem, Piet
2015-09-01
The survival time T is the longest time that a virus, a meme, or a failure can propagate in a network. Using the hitting time of the absorbing state in an uniformized embedded Markov chain of the continuous-time susceptible-infected-susceptible (SIS) Markov process, we derive an exact expression for the average survival time E [T ] of a virus in the complete graph KN and the star graph K1 ,N -1. By using the survival time, instead of the average fraction of infected nodes, we propose a new method to approximate the SIS epidemic threshold τc that, at least for KN and K1 ,N -1, correctly scales with the number of nodes N and that is superior to the epidemic threshold τc(1 )=1/λ1 of the N-intertwined mean-field approximation, where λ1 is the spectral radius of the adjacency matrix of the graph G . Although this new approximation of the epidemic threshold offers a more intuitive understanding of the SIS process, it remains difficult to compare outbreaks in different graph types. For example, the survival in an arbitrary graph seems upper bounded by the complete graph and lower bounded by the star graph as a function of the normalized effective infection rate τ/τc(1 ). However, when the average fraction of infected nodes is used as a basis for comparison, the virus will survive in the star graph longer than in any other graph, making the star graph the worst-case graph instead of the complete graph. Finally, in non-Markovian SIS, the distribution of the spreading attempts over the infectious period of a node influences the survival time, even if the expected number of spreading attempts during an infectious period (the non-Markovian equivalent of the effective infection rate) is kept constant. Both early and late infection attempts lead to shorter survival times. Interestingly, just as in Markovian SIS, the survival times appear to be exponentially distributed, regardless of the infection and curing time distributions.
Survival time of the susceptible-infected-susceptible infection process on a graph.
van de Bovenkamp, Ruud; Van Mieghem, Piet
2015-09-01
The survival time T is the longest time that a virus, a meme, or a failure can propagate in a network. Using the hitting time of the absorbing state in an uniformized embedded Markov chain of the continuous-time susceptible-infected-susceptible (SIS) Markov process, we derive an exact expression for the average survival time E[T] of a virus in the complete graph K_{N} and the star graph K_{1,N-1}. By using the survival time, instead of the average fraction of infected nodes, we propose a new method to approximate the SIS epidemic threshold τ_{c} that, at least for K_{N} and K_{1,N-1}, correctly scales with the number of nodes N and that is superior to the epidemic threshold τ_{c}^{(1)}=1/λ_{1} of the N-intertwined mean-field approximation, where λ_{1} is the spectral radius of the adjacency matrix of the graph G. Although this new approximation of the epidemic threshold offers a more intuitive understanding of the SIS process, it remains difficult to compare outbreaks in different graph types. For example, the survival in an arbitrary graph seems upper bounded by the complete graph and lower bounded by the star graph as a function of the normalized effective infection rate τ/τ_{c}^{(1)}. However, when the average fraction of infected nodes is used as a basis for comparison, the virus will survive in the star graph longer than in any other graph, making the star graph the worst-case graph instead of the complete graph. Finally, in non-Markovian SIS, the distribution of the spreading attempts over the infectious period of a node influences the survival time, even if the expected number of spreading attempts during an infectious period (the non-Markovian equivalent of the effective infection rate) is kept constant. Both early and late infection attempts lead to shorter survival times. Interestingly, just as in Markovian SIS, the survival times appear to be exponentially distributed, regardless of the infection and curing time distributions. PMID:26465527
Survival time of the susceptible-infected-susceptible infection process on a graph.
van de Bovenkamp, Ruud; Van Mieghem, Piet
2015-09-01
The survival time T is the longest time that a virus, a meme, or a failure can propagate in a network. Using the hitting time of the absorbing state in an uniformized embedded Markov chain of the continuous-time susceptible-infected-susceptible (SIS) Markov process, we derive an exact expression for the average survival time E[T] of a virus in the complete graph K_{N} and the star graph K_{1,N-1}. By using the survival time, instead of the average fraction of infected nodes, we propose a new method to approximate the SIS epidemic threshold τ_{c} that, at least for K_{N} and K_{1,N-1}, correctly scales with the number of nodes N and that is superior to the epidemic threshold τ_{c}^{(1)}=1/λ_{1} of the N-intertwined mean-field approximation, where λ_{1} is the spectral radius of the adjacency matrix of the graph G. Although this new approximation of the epidemic threshold offers a more intuitive understanding of the SIS process, it remains difficult to compare outbreaks in different graph types. For example, the survival in an arbitrary graph seems upper bounded by the complete graph and lower bounded by the star graph as a function of the normalized effective infection rate τ/τ_{c}^{(1)}. However, when the average fraction of infected nodes is used as a basis for comparison, the virus will survive in the star graph longer than in any other graph, making the star graph the worst-case graph instead of the complete graph. Finally, in non-Markovian SIS, the distribution of the spreading attempts over the infectious period of a node influences the survival time, even if the expected number of spreading attempts during an infectious period (the non-Markovian equivalent of the effective infection rate) is kept constant. Both early and late infection attempts lead to shorter survival times. Interestingly, just as in Markovian SIS, the survival times appear to be exponentially distributed, regardless of the infection and curing time distributions.
Measuring geographic segregation: a graph-based approach
NASA Astrophysics Data System (ADS)
Hong, Seong-Yun; Sadahiro, Yukio
2014-04-01
Residential segregation is a multidimensional phenomenon that encompasses several conceptually distinct aspects of geographical separation between populations. While various indices have been developed as a response to different definitions of segregation, the reliance on such single-figure indices could oversimplify the complex, multidimensional phenomena. In this regard, this paper suggests an alternative graph-based approach that provides more detailed information than simple indices: The concentration profile graphically conveys information about how evenly a population group is distributed over the study region, and the spatial proximity profile depicts the degree of clustering across different threshold levels. These graphs can also be summarized into single numbers for comparative purposes, but the interpretation can be more accurate by inspecting the additional information. To demonstrate the use of these methods, the residential patterns of three major ethnic groups in Auckland, namely Māori, Pacific peoples, and Asians, are examined using the 2006 census data.
Massive graph visualization : LDRD final report.
Wylie, Brian Neil; Moreland, Kenneth D.
2007-10-01
Graphs are a vital way of organizing data with complex correlations. A good visualization of a graph can fundamentally change human understanding of the data. Consequently, there is a rich body of work on graph visualization. Although there are many techniques that are effective on small to medium sized graphs (tens of thousands of nodes), there is a void in the research for visualizing massive graphs containing millions of nodes. Sandia is one of the few entities in the world that has the means and motivation to handle data on such a massive scale. For example, homeland security generates graphs from prolific media sources such as television, telephone, and the Internet. The purpose of this project is to provide the groundwork for visualizing such massive graphs. The research provides for two major feature gaps: a parallel, interactive visualization framework and scalable algorithms to make the framework usable to a practical application. Both the frameworks and algorithms are designed to run on distributed parallel computers, which are already available at Sandia. Some features are integrated into the ThreatView{trademark} application and future work will integrate further parallel algorithms.
Graph isomorphism and adiabatic quantum computing
NASA Astrophysics Data System (ADS)
Gaitan, Frank; Clark, Lane
2014-03-01
In the Graph Isomorphism (GI) problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and maps G --> G'. If yes (no), then G and G' are said to be isomorphic (non-isomorphic). The GI problem is an important problem in computer science and is thought to be of comparable difficulty to integer factorization. We present a quantum algorithm that solves arbitrary instances of GI, and which provides a novel approach to determining all automorphisms of a graph. The algorithm converts a GI instance to a combinatorial optimization problem that can be solved using adiabatic quantum evolution. Numerical simulation of the algorithm's quantum dynamics shows that it correctly distinguishes non-isomorphic graphs; recognizes isomorphic graphs; and finds the automorphism group of a graph. We also discuss the algorithm's experimental implementation and show how it can be leveraged to solve arbitrary instances of the NP-Complete Sub-Graph Isomorphism problem.
Sketch Matching on Topology Product Graph.
Liang, Shuang; Luo, Jun; Liu, Wenyin; Wei, Yichen
2015-08-01
Sketch matching is the fundamental problem in sketch based interfaces. After years of study, it remains challenging when there exists large irregularity and variations in the hand drawn sketch shapes. While most existing works exploit topology relations and graph representations for this problem, they are usually limited by the coarse topology exploration and heuristic (thus suboptimal) similarity metrics between graphs. We present a new sketch matching method with two novel contributions. We introduce a comprehensive definition of topology relations, which results in a rich and informative graph representation of sketches. For graph matching, we propose topology product graph that retains the full correspondence for matching two graphs. Based on it, we derive an intuitive sketch similarity metric whose exact solution is easy to compute. In addition, the graph representation and new metric naturally support partial matching, an important practical problem that received less attention in the literature. Extensive experimental results on a real challenging dataset and the superior performance of our method show that it outperforms the state-of-the-art.
Partitioning sparse matrices with eigenvectors of graphs
NASA Technical Reports Server (NTRS)
Pothen, Alex; Simon, Horst D.; Liou, Kang-Pu
1990-01-01
The problem of computing a small vertex separator in a graph arises in the context of computing a good ordering for the parallel factorization of sparse, symmetric matrices. An algebraic approach for computing vertex separators is considered in this paper. It is shown that lower bounds on separator sizes can be obtained in terms of the eigenvalues of the Laplacian matrix associated with a graph. The Laplacian eigenvectors of grid graphs can be computed from Kronecker products involving the eigenvectors of path graphs, and these eigenvectors can be used to compute good separators in grid graphs. A heuristic algorithm is designed to compute a vertex separator in a general graph by first computing an edge separator in the graph from an eigenvector of the Laplacian matrix, and then using a maximum matching in a subgraph to compute the vertex separator. Results on the quality of the separators computed by the spectral algorithm are presented, and these are compared with separators obtained from other algorithms for computing separators. Finally, the time required to compute the Laplacian eigenvector is reported, and the accuracy with which the eigenvector must be computed to obtain good separators is considered. The spectral algorithm has the advantage that it can be implemented on a medium-size multiprocessor in a straightforward manner.
Lamplighter groups, de Brujin graphs, spider-web graphs and their spectra
NASA Astrophysics Data System (ADS)
Grigorchuk, R.; Leemann, P.-H.; Nagnibeda, T.
2016-05-01
We study the infinite family of spider-web graphs \\{{{ S }}k,N,M\\}, k≥slant 2, N≥slant 0 and M≥slant 1, initiated in the 50s in the context of network theory. It was later shown in physical literature that these graphs have remarkable percolation and spectral properties. We provide a mathematical explanation of these properties by putting the spider-web graphs in the context of group theory and algebraic graph theory. Namely, we realize them as tensor products of the well-known de Bruijn graphs \\{{{ B }}k,N\\} with cyclic graphs \\{{C}M\\} and show that these graphs are described by the action of the lamplighter group {{ L }}k={Z}/k{Z}\\wr {Z} on the infinite binary tree. Our main result is the identification of the infinite limit of \\{{{ S }}k,N,M\\}, as N,M\\to ∞ , with the Cayley graph of the lamplighter group {{ L }}k which, in turn, is one of the famous Diestel–Leader graphs {{DL}}k,k. As an application we compute the spectra of all spider-web graphs and show their convergence to the discrete spectral distribution associated with the Laplacian on the lamplighter group.
Lamplighter groups, de Brujin graphs, spider-web graphs and their spectra
NASA Astrophysics Data System (ADS)
Grigorchuk, R.; Leemann, P.-H.; Nagnibeda, T.
2016-05-01
We study the infinite family of spider-web graphs \\{{{ S }}k,N,M\\}, k≥slant 2, N≥slant 0 and M≥slant 1, initiated in the 50s in the context of network theory. It was later shown in physical literature that these graphs have remarkable percolation and spectral properties. We provide a mathematical explanation of these properties by putting the spider-web graphs in the context of group theory and algebraic graph theory. Namely, we realize them as tensor products of the well-known de Bruijn graphs \\{{{ B }}k,N\\} with cyclic graphs \\{{C}M\\} and show that these graphs are described by the action of the lamplighter group {{ L }}k={Z}/k{Z}\\wr {Z} on the infinite binary tree. Our main result is the identification of the infinite limit of \\{{{ S }}k,N,M\\}, as N,M\\to ∞ , with the Cayley graph of the lamplighter group {{ L }}k which, in turn, is one of the famous Diestel-Leader graphs {{DL}}k,k. As an application we compute the spectra of all spider-web graphs and show their convergence to the discrete spectral distribution associated with the Laplacian on the lamplighter group.
BioGraphE: high-performance bionetwork analysis using the Biological Graph Environment
Chin, George; Chavarria, Daniel G; Nakamura, Grant C; Sofia, Heidi J
2008-01-01
Background Graphs and networks are common analysis representations for biological systems. Many traditional graph algorithms such as k-clique, k-coloring, and subgraph matching have great potential as analysis techniques for newly available data in biology. Yet, as the amount of genomic and bionetwork information rapidly grows, scientists need advanced new computational strategies and tools for dealing with the complexities of the bionetwork analysis and the volume of the data. Results We introduce a computational framework for graph analysis called the Biological Graph Environment (BioGraphE), which provides a general, scalable integration platform for connecting graph problems in biology to optimized computational solvers and high-performance systems. This framework enables biology researchers and computational scientists to identify and deploy network analysis applications and to easily connect them to efficient and powerful computational software and hardware that are specifically designed and tuned to solve complex graph problems. In our particular application of BioGraphE to support network analysis in genome biology, we investigate the use of a Boolean satisfiability solver known as Survey Propagation as a core computational solver executing on standard high-performance parallel systems, as well as multi-threaded architectures. Conclusion In our application of BioGraphE to conduct bionetwork analysis of homology networks, we found that BioGraphE and a custom, parallel implementation of the Survey Propagation SAT solver were capable of solving very large bionetwork problems at high rates of execution on different high-performance computing platforms. PMID:18541059
Enabling Graph Mining in RDF Triplestores using SPARQL for Holistic In-situ Graph Analysis
Lee, Sangkeun; Sukumar, Sreenivas R; Hong, Seokyong; Lim, Seung-Hwan
2016-01-01
The graph analysis is now considered as a promising technique to discover useful knowledge in data with a new perspective. We envi- sion that there are two dimensions of graph analysis: OnLine Graph Analytic Processing (OLGAP) and Graph Mining (GM) where each respectively focuses on subgraph pattern matching and automatic knowledge discovery in graph. Moreover, as these two dimensions aim to complementarily solve complex problems, holistic in-situ graph analysis which covers both OLGAP and GM in a single system is critical for minimizing the burdens of operating multiple graph systems and transferring intermediate result-sets between those systems. Nevertheless, most existing graph analysis systems are only capable of one dimension of graph analysis. In this work, we take an approach to enabling GM capabilities (e.g., PageRank, connected-component analysis, node eccentricity, etc.) in RDF triplestores, which are originally developed to store RDF datasets and provide OLGAP capability. More specifically, to achieve our goal, we implemented six representative graph mining algorithms using SPARQL. The approach allows a wide range of available RDF data sets directly applicable for holistic graph analysis within a system. For validation of our approach, we evaluate performance of our implementations with nine real-world datasets and three different computing environments - a laptop computer, an Amazon EC2 instance, and a shared-memory Cray XMT2 URIKA-GD graph-processing appliance. The experimen- tal results show that our implementation can provide promising and scalable performance for real world graph analysis in all tested environments. The developed software is publicly available in an open-source project that we initiated.
Enabling Graph Mining in RDF Triplestores using SPARQL for Holistic In-situ Graph Analysis
Lee, Sangkeun; Sukumar, Sreenivas R; Hong, Seokyong; Lim, Seung-Hwan
2016-01-01
The graph analysis is now considered as a promising technique to discover useful knowledge in data with a new perspective. We envi- sion that there are two dimensions of graph analysis: OnLine Graph Analytic Processing (OLGAP) and Graph Mining (GM) where each respectively focuses on subgraph pattern matching and automatic knowledge discovery in graph. Moreover, as these two dimensions aim to complementarily solve complex problems, holistic in-situ graph analysis which covers both OLGAP and GM in a single system is critical for minimizing the burdens of operating multiple graph systems and transferring intermediate result-sets between those systems. Nevertheless, most existingmore » graph analysis systems are only capable of one dimension of graph analysis. In this work, we take an approach to enabling GM capabilities (e.g., PageRank, connected-component analysis, node eccentricity, etc.) in RDF triplestores, which are originally developed to store RDF datasets and provide OLGAP capability. More specifically, to achieve our goal, we implemented six representative graph mining algorithms using SPARQL. The approach allows a wide range of available RDF data sets directly applicable for holistic graph analysis within a system. For validation of our approach, we evaluate performance of our implementations with nine real-world datasets and three different computing environments - a laptop computer, an Amazon EC2 instance, and a shared-memory Cray XMT2 URIKA-GD graph-processing appliance. The experimen- tal results show that our implementation can provide promising and scalable performance for real world graph analysis in all tested environments. The developed software is publicly available in an open-source project that we initiated.« less
Rapidly Mixing Gibbs Sampling for a Class of Factor Graphs Using Hierarchy Width
De Sa, Christopher; Zhang, Ce; Olukotun, Kunle; Ré, Christopher
2016-01-01
Gibbs sampling on factor graphs is a widely used inference technique, which often produces good empirical results. Theoretical guarantees for its performance are weak: even for tree structured graphs, the mixing time of Gibbs may be exponential in the number of variables. To help understand the behavior of Gibbs sampling, we introduce a new (hyper)graph property, called hierarchy width. We show that under suitable conditions on the weights, bounded hierarchy width ensures polynomial mixing time. Our study of hierarchy width is in part motivated by a class of factor graph templates, hierarchical templates, which have bounded hierarchy width—regardless of the data used to instantiate them. We demonstrate a rich application from natural language processing in which Gibbs sampling provably mixes rapidly and achieves accuracy that exceeds human volunteers. PMID:27279724
Graph-theoretic independence as a predictor of fullerene stability
NASA Astrophysics Data System (ADS)
Fajtlowicz, S.; Larson, C. E.
2003-08-01
The independence number of the graph of a fullerene, the size of the largest set of vertices such that no two are adjacent (corresponding to the largest set of atoms of the molecule, no pair of which are bonded), appears to be a useful selector in identifying stable fullerene isomers. The experimentally characterized isomers with 60, 70 and 76 atoms uniquely minimize this number among the classes of possible structures with, respectively, 60, 70 and 76 atoms. Other experimentally characterized isomers also rank extremely low with respect to this invariant. These findings were initiated by a conjecture of the computer program Graffiti.
Intelligent Graph Layout Using Many Users' Input.
Yuan, Xiaoru; Che, Limei; Hu, Yifan; Zhang, Xin
2012-12-01
In this paper, we propose a new strategy for graph drawing utilizing layouts of many sub-graphs supplied by a large group of people in a crowd sourcing manner. We developed an algorithm based on Laplacian constrained distance embedding to merge subgraphs submitted by different users, while attempting to maintain the topological information of the individual input layouts. To facilitate collection of layouts from many people, a light-weight interactive system has been designed to enable convenient dynamic viewing, modification and traversing between layouts. Compared with other existing graph layout algorithms, our approach can achieve more aesthetic and meaningful layouts with high user preference.
Line graphs for a multiplex network.
Criado, Regino; Flores, Julio; García Del Amo, Alejandro; Romance, Miguel; Barrena, Eva; Mesa, Juan A
2016-06-01
It is well known that line graphs offer a good summary of the graphs properties, which make them easier to analyze and highlight the desired properties. We extend the concept of line graph to multiplex networks in order to analyze multi-plexed and multi-layered networked systems. As these structures are very rich, different approaches to this notion are required to capture a variety of situations. Some relationships between these approaches are established. Finally, by means of some simulations, the potential utility of this concept is illustrated.
Line graphs for a multiplex network.
Criado, Regino; Flores, Julio; García Del Amo, Alejandro; Romance, Miguel; Barrena, Eva; Mesa, Juan A
2016-06-01
It is well known that line graphs offer a good summary of the graphs properties, which make them easier to analyze and highlight the desired properties. We extend the concept of line graph to multiplex networks in order to analyze multi-plexed and multi-layered networked systems. As these structures are very rich, different approaches to this notion are required to capture a variety of situations. Some relationships between these approaches are established. Finally, by means of some simulations, the potential utility of this concept is illustrated. PMID:27368798
Graph states for quantum secret sharing
NASA Astrophysics Data System (ADS)
Markham, Damian; Sanders, Barry C.
2008-10-01
We consider three broad classes of quantum secret sharing with and without eavesdropping and show how a graph state formalism unifies otherwise disparate quantum secret sharing models. In addition to the elegant unification provided by graph states, our approach provides a generalization of threshold classical secret sharing via insecure quantum channels beyond the current requirement of 100% collaboration by players to just a simple majority in the case of five players. Another innovation here is the introduction of embedded protocols within a larger graph state that serves as a one-way quantum-information processing system.
The MultiThreaded Graph Library (MTGL)
Berry, Jonathan; Leung, Vitus; McLendon, III, William; & Madduri, Kamesh
2008-07-17
The MultiThreaded Graph Library (MTGL) is a set of header files that implement graph algorithm in such a way that they can run on massively multithreaded architectures. It is based upon the Boost Graph Library, but doesnÃÂÃÂ¢ÃÂÃÂÃÂÃÂt use Boost since the latter doesnÃÂÃÂ¢ÃÂÃÂÃÂÃÂt run well on these architectures.
A heterogeneous graph-based recommendation simulator
Yeonchan, Ahn; Sungchan, Park; Lee, Matt Sangkeun; Sang-goo, Lee
2013-01-01
Heterogeneous graph-based recommendation frameworks have flexibility in that they can incorporate various recommendation algorithms and various kinds of information to produce better results. In this demonstration, we present a heterogeneous graph-based recommendation simulator which enables participants to experience the flexibility of a heterogeneous graph-based recommendation method. With our system, participants can simulate various recommendation semantics by expressing the semantics via meaningful paths like User Movie User Movie. The simulator then returns the recommendation results on the fly based on the user-customized semantics using a fast Monte Carlo algorithm.
Linear game non-contextuality and Bell inequalities—a graph-theoretic approach
NASA Astrophysics Data System (ADS)
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.
A graph-based approach for designing extensible pipelines
2012-01-01
://code.google.com/p/dynamic-pipeline. The system has been tested on Linux and Windows platforms. Conclusions Our graph-based approach enables the automatic creation of pipelines by compiling a specialised set of tools on demand, depending on the functionality required. It also allows the implementation of extensible and low-maintenance pipelines and contributes towards consolidating openness and collaboration in bioinformatics systems. It is targeted at pipeline developers and is suited for implementing applications with sequential execution steps and combined functionalities. In the format conversion application, the automatic combination of conversion tools increased both the number of possible conversions available to the user and the extensibility of the system to allow for future updates with new file formats. PMID:22788675
Hegarty, Peter; Lemieux, Anthony F; McQueen, Grant
2010-03-01
Graphs seem to connote facts more than words or tables do. Consequently, they seem unlikely places to spot implicit sexism at work. Yet, in 6 studies (N = 741), women and men constructed (Study 1) and recalled (Study 2) gender difference graphs with men's data first, and graphed powerful groups (Study 3) and individuals (Study 4) ahead of weaker ones. Participants who interpreted graph order as evidence of author "bias" inferred that the author graphed his or her own gender group first (Study 5). Women's, but not men's, preferences to graph men first were mitigated when participants graphed a difference between themselves and an opposite-sex friend prior to graphing gender differences (Study 6). Graph production and comprehension are affected by beliefs and suppositions about the groups represented in graphs to a greater degree than cognitive models of graph comprehension or realist models of scientific thinking have yet acknowledged.
A bipartite graph of Neuroendocrine System
NASA Astrophysics Data System (ADS)
Guo, Zhong-Wei; Zou, Sheng-Rong; Peng, Yu-Jing; Zhou, Ta; Gu, Chang-Gui; He, Da-Ren
2008-03-01
We present an empirical investigation on the neuroendocrine system and suggest describe it by a bipartite graph. In the net the cells can be regarded as collaboration acts and the mediators can be regarded as collaboration actors. The act degree stands for the number of the cells that secrete a single mediator. Among them bFGF (the basic fibroblast growth factor) has the largest node act degree. It is the most important mitogenic cytokine, followed by TGF-beta, IL-6, IL1-beta, VEGF, IGF-1and so on. They are critical in neuroendocrine system to maintain bodily healthiness, emotional stabilization and endocrine harmony. The act degree distribution shows a shifted power law (SPL) function forms [1]. The average act degree of neuroendocrine network is h=3.01, It means that each mediator is secreted by three cells on average. The similarity, which stands for the average probability of secreting the same mediators by all neuroendocrine cells, is observed as s=0.14. Our results may be used in the research of the medical treatment of neuroendocrine diseases. [1] Assortativity and act degree distribution of some collaboration networks, Hui Chang, Bei-Bei Su, Yue-Ping Zhou, Daren He, Physica A, 383 (2007) 687-702
Protein flexibility predictions using graph theory.
Jacobs, D J; Rader, A J; Kuhn, L A; Thorpe, M F
2001-08-01
Techniques from graph theory are applied to analyze the bond networks in proteins and identify the flexible and rigid regions. The bond network consists of distance constraints defined by the covalent and hydrogen bonds and salt bridges in the protein, identified by geometric and energetic criteria. We use an algorithm that counts the degrees of freedom within this constraint network and that identifies all the rigid and flexible substructures in the protein, including overconstrained regions (with more crosslinking bonds than are needed to rigidify the region) and underconstrained or flexible regions, in which dihedral bond rotations can occur. The number of extra constraints or remaining degrees of bond-rotational freedom within a substructure quantifies its relative rigidity/flexibility and provides a flexibility index for each bond in the structure. This novel computational procedure, first used in the analysis of glassy materials, is approximately a million times faster than molecular dynamics simulations and captures the essential conformational flexibility of the protein main and side-chains from analysis of a single, static three-dimensional structure. This approach is demonstrated by comparison with experimental measures of flexibility for three proteins in which hinge and loop motion are essential for biological function: HIV protease, adenylate kinase, and dihydrofolate reductase.
Experiments on parallel graph coloring and applications
Lewandowski, G.; Condon, A.
1994-12-31
The graph coloring problem is an NP-Complete problem with a wide array of applications, such as course scheduling, exam scheduling, register allocation, and parallelizing solutions for sparse systems of linear equations. Much theoretical effort has been put into designing heuristics that perform well on randomly generated graphs. The best sequential heuristics require large amounts of time and tuning of various parameters in the heuristics. We have used parallelism to combine exhaustive search with successful heuristic strategies to create a new heuristic, Hybrid, which does well on a wide variety of graphs, without any tuning of parameters. We have also gathered real application data and tested several heuristics on this data. Our study of real data points out some flaws in studying only random graphs and also suggests interesting new problems for study.
D'Azevedo, Ed F; Imam, Neena
2015-01-01
This document describes the effort to implement the Graph 500 benchmark using OpenSHMEM based on the MPI-2 one-side version. The Graph 500 benchmark performs a breadth-first search in parallel on a large randomly generated undirected graph and can be implemented using basic MPI-1 and MPI-2 one-sided communication. Graph 500 requires atomic bit-wise operations on unsigned long integers but neither atomic bit-wise operations nor OpenSHMEM for unsigned long are available in OpenSHEM. Such needed bit-wise atomic operations and support for unsigned long are implemented using atomic condition swap (CSWAP) on signed long integers. Preliminary results on comparing the OpenSHMEM and MPI-2 one-sided implementations on a Silicon Graphics Incorporated (SGI) cluster and the Cray XK7 are presented.
An Investigation of the Coauthor Graph.
ERIC Educational Resources Information Center
Logan, Elisabeth L.; Shaw, W. M., Jr.
1987-01-01
The role of the coauthor relationship in the structure of informal communications networks within disciplines is explored, and the validity of coauthor graphs used to map these relationships is tested for both small and large databases. (CLB)
The signed permutation group on Feynman graphs
NASA Astrophysics Data System (ADS)
Purkart, Julian
2016-08-01
The Feynman rules assign to every graph an integral which can be written as a function of a scaling parameter L. Assuming L for the process under consideration is very small, so that contributions to the renormalization group are small, we can expand the integral and only consider the lowest orders in the scaling. The aim of this article is to determine specific combinations of graphs in a scalar quantum field theory that lead to a remarkable simplification of the first non-trivial term in the perturbation series. It will be seen that the result is independent of the renormalization scheme and the scattering angles. To achieve that goal we will utilize the parametric representation of scalar Feynman integrals as well as the Hopf algebraic structure of the Feynman graphs under consideration. Moreover, we will present a formula which reduces the effort of determining the first-order term in the perturbation series for the specific combination of graphs to a minimum.
Bipartite graph partitioning and data clustering
Zha, Hongyuan; He, Xiaofeng; Ding, Chris; Gu, Ming; Simon, Horst D.
2001-05-07
Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie recommender system. In this paper, the authors propose a new data clustering method based on partitioning the underlying biopartite graph. The partition is constructed by minimizing a normalized sum of edge weights between unmatched pairs of vertices of the bipartite graph. They show that an approximate solution to the minimization problem can be obtained by computing a partial singular value decomposition (SVD) of the associated edge weight matrix of the bipartite graph. They point out the connection of their clustering algorithm to correspondence analysis used in multivariate analysis. They also briefly discuss the issue of assigning data objects to multiple clusters. In the experimental results, they apply their clustering algorithm to the problem of document clustering to illustrate its effectiveness and efficiency.
Fault-tolerant dynamic task graph scheduling
Kurt, Mehmet C.; Krishnamoorthy, Sriram; Agrawal, Kunal; Agrawal, Gagan
2014-11-16
In this paper, we present an approach to fault tolerant execution of dynamic task graphs scheduled using work stealing. In particular, we focus on selective and localized recovery of tasks in the presence of soft faults. We elicit from the user the basic task graph structure in terms of successor and predecessor relationships. The work stealing-based algorithm to schedule such a task graph is augmented to enable recovery when the data and meta-data associated with a task get corrupted. We use this redundancy, and the knowledge of the task graph structure, to selectively recover from faults with low space and time overheads. We show that the fault tolerant design retains the essential properties of the underlying work stealing-based task scheduling algorithm, and that the fault tolerant execution is asymptotically optimal when task re-execution is taken into account. Experimental evaluation demonstrates the low cost of recovery under various fault scenarios.
Teaching Waves with a Graphing Calculator.
ERIC Educational Resources Information Center
Raggett, Matthew
2000-01-01
Stresses the value of graphing and computer algebra systems calculators when teaching about waves. Discusses how to input data into these calculators. Highlights the Texas Instruments' (TI) Web site at http://www.ti.com. (YDS)
Continuous Time Group Discovery in Dynamic Graphs
Miller, K; Eliassi-Rad, T
2010-11-04
With the rise in availability and importance of graphs and networks, it has become increasingly important to have good models to describe their behavior. While much work has focused on modeling static graphs, we focus on group discovery in dynamic graphs. We adapt a dynamic extension of Latent Dirichlet Allocation to this task and demonstrate good performance on two datasets. Modeling relational data has become increasingly important in recent years. Much work has focused on static graphs - that is fixed graphs at a single point in time. Here we focus on the problem of modeling dynamic (i.e. time-evolving) graphs. We propose a scalable Bayesian approach for community discovery in dynamic graphs. Our approach is based on extensions of Latent Dirichlet Allocation (LDA). LDA is a latent variable model for topic modeling in text corpora. It was extended to deal with topic changes in discrete time and later in continuous time. These models were referred to as the discrete Dynamic Topic Model (dDTM) and the continuous Dynamic Topic Model (cDTM), respectively. When adapting these models to graphs, we take our inspiration from LDA-G and SSN-LDA, applications of LDA to static graphs that have been shown to effectively factor out community structure to explain link patterns in graphs. In this paper, we demonstrate how to adapt and apply the cDTM to the task of finding communities in dynamic networks. We use link prediction to measure the quality of the discovered community structure and apply it to two different relational datasets - DBLP author-keyword and CAIDA autonomous systems relationships. We also discuss a parallel implementation of this approach using Hadoop. In Section 2, we review LDA and LDA-G. In Section 3, we review the cDTM and introduce cDTMG, its adaptation to modeling dynamic graphs. We discuss inference for the cDTM-G and details of our parallel implementation in Section 4 and present its performance on two datasets in Section 5 before concluding in
Community detection in graphs using singular value decomposition.
Sarkar, Somwrita; Dong, Andy
2011-04-01
A spectral algorithm for community detection is presented. The algorithm consists of three stages: (1) matrix factorization of two matrix forms, square signless Laplacian for unipartite graphs and rectangular adjacency matrix for bipartite graphs, using singular value decompostion (SVD); (2) dimensionality reduction using an optimal linear approximation; and (3) clustering vertices using dot products in reduced dimensional space. The algorithm reveals communities in graphs without placing any restriction on the input network type or the output community type. It is applicable on unipartite or bipartite unweighted or weighted networks. It places no requirement on strict community membership and automatically reveals the number of clusters, their respective sizes and overlaps, and hierarchical modular organization. By representing vertices as vectors in real space, expressed as linear combinations of the orthogonal bases described by SVD, orthogonality becomes the metric for classifying vertices into communities. Results on several test and real world networks are presented, including cases where a mix of disjointed, overlapping, or hierarchical communities are known to exist in the network. PMID:21599247
Optimizing spread dynamics on graphs by message passing
NASA Astrophysics Data System (ADS)
Altarelli, F.; Braunstein, A.; Dall'Asta, L.; Zecchina, R.
2013-09-01
Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully applied to describe cascades in a large variety of contexts. Over the past decades, much effort has been devoted to understanding the typical behavior of the cascades arising from initial conditions extracted at random from some given ensemble. However, the problem of optimizing the trajectory of the system, i.e. of identifying appropriate initial conditions to maximize (or minimize) the final number of active nodes, is still considered to be practically intractable, with the only exception being models that satisfy a sort of diminishing returns property called submodularity. Submodular models can be approximately solved by means of greedy strategies, but by definition they lack cooperative characteristics which are fundamental in many real systems. Here we introduce an efficient algorithm based on statistical physics for the optimization of trajectories in cascade processes on graphs. We show that for a wide class of irreversible dynamics, even in the absence of submodularity, the spread optimization problem can be solved efficiently on large networks. Analytic and algorithmic results on random graphs are complemented by the solution of the spread maximization problem on a real-world network (the Epinions consumer reviews network).
Bipartite Graphs for Visualization Analysis of Microbiome Data
Sedlar, Karel; Videnska, Petra; Skutkova, Helena; Rychlik, Ivan; Provaznik, Ivo
2016-01-01
Visualization analysis plays an important role in metagenomics research. Proper and clear visualization can help researchers get their first insights into data and by selecting different features, also revealing and highlighting hidden relationships and drawing conclusions. To prevent the resulting presentations from becoming chaotic, visualization techniques have to properly tackle the high dimensionality of microbiome data. Although a number of different methods based on dimensionality reduction, correlations, Venn diagrams, and network representations have already been published, there is still room for further improvement, especially in the techniques that allow visual comparison of several environments or developmental stages in one environment. In this article, we represent microbiome data by bipartite graphs, where one partition stands for taxa and the other stands for samples. We demonstrated that community detection is independent of taxonomical level. Moreover, focusing on higher taxonomical levels and the appropriate merging of samples greatly helps improving graph organization and makes our presentations clearer than other graph and network visualizations. Capturing labels in the vertices also brings the possibility of clearly comparing two or more microbial communities by showing their common and unique parts. PMID:27279729
An improved approach of register allocation via graph coloring
NASA Astrophysics Data System (ADS)
Gao, Lei; Shi, Ce
2005-03-01
Register allocation is an important part of optimizing compiler. The algorithm of register allocation via graph coloring is implemented by Chaitin and his colleagues firstly and improved by Briggs and others. By abstracting register allocation to graph coloring, the allocation process is simplified. As the physical register number is limited, coloring of the interference graph can"t succeed for every node. The uncolored nodes must be spilled. There is an assumption that almost all the allocation method obeys: when a register is allocated to a variable v, it can"t be used by others before v quit even if v is not used for a long time. This may causes a waste of register resource. The authors relax this restriction under certain conditions and make some improvement. In this method, one register can be mapped to two or more interfered "living" live ranges at the same time if they satisfy some requirements. An operation named merge is defined which can arrange two interfered nodes occupy the same register with some cost. Thus, the resource of register can be used more effectively and the cost of memory access can be reduced greatly.
Pre-Service Elementary Teachers' Understandings of Graphs
ERIC Educational Resources Information Center
Alacaci, Cengiz; Lewis, Scott; O'Brien, George E.; Jiang, Zhonghong
2011-01-01
Choosing graphs to display quantitative information is a component of "graph sense". An important aspect of pre-service elementary teachers' content knowledge; ability to choose appropriate graphs in applied contexts is investigated in this study. They were given three scenarios followed by four graphs representing the same quantitative data. They…
Accelerating semantic graph databases on commodity clusters
Morari, Alessandro; Castellana, Vito G.; Haglin, David J.; Feo, John T.; Weaver, Jesse R.; Tumeo, Antonino; Villa, Oreste
2013-10-06
We are developing a full software system for accelerating semantic graph databases on commodity cluster that scales to hundreds of nodes while maintaining constant query throughput. Our framework comprises a SPARQL to C++ compiler, a library of parallel graph methods and a custom multithreaded runtime layer, which provides a Partitioned Global Address Space (PGAS) programming model with fork/join parallelism and automatic load balancing over a commodity clusters. We present preliminary results for the compiler and for the runtime.
A software tool for dataflow graph scheduling
NASA Technical Reports Server (NTRS)
Jones, Robert L., III
1994-01-01
A graph-theoretic design process and software tool is presented for selecting a multiprocessing scheduling solution for a class of computational problems. The problems of interest are those that can be described using a dataflow graph and are intended to be executed repetitively on multiple processors. The dataflow paradigm is very useful in exposing the parallelism inherent in algorithms. It provides a graphical and mathematical model which describes a partial ordering of algorithm tasks based on data precedence.
Program for Generating Graphs and Charts
NASA Technical Reports Server (NTRS)
Ackerson, C. T.
1986-01-01
Office Automation Pilot (OAP) Graphics Database system offers IBM personal computer user assistance in producing wide variety of graphs and charts and convenient data-base system, called chart base, for creating and maintaining data associated with graphs and charts. Thirteen different graphics packages available. Access graphics capabilities obtained in similar manner. User chooses creation, revision, or chartbase-maintenance options from initial menu; Enters or modifies data displayed on graphic chart. OAP graphics data-base system written in Microsoft PASCAL.
A Fermi golden rule for quantum graphs
NASA Astrophysics Data System (ADS)
Lee, Minjae; Zworski, Maciej
2016-09-01
We present a Fermi golden rule giving rates of decay of states obtained by perturbing embedded eigenvalues of a quantum graph. To illustrate the procedure in a notationally simpler setting, we first describe a Fermi golden rule for boundary value problems on surfaces with constant curvature cusps. We also provide a resonance existence result which is uniform on compact sets of energies and metric graphs. The results are illustrated by numerical experiments.
The Vertex Version of Weighted Wiener Number for Bicyclic Molecular Structures.
Gao, Wei; Wang, Weifan
2015-01-01
Graphs are used to model chemical compounds and drugs. In the graphs, each vertex represents an atom of molecule and edges between the corresponding vertices are used to represent covalent bounds between atoms. We call such a graph, which is derived from a chemical compound, a molecular graph. Evidence shows that the vertex-weighted Wiener number, which is defined over this molecular graph, is strongly correlated to both the melting point and boiling point of the compounds. In this paper, we report the extremal vertex-weighted Wiener number of bicyclic molecular graph in terms of molecular structural analysis and graph transformations. The promising prospects of the application for the chemical and pharmacy engineering are illustrated by theoretical results achieved in this paper. PMID:26640513
The Vertex Version of Weighted Wiener Number for Bicyclic Molecular Structures
Gao, Wei; Wang, Weifan
2015-01-01
Graphs are used to model chemical compounds and drugs. In the graphs, each vertex represents an atom of molecule and edges between the corresponding vertices are used to represent covalent bounds between atoms. We call such a graph, which is derived from a chemical compound, a molecular graph. Evidence shows that the vertex-weighted Wiener number, which is defined over this molecular graph, is strongly correlated to both the melting point and boiling point of the compounds. In this paper, we report the extremal vertex-weighted Wiener number of bicyclic molecular graph in terms of molecular structural analysis and graph transformations. The promising prospects of the application for the chemical and pharmacy engineering are illustrated by theoretical results achieved in this paper. PMID:26640513
Graph representation of protein free energy landscape
Li, Minghai; Duan, Mojie; Fan, Jue; Huo, Shuanghong; Han, Li
2013-11-14
The thermodynamics and kinetics of protein folding and protein conformational changes are governed by the underlying free energy landscape. However, the multidimensional nature of the free energy landscape makes it difficult to describe. We propose to use a weighted-graph approach to depict the free energy landscape with the nodes on the graph representing the conformational states and the edge weights reflecting the free energy barriers between the states. Our graph is constructed from a molecular dynamics trajectory and does not involve projecting the multi-dimensional free energy landscape onto a low-dimensional space defined by a few order parameters. The calculation of free energy barriers was based on transition-path theory using the MSMBuilder2 package. We compare our graph with the widely used transition disconnectivity graph (TRDG) which is constructed from the same trajectory and show that our approach gives more accurate description of the free energy landscape than the TRDG approach even though the latter can be organized into a simple tree representation. The weighted-graph is a general approach and can be used on any complex system.
Graph representation of protein free energy landscape.
Li, Minghai; Duan, Mojie; Fan, Jue; Han, Li; Huo, Shuanghong
2013-11-14
The thermodynamics and kinetics of protein folding and protein conformational changes are governed by the underlying free energy landscape. However, the multidimensional nature of the free energy landscape makes it difficult to describe. We propose to use a weighted-graph approach to depict the free energy landscape with the nodes on the graph representing the conformational states and the edge weights reflecting the free energy barriers between the states. Our graph is constructed from a molecular dynamics trajectory and does not involve projecting the multi-dimensional free energy landscape onto a low-dimensional space defined by a few order parameters. The calculation of free energy barriers was based on transition-path theory using the MSMBuilder2 package. We compare our graph with the widely used transition disconnectivity graph (TRDG) which is constructed from the same trajectory and show that our approach gives more accurate description of the free energy landscape than the TRDG approach even though the latter can be organized into a simple tree representation. The weighted-graph is a general approach and can be used on any complex system.
Student reasoning about graphs in different contexts
NASA Astrophysics Data System (ADS)
Ivanjek, Lana; Susac, Ana; Planinic, Maja; Andrasevic, Aneta; Milin-Sipus, Zeljka
2016-06-01
This study investigates university students' graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the Faculty of Science, University of Zagreb. Students were asked to provide explanations and/or mathematical procedures with their answers. Students' main strategies and difficulties identified through the analysis of those explanations and procedures are described. Student strategies of graph interpretation were found to be largely context dependent and domain specific. A small fraction of students have used the same strategy in all three domains (mathematics, physics, and other contexts) on most sets of parallel questions. Some students have shown indications of transfer of knowledge in the sense that they used techniques and strategies developed in physics for solving (or attempting to solve) other context problems. In physics, the preferred strategy was the use of formulas, which sometimes seemed to block the use of other, more productive strategies which students displayed in other domains. Students' answers indicated the presence of slope-height confusion and interval-point confusion in all three domains. Students generally better interpreted graph slope than the area under a graph, although the concept of slope still seemed to be quite vague for many. The interpretation of the concept of area under a graph needs more attention in both physics and mathematics teaching.
Bipartite separability and nonlocal quantum operations on graphs
NASA Astrophysics Data System (ADS)
Dutta, Supriyo; Adhikari, Bibhas; Banerjee, Subhashish; Srikanth, R.
2016-07-01
In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for separability, although there are entangled states with positive partial transpose for which the degree criterion fails. Here we introduce the concept of partially symmetric graphs and degree symmetric graphs by using the well-known concept of partial transposition of a graph and degree criteria, respectively. Thus, we provide classes of bipartite separable states of dimension m ×n arising from partially symmetric graphs. We identify partially asymmetric graphs that lack the property of partial symmetry. We develop a combinatorial procedure to create a partially asymmetric graph from a given partially symmetric graph. We show that this combinatorial operation can act as an entanglement generator for mixed states arising from partially symmetric graphs.
NASA Astrophysics Data System (ADS)
Zhou, Haijun; Wang, Chuang
2012-08-01
Graphical models for finite-dimensional spin glasses and real-world combinatorial optimization and satisfaction problems usually have an abundant number of short loops. The cluster variation method and its extension, the region graph method, are theoretical approaches for treating the complicated short-loop-induced local correlations. For graphical models represented by non-redundant or redundant region graphs, approximate free energy landscapes are constructed in this paper through the mathematical framework of region graph partition function expansion. Several free energy functionals are obtained, each of which use a set of probability distribution functions or functionals as order parameters. These probability distribution function/functionals are required to satisfy the region graph belief-propagation equation or the region graph survey-propagation equation to ensure vanishing correction contributions of region subgraphs with dangling edges. As a simple application of the general theory, we perform region graph belief-propagation simulations on the square-lattice ferromagnetic Ising model and the Edwards-Anderson model. Considerable improvements over the conventional Bethe-Peierls approximation are achieved. Collective domains of different sizes in the disordered and frustrated square lattice are identified by the message-passing procedure. Such collective domains and the frustrations among them are responsible for the low-temperature glass-like dynamical behaviors of the system.
Preserving Differential Privacy in Degree-Correlation based Graph Generation
Wang, Yue; Wu, Xintao
2014-01-01
Enabling accurate analysis of social network data while preserving differential privacy has been challenging since graph features such as cluster coefficient often have high sensitivity, which is different from traditional aggregate functions (e.g., count and sum) on tabular data. In this paper, we study the problem of enforcing edge differential privacy in graph generation. The idea is to enforce differential privacy on graph model parameters learned from the original network and then generate the graphs for releasing using the graph model with the private parameters. In particular, we develop a differential privacy preserving graph generator based on the dK-graph generation model. We first derive from the original graph various parameters (i.e., degree correlations) used in the dK-graph model, then enforce edge differential privacy on the learned parameters, and finally use the dK-graph model with the perturbed parameters to generate graphs. For the 2K-graph model, we enforce the edge differential privacy by calibrating noise based on the smooth sensitivity, rather than the global sensitivity. By doing this, we achieve the strict differential privacy guarantee with smaller magnitude noise. We conduct experiments on four real networks and compare the performance of our private dK-graph models with the stochastic Kronecker graph generation model in terms of utility and privacy tradeoff. Empirical evaluations show the developed private dK-graph generation models significantly outperform the approach based on the stochastic Kronecker generation model. PMID:24723987
Preserving Differential Privacy in Degree-Correlation based Graph Generation.
Wang, Yue; Wu, Xintao
2013-08-01
Enabling accurate analysis of social network data while preserving differential privacy has been challenging since graph features such as cluster coefficient often have high sensitivity, which is different from traditional aggregate functions (e.g., count and sum) on tabular data. In this paper, we study the problem of enforcing edge differential privacy in graph generation. The idea is to enforce differential privacy on graph model parameters learned from the original network and then generate the graphs for releasing using the graph model with the private parameters. In particular, we develop a differential privacy preserving graph generator based on the dK-graph generation model. We first derive from the original graph various parameters (i.e., degree correlations) used in the dK-graph model, then enforce edge differential privacy on the learned parameters, and finally use the dK-graph model with the perturbed parameters to generate graphs. For the 2K-graph model, we enforce the edge differential privacy by calibrating noise based on the smooth sensitivity, rather than the global sensitivity. By doing this, we achieve the strict differential privacy guarantee with smaller magnitude noise. We conduct experiments on four real networks and compare the performance of our private dK-graph models with the stochastic Kronecker graph generation model in terms of utility and privacy tradeoff. Empirical evaluations show the developed private dK-graph generation models significantly outperform the approach based on the stochastic Kronecker generation model.
A graph theoretic approach to scene matching
NASA Technical Reports Server (NTRS)
Ranganath, Heggere S.; Chipman, Laure J.
1991-01-01
The ability to match two scenes is a fundamental requirement in a variety of computer vision tasks. A graph theoretic approach to inexact scene matching is presented which is useful in dealing with problems due to imperfect image segmentation. A scene is described by a set of graphs, with nodes representing objects and arcs representing relationships between objects. Each node has a set of values representing the relations between pairs of objects, such as angle, adjacency, or distance. With this method of scene representation, the task in scene matching is to match two sets of graphs. Because of segmentation errors, variations in camera angle, illumination, and other conditions, an exact match between the sets of observed and stored graphs is usually not possible. In the developed approach, the problem is represented as an association graph, in which each node represents a possible mapping of an observed region to a stored object, and each arc represents the compatibility of two mappings. Nodes and arcs have weights indicating the merit or a region-object mapping and the degree of compatibility between two mappings. A match between the two graphs corresponds to a clique, or fully connected subgraph, in the association graph. The task is to find the clique that represents the best match. Fuzzy relaxation is used to update the node weights using the contextual information contained in the arcs and neighboring nodes. This simplifies the evaluation of cliques. A method of handling oversegmentation and undersegmentation problems is also presented. The approach is tested with a set of realistic images which exhibit many types of sementation errors.
Unraveling Protein Networks with Power Graph Analysis
Royer, Loïc; Reimann, Matthias; Andreopoulos, Bill; Schroeder, Michael
2008-01-01
Networks play a crucial role in computational biology, yet their analysis and representation is still an open problem. Power Graph Analysis is a lossless transformation of biological networks into a compact, less redundant representation, exploiting the abundance of cliques and bicliques as elementary topological motifs. We demonstrate with five examples the advantages of Power Graph Analysis. Investigating protein-protein interaction networks, we show how the catalytic subunits of the casein kinase II complex are distinguishable from the regulatory subunits, how interaction profiles and sequence phylogeny of SH3 domains correlate, and how false positive interactions among high-throughput interactions are spotted. Additionally, we demonstrate the generality of Power Graph Analysis by applying it to two other types of networks. We show how power graphs induce a clustering of both transcription factors and target genes in bipartite transcription networks, and how the erosion of a phosphatase domain in type 22 non-receptor tyrosine phosphatases is detected. We apply Power Graph Analysis to high-throughput protein interaction networks and show that up to 85% (56% on average) of the information is redundant. Experimental networks are more compressible than rewired ones of same degree distribution, indicating that experimental networks are rich in cliques and bicliques. Power Graphs are a novel representation of networks, which reduces network complexity by explicitly representing re-occurring network motifs. Power Graphs compress up to 85% of the edges in protein interaction networks and are applicable to all types of networks such as protein interactions, regulatory networks, or homology networks. PMID:18617988
ERIC Educational Resources Information Center
Deniz, Hasan; Dulger, Mehmet F.
2012-01-01
This study examined to what extent inquiry-based instruction supported with real-time graphing technology improves fourth grader's ability to interpret graphs as representations of physical science concepts such as motion and temperature. This study also examined whether there is any difference between inquiry-based instruction supported with…
ERIC Educational Resources Information Center
Gültepe, Nejla
2016-01-01
Graphing subjects in chemistry has been used to provide alternatives to verbal and algorithmic descriptions of a subject by handing students another way of improving their manipulation of concepts. Teachers should therefore know the level of students' graphing skills. Studies have identified that students have difficulty making connections with…
ERIC Educational Resources Information Center
Ubuz, Behiye
2007-01-01
This present study investigated engineering students' conceptions and misconceptions related to derivative, particularly interpreting the graph of a function and constructing its derivative graph. Participants were 147 first year engineering students from four universities enrolled in first year undergraduate calculus courses with or without the…
Counting spanning trees on fractal graphs and their asymptotic complexity
NASA Astrophysics Data System (ADS)
Anema, Jason A.; Tsougkas, Konstantinos
2016-09-01
Using the method of spectral decimation and a modified version of Kirchhoff's matrix-tree theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely ramified fractal is given in theorem 3.4. We show how spectral decimation implies the existence of the asymptotic complexity constant and obtain some bounds for it. Examples calculated include the Sierpiński gasket, a non-post critically finite analog of the Sierpiński gasket, the Diamond fractal, and the hexagasket. For each example, the asymptotic complexity constant is found.
Weighted graph based ordering techniques for preconditioned conjugate gradient methods
NASA Technical Reports Server (NTRS)
Clift, Simon S.; Tang, Wei-Pai
1994-01-01
We describe the basis of a matrix ordering heuristic for improving the incomplete factorization used in preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.
Algorithms for effective querying of compound graph-based pathway databases
2009-01-01
Background Graph-based pathway ontologies and databases are widely used to represent data about cellular processes. This representation makes it possible to programmatically integrate cellular networks and to investigate them using the well-understood concepts of graph theory in order to predict their structural and dynamic properties. An extension of this graph representation, namely hierarchically structured or compound graphs, in which a member of a biological network may recursively contain a sub-network of a somehow logically similar group of biological objects, provides many additional benefits for analysis of biological pathways, including reduction of complexity by decomposition into distinct components or modules. In this regard, it is essential to effectively query such integrated large compound networks to extract the sub-networks of interest with the help of efficient algorithms and software tools. Results Towards this goal, we developed a querying framework, along with a number of graph-theoretic algorithms from simple neighborhood queries to shortest paths to feedback loops, that is applicable to all sorts of graph-based pathway databases, from PPIs (protein-protein interactions) to metabolic and signaling pathways. The framework is unique in that it can account for compound or nested structures and ubiquitous entities present in the pathway data. In addition, the queries may be related to each other through "AND" and "OR" operators, and can be recursively organized into a tree, in which the result of one query might be a source and/or target for another, to form more complex queries. The algorithms were implemented within the querying component of a new version of the software tool PATIKAweb (Pathway Analysis Tool for Integration and Knowledge Acquisition) and have proven useful for answering a number of biologically significant questions for large graph-based pathway databases. Conclusion The PATIKA Project Web site is http
Linear Time Vertex Partitioning on Massive Graphs
Mell, Peter; Harang, Richard; Gueye, Assane
2016-01-01
The problem of optimally removing a set of vertices from a graph to minimize the size of the largest resultant component is known to be NP-complete. Prior work has provided near optimal heuristics with a high time complexity that function on up to hundreds of nodes and less optimal but faster techniques that function on up to thousands of nodes. In this work, we analyze how to perform vertex partitioning on massive graphs of tens of millions of nodes. We use a previously known and very simple heuristic technique: iteratively removing the node of largest degree and all of its edges. This approach has an apparent quadratic complexity since, upon removal of a node and adjoining set of edges, the node degree calculations must be updated prior to choosing the next node. However, we describe a linear time complexity solution using an array whose indices map to node degree and whose values are hash tables indicating the presence or absence of a node at that degree value. This approach also has a linear growth with respect to memory usage which is surprising since we lowered the time complexity from quadratic to linear. We empirically demonstrate linear scalability and linear memory usage on random graphs of up to 15000 nodes. We then demonstrate tractability on massive graphs through execution on a graph with 34 million nodes representing Internet wide router connectivity. PMID:27336059
DT-MRI segmentation using graph cuts
NASA Astrophysics Data System (ADS)
Weldeselassie, Yonas T.; Hamarneh, Ghassan
2007-03-01
An important problem in medical image analysis is the segmentation of anatomical regions of interest. Once regions of interest are segmented, one can extract shape, appearance, and structural features that can be analyzed for disease diagnosis or treatment evaluation. Diffusion tensor magnetic resonance imaging (DT-MRI) is a relatively new medical imaging modality that captures unique water diffusion properties and fiber orientation information of the imaged tissues. In this paper, we extend the interactive multidimensional graph cuts segmentation technique to operate on DT-MRI data by utilizing latest advances in tensor calculus and diffusion tensor dissimilarity metrics. The user interactively selects certain tensors as object ("obj") or background ("bkg") to provide hard constraints for the segmentation. Additional soft constraints incorporate information about both regional tissue diffusion as well as boundaries between tissues of different diffusion properties. Graph cuts are used to find globally optimal segmentation of the underlying 3D DT-MR image among all segmentations satisfying the constraints. We develop a graph structure from the underlying DT-MR image with the tensor voxels corresponding to the graph vertices and with graph edge weights computed using either Log-Euclidean or the J-divergence tensor dissimilarity metric. The topology of our segmentation is unrestricted and both obj and bkg segments may consist of several isolated parts. We test our method on synthetic DT data and apply it to real 2D and 3D MRI, providing segmentations of the corpus callosum in the brain and the ventricles of the heart.
Towards Scalable Graph Computation on Mobile Devices
Chen, Yiqi; Lin, Zhiyuan; Pienta, Robert; Kahng, Minsuk; Chau, Duen Horng
2015-01-01
Mobile devices have become increasingly central to our everyday activities, due to their portability, multi-touch capabilities, and ever-improving computational power. Such attractive features have spurred research interest in leveraging mobile devices for computation. We explore a novel approach that aims to use a single mobile device to perform scalable graph computation on large graphs that do not fit in the device's limited main memory, opening up the possibility of performing on-device analysis of large datasets, without relying on the cloud. Based on the familiar memory mapping capability provided by today's mobile operating systems, our approach to scale up computation is powerful and intentionally kept simple to maximize its applicability across the iOS and Android platforms. Our experiments demonstrate that an iPad mini can perform fast computation on large real graphs with as many as 272 million edges (Google+ social graph), at a speed that is only a few times slower than a 13″ Macbook Pro. Through creating a real world iOS app with this technique, we demonstrate the strong potential application for scalable graph computation on a single mobile device using our approach. PMID:25859564
Deformed graph laplacian for semisupervised learning.
Gong, Chen; Liu, Tongliang; Tao, Dacheng; Fu, Keren; Tu, Enmei; Yang, Jie
2015-10-01
Graph Laplacian has been widely exploited in traditional graph-based semisupervised learning (SSL) algorithms to regulate the labels of examples that vary smoothly on the graph. Although it achieves a promising performance in both transductive and inductive learning, it is not effective for handling ambiguous examples (shown in Fig. 1). This paper introduces deformed graph Laplacian (DGL) and presents label prediction via DGL (LPDGL) for SSL. The local smoothness term used in LPDGL, which regularizes examples and their neighbors locally, is able to improve classification accuracy by properly dealing with ambiguous examples. Theoretical studies reveal that LPDGL obtains the globally optimal decision function, and the free parameters are easy to tune. The generalization bound is derived based on the robustness analysis. Experiments on a variety of real-world data sets demonstrate that LPDGL achieves top-level performance on both transductive and inductive settings by comparing it with popular SSL algorithms, such as harmonic functions, AnchorGraph regularization, linear neighborhood propagation, Laplacian regularized least square, and Laplacian support vector machine.
Visualizing intelligence information using correlation graphs
NASA Astrophysics Data System (ADS)
Verma, Vivek; Gagvani, Nikhil
2005-03-01
This paper presents a new information model to help intelligence analysts in organizing, querying, and visualizing the information present in large volumes of unstructured data sources such as text reports, multi-media, and human discourse. Our primary goal is to create a system that would combine the human pattern recognition abilities of intelligence analysis with the storage and processing capabilities of computers. Our system models the collective mental map of intelligence analysts in the form of the Correlation Graph, a modified graph data structure with objects and events as nodes and subjective probabilistic correlations between them as edges. Objects are entities such as people, places, and things. Events are actions that involve the objects. A taxonomy is also associated with the model to enable intelligence domain specific querying of the data. Graph drawing techniques are used to visualize the information represented by the correlation graph. Through real world examples, we demonstrate that the resulting information model can be used for efficient representation, presentation, and querying to discover novel patterns in the intelligence data via graph visualization techniques.
Exploiting graph properties of game trees
Plaat, A.; Pijls, W.; Bruin, A. de; Schaeffer, J.
1996-12-31
The state space of most adversary games is a directed graph. However, due to the success of simple recursive algorithms based on alpha-beta, theoreticians and practitioners have concentrated on the traversal of trees, giving the field the name {open_quotes}game-tree search,{close_quotes} This paper shows that the focus on trees has obscured some important properties of the underlying graphs. One of the hallmarks of the field of game-tree search has been the notion of the minimal tree, the smallest tree that has to be searched by any algorithm to find the minimax value. In fact, for most games it is a directed graph. As demonstrated in chess and checkers, we show that the minimal graph is significantly smaller than previously thought, proving that there is more room for improvement of current algorithms. We exploit the graph properties of the search space to reduce the size of trees built in practice by at least 25%. For over a decade, fixed-depth alpha-beta searching has been considered a closed subject, with research moving on to more application-dependent techniques. This work opens up new avenues of research for further application-independent improvements.
Graph animals, subgraph sampling, and motif search in large networks
NASA Astrophysics Data System (ADS)
Baskerville, Kim; Grassberger, Peter; Paczuski, Maya
2007-09-01
We generalize a sampling algorithm for lattice animals (connected clusters on a regular lattice) to a Monte Carlo algorithm for “graph animals,” i.e., connected subgraphs in arbitrary networks. As with the algorithm in [N. Kashtan , Bioinformatics 20, 1746 (2004)], it provides a weighted sample, but the computation of the weights is much faster (linear in the size of subgraphs, instead of superexponential). This allows subgraphs with up to ten or more nodes to be sampled with very high statistics, from arbitrarily large networks. Using this together with a heuristic algorithm for rapidly classifying isomorphic graphs, we present results for two protein interaction networks obtained using the tandem affinity purification (TAP) method: one of Escherichia coli with 230 nodes and 695 links, and one for yeast (Saccharomyces cerevisiae) with roughly ten times more nodes and links. We find in both cases that most connected subgraphs are strong motifs ( Z scores >10 ) or antimotifs ( Z scores <-10 ) when the null model is the ensemble of networks with fixed degree sequence. Strong differences appear between the two networks, with dominant motifs in E. coli being (nearly) bipartite graphs and having many pairs of nodes that connect to the same neighbors, while dominant motifs in yeast tend towards completeness or contain large cliques. We also explore a number of methods that do not rely on measurements of Z scores or comparisons with null models. For instance, we discuss the influence of specific complexes like the 26S proteasome in yeast, where a small number of complexes dominate the k cores with large k and have a decisive effect on the strongest motifs with 6-8 nodes. We also present Zipf plots of counts versus rank. They show broad distributions that are not power laws, in contrast to the case when disconnected subgraphs are included.
A graph algebra for scalable visual analytics.
Shaverdian, Anna A; Zhou, Hao; Michailidis, George; Jagadish, Hosagrahar V
2012-01-01
Visual analytics (VA), which combines analytical techniques with advanced visualization features, is fast becoming a standard tool for extracting information from graph data. Researchers have developed many tools for this purpose, suggesting a need for formal methods to guide these tools' creation. Increased data demands on computing requires redesigning VA tools to consider performance and reliability in the context of analysis of exascale datasets. Furthermore, visual analysts need a way to document their analyses for reuse and results justification. A VA graph framework encapsulated in a graph algebra helps address these needs. Its atomic operators include selection and aggregation. The framework employs a visual operator and supports dynamic attributes of data to enable scalable visual exploration of data. PMID:24806630
Directed transport in quantum star graphs
NASA Astrophysics Data System (ADS)
Yusupov, Jambul; Dolgushev, Maxim; Blumen, Alexander; Mülken, Oliver
2016-04-01
We study the quantum dynamics of Gaussian wave packets on star graphs whose arms feature each a periodic potential and an external time-dependent field. Assuming that the potentials and the field can be manipulated separately for each arm of the star, we show that it is possible to manipulate the direction of the motion of a Gaussian wave packet through the bifurcation point by a suitable choice of the parameters of the external fields. In doing so, one can achieve a transmission of the wave packet into the desired arm with nearly 70 % while also keeping the shape of the wave packet approximately intact. Since a star graph is the simplest element of many other complex graphs, the obtained results can be considered as the first step to wave packet manipulations on complex networks.
Dynamic graph system for a semantic database
Mizell, David
2015-01-27
A method and system in a computer system for dynamically providing a graphical representation of a data store of entries via a matrix interface is disclosed. A dynamic graph system provides a matrix interface that exposes to an application program a graphical representation of data stored in a data store such as a semantic database storing triples. To the application program, the matrix interface represents the graph as a sparse adjacency matrix that is stored in compressed form. Each entry of the data store is considered to represent a link between nodes of the graph. Each entry has a first field and a second field identifying the nodes connected by the link and a third field with a value for the link that connects the identified nodes. The first, second, and third fields represent the rows, column, and elements of the adjacency matrix.
Interactive Web Graphs with Fewer Restrictions
NASA Technical Reports Server (NTRS)
Fiedler, James
2012-01-01
There is growing popularity for interactive, statistical web graphs and programs to generate them. However, it seems that these programs tend to be somewhat restricted in which web browsers and statistical software are supported. For example, the software might use SVG (e.g., Protovis, gridSVG) or HTML canvas, both of which exclude most versions of Internet Explorer, or the software might be made specifically for R (gridSVG, CRanvas), thus excluding users of other stats software. There are more general tools (d3, Rapha lJS) which are compatible with most browsers, but using one of these to make statistical graphs requires more coding than is probably desired, and requires learning a new tool. This talk will present a method for making interactive web graphs, which, by design, attempts to support as many browsers and as many statistical programs as possible, while also aiming to be relatively easy to use and relatively easy to extend.
A graph algebra for scalable visual analytics.
Shaverdian, Anna A; Zhou, Hao; Michailidis, George; Jagadish, Hosagrahar V
2012-01-01
Visual analytics (VA), which combines analytical techniques with advanced visualization features, is fast becoming a standard tool for extracting information from graph data. Researchers have developed many tools for this purpose, suggesting a need for formal methods to guide these tools' creation. Increased data demands on computing requires redesigning VA tools to consider performance and reliability in the context of analysis of exascale datasets. Furthermore, visual analysts need a way to document their analyses for reuse and results justification. A VA graph framework encapsulated in a graph algebra helps address these needs. Its atomic operators include selection and aggregation. The framework employs a visual operator and supports dynamic attributes of data to enable scalable visual exploration of data.
Dynamic graph system for a semantic database
Mizell, David
2016-04-12
A method and system in a computer system for dynamically providing a graphical representation of a data store of entries via a matrix interface is disclosed. A dynamic graph system provides a matrix interface that exposes to an application program a graphical representation of data stored in a data store such as a semantic database storing triples. To the application program, the matrix interface represents the graph as a sparse adjacency matrix that is stored in compressed form. Each entry of the data store is considered to represent a link between nodes of the graph. Each entry has a first field and a second field identifying the nodes connected by the link and a third field with a value for the link that connects the identified nodes. The first, second, and third fields represent the rows, column, and elements of the adjacency matrix.
The uniqueness of DMAX-matrix graph invariants.
Dehmer, Matthias; Shi, Yongtang
2014-01-01
In this paper, we examine the uniqueness (discrimination power) of a newly proposed graph invariant based on the matrix DMAX defined by Randić et al. In order to do so, we use exhaustively generated graphs instead of special graph classes such as trees only. Using these graph classes allow us to generalize the findings towards complex networks as they usually do not possess any structural constraints. We obtain that the uniqueness of this newly proposed graph invariant is approximately as low as the uniqueness of the Balaban J index on exhaustively generated (general) graphs. PMID:24392099
Graph isomorphism and adiabatic quantum computing
NASA Astrophysics Data System (ADS)
Gaitan, Frank; Clark, Lane
2014-02-01
In the graph isomorphism (GI) problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G →G'. If yes, then G and G' are said to be isomorphic; otherwise they are nonisomorphic. The GI problem is an important problem in computer science and is thought to be of comparable difficulty to integer factorization. In this paper we present a quantum algorithm that solves arbitrary instances of GI and which also provides an approach to determining all automorphisms of a given graph. We show how the GI problem can be converted to a combinatorial optimization problem that can be solved using adiabatic quantum evolution. We numerically simulate the algorithm's quantum dynamics and show that it correctly (i) distinguishes nonisomorphic graphs; (ii) recognizes isomorphic graphs and determines the permutation(s) that connect them; and (iii) finds the automorphism group of a given graph G. We then discuss the GI quantum algorithm's experimental implementation, and close by showing how it can be leveraged to give a quantum algorithm that solves arbitrary instances of the NP-complete subgraph isomorphism problem. The computational complexity of an adiabatic quantum algorithm is largely determined by the minimum energy gap Δ (N) separating the ground and first-excited states in the limit of large problem size N ≫1. Calculating Δ (N) in this limit is a fundamental open problem in adiabatic quantum computing, and so it is not possible to determine the computational complexity of adiabatic quantum algorithms in general, nor consequently, of the specific adiabatic quantum algorithms presented here. Adiabatic quantum computing has been shown to be equivalent to the circuit model of quantum computing, and so development of adiabatic quantum algorithms continues to be of great interest.
From cognitive maps to cognitive graphs.
Chrastil, Elizabeth R; Warren, William H
2014-01-01
We investigate the structure of spatial knowledge that spontaneously develops during free exploration of a novel environment. We present evidence that this structure is similar to a labeled graph: a network of topological connections between places, labeled with local metric information. In contrast to route knowledge, we find that the most frequent routes and detours to target locations had not been traveled during learning. Contrary to purely topological knowledge, participants typically traveled the shortest metric distance to a target, rather than topologically equivalent but longer paths. The results are consistent with the proposal that people learn a labeled graph of their environment.
PolyGraph: a Polymer Visualization system
NASA Astrophysics Data System (ADS)
Cutkosky, Ashok; Tarazi, Najeeb; Lieberman Aiden, Erez
2012-02-01
Rapid advances in computational hardware and parallelization have made complex simulations of large polymers increasingly ubiquitous. However, visualizing such simulations remains a challenge. Here we present PolyGraph, a Blender-powered visualization system for complex polymer simulations. As a specific example, we study molecular dynamics simulations of condensing polymers. We illustrate our initial simulation results, suggesting that formation of local beads is an initial step in the condensation process. (This finding is consistent with earlier conjectures about polymer condensation.) PolyGraph makes it possible to create precise and visually appealing clips of polymer simulations. *contributed equally
From Cognitive Maps to Cognitive Graphs
Chrastil, Elizabeth R.; Warren, William H.
2014-01-01
We investigate the structure of spatial knowledge that spontaneously develops during free exploration of a novel environment. We present evidence that this structure is similar to a labeled graph: a network of topological connections between places, labeled with local metric information. In contrast to route knowledge, we find that the most frequent routes and detours to target locations had not been traveled during learning. Contrary to purely topological knowledge, participants typically traveled the shortest metric distance to a target, rather than topologically equivalent but longer paths. The results are consistent with the proposal that people learn a labeled graph of their environment. PMID:25389769
Percolation threshold on planar Euclidean Gabriel graphs
NASA Astrophysics Data System (ADS)
Norrenbrock, Christoph
2016-04-01
In the present article, numerical simulations have been performed to find the bond and site percolation thresholds on two-dimensional Gabriel graphs (GG) for Poisson point processes. GGs belong to the family of "proximity graphs" and are discussed, e.g., in context of the construction of backbones for wireless ad-hoc networks. Finite-size scaling analyses have been performed to find the critical points and critical exponents ν, β and γ. The critical exponents obtained this way verify that the associated universality class is that of standard 2D percolation.
Isomorphisms between Petri nets and dataflow graphs
NASA Technical Reports Server (NTRS)
Kavi, Krishna M.; Buckles, Billy P.; Bhat, U. Narayan
1987-01-01
Dataflow graphs are a generalized model of computation. Uninterpreted dataflow graphs with nondeterminism resolved via probabilities are shown to be isomorphic to a class of Petri nets known as free choice nets. Petri net analysis methods are readily available in the literature and this result makes those methods accessible to dataflow research. Nevertheless, combinatorial explosion can render Petri net analysis inoperative. Using a previously known technique for decomposing free choice nets into smaller components, it is demonstrated that, in principle, it is possible to determine aspects of the overall behavior from the particular behavior of components.
Internet topology: connectivity of IP graphs
NASA Astrophysics Data System (ADS)
Broido, Andre; claffy, kc
2001-07-01
In this paper we introduce a framework for analyzing local properties of Internet connectivity. We compare BGP and probed topology data, finding that currently probed topology data yields much denser coverage of AS-level connectivity. We describe data acquisition and construction of several IP- level graphs derived from a collection of 220 M skitter traceroutes. We find that a graph consisting of IP nodes and links contains 90.5% of its 629 K nodes in the acyclic subgraph. In particular, 55% of the IP nodes are in trees. Full bidirectional connectivity is observed for a giant component containing 8.3% of IP nodes.
Lattices of processes in graphs with inputs
Shakhbazyan, K.V.
1995-09-01
This article is a continuation of others work, presenting a detailed analysis of finite lattices of processes in graphs with input nodes. Lattices of processes in such graphs are studied by representing the lattices in the form of an algebra of pairs. We define the algebra of pairs somewhat generalizing the definition. Let K and D be bounded distributive lattices. A sublattice {delta} {contained_in} K x D is called an algebra of pairs if for all K {element_of} K we have (K, 1{sub D}) {element_of} {delta} and for all d {element_of} D we have (O{sub K}).
A Similarity Search Using Molecular Topological Graphs
Fukunishi, Yoshifumi; Nakamura, Haruki
2009-01-01
A molecular similarity measure has been developed using molecular topological graphs and atomic partial charges. Two kinds of topological graphs were used. One is the ordinary adjacency matrix and the other is a matrix which represents the minimum path length between two atoms of the molecule. The ordinary adjacency matrix is suitable to compare the local structures of molecules such as functional groups, and the other matrix is suitable to compare the global structures of molecules. The combination of these two matrices gave a similarity measure. This method was applied to in silico drug screening, and the results showed that it was effective as a similarity measure. PMID:20037730
Genome alignment with graph data structures: a comparison
2014-01-01
Background Recent advances in rapid, low-cost sequencing have opened up the opportunity to study complete genome sequences. The computational approach of multiple genome alignment allows investigation of evolutionarily related genomes in an integrated fashion, providing a basis for downstream analyses such as rearrangement studies and phylogenetic inference. Graphs have proven to be a powerful tool for coping with the complexity of genome-scale sequence alignments. The potential of graphs to intuitively represent all aspects of genome alignments led to the development of graph-based approaches for genome alignment. These approaches construct a graph from a set of local alignments, and derive a genome alignment through identification and removal of graph substructures that indicate errors in the alignment. Results We compare the structures of commonly used graphs in terms of their abilities to represent alignment information. We describe how the graphs can be transformed into each other, and identify and classify graph substructures common to one or more graphs. Based on previous approaches, we compile a list of modifications that remove these substructures. Conclusion We show that crucial pieces of alignment information, associated with inversions and duplications, are not visible in the structure of all graphs. If we neglect vertex or edge labels, the graphs differ in their information content. Still, many ideas are shared among all graph-based approaches. Based on these findings, we outline a conceptual framework for graph-based genome alignment that can assist in the development of future genome alignment tools. PMID:24712884
From Many Records to One Graph: Heterogeneity Conflicts in the Linked Data Restructuring Cycle
ERIC Educational Resources Information Center
Tallerås, Kim
2013-01-01
Introduction: During the last couple of years the library community has developed a number of comprehensive metadata standardization projects inspired by the idea of linked data, such as the BIBFRAME model. Linked data is a set of best practice principles of publishing and exposing data on the Web utilizing a graph based data model powered with…
Decision graphs: a tool for developing real-time software
Kozubal, A.J.
1981-01-01
The use of decision graphs in the preparation of, in particular, real-time software is briefly described. The usefulness of decision graphs in software design, testing, and maintenance is pointed out. 2 figures. (RWR)
Graph Regularized Meta-path Based Transductive Regression in Heterogeneous Information Network
Wan, Mengting; Ouyang, Yunbo; Kaplan, Lance; Han, Jiawei
2015-01-01
A number of real-world networks are heterogeneous information networks, which are composed of different types of nodes and links. Numerical prediction in heterogeneous information networks is a challenging but significant area because network based information for unlabeled objects is usually limited to make precise estimations. In this paper, we consider a graph regularized meta-path based transductive regression model (Grempt), which combines the principal philosophies of typical graph-based transductive classification methods and transductive regression models designed for homogeneous networks. The computation of our method is time and space efficient and the precision of our model can be verified by numerical experiments. PMID:26705510
N=2 gauge theories: Congruence subgroups, coset graphs, and modular surfaces
NASA Astrophysics Data System (ADS)
He, Yang-Hui; McKay, John
2013-01-01
We establish a correspondence between generalized quiver gauge theories in four dimensions and congruence subgroups of the modular group, hinging upon the trivalent graphs, which arise in both. The gauge theories and the graphs are enumerated and their numbers are compared. The correspondence is particularly striking for genus zero torsion-free congruence subgroups as exemplified by those which arise in Moonshine. We analyze in detail the case of index 24, where modular elliptic K3 surfaces emerge: here, the elliptic j-invariants can be recast as dessins d'enfant, which dictate the Seiberg-Witten curves.
A Benes-like theorem for the shuffle-exchange graph
NASA Technical Reports Server (NTRS)
Schwabe, Eric J.
1992-01-01
One of the first theorems on permutation routing, proved by V. E. Beness (1965), shows that given a set of source-destination pairs in an N-node butterfly network with at most a constant number of sources or destinations in each column of the butterfly, there exists a set of paths of lengths O(log N) connecting each pair such that the total congestion is constant. An analogous theorem yielding constant-congestion paths for off-line routing in the shuffle-exchange graph is proved here. The necklaces of the shuffle-exchange graph play the same structural role as the columns of the butterfly in Beness' theorem.
Using Dynamic Graphs to Reveal Student Reasoning
ERIC Educational Resources Information Center
Lassak, Marshall
2009-01-01
Using dynamic graphs, future secondary mathematics teachers were able to represent and communicate their understanding of a brief mathematical investigation in a way that a symbolic proof of the problem could not. Four different student work samples are discussed. (Contains 6 figures.)
A Graphing Investigation of the Ellipse.
ERIC Educational Resources Information Center
Davis, Jennifer; Hofstetter, Elaine
1998-01-01
Discusses ways to present mathematics concepts dealing with the ellipse to high school students, particularly by using a graphing calculator. Real-world occurrences of ellipses are considered, and a one-page student worksheet on constructing an ellipse is included. (LRW)
Communication Graph Generator for Parallel Programs
2014-04-08
Graphator is a collection of relatively simple sequential programs that generate communication graphs/matrices for commonly occurring patterns in parallel programs. Currently, there is support for five communication patterns: two-dimensional 4-point stencil, four-dimensional 8-point stencil, all-to-alls over sub-communicators, random near-neighbor communication, and near-neighbor communication.
Isoperimetric graph partitioning for image segmentation.
Grady, Leo; Schwartz, Eric L
2006-03-01
Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an alternate idea that finds partitions with a small isoperimetric constant, requiring solution to a linear system rather than an eigenvector problem. This approach produces the high quality segmentations of spectral methods, but with improved speed and stability.
Examining Students' Reluctance to Use Graphs
ERIC Educational Resources Information Center
Dyke, Frances Van; White, Alexander
2004-01-01
An evaluation designed to test basic graphical-thinking skills to students entering calculus or applied calculus at American University was given to use the assessment to discover the underlying causes for student's inability to use graphs effectively. The study indicates that graphical representation is not emphasized properly in the curriculum…
Marking Student Programs Using Graph Similarity
ERIC Educational Resources Information Center
Naude, Kevin A.; Greyling, Jean H.; Vogts, Dieter
2010-01-01
We present a novel approach to the automated marking of student programming assignments. Our technique quantifies the structural similarity between unmarked student submissions and marked solutions, and is the basis by which we assign marks. This is accomplished through an efficient novel graph similarity measure ("AssignSim"). Our experiments…
An Ellipse Morphs to a Cosine Graph!
ERIC Educational Resources Information Center
King, L .R.
2013-01-01
We produce a continuum of curves all of the same length, beginning with an ellipse and ending with a cosine graph. The curves in the continuum are made by cutting and unrolling circular cones whose section is the ellipse; the initial cone is degenerate (it is the plane of the ellipse); the final cone is a circular cylinder. The curves of the…
Evolving Polygons Revisited: Inequalities and Computer Graphing
ERIC Educational Resources Information Center
Abramovich, Sergei; Brouwer, Peter
2009-01-01
This paper was developed with the goal of enhancing the mathematical preparation of secondary school teachers in the technological paradigm. It shows how two-variable inequalities can be utilized as models for the construction of geometric objects using the software Graphing Calculator 3.5 (produced by Pacific Tech) as a relation grapher. An…
Product disassembly scheduling using graph models
NASA Astrophysics Data System (ADS)
Puente Mendez, Santiago; Torres Medina, Fernando; Pomares Baeza, Jorge
2002-02-01
Disassembly problem is a current issue for industrial companies. Governments of different countries promote research in this field. This paper presents the following points. First a brief state of the art in disassembly planning. Next it exposes a solution for the disassembly problem of industrial products. It uses a combination between direct and indirect graph representation for the product, all components that have physical entity are considered as vertices of the graph. Edges of the graph represent the relationships between vertices. There are three different types of edges. First corresponds with accessibility and fastener restrictions. Second corresponds with direct relations between components without fasteners. Last one corresponds with contact relationships, which represent an indifferent choice of the vertices. Based on that representation the paper exposed a method to find the best sequence to disassemble a component. Costs of disassembling each component and of changing tool between each pair of vertices and different sequences of the disassembly are taken into consideration. This method consists in a function minimization defined in the graph domain. In the last point of the paper this method is tested with a remote control disassembly. This method gives a solution to the problem, if several solutions, with the same cost, exist then it gives all of them, and any one of these disassemble sequences could be used to achieve to the target component.
Mathematical formula recognition using graph grammar
NASA Astrophysics Data System (ADS)
Lavirotte, Stephane; Pottier, Loic
1998-04-01
This paper describes current results of Ofr, a system for extracting and understanding mathematical expressions in documents. Such a tool could be really useful to be able to re-use knowledge in scientific books which are not available in electronic form. We currently also study use of this system for direct input of formulas with a graphical tablet for computer algebra system softwares. Existing solutions for mathematical recognition have problems to analyze 2D expressions like vectors and matrices. This is because they often try to use extended classical grammar to analyze formulas, relatively to baseline. But a lot of mathematical notations do not respect rules for such a parsing and that is the reason why they fail to extend text parsing technic. We investigate graph grammar and graph rewriting as a solution to recognize 2D mathematical notations. Graph grammar provide a powerful formalism to describe structural manipulations of multi-dimensional data. The main two problems to solve are ambiguities between rules of grammar and construction of graph.
Using Tables and Graphs for Reporting Data.
Bavdekar, Sandeep B
2015-10-01
For presenting the study results, authors need to choose from one of the three formats: text, tables and graphs. The underlying consideration of any author while making the choice is to ensure that readers find it easy to understand, to assist the author present data in a way that would catch the reader's eye, hold his interest and enhance his understanding. The choice should, therefore, be based on the advantages and limitations of each of these formats. Most of the observations are reported in textual format. Tables are useful when comparisons are to be shown. Graphs attract readers' attention better and the data they depict remains in the reader's memory. The type of graph used is dependent upon the nature of data that is to be shown. Every research paper has a lot to say through the data that has been collected and analyzed. However, this data needs to be presented in a logical, coherent and easy-to-understand manner. The way data is presented can influence the reviewers' and editors' decision. It can also make the difference between a paper being appreciated by the readers or being neglected or even trashed by them. Tables and Graphs are the two important tools that authors use to make the data more presentable and easy to read and understand. PMID:27608693
Simple scale interpolator facilitates reading of graphs
NASA Technical Reports Server (NTRS)
Fazio, A.; Henry, B.; Hood, D.
1966-01-01
Set of cards with scale divisions and a scale finder permits accurate reading of the coordinates of points on linear or logarithmic graphs plotted on rectangular grids. The set contains 34 different scales for linear plotting and 28 single cycle scales for log plots.
Signals on Graphs: Uncertainty Principle and Sampling
NASA Astrophysics Data System (ADS)
Tsitsvero, Mikhail; Barbarossa, Sergio; Di Lorenzo, Paolo
2016-09-01
In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of graph signals that are maximally concentrated on the graph domain and on its dual. Then, building on this framework, we derive an uncertainty principle for graph signals and illustrate the conditions for the recovery of band-limited signals from a subset of samples. We show an interesting link between uncertainty principle and sampling and propose alternative signal recovery algorithms, including a generalization to frame-based reconstruction methods. After showing that the performance of signal recovery algorithms is significantly affected by the location of samples, we suggest and compare a few alternative sampling strategies. Finally, we provide the conditions for perfect recovery of a useful signal corrupted by sparse noise, showing that this problem is also intrinsically related to vertex-frequency localization properties.
NASA Astrophysics Data System (ADS)
Sukhoruchkin, S. I.; Soroko, Z. N.
This document is part of the Supplement containing the complete sets of data of Subvolume A `Nuclei with Z = 1 - 54' of Volume 22 `Nuclear Binding Energies and Atomic Masses' of Landolt-Börnstein - Group I `Elementary Particles, Nuclei and Atoms'. It provides a graphic representation of nucleon separation energies and residual interaction parameters for isotopes of the chemical element 53-I (Iodine, atomic number Z = 53).
Range charts and no-space graphs
Edwards, L.E.
1978-01-01
No-space graphs present one solution to the familiar problem: given data on the occurrence of fossil taxa in separate, well-sampled sections, determine a range chart; that is, a reasonable working hypothesis of the total range in the area in question of each taxon studied. The solution presented here treats only the relative sequence of biostratigraphic events (first and last occurrences of taxa) and does not attempt to determine an amount of spacing between events. Relative to a hypothesized sequence, observed events in any section may be in-place or out-of-place. Out-of-place events may indicate (1) the event in question reflects a taxon that did not fill its entire range (unfilled-range event), or (2) the event in question indicates a need for the revision of the hypothesized sequence. A graph of relative position only (no-space graph) can be used to facilitate the recognition of in-place and out-of-place events by presenting a visual comparison of the observations from each section with the hypothesized sequence. The geometry of the graph as constructed here is such that in-place events will lie along a line series and out-of-place events will lie above or below it. First-occurrence events below the line series and last-occurrence events above the line series indicate unfilled ranges. First-occurrence events above the line series and last-occurrence events below the line series indicate a need for the revision of the hypothesis. Knowing this, the stratigrapher considers alternative positionings of the line series as alternative range hypotheses and seeks the line series that best fits his geologic and paleontologic judgment. No-space graphs are used to revise an initial hypothesis until a final hypothesis is reached. In this final hypothesis every event is found in-place in at least one section, and all events in all sections may be interpreted to represent in-place events or unfilled-range events. No event may indicate a need for further range revision. The
A Graph Based Methodology for Temporal Signature Identification from HER.
Wang, Fei; Liu, Chuanren; Wang, Yajuan; Hu, Jianying; Yu, Guoqiang
2015-01-01
Data driven technology is believed to be a promising technique for transforming the current status of healthcare. Electronic Health Records (EHR) is one of the main carriers for conducting the data driven healthcare research, where the goal is to derive insights from healthcare data and utilize such insights to improve the quality of care delivery. Due to the progression nature of human disease, one important aspect for analyzing healthcare data is temporality, which suggests the temporal relationships among different healthcare events and how their values evolve over time. Sequential pattern mining is a popular tool to extract time-invariant patterns from discrete sequences and has been applied in analyzing EHR before. However, due to the complexity of EHR, those approaches usually suffers from the pattern explosion problem, which means that a huge number of patterns will be detected with improper setting of the support threshold. To address this challenge, in this paper, we develop a novel representation, namely the temporal graph, for event sequences like EHR, wherein the nodes are medical events and the edges indicate the temporal relationships among those events in patient EHRs. Based on the temporal graph representation, we further develop an approach for temporal signature identification to identify the most significant and interpretable graph bases as temporal signatures, and the expressing coefficients can be treated as the embeddings of the patients in such temporal signature space. Our temporal signature identification framework is also flexible to incorporate semi-supervised/supervised information. We validate our framework on two real-world tasks. One is predicting the onset risk of heart failure. The other is predicting the risk of heart failure related hospitalization for patients with COPD pre-condition. Our results show that the prediction performance in both tasks can be improved by the proposed approaches. PMID:26958267
A Graph Based Methodology for Temporal Signature Identification from HER.
Wang, Fei; Liu, Chuanren; Wang, Yajuan; Hu, Jianying; Yu, Guoqiang
2015-01-01
Data driven technology is believed to be a promising technique for transforming the current status of healthcare. Electronic Health Records (EHR) is one of the main carriers for conducting the data driven healthcare research, where the goal is to derive insights from healthcare data and utilize such insights to improve the quality of care delivery. Due to the progression nature of human disease, one important aspect for analyzing healthcare data is temporality, which suggests the temporal relationships among different healthcare events and how their values evolve over time. Sequential pattern mining is a popular tool to extract time-invariant patterns from discrete sequences and has been applied in analyzing EHR before. However, due to the complexity of EHR, those approaches usually suffers from the pattern explosion problem, which means that a huge number of patterns will be detected with improper setting of the support threshold. To address this challenge, in this paper, we develop a novel representation, namely the temporal graph, for event sequences like EHR, wherein the nodes are medical events and the edges indicate the temporal relationships among those events in patient EHRs. Based on the temporal graph representation, we further develop an approach for temporal signature identification to identify the most significant and interpretable graph bases as temporal signatures, and the expressing coefficients can be treated as the embeddings of the patients in such temporal signature space. Our temporal signature identification framework is also flexible to incorporate semi-supervised/supervised information. We validate our framework on two real-world tasks. One is predicting the onset risk of heart failure. The other is predicting the risk of heart failure related hospitalization for patients with COPD pre-condition. Our results show that the prediction performance in both tasks can be improved by the proposed approaches.
A Graph Based Methodology for Temporal Signature Identification from EHR
Wang, Fei; Liu, Chuanren; Wang, Yajuan; Hu, Jianying; Yu, Guoqiang
2015-01-01
Data driven technology is believed to be a promising technique for transforming the current status of healthcare. Electronic Health Records (EHR) is one of the main carriers for conducting the data driven healthcare research, where the goal is to derive insights from healthcare data and utilize such insights to improve the quality of care delivery. Due to the progression nature of human disease, one important aspect for analyzing healthcare data is temporality, which suggests the temporal relationships among different healthcare events and how their values evolve over time. Sequential pattern mining is a popular tool to extract time-invariant patterns from discrete sequences and has been applied in analyzing EHR before. However, due to the complexity of EHR, those approaches usually suffers from the pattern explosion problem, which means that a huge number of patterns will be detected with improper setting of the support threshold. To address this challenge, in this paper, we develop a novel representation, namely the temporal graph, for event sequences like EHR, wherein the nodes are medical events and the edges indicate the temporal relationships among those events in patient EHRs. Based on the temporal graph representation, we further develop an approach for temporal signature identification to identify the most significant and interpretable graph bases as temporal signatures, and the expressing coefficients can be treated as the embeddings of the patients in such temporal signature space. Our temporal signature identification framework is also flexible to incorporate semi-supervised/supervised information. We validate our framework on two real-world tasks. One is predicting the onset risk of heart failure. The other is predicting the risk of heart failure related hospitalization for patients with COPD pre-condition. Our results show that the prediction performance in both tasks can be improved by the proposed approaches. PMID:26958267
GraphPrints: Towards a Graph Analytic Method for Network Anomaly Detection
Harshaw, Chris R; Bridges, Robert A; Iannacone, Michael D; Reed, Joel W; Goodall, John R
2016-01-01
This paper introduces a novel graph-analytic approach for detecting anomalies in network flow data called \\textit{GraphPrints}. Building on foundational network-mining techniques, our method represents time slices of traffic as a graph, then counts graphlets\\textemdash small induced subgraphs that describe local topology. By performing outlier detection on the sequence of graphlet counts, anomalous intervals of traffic are identified, and furthermore, individual IPs experiencing abnormal behavior are singled-out. Initial testing of GraphPrints is performed on real network data with an implanted anomaly. Evaluation shows false positive rates bounded by 2.84\\% at the time-interval level, and 0.05\\% at the IP-level with 100\\% true positive rates at both.
Multigraph: Interactive Data Graphs on the Web
NASA Astrophysics Data System (ADS)
Phillips, M. B.
2010-12-01
Many aspects of geophysical science involve time dependent data that is often presented in the form of a graph. Considering that the web has become a primary means of communication, there are surprisingly few good tools and techniques available for presenting time-series data on the web. The most common solution is to use a desktop tool such as Excel or Matlab to create a graph which is saved as an image and then included in a web page like any other image. This technique is straightforward, but it limits the user to one particular view of the data, and disconnects the graph from the data in a way that makes updating a graph with new data an often cumbersome manual process. This situation is somewhat analogous to the state of mapping before the advent of GIS. Maps existed only in printed form, and creating a map was a laborious process. In the last several years, however, the world of mapping has experienced a revolution in the form of web-based and other interactive computer technologies, so that it is now commonplace for anyone to easily browse through gigabytes of geographic data. Multigraph seeks to bring a similar ease of access to time series data. Multigraph is a program for displaying interactive time-series data graphs in web pages that includes a simple way of configuring the appearance of the graph and the data to be included. It allows multiple data sources to be combined into a single graph, and allows the user to explore the data interactively. Multigraph lets users explore and visualize "data space" in the same way that interactive mapping applications such as Google Maps facilitate exploring and visualizing geography. Viewing a Multigraph graph is extremely simple and intuitive, and requires no instructions. Creating a new graph for inclusion in a web page involves writing a simple XML configuration file and requires no programming. Multigraph can read data in a variety of formats, and can display data from a web service, allowing users to "surf
Scaling Up Graph-Based Semisupervised Learning via Prototype Vector Machines
Zhang, Kai; Lan, Liang; Kwok, James T.; Vucetic, Slobodan; Parvin, Bahram
2014-01-01
When the amount of labeled data are limited, semi-supervised learning can improve the learner's performance by also using the often easily available unlabeled data. In particular, a popular approach requires the learned function to be smooth on the underlying data manifold. By approximating this manifold as a weighted graph, such graph-based techniques can often achieve state-of-the-art performance. However, their high time and space complexities make them less attractive on large data sets. In this paper, we propose to scale up graph-based semisupervised learning using a set of sparse prototypes derived from the data. These prototypes serve as a small set of data representatives, which can be used to approximate the graph-based regularizer and to control model complexity. Consequently, both training and testing become much more efficient. Moreover, when the Gaussian kernel is used to define the graph affinity, a simple and principled method to select the prototypes can be obtained. Experiments on a number of real-world data sets demonstrate encouraging performance and scaling properties of the proposed approach. It also compares favorably with models learned via ℓ1-regularization at the same level of model sparsity. These results demonstrate the efficacy of the proposed approach in producing highly parsimonious and accurate models for semisupervised learning. PMID:25720002
Overview and extensions of a system for routing directed graphs on SIMD architectures
NASA Technical Reports Server (NTRS)
Tomboulian, Sherryl
1988-01-01
Many problems can be described in terms of directed graphs that contain a large number of vertices where simple computations occur using data from adjacent vertices. A method is given for parallelizing such problems on an SIMD machine model that uses only nearest neighbor connections for communication, and has no facility for local indirect addressing. Each vertex of the graph will be assigned to a processor in the machine. Rules for a labeling are introduced that support the use of a simple algorithm for movement of data along the edges of the graph. Additional algorithms are defined for addition and deletion of edges. Modifying or adding a new edge takes the same time as parallel traversal. This combination of architecture and algorithms defines a system that is relatively simple to build and can do fast graph processing. All edges can be traversed in parallel in time O(T), where T is empirically proportional to the average path length in the embedding times the average degree of the graph. Additionally, researchers present an extension to the above method which allows for enhanced performance by allowing some broadcasting capabilities.
NASA Astrophysics Data System (ADS)
Bonchiş, N.; Balint, Şt.
2010-09-01
In this paper the Ramsey optimal growth of the capital stock and consumption on finite horizon is analyzed when the growth rate of consumers is strictly positive. The main purpose is to establish the dependence of the optimal capital stock and consumption evolution on the growth rate of consumers. The analysis reveals: for any initial value k0≥0 there exists a unique optimal evolution path of length N+1 for the capital stock; if k0 is strictly positive then all the elements of the optimal capital stock evolution path are strictly positives except the last one which is zero; the optimal capital stock evolution of length N+1 starting from k0≥0 satisfies the Euler equation; the value function VN is strictly increasing, strictly concave and continuous on R+. The family of functions {VN-T}T = 0…N-1 satisfies the Bellman equation and it is the unique solution of this equation which is both continuous and satisfies the transversality condition. The Mangasarian Lemma is also satisfied. For N tending to infinity the optimal evolution path of length N of the capital stock tends to those on the infinite time horizon. For any k0>0 the value function in k0 decreases when the consumers growth rate increases.
Multifractal analysis of visibility graph-based Ito-related connectivity time series.
Czechowski, Zbigniew; Lovallo, Michele; Telesca, Luciano
2016-02-01
In this study, we investigate multifractal properties of connectivity time series resulting from the visibility graph applied to normally distributed time series generated by the Ito equations with multiplicative power-law noise. We show that multifractality of the connectivity time series (i.e., the series of numbers of links outgoing any node) increases with the exponent of the power-law noise. The multifractality of the connectivity time series could be due to the width of connectivity degree distribution that can be related to the exit time of the associated Ito time series. Furthermore, the connectivity time series are characterized by persistence, although the original Ito time series are random; this is due to the procedure of visibility graph that, connecting the values of the time series, generates persistence but destroys most of the nonlinear correlations. Moreover, the visibility graph is sensitive for detecting wide "depressions" in input time series.
Consensus dynamics on random rectangular graphs
NASA Astrophysics Data System (ADS)
Estrada, Ernesto; Sheerin, Matthew
2016-06-01
A random rectangular graph (RRG) is a generalization of the random geometric graph (RGG) in which the nodes are embedded into a rectangle with side lengths a and b = 1 / a, instead of on a unit square [ 0 , 1 ] 2. Two nodes are then connected if and only if they are separated at a Euclidean distance smaller than or equal to a certain threshold radius r. When a = 1 the RRG is identical to the RGG. Here we apply the consensus dynamics model to the RRG. Our main result is a lower bound for the time of consensus, i.e., the time at which the network reaches a global consensus state. To prove this result we need first to find an upper bound for the algebraic connectivity of the RRG, i.e., the second smallest eigenvalue of the combinatorial Laplacian of the graph. This bound is based on a tight lower bound found for the graph diameter. Our results prove that as the rectangle in which the nodes are embedded becomes more elongated, the RRG becomes a 'large-world', i.e., the diameter grows to infinity, and a poorly-connected graph, i.e., the algebraic connectivity decays to zero. The main consequence of these findings is the proof that the time of consensus in RRGs grows to infinity as the rectangle becomes more elongated. In closing, consensus dynamics in RRGs strongly depend on the geometric characteristics of the embedding space, and reaching the consensus state becomes more difficult as the rectangle is more elongated.
Concepts and Misconceptions in Comprehension of Hierarchical Graphs
ERIC Educational Resources Information Center
Korner, Christof
2005-01-01
Hierarchical graphs represent relationships between objects (like computer file systems, family trees etc.). Graph nodes represent the objects and interconnecting lines represent the relationships. In two experiments we investigated what concepts are necessary for understanding hierarchical graphs, what misconceptions evolve when some of the…
Hands-on Science: Getting-to-Know-You Graphing.
ERIC Educational Resources Information Center
Kepler, Lynne
1992-01-01
Elementary teachers can use graphing to introduce students to one another. An eye color graphing activity helps students learn more about each other while experimenting with different ways of organizing and displaying information. For follow up, students can apply their graphing knowledge by collecting and displaying data from their families. (SM)
Can Comparison of Contrastive Examples Facilitate Graph Understanding?
ERIC Educational Resources Information Center
Smith, Linsey A.; Gentner, Dedre
2011-01-01
The authors explore the role of comparison in improving graph fluency. The ability to use graphs fluently is crucial for STEM achievement, but graphs are challenging to interpret and produce because they often involve integration of multiple variables, continuous change in variables over time, and omission of certain details in order to highlight…
Sharing the Spotlight: Humane Education and Bar Graphs.
ERIC Educational Resources Information Center
Dewey, Paul
1987-01-01
Promotes the use of humane education as a vehicle for teaching students how to make bar graphs. Provides ideas for bar graph activities for both primary- and intermediate-grade children that focus on different kinds of domestic and wild animals. Suggests expanded types of graphing activities involving survey techniques. (TW)
An Interactive Graphing Tool for Web-Based Courses.
ERIC Educational Resources Information Center
Kennedy, David M.; Fritze, Paul
This paper reports on a project involving the development and formative evaluation of an interactive World Wide Web-based learning tool. The interactive graphing tool (IGT) permits students to sketch a graph on screen using a mouse and responds to a wide range of common graph types. The IGT facilitates an iterative approach to understanding…
Graphing Online Searches with Lotus 1-2-3.
ERIC Educational Resources Information Center
Persson, Olle
1986-01-01
This article illustrates how Lotus 1-2-3 software can be used to create graphs using downloaded online searches as raw material, notes most commands applied, and outlines three required steps: downloading, importing the downloading file into the worksheet, and making graphs. An example in bibliometrics and sample graphs are included. (EJS)
Deterministic dense coding and faithful teleportation with multipartite graph states
Huang, C.-Y.; Yu, I-C.; Lin, F.-L.; Hsu, L.-Y.
2009-05-15
We propose schemes to perform the deterministic dense coding and faithful teleportation with multipartite graph states. We also find the sufficient and necessary condition of a viable graph state for the proposed schemes. That is, for the associated graph, the reduced adjacency matrix of the Tanner-type subgraph between senders and receivers should be invertible.
Students' Cognitive Reasoning of Graphs: Characteristics and Progression
ERIC Educational Resources Information Center
Wang, Zu Hao; Wei, Silin; Ding, Wei; Chen, Xiuyun; Wang, Xiaonan; Hu, Kaiyan
2012-01-01
Graphs are widely used to present scientific information. Information presented in graphs can be classified into three kinds: explicit information, tacit information, and conclusive information. Reading information from graphs requires not only science content knowledge and understanding but also general logical reasoning. This study examined the…
Measuring Graph Comprehension, Critique, and Construction in Science
ERIC Educational Resources Information Center
Lai, Kevin; Cabrera, Julio; Vitale, Jonathan M.; Madhok, Jacquie; Tinker, Robert; Linn, Marcia C.
2016-01-01
Interpreting and creating graphs plays a critical role in scientific practice. The K-12 Next Generation Science Standards call for students to use graphs for scientific modeling, reasoning, and communication. To measure progress on this dimension, we need valid and reliable measures of graph understanding in science. In this research, we designed…
Efficient graph algorithms for sequential and parallel computers. Doctoral thesis
Goldberg, A.V.
1987-02-01
This thesis studies graph algorithms, both in sequential and parallel contexts. In the outline of the thesis, algorithm complexities are stated in terms of the the number of vertices n, the number of edges m, the largest absolute value of capacities U, and the largest absolute value of costs C. Chapter 1 introduces a new approach to the maximum flow problem that leads to better algorithms for the problem. Chapter 2 is devoted to the minimum cost flow problem, which is a generalization of the maximum flow problem. Chapter 3 addresses implementation of parallel algorithms through a case study of an implementation of a parallel maximum flow algorithm. Parallel prefix operations play an important role in the implementation. Present experimental results achieved by the implementation are presented. Present parallel symmetry-breaking techniques are the main topic of Chapter 4.
Dimer problem for some three dimensional lattice graphs
NASA Astrophysics Data System (ADS)
Lin, Fenggen; Chen, Ailian; Lai, Jiangzhou
2016-02-01
Dimer problem for three dimensional lattice is an unsolved problem in statistical mechanics and solid-state chemistry. In this paper, we obtain asymptotical expressions of the number of close-packed dimers (perfect matchings) for two types of three dimensional lattice graphs. Let M(G) denote the number of perfect matchings of G. Then log(M(K2 ×C4 ×Pn)) ≈(- 1.171 ṡn-1.1223 + 3.146) n, and log(M(K2 ×P4 ×Pn)) ≈(- 1.164 ṡn-1.196 + 2.804) n, where log() denotes the natural logarithm. Furthermore, we obtain a sufficient condition under which the lattices with multiple cylindrical and multiple toroidal boundary conditions have the same entropy.
Analyzing microarray data with transitive directed acyclic graphs.
Phan, Vinhthuy; Olusegun George, E; Tran, Quynh T; Goodwin, Shirlean; Bodreddigari, Sridevi; Sutter, Thomas R
2009-02-01
Post hoc assignment of patterns determined by all pairwise comparisons in microarray experiments with multiple treatments has been proven to be useful in assessing treatment effects. We propose the usage of transitive directed acyclic graphs (tDAG) as the representation of these patterns and show that such representation can be useful in clustering treatment effects, annotating existing clustering methods, and analyzing sample sizes. Advantages of this approach include: (1) unique and descriptive meaning of each cluster in terms of how genes respond to all pairs of treatments; (2) insensitivity of the observed patterns to the number of genes analyzed; and (3) a combinatorial perspective to address the sample size problem by observing the rate of contractible tDAG as the number of replicates increases. The advantages and overall utility of the method in elaborating drug structure activity relationships are exemplified in a controlled study with real and simulated data. PMID:19226664