Generalized Ramsey numbers through adiabatic quantum optimization
NASA Astrophysics Data System (ADS)
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-06-01
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.
On the Ramsey numbers for complete distance graphs with vertices in {l_brace}0,1{r_brace}{sup n}
Mikhailov, Kirill A; Raigorodskii, Andrei M
2009-12-31
A new problem of Ramsey type is posed for complete distance graphs in R{sup n} with vertices in the Boolean cube. This problem is closely related to the classical Nelson-Erdos-Hadwiger problem on the chromatic number of a space. Several quite sharp estimates are obtained for certain numerical characteristics that appear in the framework of the problem. Bibliography: 15 titles.
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.
Determining Ramsey numbers on a quantum computer
NASA Astrophysics Data System (ADS)
Wang, Hefeng
2016-03-01
We present a quantum algorithm for computing the Ramsey numbers whose computational complexity grows superexponentially with the number of vertices of a graph on a classical computer. The problem is mapped to a decision problem on a quantum computer, and a probe qubit is coupled to a register that represents the problem and detects the energy levels of the problem Hamiltonian. The decision problem is solved by detecting the decay dynamics of the probe qubit.
Restricted size Ramsey number for P3 versus small paths
NASA Astrophysics Data System (ADS)
Silaban, Denny Riama; Baskoro, E. T.; Uttunggadewa, Saladin
2016-02-01
Let F, G, and H be simple graphs. We say F → (G, H) if for every 2-coloring of the edges of F there exist a monochromatic G or H in F. The Ramsey number r(G, H) is defined as min {|V (F)| : F → (G, H)}, the size Ramsey number r̂(G, H) is defined as min {|E(F)| : F → (G, H)}, and the restricted size Ramsey number r*(G, H) is defined as min {|E(F)| : F → (G, H), |V (F)| = r(G, H)}. In this paper we give a lower bound for the restricted size Ramsey number for a path P3 versus Pn. We also give the upper bound and the exact restricted size Ramsey number for some small values of n.
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.
Connected size Ramsey numbers of matchings and stars
NASA Astrophysics Data System (ADS)
Rahadjeng, Budi; Baskoro, Edy Tri; Assiyatun, Hilda
2016-02-01
Let F, G, and H be finite, simple, and undirected graphs. The notation F → (G, H) means that if the edge set of F is arbitrarily colored by red or blue, then there always exists either a red copy of G or a blue copy of H. The connected size Ramsey number r̂c(G, H) is min{|E(F)| : F → (G, H), F is connected}. In this paper, we determine the connected size Ramsey numbers r̂c(nK2, mK2), for n, m ≥ 2. Furthermore, an upper bound of r̂c(nK2, K1,m), for n ≥ 2 and m ≥ 3, and the exact value of r̂c(nK2, K1,m), for n = 2, 3, are presented.
On size tripartite Ramsey numbers of P3 versus mK1,n
NASA Astrophysics Data System (ADS)
Lusiani, Anie; Baskoro, Edy Tri; Saputro, Suhadi Wido
2016-02-01
Let Kl×t be a complete, balanced, multipartite graph consisting of l partite sets and t vertices in each partite set. For simple graphs G and H, the size multipartite Ramsey number mj (G, H) is the smallest natural number t such that any arbitrary red-blue coloring on the edges of Kl×t contains a red G or a blue H as a subgraph. In particular, if j = 3 then m3(G, H) is called the size tripartite Ramsey number of G and H. In this paper, we determine the exact values of the size tripartite numbers m3(P3, mK1,n) for all integers m ≥ 1 and n ≥ 3, where P3 is a path of order 3 and mK1,n is a disjoint union of m copies of a star K1,n.
Rainbow connection number of rocket graphs
NASA Astrophysics Data System (ADS)
Susilawati, Salman, A. N. M.
2015-09-01
All graphs in this paper are simple, finite, and undirected. The concept of rainbow coloring was introduced by Chartrand et al2. Let G be a non trivial connected graph. For k ∈ℕ , we define a coloring c :E (G )→{1 ,2 ,…,k } of the edges of G such that the adjacent can be colored the same. A path P in G is a rainbow path if no two edges of P are colored the same. A path connecting two vertices u and u in G is called u-v path. A graph G is said rainbow-connected if for every two vertices u and u of G, there exist a rainbow u-v path. In this case, the coloring c is called the rainbow k-coloring of G. The minimum k such that G has rainbow k-coloring is called the rainbow connection number of G. Clearly that diam(G )≤r c (G ) where diam(G) denotes the diameter of G. In this paper we determine the rainbow connection number of rocket graphs.
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
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.
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…
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.
NASA Astrophysics Data System (ADS)
Kupavskii, A. B.
2014-02-01
We study distance graphs with exponentially large chromatic numbers and without k-cliques, that is, complete subgraphs of size k. Explicit constructions of such graphs use vectors in the integer lattice. For a large class of graphs we find a sharp threshold for containing a k-clique. This enables us to improve the lower bounds for the maximum of the chromatic numbers of such graphs. We give a new probabilistic approach to the construction of distance graphs without k-cliques, and this yields better lower bounds for the maximum of the chromatic numbers for large k.
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.
On Vertex Covering Transversal Domination Number of Regular Graphs
Vasanthi, R.; Subramanian, K.
2016-01-01
A simple graph G = (V, E) is said to be r-regular if each vertex of G is of degree r. The vertex covering transversal domination number γvct(G) is the minimum cardinality among all vertex covering transversal dominating sets of G. In this paper, we analyse this parameter on different kinds of regular graphs especially for Qn and H3,n. Also we provide an upper bound for γvct of a connected cubic graph of order n ≥ 8. Then we try to provide a more stronger relationship between γ and γvct. PMID:27119089
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.
Spatiotemporal Directional Number Transitional Graph for Dynamic Texture Recognition.
Rivera, Adín Ramírez; Chae, Oksam
2015-10-01
Spatiotemporal image descriptors are gaining attention in the image research community for better representation of dynamic textures. In this paper, we introduce a dynamic-micro-texture descriptor, i.e., spatiotemporal directional number transitional graph (DNG), which describes both the spatial structure and motion of each local neighborhood by capturing the direction of natural flow in the temporal domain. We use the structure of the local neighborhood, given by its principal directions, and compute the transition of such directions between frames. Moreover, we present the statistics of the direction transitions in a transitional graph, which acts as a signature for a given spatiotemporal region in the dynamic texture. Furthermore, we create a sequence descriptor by dividing the spatiotemporal volume into several regions, computing a transitional graph for each of them, and represent the sequence as a set of graphs. Our results validate the robustness of the proposed descriptor in different scenarios for expression recognition and dynamic texture analysis. PMID:26340258
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.
An α-cut chromatic number of a total uncertain graph and its properties
NASA Astrophysics Data System (ADS)
Rosyida, Isnaini; Widodo, Indrati, Ch. Rini; Sugeng, Kiki A.
2016-02-01
A graph is called an edge uncertain graph if the edges are not deterministic but exist with some belief degrees described by uncertain measure. A new definition for total uncertain graph is first introduced in this paper, that is an uncertain graph in which the vertices and the edges are not deterministic. Further, we give a concept of an α-cut of a total uncertain graph and investigate some of its properties. We color a total uncertain graph via the α-cut, and obtain α-cut chromatic numbers for all α ∈ [0, 1]. Some properties of the α-cut chromatic number are also verified.
Detecting independent and recurrent copy number aberrations using interval graphs
Wu, Hsin-Ta; Hajirasouliha, Iman; Raphael, Benjamin J.
2014-01-01
Motivation: Somatic copy number aberrations (SCNAs) are frequent in cancer genomes, but many of these are random, passenger events. A common strategy to distinguish functional aberrations from passengers is to identify those aberrations that are recurrent across multiple samples. However, the extensive variability in the length and position of SCNAs makes the problem of identifying recurrent aberrations notoriously difficult. Results: We introduce a combinatorial approach to the problem of identifying independent and recurrent SCNAs, focusing on the key challenging of separating the overlaps in aberrations across individuals into independent events. We derive independent and recurrent SCNAs as maximal cliques in an interval graph constructed from overlaps between aberrations. We efficiently enumerate all such cliques, and derive a dynamic programming algorithm to find an optimal selection of non-overlapping cliques, resulting in a very fast algorithm, which we call RAIG (Recurrent Aberrations from Interval Graphs). We show that RAIG outperforms other methods on simulated data and also performs well on data from three cancer types from The Cancer Genome Atlas (TCGA). In contrast to existing approaches that employ various heuristics to select independent aberrations, RAIG optimizes a well-defined objective function. We show that this allows RAIG to identify rare aberrations that are likely functional, but are obscured by overlaps with larger passenger aberrations. Availability: http://compbio.cs.brown.edu/software. Contact: braphael@brown.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:24931984
Decomposition Optimization for Minimizing Label Overflow in Prime Number Graph Labeling
NASA Astrophysics Data System (ADS)
Kim, Jaehoon; Park, Seog
Recently, a graph labeling technique based on prime numbers has been suggested for reducing the costly transitive closure computations in RDF query languages. The suggested prime number graph labeling provides the benefit of fast query processing by a simple divisibility test of labels. However, it has an inherent problem that originates with the nature of prime numbers. Since each prime number must be used exclusively, labels can become significantly large. Therefore, in this paper, we introduce a novel optimization technique to effectively reduce the problem of label overflow. The suggested idea is based on graph decomposition. When label overflow occurs, the full graph is divided into several sub-graphs, and nodes in each sub-graph are separately labeled. Through experiments, we also analyze the effectiveness of the graph decomposition optimization, which is evaluated by the number of divisions.
Locating-coloring on Halin graphs with a certain number of inner faces
NASA Astrophysics Data System (ADS)
Purwasih, I. A.; Baskoro, E. T.; Assiyatun, H.; Suprijanto, D.
2016-02-01
For any tree T with at least four vertices and no vertices of degree two, define a Halin graph H(T) as a planar graph constructed from an embedding of T in a plane by connecting all the leaves (the vertices of degree 1) of T to form a cycle C that passes around T in the natural cyclic order defined by the embedding of T . The study of the properties of a Halin graph has received much attention. For instances, it has been shown that every Halin graph is 3-connected and Hamiltonian. A Halin graph has also treewidth at most three, so that many graph optimization problems that are NP-complete for arbitrary planar graphs may be solved in linear time on Halin graphs using dynamic programming. In this paper, we characterize all Halin graphs with 3,4,5,6, and 7 inner faces and give their locating-chromatic number. Furthermore, we show that there exist a Halin graph having locating-chromatic number k ≥ 4 with r ≥max {3 ,(k/-2) 3-(k-2 ) 2 2 +1 } inner faces.
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
Stavropoulos, Nick A.
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 on 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.
2010-01-01
Background Understanding of secondary metabolic pathway in plant is essential for finding druggable candidate enzymes. However, there are many enzymes whose functions are not yet discovered in organism-specific metabolic pathways. Towards identifying the functions of those enzymes, assignment of EC numbers to the enzymatic reactions they catalyze plays a key role, since EC numbers represent the categorization of enzymes on one hand, and the categorization of enzymatic reactions on the other hand. Results We propose reaction graph kernels for automatically assigning EC numbers to unknown enzymatic reactions in a metabolic network. Reaction graph kernels compute similarity between two chemical reactions considering the similarity of chemical compounds in reaction and their relationships. In computational experiments based on the KEGG/REACTION database, our method successfully predicted the first three digits of the EC number with 83% accuracy. We also exhaustively predicted missing EC numbers in plant's secondary metabolism pathway. The prediction results of reaction graph kernels on 36 unknown enzymatic reactions are compared with an expert's knowledge. Using the same data for evaluation, we compared our method with E-zyme, and showed its ability to assign more number of accurate EC numbers. Conclusion Reaction graph kernels are a new metric for comparing enzymatic reactions. PMID:20122204
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 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'…
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…
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.
Two-frequency Ramsey interferometry
Seidel, D.; Muga, J. G.
2007-02-15
We investigate Ramsey interferometry for two separated fields oscillating with different frequencies. It is shown that the interplay between average and relative detuning leads to interference effects not present in the standard, single-frequency setup. For a large free-flight time of ground-state atoms before entering the first field region, the Ramsey fringes with respect to the relative detuning become much narrower than the usual ones. The stability of these effects with respect to phase or velocity fluctuations is discussed.
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.
Pulse defect immune Ramsey spectroscopy
NASA Astrophysics Data System (ADS)
Sanner, Christian; Huntemann, Nils; Kuznetsov, Sergey; Lipphardt, Burghard; Tamm, Christian; Peik, Ekkehard
2016-05-01
We show that a balanced version of Ramsey's method of separated oscillatory fields is well suited for measuring unperturbed transition frequencies of atomic reference transitions that suffer from significant clock shifts in the presence of the oscillatory drive fields. Using the example of the strongly light shift affected Yb 171 + octupole transition we experimentally demonstrate the feasibility of this concept and show that no systematic clock shifts are incurred for arbitrarily detuned drive pulses. Unlike composite pulse approaches as proposed in balanced Ramsey spectroscopy can provide universal immunity to a variety of pulse aberrations and drive pulse induced shifts including phase chirps and pulse-synchronous intensity variations. In this context we also devise an experimental method addressing issues related to motional heating of the confined ion. Furthermore we report on the status of an Yb + experiment searching for signatures of spatial anisotropy.
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…
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
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
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
Single-atom and two-atom Ramsey interferometry with quantized fields
Agarwal, G.S.; Pathak, P.K.; Scully, M.O.
2003-04-01
Implications of field quantization on Ramsey interferometry are discussed and general conditions for the occurrence of interference are obtained. Interferences do not occur if the fields in two Ramsey zones have a precise number of photons. However, in this case we show how an analog of Hanbury-Brown Twiss photon-photon correlation interferometry can be used to discern a variety of interference effects as the two independent Ramsey zones get entangled by the passage of the first atom. Interferences are restored by working with fields at a single-photon level. Generation of entangled states including states such as vertical bar 2,0>+e{sup i{theta}} vertical bar 0,2> is discussed.
Ramsey County commercial, industrial, institutional waste reduction and recycling program
Lyman-Onkka, C.
1995-09-01
The Ramsey County Commercial, Industrial, Institutional Waste Reduction and Recycling Program was developed (1) to raise awareness of waste reduction and recycling opportunities for businesses, (2) to make information available to businesses, (3) to provide technical assistance to small and medium sized businesses on waste reduction and recycling, and (4) to raise awareness of Ramsey County as a technical resource. Ramsey County was founded in 1849 and is named for Alexander Ramsey, the first governor of the Minnesota Territory. Ramsey County is the smallest, most urban of all 87 counties in Minnesota. With 170 square miles and a 1990 population of 485,000, Ramsey has the most people per square mile of any county in Minnesota. There are 19 cities within the County, the largest is Saint Paul with a 1990 population of 272,000. There are no unincorporated areas in Ramsey County. This report describes the efforts directed towards raising the awareness of the county waste management, recycling program.
Mitra, Tapan; Sorger, Gerhard
2013-01-01
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
Ramsey interference in a multilevel quantum system
NASA Astrophysics Data System (ADS)
Lee, J. P.; Bennett, A. J.; Skiba-Szymanska, J.; Ellis, D. J. P.; Farrer, I.; Ritchie, D. A.; Shields, A. J.
2016-02-01
We report Ramsey interference in the excitonic population of a negatively charged quantum dot measured in resonant fluorescence. Our experiments show that the decay time of the Ramsey interference is limited by the spectral width of the transition. Applying a vertical magnetic field induces Zeeman split transitions that can be addressed by changing the laser detuning to reveal two-, three-, and four-level system behavior. We show that under finite field the phase-sensitive control of two optical pulses from a single laser can be used to prepare both population and spin states simultaneously. We also demonstrate the coherent optical manipulation of a trapped spin in a quantum dot in a Faraday geometry magnetic field.
NASA Astrophysics Data System (ADS)
Lai, Pik-Yin
Methods of statistical mechanics are applied to two important NP-complete combinatorial optimization problems. The first is the chromatic number problem which seeks the minimal number of colors necessary to color a graph such that no two sites connected by an edge have the same color. The second is partitioning of a graph into q equal subgraphs so as to minimize inter-subgraph connections. Both models are mapped into a frustrated Potts model which is related to the q-state Potts spin glass. For the first problem, we obtain very good agreement with numerical simulations and theoretical bounds using the annealed approximation. The quenched model is also discussed. For the second problem we obtain analytic and numerical results by evaluating the ground state energy of the q = 3 and 4 Potts spin glass using Parisi's replica symmetry breaking. We also performed some numerical simulations to test the theoretical result and obtained very good agreement. In the second part of the thesis, we simulate the Ising spin-glass model on a random lattice with a finite (average) coordination number and also on the Bethe lattice with various different boundary conditions. In particular, we calculate the overlap function P(q) for two independent samples. For the random lattice, the results are consistent with a spin-glass transition above which P(q) converges to a Dirac delta -function for large N (number of sites) and below which P(q) has in addition a long tail similar to previous results obtained for the infinite ranged model. For the Bethe lattice, we obtain results in the interior by discarding the two outer shells of the Cayley tree when calculating the thermal averages. For fixed (uncorrelated) boundary conditions, P(q) seems to converge to a delta -function even below the spin-glass transition whereas for a "closed" lattice (correlated boundary conditions) P(q) has a long tail similar to its behavior in the random lattice case.
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.
Ramsey interferometry with an atom laser.
Döring, D; Debs, J E; Robins, N P; Figl, C; Altin, P A; Close, J D
2009-11-01
We present results on a free-space atom interferometer operating on the first order magnetically insensitive |F = 1,mF = 0) --> |F = 2,mF = 0) ground state transition of Bose-condensed (87)Rb atoms. A pulsed atom laser is output-coupled from a Bose-Einstein condensate and propagates through a sequence of two internal state beam splitters, realized via coherent Raman transitions between the two interfering states. We observe Ramsey fringes with a visibility close to 100% and determine the current and the potentially achievable interferometric phase sensitivity. This system is well suited to testing recent proposals for generating and detecting squeezed atomic states. PMID:19997295
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.
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
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.
ERIC Educational Resources Information Center
Noble, Tracy; And Others
Graphs without a time axis, such as velocity-versus-position graphs, offer interesting possibilities for exploring graphing and motion. Relations depicted by these graphs are not limited to functions. Interviews with a high school student named Olivia, who uses a motion detector to create such graphs, indicate that she uses thought experiments as…
Mulet, R; Pagnani, A; Weigt, M; Zecchina, R
2002-12-23
We study the graph coloring problem over random graphs of finite average connectivity c. Given a number q of available colors, we find that graphs with low connectivity admit almost always a proper coloring, whereas graphs with high connectivity are uncolorable. Depending on q, we find the precise value of the critical average connectivity c(q). Moreover, we show that below c(q) there exists a clustering phase c in [c(d),c(q)] in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity in local search algorithms. PMID:12484862
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.
Robust Ramsey sequences with Raman adiabatic rapid passage
NASA Astrophysics Data System (ADS)
Kotru, Krish; Brown, Justin M.; Butts, David L.; Kinast, Joseph M.; Stoner, Richard E.
2014-11-01
We present a method for robust timekeeping in which alkali-metal atoms are interrogated in a Ramsey sequence based on stimulated Raman transitions with optical photons. To suppress systematic effects introduced by differential ac Stark shifts and optical intensity gradients, we employ atom optics derived from Raman adiabatic rapid passage (ARP). Raman ARP drives coherent transfer between the alkali-metal hyperfine ground states via a sweep of the Raman detuning through the two-photon resonance. Our experimental implementation of Raman ARP reduced the phase sensitivity of Ramsey sequences to Stark shifts in 133Cs atoms by about two orders of magnitude, relative to fixed-frequency Raman transitions. This technique also preserved Ramsey fringe contrast for cloud displacements reaching the 1 /e2 intensity radius of the laser beam. In a magnetically unshielded apparatus, second-order Zeeman shifts limited the fractional frequency uncertainty to ˜3.5 ×10-12 after about 2500 s of averaging.
Ramsey fringes and time-domain multiple-slit interference from vacuum.
Akkermans, Eric; Dunne, Gerald V
2012-01-20
Sequences of alternating-sign time-dependent electric field pulses lead to coherent interference effects in Schwinger vacuum pair production, producing a Ramsey interferometer, an all-optical time-domain realization of the multiple-slit interference effect, directly from the quantum vacuum. The interference, obeying fermionic quantum statistics, is manifest in the momentum dependence of the number of produced electrons and positrons along the linearly polarized electric field. The central value grows like N(2) for N pulses [i.e., N "slits"], and the functional form is well described by a coherent multiple-slit expression. This behavior is generic for many driven quantum systems. PMID:22400718
Federal Register 2010, 2011, 2012, 2013, 2014
2013-07-19
... Surface Transportation Board Ramsey County Regional Railroad Authority--Acquisition Exemption--Right to Restore Rail Service Over a Railbanked Right-of-Way in Ramsey County, Minn. Ramsey County Regional..., and milepost 6.52, approximately 50 feet north of Beam Avenue in the City (the line), in Ramsey...
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.}
Anoka Ramsey Community College, Exploring America's Communities. Progress Report.
ERIC Educational Resources Information Center
Anoka Ramsey Community Coll., Coon Rapids, MN.
In 1996, Minnesota's Anoka Ramsey Community College (ARCC) participated in the Exploring America's Communities project sponsored by the American Association of Community Colleges. The project works to strengthen the teaching and learning of American History, literature, and culture at U.S. community colleges. The grant application from the ARCC…
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.
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.
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.
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
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.
Random graphs with hidden color.
Söderberg, Bo
2003-07-01
We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, random graphs with a given degree distribution, in a way that admits a nontrivial correlation structure in the resulting graphs. The approach unifies a number of existing random graph ensembles within a common general formalism, and allows for the analytic calculation of observable graph characteristics. In particular, generating function techniques are used to derive the size distribution of connected components (clusters) as well as the location of the percolation threshold where a giant component appears. PMID:12935185
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…
ERIC Educational Resources Information Center
Auspos, Patricia; Miller, Cynthia; Hunter, Jo Anna
This report examines implementation and impacts of Ramsey County's Minnesota Family Investment Program (MFIP), a "work first" program. Chapter 1 lists key findings, provides an overview of the Ramsey County variant (MFIP-R) evaluation, and policy relevance of MFIP-R. Chapter 2 describes key features of MFIP-R and compares them with features of…
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.
Ohtsuki, Hisashi; Nowak, Martin A.
2008-01-01
Direct reciprocity is a mechanism for the evolution of cooperation based on the idea of repeated encounters between the same two individuals. Here we examine direct reciprocity in structured populations, where individuals occupy the vertices of a graph. The edges denote who interacts with whom. The graph represents spatial structure or a social network. For birth-death or pairwise comparison updating, we find that evolutionary stability of direct reciprocity is more restrictive on a graph than in a well-mixed population, but the condition for reciprocators to be advantageous is less restrictive on a graph. For death-birth and imitation updating, in contrast, both conditions are easier to fulfill on a graph. Moreover, for all four update mechanisms, reciprocators can dominate defectors on a graph, which is never possible in a well-mixed population. We also study the effect of an error rate, which increases with the number of links per individual; interacting with more people simultaneously enhances the probability of making mistakes. We provide analytic derivations for all results. PMID:17466339
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.
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.
Improving Ramsey spectroscopy in the extreme-ultraviolet region with a random-sampling approach
Eramo, R.; Bellini, M.; Corsi, C.; Liontos, I.; Cavalieri, S.
2011-04-15
Ramsey-like techniques, based on the coherent excitation of a sample by delayed and phase-correlated pulses, are promising tools for high-precision spectroscopic tests of QED in the extreme-ultraviolet (xuv) spectral region, but currently suffer experimental limitations related to long acquisition times and critical stability issues. Here we propose a random subsampling approach to Ramsey spectroscopy that, by allowing experimentalists to reach a given spectral resolution goal in a fraction of the usual acquisition time, leads to substantial improvements in high-resolution spectroscopy and may open the way to a widespread application of Ramsey-like techniques to precision measurements in the xuv spectral region.
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.
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.
Multiphoton- and simultaneous conjugate Ramsey-Borde atom interferometers
Mueller, Holger; Chiow, Sheng-wey; Herrmann, Sven; Chu, Steven
2008-03-06
We report on our experiment to measure h/M, the ratio of the Planck constant to the mass of Cs atoms, and thereby the fine-structure constant. The target accuracy is 1 part per billion or better. We focus on two recent milestones: (i) The first realization of atom interferometers based on light-pulse beam splitters that transfer the momentum of up to 12 photon pairs, which increases the useful signal (matter wave phase shift) by a factor of 144 compared to the beam splitters used in the best present atom interferometers. Moreover, they lead to a cancellation of important systematic effects. (ii) The first realization of a simultaneous pair of conjugate Ramsey-Borde interferometers. In these, the relative sign of the inertial term is reversed so that it can be cancelled. Simultaneous operation means that this holds for a time-dependent inertial term (vibrations) too, which promises a substantial improvement in the signal to noise ratio.
Magnetic tensor gradiometry using Ramsey interferometry of spinor condensates
NASA Astrophysics Data System (ADS)
Wood, A. A.; Bennie, L. M.; Duong, A.; Jasperse, M.; Turner, L. D.; Anderson, R. P.
2015-11-01
We have realized a magnetic tensor gradiometer by interferometrically measuring the relative phase between two spatially separated Bose-Einstein condensates (BECs). We perform simultaneous Ramsey interferometry of the proximate 87Rb spin-1 condensates in free fall and infer their relative Larmor phase, and thus the differential magnetic-field strength, with a common-mode phase noise suppression exceeding 50 dB . By appropriately biasing the magnetic field and separating the BECs along orthogonal directions, we measure in vacuo the magnetic-field-gradient tensor of ambient and applied magnetic fields with a nominal precision of 0.30 nT mm-1 and a sensor volume of 2 ×10-5mm3 . We predict a spin-projection noise-limited magnetic energy resolution of order ˜10 ℏ for typical Zeeman coherence times of trapped condensates with this scheme, even with the low measurement duty cycle of current BEC experiments.
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…
Park, Young-Ho; Lee, Soo Heyong; Park, Sang Eon; Lee, Ho Seong; Kwon, Taeg Yong
2007-04-23
The authors report on a method to determine the Rabi frequency and transit time distribution of atoms that are essential for proper operation of atomic beam frequency standards. Their method, which employs alternative regularized inverse on two Ramsey spectra measured at different microwave powers, can be used for the frequency standards with short Ramsey cavity as well as long ones. The authors demonstrate that uncertainty in Rabi frequency obtained from their method is 0.02%.
Optical Ramsey spectroscopy of a single trapped {sup 88}Sr{sup +} ion
Letchumanan, V.; Gill, P.; Sinclair, A.G.; Riis, E.
2004-09-01
Coherent optical spectroscopy has been performed on the narrow 5s {sup 2}S{sub 1/2}-4d {sup 2}D{sub 5/2} quadrupole transition in a single Doppler-cooled and trapped {sup 88}Sr{sup +} ion. High-contrast optical Ramsey spectra have been observed with fringe visibilities up to {approx}90%. The visibility decreased as the free precession period was increased, and was limited by the interrogation laser's coherence. The effect of varying the relative phase of the second Ramsey pulse was investigated. By measuring the difference in excitation probability on reversing a 90 deg. relative phase shift between the two Ramsey pulses, we have demonstrated Ramsey's anti-symmetric line shape in the optical domain. A significant advantage of this line shape is the zero crossing at line center and the independence of this center frequency on drifts in signal amplitude. This optical Ramsey line shape is suitable for stabilizing a local oscillator to an atomic reference transition in an optical frequency standard. All observed optical Ramsey signals are well described by a model using the optical Bloch equations.
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
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.
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.
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…
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.
The Bryant-Anthony-Ramsey (B-A-R) Project: An Evaluation. Report C-73-2.
ERIC Educational Resources Information Center
Mueller, Mildred K.
The Bryant-Anthony-Ramsey (B-A-R) Project is a desegregation/integration project aimed at assuring a smooth transition from a predominately segregated school environment to a desegregated or integrated environment. The Bryant, Anthony, and Ramsey Junior High Schools are participants in a desegregation effort that is one part of an overall…
Graph Coloring Used to Model Traffic Lights.
ERIC Educational Resources Information Center
Williams, John
1992-01-01
Two scheduling problems, one involving setting up an examination schedule and the other describing traffic light problems, are modeled as colorings of graphs consisting of a set of vertices and edges. The chromatic number, the least number of colors necessary for coloring a graph, is employed in the solutions. (MDH)
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.
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…
NASA Astrophysics Data System (ADS)
Diot, Emilie; Gavoille, Cyril
In this paper we investigate the structural properties of k-path separable graphs, that are the graphs that can be separated by a set of k shortest paths. We identify several graph families having such path separability, and we show that this property is closed under minor taking. In particular we establish a list of forbidden minors for 1-path separable graphs.
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. PMID:20431140
Single Parent Families: A Needs Assessment Survey of Single Parents, Ramsey County, Minnesota.
ERIC Educational Resources Information Center
Chase, Richard A.; And Others
This report provides findings of an in-person survey of single parents in Ramsey County, Minnesota. The report is organized into seven chapters. Chapter 1 provides a current demographic, educational, and economic profile of single parents and examines whether the backgrounds of single parents relate to their present conditions. Chapter 2 describes…
ERIC Educational Resources Information Center
Sandell, Elizabeth J., Ed.
This report describes the initial plan, participants, and evaluation of Saint Paul (Minnesota) Children's Initiative (SPCI) during 1993. The SPCI is a family-community program to improve child health, child development, school performance, and to enhance family functioning through formal and informal support systems in Saint Paul/Ramsey county. At…
An Evaluation of the Pilot Child Care Sliding Fee Program in Ramsey County.
ERIC Educational Resources Information Center
Ramsey County Child Care Council, Inc., St. Paul, Minn.
This study was designed to assess the monetary and human costs and benefits of the Pilot Child Care Sliding Fee Program in Ramsey County, Minnesota. A 21-item questionnaire was used to survey 53 of the 161 families who had participated in the program. The vast majority of the sample consisted of single, female, working-parent families with from…
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…
Report on Child Care Services in Ramsey County: Fees Charged and Rates of Utilization.
ERIC Educational Resources Information Center
Ramsey County Child Care Council, Inc., St. Paul, Minn.
This report describes the second annual survey of utilization of child care services (day care homes and day care centers) in Ramsey County, Minnesota. Information about fees charged is included. Data from day care homes and centers were collected by mail or telephone. The rate of utilization of child care services was determined by county, county…
Inferring Pedigree Graphs from Genetic Distances
NASA Astrophysics Data System (ADS)
Tamura, Takeyuki; Ito, Hiro
In this paper, we study a problem of inferring blood relationships which satisfy a given matrix of genetic distances between all pairs of n nodes. Blood relationships are represented by our proposed graph class, which is called a pedigree graph. A pedigree graph is a directed acyclic graph in which the maximum indegree is at most two. We show that the number of pedigree graphs which satisfy the condition of given genetic distances may be exponential, but they can be represented by one directed acyclic graph with n nodes. Moreover, an O(n3) time algorithm which solves the problem is also given. Although phylogenetic trees and phylogenetic networks are similar data structures to pedigree graphs, it seems that inferring methods for phylogenetic trees and networks cannot be applied to infer pedigree graphs since nodes of phylogenetic trees and networks represent species whereas nodes of pedigree graphs represent individuals. We also show an O(n2) time algorithm which detects a contradiction between a given pedigreee graph and distance matrix of genetic distances.
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 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
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
2015-01-01
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 𝒪(n(logn)2). As a practical example we show how to generate samples of power-law degree distribution graphs with tunable assortativity. PMID:26356296
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. PMID:25314272
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.
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…
Acyclic colorings of graphs with bounded degree
NASA Astrophysics Data System (ADS)
Fiedorowicz, Anna; Sidorowicz, Elżbieta
2016-07-01
A $k$-colouring (not necessarily proper) of vertices of a graph is called {\\it acyclic}, if for every pair of distinct colours $i$ and $j$ the subgraph induced by the edges whose endpoints have colours $i$ and $j$ is acyclic. In the paper we consider some generalised acyclic $k$-colourings, namely, we require that each colour class induces an acyclic or bounded degree graph. Mainly we focus on graphs with maximum degree 5. We prove that any such graph has an acyclic $5$-colouring such that each colour class induces an acyclic graph with maximum degree at most 4. We prove that the problem of deciding whether a graph $G$ has an acyclic 2-colouring in which each colour class induces a graph with maximum degree at most 3 is NP-complete, even for graphs with maximum degree 5. We also give a linear-time algorithm for an acyclic $t$-improper colouring of any graph with maximum degree $d$ assuming that the number of colors is large enough.
ERIC Educational Resources Information Center
VanDoren, Sandra Shaffer
This paper describes the cataloging, shelf arrangement, and preservation of Wayne State University's Eloise Ramsey collection of children's books. It also outlines Wayne State's efforts to consolidate the collection and to make it accessible to the public. (FM)
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)
Optimal preparation of graph states
Cabello, Adan; Lopez-Tarrida, Antonio J.; Danielsen, Lars Eirik; Portillo, Jose R.
2011-04-15
We show how to prepare any graph state of up to 12 qubits with (a) the minimum number of controlled-Z gates and (b) the minimum preparation depth. We assume only one-qubit and controlled-Z gates. The method exploits the fact that any graph state belongs to an equivalence class under local Clifford operations. We extend up to 12 qubits the classification of graph states according to their entanglement properties, and identify each class using only a reduced set of invariants. For any state, we provide a circuit with both properties (a) and (b), if it does exist, or, if it does not, one circuit with property (a) and one with property (b), including the explicit one-qubit gates needed.
ERIC Educational Resources Information Center
Beineke, Lowell W.
1989-01-01
Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)
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…
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 Astrophysics Data System (ADS)
Prudente, Matthew James
Given a graph G with pebbles on the vertices, we define a pebbling move as removing two pebbles from a vertex u, placing one pebble on a neighbor v, and discarding the other pebble, like a toll. The pebbling number pi( G) is the least number of pebbles needed so that every arrangement of pi(G) pebbles can place a pebble on any vertex through a sequence of pebbling moves. We introduce a new variation on graph pebbling called two-player pebbling. In this, players called the mover and the defender alternate moves, with the stipulation that the defender cannot reverse the previous move. The mover wins only if they can place a pebble on a specified vertex and the defender wins if the mover cannot. We define η(G), analogously, as the minimum number of pebbles such that given every configuration of the η( G) pebbles and every specified vertex r, the mover has a winning strategy. First, we will investigate upper bounds for η( G) on various classes of graphs and find a certain structure for which the defender has a winning strategy, no matter how many pebbles are in a configuration. Then, we characterize winning configurations for both players on a special class of diameter 2 graphs. Finally, we show winning configurations for the mover on paths using a recursive argument.
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. PMID:23005495
Detecting alternative graph clusterings
NASA Astrophysics Data System (ADS)
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.
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.
Effect of atomic diffusion on the Raman-Ramsey coherent population trapping resonances
NASA Astrophysics Data System (ADS)
Kuchina, Elena; Mikhailov, Eugeniy E.; Novikova, Irina
2016-04-01
We experimentally investigated the characteristics of two-photon transmission resonances in Rb vapor cells with different amount of buffer gas under the conditions of steady-state coherent population trapping (CPT) and pulsed Raman-Ramsey (RR-) CPT interrogation scheme. We particularly focused on the influence of the Rb atoms diffusing in and out of the laser beam. We showed that this effect modifies the shape of both CPT and Raman-Ramsey resonances, as well as their projected performance for CPT clock applications. In particular we found that at moderate buffer gas pressures RR-CPT did not improved the projected atomic clock stability compare to the regular steady-state CPT resonance.
Zanon, T.; Guerandel, S.; Clercq, E. de; Holleville, D.; Dimarcq, N.; Clairon, A.
2005-05-20
We report the observation of Raman-Ramsey fringes using a double lambda scheme creating coherent population trapping in an atomic ensemble combined with pulsed optical radiations. The observation was made in a Cs vapor mixed with N{sub 2} buffer gas in a closed cell. The double lambda scheme is created with lin perpendicular lin polarized laser beams leading to higher contrast than the usual simple lambda scheme. The pulsed trapping technique leads to narrow fringe widths scaling as 1/(2T) with high contrasts which are no longer limited by the saturation effect. This technique operates in a different way from the classical Ramsey sequence: the signal is done by applying a long trapping pulse to prepare the atomic state superposition, and fringe detection is accomplished by optical transmission during a short second trapping pulse without any perturbation of the dark state.
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.
Coloring random graphs and maximizing local diversity.
Bounkong, S; van Mourik, J; Saad, D
2006-11-01
We study a variation of the graph coloring problem on random graphs of finite average connectivity. Given the number of colors, we aim to maximize the number of different colors at neighboring vertices (i.e., one edge distance) of any vertex. Two efficient algorithms, belief propagation and Walksat, are adapted to carry out this task. We present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution. The problem and the suggested algorithms have practical relevance since various applications, such as distributed storage, can be mapped onto this problem. PMID:17280022
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.
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.
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.
NASA Astrophysics Data System (ADS)
Aldecoa, Rodrigo; Orsini, Chiara; Krioukov, Dmitri
2015-11-01
Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks can be adequately modeled as random geometric graphs in hyperbolic spaces. In this paper, we present a computer program to generate such graphs. Besides real-world-like networks, the program can generate random graphs from other well-known graph ensembles, such as the soft configuration model, random geometric graphs on a circle, or Erdős-Rényi random graphs. The simulations show a good match between the expected values of different network structural properties and the corresponding empirical values measured in generated graphs, confirming the accurate behavior of the program.
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.
Understanding the role of spin-motion coupling in Ramsey spectroscopy
NASA Astrophysics Data System (ADS)
Koller, Andrew; Beverland, Michael; Mundinger, Joshua; Gorshkov, Alexey; Rey, Ana Maria
2014-05-01
Ramsey spectroscopy has become a powerful technique for probing non-equilibrium dynamics of internal (pseudospin) degrees of freedom of interacting systems. In many theoretical treatments, the key to understanding the dynamics has been to assume the external (motional) degrees of freedom are decoupled from the pseudospin degrees of freedom. Determining the validity of this approximation - known as the spin model approximation - has not been addressed in detail. We shed light in this direction by calculating Ramsey dynamics exactly for two interacting spin-1/2 particles in a harmonic trap. We find that in 1D the spin model assumption works well over a wide range of experimentally-relevant conditions, but can fail at time scales longer than those set by the mean interaction energy. Surprisingly, in 2D a modified version of the spin model is exact to first order in the interaction strength. This analysis is important for a correct interpretation of Ramsey spectroscopy and has broad applications ranging from precision measurements to quantum information and to fundamental probes of many-body systems. Supported by NSF, ARO-DARPA-OLE, AFOSR, NIST, the Lee A. DuBridge and Gordon and Betty Moore Foundations, and the NDSEG program.
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.
Pattern vectors from algebraic graph theory.
Wilson, Richard C; Hancock, Edwin R; Luo, Bin
2005-07-01
Graph structures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low-dimensional space using a number of alternative strategies, including principal components analysis (PCA), multidimensional scaling (MDS), and locality preserving projection (LPP). Experimentally, we demonstrate that the embeddings result in well-defined graph clusters. Our experiments with the spectral representation involve both synthetic and real-world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real-world experiments show that the method can be used to locate clusters of graphs. PMID:16013758
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.
Scale-invariant geometric random graphs
NASA Astrophysics Data System (ADS)
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.
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
Moody, Adam
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. It is also useful to characterize how interconnect performance changes with different settings or how one interconnect type compares to another.
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.
Models of random graph hierarchies
NASA Astrophysics Data System (ADS)
Paluch, Robert; Suchecki, Krzysztof; Hołyst, Janusz A.
2015-10-01
We introduce two models of inclusion hierarchies: random graph hierarchy (RGH) and limited random graph hierarchy (LRGH). In both models a set of nodes at a given hierarchy level is connected randomly, as in the Erdős-Rényi random graph, with a fixed average degree equal to a system parameter c. Clusters of the resulting network are treated as nodes at the next hierarchy level and they are connected again at this level and so on, until the process cannot continue. In the RGH model we use all clusters, including those of size 1, when building the next hierarchy level, while in the LRGH model clusters of size 1 stop participating in further steps. We find that in both models the number of nodes at a given hierarchy level h decreases approximately exponentially with h. The height of the hierarchy H, i.e. the number of all hierarchy levels, increases logarithmically with the system size N, i.e. with the number of nodes at the first level. The height H decreases monotonically with the connectivity parameter c in the RGH model and it reaches a maximum for a certain c max in the LRGH model. The distribution of separate cluster sizes in the LRGH model is a power law with an exponent about - 1.25. The above results follow from approximate analytical calculations and have been confirmed by numerical simulations.
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
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
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
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
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
De Jong, Marvin L.
1993-01-01
Describes the powerful graphing ability of computer algebra systems (CAS) to create three-dimensional graphs or surface graphics of electric potentials. Provides equations along with examples of the printouts. Lists the programs Mathematica, Maple, Derive, Theorist, MathCad, and MATLAB as promising CAS systems. (MVL)
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)
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
ERIC Educational Resources Information Center
Shaw, Jean M.
1984-01-01
Reasons for having students make graphs are noted. Then specific graphing topics and materials appropriate for young learners are presented, including life-sized, floor, clothespin, felt-face, block, and magnetic graphs, and polls of pupils. (MNS)
Evolutionary stability on graphs
Ohtsuki, Hisashi; Nowak, Martin A.
2008-01-01
Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs. We obtain analytical conditions for regular graphs of degree k > 2. Those theoretical predictions are compared with computer simulations for random regular graphs and for lattices. We study three different update rules: birth-death (BD), death-birth (DB), and imitation (IM) updating. Evolutionary stability on sparse graphs does not imply evolutionary stability in a well-mixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs. PMID:18295801
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.
Kitagawa, Takuya; Pielawa, Susanne; Demler, Eugene; Imambekov, Adilet; Schmiedmayer, Joerg; Gritsev, Vladimir
2010-06-25
We theoretically analyze Ramsey interference experiments in one-dimensional quasicondensates and obtain explicit expressions for the time evolution of full distribution functions of fringe contrast. We show that distribution functions contain unique signatures of the many-body mechanism of decoherence. We argue that Ramsey interference experiments provide a powerful tool for analyzing strongly correlated nature of 1D interacting systems.
Ramsey spectroscopy of high-contrast CPT resonances with push-pull optical pumping in Cs vapor.
Liu, X; Mérolla, J-M; Guérandel, S; de Clercq, E; Boudot, R
2013-05-20
We report on the detection of high-contrast and narrow Coherent Population Trapping (CPT) Ramsey fringes in a Cs vapor cell using a simple-architecture laser system. The latter allows the combination of push-pull optical pumping (PPOP) and a temporal Ramsey-like pulsed interrogation. An originality of the optics package is the use of a single Mach-Zehnder electro-optic modulator (MZ EOM) both for optical sidebands generation and light switch for pulsed interaction. Typical Ramsey fringes with a linewidth of 166 Hz and a contrast of 33 % are detected in a cm-scale buffer-gas filled Cs vapor cell. This technique could be interesting for the development of high-performance and low power consumption compact vapor cell clocks based on CPT. PMID:23736464
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. PMID:18827098
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.
The Ramsey phase-change hypothesis. [for development of earth core
NASA Technical Reports Server (NTRS)
Lyttleton, R. A.
1978-01-01
Ramsey's (1948, 1949, 1950, 1954) arguments for the phase-change interpretation of the nature of the terrestrial core are summarized. Some of the successes of the phase-change theory in accounting for hitherto unexplained properties of earth's interior are discussed. Evidence in favor of the phase-change theory is reviewed, and calculations are examined which indicate that the liquid-core material is far more compressible at any relevant pressure than is the mantle material. Implications of the phase-change theory for Venus, Mars, Mercury, and the moon are considered.
Modified hyper-Ramsey methods for the elimination of probe shifts in optical clocks
NASA Astrophysics Data System (ADS)
Hobson, R.; Bowden, W.; King, S. A.; Baird, P. E. G.; Hill, I. R.; Gill, P.
2016-01-01
We develop a method of modified hyper-Ramsey spectroscopy in optical clocks, achieving complete immunity to the frequency shifts induced by the probing fields themselves. Using particular pulse sequences with tailored phases, frequencies, and durations, we can derive an error signal centered exactly at the unperturbed atomic resonance with a steep discriminant which is robust against variations in the probe shift. We experimentally investigate the scheme using the magnetically induced 1S0-3P0 transition in 88Sr, demonstrating automatic suppression of a sizable 2 ×10-13 probe Stark shift to below 1 ×10-16 even with very large errors in shift compensation.
Encoding the core electrons with graph concepts.
Pogliani, Lionello
2004-01-01
The core electron problem of atoms in chemical graph studies has always been considered as a minor problem. Usually, chemical graphs had to encode just a small set of second row atoms, i.e., C, N, O, and F, thus, graph and, in some cases, pseudograph concepts were enough to "graph" encode the molecules at hand. Molecular connectivity theory, together with its side-branch the electrotopological state, introduced two "ad hoc" algorithms for the core electrons of higher-row atoms based, mainly, on quantum concepts alike. Recently, complete graphs, and, especially, odd complete graphs have been introduced to encode the core electrons of higher-row atoms. By the aid of these types of graphs a double-valued algorithm has been proposed for the valence delta, deltav, of any type of atoms of the periodic table with a principal quantum number n > or =2. The new algorithm is centered on an invariant suggested by the hand-shaking theorem, and the values it gives rise to parallel in some way the values derived by the aid of the two old "quantum" algorithms. A thorough comparative analysis of the newly proposed algorithms has been undertaken for atoms of the group 1A-7A of the periodic table. This comparative study includes the electronegativity, the size of the atoms, the first ionization energy, and the electron affinity. The given algorithm has also been tested with sequential complete graphs, while the even complete graphs give rise to conceptual difficulties. QSAR/QSPR studies do not show a clear-cut preference for any of the two values the algorithm gives rise to, even if recent results seem to prefer one of the two values. PMID:14741009
The Effect of Using Graphing Calculators in Complex Function Graphs
ERIC Educational Resources Information Center
Ocak, Mehmet Akif
2008-01-01
This study investigates the role of graphing calculators in multiple representations for knowledge transfer and the omission of oversimplification in complex function graphs. The main aim is to examine whether graphing calculators were used efficiently to see different cases and multiple perspectives among complex function graphs, or whether…
Ramsey effects in coherent resonances at closed transition Fg = 2 → Fe = 3 of 87Rb
NASA Astrophysics Data System (ADS)
Grujić, Z. D.; Lekić, M. M.; Radonjić, M.; Arsenović, D.; Jelenković, B. M.
2012-12-01
Experimental and theoretical investigations show the strong effect of the pump beam, spatially separated from the probe beam, on the probe's electromagnetically induced absorption (EIA) and nonlinear magneto-optical rotation (NMOR). Linearly polarized pump and probe laser beams are locked to the Fg = 2 → Fe = 3 transition of the 87Rb D2 line and pass a vacuum Rb gas cell coaxially. We show that the observed narrowing of EIA and NMOR resonances is due to the Ramsey effect. Linewidths of the resonances decrease when the size of the dark region between pump and probe lasers increases. Variation of the angle between pump and probe linear polarizations strongly influences the phases of atomic coherences generated by the pump beam and consequently the line-shapes of the probe EIA and NMOR resonances. Complete change of the resonance sign is possible if the phases of the ground state coherences, Δmg = 2, are altered by π. The central EIA fringe becomes less pronounced if the probe intensity increases, due to the larger probe contribution to atomic evolution. Ramsey-like interference is a manifestation of the evolution of ground state Zeeman coherences, required for EIA, in the dark region in the presence of a small magnetic field.
ERIC Educational Resources Information Center
Schlick, Deborah
Concerns about the growing waiting list for the child care assistance program in Ramsey County, Minnesota precipitated a telephone survey study of the experiences and attitudes of families on the waiting list. Participating in the study were 270 families randomly selected as a representative sample of individuals on the waiting list for March…
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
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).
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.
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. PMID:24483542
Higher-order graph wavelets and sparsity on circulant graphs
NASA Astrophysics Data System (ADS)
Kotzagiannidis, Madeleine S.; Dragotti, Pier Luigi
2015-08-01
The notion of a graph wavelet gives rise to more advanced processing of data on graphs due to its ability to operate in a localized manner, across newly arising data-dependency structures, with respect to the graph signal and underlying graph structure, thereby taking into consideration the inherent geometry of the data. In this work, we tackle the problem of creating graph wavelet filterbanks on circulant graphs for a sparse representation of certain classes of graph signals. The underlying graph can hereby be data-driven as well as fixed, for applications including image processing and social network theory, whereby clusters can be modelled as circulant graphs, respectively. We present a set of novel graph wavelet filter-bank constructions, which annihilate higher-order polynomial graph signals (up to a border effect) defined on the vertices of undirected, circulant graphs, and are localised in the vertex domain. We give preliminary results on their performance for non-linear graph signal approximation and denoising. Furthermore, we provide extensions to our previously developed segmentation-inspired graph wavelet framework for non-linear image approximation, by incorporating notions of smoothness and vanishing moments, which further improve performance compared to traditional methods.
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. PMID:25822506
ASK-GraphView: A large scale graph visualization system.
Abello, James; van Ham, Frank; Krishnan, Neeraj
2006-01-01
We describe ASK-GraphView, a node-link-based graph visualization system that allows clustering and interactive navigation of large graphs, ranging in size up to 16 million edges. The system uses a scalable architecture and a series of increasingly sophisticated clustering algorithms to construct a hierarchy on an arbitrary, weighted undirected input graph. By lowering the interactivity requirements we can scale to substantially bigger graphs. The user is allowed to navigate this hierarchy in a top down manner by interactively expanding individual clusters. ASK-GraphView also provides facilities for filtering and coloring, annotation and cluster labeling. PMID:17080786
New Graph Calculi for Planar Non-3-Colorable Graphs
NASA Astrophysics Data System (ADS)
Hanatani, Yoichi; Horiyama, Takashi; Iwama, Kazuo; Tamaki, Suguru
The Hajós calculus is a nondeterministic procedure which generates the class of non-3-colorable graphs. If all non-3-colorable graphs can be constructed in polynomial steps by the calculus, then NP=co-NP holds. Up to date, however, it remains open whether there exists a family of graphs that cannot be generated in polynomial steps. To attack this problem, we propose two graph calculi PHC and PHC* that generate non-3-colorable planar graphs, where intermediate graphs in the calculi are also restricted to be planar. Then we prove that PHC and PHC* are sound and complete. We also show that PHC* can polynomially simulate PHC.
Graphing. USMES Beginning "How To" Set.
ERIC Educational Resources Information Center
Agro, Sally; And Others
In this set of eight booklets on graphing, primary grade students learn how to choose which graph to make and how to make a bar graph, bar graph histogram, conversion graph, line chart, line graph, scatter graph, and slope diagram. The major emphasis in all Unified Sciences and Mathematics for Elementary Schools (USMES) units is on open-ended,…
Probing Real-Space and Time-Resolved Correlation Functions with Many-Body Ramsey Interferometry
NASA Astrophysics Data System (ADS)
Knap, Michael; Kantian, Adrian; Giamarchi, Thierry; Bloch, Immanuel; Lukin, Mikhail D.; Demler, Eugene
2013-10-01
We propose to use Ramsey interferometry and single-site addressability, available in synthetic matter such as cold atoms or trapped ions, to measure real-space and time-resolved spin correlation functions. These correlation functions directly probe the excitations of the system, which makes it possible to characterize the underlying many-body states. Moreover, they contain valuable information about phase transitions where they exhibit scale invariance. We also discuss experimental imperfections and show that a spin-echo protocol can be used to cancel slow fluctuations in the magnetic field. We explicitly consider examples of the two-dimensional, antiferromagnetic Heisenberg model and the one-dimensional, long-range transverse field Ising model to illustrate the technique.
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.
Quantum-projection-noise-limited interferometry with coherent atoms in a Ramsey-type setup
Doering, D.; McDonald, G.; Debs, J. E.; Figl, C.; Altin, P. A.; Bachor, H.-A.; Robins, N. P.; Close, J. D.
2010-04-15
Every measurement of the population in an uncorrelated ensemble of two-level systems is limited by what is known as the quantum projection noise limit. Here, we present quantum-projection-noise-limited performance of a Ramsey-type interferometer using freely propagating coherent atoms. The experimental setup is based on an electro-optic modulator in an inherently stable Sagnac interferometer, optically coupling the two interfering atomic states via a two-photon Raman transition. Going beyond the quantum projection noise limit requires the use of reduced quantum uncertainty (squeezed) states. The experiment described demonstrates atom interferometry at the fundamental noise level and allows the observation of possible squeezing effects in an atom laser, potentially leading to improved sensitivity in atom interferometers.
Probe light-shift elimination in generalized hyper-Ramsey quantum clocks
NASA Astrophysics Data System (ADS)
Zanon-Willette, T.; de Clercq, E.; Arimondo, E.
2016-04-01
We present an interrogation scheme for the next generation of quantum clocks to suppress frequency shifts induced by laser probing fields that are themselves based on generalized hyper-Ramsey resonances. Sequences of composite laser pulses with a specific selection of phases, frequency detunings, and durations are combined to generate a very efficient and robust frequency locking signal with an almost perfect elimination of the light shift from off-resonant states and to decouple the unperturbed frequency measurement from the laser's intensity. The frequency lock point generated from synthesized error signals using either π /4 or 3 π /4 laser phase steps during the intermediate pulse is tightly protected against large laser-pulse area variations and errors in potentially applied frequency shift compensations. Quantum clocks based on weakly allowed or completely forbidden optical transitions in atoms, ions, molecules, and nuclei will benefit from these hyperstable laser frequency stabilization schemes to reach relative accuracies below the 10-18 level.
Space Time Reversal Experiment by Use of Pulsed Neutron Ramsey Resonance
Masuda, Y.; Jeong, S. C.; Watanabe, Y.; Skoy, V.; Ino, T.
2007-06-13
We have developed a pulsed neutron Ramsey resonance for a T-violation experiment on polarized neutron transmission through a polarized nuclear target. Two separated oscillatory fields were placed in a pulsed neutron beam line, which were synchronized with a neutron pulse for precision neutron spin manipulation. We observed neutron Larmor precession between the two oscillatory fields as a function of a neutron time of flight (TOF). We modulated the phase of the second oscillatory field with respect to the first oscillatory field. The effect of the phase modulation was found in a neutron intensity modulation as a function of the TOF. From the neutron intensity modulation, the neutron spin direction as well as the neutron velocity between the two oscillatory fields was precisely obtained.
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).
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…
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
On the length of the drift region in the Ramsey cavity
NASA Technical Reports Server (NTRS)
Thomann, Pierre
1990-01-01
The interaction of atoms in a beam with the microwave field in a separated field geometry such as a Ramsey cavity is generally described in terms of the three regions traversed successively by the atoms, namely two interaction regions of length (l) separated by a drift, or free precession, region of length L. For a monokinetic beam of velocity v, the linewidth of the central fringe in the Ramsey resonance pattern is usually expressed as delta omega equals pi v/L. A more detailed calculation shows, however, that the linewidth is equal to pi v/L asterisk, where the equivalent drift L asterisk is larger than L by an amount of the order of l/L. The correction depends on the field distribution in the interaction regions. Its origin lies in the fact that atomic precession is not limited to the field-free regions but also occurs in the interaction regions, where atomic coherence builds up or decreases continuously. Although the correction to the equivalent length of the drift region is small, it may be relevant to the evaluation of the second-order Doppler effect bias in primary cesium-beam standards to the extent that the atomic velocity is deduced from the lineshape and from the geometrical parameters of the cavity. It is shown that in current and projected standards with atoms of average thermal velocity, use of corrected dimensions may lead to a change of the calculated bias of the order of 10(exp -14), which is significant at the levels of accuracy considered nowadays.
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.
NASA Astrophysics Data System (ADS)
Gnutzmann, S.; Keating, J. P.; Piotet, F.
2008-12-01
We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for large well-connected graphs. We use an exact field-theoretic expression in terms of a variant of the supersymmetric nonlinear σ model. Our estimate is based on a saddle-point analysis of this expression and leads to a criterion for when equidistribution emerges asymptotically in the limit of large graphs. Our theory predicts a rate of convergence that is a significant refinement of previous estimates, long assumed to be valid for quantum chaotic systems, agreeing with them in some situations but not all. We discuss specific examples for which the theory is tested numerically.
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.
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.
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. PMID:26415154
Graph ranking for exploratory gene data analysis
2009-01-01
Background Microarray technology has made it possible to simultaneously monitor the expression levels of thousands of genes in a single experiment. However, the large number of genes greatly increases the challenges of analyzing, comprehending and interpreting the resulting mass of data. Selecting a subset of important genes is inevitable to address the challenge. Gene selection has been investigated extensively over the last decade. Most selection procedures, however, are not sufficient for accurate inference of underlying biology, because biological significance does not necessarily have to be statistically significant. Additional biological knowledge needs to be integrated into the gene selection procedure. Results We propose a general framework for gene ranking. We construct a bipartite graph from the Gene Ontology (GO) and gene expression data. The graph describes the relationship between genes and their associated molecular functions. Under a species condition, edge weights of the graph are assigned to be gene expression level. Such a graph provides a mathematical means to represent both species-independent and species-dependent biological information. We also develop a new ranking algorithm to analyze the weighted graph via a kernelized spatial depth (KSD) approach. Consequently, the importance of gene and molecular function can be simultaneously ranked by a real-valued measure, KSD, which incorporates the global and local structure of the graph. Over-expressed and under-regulated genes also can be separately ranked. Conclusion The gene-function bigraph integrates molecular function annotations into gene expression data. The relevance of genes is described in the graph (through a common function). The proposed method provides an exploratory framework for gene data analysis. PMID:19811684
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.
Polynomial iterative algorithms for coloring and analyzing random graphs.
Braunstein, A; Mulet, R; Pagnani, A; Weigt, M; Zecchina, R
2003-09-01
We study the graph coloring problem over random graphs of finite average connectivity c. Given a number q of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable. Depending on q, we find with a one-step replica-symmetry breaking approximation the precise value of the critical average connectivity c(q). Moreover, we show that below c(q) there exists a clustering phase c in [c(d),c(q)] in which ground states spontaneously divide into an exponential number of clusters. Furthermore, we extended our considerations to the case of single instances showing consistent results. This leads us to propose a different algorithm that is able to color in polynomial time random graphs in the hard but colorable region, i.e., when c in [c(d),c(q)]. PMID:14524921
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.
NASA Astrophysics Data System (ADS)
Sui, Xiukai; Wu, Bin; Wang, Long
2015-12-01
The likelihood that a mutant fixates in the wild population, i.e., fixation probability, has been intensively studied in evolutionary game theory, where individuals' fitness is frequency dependent. However, it is of limited interest when it takes long to take over. Thus the speed of evolution becomes an important issue. In general, it is still unclear how fixation times are affected by the population structure, although the fixation times have already been addressed in the well-mixed populations. Here we theoretically address this issue by pair approximation and diffusion approximation on regular graphs. It is shown (i) that under neutral selection, both unconditional and conditional fixation time are shortened by increasing the number of neighbors; (ii) that under weak selection, for the simplified prisoner's dilemma game, if benefit-to-cost ratio exceeds the degree of the graph, then the unconditional fixation time of a single cooperator is slower than that in the neutral case; and (iii) that under weak selection, for the conditional fixation time, limited neighbor size dilutes the counterintuitive stochastic slowdown which was found in well-mixed populations. Interestingly, we find that all of our results can be interpreted as that in the well-mixed population with a transformed payoff matrix. This interpretation is also valid for both death-birth and birth-death processes on graphs. This interpretation bridges the fixation time in the structured population and that in the well-mixed population. Thus it opens the avenue to investigate the challenging fixation time in structured populations by the known results in well-mixed populations.
ERIC Educational Resources Information Center
Nemirovsky, Ricardo; Tierney, Cornelia; Wright, Tracy
1998-01-01
Analyzed two children's use of a computer-based motion detector to make sense of symbolic expressions (Cartesian graphs). Found three themes: (1) tool perspectives, efforts to understand graphical responses to body motion; (2) fusion, emergent ways of talking and behaving that merge symbols and referents; and (3) graphical spaces, when changing…
ERIC Educational Resources Information Center
Beckmann, Charlene E.; Rozanski, Kara
1999-01-01
Presents a lesson that uses a motion detector in order for students to experience the interplay between motion and its graphical representation of the slope. Focuses on the change in the appearance of the graph with regard to changing speed. (ASK)
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
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…
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
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.
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,
Clustering gene expression data using graph separators.
Kaba, Bangaly; Pinet, Nicolas; Lelandais, Gaëlle; Sigayret, Alain; Berry, Anne
2007-01-01
Recent work has used graphs to modelize expression data from microarray experiments, in view of partitioning the genes into clusters. In this paper, we introduce the use of a decomposition by clique separators. Our aim is to improve the classical clustering methods in two ways: first we want to allow an overlap between clusters, as this seems biologically sound, and second we want to be guided by the structure of the graph to define the number of clusters. We test this approach with a well-known yeast database (Saccharomyces cerevisiae). Our results are good, as the expression profiles of the clusters we find are very coherent. Moreover, we are able to organize into another graph the clusters we find, and order them in a fashion which turns out to respect the chronological order defined by the the sporulation process. PMID:18391236
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.
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…
Using Combinatorica/Mathematica for Student Projects in Random Graph Theory
ERIC Educational Resources Information Center
Pfaff, Thomas J.; Zaret, Michele
2006-01-01
We give an example of a student project that experimentally explores a topic in random graph theory. We use the "Combinatorica" package in "Mathematica" to estimate the minimum number of edges needed in a random graph to have a 50 percent chance that the graph is connected. We provide the "Mathematica" code and compare it to the known theoretical…
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. PMID:25616091
NASA Astrophysics Data System (ADS)
Cooper, Colin; Frieze, Alan
The aim of this article is to discuss some of the notions and applications of random walks on finite graphs, especially as they apply to random graphs. In this section we give some basic definitions, in Section 2 we review applications of random walks in computer science, and in Section 3 we focus on walks in random graphs.
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.
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.…
ERIC Educational Resources Information Center
Hopkins, Brian
2004-01-01
The interconnected world of actors and movies is a familiar, rich example for graph theory. This paper gives the history of the "Kevin Bacon Game" and makes extensive use of a Web site to analyze the underlying graph. The main content is the classroom development of the weighted average to determine the best choice of "center" for the graph. The…
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.
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…
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.
Graphing. USMES Intermediate "How To" Set.
ERIC Educational Resources Information Center
Agro, Sally; And Others
In this set of six booklets on graphing, intermediate grade students learn how to choose which kind of graph to make; make bar graphs, histograms, line graphs, and conversion graphs; and use graphs to compare two sets of data. The major emphasis in all Unified Sciences and Mathematics for Elementary Schools (USMES) units is on open-ended,…
Multithreaded Algorithms for Graph Coloring
Catalyurek, Umit V.; Feo, John T.; Gebremedhin, Assefaw H.; Halappanavar, Mahantesh; Pothen, Alex
2012-10-21
Graph algorithms are challenging to parallelize when high performance and scalability are primary goals. Low concurrency, poor data locality, irregular access pattern, and high data access to computation ratio are among the chief reasons for the challenge. The performance implication of these features is exasperated on distributed memory machines. More success is being achieved on shared-memory, multi-core architectures supporting multithreading. We consider a prototypical graph problem, coloring, and show how a greedy algorithm for solving it can be e*ectively parallelized on multithreaded architectures. We present in particular two di*erent parallel algorithms. The first relies on speculation and iteration, and is suitable for any shared-memory, multithreaded system. The second uses data ow principles and is targeted at the massively multithreaded Cray XMT system. We benchmark the algorithms on three di*erent platforms and demonstrate scalable runtime performance. In terms of quality of solution, both algorithms use nearly the same number of colors as the serial algorithm.
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.
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…
Huber, Wolfgang; Carey, Vincent J; Long, Li; Falcon, Seth; Gentleman, Robert
2007-01-01
Graph theoretical concepts are useful for the description and analysis of interactions and relationships in biological systems. We give a brief introduction into some of the concepts and their areas of application in molecular biology. We discuss software that is available through the Bioconductor project and present a simple example application to the integration of a protein-protein interaction and a co-expression network. PMID:17903289
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.
Entanglement witnesses for graph states: General theory and examples
Jungnitsch, Bastian; Moroder, Tobias; Guehne, Otfried
2011-09-15
We present a general theory for the construction of witnesses that detect genuine multipartite entanglement in graph states. First, we present explicit witnesses for all graph states of up to six qubits which are better than all criteria so far. Therefore, lower fidelities are required in experiments that aim at the preparation of graph states. Building on these results, we develop analytical methods to construct two different types of entanglement witnesses for general graph states. For many classes of states, these operators exhibit white noise tolerances that converge to 1 when increasing the number of particles. We illustrate our approach for states such as the linear and the 2D cluster state. Finally, we study an entanglement monotone motivated by our approach for graph states.
NASA Astrophysics Data System (ADS)
Fortunato, Santo
2010-02-01
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i.e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e.g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.
NASA Astrophysics Data System (ADS)
Rudinger, Kenneth; Gamble, John King; Wellons, Mark; Bach, Eric; Friesen, Mark; Joynt, Robert; Coppersmith, S. N.
2012-08-01
We investigate the quantum dynamics of particles on graphs (“quantum random walks”), with the aim of developing quantum algorithms for determining if two graphs are isomorphic (related to each other by a relabeling of vertices). We focus on quantum random walks of multiple noninteracting particles on strongly regular graphs (SRGs), a class of graphs with high symmetry that is known to have pairs of graphs that are hard to distinguish. Previous work has already demonstrated analytically that two-particle noninteracting quantum walks cannot distinguish nonisomorphic SRGs of the same family. Here, we demonstrate numerically that three-particle noninteracting quantum walks have significant, but not universal, distinguishing power for pairs of SRGs, proving a fundamental difference between the distinguishing power of two-particle and three-particle noninteracting walks. We show analytically why this distinguishing power is possible, whereas it is forbidden for two-particle noninteracting walks. Based on sampling of SRGs with up to 64 vertices, we find no difference in the distinguishing power of bosonic and fermionic walks. In addition, we find that the four-fermion noninteracting walk has greater distinguishing power than the three-particle walk on SRGs, showing that increasing the particle number increases the distinguishing power. However, we also show analytically that no noninteracting walk with a fixed number of particles can distinguish all SRGs, thus demonstrating a potential fundamental difference in the distinguishing power of interacting versus noninteracting walks.
Join-Graph Propagation Algorithms
Mateescu, Robert; Kask, Kalev; Gogate, Vibhav; Dechter, Rina
2010-01-01
The paper investigates parameterized approximate message-passing schemes that are based on bounded inference and are inspired by Pearl's belief propagation algorithm (BP). We start with the bounded inference mini-clustering algorithm and then move to the iterative scheme called Iterative Join-Graph Propagation (IJGP), that combines both iteration and bounded inference. Algorithm IJGP belongs to the class of Generalized Belief Propagation algorithms, a framework that allowed connections with approximate algorithms from statistical physics and is shown empirically to surpass the performance of mini-clustering and belief propagation, as well as a number of other state-of-the-art algorithms on several classes of networks. We also provide insight into the accuracy of iterative BP and IJGP by relating these algorithms to well known classes of constraint propagation schemes. PMID:20740057
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.
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.
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.
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
Cactus Graphs for Genome Comparisons
NASA Astrophysics Data System (ADS)
Paten, Benedict; Diekhans, Mark; Earl, Dent; St. John, John; Ma, Jian; Suh, Bernard; Haussler, David
We introduce a data structure, analysis and visualization scheme called a cactus graph for comparing sets of related genomes. Cactus graphs capture some of the advantages of de Bruijn and breakpoint graphs in one unified framework. They naturally decompose the common substructures in a set of related genomes into a hierarchy of chains that can be visualized as multiple alignments and nets that can be visualized in circular genome plots.
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
The first eigenvalue of the p- Laplacian on quantum graphs
NASA Astrophysics Data System (ADS)
Del Pezzo, Leandro M.; Rossi, Julio D.
2016-01-01
We study the first eigenvalue of the p- Laplacian (with 1
graph with Dirichlet or Kirchoff boundary conditions on the nodes. We find lower and upper bounds for this eigenvalue when we prescribe the total sum of the lengths of the edges and the number of Dirichlet nodes of the graph. Also we find a formula for the shape derivative of the first eigenvalue (assuming that it is simple) when we perturb the graph by changing the length of an edge. Finally, we study in detail the limit cases p→ ∞ and p→ 1.
Graph-based algorithms for Boolean function manipulation
Bryant, R.E.
1986-08-01
In this paper the authors present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. The algorithms have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large. The authors present experimental results from applying these algorithms to problems in logic design verification that demonstrate the practicality of the approach.
DNA solution of a graph coloring problem.
Liu, Yachun; Xu, Jin; Pan, Linqiang; Wang, Shiying
2002-01-01
The graph-theoretic parameter that has probably received the most attention over the years is the chromatic number. As is well-known, the coloring problem is an NP-Complete problem. In this paper, it has been solved by means of molecular biology techniques. The algorithm is highly parallel and has satisfactory fidelity. This work shows further evidence for the ability of DNA computing to solve NP-Complete problems. PMID:12086509
Statistics of Gaussian packets on metric and decorated graphs
Chernyshev, V. L.; Shafarevich, A. I.
2014-01-01
We study a semiclassical asymptotics of the Cauchy problem for a time-dependent Schrödinger equation on metric and decorated graphs with a localized initial function. A decorated graph is a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds. The main term of an asymptotic solution at an arbitrary finite time is a sum of Gaussian packets and generalized Gaussian packets (localized near a certain set of codimension one). We study the number of packets as time tends to infinity. We prove that under certain assumptions this number grows in time as a polynomial and packets fill the graph uniformly. We discuss a simple example of the opposite situation: in this case, a numerical experiment shows a subexponential growth. PMID:24344346
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.
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(N(2))], 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. PMID:25122337
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.
Graph Visualization for RDF Graphs with SPARQL-EndPoints
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.
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%.
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.
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.
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.
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.
Bootstrap Percolation in Power-Law Random Graphs
NASA Astrophysics Data System (ADS)
Amini, Hamed; Fountoulakis, Nikolaos
2014-04-01
A bootstrap percolation process on a graph is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least infected neighbours becomes infected and remains so forever. The parameter is fixed. Such processes have been used as models for the spread of ideas or trends within a network of individuals. We analyse this process in the case where the underlying graph is an inhomogeneous random graph, which exhibits a power-law degree distribution, and initially there are randomly infected nodes. The main focus of this paper is the number of vertices that will have been infected by the end of the process. The main result of this work is that if the degree sequence of the random graph follows a power law with exponent , where , then a sublinear number of initially infected vertices is enough to spread the infection over a linear fraction of the nodes of the random graph, with high probability. More specifically, we determine explicitly a critical function such that with the following property. Assuming that is the number of vertices of the underlying random graph, if , then the process does not evolve at all, with high probability as grows, whereas if , then there is a constant such that, with high probability, the final set of infected vertices has size at least . This behaviour is in sharp contrast with the case where the underlying graph is a random graph with . It follows from an observation of Balogh and Bollobás that in this case if the number of initially infected vertices is sublinear, then there is lack of evolution of the process. It turns out that when the maximum degree is , then depends also on . But when the maximum degree is , then.
Guide to graphing data and taking action.
1992-01-01
3 kinds of graphs are presented as instructional examples of how to display data collected on family planning (FP) programs. The first is a trend analysis of new acceptors and requires monthly summaries of new acceptors serviced by the clinic. The objective is to gauge declines or increases over time in new acceptors for each contraceptive method offered. The second graph requires a monthly summary of new acceptors by method mix. The third graph needs data on the reason for attending the particular FP clinic. IEC activities can be enhanced with this information. In the example for graph 1, new acceptors over an 18-month-period are plotted on one axis by monthly units, and the other axis by number of new acceptors. The connection of dots reflects the trend over time. There is a specific example with data from Yena clinic over a 12-month-period; the interpretations and possible actions are indicated. Instructions for presenting a pie chart are also given for new acceptors by method mix; the example is given for data from Yena Clinic and possible interpretations and actions are indicated. A visual presentation of the data worksheet needed for a pie chart is provided. Calculations must be made for the fraction of new acceptors out of total acceptors and the percent of total new acceptors for each method. An explanation is given for constructing a bar chart; again an example is given of a completed bar chart with data and the accompanying data sheet. A checklist identifies important guidelines for developing and using line graphs, bar charts, and pie charts. PMID:12318345
Young Students Investigate Number Cubes.
ERIC Educational Resources Information Center
Friedlander, Alex
1997-01-01
Describes a series of learning activities built around number cubes. Sample activities introduce elementary properties of the cube, the magic rule of seven, and basic concepts related to graphs in the plane coordinate system. (PVD)
2010-01-01
Background Oncidium spp. produce commercially important orchid cut flowers. However, they are amenable to intergeneric and inter-specific crossing making phylogenetic identification very difficult. Molecular markers derived from the chloroplast genome can provide useful tools for phylogenetic resolution. Results The complete chloroplast genome of the economically important Oncidium variety Onc. Gower Ramsey (Accession no. GQ324949) was determined using a polymerase chain reaction (PCR) and Sanger based ABI sequencing. The length of the Oncidium chloroplast genome is 146,484 bp. Genome structure, gene order and orientation are similar to Phalaenopsis, but differ from typical Poaceae, other monocots for which there are several published chloroplast (cp) genome. The Onc. Gower Ramsey chloroplast-encoded NADH dehydrogenase (ndh) genes, except ndhE, lack apparent functions. Deletion and other types of mutations were also found in the ndh genes of 15 other economically important Oncidiinae varieties, except ndhE in some species. The positions of some species in the evolution and taxonomy of Oncidiinae are difficult to identify. To identify the relationships between the 15 Oncidiinae hybrids, eight regions of the Onc. Gower Ramsey chloroplast genome were amplified by PCR for phylogenetic analysis. A total of 7042 bp derived from the eight regions could identify the relationships at the species level, which were supported by high bootstrap values. One particular 1846 bp region, derived from two PCR products (trnHGUG -psbA and trnFGAA-ndhJ) was adequate for correct phylogenetic placement of 13 of the 15 varieties (with the exception of Degarmoara Flying High and Odontoglossum Violetta von Holm). Thus the chloroplast genome provides a useful molecular marker for species identifications. Conclusion In this report, we used Phalaenopsis. aphrodite as a prototype for primer design to complete the Onc. Gower Ramsey genome sequence. Gene annotation showed that most of the ndh
CANCER MORTALITY MAPS AND GRAPHS
The Cancer Mortality Maps & Graph Web Site provides interactive maps, graphs (which are accessible to the blind and visually-impaired), text, tables and figures showing geographic patterns and time trends of cancer death rates for the time period 1950-1994 for more than 40 cancer...
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)
Graph models of habitat mosaics.
Urban, Dean L; Minor, Emily S; Treml, Eric A; Schick, Robert S
2009-03-01
Graph theory is a body of mathematics dealing with problems of connectivity, flow, and routing in networks ranging from social groups to computer networks. Recently, network applications have erupted in many fields, and graph models are now being applied in landscape ecology and conservation biology, particularly for applications couched in metapopulation theory. In these applications, graph nodes represent habitat patches or local populations and links indicate functional connections among populations (i.e. via dispersal). Graphs are models of more complicated real systems, and so it is appropriate to review these applications from the perspective of modelling in general. Here we review recent applications of network theory to habitat patches in landscape mosaics. We consider (1) the conceptual model underlying these applications; (2) formalization and implementation of the graph model; (3) model parameterization; (4) model testing, insights, and predictions available through graph analyses; and (5) potential implications for conservation biology and related applications. In general, and for a variety of ecological systems, we find the graph model a remarkably robust framework for applications concerned with habitat connectivity. We close with suggestions for further work on the parameterization and validation of graph models, and point to some promising analytic insights. PMID:19161432
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…
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.
Graphs on uniform points in [0,1]d
NASA Astrophysics Data System (ADS)
Appel, Martin J. B.; Russo, Ralph P.; Yang, King J.
1995-06-01
Statistical problems in pattern or structure recognition for a random multidimensional point set may be addressed by variations on the random graph model of Erdos and Renyui. The imposition of graph structure with a variable edge criterion on a large random point set allows a search for signature quantities or behavior under the given distributional hypothesis. The work is motivated by the question of how to make statistical inferences from sensed mine field data. This article describes recent results obtained in the following special cases. On independent random points U1,...,Un distributed uniformly on [0,1]d, a random graph Gn(x) is constructed in which two distinct such points are joined by an edge if the l(infinity )-distance between them is at most some prescribed value 0
A parallel graph coloring heuristic
Jones, M.T.; Plassmann, P.E. )
1993-05-01
The problem of computing good graph colorings arises in many diverse applications, such as in the estimation of sparse Jacobians and in the development of efficient, parallel iterative methods for solving sparse linear systems. This paper presents an asynchronous graph coloring heuristic well suited to distributed memory parallel computers. Experimental results obtained on an Intel iPSC/860 are presented, which demonstrate that, for graphs arising from finite element applications, the heuristic exhibits scalable performance and generates colorings usually within three or four colors of the best-known linear time sequential heuristics. For bounded degree graphs, it is shown that the expected running time of the heuristic under the P-Ram computation model is bounded by EO(log(n)/log log(n)). This bound is an improvement over the previously known best upper bound for the expected running time of a random heuristic for the graph coloring problem.
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
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
Graph hierarchies for phylogeography.
Cybis, Gabriela B; Sinsheimer, Janet S; Lemey, Philippe; Suchard, Marc A
2013-03-19
Bayesian phylogeographic methods simultaneously integrate geographical and evolutionary modelling, and have demonstrated value in assessing spatial spread patterns of measurably evolving organisms. We improve on existing phylogeographic methods by combining information from multiple phylogeographic datasets in a hierarchical setting. Consider N exchangeable datasets or strata consisting of viral sequences and locations, each evolving along its own phylogenetic tree and according to a conditionally independent geographical process. At the hierarchical level, a random graph summarizes the overall dispersion process by informing which migration rates between sampling locations are likely to be relevant in the strata. This approach provides an efficient and improved framework for analysing inherently hierarchical datasets. We first examine the evolutionary history of multiple serotypes of dengue virus in the Americas to showcase our method. Additionally, we explore an application to intrahost HIV evolution across multiple patients. PMID:23382428
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.
The asymptotics of large constrained graphs
NASA Astrophysics Data System (ADS)
Radin, Charles; Ren, Kui; Sadun, Lorenzo
2014-05-01
We show, through local estimates and simulation, that if one constrains simple graphs by their densities ɛ of edges and τ of triangles, then asymptotically (in the number of vertices) for over 95% of the possible range of those densities there is a well-defined typical graph, and it has a very simple structure: the vertices are decomposed into two subsets V1 and V2 of fixed relative size c and 1 - c, and there are well-defined probabilities of edges, gjk, between vj ∈ Vj, and vk ∈ Vk. Furthermore the four parameters c, g11, g22 and g12 are smooth functions of (ɛ, τ) except at two smooth ‘phase transition’ curves.
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.
Flying through Graphs: An Introduction to Graph Theory.
ERIC Educational Resources Information Center
McDuffie, Amy Roth
2001-01-01
Presents an activity incorporating basic terminology, concepts, and solution methods of graph theory in the context of solving problems related to air travel. Discusses prerequisite knowledge and resources and includes a teacher's guide with a student worksheet. (KHR)
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)
Shahid, Nauman; Perraudin, Nathanael; Kalofolias, Vassilis; Puy, Gilles; Vandergheynst, Pierre
2016-06-01
Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role to overcome the curse of dimensionality. However, often such methods are accompanied with three different problems: high computational complexity (usually associated with the nuclear norm minimization), non-convexity (for matrix factorization methods) and susceptibility to gross corruptions in the data. In this paper we propose a principal component analysis (PCA) based solution that overcomes these three issues and approximates a low-rank recovery method for high dimensional datasets. We target the low-rank recovery by enforcing two types of graph smoothness assumptions, one on the data samples and the other on the features by designing a convex optimization problem. The resulting algorithm is fast, efficient and scalable for huge datasets with O(nlog(n)) computational complexity in the number of data samples. It is also robust to gross corruptions in the dataset as well as to the model parameters. Clustering experiments on 7 benchmark datasets with different types of corruptions and background separation experiments on 3 video datasets show that our proposed model outperforms 10 state-of-the-art dimensionality reduction models. Our theoretical analysis proves that the proposed model is able to recover approximate low-rank representations with a bounded error for clusterable data.
NASA Astrophysics Data System (ADS)
Szabó, György; Fáth, Gábor
2007-07-01
Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by non-mean-field-type social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Stacked graphs--geometry & aesthetics.
Byron, Lee; Wattenberg, Martin
2008-01-01
In February 2008, the New York Times published an unusual chart of box office revenues for 7500 movies over 21 years. The chart was based on a similar visualization, developed by the first author, that displayed trends in music listening. This paper describes the design decisions and algorithms behind these graphics, and discusses the reaction on the Web. We suggest that this type of complex layered graph is effective for displaying large data sets to a mass audience. We provide a mathematical analysis of how this layered graph relates to traditional stacked graphs and to techniques such as ThemeRiver, showing how each method is optimizing a different "energy function". Finally, we discuss techniques for coloring and ordering the layers of such graphs. Throughout the paper, we emphasize the interplay between considerations of aesthetics and legibility. PMID:18988970
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…
NASA Astrophysics Data System (ADS)
Marinari, Enzo; Semerjian, Guilhem; van Kerrebroeck, Valery
2007-06-01
We analyze the problem of discovering long cycles inside a graph. We propose and test two algorithms for this task. The first one is based on recent advances in statistical mechanics and relies on a message passing procedure. The second follows a more standard Monte Carlo Markov chain strategy. Special attention is devoted to Hamiltonian cycles of (nonregular) random graphs of minimal connectivity equal to 3.
Zeta functions of quantum graphs
NASA Astrophysics Data System (ADS)
Harrison, J. M.; Kirsten, K.
2011-06-01
In this paper, we construct zeta functions of quantum graphs using a contour integral technique based on the argument principle. We start by considering the special case of the star graph with Neumann matching conditions at the center of the star. We then extend the technique to allow any matching conditions at the center for which the Laplace operator is self-adjoint and finally obtain an expression for the zeta function of any graph with general vertex matching conditions. In the process, it is convenient to work with new forms for the secular equation of a quantum graph that extend the well-known secular equation of the Neumann star graph. In the second half of this paper, we apply the zeta function to obtain new results for the spectral determinant, vacuum energy and heat kernel coefficients of quantum graphs. These have all been topics of current research in their own right and in each case this unified approach significantly expands results in the literature.
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.
Iterated greedy graph coloring and the coloring landscape
Culberson, J.
1994-12-31
The Iterated Greedy (IG) graph coloring algorithm uses the greedy, or simple sequential, graph coloring algorithm repeatedly to obtain ever better colorings. On each iteration, the permutation presented to the greedy algorithm is generated so that the vertices of the independent sets identified in the previous coloring are adjacent in the permutation. It is trivial to prove that this ensures that the new coloring will use no more colors than the previous coloring. On random graphs the algorithm does not perform as well as TABU or semi-exhaustive independent set approaches. It does offer some improvements when combined with these. On k-colorable graphs it seems quite effective, and offers a robustness over a wide range of k, n, p values the other algorithms seem not to have. In particular, evidence indicates that one setting of parameters seems to be {open_quotes}near best{close_quotes} over most of these classes. Evidence also indicates that graphs in the classes we consider that are harder for this algorithm are also more difficult for TABU and semi-exhaustive independent set approaches. Thus, the number of iterations required gives a natural measure of difficulty of the graphs, independent of machine characteristics and many details of implementation.
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)
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.
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.
Numerical investigations of quantum walks with hard-core bosons and the graph isomorphism problem
NASA Astrophysics Data System (ADS)
Wellons, Mark; Gamble, John; Bach, Eric; Friesen, Mark; Joynt, Robert; Rudinger, Kenneth; Zhou, Dong; Coppersmith, Susan
2011-03-01
Gamble et al. investigated quantum walks of two hard-core bosons on a class of highly symmetric graphs called strongly regular graphs (SRGs) and showed that these walks will distinguish nonisomorphic graphs from the same family. However, J. Smith (arXiv:1004.0206) has shown that pairs of nonisomorphic graphs exist that cannot be distinguished by such quantum walks. Here we construct explicit counterexample graph pairs for 2 and 3-particle interacting and non-interacting walks. We also describe an algorithm that, given k particles, generates two graphs indistinguishable by a k -boson quantum walk. We find that these indistinguishable graph pairs generated by our algorithm scale in size quadratically with the number of particles. It follows that distinguishing graphs via simulating quantum walks with classical computers will likely require exponential time in the size of the graph, while leaving open the possibility that a quantum computer could distinguish the graphs in polynomial time. This work was supported by ARO and DOD (W911NF-09-1-0439) and NSF (CCF-0635355). J.K.G. acknowledges support from the NSF.
Bonabeau model on a fully connected graph
NASA Astrophysics Data System (ADS)
Malarz, K.; Stauffer, D.; Kułakowski, K.
2006-03-01
Numerical simulations are reported on the Bonabeau model on a fully connected graph, where spatial degrees of freedom are absent. The control parameter is the memory factor f. The phase transition is observed at the dispersion of the agents power hi. The critical value fC shows a hysteretic behavior with respect to the initial distribution of hi. fC decreases with the system size; this decrease can be compensated by a greater number of fights between a global reduction of the distribution width of hi. The latter step is equivalent to a partial forgetting.
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.
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.
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.
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.
Graph transformation expert system (GTES)
NASA Astrophysics Data System (ADS)
Li, Guiquing; Ge, Qihong; Zhong, Luo; Xie, Weiping
1996-03-01
The design of many industrial and engineering systems can often be accomplished using flow graphs of various types. Examples include manufacturing processes and data processing applications, Graph Transformation Expert System, is an expert system which has been developed by WUT for applying techniques of artificial intelligence to the architectural design of data and signal processing systems. Software and hardware architectures may be defined for such systems using data flow graphs, in which nodes represent data processing steps and directed areas represent the `flow' of data between the processing steps. Starting with a user- defined generic processing graphic, this expert will transform the graph by applying transformation rules in order to specialize the processing graph to satisfy specified design goals and/or hardware constraints. Although the particular application for which this expert is designed is that of data and signal processing systems, it can provide an expert system framework for other problems specified graphically; for example, manufacturing systems, information systems, and product distribution systems.
Eigenfunction statistics on quantum graphs
Gnutzmann, S.; Keating, J.P.; Piotet, F.
2010-12-15
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric {sigma} model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.
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.
Discrete Signal Processing on Graphs: Sampling Theory
NASA Astrophysics Data System (ADS)
Chen, Siheng; Varma, Rohan; Sandryhaila, Aliaksei; Kovacevic, Jelena
2015-12-01
We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that perfect recovery is possible for graph signals bandlimited under the graph Fourier transform. The sampled signal coefficients form a new graph signal, whose corresponding graph structure preserves the first-order difference of the original graph signal. For general graphs, an optimal sampling operator based on experimentally designed sampling is proposed to guarantee perfect recovery and robustness to noise; for graphs whose graph Fourier transforms are frames with maximal robustness to erasures as well as for Erd\\H{o}s-R\\'enyi graphs, random sampling leads to perfect recovery with high probability. We further establish the connection to the sampling theory of finite discrete-time signal processing and previous work on signal recovery on graphs. To handle full-band graph signals, we propose a graph filter bank based on sampling theory on graphs. Finally, we apply the proposed sampling theory to semi-supervised classification on online blogs and digit images, where we achieve similar or better performance with fewer labeled samples compared to previous work.
ERIC Educational Resources Information Center
Lo, Ya-yu; Starling, A. Leyf Peirce
2009-01-01
This study examined the effects of a graphing task analysis using the Microsoft[R] Office Excel 2007 program on the single-subject multiple baseline graphing skills of three university graduate students. Using a multiple probe across participants design, the study demonstrated a functional relationship between the number of correct graphing…
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…
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.
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.
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.
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.
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.
Interacting particle systems on graphs
NASA Astrophysics Data System (ADS)
Sood, Vishal
In this dissertation, the dynamics of socially or biologically interacting populations are investigated. The individual members of the population are treated as particles that interact via links on a social or biological network represented as a graph. The effect of the structure of the graph on the properties of the interacting particle system is studied using statistical physics techniques. In the first chapter, the central concepts of graph theory and social and biological networks are presented. Next, interacting particle systems that are drawn from physics, mathematics and biology are discussed in the second chapter. In the third chapter, the random walk on a graph is studied. The mean time for a random walk to traverse between two arbitrary sites of a random graph is evaluated. Using an effective medium approximation it is found that the mean first-passage time between pairs of sites, as well as all moments of this first-passage time, are insensitive to the density of links in the graph. The inverse of the mean-first passage time varies non-monotonically with the density of links near the percolation transition of the random graph. Much of the behavior can be understood by simple heuristic arguments. Evolutionary dynamics, by which mutants overspread an otherwise uniform population on heterogeneous graphs, are studied in the fourth chapter. Such a process underlies' epidemic propagation, emergence of fads, social cooperation or invasion of an ecological niche by a new species. The first part of this chapter is devoted to neutral dynamics, in which the mutant genotype does not have a selective advantage over the resident genotype. The time to extinction of one of the two genotypes is derived. In the second part of this chapter, selective advantage or fitness is introduced such that the mutant genotype has a higher birth rate or a lower death rate. This selective advantage leads to a dynamical competition in which selection dominates for large populations
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.
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.
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
Bose and Fermi walk configurations on planar graphs
NASA Astrophysics Data System (ADS)
Arrowsmith, D. K.; Bhatti, F. M.; Essam, J. W.
2012-06-01
The number, fCn(H), of n-walk configurations of type C is investigated on certain two-rooted directed planar graphs H which will be always realized as plane graphs in R2. C may be Bose or Fermi as defined by Inui and Katori. Both types of configuration are collections of non-crossing walks which follow the directed paths between the roots of the plane graph H. In the case of configurations of Fermi type each walk may be included only once. The number fBosen(H) is shown to be a polynomial in n of degree nmax - 1 where nmax is the maximum number of walks in a Fermi configuration. The coefficient of the highest power of n in this polynomial is simply related to the number of maximal Fermi walk configurations. It is also shown that nmax = c(H) + 1 where c(H) is the number of finite faces on H. Extension of these results to multi-rooted graphs is also discussed. When H is the union of paths between two sites of the directed square lattice subject to various boundary conditions Kreweras showed that the number of Bose configurations is equal to the number of n-element multi-chains on segments of Young’s lattice. He expressed this number as a determinant the elements of which are polynomials in n. We evaluate this determinant by the method of LU decomposition in the case of ‘watermelon’ configurations above a wall. In this case the polynomial is a product of linear factors but on introducing a second wall the polynomial does not completely factorize but has a factor which is the number of watermelon configurations on the largest rectangular subgraph. The number of two-rooted ‘star’ configurations is found to be the product of the numbers of watermelon configurations on the three rectangular subgraphs into which it may be partitioned.
ERIC Educational Resources Information Center
Browning, Christine A.; Garza-Kling, Gina
2010-01-01
Middle school mathematics classrooms are changing. The curriculum has changed as well. Instead of an annual return to previously encountered topics, many middle school students encounter mathematics of a varying nature, characterized in "Principles and Standards for School Mathematics" (NCTM 2000) as the five Content Standards of Number and…
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.
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.
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.
Sorting: Groups and Graphs. Used Numbers. Grades 2-3.
ERIC Educational Resources Information Center
Russell, Susan Jo; Corwin, Rebecca B.
A unit of study that introduces sorting and classification as a way of organizing data is presented. Suitable for students in grades 2 and 3, it provides a foundation for further work in statistics and data analysis. The investigations may extend from one to five class sessions and are grouped into three parts: "Introduction to Sorting"; "Sorting…
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
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)
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...
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
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)
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.
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.
Labeling RDF Graphs for Linear Time and Space Querying
NASA Astrophysics Data System (ADS)
Furche, Tim; Weinzierl, Antonius; Bry, François
Indices and data structures for web querying have mostly considered tree shaped data, reflecting the view of XML documents as tree-shaped. However, for RDF (and when querying ID/IDREF constraints in XML) data is indisputably graph-shaped. In this chapter, we first study existing indexing and labeling schemes for RDF and other graph datawith focus on support for efficient adjacency and reachability queries. For XML, labeling schemes are an important part of the widespread adoption of XML, in particular for mapping XML to existing (relational) database technology. However, the existing indexing and labeling schemes for RDF (and graph data in general) sacrifice one of the most attractive properties of XML labeling schemes, the constant time (and per-node space) test for adjacency (child) and reachability (descendant). In the second part, we introduce the first labeling scheme for RDF data that retains this property and thus achieves linear time and space processing of acyclic RDF queries on a significantly larger class of graphs than previous approaches (which are mostly limited to tree-shaped data). Finally, we show how this labeling scheme can be applied to (acyclic) SPARQL queries to obtain an evaluation algorithm with time and space complexity linear in the number of resources in the queried RDF graph.
Dynamic modeling of electrochemical systems using linear graph theory
NASA Astrophysics Data System (ADS)
Dao, Thanh-Son; McPhee, John
An electrochemical cell is a multidisciplinary system which involves complex chemical, electrical, and thermodynamical processes. The primary objective of this paper is to develop a linear graph-theoretical modeling for the dynamic description of electrochemical systems through the representation of the system topologies. After a brief introduction to the topic and a review of linear graphs, an approach to develop linear graphs for electrochemical systems using a circuitry representation is discussed, followed in turn by the use of the branch and chord transformation techniques to generate final dynamic equations governing the system. As an example, the application of linear graph theory to modeling a nickel metal hydride (NiMH) battery will be presented. Results show that not only the number of equations are reduced significantly, but also the linear graph model simulates faster compared to the original lumped parameter model. The approach presented in this paper can be extended to modeling complex systems such as an electric or hybrid electric vehicle where a battery pack is interconnected with other components in many different domains.
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.
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)
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…
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…
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)
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…
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
Graph-state formalism for mutually unbiased bases
NASA Astrophysics Data System (ADS)
Spengler, Christoph; Kraus, Barbara
2013-11-01
A pair of orthonormal bases is called mutually unbiased if all mutual overlaps between any element of one basis and an arbitrary element of the other basis coincide. In case the dimension, d, of the considered Hilbert space is a power of a prime number, complete sets of d+1 mutually unbiased bases (MUBs) exist. Here we present a method based on the graph-state formalism to construct such sets of MUBs. We show that for n p-level systems, with p being prime, one particular graph suffices to easily construct a set of pn+1 MUBs. In fact, we show that a single n-dimensional vector, which is associated with this graph, can be used to generate a complete set of MUBs and demonstrate that this vector can be easily determined. Finally, we discuss some advantages of our formalism regarding the analysis of entanglement structures in MUBs, as well as experimental realizations.
Better Polynomial Algorithms on Graphs of Bounded Rank-Width
NASA Astrophysics Data System (ADS)
Ganian, Robert; Hliněný, Petr
Although there exist many polynomial algorithms for NP-hard problems running on a bounded clique-width expression of the input graph, there exists only little comparable work on such algorithms for rank-width. We believe that one reason for this is the somewhat obscure and hard-to-grasp nature of rank-decompositions. Nevertheless, strong arguments for using the rank-width parameter have been given by recent formalisms independently developed by Courcelle and Kanté, by the authors, and by Bui-Xuan et al. This article focuses on designing formally clean and understandable "pseudopolynomial" (XP) algorithms solving "hard" problems (non-FPT) on graphs of bounded rank-width. Those include computing the chromatic number and polynomial or testing the Hamiltonicity of a graph and are extendable to many other problems.
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.
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)
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.
Around the Sun in a Graphing Calculator.
ERIC Educational Resources Information Center
Demana, Franklin; Waits, Bert K.
1989-01-01
Discusses the use of graphing calculators for polar and parametric equations. Presents eight lines of the program for the graph of a parametric equation and 11 lines of the program for a graph of a polar equation. Illustrates the application of the programs for planetary motion and free-fall motion. (YP)
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...
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…
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...
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…
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, 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, 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...
Some Applications of Graph Theory to Clustering
ERIC Educational Resources Information Center
Hubert, Lawrence J.
1974-01-01
The connection between graph theory and clustering is reviewed and extended. Major emphasis is on restating, in a graph-theoretic context, selected past work in clustering, and conversely, developing alternative strategies from several standard concepts used in graph theory per se. (Author/RC)
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…
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. PMID:21647928
NASA Astrophysics Data System (ADS)
Xiong, B.; Oude Elberink, S.; Vosselman, G.
2014-07-01
In the task of 3D building model reconstruction from point clouds we face the problem of recovering a roof topology graph in the presence of noise, small roof faces and low point densities. Errors in roof topology graphs will seriously affect the final modelling results. The aim of this research is to automatically correct these errors. We define the graph correction as a graph-to-graph problem, similar to the spelling correction problem (also called the string-to-string problem). The graph correction is more complex than string correction, as the graphs are 2D while strings are only 1D. We design a strategy based on a dictionary of graph edit operations to automatically identify and correct the errors in the input graph. For each type of error the graph edit dictionary stores a representative erroneous subgraph as well as the corrected version. As an erroneous roof topology graph may contain several errors, a heuristic search is applied to find the optimum sequence of graph edits to correct the errors one by one. The graph edit dictionary can be expanded to include entries needed to cope with errors that were previously not encountered. Experiments show that the dictionary with only fifteen entries already properly corrects one quarter of erroneous graphs in about 4500 buildings, and even half of the erroneous graphs in one test area, achieving as high as a 95% acceptance rate of the reconstructed models.
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.
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.
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.
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
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
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.
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.
Choosability of P 5-Free Graphs
NASA Astrophysics Data System (ADS)
Golovach, Petr A.; Heggernes, Pinar
A graph is k-choosable if it admits a proper coloring of its vertices for every assignment of k (possibly different) allowed colors to choose from for each vertex. It is NP-hard to decide whether a given graph is k-choosable for k ≥ 3, and this problem is considered strictly harder than the k-coloring problem. Only few positive results are known on input graphs with a given structure. Here, we prove that the problem is fixed parameter tractable on P 5-free graphs when parameterized by k. This graph class contains the well known and widely studied class of cographs. Our result is surprising since the parameterized complexity of k-coloring is still open on P 5-free graphs. To give a complete picture, we show that the problem remains NP-hard on P 5-free graphs when k is a part of the input.
The weighted random graph model
NASA Astrophysics Data System (ADS)
Garlaschelli, Diego
2009-07-01
We introduce the weighted random graph (WRG) model, which represents the weighted counterpart of the Erdos-Renyi random graph and provides fundamental insights into more complicated weighted networks. We find analytically that the WRG is characterized by a geometric weight distribution, a binomial degree distribution and a negative binomial strength distribution. We also characterize exactly the percolation phase transitions associated with edge removal and with the appearance of weighted subgraphs of any order and intensity. We find that even this completely null model displays a percolation behaviour similar to what is observed in real weighted networks, implying that edge removal cannot be used to detect community structure empirically. By contrast, the analysis of clustering successfully reveals different patterns between the WRG and real networks.
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.
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.
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.
Fast Dynamic Meshing Method Based on Delaunay Graph and Inverse Distance Weighting Interpolation
NASA Astrophysics Data System (ADS)
Wang, Yibin; Qin, Ning; Zhao, Ning
2016-06-01
A novel mesh deformation technique is developed based on the Delaunay graph mapping method and the inverse distance weighting (IDW) interpolation. The algorithm maintains the advantages of the efficiency of Delaunay-graph-mapping mesh deformation while possess the ability for better controlling the near surface mesh quality. The Delaunay graph is used to divide the mesh domain into a number of sub-domains. On each of the sub-domains, the inverse distance weighting interpolation is applied to build a much smaller sized translation matrix between the original mesh and the deformed mesh, resulting a similar efficiency for the mesh deformation as compared to the fast Delaunay graph mapping method. The paper will show how the near-wall mesh quality is controlled and improved by the new method while the computational time is compared with the original Delaunay graph mapping method.
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
2011-01-01
Background Orchids comprise one of the largest families of flowering plants and generate commercially important flowers. However, model plants, such as Arabidopsis thaliana do not contain all plant genes, and agronomic and horticulturally important genera and species must be individually studied. Results Several molecular biology tools were used to isolate flower-specific gene promoters from Oncidium 'Gower Ramsey' (Onc. GR). A cDNA library of reproductive tissues was used to construct a microarray in order to compare gene expression in flowers and leaves. Five genes were highly expressed in flower tissues, and the subcellular locations of the corresponding proteins were identified using lip transient transformation with fluorescent protein-fusion constructs. BAC clones of the 5 genes, together with 7 previously published flower- and reproductive growth-specific genes in Onc. GR, were identified for cloning of their promoter regions. Interestingly, 3 of the 5 novel flower-abundant genes were putative trypsin inhibitor (TI) genes (OnTI1, OnTI2 and OnTI3), which were tandemly duplicated in the same BAC clone. Their promoters were identified using transient GUS reporter gene transformation and stable A. thaliana transformation analyses. Conclusions By combining cDNA microarray, BAC library, and bombardment assay techniques, we successfully identified flower-directed orchid genes and promoters. PMID:21473751
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.
Refactorable Numbers - A Machine Invention
NASA Astrophysics Data System (ADS)
Colton, Simon
1999-02-01
The HR (or Hardy-Ramanujan) program invents and analyses definitions in areas of pure mathematics, including finite algebras, graph theory and number theory. While working in number theory, HR recently invented a new integer sequence, the refactorable numbers, which are defined and developed here. A discussion of how HR works, along with details of well known sequences reinvented by HR and other new sequences invented by HR is also given.
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
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.
An area change detection method of remote sensing image using historical land use graph
NASA Astrophysics Data System (ADS)
Li, Xiangjun; Deng, Xiaolian; Niu, Zheng; Ye, Famao
2005-11-01
Kinds of historical vector graphs have been gradually accumulated by ground truth data or other reliable sources, but these data have not been fully adopted to detect change in remote sensing circle. In this paper we describe a novel change detection method. The key feature of the new method is the use of a piece of historical land using vector graph. By combing one satellite image and the vector graph after necessary geometric rectification, we could detect change region of the satellite image corresponding to patches in the vector graph. Through adopting coefficient of part change and coefficient of entire change, the study calculates statistics indexes of image corresponding to patches of vector graph with different coefficient groups and assesses the computing results by kappa matrix. According to analytical results, the coefficient of entire change is more important to the number of commission error than the coefficient of part change. This method is benefit to the reuse of historical vector graphs. As the image-processing work of this method is based on patches of historical vector graph, it helps to the development of different vector graphs.
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.
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
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.
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.
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…
Smit, Dirk J A; de Geus, Eco J C; Boersma, Maria; Boomsma, Dorret I; Stam, Cornelis J
2016-05-01
Graph analysis of electroencephalography (EEG) has previously revealed developmental increases in connectivity between distant brain areas and a decrease in randomness and increased integration in the brain network with concurrent increased modularity. Comparisons of graph parameters across age groups, however, may be confounded with network degree distributions. In this study, we analyzed graph parameters from minimum spanning tree (MST) graphs and compared their developmental trajectories to those of graph parameters based on full graphs published previously. MST graphs are constructed by selecting only the strongest available connections avoiding loops, resulting in a backbone graph that is thought to reflect the major qualitative properties of the network, while allowing a better comparison across age groups by avoiding the degree of distribution confound. EEG was recorded in a large (n = 1500) population-based sample aged 5-71 years. Connectivity was assessed using phase lag index to reduce effects of volume conduction. Connectivity in the MST graph increased significantly from childhood to adolescence, continuing to grow nonsignificantly into adulthood, and decreasing significantly about 57 years of age. Leaf number, degree, degree correlation, and maximum centrality from the MST graph indicated a pattern of increased integration and decreased randomness from childhood into early adulthood. The observed development in network topology suggested that maturation at the neuronal level is aimed to increase connectivity as well as increase integration of the brain network. We confirm that brain network connectivity shows quantitative changes across the life span and additionally demonstrate parallel qualitative changes in the connectivity pattern. PMID:26885699
API Requirements for Dynamic Graph Prediction
Gallagher, B; Eliassi-Rad, T
2006-10-13
Given a large-scale time-evolving multi-modal and multi-relational complex network (a.k.a., a large-scale dynamic semantic graph), we want to implement algorithms that discover patterns of activities on the graph and learn predictive models of those discovered patterns. This document outlines the application programming interface (API) requirements for fast prototyping of feature extraction, learning, and prediction algorithms on large dynamic semantic graphs. Since our algorithms must operate on large-scale dynamic semantic graphs, we have chosen to use the graph API developed in the CASC Complex Networks Project. This API is supported on the back end by a semantic graph database (developed by Scott Kohn and his team). The advantages of using this API are (i) we have full-control of its development and (ii) the current API meets almost all of the requirements outlined in this document.
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 .
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
Experimental quantum annealing: case study involving the graph isomorphism problem
NASA Astrophysics Data System (ADS)
Zick, Kenneth M.; Shehab, Omar; French, Matthew
2015-06-01
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.
Antimagic covering on double star and related graphs
NASA Astrophysics Data System (ADS)
Roswitha, Mania; Kuntari, Sri; Suraningsih, Dwi; Martini, Titin Sri; Kusmayadi, Tri Atmojo
2016-02-01
A graph G(V, E) admits an (a, d)-H-antimagic covering if every edge in E(G) belongs to H' subgraph of G that is isomorphic to H and there exists a bijective function f : V (G) ∪ E(G) → 1, 2,…, |V (G)| + |E(G)| such that for all subgraphs H' isomorphic to H, the H'-weights, w(H') = ∑vɛV (H') f (v) + ∑eɛE(H') f(e) constitutes an arithmetic progression a, a + d,…, a + (t - 1)d, where a and d are some positive integers and t is the number of subgraphs isomorphic to H. If the label of vertices are {1, 2, …, |V (G)|}, then it is called super (a, d)-H-antimagic covering. In this paper we find super (a, d)-H-antimagic covering on double star graph Sn,n, union of star graph mSn and union of double star graph mSn,n.
Weight of quadratic forms and graph states
NASA Astrophysics Data System (ADS)
Cosentino, Alessandro; Severini, Simone
2009-11-01
We prove a connection between Schmidt rank and weight of quadratic forms. This provides a new tool for the classification of graph states based on entanglement. Our main tool arises from a reformulation of previously known results concerning the weight of quadratic forms in terms of graph states properties. As a byproduct, we obtain a straightforward characterization of the weight of functions associated with pivot-minor of bipartite graphs.
Maksimov, Dmitry; Hesser, Jürgen; Brockmann, Carolin; Jochum, Susanne; Dietz, Tiina; Schnitzer, Andreas; Düber, Christoph; Schoenberg, Stefan O; Diehl, Steffen
2009-12-01
Separating bone, calcification, and vessels in computer tomography angiography (CTA) allows for a detailed diagnosis of vessel stenosis. This paper presents a new, graph-based technique that solves this difficult problem with high accuracy. The approach requires one native data set and one that is contrast enhanced. On each data set, an attributed level-graph is derived and both graphs are matched by dynamic programming to differentiate between bone, on one hand side, and vessel/calcification on the other hand side. Lumen and calcified regions are then separated by a profile technique. Evaluation is based on data from vessels of pelvis and lower extremities of elderly patients. Due to substantial calcification and motion of patients between and during the acquisitions, the underlying approach is tested on a class of difficult cases. Analysis requires 3-5 min on a Pentium IV 3 GHz for a 700 MByte data set. Among 37 patients, our approach correctly identifies all three components in 80% of cases correctly compared to visual control. Critical inconsistencies with visual inspection were found in 6% of all cases; 70% of these inconsistencies are due to small vessels that have 1) a diameter near the resolution of the CT and 2) are passing next to bony structures. All other remaining deviations are found in an incorrect handling of the iliac artery since the slice thickness is near the diameter of this vessel and since the orientation is not in cranio-caudal direction. Increasing resolution is thus expected to solve many the aforementioned difficulties. PMID:19574161
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.
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.
On designing heteroclinic networks from graphs
NASA Astrophysics Data System (ADS)
Ashwin, Peter; Postlethwaite, Claire
2013-12-01
Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a complicated structure determined to a large extent by the constraints and dimension of the system. As these networks are of great interest as dynamical models of biological and cognitive processes, it is useful to understand how particular directed graphs can be realised as attracting robust heteroclinic networks between states in phase space. This paper presents two methods of realising arbitrarily complex directed graphs as robust heteroclinic networks for flows generated by ODEs-we say the ODEs realise the graphs as heteroclinic networks between equilibria that represent the vertices. Suppose we have a directed graph on nv vertices with ne edges. The “simplex realisation” embeds the graph as an invariant set of a flow on an (nv-1)-simplex. This method realises the graph as long as it is one- and two-cycle free. The “cylinder realisation” embeds a graph as an invariant set of a flow on a (ne+1)-dimensional space. This method realises the graph as long as it is one-cycle free. In both cases we realise the graph as an invariant set within an attractor, and discuss some illustrative examples, including the influence of noise and parameters on the dynamics. In particular we show that the resulting heteroclinic network may or may not display “memory” of the vertices visited.
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
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
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.
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.
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.
Chiou, Chung-Yi; Yeh, Kai-Wun
2008-03-01
The yellow coloration pattern in Oncidium floral lip associated with red sepal and petal tissues is an ideal model to study coordinate regulation of anthocyanin synthesis. In this study, chromatography analysis revealed that the red coloration in floral tissues was composed of malvidin-3-O-galactoside, peonidin-3-O-glucoside, delphinidin-3-O-glucoside and cyanidin-3-O-glucoside compounds. By contrary, these pigments were not detected in yellow lip tissue. Four key genes involved in anthocyanin biosynthetic pathway, i.e. chalcone synthase (OgCHS), chalcone isomerase (OgCHI), dihydroflavonol 4-reductase (OgDFR) and anthocyanidin synthase (OgANS) were isolated and their expression patterns were characterized. Northern blot analysis confirmed that although they are active during floral development, OgCHI and OgDFR genes are specifically down-regulated in yellow lip tissue. Bombardment with OgCHI and OgDFR genes into lip tissue driven by a flower-specific promoter, Pchrc (chromoplast-specific carotenoid-associated gene), demonstrated that transient expression of these two genes resulted in anthocyanin production in yellow lip. Further analysis of a R2R3 MYB transcription factor, OgMYB1, revealed that although it is actively expressed during floral development, it is not expressed in yellow lip tissue. Transient expression of OgMYB1 in lip tissues by bombardment can also induce formation of red pigments through the activation of OgCHI and OgDFR transcription. These results demonstrate that differential expression of OgMYB1 is critical to determine the color pattern of floral organ in Oncidium Gower Ramsey. PMID:18161007
Acyclic and star colorings of joins of graphs and an algorithm for cographs.
Lyons, A.; Mathematics and Computer Science; Univ. of Chicago
2009-01-01
An acyclic coloring of a graph is a proper vertex coloring such that the subgraph induced by the union of any two color classes is a disjoint collection of trees. The more restricted notion of star coloring requires that the union of any two color classes induces a disjoint collection of stars. The acyclic and star chromatic numbers of a graph G are defined analogously to the chromatic number {chi}(G) and are denoted by {chi}{sub a}(G) and {chi}{sub s}(G), respectively. In this paper, we consider acyclic and star colorings of graphs that are decomposable with respect to the join operation, which builds a new graph from a collection of two or more disjoint graphs by adding all possible edges between them. In particular, we present a recursive formula for the acyclic chromatic number of joins of graphs and show that a similar formula holds for the star chromatic number. We also demonstrate the algorithmic implications of our results for the cographs, which have the unique property that they are recursively decomposable with respect to the join and disjoint union operations.
Structural pursuit over multiple undirected graphs*
Zhu, Yunzhang; Shen, Xiaotong; Pan, Wei
2014-01-01
Summary Gaussian graphical models are useful to analyze and visualize conditional dependence relationships between interacting units. Motivated from network analysis under di erent experimental conditions, such as gene networks for disparate cancer subtypes, we model structural changes over multiple networks with possible heterogeneities. In particular, we estimate multiple precision matrices describing dependencies among interacting units through maximum penalized likelihood. Of particular interest are homogeneous groups of similar entries across and zero-entries of these matrices, referred to as clustering and sparseness structures, respectively. A non-convex method is proposed to seek a sparse representation for each matrix and identify clusters of the entries across the matrices. Computationally, we develop an e cient method on the basis of di erence convex programming, the augmented Lagrangian method and the block-wise coordinate descent method, which is scalable to hundreds of graphs of thousands nodes through a simple necessary and sufficient partition rule, which divides nodes into smaller disjoint subproblems excluding zero-coe cients nodes for arbitrary graphs with convex relaxation. Theoretically, a finite-sample error bound is derived for the proposed method to reconstruct the clustering and sparseness structures. This leads to consistent reconstruction of these two structures simultaneously, permitting the number of unknown parameters to be exponential in the sample size, and yielding the optimal performance of the oracle estimator as if the true structures were given a priori. Simulation studies suggest that the method enjoys the benefit of pursuing these two disparate kinds of structures, and compares favorably against its convex counterpart in the accuracy of structure pursuit and parameter estimation. PMID:25642006
Graph states of prime-power dimension from generalized CNOT quantum circuit
NASA Astrophysics Data System (ADS)
Chen, Lin; Zhou, D. L.
2016-06-01
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.
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
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.
Phase unwrapping via graph cuts.
Bioucas-Dias, José M; Valadão, Gonçalo
2007-03-01
Phase unwrapping is the inference of absolute phase from modulo-2pi phase. This paper introduces a new energy minimization framework for phase unwrapping. The considered objective functions are first-order Markov random fields. We provide an exact energy minimization algorithm, whenever the corresponding clique potentials are convex, namely for the phase unwrapping classical Lp norm, with p > or = 1. Its complexity is KT (n, 3n), where K is the length of the absolute phase domain measured in 2pi units and T (n, m) is the complexity of a max-flow computation in a graph with n nodes and m edges. For nonconvex clique potentials, often used owing to their discontinuity preserving ability, we face an NP-hard problem for which we devise an approximate solution. Both algorithms solve integer optimization problems by computing a sequence of binary optimizations, each one solved by graph cut techniques. Accordingly, we name the two algorithms PUMA, for phase unwrappping max-flow/min-cut. A set of experimental results illustrates the effectiveness of the proposed approach and its competitiveness in comparison with state-of-the-art phase unwrapping algorithms. PMID:17357730
Clique percolation in random graphs.
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
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
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.
pGraph: Efficient Parallel Construction of Large-Scale Protein Sequence Homology Graphs
Wu, Changjun; Kalyanaraman, Anantharaman; Cannon, William R.
2012-09-15
Detecting sequence homology between protein sequences is a fundamental problem in computational molecular biology, with a pervasive application in nearly all analyses that aim to structurally and functionally characterize protein molecules. While detecting the homology between two protein sequences is relatively inexpensive, detecting pairwise homology for a large number of protein sequences can become computationally prohibitive for modern inputs, often requiring millions of CPU hours. Yet, there is currently no robust support to parallelize this kernel. In this paper, we identify the key characteristics that make this problemparticularly hard to parallelize, and then propose a new parallel algorithm that is suited for detecting homology on large data sets using distributed memory parallel computers. Our method, called pGraph, is a novel hybrid between the hierarchical multiple-master/worker model and producer-consumer model, and is designed to break the irregularities imposed by alignment computation and work generation. Experimental results show that pGraph achieves linear scaling on a 2,048 processor distributed memory cluster for a wide range of inputs ranging from as small as 20,000 sequences to 2,560,000 sequences. In addition to demonstrating strong scaling, we present an extensive report on the performance of the various system components and related parametric studies.
NASA Astrophysics Data System (ADS)
Jefferts, S. R.; Heavner, T. P.; Barlow, S. E.; Ashby, N.
2015-06-01
The theory of a frequency shift in primary frequency standards due to microwave lensing in Gibble [Phys. Rev. A 90, 015601 (2014), 10.1103/PhysRevA.90.015601] contains a number of problems that undermine its validity. Furthermore, because the exposition of the theory has multiple errors and because the shift has never been experimentally observed, we believe this possible shift should not be included as a correction to primary frequency standards contributing to international atomic time. Although the theory may describe the basic mechanisms of a possible frequency shift, we argue it is not possible to use this theory to make reliable corrections to a primary frequency standard at the δ f /f ˜10-16 level.
Feynman graph generation and calculations in the Hopf algebra of Feynman graphs
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2014-12-01
Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for Yang-Mills, QED and φk theories. Using dedicated graph theoretic tools feyngen can generate graphs of comparatively high loop orders. feyncop implements the Hopf algebra of those Feynman graphs which incorporates the renormalization procedure necessary to calculate finite results in perturbation theory of the underlying quantum field theory. feyngen is validated by comparison to explicit calculations of zero dimensional quantum field theories and feyncop is validated using a combinatorial identity on the Hopf algebra of graphs.
Stereo Vision By Pyramidal Bli Graph Matching
NASA Astrophysics Data System (ADS)
Shen, Jun; Castan, Serge; Zhao, Jian
1988-04-01
We propose the pyramidal BLI (Binary Laplacian Image) graph matching method for stereo vision, which uses the local as well as the global similarities to assure a good precision of matching results and to eliminate the ambiguities. Because the BLI is detected by DRF method which has a fast realization and matching between graphs is fast, a pseudo-real time system is possible.
This Is Us! Great Graphs for Kids.
ERIC Educational Resources Information Center
Sullivan, Delia; O'Neil, Mary Ann
1980-01-01
Described are graphing activities which can be instrumental in introducing the mathematics concepts of counting, sorting, grouping, and comparing on the primary level. On the intermediate level, these activites can be used to introduce collecting and sorting unorganized data, and creating graphs to represent the data. (Author/TG)
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…
Body Motion and Graphing. Working Paper.
ERIC Educational Resources Information Center
Nemirovsky, Ricardo; Tierney, Cornelia; Wright, Tracey
This paper explores children's efforts to make sense of graphs by analyzing two students' use of a computer-based motion detector. The analysis focuses on the students' growing understanding of the motion detector which enables them to plan their movements in order to create graphs and interpret them in terms of kinesthetic actions. Students…
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,…
Generative Graph Prototypes from Information Theory.
Han, Lin; Wilson, Richard C; Hancock, Edwin R
2015-10-01
In this paper we present a method for constructing a generative prototype for a set of graphs by adopting a minimum description length approach. The method is posed in terms of learning a generative supergraph model from which the new samples can be obtained by an appropriate sampling mechanism. We commence by constructing a probability distribution for the occurrence of nodes and edges over the supergraph. We encode the complexity of the supergraph using an approximate Von Neumann entropy. A variant of the EM algorithm is developed to minimize the description length criterion in which the structure of the supergraph and the node correspondences between the sample graphs and the supergraph are treated as missing data. To generate new graphs, we assume that the nodes and edges of graphs arise under independent Bernoulli distributions and sample new graphs according to their node and edge occurrence probabilities. Empirical evaluations on real-world databases demonstrate the practical utility of the proposed algorithm and show the effectiveness of the generative model for the tasks of graph classification, graph clustering and generating new sample graphs. PMID:26340255
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.
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)
Qualitative Graphing: A Construction in Mathematics.
ERIC Educational Resources Information Center
Narode, Ronald
This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…
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…
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…
Critiquing the Culture of Computer Graphing Practices.
ERIC Educational Resources Information Center
Brasseur, Lee
2001-01-01
Argues that current approaches to computer graphing practices are ill suited to meet the complex needs of real users. Offers an overview of work in two major areas of graphing theory and research: the sociology of science and the educational research of mathematics and scientific students. Suggests what technical communicators can do to improve…
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…
Adolescents' Graphing Skills: A Descriptive Analysis.
ERIC Educational Resources Information Center
Clement, John; And Others
Clinical interviews were conducted with 25 seventh- and eighth-grade students to determine: (1) the extent to which they could produce correct graphical representations of familiar situations; (2) to what extent they could infer relationships from graphs; (3) what are the most commonly held graphing misconceptions and how stable they are; and (4)…
ON CLUSTERING TECHNIQUES OF CITATION GRAPHS.
ERIC Educational Resources Information Center
CHIEN, R.T.; PREPARATA, F.P.
ONE OF THE PROBLEMS ENCOUNTERED IN CLUSTERING TECHNIQUES AS APPLIED TO DOCUMENT RETRIEVAL SYSTEMS USING BIBLIOGRAPHIC COUPLING DEVICES IS THAT THE COMPUTATIONAL EFFORT REQUIRED GROWS ROUGHLY AS THE SQUARE OF THE COLLECTION SIZE. IN THIS STUDY GRAPH THEORY IS APPLIED TO THIS PROBLEM BY FIRST MAPPING THE CITATION GRAPH OF THE DOCUMENT COLLECTION…
Attitudes towards Graphing Calculators in Developmental Mathematics
ERIC Educational Resources Information Center
Rajan, Shaun Thomas
2013-01-01
The purpose of this exploratory study was to examine instructor and student attitudes towards the use of the graphing calculator in the developmental mathematics classroom. A focus of the study was to see if instructors or students believed there were changes in the conceptual understanding of mathematics as a result of graphing calculator…
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…
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…
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.
NASA Astrophysics Data System (ADS)
Dafik, Agustin, Ika Hesti; Khuri Faridatun, N.
2016-02-01
All graph in this paper are finite, simple and undirected. Let G = (V (G), E(G)) be a graph of order p and size q. Graph G admits a H-covering, if every edge in E(G) belongs to at least one subgraph of G isomorphic to a given graph H. A graph G is said to be an (a, d)-H-antimagic total labeling if there exist a bijective function f : V (G) ∪ E(G) → {1, 2,…, |V(G)| + |E(G)|} such that for all subgraphs H' isomorphic to H, the total H-weights w(H) = ∑v∈V (H') f (v) + ∑e∈E(H') f (e) form an arithmetic sequence {a, a + d, a + 2d, …, a + (t - 1)d}, where a and d are positive integers and t is the number of all subgraphs H' isomorphic to H. Such a labeling is called a super if the smallest labels appear in the vertices. This paper studies the super (a, d)-Fn-antimagic total labeling for a connected and disconnected amalgamation of fan graphs. We can prove that, for some feasible d, a connected and disconnected amalgamation of fan graphs admit a super (a, d) - Fn-antimagic total labeling.
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
2016-01-01
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
Quantum Random Walks of Non-Interacting Bosons on Strongly Regular Graphs
NASA Astrophysics Data System (ADS)
Rudinger, Kenneth; Gamble, John King; Wellons, Mark; Friesen, Mark; Zhou, Dong; Bach, Eric; Joynt, Robert; Coppersmith, S. N.
2011-03-01
We investigate the quantum dynamics of particles on graphs (``quantum walks"), with the aim of developing quantum algorithms for determining if two graphs are isomorphic and show that there are fundamental differences between the distinguishing power of two-particle and three-particle non-interacting quantum walks. We investigate quantum walks on strongly regular graphs (SRGs), a class of graphs with high symmetry. We show analytically that the two-particle walk always fails to distinguish non-isomorphic members of the same SRG family. We show numerically that the three-boson walk is able to distinguish 99.6% of 70,712 SRG comparisons made and that this distinguishing power comes from different multiplicities of certain graph substructures in non-isomorphic graphs. We identify certain distinguishing substructures and examine ones that appear in the four-boson walk, discovering they are able to distinguish almost all of the graphs that the three-boson walk failed on. This indicates a positive correlation between number of bosons in the walk and distinguishing power. This work was supported by ARO and DOD (W911NF-09-1-0439) and NSF (CCF-0635355). J.K.G. acknowledges support from the NSF.
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.
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.
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.
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.
Quantum walk search on Johnson graphs
NASA Astrophysics Data System (ADS)
Wong, Thomas G.
2016-05-01
The Johnson graph J(n,k) is defined by n symbols, where vertices are k-element subsets of the symbols, and vertices are adjacent if they differ in exactly one symbol. In particular, J(n,1) is the complete graph K n , and J(n,2) is the strongly regular triangular graph T n , both of which are known to support fast spatial search by continuous-time quantum walk. In this paper, we prove that J(n,3), which is the n-tetrahedral graph, also supports fast search. In the process, we show that a change of basis is needed for degenerate perturbation theory to accurately describe the dynamics. This method can also be applied to general Johnson graphs J(n,k) with fixed k.
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.
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
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.
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.
Degree distribution and assortativity in line graphs of complex networks
NASA Astrophysics Data System (ADS)
Wang, Xiangrong; Trajanovski, Stojan; Kooij, Robert E.; Van Mieghem, Piet
2016-03-01
Topological characteristics of links of complex networks influence the dynamical processes executed on networks triggered by links, such as cascading failures triggered by links in power grids and epidemic spread due to link infection. The line graph transforms links in the original graph into nodes. In this paper, we investigate how graph metrics in the original graph are mapped into those for its line graph. In particular, we study the degree distribution and the assortativity of a graph and its line graph. Specifically, we show, both analytically and numerically, the degree distribution of the line graph of an Erdős-Rényi graph follows the same distribution as its original graph. We derive a formula for the assortativity of line graphs and indicate that the assortativity of a line graph is not linearly related to its original graph. Additionally, line graphs of various graphs, e.g. Erdős-Rényi graphs, scale-free graphs, show positive assortativity. In contrast, we find certain types of trees and non-trees whose line graphs have negative assortativity.
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.
Application of Graph Based Database in Geoinformatics: A Sinoprobe Example
NASA Astrophysics Data System (ADS)
Chen, Z.; Guan, Y.; Cheng, M.; Chen, G.
2011-12-01
Most geospatial databases used are based on extension of the traditional relational databases. The data model based on these databases must represent the data into a number of interconnected tables linked through creating "artificial" ids, which imposes inflexible and rigid data structures. We propose here to use graph based database to store data in a way that semantically represents its own structure, leading to a natural flexible and schema free data store that is easily expandable and maintainable, more importantly semantic friendly. Specifically we use the high-performance graph engine Neo4J spatial and GeoServer to explore this emerging new technology in geosciences applications and study the feasibility of using this technology to build a future semantic web for the Sinoprobe program. An example application is built using the Sinoprobe data center data.
NASA Astrophysics Data System (ADS)
Kabcenell, Aaron; Kominis, Iannis; Romalis, Michael
2012-06-01
Noble gas co-magnetometers have been used for many precision measurements, but their sensitivity is still very far from fundamental limits. We are exploring a new approach for operation of a ^3He-^129Xe co-magnetometer that uses a sensitive Rb-K magnetometer as a spin detector. By placing the noble gas atoms inside the magnetometer cell we can increase their magnetic signal using the Fermi-contact interaction, representing a gain of nearly 500 for ^129Xe, and achieve nearly quantum-noise limited detection of nuclear spins. In order to take advantage of the long coherence times of ^3He and^129Xe, the precession measurement is based on the Ramsey method of separated oscillatory fields and will be performed in an alkali-metal-free volume. The gas is then transported to the spin detector using techniques developed for remote NMR detection. The sensitivity of this approach is estimated to be on the order of 10-13 Hz/day^1/2, making it several orders of magnitude more sensitive than the best existing co-magnetometers. We are currently performing tests of the Ramsey measurement method and the sensitivity of the spin detector.
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.
Less is less: a systematic review of graph use in meta-analyses.
Schild, Anne H E; Voracek, Martin
2013-09-01
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 (medicine, psychology, and business) and nine journals was conducted. Interdisciplinary differences, which are mirrored in the respective journals, were revealed, that is, graph use correlates with external factors rather than methodological considerations. There was only limited variation in graph types (with forest plots as the most important representatives), and diagnostic plots were very rare. Although an increase in graph use over time could be observed, it is unlikely that this phenomenon is specific to meta-analyses. There is a gaping discrepancy between available graphic methods and their application in meta-analyses. This may be rooted in a number of factors, namely, (i) insufficient dissemination of new developments, (ii) unsatisfactory implementation in software packages, and (iii) minor attention on graphics in meta-analysis reporting guidelines. Using visualization methods to their full capacity is a further step in using meta-analysis to its full potential. PMID:26053841
Approximate von Neumann entropy for directed graphs.
Ye, Cheng; Wilson, Richard C; Comin, César H; Costa, Luciano da F; Hancock, Edwin R
2014-05-01
In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks. PMID:25353841
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.
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.
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.
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; Chavarría-Miranda, Daniel; Nakamura, Grant C.; Sofia, Heidi J.
2008-05-28
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. 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 and high-performance parallel systems that utilize multi-threaded architectures. 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.
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
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.
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.
Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory
van Wijk, Bernadette C. M.; Stam, Cornelis J.; Daffertshofer, Andreas
2010-01-01
Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) non-significant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others. PMID:21060892
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
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.
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. PMID:26357179
Spectral statistics of nearly unidirectional quantum graphs
NASA Astrophysics Data System (ADS)
Akila, Maram; Gutkin, Boris
2015-08-01
The energy levels of a quantum graph with time reversal symmetry and unidirectional classical dynamics are doubly degenerate and obey the spectral statistics of the Gaussian unitary ensemble. These degeneracies, however, are lifted when the unidirectionality is broken in one of the graph’s vertices by a singular perturbation. Based on a random matrix model we derive an analytic expression for the nearest neighbour distribution between energy levels of such systems. As we demonstrate the result agrees excellently with the actual statistics for graphs with a uniform distribution of eigenfunctions. Yet, it exhibits quite substantial deviations for classes of graphs which show strong scarring.
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.
Finite Frames and Graph Theoretic Uncertainty Principles
NASA Astrophysics Data System (ADS)
Koprowski, Paul J.
The subject of analytical uncertainty principles is an important field within harmonic analysis, quantum physics, and electrical engineering. We explore uncertainty principles in the context of the graph Fourier transform, and we prove additive results analogous to the multiplicative version of the classical uncertainty principle. We establish additive uncertainty principles for finite Parseval frames. Lastly, we examine the feasibility region of simultaneous values of the norms of a graph differential operator acting on a function f ∈ l2(G) and its graph Fourier transform.
Line graphs for a multiplex network
NASA Astrophysics Data System (ADS)
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.
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
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
ERIC Educational Resources Information Center
Saint Paul Foundation, St. Paul, MN.
The Words Work! early literacy initiative, in Ramsey Action Program (RAP) Head Start centers, was initiated to prepare children to be successful third-grade readers and mathematicians. These reports reflect the standardized test results collected in years 1 and 2 for the first cohort of Words Work! children from four RAP Head Start centers who…
Data graphs and mechanistic explanation.
Burnston, Daniel C
2016-06-01
It is a widespread assumption in philosophy of science that representations of data are not explanatory-that they are mere stepping stones towards an explanation, such as a representation of a mechanism. I draw on instances of representational and explanatory practice from mammalian chronobiology to suggest that this assumption is unsustainable. In many instances, biologists employ representations of data in explanatory ways that are not reducible to constraints on or evidence for representations of mechanisms. Data graphs are used to represent relationships between quantities across conditions, and often these representations are necessary for explaining particular aspects of the phenomena under study. The benefit of the analysis is two-fold. First, it provides a more accurate account of explanatory practice in broadly mechanistic investigation in biology. Second, it suggests that there is not an explanatorily "fundamental" type of representation in biology. Rather, the practice of explanation consists in the construction of different types of representations and their employment for distinct explanatory purposes. PMID:26871740
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
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
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
Signals on graphs: Transforms and tomograms
NASA Astrophysics Data System (ADS)
Vilela Mendes, R.; Mendes, Hugo C.; Araújo, Tanya
2016-05-01
Development of efficient tools for the representation of large datasets is a precondition for the study of dynamics on networks. Generalizations of the Fourier transform on graphs have been constructed through projections on the eigenvectors of graph matrices. By exploring mappings of the spectrum of these matrices we show how to construct more general transforms, in particular wavelet-like transforms on graphs. For time-series, tomograms, a generalization of the Radon transforms to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signals and are robust in the presence of noise. Here the notion of tomogram is also extended to signals on arbitrary graphs.
Trivalent Graphs, Volume Conjectures and Character Varieties
NASA Astrophysics Data System (ADS)
Nawata, Satoshi; Pichai, Ramadevi; Zodinmawia
2014-10-01
The generalized volume conjecture and the AJ conjecture (a.k.a. the quantum volume conjecture) are extended to colored quantum invariants of the theta and tetrahedron graph. The character variety of the fundamental group of the complement of a trivalent graph with E edges in S 3 is a Lagrangian subvariety of the Hitchin moduli space over the Riemann surface of genus g = E/3 + 1. For the theta and tetrahedron graph, we conjecture that the configuration of the character variety is locally determined by large color asymptotics of the quantum invariants of the trivalent graph in terms of complex Fenchel-Nielsen coordinates. Moreover, the q-holonomic difference equation of the quantum invariants provides the quantization of the character variety.
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.
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.
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)
Bipartite Graphs of Large Clique-Width
NASA Astrophysics Data System (ADS)
Korpelainen, Nicholas; Lozin, Vadim V.
Recently, several constructions of bipartite graphs of large clique-width have been discovered in the literature. In the present paper, we propose a general framework for developing such constructions and use it to obtain new results on this topic.
Graph Theory and the High School Student.
ERIC Educational Resources Information Center
Chartrand, Gary; Wall, Curtiss E.
1980-01-01
Graph theory is presented as a tool to instruct high school mathematics students. A variety of real world problems can be modeled which help students recognize the importance and difficulty of applying mathematics. (MP)
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.
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.
Exploring Hill Ciphers with Graphing Calculators.
ERIC Educational Resources Information Center
St. John, Dennis
1998-01-01
Explains how to code and decode messages using Hill ciphers which combine matrix multiplication and modular arithmetic. Discusses how a graphing calculator can facilitate the matrix and modular arithmetic used in the coding and decoding procedures. (ASK)
Note on resolution, connection graphs, and subsumption
De Champeaux, D.
1982-07-01
Completeness is endangered by the combination in connection graph of subsumption deletion rules and the run time pure literal rule. With some care completeness can be restored. How this can be achieved is briefly discussed. 3 references.
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…
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
Understanding graphs with two independent variables
NASA Astrophysics Data System (ADS)
Cooper, Jennifer L.
Adults are not necessarily competent users of graphs with two independent variables, despite the frequency of this representational format. The three tasks in this thesis address the impact of interpretation statements and graph patterns. Interpretation statements were based on the statistical effects -- simple effects, main effects, and interactions. Graph patterns were systematically varied based on a novel classification scheme of graphs with two IVs. I suggest that the complexity of a graph's data pattern depends on the consistency of the simple effects' directions and magnitudes. In the first study, undergraduates constructed graphs based on statements about data patterns. Errors reflected a misunderstanding of how two IVs could be combined and represented graphically. When the experimental group had graph-relevant information added (variable labels spatially located on axes), the ability to represent the relationships among the IVs significantly increased. The ability to satisfy the constraints imposed by the statements was not affected. Adding labels specifically targeted skills relevant to graphical literacy. Transfer to a third trial was stronger for those of higher math abilities. The second study focused on the effect of an introductory statistics course. Overall, undergraduates performed well on statements describing the simple effects of the IVs. However, even though they improved from Time 1 to Time 2 for interaction statements, performance on statements about main effects and interactions still showed considerable room for improvement. In the third study, repeated trials of the 20 patterns proposed by the simple effects consistency model established that the proposed classification scheme addresses additional sources of variability in reasoning with graphs (i.e., sources not captured by traditional classification schemes). As the complexity level of the data pattern increased, performance (based on accuracy and RT) decreased, with parallel impacts on
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.
Capacitated max -Batching with Interval Graph Compatibilities
NASA Astrophysics Data System (ADS)
Nonner, Tim
We consider the problem of partitioning interval graphs into cliques of bounded size. Each interval has a weight, and the weight of a clique is the maximum weight of any interval in the clique. This natural graph problem can be interpreted as a batch scheduling problem. Solving a long-standing open problem, we show NP-hardness, even if the bound on the clique sizes is constant. Moreover, we give a PTAS based on a novel dynamic programming technique for this case.
Inverse scattering problem for quantum graph vertices
Cheon, Taksu; Turek, Ondrej; Exner, Pavel
2011-06-15
We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of the Hermitian unitary matrix when the vertex coupling is of the scale-invariant (or Fueloep-Tsutsui) form. This enables the construction of quantum graphs with desired properties in a tailor-made fashion. The procedure is illustrated on the example of quantum vertices with equal transmission probabilities.
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.
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.