Optimal Embeddings of Distance Regular Graphs into Euclidean Spaces
F. Vallentin (Frank)
2008-01-01
htmlabstractIn this paper we give a lower bound for the least distortion embedding of a distance regular graph into Euclidean space. We use the lower bound for finding the least distortion for Hamming graphs, Johnson graphs, and all strongly regular graphs. Our technique involves semidefinite
Draisma, J.; Horobet, E.; Ottaviani, G.; Sturmfels, B.; Thomas, R.R.; Zhi, L.; Watt, M.
2014-01-01
The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest
Mixed Volume and Distance Geometry Techniques for Counting Euclidean Embeddings of Rigid Graphs
I.Z. Emiris; E.P. Tsigaridas; A. Varvitsiotis (Antonios); A. Mucherino (Antonio); C. Lavor; L. Liberti; N. Maculan
2013-01-01
htmlabstractA graph G is called generically minimally rigid in Rd if, for any choice of sufficiently generic edge lengths, it can be embedded in Rd in a finite number of distinct ways, modulo rigid transformations. Here, we deal with the problem of determining tight bounds on the number of such
Fast Exact Euclidean Distance (FEED) Transformation
Schouten, Theo; Kittler, J.; van den Broek, Egon; Petrou, M.; Nixon, M.
2004-01-01
Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number
Euclidean distance geometry an introduction
Liberti, Leo
2017-01-01
This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several. Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.
Euclidean distance degrees of real algebraic groups
Baaijens, J.A.; Draisma, J.
2015-01-01
We study the problem of finding, in a real algebraic matrix group, the matrix closest to a given data matrix. We do so from the algebro-geometric perspective of Euclidean distance degrees. We recover several classical results; and among the new results that we prove is a formula for the Euclidean
Euclidean distance degrees of real algebraic groups
Baaijens, J.A.; Draisma, J.
2014-01-01
We study the problem of finding, in a real algebraic matrix group, the matrix closest to a given data matrix. We do so from the algebro-geometric perspective of Euclidean distance degrees. We recover several classical results; and among the new results that we prove is a formula for the Euclidean
PERBANDINGAN EUCLIDEAN DISTANCE DENGAN CANBERRA DISTANCE PADA FACE RECOGNITION
Sendhy Rachmat Wurdianarto
2014-08-01
Full Text Available Perkembangan ilmu pada dunia komputer sangatlah pesat. Salah satu yang menandai hal ini adalah ilmu komputer telah merambah pada dunia biometrik. Arti biometrik sendiri adalah karakter-karakter manusia yang dapat digunakan untuk membedakan antara orang yang satu dengan yang lainnya. Salah satu pemanfaatan karakter / organ tubuh pada setiap manusia yang digunakan untuk identifikasi (pengenalan adalah dengan memanfaatkan wajah. Dari permasalahan diatas dalam pengenalan lebih tentang aplikasi Matlab pada Face Recognation menggunakan metode Euclidean Distance dan Canberra Distance. Model pengembangan aplikasi yang digunakan adalah model waterfall. Model waterfall beriisi rangkaian aktivitas proses yang disajikan dalam proses analisa kebutuhan, desain menggunakan UML (Unified Modeling Language, inputan objek gambar diproses menggunakan Euclidean Distance dan Canberra Distance. Kesimpulan yang dapat ditarik adalah aplikasi face Recognation menggunakan metode euclidean Distance dan Canverra Distance terdapat kelebihan dan kekurangan masing-masing. Untuk kedepannya aplikasi tersebut dapat dikembangkan dengan menggunakan objek berupa video ataupun objek lainnya. Kata kunci : Euclidean Distance, Face Recognition, Biometrik, Canberra Distance
van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime
2016-01-01
This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,
The Minimum Distance of Graph Codes
Høholdt, Tom; Justesen, Jørn
2011-01-01
We study codes constructed from graphs where the code symbols are associated with the edges and the symbols connected to a given vertex are restricted to be codewords in a component code. In particular we treat such codes from bipartite expander graphs coming from Euclidean planes and other...... geometries. We give results on the minimum distances of the codes....
Algebraic Methods for Counting Euclidean Embeddings of Rigid Graphs
I.Z. Emiris; E.P. Tsigaridas; A. Varvitsiotis (Antonios); E.R. Gasner
2009-01-01
textabstract The study of (minimally) rigid graphs is motivated by numerous applications, mostly in robotics and bioinformatics. A major open problem concerns the number of embeddings of such graphs, up to rigid motions, in Euclidean space. We capture embeddability by polynomial systems
Cohen, A.M.; Beineke, L.W.; Wilson, R.J.; Cameron, P.J.
2004-01-01
In this chapter we investigate the classification of distance-transitive graphs: these are graphs whose automorphism groups are transitive on each of the sets of pairs of vertices at distance i, for i = 0, 1,.... We provide an introduction into the field. By use of the classification of finite
Matrices and Graphs in Euclidean Geometry
Fiedler, Miroslav
2005-01-01
Roč. 14, - (2005), s. 51-58 E-ISSN 1081-3810 R&D Projects: GA AV ČR IAA1030302 Institutional research plan: CEZ:AV0Z10300504 Keywords : Euclidean space * Gram matrix * biorthogonal bases * simplex * interior angle * Steiner circumscribed ellipsoid * right simplex Subject RIV: BA - General Mathematics http://www.math.technion.ac.il/iic/ ela / ela -articles/14.html
MEDOF - MINIMUM EUCLIDEAN DISTANCE OPTIMAL FILTER
Barton, R. S.
1994-01-01
The Minimum Euclidean Distance Optimal Filter program, MEDOF, generates filters for use in optical correlators. The algorithm implemented in MEDOF follows theory put forth by Richard D. Juday of NASA/JSC. This program analytically optimizes filters on arbitrary spatial light modulators such as coupled, binary, full complex, and fractional 2pi phase. MEDOF optimizes these modulators on a number of metrics including: correlation peak intensity at the origin for the centered appearance of the reference image in the input plane, signal to noise ratio including the correlation detector noise as well as the colored additive input noise, peak to correlation energy defined as the fraction of the signal energy passed by the filter that shows up in the correlation spot, and the peak to total energy which is a generalization of PCE that adds the passed colored input noise to the input image's passed energy. The user of MEDOF supplies the functions that describe the following quantities: 1) the reference signal, 2) the realizable complex encodings of both the input and filter SLM, 3) the noise model, possibly colored, as it adds at the reference image and at the correlation detection plane, and 4) the metric to analyze, here taken to be one of the analytical ones like SNR (signal to noise ratio) or PCE (peak to correlation energy) rather than peak to secondary ratio. MEDOF calculates filters for arbitrary modulators and a wide range of metrics as described above. MEDOF examines the statistics of the encoded input image's noise (if SNR or PCE is selected) and the filter SLM's (Spatial Light Modulator) available values. These statistics are used as the basis of a range for searching for the magnitude and phase of k, a pragmatically based complex constant for computing the filter transmittance from the electric field. The filter is produced for the mesh points in those ranges and the value of the metric that results from these points is computed. When the search is concluded, the
Timed Fast Exact Euclidean Distance (tFEED) maps
Kehtarnavaz, Nasser; Schouten, Theo E.; Laplante, Philip A.; Kuppens, Harco; van den Broek, Egon
2005-01-01
In image and video analysis, distance maps are frequently used. They provide the (Euclidean) distance (ED) of background pixels to the nearest object pixel. In a naive implementation, each object pixel feeds its (exact) ED to each background pixel; then the minimum of these values denotes the ED to
Change of Measure between Light Travel Time and Euclidean Distances
Heymann Y.
2013-04-01
Full Text Available The problem of cosmological distances is approached using a method based on the propagation of light in an expanding Universe. From the chan ge of measure between Light Travel Time and Euclidean Distances, a formula is deri ved to compute distances as a function of redshift. This formula is identical to Matti g’s formula (with q 0 = 1 / 2 which is based on Friedmann’s equations of general relativi ty.
The Euclidean distance degree of an algebraic variety
Draisma, J.; Horobet, E.; Ottaviani, G.; Sturmfels, B.; Thomas, R.R.
2013-01-01
The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest
The Euclidean distance degree of an algebraic variety
Draisma, J.; Horobet, E.; Ottaviani, G.; Sturmfels, B.; Thomas, R.R.
The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low-rank matrices, the Eckart–Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest
Complex networks in the Euclidean space of communicability distances
Estrada, Ernesto
2012-06-01
We study the properties of complex networks embedded in a Euclidean space of communicability distances. The communicability distance between two nodes is defined as the difference between the weighted sum of walks self-returning to the nodes and the weighted sum of walks going from one node to the other. We give some indications that the communicability distance identifies the least crowded routes in networks where simultaneous submission of packages is taking place. We define an index Q based on communicability and shortest path distances, which allows reinterpreting the “small-world” phenomenon as the region of minimum Q in the Watts-Strogatz model. It also allows the classification and analysis of networks with different efficiency of spatial uses. Consequently, the communicability distance displays unique features for the analysis of complex networks in different scenarios.
Speckle Suppression by Weighted Euclidean Distance Anisotropic Diffusion
Fengcheng Guo
2018-05-01
Full Text Available To better reduce image speckle noise while also maintaining edge information in synthetic aperture radar (SAR images, we propose a novel anisotropic diffusion algorithm using weighted Euclidean distance (WEDAD. Presented here is a modified speckle reducing anisotropic diffusion (SRAD method, which constructs a new edge detection operator using weighted Euclidean distances. The new edge detection operator can adaptively distinguish between homogenous and heterogeneous image regions, effectively generate anisotropic diffusion coefficients for each image pixel, and filter each pixel at different scales. Additionally, the effects of two different weighting methods (Gaussian weighting and non-linear weighting of de-noising were analyzed. The effect of different adjustment coefficient settings on speckle suppression was also explored. A series of experiments were conducted using an added noise image, GF-3 SAR image, and YG-29 SAR image. The experimental results demonstrate that the proposed method can not only significantly suppress speckle, thus improving the visual effects, but also better preserve the edge information of images.
Fast Exact Euclidean Distance (FEED): A new class of adaptable distance transforms
Schouten, Theo E.; van den Broek, Egon
2014-01-01
A new unique class of foldable distance transforms of digital images (DT) is introduced, baptized: Fast Exact Euclidean Distance (FEED) transforms. FEED class algorithms calculate the DT starting directly from the definition or rather its inverse. The principle of FEED class algorithms is
Fast Exact Euclidean Distance (FEED) : A new class of adaptable distance transforms
Schouten, Theo E.; van den Broek, Egon L.
2014-01-01
A new unique class of foldable distance transforms of digital images (DT) is introduced, baptized: Fast Exact Euclidean Distance (FEED) transforms. FEED class algorithms calculate the DT startingdirectly from the definition or rather its inverse. The principle of FEED class algorithms is introduced,
Steiner Distance in Graphs--A Survey
Mao, Yaping
2017-01-01
For a connected graph $G$ of order at least $2$ and $S\\subseteq V(G)$, the \\emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. In this paper, we summarize the known results on the Steiner distance parameters, including Steiner distance, Steiner diameter, Steiner center, Steiner median, Steiner interval, Steiner distance hereditary graph, Steiner distance stable graph, average Steiner distance, and Steiner ...
Squared Euclidean distance: a statistical test to evaluate plant community change
Raymond D. Ratliff; Sylvia R. Mori
1993-01-01
The concepts and a procedure for evaluating plant community change using the squared Euclidean distance (SED) resemblance function are described. Analyses are based on the concept that Euclidean distances constitute a sample from a population of distances between sampling units (SUs) for a specific number of times and SUs. With different times, the distances will be...
Three Dimensional Fast Exact Euclidean Distance (3D-FEED) Maps
Latecki, L.J.; Schouten, Theo E.; Mount, D.M.; Kuppens, Harco C.; Wu, A.Y.; van den Broek, Egon
2006-01-01
In image and video analysis, distance maps are frequently used. They provide the (Euclidean) distance (ED) of background pixels to the nearest object pixel. Recently, the Fast Exact Euclidean Distance (FEED) transformation was launched. In this paper, we present the three dimensional (3D) version of
Efficient gamma index calculation using fast Euclidean distance transform
Chen Mingli; Lu Weiguo; Chen Quan; Ruchala, Kenneth; Olivera, Gustavo [TomoTherapy Inc., 1240 Deming Way, Madison, WI 53717 (United States)], E-mail: wlu@tomotherapy.com
2009-04-07
The gamma index is a tool for dose distribution comparison. It combines both dose difference (DD) and distance to agreement (DTA) into a single quantity. Though it is an effective measure, making up for the inadequacy of DD or DTA alone, its calculation can be very time-consuming. For a k-D space with N quantization levels in each dimension, the complexity of the exhaustive search is O(N{sup 2k}). In this work, we proposed an efficient method that reduces the complexity from O(N{sup 2k}) to O(N{sup k}M), where M is the number of discretized dose values and is comparable to N. More precisely, by embedding the reference dose distribution in a (k+1)-D spatial-dose space, we can use fast Euclidean distance transform with linear complexity to obtain a table of gamma indices evaluated over a range of the (k+1)-D spatial-dose space. Then, to obtain gamma indices for the test dose distribution, it requires only table lookup with complexity O(N{sup k}). Such a table can also be used for other test dose distributions as long as the reference dose distribution is the same. Simulations demonstrated the efficiency of our proposed method. The speedup for 3D gamma index calculation is expected to be on the order of tens of thousands (from O(N{sup 6}) to O(N{sup 3}M)) if N is a few hundreds, which makes clinical usage of the 3D gamma index feasible. A byproduct of the gamma index table is that the gradient of the gamma index with respect to either the spatial or dose dimension can be easily derived. The gradient can be used to identify the main causes of the discrepancy from the reference distribution at any dose point in the test distribution or incorporated in treatment planning and machine parameter optimization.
Distance matrices and quadratic embedding of graphs
Nobuaki Obata
2018-04-01
Full Text Available A connected graph is said to be of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently, if the distance matrix is conditionally negative definite. Several criteria for a graph to be of QE class are derived from the point of view of graph operations. For a quantitative criterion the QE constant is introduced and concrete examples are shown with explicit calculation. If the distance matrix admits a constant row sum, the QE constant coincides with the second largest eigenvalue of the distance matrix. The QE constants are determined for all graphs on $n$ vertices with $n\\le5$, among which two are not of QE class.
Equivalence of massive propagator distance and mathematical distance on graphs
Filk, T.
1992-01-01
It is shown in this paper that the assignment of distance according to the massive propagator method and according to the mathematical definition (length of minimal path) on arbitrary graphs with a bound on the degree leads to equivalent large scale properties of the graph. Especially, the internal scaling dimension is the same for both definitions. This result holds for any fixed, non-vanishing mass, so that a really inequivalent definition of distance requires the limit m → 0
Geodesic distance in planar graphs
Bouttier, J.; Di Francesco, P.; Guitter, E.
2003-01-01
We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection with decorated trees, leading to a recursion relation on the geodesic distance. The latter is solved exactly in terms of discrete soliton-like expressions, suggesting an underlying integrable structure. We extract from this solution the fractal dimensions at the various (multi)-critical points, as well as the precise scaling forms of the continuum two-point functions and the probability distributions for the geodesic distance in (multi)-critical random surfaces. The two-point functions are shown to obey differential equations involving the residues of the KdV hierarchy
Resistance Distances in Vertex-Face Graphs
Shangguan, Yingmin; Chen, Haiyan
2018-01-01
The computation of two-point resistances in networks is a classical problem in electric circuit theory and graph theory. Let G be a triangulation graph with n vertices embedded on an orientable surface. Define K(G) to be the graph obtained from G by inserting a new vertex vϕ to each face ϕ of G and adding three new edges (u, vϕ), (v, vϕ) and (w, vϕ), where u, v and w are three vertices on the boundary of ϕ. In this paper, using star-triangle transformation and resistance local-sum rules, explicit relations between resistance distances in K(G) and those in G are obtained. These relations enable us to compute resistance distance between any two points of Kk(G) recursively. As explanation examples, some resistances in several networks are computed, including the modified Apollonian network and networks constructed from tetrahedron, octahedron and icosahedron, respectively.
Distance 2-Domination in Prisms of Graphs
Hurtado Ferran
2017-05-01
Full Text Available A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ∊ (V (G − D and D is at most two. Let γ2(G denote the size of a smallest distance 2-dominating set of G. For any permutation π of the vertex set of G, the prism of G with respect to π is the graph πG obtained from G and a copy G′ of G by joining u ∊ V(G with v′ ∊ V(G′ if and only if v′ = π(u. If γ2(πG = γ2(G for any permutation π of V(G, then G is called a universal γ2-fixer. In this work we characterize the cycles and paths that are universal γ2-fixers.
On the sizes of expander graphs and minimum distances of graph codes
Høholdt, Tom; Justesen, Jørn
2014-01-01
We give lower bounds for the minimum distances of graph codes based on expander graphs. The bounds depend only on the second eigenvalue of the graph and the parameters of the component codes. We also give an upper bound on the size of a degree regular graph with given second eigenvalue....
Steiner tree heuristic in the Euclidean d-space using bottleneck distances
Lorenzen, Stephan Sloth; Winter, Pawel
2016-01-01
Some of the most efficient heuristics for the Euclidean Steiner minimal tree problem in the d-dimensional space, d ≥2, use Delaunay tessellations and minimum spanning trees to determine small subsets of geometrically close terminals. Their low-cost Steiner trees are determined and concatenated...... in a greedy fashion to obtain a low cost tree spanning all terminals. The weakness of this approach is that obtained solutions are topologically related to minimum spanning trees. To avoid this and to obtain even better solutions, bottleneck distances are utilized to determine good subsets of terminals...
Meng, Weizhi; Li, Wenjuan; Wang, Yu
2017-01-01
and healthcare personnel. The underlying network architecture to support such devices is also referred to as medical smartphone networks (MSNs). Similar to other networks, MSNs also suffer from various attacks like insider attacks (e.g., leakage of sensitive patient information by a malicious insider......). In this work, we focus on MSNs and design a trust-based intrusion detection approach through Euclidean distance-based behavioral profiling to detect malicious devices (or called nodes). In the evaluation, we collaborate with healthcare organizations and implement our approach in a real simulated MSN...
Septa Cahyani
2018-04-01
Full Text Available The human ability to recognize a variety of objects, however complex the object, is the special ability that humans possess. Any normal human will have no difficulty in recognizing handwriting objects between an author and another author. With the rapid development of digital technology, the human ability to recognize handwriting objects has been applied in a program known as Computer Vision. This study aims to create identification system different types of handwriting capital letters that have different sizes, thickness, shape, and tilt (distinctive features in handwriting using Linear Discriminant Analysis (LDA and Euclidean Distance methods. LDA is used to obtain characteristic characteristics of the image and provide the distance between the classes becomes larger, while the distance between training data in one class becomes smaller, so that the introduction time of digital image of handwritten capital letter using Euclidean Distance becomes faster computation time (by searching closest distance between training data and data testing. The results of testing the sample data showed that the image resolution of 50x50 pixels is the exact image resolution used for data as much as 1560 handwritten capital letter data compared to image resolution 25x25 pixels and 40x40 pixels. While the test data and training data testing using the method of 10-fold cross validation where 1404 for training data and 156 for data testing showed identification of digital image handwriting capital letter has an average effectiveness of the accuracy rate of 75.39% with the average time computing of 0.4199 seconds.
Lambert Marie-Ève
2012-06-01
Full Text Available Abstract Background Porcine reproductive and respiratory syndrome (PRRS is a viral disease that has a major economic impact for the swine industry. Its control is mostly directed towards preventing its spread which requires a better understanding of the mechanisms of transmission of the virus between herds. The objectives of this study were to describe the genetic diversity and to assess the correlation among genetic, Euclidean and temporal distances and ownership to better understand pathways of transmission. Results A cross-sectional study was conducted on sites located in a high density area of swine production in Quebec. Geographical coordinates (longitude/latitude, date of submission and ownership were obtained for each site. ORF5 sequencing was attempted on PRRSV positive sites. Proportion of pairwise combinations of strains having ≥98% genetic homology were analysed according to Euclidean distances and ownership. Correlations between genetic, Euclidean and temporal distances and ownership were assessed using Mantel tests on continuous and binary matrices. Sensitivity of the correlations between genetic and Euclidean as well as temporal distances was evaluated for different Euclidean and temporal distance thresholds. An ORF5 sequence was identified for 132 of the 176 (75% PRRSV positive sites; 122 were wild-type strains. The mean (min-max genetic, Euclidean and temporal pairwise distances were 11.6% (0–18.7, 15.0 km (0.04-45.7 and 218 days (0–852, respectively. Significant positive correlations were observed between genetic and ownership, genetic and Euclidean and between genetic and temporal binary distances. The relationship between genetic and ownership suggests either common sources of animals or semen, employees, technical services or vehicles, whereas that between genetic and Euclidean binary distances is compatible with area spread of the virus. The latter correlation was observed only up to 5 km. Conclusions This study
Overlapping community detection based on link graph using distance dynamics
Chen, Lei; Zhang, Jing; Cai, Li-Jun
2018-01-01
The distance dynamics model was recently proposed to detect the disjoint community of a complex network. To identify the overlapping structure of a network using the distance dynamics model, an overlapping community detection algorithm, called L-Attractor, is proposed in this paper. The process of L-Attractor mainly consists of three phases. In the first phase, L-Attractor transforms the original graph to a link graph (a new edge graph) to assure that one node has multiple distances. In the second phase, using the improved distance dynamics model, a dynamic interaction process is introduced to simulate the distance dynamics (shrink or stretch). Through the dynamic interaction process, all distances converge, and the disjoint community structure of the link graph naturally manifests itself. In the third phase, a recovery method is designed to convert the disjoint community structure of the link graph to the overlapping community structure of the original graph. Extensive experiments are conducted on the LFR benchmark networks as well as real-world networks. Based on the results, our algorithm demonstrates higher accuracy and quality than other state-of-the-art algorithms.
Q. Zhou
2017-07-01
Full Text Available Visual Odometry (VO is a critical component for planetary robot navigation and safety. It estimates the ego-motion using stereo images frame by frame. Feature points extraction and matching is one of the key steps for robotic motion estimation which largely influences the precision and robustness. In this work, we choose the Oriented FAST and Rotated BRIEF (ORB features by considering both accuracy and speed issues. For more robustness in challenging environment e.g., rough terrain or planetary surface, this paper presents a robust outliers elimination method based on Euclidean Distance Constraint (EDC and Random Sample Consensus (RANSAC algorithm. In the matching process, a set of ORB feature points are extracted from the current left and right synchronous images and the Brute Force (BF matcher is used to find the correspondences between the two images for the Space Intersection. Then the EDC and RANSAC algorithms are carried out to eliminate mismatches whose distances are beyond a predefined threshold. Similarly, when the left image of the next time matches the feature points with the current left images, the EDC and RANSAC are iteratively performed. After the above mentioned, there are exceptional remaining mismatched points in some cases, for which the third time RANSAC is applied to eliminate the effects of those outliers in the estimation of the ego-motion parameters (Interior Orientation and Exterior Orientation. The proposed approach has been tested on a real-world vehicle dataset and the result benefits from its high robustness.
Durato, M. V.; Albano, A. M.; Rapp, P. E.; Nawang, S. A.
2015-06-01
The validity of ERPs as indices of stable neurophysiological traits is partially dependent on their stability over time. Previous studies on ERP stability, however, have reported diverse stability estimates despite using the same component scoring methods. This present study explores a novel approach in investigating the longitudinal stability of average ERPs—that is, by treating the ERP waveform as a time series and then applying Euclidean Distance and Kolmogorov-Smirnov analyses to evaluate the similarity or dissimilarity between the ERP time series of different sessions or run pairs. Nonlinear dynamical analysis show that in the absence of a change in medical condition, the average ERPs of healthy human adults are highly longitudinally stable—as evaluated by both the Euclidean distance and the Kolmogorov-Smirnov test.
Durato, M V; Nawang, S A; Albano, A M; Rapp, P E
2015-01-01
The validity of ERPs as indices of stable neurophysiological traits is partially dependent on their stability over time. Previous studies on ERP stability, however, have reported diverse stability estimates despite using the same component scoring methods. This present study explores a novel approach in investigating the longitudinal stability of average ERPs—that is, by treating the ERP waveform as a time series and then applying Euclidean Distance and Kolmogorov-Smirnov analyses to evaluate the similarity or dissimilarity between the ERP time series of different sessions or run pairs. Nonlinear dynamical analysis show that in the absence of a change in medical condition, the average ERPs of healthy human adults are highly longitudinally stable—as evaluated by both the Euclidean distance and the Kolmogorov-Smirnov test. (paper)
The Eccentric-distance Sum of Some Graphs
P, Padmapriya; Mathad, Veena
2017-01-01
Let $G = (V,E)$ be a simple connected graph. Theeccentric-distance sum of $G$ is defined as$\\xi^{ds}(G) =\\ds\\sum_{\\{u,v\\}\\subseteq V(G)} [e(u)+e(v)] d(u,v)$, where $e(u)$ %\\dsis the eccentricity of the vertex $u$ in $G$ and $d(u,v)$ is thedistance between $u$ and $v$. In this paper, we establish formulaeto calculate the eccentric-distance sum for some graphs, namelywheel, star, broom, lollipop, double star, friendship, multi-stargraph and the join of $P_{n-2}$ and $P_2$.
The eccentric-distance sum of some graphs
Padmapriya P
2017-04-01
Full Text Available Let $G = (V,E$ be a simple connected graph. Theeccentric-distance sum of $G$ is defined as$\\xi^{ds}(G =\\ds\\sum_{\\{u,v\\}\\subseteq V(G} [e(u+e(v] d(u,v$, where $e(u$ %\\dsis the eccentricity of the vertex $u$ in $G$ and $d(u,v$ is thedistance between $u$ and $v$. In this paper, we establish formulaeto calculate the eccentric-distance sum for some graphs, namelywheel, star, broom, lollipop, double star, friendship, multi-stargraph and the join of $P_{n-2}$ and $P_2$.
Distance spectrum of Indu–Bala product of graphs
G. Indulal
2016-12-01
Full Text Available The D-eigenvalues μ1,μ2,…,μn of a graph G of order n are the eigenvalues of its distance matrix D and form the distance spectrum or D-spectrum of G denoted by SpecD(G. Let G1 and G2 be two regular graphs. The Indu–Bala product of G1 and G2 is denoted by G1▾G2 and is obtained from two disjoint copies of the join G1∨G2 of G1 and G2 by joining the corresponding vertices in the two copies of G2. In this paper we obtain the distance spectrum of G1▾G2 in terms of the adjacency spectra of G1 and G2. We use this result to obtain a new class of distance equienergetic graphs of diameter 3. We also prove that the class of graphs Kn¯▾Kn+1¯ has integral distance spectrum.
Gómez, Daviel; Hernández, L Ázaro; Yabor, Lourdes; Beemster, Gerrit T S; Tebbe, Christoph C; Papenbrock, Jutta; Lorenzo, José Carlos
2018-03-15
Plant scientists usually record several indicators in their abiotic factor experiments. The common statistical management involves univariate analyses. Such analyses generally create a split picture of the effects of experimental treatments since each indicator is addressed independently. The Euclidean distance combined with the information of the control treatment could have potential as an integrating indicator. The Euclidean distance has demonstrated its usefulness in many scientific fields but, as far as we know, it has not yet been employed for plant experimental analyses. To exemplify the use of the Euclidean distance in this field, we performed an experiment focused on the effects of mannitol on sugarcane micropropagation in temporary immersion bioreactors. Five mannitol concentrations were compared: 0, 50, 100, 150 and 200 mM. As dependent variables we recorded shoot multiplication rate, fresh weight, and levels of aldehydes, chlorophylls, carotenoids and phenolics. The statistical protocol which we then carried out integrated all dependent variables to easily identify the mannitol concentration that produced the most remarkable integral effect. Results provided by the Euclidean distance demonstrate a gradually increasing distance from the control in function of increasing mannitol concentrations. 200 mM mannitol caused the most significant alteration of sugarcane biochemistry and physiology under the experimental conditions described here. This treatment showed the longest statistically significant Euclidean distance to the control treatment (2.38). In contrast, 50 and 100 mM mannitol showed the lowest Euclidean distances (0.61 and 0.84, respectively) and thus poor integrated effects of mannitol. The analysis shown here indicates that the use of the Euclidean distance can contribute to establishing a more integrated evaluation of the contrasting mannitol treatments.
Yuxian Zhang
2015-01-01
Full Text Available The quality index model in slashing process is difficult to build by reason of the outliers and noise data from original data. To the above problem, a fuzzy neural network based on non-Euclidean distance clustering is proposed in which the input space is partitioned into many local regions by the fuzzy clustering based on non-Euclidean distance so that the computation complexity is decreased, and fuzzy rule number is determined by validity function based on both the separation and the compactness among clusterings. Then, the premise parameters and consequent parameters are trained by hybrid learning algorithm. The parameters identification is realized; meanwhile the convergence condition of consequent parameters is obtained by Lyapunov function. Finally, the proposed method is applied to build the quality index model in slashing process in which the experimental data come from the actual slashing process. The experiment results show that the proposed fuzzy neural network for quality index model has lower computation complexity and faster convergence time, comparing with GP-FNN, BPNN, and RBFNN.
Entity-Linking via Graph-Distance Minimization
Roi Blanco
2014-07-01
Full Text Available Entity-linking is a natural-language–processing task that consists in identifying the entities mentioned in a piece of text, linking each to an appropriate item in some knowledge base; when the knowledge base is Wikipedia, the problem comes to be known as wikification (in this case, items are wikipedia articles. One instance of entity-linking can be formalized as an optimization problem on the underlying concept graph, where the quantity to be optimized is the average distance between chosen items. Inspired by this application, we define a new graph problem which is a natural variant of the Maximum Capacity Representative Set. We prove that our problem is NP-hard for general graphs; nonetheless, under some restrictive assumptions, it turns out to be solvable in linear time. For the general case, we propose two heuristics: one tries to enforce the above assumptions and another one is based on the notion of hitting distance; we show experimentally how these approaches perform with respect to some baselines on a real-world dataset.
High Girth Column-Weight-Two LDPC Codes Based on Distance Graphs
Gabofetswe Malema
2007-01-01
Full Text Available LDPC codes of column weight of two are constructed from minimal distance graphs or cages. Distance graphs are used to represent LDPC code matrices such that graph vertices that represent rows and edges are columns. The conversion of a distance graph into matrix form produces an adjacency matrix with column weight of two and girth double that of the graph. The number of 1's in each row (row weight is equal to the degree of the corresponding vertex. By constructing graphs with different vertex degrees, we can vary the rate of corresponding LDPC code matrices. Cage graphs are used as examples of distance graphs to design codes with different girths and rates. Performance of obtained codes depends on girth and structure of the corresponding distance graphs.
Distance Magic-Type and Distance Antimagic-Type Labelings of Graphs
Freyberg, Bryan J.
Generally speaking, a distance magic-type labeling of a graph G of order n is a bijection l from the vertex set of the graph to the first n natural numbers or to the elements of a group of order n, with the property that the weight of each vertex is the same. The weight of a vertex x is defined as the sum (or appropriate group operation) of all the labels of vertices adjacent to x. If instead we require that all weights differ, then we refer to the labeling as a distance antimagic-type labeling. This idea can be generalized for directed graphs; the weight will take into consideration the direction of the arcs. In this manuscript, we provide new results for d-handicap labeling, a distance antimagic-type labeling, and introduce a new distance magic-type labeling called orientable Gamma-distance magic labeling. A d-handicap distance antimagic labeling (or just d-handicap labeling for short) of a graph G = ( V,E) of order n is a bijection l from V to the set {1,2,...,n} with induced weight function [special characters omitted]. such that l(xi) = i and the sequence of weights w(x 1),w(x2),...,w (xn) forms an arithmetic sequence with constant difference d at least 1. If a graph G admits a d-handicap labeling, we say G is a d-handicap graph. A d-handicap incomplete tournament, H(n,k,d ) is an incomplete tournament of n teams ranked with the first n natural numbers such that each team plays exactly k games and the strength of schedule of the ith ranked team is d more than the i + 1st ranked team. That is, strength of schedule increases arithmetically with strength of team. Constructing an H(n,k,d) is equivalent to finding a d-handicap labeling of a k-regular graph of order n.. In Chapter 2 we provide general constructions for every d for large classes of both n and k, providing breadfth and depth to the catalog of known H(n,k,d)'s. In Chapters 3 - 6, we introduce a new type of labeling called orientable Gamma-distance magic labeling. Let Gamma be an abelian group of order
Oblakov, Konstantin I; Oblakova, Tat' yana A [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
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.
Distances in zero-divisor and total graphs from commutative rings–A survey
T. Tamizh Chelvam
2016-12-01
Full Text Available There are so many ways to construct graphs from algebraic structures. Most popular constructions are Cayley graphs, commuting graphs and non-commuting graphs from finite groups and zero-divisor graphs and total graphs from commutative rings. For a commutative ring R with non-zero identity, we denote the set of zero-divisors and unit elements of R by Z(R and U(R, respectively. One of the associated graphs to a ring R is the zero-divisor graph; it is a simple graph with vertex set Z(R∖{0}, and two vertices x and y are adjacent if and only if xy=0. This graph was first introduced by Beck, where all the elements of R are considered as the vertices. Anderson and Badawi, introduced the total graph of R, as the simple graph with all elements of R as vertices, and two distinct vertices x and y are adjacent if and only if x+y∈Z(R. For a given graph G, the concept of connectedness, diameter and girth are always of great interest. Several authors extensively studied about the zero-divisor and total graphs from commutative rings. In this paper, we present a survey of results obtained with regard to distances in zero-divisor and total graphs.
A linear time algorithm for minimum fill-in and treewidth for distance heredity graphs
Broersma, Haitze J.; Dahlhaus, E.; Kloks, A.J.J.; Kloks, T.
2000-01-01
A graph is distance hereditary if it preserves distances in all its connected induced subgraphs. The MINIMUM FILL-IN problem is the problem of finding a chordal supergraph with the smallest possible number of edges. The TREEWIDTH problem is the problem of finding a chordal embedding of the graph
Kupavskii, A B; Raigorodskii, A M [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2013-10-31
We investigate in detail some properties of distance graphs constructed on the integer lattice. Such graphs find wide applications in problems of combinatorial geometry, in particular, such graphs were employed to answer Borsuk's question in the negative and to obtain exponential estimates for the chromatic number of the space. This work is devoted to the study of the number of cliques and the chromatic number of such graphs under certain conditions. Constructions of sequences of distance graphs are given, in which the graphs have unit length edges and contain a large number of triangles that lie on a sphere of radius 1/√3 (which is the minimum possible). At the same time, the chromatic numbers of the graphs depend exponentially on their dimension. The results of this work strengthen and generalize some of the results obtained in a series of papers devoted to related issues. Bibliography: 29 titles.
Algorithms for Planar Graphs and Graphs in Metric Spaces
Wulff-Nilsen, Christian
structural properties that can be exploited. For instance, a road network or a wire layout on a microchip is typically (near-)planar and distances in the network are often defined w.r.t. the Euclidean or the rectilinear metric. Specialized algorithms that take advantage of such properties are often orders...... of magnitude faster than the corresponding algorithms for general graphs. The first and main part of this thesis focuses on the development of efficient planar graph algorithms. The most important contributions include a faster single-source shortest path algorithm, a distance oracle with subquadratic...... for geometric graphs and graphs embedded in metric spaces. Roughly speaking, the stretch factor is a real value expressing how well a (geo-)metric graph approximates the underlying complete graph w.r.t. distances. We give improved algorithms for computing the stretch factor of a given graph and for augmenting...
Sum of All-Pairs Shortest Path Distances in a Planar Graph in Subquadratic Time
Wulff-Nilsen, Christian
2008-01-01
We consider the problem of computing the Wiener index of a graph, defined as the sum of distances between all pairs of its vertices. It is an open problem whether the Wiener index of a planar graph can be found in subquadratic time. We solve this problem by presenting an algorithm with O(n^2*log...
On The Determinant of q-Distance Matrix of a Graph
Li Hong-Hai
2014-02-01
Full Text Available In this note, we show how the determinant of the q-distance matrix Dq(T of a weighted directed graph G can be expressed in terms of the corresponding determinants for the blocks of G, and thus generalize the results obtained by Graham et al. [R.L. Graham, A.J. Hoffman and H. Hosoya, On the distance matrix of a directed graph, J. Graph Theory 1 (1977 85-88]. Further, by means of the result, we determine the determinant of the q-distance matrix of the graph obtained from a connected weighted graph G by adding the weighted branches to G, and so generalize in part the results obtained by Bapat et al. [R.B. Bapat, S. Kirkland and M. Neumann, On distance matrices and Laplacians, Linear Algebra Appl. 401 (2005 193- 209]. In particular, as a consequence, determinantal formulae of q-distance matrices for unicyclic graphs and one class of bicyclic graphs are presented.
A weak zero-one law for sequences of random distance graphs
Zhukovskii, Maksim E [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2012-07-31
We study zero-one laws for properties of random distance graphs. Properties written in a first-order language are considered. For p(N) such that pN{sup {alpha}}{yields}{infinity} as N{yields}{infinity}, and (1-p)N{sup {alpha}} {yields} {infinity} as N {yields} {infinity} for any {alpha}>0, we succeed in refuting the law. In this connection, we consider a weak zero-one j-law. For this law, we obtain results for random distance graphs which are similar to the assertions concerning the classical zero-one law for random graphs. Bibliography: 18 titles.
de Wit, Bernard; Reys, Valentin
2017-12-01
Supergravity with eight supercharges in a four-dimensional Euclidean space is constructed at the full non-linear level by performing an off-shell time-like reduction of five-dimensional supergravity. The resulting four-dimensional theory is realized off-shell with the Weyl, vector and tensor supermultiplets and a corresponding multiplet calculus. Hypermultiplets are included as well, but they are themselves only realized with on-shell supersymmetry. We also briefly discuss the non-linear supermultiplet. The off-shell reduction leads to a full understanding of the Euclidean theory. A complete multiplet calculus is presented along the lines of the Minkowskian theory. Unlike in Minkowski space, chiral and anti-chiral multiplets are real and supersymmetric actions are generally unbounded from below. Precisely as in the Minkowski case, where one has different formulations of Poincaré supergravity upon introducing different compensating supermultiplets, one can also obtain different versions of Euclidean supergravity.
Sequence of maximal distance codes in graphs or other metric spaces
Charles Delorme
2013-11-01
Full Text Available Given a subset C in a metric space E, its successor is the subset s(C of points at maximum distance from C in E. We study some properties of the sequence obtained by iterating this operation. Graphs with their usual distance provide already typical examples.
Trudeau, Richard J
1994-01-01
Preface1. Pure Mathematics Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. Graphs Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics The Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar Graphs Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions; Kuratowski's Theorem; Determining Whether a Graph is Planar or
Approximate distance oracles for planar graphs with improved query time-space tradeoff
Wulff-Nilsen, Christian
2016-01-01
We consider approximate distance oracles for edge-weighted n-vertex undirected planar graphs. Given fixed ϵ > 0, we present a (1 + ϵ)-approximate distance oracle with O(n(log log n)2) space and O((loglogr?,)3) query time. This improves the previous best product of query time and space...... of the oracles of Thorup (FOCS 2001, J. ACM 2004) and Klein (SODA 2002) from O(nlogn) to O(n(loglogn)5)....
A linear-time algorithm for Euclidean feature transform sets
Hesselink, Wim H.
2007-01-01
The Euclidean distance transform of a binary image is the function that assigns to every pixel the Euclidean distance to the background. The Euclidean feature transform is the function that assigns to every pixel the set of background pixels with this distance. We present an algorithm to compute the
Scaling limits of Euclidean quantum fields
Enss, V.
1981-01-01
The author studies the long-distance and short-distance behaviour of generalized random processes which arise in Euclidean Boson field theories. Among them are Wick-polynomials of free fields and P(PHI) 2 -models. (Auth.)
Constant time distance queries in planar unweighted graphs with subquadratic preprocessing time
Wulff-Nilsen, C.
2013-01-01
Let G be an n-vertex planar, undirected, and unweighted graph. It was stated as open problems whether the Wiener index, defined as the sum of all-pairs shortest path distances, and the diameter of G can be computed in o(n(2)) time. We show that both problems can be solved in O(n(2) log log n/log n......) time with O(n) space. The techniques that we apply allow us to build, within the same time bound, an oracle for exact distance queries in G. More generally, for any parameter S is an element of [(log n/log log n)(2), n(2/5)], distance queries can be answered in O (root S log S/log n) time per query...... with O(n(2)/root S) preprocessing time and space requirement. With respect to running time, this is better than previous algorithms when log S = o(log n). All algorithms have linear space requirement. Our results generalize to a larger class of graphs including those with a fixed excluded minor. (C) 2012...
Isotropic covariance functions on graphs and their edges
Anderes, E.; Møller, Jesper; Rasmussen, Jakob Gulddahl
We develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, i.e., graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to consider points on the graph which are vertices or points...... on an edge. Our covariance functions are defined on the vertices and edge points of these graphs and are isotropic in the sense that they depend only on the geodesic distance or on a new metric called the resistance metric (which extends the classical resistance metric developed in electrical network theory...... functions in the spatial statistics literature (the power exponential, Matérn, generalized Cauchy, and Dagum classes) are shown to be valid with respect to the resistance metric for any graph with Euclidean edges, whilst they are only valid with respect to the geodesic metric in more special cases....
Learning Euclidean Embeddings for Indexing and Classification
Athitsos, Vassilis; Alon, Joni; Sclaroff, Stan; Kollios, George
2004-01-01
BoostMap is a recently proposed method for efficient approximate nearest neighbor retrieval in arbitrary non-Euclidean spaces with computationally expensive and possibly non-metric distance measures...
Wiener Index, Diameter, and Stretch Factor of a Weighted Planar Graph in Subquadratic Time
Wulff-Nilsen, Christian
over all pairs of distinct vertices of the ratio between the graph distance and the Euclidean distance between the two vertices). More specifically, we show that the Wiener index and diameter can be found in O(n^2*(log log n)^4/log n) worst-case time and that the stretch factor can be found in O(n^2......We solve three open problems: the existence of subquadratic time algorithms for computing the Wiener index (sum of APSP distances) and the diameter (maximum distance between any vertex pair) of a planar graph with non-negative edge weights and the stretch factor of a plane geometric graph (maximum...
Dey, Soumyabrata; Rao, A Ravishankar; Shah, Mubarak
2014-01-01
Attention Deficit Hyperactive Disorder (ADHD) is getting a lot of attention recently for two reasons. First, it is one of the most commonly found childhood disorders and second, the root cause of the problem is still unknown. Functional Magnetic Resonance Imaging (fMRI) data has become a popular tool for the analysis of ADHD, which is the focus of our current research. In this paper we propose a novel framework for the automatic classification of the ADHD subjects using their resting state fMRI (rs-fMRI) data of the brain. We construct brain functional connectivity networks for all the subjects. The nodes of the network are constructed with clusters of highly active voxels and edges between any pair of nodes represent the correlations between their average fMRI time series. The activity level of the voxels are measured based on the average power of their corresponding fMRI time-series. For each node of the networks, a local descriptor comprising of a set of attributes of the node is computed. Next, the Multi-Dimensional Scaling (MDS) technique is used to project all the subjects from the unknown graph-space to a low dimensional space based on their inter-graph distance measures. Finally, the Support Vector Machine (SVM) classifier is used on the low dimensional projected space for automatic classification of the ADHD subjects. Exhaustive experimental validation of the proposed method is performed using the data set released for the ADHD-200 competition. Our method shows promise as we achieve impressive classification accuracies on the training (70.49%) and test data sets (73.55%). Our results reveal that the detection rates are higher when classification is performed separately on the male and female groups of subjects.
Soumyabrata eDey
2014-06-01
Full Text Available Attention Deficit Hyperactive Disorder (ADHD is getting a lot of attention recently for two reasons. First, it is one of the most commonly found childhood disorders and second, the root cause of the problem is still unknown. Functional Magnetic Resonance Imaging (fMRI data has become a popular tool for the analysis of ADHD, which is the focus of our current research. In this paper we propose a novel framework for the automatic classification of the ADHD subjects using their resting state fMRI (rs-fMRI data of the brain. We construct brain functional connectivity networks for all the subjects. The nodes of the network are constructed with clusters of highly active voxels and edges between any pair of nodes represent the correlations between their average fMRI time series. The activity level of the voxels are measured based on the average power of their corresponding fMRI time-series. For each node of the networks, a local descriptor comprising of a set of attributes of the node is computed. Next, the Multi-Dimensional Scaling (MDS technique is used to project all the subjects from the unknown graph-space to a low dimensional space based on their inter-graph distance measures. Finally, the Support Vector Machine (SVM classifier is used on the low dimensional projected space for automatic classification of the ADHD subjects. Exhaustive experimental validation of the proposed method is performed using the data set released for the ADHD-200 competition. Our method shows promise as we achieve impressive classification accuracies on the training (70.49% and test data sets (73.55%. Our results reveal that the detection rates are higher when classification is performed separately on the male and female groups of subjects.
Coloring geographical threshold graphs
Bradonjic, Milan [Los Alamos National Laboratory; Percus, Allon [Los Alamos National Laboratory; Muller, Tobias [EINDHOVEN UNIV. OF TECH
2008-01-01
We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
Fubiao Feng
2017-03-01
Full Text Available Recently, graph embedding has drawn great attention for dimensionality reduction in hyperspectral imagery. For example, locality preserving projection (LPP utilizes typical Euclidean distance in a heat kernel to create an affinity matrix and projects the high-dimensional data into a lower-dimensional space. However, the Euclidean distance is not sufficiently correlated with intrinsic spectral variation of a material, which may result in inappropriate graph representation. In this work, a graph-based discriminant analysis with spectral similarity (denoted as GDA-SS measurement is proposed, which fully considers curves changing description among spectral bands. Experimental results based on real hyperspectral images demonstrate that the proposed method is superior to traditional methods, such as supervised LPP, and the state-of-the-art sparse graph-based discriminant analysis (SGDA.
Phylogenetic trees and Euclidean embeddings.
Layer, Mark; Rhodes, John A
2017-01-01
It was recently observed by de Vienne et al. (Syst Biol 60(6):826-832, 2011) that a simple square root transformation of distances between taxa on a phylogenetic tree allowed for an embedding of the taxa into Euclidean space. While the justification for this was based on a diffusion model of continuous character evolution along the tree, here we give a direct and elementary explanation for it that provides substantial additional insight. We use this embedding to reinterpret the differences between the NJ and BIONJ tree building algorithms, providing one illustration of how this embedding reflects tree structures in data.
On the stretch factor of convex Delaunay graphs
Prosenjit Bose
2010-06-01
Full Text Available Let C be a compact and convex set in the plane that contains the origin in its interior, and let S be a finite set of points in the plane. The Delaunay graph DGC(S of S is defined to be the dual of the Voronoi diagram of S with respect to the convex distance function defined by C. We prove that DGC(S is a t-spanner for S, for some constant t that depends only on the shape of the set C. Thus, for any two points p and q in S, the graph DGC(S contains a path between p and q whose Euclidean length is at most t times the Euclidean distance between p and q.
The Role of Microcomputer-Based Laboratories in Learning To Make Graphs of Distance and Velocity.
Brasell, Heather
Two questions about the effects of microcomputer-based laboratory (MBL) activities on graphing skills were addressed in this study: (1) the extent to which activities help students link their concrete experiences with motion with graphic representations of these experiences; and (2) the degree of importance of the real-time aspect of the MBL in…
On the spectrum of a class of distance-transitive graphs
Seyed Morteza Mirafzal
2017-04-01
Full Text Available Let $\\Gamma=Cay(\\mathbb{Z}_n, S_k$ be the Cayley graph on the cyclic additive group $\\mathbb{Z}_n$ $(n\\geq 4,$ where $S_1=\\{1, n-1\\}$, \\dots , $S_k=S_ {k-1}\\cup\\{k, n-k\\}$ are the inverse-closed subsets of $\\mathbb{Z}_n-\\{0\\}$ for any $k\\in \\mathbb{N}$, $1\\leq k\\leq [\\frac{n}{2}]-1$. In this paper, we will show that $\\chi(\\Gamma = \\omega(\\Gamma=k+1$ if and only if $k+1|n$. Also, we will show that if $n$ is an even integer and $k=\\frac{n}{2}-1$ then $Aut(\\Gamma\\cong\\mathbb{Z}_2 wr_{I} {Sym}(k+1$ where $I=\\{1, \\dots , k+1\\}$ and in this case, we show that $\\Gamma$ is an integral graph.
Coxeter, HSM
1965-01-01
This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
On the mixing time of geographical threshold graphs
Bradonjic, Milan [Los Alamos National Laboratory
2009-01-01
In this paper, we study the mixing time of 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). We specifically study the mixing times of random walks on 2-dimensional GTGs near the connectivity threshold. We provide a set of criteria on the distribution of vertex weights that guarantees that the mixing time is {Theta}(n log n).
Kulczycki, Stefan
2008-01-01
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff
Hoffman, Kenneth
2007-01-01
Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory.Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Subsequent chapters cover seq
Non-euclidean simplex optimization
Silver, G.L.
1977-01-01
Geometric optimization techniques useful for studying chemical equilibrium traditionally rely upon principles of euclidean geometry, but such algorithms may also be based upon principles of a non-euclidean geometry. The sequential simplex method is adapted to the hyperbolic plane, and application of optimization to problems such as the potentiometric titration of plutonium is suggested
Improvement in quality testing of Braille printer output with Euclidean ...
This paper focuses on quality testing of Braille printed paper using calibrated camera by detecting dots and measuring the Euclidean distances between them with equal gap, vertically and horizontally. For higher accuracy, camera calibration is essential to observe a planar checker board pattern from different distances and ...
Chartrand, Gary; Rosen, Kenneth H
2008-01-01
Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex coloring...
Micrononcasual Euclidean wave functions
Enatsu, H.; Takenaka, A.; Okazaki, M.
1978-01-01
A theory which describes the internal attributes of hadrons in terms of space-time wave functions is presented. In order to develop the theory on the basis of a rather realistic model, covariant wave equations are first derived for the deuteron, in which the co-ordinates of the centre of mass of two nucleons can be defined unambiguously. Then the micro-noncasual behaviour of virtual mesons mediating between the two nucleons is expressed by means of wave functions depending only on the relative Euclidean co-ordinates with respect to the centre of mass of the two nucleons; the wave functions are assumed to obey the 0 4 and SU 2 x SU 2 groups. The properties of the wave functions under space inversion, time reversal and particle-antiparticle conjugation are investigated. It is found that the internal attributes of the mesons, such as spin, isospin, strangeness, intrinsic parity, charge parity and G-parity are explained consistently. The theory is applicable also to the case of baryons
Quantitative graph theory mathematical foundations and applications
Dehmer, Matthias
2014-01-01
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat
Uniform Page Migration Problem in Euclidean Space
Amanj Khorramian
2016-08-01
Full Text Available The page migration problem in Euclidean space is revisited. In this problem, online requests occur at any location to access a single page located at a server. Every request must be served, and the server has the choice to migrate from its current location to a new location in space. Each service costs the Euclidean distance between the server and request. A migration costs the distance between the former and the new server location, multiplied by the page size. We study the problem in the uniform model, in which the page has size D = 1 . All request locations are not known in advance; however, they are sequentially presented in an online fashion. We design a 2.75 -competitive online algorithm that improves the current best upper bound for the problem with the unit page size. We also provide a lower bound of 2.732 for our algorithm. It was already known that 2.5 is a lower bound for this problem.
Large parallel volumes of finite and compact sets in d-dimensional Euclidean space
Kampf, Jürgen; Kiderlen, Markus
The r-parallel volume V (Cr) of a compact subset C in d-dimensional Euclidean space is the volume of the set Cr of all points of Euclidean distance at most r > 0 from C. According to Steiner’s formula, V (Cr) is a polynomial in r when C is convex. For finite sets C satisfying a certain geometric...
C. Dalfo
2015-10-01
Full Text Available We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors.
Bapat, Ravindra B
2014-01-01
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...
Ideas of space. Euclidean, non-Euclidean and relativistic
Gray, J
1979-01-01
An historical and chronological account of mathematics is presented in which familiarity with simple equations and elements of trigonometry is needed but no specialist knowledge is assumed although difficult problems are discussed. By discussion of the difficulties and confusions it is hoped to understand mathematics as a dynamic activity. Beginning with early Greek mathematics, the Eastern legacy and the transition to deductive and geometric thinking the problem of parallels is then encountered and discussed. The second part of the book takes the story from Wallis, Saccheri and Lambert through to its resolution by Gauss, Lobachevskii, Bolyai, Riemann and Bettrami. The background of the 19th century theory of surfaces is given. The third part gives an account of Einstein's theories based on what has gone before, moving from a Newtonian-Euclidean picture to an Einsteinian-nonEuclidean one. A brief account of gravitation, the nature of space and black holes concludes the book.
Asymptotic analysis of fundamental solutions of Dirac operators on even dimensional Euclidean spaces
Arai, A.
1985-01-01
We analyze the short distance asymptotic behavior of some quantities formed out of fundamental solutions of Dirac operators on even dimensional Euclidean spaces with finite dimensional matrix-valued potentials. (orig.)
Euclidean geometry and its subgeometries
Specht, Edward John; Calkins, Keith G; Rhoads, Donald H
2015-01-01
In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...
Trudeau, Richard J
1986-01-01
How unique and definitive is Euclidean geometry in describing the "real" space in which we live? Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world. Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world. A portion of the book won the Pólya Prize, a distinguished award from the Mathematical Association of America. "Trudeau meets the challenge of reaching a broad audience in clever ways...(The book) is a good addition to our literature o...
Variational submanifolds of Euclidean spaces
Krupka, D.; Urban, Z.; Volná, J.
2018-03-01
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given non-variational system, conditions assuring variationality (the Helmholtz conditions) of the induced system with respect to a submanifold of a Euclidean space are studied, and the problem of existence of these "variational submanifolds" is formulated in general and solved for second-order systems. The variational sequence theory on sheaves of differential forms is employed as a main tool for the analysis of local and global aspects (variationality and variational triviality). The theory is illustrated by examples of holonomic constraints (submanifolds of a configuration Euclidean space) which are variational submanifolds in geometry and mechanics.
Random walks in Euclidean space
Varjú, Péter Pál
2012-01-01
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove a local limit theorem under a suitable moment condition and a necessary non-degeneracy condition. Under stronger hypothesis, we prove a limit theorem on a wide range of scales: between e^(-cl^(1/4)) and l^(1/2), where l is the number of steps.
Noncommutative products of Euclidean spaces
Dubois-Violette, Michel; Landi, Giovanni
2018-05-01
We present natural families of coordinate algebras on noncommutative products of Euclidean spaces R^{N_1} × _R R^{N_2} . These coordinate algebras are quadratic ones associated with an R -matrix which is involutive and satisfies the Yang-Baxter equations. As a consequence, they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have eight-dimensional noncommutative euclidean spaces R4 × _R R4 . Among these, particularly well behaved ones have deformation parameter u \\in S^2 . Quotients include seven spheres S7_u as well as noncommutative quaternionic tori TH_u = S^3 × _u S^3 . There is invariance for an action of {{SU}}(2) × {{SU}}(2) on the torus TH_u in parallel with the action of U(1) × U(1) on a `complex' noncommutative torus T^2_θ which allows one to construct quaternionic toric noncommutative manifolds. Additional classes of solutions are disjoint from the classical case.
Amine Labriji
2017-07-01
Full Text Available The topic of identifying the similarity of graphs was considered as highly recommended research field in the Web semantic, artificial intelligence, the shape recognition and information research. One of the fundamental problems of graph databases is finding similar graphs to a graph query. Existing approaches dealing with this problem are usually based on the nodes and arcs of the two graphs, regardless of parental semantic links. For instance, a common connection is not identified as being part of the similarity of two graphs in cases like two graphs without common concepts, the measure of similarity based on the union of two graphs, or the one based on the notion of maximum common sub-graph (SCM, or the distance of edition of graphs. This leads to an inadequate situation in the context of information research. To overcome this problem, we suggest a new measure of similarity between graphs, based on the similarity measure of Wu and Palmer. We have shown that this new measure satisfies the properties of a measure of similarities and we applied this new measure on examples. The results show that our measure provides a run time with a gain of time compared to existing approaches. In addition, we compared the relevance of the similarity values obtained, it appears that this new graphs measure is advantageous and offers a contribution to solving the problem mentioned above.
On an edge partition and root graphs of some classes of line graphs
K Pravas
2017-04-01
Full Text Available The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line graph of a graph $G$ into the edge sets of the Gallai and anti-Gallai graphs of $G$. Based on this, an optimal algorithm to find the root graph of a line graph is obtained. Moreover, root graphs of diameter-maximal, distance-hereditary, Ptolemaic and chordal graphs are also discussed.
Clustering by Partitioning around Medoids using Distance-Based ...
OLUWASOGO
outperforms both the Euclidean and Manhattan distance metrics in certain situations. KEYWORDS: PAM ... version of a dataset, compare the quality of clusters obtained from the Euclidean .... B. Theoretical Framework and Methodology.
Endriss, U.; Grandi, U.
Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference
Euclidean supersymmetry, twisting and topological sigma models
Hull, C.M.; Lindstroem, U.; Santos, L. Melo dos; Zabzine, M.; Unge, R. von
2008-01-01
We discuss two dimensional N-extended supersymmetry in Euclidean signature and its R-symmetry. For N = 2, the R-symmetry is SO(2) x SO(1, 1), so that only an A-twist is possible. To formulate a B-twist, or to construct Euclidean N = 2 models with H-flux so that the target geometry is generalised Kahler, it is necessary to work with a complexification of the sigma models. These issues are related to the obstructions to the existence of non-trivial twisted chiral superfields in Euclidean superspace.
Local algebras in Euclidean quantum field theory
Guerra, Francesco.
1975-06-01
The general structure of the local observable algebras of Euclidean quantum field theory is described, considering the very simple examples of the free scalar field, the vector meson field, and the electromagnetic field. The role of Markov properties, and the relations between Euclidean theory and Hamiltonian theory in Minkowski space-time are especially emphasized. No conflict appears between covariance (in the Euclidean sense) and locality (in the Markov sense) on one hand and positive definiteness of the metric on the other hand [fr
The elements of non-Euclidean geometry
Sommerville, D MY
2012-01-01
Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.
Axioms for Euclidean Green's functions. Pt. 2
Osterwalder, K.; Schrader, R.
1975-01-01
We give new (necessary and) sufficient conditions for Euclidean Green's functions to have analytic continuations to a relativistic field theory. These results extend and correct a previous paper. (orig.) [de
Constructive curves in non-Euclidean planes
Horváth, Ákos G.
2016-01-01
In this paper we overview the theory of conics and roulettes in four non-Euclidean planes. We collect the literature about these classical concepts, from the eighteenth century to the present, including papers available only on arXiv. The comparison of the four non-Euclidean planes, in terms of the known results on conics and roulettes, reflects only the very subjective view of the author.
Classical geometry Euclidean, transformational, inversive, and projective
Leonard, I E; Liu, A C F; Tokarsky, G W
2014-01-01
Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which p
Zhang, L.-C.; Patone, M.
2017-01-01
We synthesise the existing theory of graph sampling. We propose a formal definition of sampling in finite graphs, and provide a classification of potential graph parameters. We develop a general approach of Horvitz–Thompson estimation to T-stage snowball sampling, and present various reformulations of some common network sampling methods in the literature in terms of the outlined graph sampling theory.
Chordal Graphs and Semidefinite Optimization
Vandenberghe, Lieven; Andersen, Martin Skovgaard
2015-01-01
of a sparse positive definite matrix, positive semidefinite and Euclidean distance matrix completion problems, and the evaluation of gradients and Hessians of logarithmic barriers for cones of sparse positive semidefinite matrices and their dual cones. The purpose of the survey is to show how these techniques...
Reduction of product platform complexity by vectorial Euclidean algorithm
Navarrete, Israel Aguilera; Guzman, Alejandro A. Lozano
2013-01-01
In traditional machine, equipment and devices design, technical solutions are practically independent, thus increasing designs cost and complexity. Overcoming this situation has been tackled just using designer's experience. In this work, a product platform complexity reduction is presented based on a matrix representation of technical solutions versus product properties. This matrix represents the product platform. From this matrix, the Euclidean distances among technical solutions are obtained. Thus, the vectorial distances among technical solutions are identified in a new matrix of order of the number of technical solutions identified. This new matrix can be reorganized in groups with a hierarchical structure, in such a way that modular design of products is now more tractable. As a result of this procedure, the minimum vector distances are found thus being possible to identify the best technical solutions for the design problem raised. Application of these concepts is shown with two examples.
Using Graph and Vertex Entropy to Compare Empirical Graphs with Theoretical Graph Models
Tomasz Kajdanowicz
2016-09-01
Full Text Available Over the years, several theoretical graph generation models have been proposed. Among the most prominent are: the Erdős–Renyi random graph model, Watts–Strogatz small world model, Albert–Barabási preferential attachment model, Price citation model, and many more. Often, researchers working with real-world data are interested in understanding the generative phenomena underlying their empirical graphs. They want to know which of the theoretical graph generation models would most probably generate a particular empirical graph. In other words, they expect some similarity assessment between the empirical graph and graphs artificially created from theoretical graph generation models. Usually, in order to assess the similarity of two graphs, centrality measure distributions are compared. For a theoretical graph model this means comparing the empirical graph to a single realization of a theoretical graph model, where the realization is generated from the given model using an arbitrary set of parameters. The similarity between centrality measure distributions can be measured using standard statistical tests, e.g., the Kolmogorov–Smirnov test of distances between cumulative distributions. However, this approach is both error-prone and leads to incorrect conclusions, as we show in our experiments. Therefore, we propose a new method for graph comparison and type classification by comparing the entropies of centrality measure distributions (degree centrality, betweenness centrality, closeness centrality. We demonstrate that our approach can help assign the empirical graph to the most similar theoretical model using a simple unsupervised learning method.
Assessment of the Log-Euclidean Metric Performance in Diffusion Tensor Image Segmentation
Mostafa Charmi
2010-06-01
Full Text Available Introduction: Appropriate definition of the distance measure between diffusion tensors has a deep impact on Diffusion Tensor Image (DTI segmentation results. The geodesic metric is the best distance measure since it yields high-quality segmentation results. However, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. The main goal of this paper is to assess the possible substitution of the geodesic metric with the Log-Euclidean one to reduce the computational cost of a statistical surface evolution algorithm. Materials and Methods: We incorporated the Log-Euclidean metric in the statistical surface evolution algorithm framework. To achieve this goal, the statistics and gradients of diffusion tensor images were defined using the Log-Euclidean metric. Numerical implementation of the segmentation algorithm was performed in the MATLAB software using the finite difference techniques. Results: In the statistical surface evolution framework, the Log-Euclidean metric was able to discriminate the torus and helix patterns in synthesis datasets and rat spinal cords in biological phantom datasets from the background better than the Euclidean and J-divergence metrics. In addition, similar results were obtained with the geodesic metric. However, the main advantage of the Log-Euclidean metric over the geodesic metric was the dramatic reduction of computational cost of the segmentation algorithm, at least by 70 times. Discussion and Conclusion: The qualitative and quantitative results have shown that the Log-Euclidean metric is a good substitute for the geodesic metric when using a statistical surface evolution algorithm in DTIs segmentation.
Brouwer, A.E.; Haemers, W.H.; Brouwer, A.E.; Haemers, W.H.
2012-01-01
This chapter presents some simple results on graph spectra.We assume the reader is familiar with elementary linear algebra and graph theory. Throughout, J will denote the all-1 matrix, and 1 is the all-1 vector.
Fuzzy Euclidean wormholes in de Sitter space
Chen, Pisin; Hu, Yao-Chieh; Yeom, Dong-han, E-mail: pisinchen@phys.ntu.edu.tw, E-mail: r04244003@ntu.edu.tw, E-mail: innocent.yeom@gmail.com [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)
2017-07-01
We investigate Euclidean wormholes in Einstein gravity with a massless scalar field in de Sitter space. Euclidean wormholes are possible due to the analytic continuation of the time as well as complexification of fields, where we need to impose the classicality after the Wick-rotation to the Lorentzian signatures. For some parameters, wormholes are preferred than Hawking-Moss instantons, and hence wormholes can be more fundamental than Hawking-Moss type instantons. Euclidean wormholes can be interpreted in three ways: (1) classical big bounce, (2) either tunneling from a small to a large universe or a creation of a collapsing and an expanding universe from nothing, and (3) either a transition from a contracting to a bouncing phase or a creation of two expanding universes from nothing. These various interpretations shed some light on challenges of singularities. In addition, these will help to understand tensions between various kinds of quantum gravity theories.
Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
Joseph Matthieu
2017-11-01
Full Text Available We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance d such that the product of snowflaked Euclidean lines looks down on (RN , d, but not vice versa.
Lorentz violations and Euclidean signature metrics
Barbero G, J. Fernando; Villasenor, Eduardo J.S.
2003-01-01
We show that the families of effective actions considered by Jacobson et al. to study Lorentz invariance violations contain a class of models that represent pure general relativity with a Euclidean signature. We also point out that some members of this family of actions preserve Lorentz invariance in a generalized sense
Majorization in Euclidean Geometry and Beyond
Fiedler, Miroslav
2015-01-01
Roč. 466, 1 February (2015), s. 233-240 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : Majorization * Doubly stochastic matrix * Euclidean simplex * Star * Regular simplex * Volume of a simplex Subject RIV: BA - General Mathematics Impact factor: 0.965, year: 2015
Saveliev, M.V.
1983-01-01
In the framework of the algebraic approach a construction of exactly integrable two-dimensional Riemannian manifolds embedded into enveloping Euclidean (pseudo-Euclidean) space Rsub(N) of an arbitrary dimension is presented. The construction is based on a reformulation of the Gauss, Peterson-Codazzi and Ricci equations in the form of a Lax-type representation in two-dimensional space. Here the Lax pair operators take the values in algebra SO(N)
Texture classification using non-Euclidean Minkowski dilation
Florindo, Joao B.; Bruno, Odemir M.
2018-03-01
This study presents a new method to extract meaningful descriptors of gray-scale texture images using Minkowski morphological dilation based on the Lp metric. The proposed approach is motivated by the success previously achieved by Bouligand-Minkowski fractal descriptors on texture classification. In essence, such descriptors are directly derived from the morphological dilation of a three-dimensional representation of the gray-level pixels using the classical Euclidean metric. In this way, we generalize the dilation for different values of p in the Lp metric (Euclidean is a particular case when p = 2) and obtain the descriptors from the cumulated distribution of the distance transform computed over the texture image. The proposed method is compared to other state-of-the-art approaches (such as local binary patterns and textons for example) in the classification of two benchmark data sets (UIUC and Outex). The proposed descriptors outperformed all the other approaches in terms of rate of images correctly classified. The interesting results suggest the potential of these descriptors in this type of task, with a wide range of possible applications to real-world problems.
Modelling non-Euclidean movement and landscape connectivity in highly structured ecological networks
Sutherland, Christopher; Fuller, Angela K.; Royle, J. Andrew
2015-01-01
Movement is influenced by landscape structure, configuration and geometry, but measuring distance as perceived by animals poses technical and logistical challenges. Instead, movement is typically measured using Euclidean distance, irrespective of location or landscape structure, or is based on arbitrary cost surfaces. A recently proposed extension of spatial capture-recapture (SCR) models resolves this issue using spatial encounter histories of individuals to calculate least-cost paths (ecological distance: Ecology, 94, 2013, 287) thereby relaxing the Euclidean assumption. We evaluate the consequences of not accounting for movement heterogeneity when estimating abundance in highly structured landscapes, and demonstrate the value of this approach for estimating biologically realistic space-use patterns and landscape connectivity.
Overlapping communities detection based on spectral analysis of line graphs
Gui, Chun; Zhang, Ruisheng; Hu, Rongjing; Huang, Guoming; Wei, Jiaxuan
2018-05-01
Community in networks are often overlapping where one vertex belongs to several clusters. Meanwhile, many networks show hierarchical structure such that community is recursively grouped into hierarchical organization. In order to obtain overlapping communities from a global hierarchy of vertices, a new algorithm (named SAoLG) is proposed to build the hierarchical organization along with detecting the overlap of community structure. SAoLG applies the spectral analysis into line graphs to unify the overlap and hierarchical structure of the communities. In order to avoid the limitation of absolute distance such as Euclidean distance, SAoLG employs Angular distance to compute the similarity between vertices. Furthermore, we make a micro-improvement partition density to evaluate the quality of community structure and use it to obtain the more reasonable and sensible community numbers. The proposed SAoLG algorithm achieves a balance between overlap and hierarchy by applying spectral analysis to edge community detection. The experimental results on one standard network and six real-world networks show that the SAoLG algorithm achieves higher modularity and reasonable community number values than those generated by Ahn's algorithm, the classical CPM and GN ones.
Euclidean wormholes with minimally coupled scalar fields
Ruz, Soumendranath; Modak, Bijan; Debnath, Subhra; Sanyal, Abhik Kumar
2013-01-01
A detailed study of quantum and semiclassical Euclidean wormholes for Einstein's theory with a minimally coupled scalar field has been performed for a class of potentials. Massless, constant, massive (quadratic in the scalar field) and inverse (linear) potentials admit the Hawking and Page wormhole boundary condition both in the classically forbidden and allowed regions. An inverse quartic potential has been found to exhibit a semiclassical wormhole configuration. Classical wormholes under a suitable back-reaction leading to a finite radius of the throat, where the strong energy condition is satisfied, have been found for the zero, constant, quadratic and exponential potentials. Treating such classical Euclidean wormholes as an initial condition, a late stage of cosmological evolution has been found to remain unaltered from standard Friedmann cosmology, except for the constant potential which under the back-reaction produces a term like a negative cosmological constant. (paper)
Calculus and analysis in Euclidean space
Shurman, Jerry
2016-01-01
The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skil...
Euclidean fields: vector mesons and photons
Loffelholz, J.
1979-01-01
Free transverse vector fields of mass >= 0 are studied. The model is related to the usual free vector meson and electromagnetic quantum field theories by extension of the field operators from transverse to arbitrary test functions. The one-particle states in transverse gauge and their localization are described. Reflexion positivity is proved and derived are free Feynman-Kac-Nelson formulas. An Euclidean approach to a photon field in a spherical world using dilatation covariance and inversions is given
Vestergaard, Preben Dahl; Hartnell, Bert L.
2006-01-01
There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done, the gr...
Sphere and dot product representations of graphs
R.J. Kang (Ross); T. Müller (Tobias)
2012-01-01
textabstractA graph $G$ is a $k$-sphere graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such that $ij\\in E(G)$ if and only if the distance between $v_i$ and $v_j$ is at most $1$. A graph $G$ is a $k$-dot product graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such
Multivariate Welch t-test on distances
Alekseyenko, Alexander V.
2016-01-01
Motivation: Permutational non-Euclidean analysis of variance, PERMANOVA, is routinely used in exploratory analysis of multivariate datasets to draw conclusions about the significance of patterns visualized through dimension reduction. This method recognizes that pairwise distance matrix between observations is sufficient to compute within and between group sums of squares necessary to form the (pseudo) F statistic. Moreover, not only Euclidean, but arbitrary distances can be used. This method...
Hubble expansion in a Euclidean framework
Alfven, H.
1979-01-01
There now seems to be strong evidence for a non-cosmological interpretation of the QSO redshift - in any case, so strong that it is of interest to investigate the consequences. The purpose of this paper is to construct a model of the Hubble expansion which is as far as possible from the conventional Big Bang model without coming in conflict with any well-established observational results (while introducing no new laws of physics). This leads to an essentially Euclidean metagalactic model (see Table I) with very little mass outside one-third or half of the Hubble radius. The total kinetic energy of the Hubble expansion need only to be about 5% of the rest mass energy. Present observations support backwards in time extrapolation of the Hubble expansion to a 'minimum size galaxy' Rsub(m), which may have any value in 0 26 cm. Other arguments speak in favor of a size close to the upper value, say Rsub(m) = 10 26 cm (Table II). As this size is probably about 100 times the Schwarzschild limit, an essentially Euclidean description is allowed. The kinetic energy of the Hubble expansion may derive from an intense QSO-like activity in the minimum size metagalaxy, with an energy release corresponding to the annihilation of a few solar masses per galaxy per year. Some of the conclusions based on the Big Bang hypothesis are criticized and in several cases alternative interpretations are suggested. A comparison between the Euclidean and the conventional models is given in Table III. (orig.)
Exploring Concepts of Geometry not Euclidean
Luiz Ambrozi
2016-02-01
Full Text Available With this article we intend to propose different situations of teaching and learning, how they can be applied in schools, mediated by the use of concrete materials and Geogebra software, emphasizing the use of technology in the classroom, that this proposal has the role of assisting in the conceptualization and identification of elements of non-Euclidean geometry. In addition, this short course is designed to be a time of current and continuing education for teachers, with activities to be developed with dynamic geometry and based on the theory of Conceptual Fields of Vergnaud.
Bochner-Riesz means on Euclidean spaces
Lu, Shanzhen
2013-01-01
This book mainly deals with the Bochner-Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner-Riesz means and important achievements attained in the last 50 years. For the Bochner-Riesz means of multiple Fourier integral, it includes the Fefferman theorem which negates the Disc multiplier conjecture, the famous Carleson-Sjölin theorem, and Carbery-Rubio de Francia-Vega's work on almost everywhere convergence of the Bochner-Riesz means below the critical index. For the Bochner-Riesz means o
Euclidean approach to the inflationary universe
Hawking, S.W.
1983-01-01
The aim of this article is to show how the Euclidean approach can be used to study the inflationary universe. Although this formulation may appear counterintuitive in some respects, it has the advantage that it defines a definite quantum state and provides a framework for calculating quantities of interest such as correlation functions or tunnelling probabilities. By contrast, in the more usual approach in real Lorentzian spacetime, it is not so clear what the quantum state should be or how to evaluate such quantities. (author)
Introduction to non-Euclidean geometry
Wolfe, Harold E
2012-01-01
One of the first college-level texts for elementary courses in non-Euclidean geometry, this concise, readable volume is geared toward students familiar with calculus. A full treatment of the historical background explores the centuries-long efforts to prove Euclid's parallel postulate and their triumphant conclusion. Numerous original exercises form an integral part of the book.Topics include hyperbolic plane geometry and hyperbolic plane trigonometry, applications of calculus to the solutions of some problems in hyperbolic geometry, elliptic plane geometry and trigonometry, and the consistenc
Broadband invisibility by non-Euclidean cloaking.
Leonhardt, Ulf; Tyc, Tomás
2009-01-02
Invisibility and negative refraction are both applications of transformation optics where the material of a device performs a coordinate transformation for electromagnetic fields. The device creates the illusion that light propagates through empty flat space, whereas in physical space, light is bent around a hidden interior or seems to run backward in space or time. All of the previous proposals for invisibility require materials with extreme properties. Here we show that transformation optics of a curved, non-Euclidean space (such as the surface of a virtual sphere) relax these requirements and can lead to invisibility in a broad band of the spectrum.
Non-Euclidean Geometry and Gravitation
Stavroulakis N.
2006-04-01
Full Text Available A great deal of misunderstandings and mathematical errors are involved in the currently accepted theory of the gravitational field generated by an isotropic spherical mass. The purpose of the present paper is to provide a short account of the rigorous mathematical theory and exhibit a new formulation of the problem. The solution of the corresponding equations of gravitation points out several new and unusual features of the stationary gravitational field which are related to the non-Euclidean structure of the space. Moreover it precludes the black hole from being a mathematical and physical notion.
Deza, Michel Marie
2016-01-01
This 4th edition of the leading reference volume on distance metrics is characterized by updated and rewritten sections on some items suggested by experts and readers, as well a general streamlining of content and the addition of essential new topics. Though the structure remains unchanged, the new edition also explores recent advances in the use of distances and metrics for e.g. generalized distances, probability theory, graph theory, coding theory, data analysis. New topics in the purely mathematical sections include e.g. the Vitanyi multiset-metric, algebraic point-conic distance, triangular ratio metric, Rossi-Hamming metric, Taneja distance, spectral semimetric between graphs, channel metrization, and Maryland bridge distance. The multidisciplinary sections have also been supplemented with new topics, including: dynamic time wrapping distance, memory distance, allometry, atmospheric depth, elliptic orbit distance, VLBI distance measurements, the astronomical system of units, and walkability distance. Lea...
Statistical mechanics, gravity, and Euclidean theory
Fursaev, Dmitri V.
2002-01-01
A review of computations of free energy for Gibbs states on stationary but not static gravitational and gauge backgrounds is given. On these backgrounds wave equations for free fields are reduced to eigenvalue problems which depend non-linearly on the spectral parameter. We present a method to deal with such problems. In particular, we demonstrate how some results of the spectral theory of second-order elliptic operators, such as heat kernel asymptotics, can be extended to a class of non-linear spectral problems. The method is used to trace down the relation between the canonical definition of the free energy based on summation over the modes and the covariant definition given in Euclidean quantum gravity. As an application, high-temperature asymptotics of the free energy and of the thermal part of the stress-energy tensor in the presence of rotation are derived. We also discuss statistical mechanics in the presence of Killing horizons where canonical and Euclidean theories are related in a non-trivial way
On the scaling limits in the Euclidean (quantum) field theory
Gielerak, R.
1983-01-01
The author studies the concept of scaling limits in the context of the constructive field theory. He finds that the domain of attraction of a free massless Euclidean scalar field in the two-dimensional space time contains almost all Euclidean self-interacting models of quantum fields so far constructed. The renormalized scaling limit of the Wick polynomials of several self-interacting Euclidean field theory models are shown to be the same as in the free field theory. (Auth.)
Graph reconstruction with a betweenness oracle
Abrahamsen, Mikkel; Bodwin, Greg; Rotenberg, Eva
2016-01-01
Graph reconstruction algorithms seek to learn a hidden graph by repeatedly querying a blackbox oracle for information about the graph structure. Perhaps the most well studied and applied version of the problem uses a distance oracle, which can report the shortest path distance between any pair...... of nodes. We introduce and study the betweenness oracle, where bet(a, m, z) is true iff m lies on a shortest path between a and z. This oracle is strictly weaker than a distance oracle, in the sense that a betweenness query can be simulated by a constant number of distance queries, but not vice versa...
Founding Gravitation in 4D Euclidean Space-Time Geometry
Winkler, Franz-Guenter
2010-01-01
The Euclidean interpretation of special relativity which has been suggested by the author is a formulation of special relativity in ordinary 4D Euclidean space-time geometry. The natural and geometrically intuitive generalization of this view involves variations of the speed of light (depending on location and direction) and a Euclidean principle of general covariance. In this article, a gravitation model by Jan Broekaert, which implements a view of relativity theory in the spirit of Lorentz and Poincare, is reconstructed and shown to fulfill the principles of the Euclidean approach after an appropriate reinterpretation.
Ait-Haddou, Rachid
2015-01-01
We show that the best degree reduction of a given polynomial P from degree n to m with respect to the discrete (Formula presented.)-norm is equivalent to the best Euclidean distance of the vector of h-Bézier coefficients of P from the vector
Seiller, Thomas
2016-01-01
Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should...... be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define...... "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite...
Euclidean supergravity and multi-centered solutions
W.A. Sabra
2017-04-01
Full Text Available In ungauged supergravity theories, the no-force condition for BPS states implies the existence of stable static multi-centered solutions. The first solutions to Einstein–Maxwell theory with a positive cosmological constant describing an arbitrary number of charged black holes were found by Kastor and Traschen. Generalisations to five and higher dimensional theories were obtained by London. Multi-centered solutions in gauged supergravity, even with time-dependence allowed, have yet to be constructed. In this letter we construct supersymmetry-preserving multi-centered solutions for the case of D=5, N=2 Euclidean gauged supergravity coupled to an arbitrary number of vector multiplets. Higher dimensional Einstein–Maxwell multi-centered solutions are also presented.
Euclidean Monte Carlo simulation of nuclear interactions
Montvay, Istvan; Bonn Univ.; Urbach, Carsten
2011-05-01
We present an exploratory study of chiral effective theories of nuclei with methods adopted from lattice quantum chromodynamics (QCD). We show that the simulations in the Euclidean path integral approach are feasible and that we can determine the energy of the two nucleon state. By varying the parameters and the simulated volumes phase shifts can be determined in principle and hopefully tuned to their physical values in the future. The physical cut-off of the theory is realised by blocking of the lattice fields. By keeping this physical cut-off fixed in physical units the lattice cut-off can be changed and in this way the lattice artefacts can be eliminated. (orig.)
莫建文; 王朝选; 首照宇; 张彤; 陈利霞
2013-01-01
针对Graph-Based方法容易出现欠合并现象的不足,结合L*a*b*颜色空间,提出一种改进的Graph-Based图像分割方法.该方法首先将图像由RGB空间转换到L*a*b*颜色空间,接着将每个像素作为节点构造带权无向图,相邻节点之间的欧氏距离作为图的权值,表征相邻像素间的颜色差异；同时,引入一个常数s用于控制颜色差异程度.实验证明,该方法效率高,分割效果良好.%In view of the deficiency of Graph-Based method that it is easy to appear the less merging, in combination with L * a * b * colour space, we propose an improved Graph-Based image segmentation algorithm. First, the method converts the image from RGB colour space to L * a * b * colour space. Then, it takes every pixel as the node to construct the weighted undirected graph, to be the weight of the graph, the Euclidean distance between adjacent nodes is used to represent the colour difference between adjacent pixels; At the same time, a constant S is introduced for the control of the colour difference degree. Experiments show that the method has high efficiency and very good segmentation results.
The relation between Euclidean and Lorentzian 2D quantum gravity
Ambjørn, J.; Correia, J.; Kristjansen, C.; Loll, R.
1999-01-01
Starting from 2D Euclidean quantum gravity, we show that one recovers 2D Lorentzian quantum gravity by removing all baby universes. Using a peeling procedure to decompose the discrete, triangulated geometries along a one-dimensional path, we explicitly associate with each Euclidean space-time a
Euclidean null controllability of perturbed infinite delay systems with ...
Euclidean null controllability of perturbed infinite delay systems with limited control. ... Open Access DOWNLOAD FULL TEXT ... The results are established by placing conditions on the perturbation function which guarantee that, if the linear control base system is completely Euclidean controllable, then the perturbed system ...
Euclidean null controllability of nonlinear infinite delay systems with ...
Sufficient conditions for the Euclidean null controllability of non-linear delay systems with time varying multiple delays in the control and implicit derivative are derived. If the uncontrolled system is uniformly asymptotically stable and if the control system is controllable, then the non-linear infinite delay system is Euclidean null ...
Euclidean null controllability of linear systems with delays in state ...
Sufficient conditions are developed for the Euclidean controllability of linear systems with delay in state and in control. Namely, if the uncontrolled system is uniformly asymptotically stable and the control equation proper, then the control system is Euclidean null controllable. Journal of the Nigerian Association of ...
Diestel, Reinhard
2017-01-01
This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...
Extended supersymmetry in four-dimensional Euclidean space
McKeon, D.G.C.; Sherry, T.N.
2000-01-01
Since the generators of the two SU(2) groups which comprise SO(4) are not Hermitian conjugates of each other, the simplest supersymmetry algebra in four-dimensional Euclidean space more closely resembles the N=2 than the N=1 supersymmetry algebra in four-dimensional Minkowski space. An extended supersymmetry algebra in four-dimensional Euclidean space is considered in this paper; its structure resembles that of N=4 supersymmetry in four-dimensional Minkowski space. The relationship of this algebra to the algebra found by dimensionally reducing the N=1 supersymmetry algebra in ten-dimensional Euclidean space to four-dimensional Euclidean space is examined. The dimensional reduction of N=1 super Yang-Mills theory in ten-dimensional Minkowski space to four-dimensional Euclidean space is also considered
Walwyn, Amy L.; Navarro, Daniel J.
2010-01-01
An experiment is reported comparing human performance on two kinds of visually presented traveling salesperson problems (TSPs), those reliant on Euclidean geometry and those reliant on city block geometry. Across multiple array sizes, human performance was near-optimal in both geometries, but was slightly better in the Euclidean format. Even so,…
Gould, Ronald
2012-01-01
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S
Rao, R Venkata
2013-01-01
Decision Making in Manufacturing Environment Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods presents the concepts and details of applications of MADM methods. A range of methods are covered including Analytic Hierarchy Process (AHP), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VIšekriterijumsko KOmpromisno Rangiranje (VIKOR), Data Envelopment Analysis (DEA), Preference Ranking METHod for Enrichment Evaluations (PROMETHEE), ELimination Et Choix Traduisant la Realité (ELECTRE), COmplex PRoportional ASsessment (COPRAS), Grey Relational Analysis (GRA), UTility Additive (UTA), and Ordered Weighted Averaging (OWA). The existing MADM methods are improved upon and three novel multiple attribute decision making methods for solving the decision making problems of the manufacturing environment are proposed. The concept of integrated weights is introduced in the proposed subjective and objective integrated weights (SOIW) method and the weighted Euclidean distance ba...
Chartrand, Gary; Zhang, Ping
2010-01-01
Gary Chartrand has influenced the world of Graph Theory for almost half a century. He has supervised more than a score of Ph.D. dissertations and written several books on the subject. The most widely known of these texts, Graphs and Digraphs, … has much to recommend it, with clear exposition, and numerous challenging examples [that] make it an ideal textbook for the advanced undergraduate or beginning graduate course. The authors have updated their notation to reflect the current practice in this still-growing area of study. By the authors' estimation, the 5th edition is approximately 50% longer than the 4th edition. … the legendary Frank Harary, author of the second graph theory text ever produced, is one of the figures profiled. His book was the standard in the discipline for several decades. Chartrand, Lesniak and Zhang have produced a worthy successor.-John T. Saccoman, MAA Reviews, June 2012 (This book is in the MAA's basic library list.)As with the earlier editions, the current text emphasizes clear...
Spinors in euclidean field theory, complex structures and discrete symmetries
Wetterich, C.
2011-01-01
We discuss fermions for arbitrary dimensions and signature of the metric, with special emphasis on euclidean space. Generalized Majorana spinors are defined for d=2,3,4,8,9mod8, independently of the signature. These objects permit a consistent analytic continuation of Majorana spinors in Minkowski space to euclidean signature. Compatibility of charge conjugation with complex conjugation requires for euclidean signature a new complex structure which involves a reflection in euclidean time. The possible complex structures for Minkowski and euclidean signature can be understood in terms of a modulo two periodicity in the signature. The concepts of a real action and hermitean observables depend on the choice of the complex structure. For a real action the expectation values of all hermitean multi-fermion observables are real. This holds for arbitrary signature, including euclidean space. In particular, a chemical potential is compatible with a real action for the euclidean theory. We also discuss the discrete symmetries of parity, time reversal and charge conjugation for arbitrary dimension and signature.
Some remarks on definability of process graphs
Grabmayer, C.A.; Klop, J.W.; Luttik, B.; Baier, C.; Hermanns, H.
2006-01-01
We propose the notions of "density" and "connectivity" of infinite process graphs and investigate them in the context of the wellknown process algebras BPA and BPP. For a process graph G, the density function in a state s maps a natural number n to the number of states of G with distance less or
Quaternion analyticity and conformally Kaehlerian structure in Euclidean gravity
Guersey, F.; Chia-Hsiung Tze
1984-01-01
Starting from the fact that the d = 4 Euclidean flat spacetime is conformally related to the Kaehler manifold H 2 xS 2 , we show the Euclidean Schwarzschild metric to be conformally related to another Kaehler manifold M 2 xS 2 with M 2 being conformal to H 2 in two dimensions. Both metrics which are conformally Kaehlerian, are form-invariant under the infinite parameter Fueter group, the Euclidean counterpart of Milne's group of clock regraduation. The associated Einstein's equations translate into Fueter's quaternionic analyticity. The latter leads to an infinite number of local continuity equations. (orig.)
New solutions of euclidean SU(2) gauge theory
Khan, I.
1983-08-01
New solutions of the Euclidean SU(2) gauge theory having finite field strength everywhere are presented. The solutions are self dual or antidual and constitute a two-parameter family which includes the instantons. (author)
On the invariant theory of Weingarten surfaces in Euclidean space
Ganchev, Georgi; Mihova, Vesselka
2010-01-01
On any Weingarten surface in Euclidean space (strongly regular or rotational), we introduce locally geometric principal parameters and prove that such a surface is determined uniquely up to a motion by a special invariant function, which satisfies a natural nonlinear partial differential equation. This result can be interpreted as a solution to the Lund-Regge reduction problem for Weingarten surfaces in Euclidean space. We apply this theory to fractional-linear Weingarten surfaces and obtain the nonlinear partial differential equations describing them.
Non-Euclidean geometry and curvature two-dimensional spaces, volume 3
Cannon, James W
2017-01-01
This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. Einstein showed how to interpret gravity as the dynamic response to the curvature of space-time. Bill Thurston showed us that non-Euclidean geometries and curvature are essential to the understanding of low-dimensional spaces. This third and final volume aims to give the reader a firm intuitive understanding of these concepts in dimension 2. The volume first demonstrates a number of the most important properties of non-Euclidean geometry by means of simple infinite graphs that approximate that geometry. This is followed by a long chapter taken from lectures the author gave at MSRI, wh...
Two-stage sparse coding of region covariance via Log-Euclidean kernels to detect saliency.
Zhang, Ying-Ying; Yang, Cai; Zhang, Ping
2017-05-01
In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods-highlight-inhibition function, context-based saliency weighting, and the graph cut-are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.
Xu, Kexiang; Trinajstić, Nenad
2015-01-01
This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921—2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number o...
The Partial Mapping of the Web Graph
Kristina Machova
2009-06-01
Full Text Available The paper presents an approach to partial mapping of a web sub-graph. This sub-graph contains the nearest surroundings of an actual web page. Our work deals with acquiring relevant Hyperlinks of a base web site, generation of adjacency matrix, the nearest distance matrix and matrix of converted distances of Hyperlinks, detection of compactness of web representation, and visualization of its graphical representation. The paper introduces an LWP algorithm – a technique for Hyperlink filtration. This work attempts to help users with the orientation within the web graph.
Catoni, Francesco; Cannata, Roberto; Zampetti, Paolo
2005-08-01
The Riemann and Lorentz constant curvature surfaces are investigated from an Euclidean point of view. The four surfaces (constant positive and constant negative curvatures with definite and non-definite fine elements) are represented as surfaces in a Riemannian or in a particular semi-Riemannian flat space and it is shown that the complex and the hyperbolic numbers allow to obtain the same equations for the corresponding Riemann and Lorentz surfaces, respectively. Moreover it is shown that the geodesics on the Lorentz surfaces states, from a physical point of view, a link between curvature and fields. This result is obtained just as a consequence of the space-time geometrical symmetry, without invoking the famous Einstein general relativity postulate [it
Flexible intuitions of Euclidean geometry in an Amazonian indigene group
Izard, Véronique; Pica, Pierre; Spelke, Elizabeth S.; Dehaene, Stanislas
2011-01-01
Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. PMID:21606377
Feder, Tomá s; Motwani, Rajeev
2009-01-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Feder, Tomás
2009-06-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Some nonunitary, indecomposable representations of the Euclidean algebra e(3)
Douglas, Andrew; De Guise, Hubert
2010-01-01
The Euclidean group E(3) is the noncompact, semidirect product group E(3)≅R 3 x SO(3). It is the Lie group of orientation-preserving isometries of three-dimensional Euclidean space. The Euclidean algebra e(3) is the complexification of the Lie algebra of E(3). We construct three distinct families of finite-dimensional, nonunitary representations of e(3) and show that each representation is indecomposable. The representations of the first family are explicitly realized as subspaces of the polynomial ring F[X,Y,Z] with the action of e(3) given by differential operators. The other families are constructed via duals and tensor products of the representations within the first family. We describe subrepresentations, quotients and duals of these indecomposable representations.
Growth Modeling of Human Mandibles using Non-Euclidean Metrics
Hilger, Klaus Baggesen; Larsen, Rasmus; Wrobel, Mark
2003-01-01
From a set of 31 three-dimensional CT scans we model the temporal shape and size of the human mandible. Each anatomical structure is represented using 14851 semi-landmarks, and mapped into Procrustes tangent space. Exploratory subspace analyses are performed leading to linear models of mandible...... shape evolution in Procrustes space. The traditional variance analysis results in a one-dimensional growth model. However, working in a non-Euclidean metric results in a multimodal model with uncorrelated modes of biological variation. The applied non-Euclidean metric is governed by the correlation...... structure of the estimated noise in the data. The generative models are compared, and evaluated on the basis of a cross validation study. The new non-Euclidean analysis is completely data driven. It not only gives comparable results w.r.t. to previous studies of the mean modelling error, but in addition...
Measuring and testing dependence by correlation of distances
Székely, Gábor J.; Rizzo, Maria L.; Bakirov, Nail K.
2007-01-01
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the clas...
TOPSIS with statistical distances: A new approach to MADM
Vijaya Babu Vommi
2017-01-01
Full Text Available Multiple attribute decision making (MADM methods are very useful in choosing the best alternative among the available finite but conflicting alternatives. TOPSIS is one of the MADM methods, which is simple in its methodology and logic. In TOPSIS, Euclidean distances of each alternative from the positive and negative ideal solutions are utilized to find the best alternative. In literature, apart from Euclidean distances, the city block distances have also been tried to find the separations measures. In general, the attribute data are distributed with unequal ranges and also possess moderate to high correlations. Hence, in the present paper, use of statistical distances is proposed in place of Euclidean distances. Procedures to find the best alternatives are developed using statistical and weighted statistical distances respectively. The proposed methods are illustrated with some industrial problems taken from literature. Results show that the proposed methods can be used as new alternatives in MADM for choosing the best solutions.
Deza, Michel Marie
2014-01-01
This updated and revised third edition of the leading reference volume on distance metrics includes new items from very active research areas in the use of distances and metrics such as geometry, graph theory, probability theory and analysis. Among the new topics included are, for example, polyhedral metric space, nearness matrix problems, distances between belief assignments, distance-related animal settings, diamond-cutting distances, natural units of length, Heidegger’s de-severance distance, and brain distances. The publication of this volume coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval. Leaving aside the practical questions that arise during the selection of a ‘good’ distance function, this work focuses on providing the research community with an invaluable comprehensive listing of the main available di...
Graph visualization (Invited talk)
Wijk, van J.J.; Kreveld, van M.J.; Speckmann, B.
2012-01-01
Black and white node link diagrams are the classic method to depict graphs, but these often fall short to give insight in large graphs or when attributes of nodes and edges play an important role. Graph visualization aims obtaining insight in such graphs using interactive graphical representations.
What if? Exploring the multiverse through Euclidean wormholes
Bouhmadi-López, Mariam; Krämer, Manuel; Morais, João; Robles-Pérez, Salvador
2017-10-01
We present Euclidean wormhole solutions describing possible bridges within the multiverse. The study is carried out in the framework of third quantisation. The matter content is modelled through a scalar field which supports the existence of a whole collection of universes. The instanton solutions describe Euclidean solutions that connect baby universes with asymptotically de Sitter universes. We compute the tunnelling probability of these processes. Considering the current bounds on the energy scale of inflation and assuming that all the baby universes are nucleated with the same probability, we draw some conclusions about which universes are more likely to tunnel and therefore undergo a standard inflationary era.
What if? Exploring the multiverse through Euclidean wormholes
Bouhmadi-Lopez, Mariam; Kraemer, Manuel; Morais, Joao; Robles-Perez, Salvador
2017-01-01
We present Euclidean wormhole solutions describing possible bridges within the multiverse. The study is carried out in the framework of third quantisation. The matter content is modelled through a scalar field which supports the existence of a whole collection of universes. The instanton solutions describe Euclidean solutions that connect baby universes with asymptotically de Sitter universes. We compute the tunnelling probability of these processes. Considering the current bounds on the energy scale of inflation and assuming that all the baby universes are nucleated with the same probability, we draw some conclusions about which universes are more likely to tunnel and therefore undergo a standard inflationary era. (orig.)
What if? Exploring the multiverse through Euclidean wormholes
Bouhmadi-Lopez, Mariam [University of the Basque Country UPV/EHU, Department of Theoretical Physics, Bilbao (Spain); Ikerbasque, Basque Foundation for Science, Bilbao (Spain); Kraemer, Manuel [University of Szczecin, Institute of Physics, Szczecin (Poland); Morais, Joao [University of the Basque Country UPV/EHU, Department of Theoretical Physics, Bilbao (Spain); Robles-Perez, Salvador [Instituto de Fisica Fundamental, CSIC, Madrid (Spain); Estacion Ecologica de Biocosmologia, Medellin (Spain)
2017-10-15
We present Euclidean wormhole solutions describing possible bridges within the multiverse. The study is carried out in the framework of third quantisation. The matter content is modelled through a scalar field which supports the existence of a whole collection of universes. The instanton solutions describe Euclidean solutions that connect baby universes with asymptotically de Sitter universes. We compute the tunnelling probability of these processes. Considering the current bounds on the energy scale of inflation and assuming that all the baby universes are nucleated with the same probability, we draw some conclusions about which universes are more likely to tunnel and therefore undergo a standard inflationary era. (orig.)
Jégat , Alain
2014-01-01
The usual framework for Einstein’s special theory of relativity is the pseudo-euclidean spacetime proposed by Hermann Minkowski. This article aims at proposing a different model.The framework is an euclidean four-dimensional space in which all the objects move regularly (it means that, between two observations, whatever their trajectories, they cover the same distance), but where the events are seen in projection according to a privileged direction, as we are going to explain. The remark, rat...
Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
Solution for a bipartite Euclidean traveling-salesman problem in one dimension
Caracciolo, Sergio; Di Gioacchino, Andrea; Gherardi, Marco; Malatesta, Enrico M.
2018-05-01
The traveling-salesman problem is one of the most studied combinatorial optimization problems, because of the simplicity in its statement and the difficulty in its solution. We characterize the optimal cycle for every convex and increasing cost function when the points are thrown independently and with an identical probability distribution in a compact interval. We compute the average optimal cost for every number of points when the distance function is the square of the Euclidean distance. We also show that the average optimal cost is not a self-averaging quantity by explicitly computing the variance of its distribution in the thermodynamic limit. Moreover, we prove that the cost of the optimal cycle is not smaller than twice the cost of the optimal assignment of the same set of points. Interestingly, this bound is saturated in the thermodynamic limit.
Pragmatic Graph Rewriting Modifications
Rodgers, Peter; Vidal, Natalia
1999-01-01
We present new pragmatic constructs for easing programming in visual graph rewriting programming languages. The first is a modification to the rewriting process for nodes the host graph, where nodes specified as 'Once Only' in the LHS of a rewrite match at most once with a corresponding node in the host graph. This reduces the previously common use of tags to indicate the progress of matching in the graph. The second modification controls the application of LHS graphs, where those specified a...
Computing Best and Worst Shortcuts of Graphs Embedded in Metric Spaces
Wulff-Nilsen, Christian; Luo, Jun
2008-01-01
Given a graph embedded in a metric space, its dilation is the maximum over all distinct pairs of vertices of the ratio between their distance in the graph and the metric distance between them. Given such a graph G with n vertices and m edges and consisting of at most two connected components, we ...
Mutual proximity graphs for improved reachability in music recommendation.
Flexer, Arthur; Stevens, Jeff
2018-01-01
This paper is concerned with the impact of hubness, a general problem of machine learning in high-dimensional spaces, on a real-world music recommendation system based on visualisation of a k-nearest neighbour (knn) graph. Due to a problem of measuring distances in high dimensions, hub objects are recommended over and over again while anti-hubs are nonexistent in recommendation lists, resulting in poor reachability of the music catalogue. We present mutual proximity graphs, which are an alternative to knn and mutual knn graphs, and are able to avoid hub vertices having abnormally high connectivity. We show that mutual proximity graphs yield much better graph connectivity resulting in improved reachability compared to knn graphs, mutual knn graphs and mutual knn graphs enhanced with minimum spanning trees, while simultaneously reducing the negative effects of hubness.
What does the Euclidean pseudoparticle do in Minkowski space
Ju, I.
1978-08-01
Self dual pseudoparticle solutions for the classical Yang--Mills field equation with finite action have been constructed in Minkowski space. It is shown that the topological structures apparent in Euclidean space are no longer present in Minkowski space. Topological charges become fractional leading to the unquantized axial charge violation in the process involving fermions. 17 references
Euclidean self-dual Yang-Mills field configurations
Sartori, G.
1980-01-01
The determination of a large class of regular and singular Euclidean self-dual Yang-Mills field configurations is reduced to the solution of a set of linear algebraic equations. The matrix of the coefficients is a polynomial functions of x and the rules for its construction are elementary. (author)
The toroidal Hausdorff dimension of 2d Euclidean quantum gravity
Ambjorn, Jan; Budd, Timothy George
2013-01-01
The lengths of shortest non-contractible loops are studied numerically in 2d Euclidean quantum gravity on a torus coupled to conformal field theories with central charge less than one. We find that the distribution of these geodesic lengths displays a scaling in agreement with a Hausdorff dimension...
Fisher type inequalities for Euclidean t-designs
Delsarte, Ph.; Seidel, J.J.
1989-01-01
The notion of a Euclidean t-design is analyzed in the framework of appropriate inner product spaces of polynomial functions. Some Fisher type inequalities are obtained in a simple manner by this method. The same approach is used to deal with certain analogous combinatorial designs.
Superconvergent perturbation theory for euclidean scalar field theories
Ushveridze, A.G.
1984-01-01
It is shown that the bare (unrenormalized) correlation functions in the euclidean scalar field theories can be expanded in a series whose terms, being computable in a relatively simple way, are free from ultraviolet and infrared divergencies. This series is convergent (divergent) for finite (infinite) values of the correlation functions. (orig.)
The Role of Structure in Learning Non-Euclidean Geometry
Asmuth, Jennifer A.
2009-01-01
How do people learn novel mathematical information that contradicts prior knowledge? The focus of this thesis is the role of structure in the acquisition of knowledge about hyperbolic geometry, a non-Euclidean geometry. In a series of three experiments, I contrast a more holistic structure--training based on closed figures--with a mathematically…
Euclidean Primes Have the Minimum Number of Primitive Roots
Křížek, Michal; Somer, L.
2008-01-01
Roč. 12, č. 1 (2008), s. 121-127 ISSN 0972-5555 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : Euclidean primes * Fermat primes * Sophie Germain primes Subject RIV: BA - General Mathematics
The many faces of graph dynamics
Pignolet, Yvonne Anne; Roy, Matthieu; Schmid, Stefan; Tredan, Gilles
2017-06-01
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a ‘one fits it all’ model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.
ORDERED WEIGHTED DISTANCE MEASURE
Zeshui XU; Jian CHEN
2008-01-01
The aim of this paper is to develop an ordered weighted distance (OWD) measure, which is thegeneralization of some widely used distance measures, including the normalized Hamming distance, the normalized Euclidean distance, the normalized geometric distance, the max distance, the median distance and the min distance, etc. Moreover, the ordered weighted averaging operator, the generalized ordered weighted aggregation operator, the ordered weighted geometric operator, the averaging operator, the geometric mean operator, the ordered weighted square root operator, the square root operator, the max operator, the median operator and the min operator axe also the special cases of the OWD measure. Some methods depending on the input arguments are given to determine the weights associated with the OWD measure. The prominent characteristic of the OWD measure is that it can relieve (or intensify) the influence of unduly large or unduly small deviations on the aggregation results by assigning them low (or high) weights. This desirable characteristic makes the OWD measure very suitable to be used in many actual fields, including group decision making, medical diagnosis, data mining, and pattern recognition, etc. Finally, based on the OWD measure, we develop a group decision making approach, and illustrate it with a numerical example.
Adaptive Graph Convolutional Neural Networks
Li, Ruoyu; Wang, Sheng; Zhu, Feiyun; Huang, Junzhou
2018-01-01
Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for eac...
Central limit theorems for large graphs: Method of quantum decomposition
Hashimoto, Yukihiro; Hora, Akihito; Obata, Nobuaki
2003-01-01
A new method is proposed for investigating spectral distribution of the combinatorial Laplacian (adjacency matrix) of a large regular graph on the basis of quantum decomposition and quantum central limit theorem. General results are proved for Cayley graphs of discrete groups and for distance-regular graphs. The Coxeter groups and the Johnson graphs are discussed in detail by way of illustration. In particular, the limit distributions obtained from the Johnson graphs are characterized by the Meixner polynomials which form a one-parameter deformation of the Laguerre polynomials
Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces
Fu, Yu, E-mail: yufudufe@gmail.com [Dongbei University of Finance and Economics, School of Mathematics and Quantitative Economics (China)
2013-12-15
In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces.
Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces
Fu, Yu
2013-01-01
In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces
Representing distance, consuming distance
Larsen, Gunvor Riber
Title: Representing Distance, Consuming Distance Abstract: Distance is a condition for corporeal and virtual mobilities, for desired and actual travel, but yet it has received relatively little attention as a theoretical entity in its own right. Understandings of and assumptions about distance...... are being consumed in the contemporary society, in the same way as places, media, cultures and status are being consumed (Urry 1995, Featherstone 2007). An exploration of distance and its representations through contemporary consumption theory could expose what role distance plays in forming...
An adaptive distance measure for use with nonparametric models
Garvey, D. R.; Hines, J. W.
2006-01-01
Distance measures perform a critical task in nonparametric, locally weighted regression. Locally weighted regression (LWR) models are a form of 'lazy learning' which construct a local model 'on the fly' by comparing a query vector to historical, exemplar vectors according to a three step process. First, the distance of the query vector to each of the exemplar vectors is calculated. Next, these distances are passed to a kernel function, which converts the distances to similarities or weights. Finally, the model output or response is calculated by performing locally weighted polynomial regression. To date, traditional distance measures, such as the Euclidean, weighted Euclidean, and L1-norm have been used as the first step in the prediction process. Since these measures do not take into consideration sensor failures and drift, they are inherently ill-suited for application to 'real world' systems. This paper describes one such LWR model, namely auto associative kernel regression (AAKR), and describes a new, Adaptive Euclidean distance measure that can be used to dynamically compensate for faulty sensor inputs. In this new distance measure, the query observations that lie outside of the training range (i.e. outside the minimum and maximum input exemplars) are dropped from the distance calculation. This allows for the distance calculation to be robust to sensor drifts and failures, in addition to providing a method for managing inputs that exceed the training range. In this paper, AAKR models using the standard and Adaptive Euclidean distance are developed and compared for the pressure system of an operating nuclear power plant. It is shown that using the standard Euclidean distance for data with failed inputs, significant errors in the AAKR predictions can result. By using the Adaptive Euclidean distance it is shown that high fidelity predictions are possible, in spite of the input failure. In fact, it is shown that with the Adaptive Euclidean distance prediction
Soetevent, A.R.
2010-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial
Graphing Inequalities, Connecting Meaning
Switzer, J. Matt
2014-01-01
Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…
Fuzzy Graph Language Recognizability
Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros
2012-01-01
Part 5: Fuzzy Logic; International audience; Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.
Brouwer, A.E.; Haemers, W.H.
2012-01-01
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association
Regular graph construction for semi-supervised learning
Vega-Oliveros, Didier A; Berton, Lilian; Eberle, Andre Mantini; Lopes, Alneu de Andrade; Zhao, Liang
2014-01-01
Semi-supervised learning (SSL) stands out for using a small amount of labeled points for data clustering and classification. In this scenario graph-based methods allow the analysis of local and global characteristics of the available data by identifying classes or groups regardless data distribution and representing submanifold in Euclidean space. Most of methods used in literature for SSL classification do not worry about graph construction. However, regular graphs can obtain better classification accuracy compared to traditional methods such as k-nearest neighbor (kNN), since kNN benefits the generation of hubs and it is not appropriate for high-dimensionality data. Nevertheless, methods commonly used for generating regular graphs have high computational cost. We tackle this problem introducing an alternative method for generation of regular graphs with better runtime performance compared to methods usually find in the area. Our technique is based on the preferential selection of vertices according some topological measures, like closeness, generating at the end of the process a regular graph. Experiments using the global and local consistency method for label propagation show that our method provides better or equal classification rate in comparison with kNN
Lisonek, Petr
1996-01-01
A two-distance set in E^d is a point set X inthe d-dimensional Euclidean spacesuch that the distances between distinct points in Xassume only two different non-zero values. Based on results from classical distance geometry, we developan algorithm to classify, for a given dimension, all maximal...... (largest possible)two-distance sets in E^d.Using this algorithm we have completed the full classificationfor all dimensions less than or equal to 7, andwe have found one set in E^8 whosemaximality follows from Blokhuis' upper bound on sizes of s-distance sets.While in the dimensions less than or equal to 6...
Euclidean to Minkowski Bethe-Salpeter amplitude and observables
Carbonell, J.; Frederico, T.; Karmanov, V.A.
2017-01-01
We propose a method to reconstruct the Bethe-Salpeter amplitude in Minkowski space given the Euclidean Bethe-Salpeter amplitude - or alternatively the light-front wave function - as input. The method is based on the numerical inversion of the Nakanishi integral representation and computing the corresponding weight function. This inversion procedure is, in general, rather unstable, and we propose several ways to considerably reduce the instabilities. In terms of the Nakanishi weight function, one can easily compute the BS amplitude, the LF wave function and the electromagnetic form factor. The latter ones are very stable in spite of residual instabilities in the weight function. This procedure allows both, to continue the Euclidean BS solution in the Minkowski space and to obtain a BS amplitude from a LF wave function. (orig.)
Tunneling in expanding Universe: Euclidean and Hamiltonian approaches
Goncharov, A.S.; Linde, A.D.
1986-01-01
The theory of the false vacuum decay in de Sitter space and in the inflationary Universe, and also the theory of the Universe creation ''from nothing'' are discussed. This explained why tunneling in the inflationary Universe differs from that in de Sitter space and cannot be exactly homogeneous. It is shown that in several important cases the Euclidean approach should be considerably modified or is absolutely inapplicable for the description of tunneling in the expanding Universe and of the process of the quantum creation of the Universe. The Hamiltonian approach to the theory of tunneling in expanding Universe is developed. The results obtained by this method are compared with the results obtained by the Euclidean approach
Euclidean to Minkowski Bethe-Salpeter amplitude and observables
Carbonell, J. [Universite Paris-Sud, IN2P3-CNRS, Institut de Physique Nucleaire, Orsay Cedex (France); Frederico, T. [Instituto Tecnologico de Aeronautica, DCTA, Sao Jose dos Campos (Brazil); Karmanov, V.A. [Lebedev Physical Institute, Moscow (Russian Federation)
2017-01-15
We propose a method to reconstruct the Bethe-Salpeter amplitude in Minkowski space given the Euclidean Bethe-Salpeter amplitude - or alternatively the light-front wave function - as input. The method is based on the numerical inversion of the Nakanishi integral representation and computing the corresponding weight function. This inversion procedure is, in general, rather unstable, and we propose several ways to considerably reduce the instabilities. In terms of the Nakanishi weight function, one can easily compute the BS amplitude, the LF wave function and the electromagnetic form factor. The latter ones are very stable in spite of residual instabilities in the weight function. This procedure allows both, to continue the Euclidean BS solution in the Minkowski space and to obtain a BS amplitude from a LF wave function. (orig.)
Euclidean scalar field theory in the bilocal approximation
Nagy, S.; Polonyi, J.; Steib, I.
2018-04-01
The blocking step of the renormalization group method is usually carried out by restricting it to fluctuations and to local blocked action. The tree-level, bilocal saddle point contribution to the blocking, defined by the infinitesimal decrease of the sharp cutoff in momentum space, is followed within the three dimensional Euclidean ϕ6 model in this work. The phase structure is changed, new phases and relevant operators are found, and certain universality classes are restricted by the bilocal saddle point.
General Nth order integrals of motion in the Euclidean plane
Post, S; Winternitz, P
2015-01-01
The general form of an integral of motion that is a polynomial of order N in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean space. The classical and the quantum cases are treated separately, emphasizing both the similarities and the differences between the two. The main application will be to study Nth order superintegrable systems that allow separation of variables in the Hamilton–Jacobi and Schrödinger equations, respectively. (paper)
Optimal recovery of linear operators in non-Euclidean metrics
Osipenko, K Yu [Moscow State Aviation Technological University, Moscow (Russian Federation)
2014-10-31
The paper looks at problems concerning the recovery of operators from noisy information in non-Euclidean metrics. A number of general theorems are proved and applied to recovery problems for functions and their derivatives from the noisy Fourier transform. In some cases, a family of optimal methods is found, from which the methods requiring the least amount of original information are singled out. Bibliography: 25 titles.
Hell, Pavol
2004-01-01
This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics.Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level an
Simplicial complexes of graphs
Jonsson, Jakob
2008-01-01
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
Introduction to quantum graphs
Berkolaiko, Gregory
2012-01-01
A "quantum graph" is a graph considered as a one-dimensional complex and equipped with a differential operator ("Hamiltonian"). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., "meso-" or "nano-scale") system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on qu...
Shape anisotropy: tensor distance to anisotropy measure
Weldeselassie, Yonas T.; El-Hilo, Saba; Atkins, M. S.
2011-03-01
Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite its extensive use in DT-MRI community, however, not much attention has been given to the mathematical correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space. But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor, its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically show that it has a higher signal to noise ratio than fractional anisotropy.
Zhang, Ying-Ying; Yang, Cai; Zhang, Ping
2017-08-01
In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods-highlight-inhibition function, context-based saliency weighting, and the graph cut-are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.
Renormalized G-convolution of n-point functions in quantum field theory. I. The Euclidean case
Bros, Jacques; Manolessou-Grammaticou, Marietta.
1977-01-01
The notion of Feynman amplitude associated with a graph G in perturbative quantum field theory admits a generalized version in which each vertex v of G is associated with a general (non-perturbative) nsub(v)-point function Hsup(nsub(v)), nsub(v) denoting the number of lines which are incident to v in G. In the case where no ultraviolet divergence occurs, this has been performed directly in complex momentum space through Bros-Lassalle's G-convolution procedure. The authors propose a generalization of G-convolution which includes the case when the functions Hsup(nsub(v)) are not integrable at infinity but belong to a suitable class of slowly increasing functions. A finite part of the G-convolution integral is then defined through an algorithm which closely follows Zimmermann's renormalization scheme. The case of Euclidean four-momentum configurations is only treated
Graphing trillions of triangles.
Burkhardt, Paul
2017-07-01
The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.
Some Properties of the Distance Function and a Conjecture of De Giorgi
Eminenti, Manolo; Mantegazza, Carlo
2003-01-01
We analyse the geometric properties of the high derivatives of the distance function from a submanifold of the Euclidean space. In particular, we show some relations with the second fundamental form and its covariant derivatives of independent interest. As an application we prove a conjecture of Ennio De Giorgi on the evolution of submanifolds of the Euclidean space by the gradient of functionals depending on the derivatives of the distance function.
Ait-Haddou, Rachid
2015-06-04
We show that the best degree reduction of a given polynomial P from degree n to m with respect to the discrete (Formula presented.)-norm is equivalent to the best Euclidean distance of the vector of h-Bézier coefficients of P from the vector of degree raised h-Bézier coefficients of polynomials of degree m. Moreover, we demonstrate the adequacy of h-Bézier curves for approaching the problem of weighted discrete least squares approximation. Applications to discrete orthogonal polynomials are also presented. © 2015 Springer Science+Business Media Dordrecht
Chartrand, Gary
1984-01-01
Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap
A heuristic derivation of Minkowski distance and Lorentz transformation
Hassani, Sadri
2008-01-01
Students learn new abstract concepts best when these concepts are connected through a well-designed analogy, to familiar ideas. Since the concept of the relativistic spacetime distance is highly abstract, it would be desirable to connect it to the familiar Euclidean distance, but present the latter in such a way that it makes a transparent contact with the former. Starting with some intuitive and 'obvious' assumptions concerning distance in one dimension, we 'derive' the two-dimensional Euclidean distance between two points in terms of their coordinates. Then, assuming the invariance of this distance, we deduce the (familiar) two-dimensional orthogonal coordinate transformation. We present the derivation in such a way that the transition to spacetime becomes 'self-evident.' Thus, following exactly the same procedure, we derive the Minkowskian distance and the corresponding transformation that respects the invariance of that distance, i.e., the Lorentz transformation
Adriaan R. Soetevent
2010-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial discontinuities in firm-level demand may occur. I show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs. I conjecture that this non-existence result holds...
Pim Heijnen; Adriaan Soetevent
2014-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. We derive an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. These graph models of price competition may lead to spatial discontinuities in firm-level demand. We show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs and conjecture that this non-existence result holds more general...
Aleks Kissinger
2014-03-01
Full Text Available String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes", on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.
Gelfand, I M; Shnol, E E
1969-01-01
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu
Creating more effective graphs
Robbins, Naomi B
2012-01-01
A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr
Lothian, Joshua [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sullivan, Blair D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Baker, Matthew B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Schrock, Jonathan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Poole, Stephen W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2013-10-01
The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of different application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.
Mansutti, Alessio; Miculan, Marino; Peressotti, Marco
2017-01-01
We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly...... also problems which are “mixed” instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give...
Alberto Apostolico
2009-08-01
Full Text Available The Web Graph is a large-scale graph that does not fit in main memory, so that lossless compression methods have been proposed for it. This paper introduces a compression scheme that combines efficient storage with fast retrieval for the information in a node. The scheme exploits the properties of the Web Graph without assuming an ordering of the URLs, so that it may be applied to more general graphs. Tests on some datasets of use achieve space savings of about 10% over existing methods.
Spinors and supersymmetry in four-dimensional Euclidean space
McKeon, D.G.C.; Sherry, T.N.
2001-01-01
Spinors in four-dimensional Euclidean space are treated using the decomposition of the Euclidean space SO(4) symmetry group into SU(2)xSU(2). Both 2- and 4-spinor representations of this SO(4) symmetry group are shown to differ significantly from the corresponding spinor representations of the SO(3, 1) symmetry group in Minkowski space. The simplest self conjugate supersymmetry algebra allowed in four-dimensional Euclidean space is demonstrated to be an N=2 supersymmetry algebra which resembles the N=2 supersymmetry algebra in four-dimensional Minkowski space. The differences between the two supersymmetry algebras gives rise to different representations; in particular an analysis of the Clifford algebra structure shows that the momentum invariant is bounded above by the central charges in 4dE, while in 4dM the central charges bound the momentum invariant from below. Dimensional reduction of the N=1 SUSY algebra in six-dimensional Minkowski space (6dM) to 4dE reproduces our SUSY algebra in 4dE. This dimensional reduction can be used to introduce additional generators into the SUSY algebra in 4dE. Well known interpolating maps are used to relate the N=2 SUSY algebra in 4dE derived in this paper to the N=2 SUSY algebra in 4dM. The nature of the spinors in 4dE allows us to write an axially gauge invariant model which is shown to be both Hermitian and anomaly-free. No equivalent model exists in 4dM. Useful formulae in 4dE are collected together in two appendixes
Representation of activity in images using geospatial temporal graphs
Brost, Randolph; McLendon, III, William C.; Parekh, Ojas D.; Rintoul, Mark Daniel; Watson, Jean-Paul; Strip, David R.; Diegert, Carl
2018-05-01
Various technologies pertaining to modeling patterns of activity observed in remote sensing images using geospatial-temporal graphs are described herein. Graphs are constructed by representing objects in remote sensing images as nodes, and connecting nodes with undirected edges representing either distance or adjacency relationships between objects and directed edges representing changes in time. Activity patterns may be discerned from the graphs by coding nodes representing persistent objects like buildings differently from nodes representing ephemeral objects like vehicles, and examining the geospatial-temporal relationships of ephemeral nodes within the graph.
Searches over graphs representing geospatial-temporal remote sensing data
Brost, Randolph; Perkins, David Nikolaus
2018-03-06
Various technologies pertaining to identifying objects of interest in remote sensing images by searching over geospatial-temporal graph representations are described herein. Graphs are constructed by representing objects in remote sensing images as nodes, and connecting nodes with undirected edges representing either distance or adjacency relationships between objects and directed edges representing changes in time. Geospatial-temporal graph searches are made computationally efficient by taking advantage of characteristics of geospatial-temporal data in remote sensing images through the application of various graph search techniques.
Graph-based clustering and data visualization algorithms
Vathy-Fogarassy, Ágnes
2013-01-01
This work presents a data visualization technique that combines graph-based topology representation and dimensionality reduction methods to visualize the intrinsic data structure in a low-dimensional vector space. The application of graphs in clustering and visualization has several advantages. A graph of important edges (where edges characterize relations and weights represent similarities or distances) provides a compact representation of the entire complex data set. This text describes clustering and visualization methods that are able to utilize information hidden in these graphs, based on
Convergent perturbation expansions for Euclidean quantum field theory
Mack, G.; Pordt, A.
1984-09-01
Mayer perturbation theory is designed to provide computable convergent expansions which permit calculation of Greens functions in Euclidean Quantum Field Theory to arbitrary accuracy, including 'nonperturbative' contributions from large field fluctuations. Here we describe the expansions at the example of 3-dimensional lambdaphi 4 -theory (in continuous space). They are not essentially more complicated than standard perturbation theory. The n-th order term is expressed in terms of 0(n)-dimensional integrals, and is of order lambda 4 if 4k-3<=n<=4k. (orig.)
Euclidean D-branes and higher-dimensional gauge theory
Acharya, B.S.; Figueroa-O'Farrill, J.M.; Spence, B.; O'Loughlin, M.
1997-07-01
We consider euclidean D-branes wrapping around manifolds of exceptional holonomy in dimensions seven and eight. The resulting theory on the D-brane-that is, the dimensional reduction of 10-dimensional supersymmetric Yang-Mills theory-is a cohomological field theory which describes the topology of the moduli space of instantons. The 7-dimensional theory is an N T =2 (or balanced) cohomological theory given by an action potential of Chern-Simons type. As a by-product of this method, we construct a related cohomological field theory which describes the monopole moduli space on a 7-manifold of G 2 holonomy. (author). 22 refs, 3 tabs
The G_Newton --> 0 Limit of Euclidean Quantum Gravity
Smolin, Lee
1992-01-01
Using the Ashtekar formulation, it is shown that the G_{Newton} --> 0 limit of Euclidean or complexified general relativity is not a free field theory, but is a theory that describes a linearized self-dual connection propagating on an arbitrary anti-self-dual background. This theory is quantized in the loop representation and, as in the full theory, an infinite dimnensional space of exact solutions to the constraint is found. An inner product is also proposed. The path integral is constructed...
Multi-stability in folded shells: non-Euclidean origami
Evans, Arthur
2015-03-01
Both natural and man-made structures benefit from having multiple mechanically stable states, from the quick snapping motion of hummingbird beaks to micro-textured surfaces with tunable roughness. Rather than discuss special fabrication techniques for creating bi-stability through material anisotropy, in this talk I will present several examples of how folding a structure can modify the energy landscape and thus lead to multiple stable states. Using ideas from origami and differential geometry, I will discuss how deforming a non-Euclidean surface can be done either continuously or discontinuously, and explore the effects that global constraints have on the ultimate stability of the surface.
ILUCG algorithm which minimizes in the Euclidean norm
Petravic, M.; Kuo-Petravic, G.
1978-07-01
An algroithm is presented which solves sparse systems of linear equations of the form Ax = Y, where A is non-symmetric, by the Incomplete LU Decomposition-Conjugate Gradient (ILUCG) method. The algorithm minimizes the error in the Euclidean norm vertical bar x/sub i/ - x vertical bar 2 , where x/sub i/ is the solution vector after the i/sup th/ iteration and x the exact solution vector. The results of a test on one real problem indicate that the algorithm is likely to be competitive with the best existing algorithms of its type
A Class of Weingarten Surfaces in Euclidean 3-Space
Yu Fu
2013-01-01
Full Text Available The class of biconservative surfaces in Euclidean 3-space 3 are defined in (Caddeo et al., 2012 by the equation A(grad H=-H grad H for the mean curvature function H and the Weingarten operator A. In this paper, we consider the more general case that surfaces in 3 satisfying A(grad H=kH grad H for some constant k are called generalized bi-conservative surfaces. We show that this class of surfaces are linear Weingarten surfaces. We also give a complete classification of generalized bi-conservative surfaces in 3.
A strong coupling simulation of Euclidean quantum gravity
Berg, B.; Hamburg Univ.
1984-12-01
Relying on Regge calculus a systematic numerical investigation of models of 4d Euclidean gravity is proposed. The scale a = 1 0 is set by fixing the expectation value of a length. Possible universality of such models is discussed. The strong coupling limit is defined by taking Planck mass msub(p) -> 0 (in units of 1 0 -1 ). The zero order approximation msub(p) = 0 is called 'fluctuating space' and investigated numerically in two 4d models. Canonical dimensions are realized and both models give a negative expectation value for the scalar curvature density. (orig.)
Graph Theory. 1. Fragmentation of Structural Graphs
Lorentz JÄNTSCHI
2002-12-01
Full Text Available The investigation of structural graphs has many fields of applications in engineering, especially in applied sciences like as applied chemistry and physics, computer sciences and automation, electronics and telecommunication. The main subject of the paper is to express fragmentation criteria in graph using a new method of investigation: terminal paths. Using terminal paths are defined most of the fragmentation criteria that are in use in molecular topology, but the fields of applications are more generally than that, as I mentioned before. Graphical examples of fragmentation are given for every fragmentation criteria. Note that all fragmentation is made with a computer program that implements a routine for every criterion.[1] A web routine for tracing all terminal paths in graph can be found at the address: http://vl.academicdirect.ro/molecular_topology/tpaths/ [1] M. V. Diudea, I. Gutman, L. Jäntschi, Molecular Topology, Nova Science, Commack, New York, 2001, 2002.
W.Janke
2006-01-01
Full Text Available This paper gives a brief introduction to using two-dimensional discrete and Euclidean quantum gravity approaches as a laboratory for studying the properties of fluctuating and frozen random graphs in interaction with "matter fields" represented by simple spin or vertex models. Due to the existence of numerous exact analytical results and predictions for comparison with simulational work, this is an interesting and useful enterprise.
GRAMI: Generalized Frequent Subgraph Mining in Large Graphs
El Saeedy, Mohammed El Sayed
2011-07-24
Mining frequent subgraphs is an important operation on graphs. Most existing work assumes a database of many small graphs, but modern applications, such as social networks, citation graphs or protein-protein interaction in bioinformatics, are modeled as a single large graph. Interesting interactions in such applications may be transitive (e.g., friend of a friend). Existing methods, however, search for frequent isomorphic (i.e., exact match) subgraphs and cannot discover many useful patterns. In this paper we propose GRAMI, a framework that generalizes frequent subgraph mining in a large single graph. GRAMI discovers frequent patterns. A pattern is a graph where edges are generalized to distance-constrained paths. Depending on the definition of the distance function, many instantiations of the framework are possible. Both directed and undirected graphs, as well as multiple labels per vertex, are supported. We developed an efficient implementation of the framework that models the frequency resolution phase as a constraint satisfaction problem, in order to avoid the costly enumeration of all instances of each pattern in the graph. We also implemented CGRAMI, a version that supports structural and semantic constraints; and AGRAMI, an approximate version that supports very large graphs. Our experiments on real data demonstrate that our framework is up to 3 orders of magnitude faster and discovers more interesting patterns than existing approaches.
Tan, Zhiyuan; Jamdagni, Aruna; He, Xiangjian; Nanda, Priyadarsi; Liu, Ren Ping; Qing, Sihan; Susilo, Willy; Wang, Guilin; Liu, Dongmei
2011-01-01
The quality of feature has significant impact on the performance of detection techniques used for Denial-of-Service (DoS) attack. The features that fail to provide accurate characterization for network traffic records make the techniques suffer from low accuracy in detection. Although researches
A graph rewriting programming language for graph drawing
Rodgers, Peter
1998-01-01
This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computationally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools are all text based. Recent developments in graph rewriting systems have produced computationally com...
On the Schroedinger representation of the Euclidean quantum field theory
Semmler, U.
1987-04-01
The theme of the present thesis is the Schroedinger representation of the Euclidean quantum field theory: We define the time development of the quantum field states as functional integral in a novel, mathematically precise way. In the following we discuss the consequences which result from this approach to the Euclidean quantum field theory. Chapter 1 introduces the theory of abstract Wiener spaces which is here proved as suitable mathematical tool for the treatment of the physical problems. In chapter 2 the diffusion theory is formulated in the framework of abstract Wiener spaces. In chapter 3 we define the field functional ψ 5 u, t 7 as functional integral, determine the functional differential equation which ψ satisfies (Schroedinger equation), and summarize the consequences resulting from this. Chapter 4 is dedicated to the attempt to determine the kernel of the time-development operator, by the knowledge of which the time development of each initial state is fixed. In chapter 5 the consequences of the theory presented in chapter 3 and 4 are discussed by means of simple examples. In chapter 6 the renormalization which results for the φ 4 potential from the definition of the functional integral in chapter 3 is calculated up to the first-order perturbation theory, and it is shown that the problems in the Symanzik renormalization procedure can be removed. (orig./HSI) [de
Euclidean and Minkowski space formulations of linearized gravitational potential in various gauges
Lim, S.C.
1979-01-01
We show that there exists a unitary map connecting linearized theories of gravitational potential in vacuum, formulated in various covariant gauges and noncovariant radiation gauge. The free Euclidean gravitational potentials in covariant gauges satisfy the Markov property of Nelson, but are nonreflexive. For the noncovariant radiation gauge, the corresponding Euclidean field is reflexive but it only satisfies the Markov property with respect to special half spaces. The Feynman--Kac--Nelson formula is established for the Euclidean gravitational potential in radiation gauge
Isometric immersions and embeddings of locally Euclidean metrics in R2
Sabitov, I Kh
1999-01-01
This paper deals with the problem of isometric immersions and embeddings of two-dimensional locally Euclidean metrics in the Euclidean plane. We find explicit formulae for the immersions of metrics defined on a simply connected domain and a number of sufficient conditions for the existence of isometric embeddings. In the case when the domain is multiply connected we find necessary conditions for the existence of isometric immersions and classify the cases when the metric admits no isometric immersion in the Euclidean plane
de Mol, M.J.; Rensink, Arend; Hunt, James J.
This paper introduces an approach for adding graph transformation-based functionality to existing JAVA programs. The approach relies on a set of annotations to identify the intended graph structure, as well as on user methods to manipulate that structure, within the user’s own JAVA class
Joyner, W David
2017-01-01
This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards ad...
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
Husfeldt, Thore
2015-01-01
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...
Packing Degenerate Graphs Greedily
Allen, P.; Böttcher, J.; Hladký, J.; Piguet, Diana
2017-01-01
Roč. 61, August (2017), s. 45-51 ISSN 1571-0653 R&D Projects: GA ČR GJ16-07822Y Institutional support: RVO:67985807 Keywords : tree packing conjecture * graph packing * graph processes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics
Generalized connectivity of graphs
Li, Xueliang
2016-01-01
Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Autoregressive Moving Average Graph Filtering
Isufi, Elvin; Loukas, Andreas; Simonetto, Andrea; Leus, Geert
2016-01-01
One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation. The design phi...
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar
2017-03-06
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar; Leus, Geert
2017-01-01
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Bollobas, Bela
2004-01-01
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A
SLE as a Mating of Trees in Euclidean Geometry
Holden, Nina; Sun, Xin
2018-05-01
The mating of trees approach to Schramm-Loewner evolution (SLE) in the random geometry of Liouville quantum gravity (LQG) has been recently developed by Duplantier et al. (Liouville quantum gravity as a mating of trees, 2014. arXiv:1409.7055). In this paper we consider the mating of trees approach to SLE in Euclidean geometry. Let {η} be a whole-plane space-filling SLE with parameter {κ > 4} , parameterized by Lebesgue measure. The main observable in the mating of trees approach is the contour function, a two-dimensional continuous process describing the evolution of the Minkowski content of the left and right frontier of {η} . We prove regularity properties of the contour function and show that (as in the LQG case) it encodes all the information about the curve {η} . We also prove that the uniform spanning tree on {Z^2} converges to SLE8 in the natural topology associated with the mating of trees approach.
Curvature-driven morphing of non-Euclidean shells
Pezzulla, Matteo; Stoop, Norbert; Jiang, Xin; Holmes, D. P.
2017-05-01
We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive an effective model that reduces a three-dimensional stimulus to the natural fundamental forms of the mid-surface of the structure, incorporating expansion, or growth, in the thickness. Then, we apply the model to a variety of thin bodies, from flat plates to spherical shells, obtaining excellent agreement between theory and numerics. We show how cylinders and cones can either bend more or unroll, and eventually snap and rotate. We also study the nearly isometric deformations of a spherical shell and describe how this shape change is ruled by the geometry of a spindle. As the derived results stem from a purely geometrical model, they are general and scalable.
Buckling transition and boundary layer in non-Euclidean plates.
Efrati, Efi; Sharon, Eran; Kupferman, Raz
2009-07-01
Non-Euclidean plates are thin elastic bodies having no stress-free configuration, hence exhibiting residual stresses in the absence of external constraints. These bodies are endowed with a three-dimensional reference metric, which may not necessarily be immersible in physical space. Here, based on a recently developed theory for such bodies, we characterize the transition from flat to buckled equilibrium configurations at a critical value of the plate thickness. Depending on the reference metric, the buckling transition may be either continuous or discontinuous. In the infinitely thin plate limit, under the assumption that a limiting configuration exists, we show that the limit is a configuration that minimizes the bending content, among all configurations with zero stretching content (isometric immersions of the midsurface). For small but finite plate thickness, we show the formation of a boundary layer, whose size scales with the square root of the plate thickness and whose shape is determined by a balance between stretching and bending energies.
Defects and boundary layers in non-Euclidean plates
Gemmer, J A; Venkataramani, S C
2012-01-01
We investigate the behaviour of non-Euclidean plates with constant negative Gaussian curvature using the Föppl–von Kármán reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In particular we show that are only two types of global minimizers—deformations that remain flat and saddle shaped deformations with isolated regions of stretching near the edge of the annulus. We also show that there exist local minimizers with a periodic profile that have additional boundary layers near their lines of inflection. These additional boundary layers are a new phenomenon in thin elastic sheets and are necessary to regularize jump discontinuities in the azimuthal curvature across lines of inflection. We rigorously derive scaling laws for the width of these boundary layers as a function of the thickness of the sheet. (paper)
Geometry through history Euclidean, hyperbolic, and projective geometries
Dillon, Meighan I
2018-01-01
Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...
Euclidean mirrors: enhanced vacuum decay from reflected instantons
Akal, Ibrahim; Moortgat-Pick, Gudrid
2018-05-01
We study the tunnelling of virtual matter–antimatter pairs from the quantum vacuum in the presence of a spatially uniform, time-dependent electric background composed of a strong, slow field superimposed with a weak, rapid field. After analytic continuation to Euclidean spacetime, we obtain from the instanton equations two critical points. While one of them is the closing point of the instanton path, the other serves as an Euclidean mirror which reflects and squeezes the instanton. It is this reflection and shrinking which is responsible for an enormous enhancement of the vacuum pair production rate. We discuss how important features of two different mechanisms can be analysed and understood via such a rotation in the complex plane. (a) Consistent with previous studies, we first discuss the standard assisted mechanism with a static strong field and certain weak fields with a distinct pole structure in order to show that the reflection takes place exactly at the poles. We also discuss the effect of possible sub-cycle structures. We extend this reflection picture then to weak fields which have no poles present and illustrate the effective reflections with explicit examples. An additional field strength dependence for the rate occurs in such cases. We analytically compute the characteristic threshold for the assisted mechanism given by the critical combined Keldysh parameter. We discuss significant differences between these two types of fields. For various backgrounds, we present the contributing instantons and perform analytical computations for the corresponding rates treating both fields nonperturbatively. (b) In addition, we also study the case with a nonstatic strong field which gives rise to the assisted dynamical mechanism. For different strong field profiles we investigate the impact on the critical combined Keldysh parameter. As an explicit example, we analytically compute the rate by employing the exact reflection points. The validity of the predictions
Euclidean mirrors. Enhanced vacuum decay from reflected instantons
Akal, Ibrahim [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Moortgat-Pick, Gudrid [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2017-06-15
We study the tunneling of virtual matter-antimatter pairs from the quantum vacuum in the presence of a spatially uniform temporal electric background composed of of a strong slow field superimposed with a weak rapid field. After analytic continuation to Euclidean spacetime we obtain from the instanton equations two critical points. While one of them is the closing point of the instanton path, the other serves as an Euclidean mirror which reflects and squeezes the instanton. It is this reflection and shrinking which is responsible for an enormous enhancement of the vacuum pair production rate. We discuss how important features of this mechanism can be analysed and understood via such a rotation in the complex plane. Consistent with previous studies, we consider certain examples where we apply weak fields with a distinct pole structure in order to show that the reflection takes place exactly at the poles. We also discuss the effect of possible sub-cycle structures. We extend this reflection picture to fields which have no poles present and illustrate the effective reflections with explicit examples. An additional field strength dependence for the rate occurs in such cases. We analytically compute the characteristic threshold for this mechanism given by the critical combined Keldysh parameter. We discuss significant differences between these two types of fields. For various backgrounds, we present the contributing instantons and perform analytical computations for the corresponding rates treating both fields nonperturbatively. The validity of the results is confirmed by numerical computations. Considering different profiles for the strong field, we also discuss its impact on the critical combined Keldysh parameter.
Uniqueness of Gibbs states and global Markov property for Euclidean fields
Albeverio, S.; Hoeegh-Krohn, R.
1981-01-01
The authors briefly discuss the proof of the uniqueness of solutions of the DLR equations (uniqueness of Gibbs states) in the class of regular generalized random fields (in the sense of having second moments bounded by those of some Euclidean field), for the Euclidean fields with trigonometric interaction. (Auth.)
Non-euclidean simplex optimization. [Application to potentiometric titration of Pu
Silver, G.L.
1977-08-15
Geometric optimization techniques useful for studying chemical equilibrium traditionally rely upon principles of euclidean geometry, but such algorithms may also be based upon principles of a non-euclidean geometry. The sequential simplex method is adapted to the hyperbolic plane, and application of optimization to problems such as the potentiometric titration of plutonium is suggested.
Haynes Teresa W.
2014-08-01
Full Text Available A path π = (v1, v2, . . . , vk+1 in a graph G = (V,E is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi ≥ deg(vi+1, where deg(vi denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds
Tailored Random Graph Ensembles
Roberts, E S; Annibale, A; Coolen, A C C
2013-01-01
Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.
Alspach, BR
1985-01-01
This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.
Wilson, Robin J
1985-01-01
Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. This book provides a comprehensive introduction to the subject.
Hyperbolicity in median graphs
mic problems in hyperbolic spaces and hyperbolic graphs have been .... that in general the main obstacle is that we do not know the location of ...... [25] Jonckheere E and Lohsoonthorn P, A hyperbolic geometry approach to multipath routing,.
Uniform Single Valued Neutrosophic Graphs
S. Broumi
2017-09-01
Full Text Available In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.
Collective Rationality in Graph Aggregation
Endriss, U.; Grandi, U.; Schaub, T.; Friedrich, G.; O'Sullivan, B.
2014-01-01
Suppose a number of agents each provide us with a directed graph over a common set of vertices. Graph aggregation is the problem of computing a single “collective” graph that best represents the information inherent in this profile of individual graphs. We consider this aggregation problem from the
Barra, F.; Gaspard, P.
2001-01-01
We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator that generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms that decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs that converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system that undergoes a diffusion process before it escapes
Bollobás, Béla
1998-01-01
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...
Community detection by graph Voronoi diagrams
Deritei, Dávid; Lázár, Zsolt I.; Papp, István; Járai-Szabó, Ferenc; Sumi, Róbert; Varga, Levente; Ravasz Regan, Erzsébet; Ercsey-Ravasz, Mária
2014-06-01
Accurate and efficient community detection in networks is a key challenge for complex network theory and its applications. The problem is analogous to cluster analysis in data mining, a field rich in metric space-based methods. Common to these methods is a geometric, distance-based definition of clusters or communities. Here we propose a new geometric approach to graph community detection based on graph Voronoi diagrams. Our method serves as proof of principle that the definition of appropriate distance metrics on graphs can bring a rich set of metric space-based clustering methods to network science. We employ a simple edge metric that reflects the intra- or inter-community character of edges, and a graph density-based rule to identify seed nodes of Voronoi cells. Our algorithm outperforms most network community detection methods applicable to large networks on benchmark as well as real-world networks. In addition to offering a computationally efficient alternative for community detection, our method opens new avenues for adapting a wide range of data mining algorithms to complex networks from the class of centroid- and density-based clustering methods.
On the Distribution of Random Geometric Graphs
Badiu, Mihai Alin; Coon, Justin P.
2018-01-01
as a measure of the graph’s topological uncertainty (or information content). Moreover, the distribution is also relevant for determining average network performance or designing protocols. However, a major impediment in deducing the graph distribution is that it requires the joint probability distribution......Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random topology, properties (e.g., connectedness), or Shannon entropy...... of the n(n − 1)/2 distances between n nodes randomly distributed in a bounded domain. As no such result exists in the literature, we make progress by obtaining the joint distribution of the distances between three nodes confined in a disk in R 2. This enables the calculation of the probability distribution...
A general Euclidean connection for so(n,m) lie algebra and the algebraic approach to scattering
Ionescu, R.A.
1994-11-01
We obtain a general Euclidean connection for so(n,m). This Euclidean connection allows an algebraic derivation of the S matrix and it reduces to the known one in suitable circumstances. (author). 8 refs
Distance of Sample Measurement Points to Prototype Catalog Curve
Hjorth, Poul G.; Karamehmedovic, Mirza; Perram, John
2006-01-01
We discuss strategies for comparing discrete data points to a catalog (reference) curve by means of the Euclidean distance from each point to the curve in a pump's head H vs. flow Qdiagram. In particular we find that a method currently in use is inaccurate. We propose several alternatives...
Proxy Graph: Visual Quality Metrics of Big Graph Sampling.
Nguyen, Quan Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra
2017-06-01
Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.
The R{sup ∗}-operation for Feynman graphs with generic numerators
Herzog, Franz [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Ruijl, Ben [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Leiden University,Niels Bohrweg 1, 2333 CA Leiden (Netherlands)
2017-05-08
The R{sup ∗}-operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ R-operation, which subtracts both ultraviolet and infrared divergences of euclidean Feynman graphs with non-exceptional external momenta. It can be used to compute the divergent parts of such Feynman graphs from products of simpler Feynman graphs of lower loops. In this paper we extend the R{sup ∗}-operation to Feynman graphs with arbitrary numerators, including tensors. We also provide a novel way of defining infrared counterterms which closely resembles the definition of its ultraviolet counterpart. We further express both infrared and ultraviolet counterterms in terms of scaleless vacuum graphs with a logarithmic degree of divergence. By exploiting symmetries, integrand and integral relations, which the counterterms of scaleless vacuum graphs satisfy, we can vastly reduce their number and complexity. A FORM implementation of this method was used to compute the five loop beta function in QCD for a general gauge group. To illustrate the procedure, we compute the poles in the dimensional regulator of all top-level propagator graphs at five loops in four dimensional ϕ{sup 3} theory.
$O(N)$ model in Euclidean de Sitter space: beyond the leading infrared approximation
Nacir, Diana López; Trombetta, Leonardo G
2016-01-01
We consider an $O(N)$ scalar field model with quartic interaction in $d$-dimensional Euclidean de Sitter space. In order to avoid the problems of the standard perturbative calculations for light and massless fields, we generalize to the $O(N)$ theory a systematic method introduced previously for a single field, which treats the zero modes exactly and the nonzero modes perturbatively. We compute the two-point functions taking into account not only the leading infrared contribution, coming from the self-interaction of the zero modes, but also corrections due to the interaction of the ultraviolet modes. For the model defined in the corresponding Lorentzian de Sitter spacetime, we obtain the two-point functions by analytical continuation. We point out that a partial resummation of the leading secular terms (which necessarily involves nonzero modes) is required to obtain a decay at large distances for massless fields. We implement this resummation along with a systematic double expansion in an effective coupling c...
Braddock, Joseph
1997-01-01
A study reviewing the existing Army Distance Learning Plan (ADLP) and current Distance Learning practices, with a focus on the Army's training and educational challenges and the benefits of applying Distance Learning techniques...
On some covering graphs of a graph
Shariefuddin Pirzada
2016-10-01
Full Text Available For a graph $G$ with vertex set $V(G=\\{v_1, v_2, \\dots, v_n\\}$, let $S$ be the covering set of $G$ having the maximum degree over all the minimum covering sets of $G$. Let $N_S[v]=\\{u\\in S : uv \\in E(G \\}\\cup \\{v\\}$ be the closed neighbourhood of the vertex $v$ with respect to $S.$ We define a square matrix $A_S(G= (a_{ij},$ by $a_{ij}=1,$ if $\\left |N_S[v_i]\\cap N_S[v_j] \\right| \\geq 1, i\
Dynamic hyperbolic geometry: building intuition and understanding mediated by a Euclidean model
Moreno-Armella, Luis; Brady, Corey; Elizondo-Ramirez, Rubén
2018-05-01
This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become thinkable the mathematical community needed to accumulate over twenty centuries of reflection and effort: a precious instance of distributed intelligence at the cultural level. In geometry education after this crisis, relations between intuitions and geometrical reasoning must be established philosophically, rather than taken for granted. One approach seeks intuitive supports only for Euclidean explorations, viewing non-Euclidean inquiry as fundamentally non-intuitive in nature. We argue for moving beyond such an impoverished approach, using dynamic geometry environments to develop new intuitions even in the extremely challenging setting of hyperbolic geometry. Our efforts reverse the typical direction, using formal structures as a source for a new family of intuitions that emerge from exploring a digital model of hyperbolic geometry. This digital model is elaborated within a Euclidean dynamic geometry environment, enabling a conceptual dance that re-configures Euclidean knowledge as a support for building intuitions in hyperbolic space-intuitions based not directly on physical experience but on analogies extending Euclidean concepts.
Fundamentals of algebraic graph transformation
Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele
2006-01-01
Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...
The STAPL Parallel Graph Library
Harshvardhan,
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.
Entropy, extremality, euclidean variations, and the equations of motion
Dong, Xi; Lewkowycz, Aitor
2018-01-01
We study the Euclidean gravitational path integral computing the Rényi entropy and analyze its behavior under small variations. We argue that, in Einstein gravity, the extremality condition can be understood from the variational principle at the level of the action, without having to solve explicitly the equations of motion. This set-up is then generalized to arbitrary theories of gravity, where we show that the respective entanglement entropy functional needs to be extremized. We also extend this result to all orders in Newton's constant G N , providing a derivation of quantum extremality. Understanding quantum extremality for mixtures of states provides a generalization of the dual of the boundary modular Hamiltonian which is given by the bulk modular Hamiltonian plus the area operator, evaluated on the so-called modular extremal surface. This gives a bulk prescription for computing the relative entropies to all orders in G N . We also comment on how these ideas can be used to derive an integrated version of the equations of motion, linearized around arbitrary states.
Non-Euclidean Geometry, Nontrivial Topology and Quantum Vacuum Effects
Yurii A. Sitenko
2018-01-01
Full Text Available Space out of a topological defect of the Abrikosov–Nielsen–Olesen (ANO vortex type is locally flat but non-Euclidean. If a spinor field is quantized in such a space, then a variety of quantum effects are induced in the vacuum. On the basis of the continuum model for long-wavelength electronic excitations originating in the tight-binding approximation for the nearest-neighbor interaction of atoms in the crystal lattice, we consider quantum ground-state effects in Dirac materials with two-dimensional monolayer structures warped into nanocones by a disclination; the nonzero size of the disclination is taken into account, and a boundary condition at the edge of the disclination is chosen to ensure self-adjointness of the Dirac–Weyl Hamiltonian operator. We show that the quantum ground-state effects are independent of the disclination size, and we find circumstances in which they are independent of parameters of the boundary condition.
Biased discriminant euclidean embedding for content-based image retrieval.
Bian, Wei; Tao, Dacheng
2010-02-01
With many potential multimedia applications, content-based image retrieval (CBIR) has recently gained more attention for image management and web search. A wide variety of relevance feedback (RF) algorithms have been developed in recent years to improve the performance of CBIR systems. These RF algorithms capture user's preferences and bridge the semantic gap. However, there is still a big room to further the RF performance, because the popular RF algorithms ignore the manifold structure of image low-level visual features. In this paper, we propose the biased discriminative Euclidean embedding (BDEE) which parameterises samples in the original high-dimensional ambient space to discover the intrinsic coordinate of image low-level visual features. BDEE precisely models both the intraclass geometry and interclass discrimination and never meets the undersampled problem. To consider unlabelled samples, a manifold regularization-based item is introduced and combined with BDEE to form the semi-supervised BDEE, or semi-BDEE for short. To justify the effectiveness of the proposed BDEE and semi-BDEE, we compare them against the conventional RF algorithms and show a significant improvement in terms of accuracy and stability based on a subset of the Corel image gallery.
Euclidean quantum field theory and the Hawking effect
Lapedes, A.S.
1978-01-01
Complex analytic continuation in a time variable in order to define a Feynman propagator is investigated in a general relativistic context. When external electric fields are present a complex analytic continuation in the electric charge is also introduced. The new Euclidean formalism is checked by reproducing Schwinger's special relativistic result for pair creation by an external, homogenous, electric field, and then applied to the Robinson-Bertotti universe. The Robinson-Bertotti universe, although unphysical, provides an interesting theoretical laboratory in which to investigate quantum effects, much as the unphysical Taub-NUT (Newman-Unti-Tamburino) universe does for purely classical general relativity. A conformally related problem of pair creation by a supercritically charged nucleus is also considered, and a sensible resolution is obtained to this classic problem. The essential mathematical point throughout is the use of the Feynman path-integral form of the propagator to motivate replacing hyperbolic equations by elliptic equations. The unique, bounded solution for the elliptic Green's function is then analytically continued back to physical values to define the Feynman Green's function
Euclidean supersymmetric solutions with the self-dual Weyl tensor
Masato Nozawa
2017-07-01
Full Text Available We explore the Euclidean supersymmetric solutions admitting the self-dual gauge field in the framework of N=2 minimal gauged supergravity in four dimensions. According to the classification scheme utilizing the spinorial geometry or the bilinears of Killing spinors, the general solution preserves one quarter of supersymmetry and is described by the Przanowski–Tod class with the self-dual Weyl tensor. We demonstrate that there exists an additional Killing spinor, provided the Przanowski–Tod metric admits a Killing vector that commutes with the principal one. The proof proceeds by recasting the metric into another Przanowski–Tod form. This formalism enables us to show that the self-dual Reissner–Nordström–Taub–NUT–AdS metric possesses a second Killing spinor, which has been missed over many years. We also address the supersymmetry when the Przanowski–Tod space is conformal to each of the self-dual ambi-toric Kähler metrics. It turns out that three classes of solutions are all reduced to the self-dual Carter family, by virtue of the nondegenerate Killing–Yano tensor.
Numerical evaluation of tensor Feynman integrals in Euclidean kinematics
Gluza, J.; Kajda [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, T.; Yundin, V. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2010-10-15
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4-2{epsilon} dimensions. One method uses Mellin-Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop {epsilon}-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sectordecomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin-Barnes representations and sector decompositions, is compared. The computational packages are publicly available. (orig.)
White, AT
1985-01-01
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.
Ribes, Luis
2017-01-01
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open quest...
Subdominant pseudoultrametric on graphs
Dovgoshei, A A; Petrov, E A [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)
2013-08-31
Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.
Cheung, King Sing
2014-01-01
Petri nets are a formal and theoretically rich model for the modelling and analysis of systems. A subclass of Petri nets, augmented marked graphs possess a structure that is especially desirable for the modelling and analysis of systems with concurrent processes and shared resources.This monograph consists of three parts: Part I provides the conceptual background for readers who have no prior knowledge on Petri nets; Part II elaborates the theory of augmented marked graphs; finally, Part III discusses the application to system integration. The book is suitable as a first self-contained volume
Dayal, Amit; Brock, David
2018-01-01
Prashant Chandrasekar, a lead developer for the Social Interactome project, has tasked the team with creating a graph representation of the data collected from the social networks involved in that project. The data is currently stored in a MySQL database. The client requested that the graph database be Cayley, but after a literature review, Neo4j was chosen. The reasons for this shift will be explained in the design section. Secondarily, the team was tasked with coming up with three scena...
Stevanovic, Dragan
2015-01-01
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the
Space-efficient path-reporting approximate distance oracles
Elkin, Michael; Neiman, Ofer; Wulff-Nilsen, Christian
2016-01-01
We consider approximate path-reporting distance oracles, distance labeling and labeled routing with extremely low space requirements, for general undirected graphs. For distance oracles, we show how to break the nlogn space bound of Thorup and Zwick if approximate paths rather than distances need...
Dynamic airspace configuration method based on a weighted graph model
Chen Yangzhou
2014-08-01
Full Text Available This paper proposes a new method for dynamic airspace configuration based on a weighted graph model. The method begins with the construction of an undirected graph for the given airspace, where the vertices represent those key points such as airports, waypoints, and the edges represent those air routes. Those vertices are used as the sites of Voronoi diagram, which divides the airspace into units called as cells. Then, aircraft counts of both each cell and of each air-route are computed. Thus, by assigning both the vertices and the edges with those aircraft counts, a weighted graph model comes into being. Accordingly the airspace configuration problem is described as a weighted graph partitioning problem. Then, the problem is solved by a graph partitioning algorithm, which is a mixture of general weighted graph cuts algorithm, an optimal dynamic load balancing algorithm and a heuristic algorithm. After the cuts algorithm partitions the model into sub-graphs, the load balancing algorithm together with the heuristic algorithm transfers aircraft counts to balance workload among sub-graphs. Lastly, airspace configuration is completed by determining the sector boundaries. The simulation result shows that the designed sectors satisfy not only workload balancing condition, but also the constraints such as convexity, connectivity, as well as minimum distance constraint.
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-01-01
Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most
Handbook of graph grammars and computing by graph transformation
Engels, G; Kreowski, H J; Rozenberg, G
1999-01-01
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran
Topics in graph theory graphs and their Cartesian product
Imrich, Wilfried; Rall, Douglas F
2008-01-01
From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.
Local adjacency metric dimension of sun graph and stacked book graph
Yulisda Badri, Alifiah; Darmaji
2018-03-01
A graph is a mathematical system consisting of a non-empty set of nodes and a set of empty sides. One of the topics to be studied in graph theory is the metric dimension. Application in the metric dimension is the navigation robot system on a path. Robot moves from one vertex to another vertex in the field by minimizing the errors that occur in translating the instructions (code) obtained from the vertices of that location. To move the robot must give different instructions (code). In order for the robot to move efficiently, the robot must be fast to translate the code of the nodes of the location it passes. so that the location vertex has a minimum distance. However, if the robot must move with the vertex location on a very large field, so the robot can not detect because the distance is too far.[6] In this case, the robot can determine its position by utilizing location vertices based on adjacency. The problem is to find the minimum cardinality of the required location vertex, and where to put, so that the robot can determine its location. The solution to this problem is the dimension of adjacency metric and adjacency metric bases. Rodrguez-Velzquez and Fernau combine the adjacency metric dimensions with local metric dimensions, thus becoming the local adjacency metric dimension. In the local adjacency metric dimension each vertex in the graph may have the same adjacency representation as the terms of the vertices. To obtain the local metric dimension of values in the graph of the Sun and the stacked book graph is used the construction method by considering the representation of each adjacent vertex of the graph.
Bisseling, R.H.; Byrka, J.; Cerav-Erbas, S.; Gvozdenovic, N.; Lorenz, M.; Pendavingh, R.A.; Reeves, C.; Röger, M.; Verhoeven, A.; Berg, van den J.B.; Bhulai, S.; Hulshof, J.; Koole, G.; Quant, C.; Williams, J.F.
2006-01-01
Splitting a large software system into smaller and more manageable units has become an important problem for many organizations. The basic structure of a software system is given by a directed graph with vertices representing the programs of the system and arcs representing calls from one program to
Budhiraja, A.S.; Mukherjee, D.; Wu, R.
2017-01-01
We consider a variation of the supermarket model in which the servers can communicate with their neighbors and where the neighborhood relationships are described in terms of a suitable graph. Tasks with unit-exponential service time distributions arrive at each vertex as independent Poisson
Kucharik, Marcel; Hofacker, Ivo; Stadler, Peter
2014-01-01
of the folding free energy landscape, however, can provide the relevant information. Results We introduce the basin hopping graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect...
The partition dimension of cycle books graph
Santoso, Jaya; Darmaji
2018-03-01
Let G be a nontrivial and connected graph with vertex set V(G), edge set E(G) and S ⊆ V(G) with v ∈ V(G), the distance between v and S is d(v,S) = min{d(v,x)|x ∈ S}. For an ordered partition ∏ = {S 1, S 2, S 3,…, Sk } of V(G), the representation of v with respect to ∏ is defined by r(v|∏) = (d(v, S 1), d(v, S 2),…, d(v, Sk )). The partition ∏ is called a resolving partition of G if all representations of vertices are distinct. The partition dimension pd(G) is the smallest integer k such that G has a resolving partition set with k members. In this research, we will determine the partition dimension of Cycle Books {B}{Cr,m}. Cycle books graph {B}{Cr,m} is a graph consisting of m copies cycle Cr with the common path P 2. It is shown that the partition dimension of cycle books graph, pd({B}{C3,m}) is 3 for m = 2, 3, and m for m ≥ 4. pd({B}{C4,m}) is 3 + 2k for m = 3k + 2, 4 + 2(k ‑ 1) for m = 3k + 1, and 3 + 2(k ‑ 1) for m = 3k. pd({B}{C5,m}) is m + 1.
The STAPL Parallel Graph Library
Harshvardhan,; Fidel, Adam; Amato, Nancy M.; Rauchwerger, Lawrence
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable
Variational estimates for the mass gap of SU(2) Euclidean lattice gauge theory
Hari Dass, N.D.
1984-10-01
The purpose of this letter is to report on the progress made in our understanding of series expansions for the masses in lattice gauge theories by the application of variational techniques to the Euclidean SU(2) lattice gauge theory. (Auth.)
Euclidean action for vacuum decay in a de Sitter universe
Balek, V.; Demetrian, M.
2005-01-01
The behavior of the action of the instantons describing vacuum decay in a de Sitter is investigated. For a near-to-limit instanton (a Coleman-de Luccia instanton close to some Hawking-Moss instanton) we find approximate formulas for the Euclidean action by expanding the scalar field and the metric of the instanton in the powers of the scalar field amplitude. The order of the magnitude of the correction to the Hawking-Moss action depends on the order of the instanton (the number of crossings of the barrier by the scalar field): for instantons of odd and even orders the correction is of the fourth and third order in the scalar field amplitude, respectively. If a near-to-limit instanton of the first order exists in a potential with the curvature at the top of the barrier greater than 4x(Hubble constant) 2 , which is the case if the fourth derivative of the potential at the top of the barrier is greater than some negative limit value, the action of the instanton is less than the Hawking-Moss action and, consequently, the instanton determines the outcome of the vacuum decay if no other Coleman-de Luccia instanton is admitted by the potential. A numerical study shows that for the quartic potential the physical mode of the vacuum decay is given by the Coleman-de Luccia instanton of the first order also in the region of parameters in which the potential admits two instantons of the second order
Winlaw, Manda [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); De Sterck, Hans [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoffrey [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-26
In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.
Groupies in multitype random graphs
Shang, Yilun
2016-01-01
A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erd?s-R?nyi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.
Groupies in multitype random graphs.
Shang, Yilun
2016-01-01
A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erdős-Rényi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.
Temporal Representation in Semantic Graphs
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.
2007-01-01
A discrete-time quantum walk on a graph Γ is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup
Manton, Jonathan H.
2012-01-01
The Newton iteration is a popular method for minimising a cost function on Euclidean space. Various generalisations to cost functions defined on manifolds appear in the literature. In each case, the convergence rate of the generalised Newton iteration needed establishing from first principles. The present paper presents a framework for generalising iterative methods from Euclidean space to manifolds that ensures local convergence rates are preserved. It applies to any (memoryless) iterative m...
Classical and quantum integrability of 2D dilaton gravities in Euclidean space
Bergamin, L; Grumiller, D; Kummer, W; Vassilevich, D V
2005-01-01
Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a restricted class of topologies is consistent with the metric and the dilaton. A particular case of string motivated Liouville gravity is studied in detail. Path integral quantization in generic Euclidean dilaton gravity is performed non-perturbatively by analogy to the Minkowskian case
Euclidean Geometry Codes, minimum weight words and decodable error-patterns using bit-flipping
Høholdt, Tom; Justesen, Jørn; Jonsson, Bergtor
2005-01-01
We determine the number of minimum wigth words in a class of Euclidean Geometry codes and link the performance of the bit-flipping decoding algorithm to the geometry of the error patterns.......We determine the number of minimum wigth words in a class of Euclidean Geometry codes and link the performance of the bit-flipping decoding algorithm to the geometry of the error patterns....
Linearization of Euclidean Norm Dependent Inequalities Applied to Multibeam Satellites Design
Camino , Jean-Thomas; Artigues , Christian; Houssin , Laurent; Mourgues , Stéphane
2016-01-01
Euclidean norm computations over continuous variables appear naturally in the constraints or in the objective of many problems in the optimization literature, possibly defining non-convex feasible regions or cost functions. When some other variables have discrete domains, it positions the problem in the challenging Mixed Integer Nonlinear Programming (MINLP) class. For any MINLP where the nonlinearity is only present in the form of inequality constraints involving the Euclidean norm, we propo...
General Rotational Surfaces in Pseudo-Euclidean 4-Space with Neutral Metric
Aleksieva, Yana; Milousheva, Velichka; Turgay, Nurettin Cenk
2016-01-01
We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general rotational surfaces with plane meridian curves and give the complete classification of minimal general rotational surfaces of elliptic and hyperbolic type, general rotational surfaces with parallel normalized mean curvature vector field, flat general rotati...
A generalization of total graphs
M Afkhami
2018-04-12
Apr 12, 2018 ... product of any lower triangular matrix with the transpose of any element of U belongs to U. The ... total graph of R, which is denoted by T( (R)), is a simple graph with all elements of R as vertices, and ...... [9] Badawi A, On dot-product graph of a commutative ring, Communications in Algebra 43 (2015). 43–50.
Graph transformation tool contest 2008
Rensink, Arend; van Gorp, Pieter
This special section is the outcome of the graph transformation tool contest organised during the Graph-Based Tools (GraBaTs) 2008 workshop, which took place as a satellite event of the International Conference on Graph Transformation (ICGT) 2008. The contest involved two parts: three “off-line case
On dominator colorings in graphs
colors required for a dominator coloring of G is called the dominator .... Theorem 1.3 shows that the complete graph Kn is the only connected graph of order n ... Conversely, if a graph G satisfies condition (i) or (ii), it is easy to see that χd(G) =.
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.
Kim, Won Hwa; Chung, Moo K; Singh, Vikas
2013-01-01
The analysis of 3-D shape meshes is a fundamental problem in computer vision, graphics, and medical imaging. Frequently, the needs of the application require that our analysis take a multi-resolution view of the shape's local and global topology, and that the solution is consistent across multiple scales. Unfortunately, the preferred mathematical construct which offers this behavior in classical image/signal processing, Wavelets, is no longer applicable in this general setting (data with non-uniform topology). In particular, the traditional definition does not allow writing out an expansion for graphs that do not correspond to the uniformly sampled lattice (e.g., images). In this paper, we adapt recent results in harmonic analysis, to derive Non-Euclidean Wavelets based algorithms for a range of shape analysis problems in vision and medical imaging. We show how descriptors derived from the dual domain representation offer native multi-resolution behavior for characterizing local/global topology around vertices. With only minor modifications, the framework yields a method for extracting interest/key points from shapes, a surprisingly simple algorithm for 3-D shape segmentation (competitive with state of the art), and a method for surface alignment (without landmarks). We give an extensive set of comparison results on a large shape segmentation benchmark and derive a uniqueness theorem for the surface alignment problem.
Wiener index and Diameter of a Planar Graph in Subquadratic Time
Wulff-Nilsen, Christian
2009-01-01
Consider the problem of computing the sum of distances between each pair of vertices of an unweighted graph. This sum is also known as the Wiener index of the graph, a generalization of a definition given by H. Wiener in 1947. A molecular topological index is a value obtained from the graph...... structure of a molecule such that this value (hopefully) correlates with physical and/or chemical properties of the molecule. The Wiener index is perhaps the most studied molecular topological index with more than a thousand publications. It is open whether the Wiener index of a planar graph can be obtained...... in subquadratic time. In my talk, I will solve this open problem by exhibiting an O(n2 log log n / log n) time algorithm, where n is the size of the graph. A simple modification yields an algorithm with the same time bound that computes the diameter (maximum distance between any vertex pair) of a planar graph. I...
Cyclic labellings with constraints at two distances
Leese, R; Noble, S D
2004-01-01
Motivated by problems in radio channel assignment, we consider the vertex-labelling of graphs with non-negative integers. The objective is to minimise the span of the labelling, subject to constraints imposed at graph distances one and two. We show that the minimum span is (up to rounding) a piecewise linear function of the constraints, and give a complete specification, together with associated optimal assignments, for trees and cycles.
Harary, Frank
2015-01-01
Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc
Spectral fluctuations of quantum graphs
Pluhař, Z.; Weidenmüller, H. A.
2014-01-01
We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry
Dynamic Representations of Sparse Graphs
Brodal, Gerth Stølting; Fagerberg, Rolf
1999-01-01
We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....
Domination criticality in product graphs
M.R. Chithra
2015-07-01
Full Text Available A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G with connected domination number, γc(G=2,3 and characterize such graphs. Also, we characterize the k−γ-vertex (edge critical graphs and k−γc-vertex (edge critical graphs for k=2,3 where γ denotes the domination number of G. We also discuss the vertex criticality in grids.
Graph Creation, Visualisation and Transformation
Maribel Fernández
2010-03-01
Full Text Available We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting.
Study of Chromatic parameters of Line, Total, Middle graphs and Graph operators of Bipartite graph
Nagarathinam, R.; Parvathi, N.
2018-04-01
Chromatic parameters have been explored on the basis of graph coloring process in which a couple of adjacent nodes receives different colors. But the Grundy and b-coloring executes maximum colors under certain restrictions. In this paper, Chromatic, b-chromatic and Grundy number of some graph operators of bipartite graph has been investigat
Random geometric graphs with general connection functions
Dettmann, Carl P.; Georgiou, Orestis
2016-03-01
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H (r ) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.
Graph Sampling for Covariance Estimation
Chepuri, Sundeep Prabhakar
2017-04-25
In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non-parametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.
Hendrix, William; Jenkins, John; Padmanabhan, Kanchana; Chakraborty, Arpan
2014-01-01
Practical Graph Mining with R presents a "do-it-yourself" approach to extracting interesting patterns from graph data. It covers many basic and advanced techniques for the identification of anomalous or frequently recurring patterns in a graph, the discovery of groups or clusters of nodes that share common patterns of attributes and relationships, the extraction of patterns that distinguish one category of graphs from another, and the use of those patterns to predict the category of new graphs. Hands-On Application of Graph Data Mining Each chapter in the book focuses on a graph mining task, such as link analysis, cluster analysis, and classification. Through applications using real data sets, the book demonstrates how computational techniques can help solve real-world problems. The applications covered include network intrusion detection, tumor cell diagnostics, face recognition, predictive toxicology, mining metabolic and protein-protein interaction networks, and community detection in social networks. De...
Canonical Labelling of Site Graphs
Nicolas Oury
2013-06-01
Full Text Available We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an extension of Hopcroft's partition refinement algorithm. All run in quadratic worst case time individually. However, one of the edge enumeration algorithms runs in sub-quadratic time for graphs with "many" automorphisms, and the partition refinement algorithm runs in sub-quadratic time for graphs with "few" bisimulation equivalences. This suite of algorithms was chosen based on the expectation that graphs fall in one of those two categories. If that is the case, a combined algorithm runs in sub-quadratic worst case time. Whether this expectation is reasonable remains an interesting open problem.
Learning heat diffusion graphs
Thanou, Dorina; Dong, Xiaowen; Kressner, Daniel; Frossard, Pascal
2016-01-01
Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or pre-determined sensing arrangements, like in road transportation networks for example. In general though, the data structure is not readily available and becomes pretty difficult to define. In particular, the global smoothness assumptions, that most of the...
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Understanding Charts and Graphs.
1987-07-28
Farenheit degrees, which have no Onaturalo zero ); finally, ratio scales have numbers that are ordered so that the magnitudes of differences are important and...system. They have to do with the very nature of how marks serve as meaningful symbols. In the ideal case, a chart or graph will be absolutely unambiguous...and these laws comprise this principle (see Stevens, 1974). Absolute discriminability: A minimal magnitude of a mark is necessary for it to be detected
On the Additively Weighted Harary Index of Some Composite Graphs
Behrooz Khosravi
2017-03-01
Full Text Available The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. The additively weighted Harary index H A ( G is a modification of the Harary index in which the contributions of vertex pairs are weighted by the sum of their degrees. This new invariant was introduced in (Alizadeh, Iranmanesh and Došlić. Additively weighted Harary index of some composite graphs, Discrete Math, 2013 and they posed the following question: What is the behavior of H A ( G when G is a composite graph resulting for example by: splice, link, corona and rooted product? We investigate the additively weighted Harary index for these standard graph products. Then we obtain lower and upper bounds for some of them.
Measuring the Accuracy of Simple Evolving Connectionist System with Varying Distance Formulas
Al-Khowarizmi; Sitompul, O. S.; Suherman; Nababan, E. B.
2017-12-01
Simple Evolving Connectionist System (SECoS) is a minimal implementation of Evolving Connectionist Systems (ECoS) in artificial neural networks. The three-layer network architecture of the SECoS could be built based on the given input. In this study, the activation value for the SECoS learning process, which is commonly calculated using normalized Hamming distance, is also calculated using normalized Manhattan distance and normalized Euclidean distance in order to compare the smallest error value and best learning rate obtained. The accuracy of measurement resulted by the three distance formulas are calculated using mean absolute percentage error. In the training phase with several parameters, such as sensitivity threshold, error threshold, first learning rate, and second learning rate, it was found that normalized Euclidean distance is more accurate than both normalized Hamming distance and normalized Manhattan distance. In the case of beta fibrinogen gene -455 G/A polymorphism patients used as training data, the highest mean absolute percentage error value is obtained with normalized Manhattan distance compared to normalized Euclidean distance and normalized Hamming distance. However, the differences are very small that it can be concluded that the three distance formulas used in SECoS do not have a significant effect on the accuracy of the training results.
On approximately fair cost allocation in Euclidean TSP games
Faigle, U.; Fekete, Sándor P.; Hochstättler, Winfried; Kern, Walter
1998-01-01
We consider the problem of allocating the cost of an optimal traveling salesman tour in a fair way among the nodes visited; in particular, we focus on the case where the distance matrix of the underlying TSP problem satisfies the triangle inequality. We thereby use the model of TSP games in the
Graphs cospectral with a friendship graph or its complement
Alireza Abdollahi
2013-12-01
Full Text Available Let $n$ be any positive integer and let $F_n$ be the friendship (or Dutch windmill graph with $2n+1$ vertices and $3n$ edges. Here we study graphs with the same adjacency spectrum as the $F_n$. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let $G$ be a graph cospectral with $F_n$. Here we prove that if $G$ has no cycle of length $4$ or $5$, then $Gcong F_n$. Moreover if $G$ is connected and planar then $Gcong F_n$.All but one of connected components of $G$ are isomorphic to $K_2$.The complement $overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues, that is, if $overline{F_n}$ is cospectral with a graph $H$, then $Hcong overline{F_n}$.
Video surveillance using distance maps
Schouten, Theo E.; Kuppens, Harco C.; van den Broek, Egon L.
2006-02-01
Human vigilance is limited; hence, automatic motion and distance detection is one of the central issues in video surveillance. Hereby, many aspects are of importance, this paper specially addresses: efficiency, achieving real-time performance, accuracy, and robustness against various noise factors. To obtain fully controlled test environments, an artificial development center for robot navigation is introduced in which several parameters can be set (e.g., number of objects, trajectories and type and amount of noise). In the videos, for each following frame, movement of stationary objects is detected and pixels of moving objects are located from which moving objects are identified in a robust way. An Exact Euclidean Distance Map (E2DM) is utilized to determine accurately the distances between moving and stationary objects. Together with the determined distances between moving objects and the detected movement of stationary objects, this provides the input for detecting unwanted situations in the scene. Further, each intelligent object (e.g., a robot), is provided with its E2DM, allowing the object to plan its course of action. Timing results are specified for each program block of the processing chain for 20 different setups. So, the current paper presents extensive, experimentally controlled research on real-time, accurate, and robust motion detection for video surveillance, using E2DMs, which makes it a unique approach.
Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs
Bensmail, Julien; Renault, Gabriel
2016-01-01
An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪⋯∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently co...
X-Graphs: Language and Algorithms for Heterogeneous Graph Streams
2017-09-01
are widely used by academia and industry. 15. SUBJECT TERMS Data Analytics, Graph Analytics, High-Performance Computing 16. SECURITY CLASSIFICATION...form the core of the DeepDive Knowledge Construction System. 2 INTRODUCTION The goal of the X-Graphs project was to develop computational techniques...memory multicore machine. Ringo is based on Snap.py and SNAP, and uses Python . Ringo now allows the integration of Delite DSL Framework Graph
Hajime Matsui
2017-12-01
Full Text Available In this study, we consider codes over Euclidean domains modulo their ideals. In the first half of the study, we deal with arbitrary Euclidean domains. We show that the product of generator matrices of codes over the rings mod a and mod b produces generator matrices of all codes over the ring mod a b , i.e., this correspondence is onto. Moreover, we show that if a and b are coprime, then this correspondence is one-to-one, i.e., there exist unique codes over the rings mod a and mod b that produce any given code over the ring mod a b through the product of their generator matrices. In the second half of the study, we focus on the typical Euclidean domains such as the rational integer ring, one-variable polynomial rings, rings of Gaussian and Eisenstein integers, p-adic integer rings and rings of one-variable formal power series. We define the reduced generator matrices of codes over Euclidean domains modulo their ideals and show their uniqueness. Finally, we apply our theory of reduced generator matrices to the Hecke rings of matrices over these Euclidean domains.
Epileptic Seizure Detection with Log-Euclidean Gaussian Kernel-Based Sparse Representation.
Yuan, Shasha; Zhou, Weidong; Wu, Qi; Zhang, Yanli
2016-05-01
Epileptic seizure detection plays an important role in the diagnosis of epilepsy and reducing the massive workload of reviewing electroencephalography (EEG) recordings. In this work, a novel algorithm is developed to detect seizures employing log-Euclidean Gaussian kernel-based sparse representation (SR) in long-term EEG recordings. Unlike the traditional SR for vector data in Euclidean space, the log-Euclidean Gaussian kernel-based SR framework is proposed for seizure detection in the space of the symmetric positive definite (SPD) matrices, which form a Riemannian manifold. Since the Riemannian manifold is nonlinear, the log-Euclidean Gaussian kernel function is applied to embed it into a reproducing kernel Hilbert space (RKHS) for performing SR. The EEG signals of all channels are divided into epochs and the SPD matrices representing EEG epochs are generated by covariance descriptors. Then, the testing samples are sparsely coded over the dictionary composed by training samples utilizing log-Euclidean Gaussian kernel-based SR. The classification of testing samples is achieved by computing the minimal reconstructed residuals. The proposed method is evaluated on the Freiburg EEG dataset of 21 patients and shows its notable performance on both epoch-based and event-based assessments. Moreover, this method handles multiple channels of EEG recordings synchronously which is more speedy and efficient than traditional seizure detection methods.
Generalizing a Categorization of Students' Interpretations of Linear Kinematics Graphs
Bollen, Laurens; De Cock, Mieke; Zuza, Kristina; Guisasola, Jenaro; van Kampen, Paul
2016-01-01
We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque…
Endomorphisms of graph algebras
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D...... that the restriction to the diagonal MASA of an automorphism which globally preserves both D_E and the core AF-subalgebra eventually commutes with the corresponding one-sided shift. Secondly, we exhibit several properties of proper endomorphisms, investigate invertibility of localized endomorphisms both on C...
Yap, Hian-Poh
1996-01-01
This book provides an up-to-date and rapid introduction to an important and currently active topic in graph theory. The author leads the reader to the forefront of research in this area. Complete and easily readable proofs of all the main theorems, together with numerous examples, exercises and open problems are given. The book is suitable for use as a textbook or as seminar material for advanced undergraduate and graduate students. The references are comprehensive and so it will also be useful for researchers as a handbook.
Graph Algorithm Animation with Grrr
Rodgers, Peter; Vidal, Natalia
2000-01-01
We discuss geometric positioning, highlighting of visited nodes and user defined highlighting that form the algorithm animation facilities in the Grrr graph rewriting programming language. The main purpose of animation was initially for the debugging and profiling of Grrr code, but recently it has been extended for the purpose of teaching algorithms to undergraduate students. The animation is restricted to graph based algorithms such as graph drawing, list manipulation or more traditional gra...
Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing.
Elmoataz, Abderrahim; Lezoray, Olivier; Bougleux, Sébastien
2008-07-01
We introduce a nonlocal discrete regularization framework on weighted graphs of the arbitrary topologies for image and manifold processing. The approach considers the problem as a variational one, which consists of minimizing a weighted sum of two energy terms: a regularization one that uses a discrete weighted p-Dirichlet energy and an approximation one. This is the discrete analogue of recent continuous Euclidean nonlocal regularization functionals. The proposed formulation leads to a family of simple and fast nonlinear processing methods based on the weighted p-Laplace operator, parameterized by the degree p of regularity, the graph structure and the graph weight function. These discrete processing methods provide a graph-based version of recently proposed semi-local or nonlocal processing methods used in image and mesh processing, such as the bilateral filter, the TV digital filter or the nonlocal means filter. It works with equal ease on regular 2-D and 3-D images, manifolds or any data. We illustrate the abilities of the approach by applying it to various types of images, meshes, manifolds, and data represented as graphs.
Detection at a distance of atomic bomb tests
Nahmias, M E
1954-01-01
Nahmias describes the radioassay of air, rain, and snowfall as the basis for detecting atomic bomb tests. Tables and graphs give time vs. Ra equivalents, distance vs Roentgens/h of radiation, and distribution of radioelements which can be expected.
Generalized hypercube graph $\\Q_n(S$, graph products and self-orthogonal codes
Pani Seneviratne
2016-01-01
Full Text Available A generalized hypercube graph $\\Q_n(S$ has $\\F_{2}^{n}=\\{0,1\\}^n$ as the vertex set and two vertices being adjacent whenever their mutual Hamming distance belongs to $S$, where $n \\ge 1$ and $S\\subseteq \\{1,2,\\ldots, n\\}$. The graph $\\Q_n(\\{1\\}$ is the $n$-cube, usually denoted by $\\Q_n$.We study graph boolean products $G_1 = \\Q_n(S\\times \\Q_1, G_2 = \\Q_{n}(S\\wedge \\Q_1$, $G_3 = \\Q_{n}(S[\\Q_1]$ and show that binary codes from neighborhood designs of $G_1, G_2$ and $G_3$ are self-orthogonal for all choices of $n$ and $S$. More over, we show that the class of codes $C_1$ are self-dual. Further we find subgroups of the automorphism group of these graphs and use these subgroups to obtain PD-sets for permutation decoding. As an example we find a full error-correcting PD set for the binary $[32, 16, 8]$ extremal self-dual code.
Optimization Problems on Threshold Graphs
Elena Nechita
2010-06-01
Full Text Available During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predeterminate properties, as well as combinations of such decompositions. In this paper we characterize threshold graphs using the weakly decomposition, determine: density and stability number, Wiener index and Wiener polynomial for threshold graphs.
Eulerian Graphs and Related Topics
Fleischner, Herbert
1990-01-01
The two volumes comprising Part 1 of this work embrace the theme of Eulerian trails and covering walks. They should appeal both to researchers and students, as they contain enough material for an undergraduate or graduate graph theory course which emphasizes Eulerian graphs, and thus can be read by any mathematician not yet familiar with graph theory. But they are also of interest to researchers in graph theory because they contain many recent results, some of which are only partial solutions to more general problems. A number of conjectures have been included as well. Various problems (such a
Robert F. Love
2001-01-01
Full Text Available Distance predicting functions may be used in a variety of applications for estimating travel distances between points. To evaluate the accuracy of a distance predicting function and to determine its parameters, a goodness-of-fit criteria is employed. AD (Absolute Deviations, SD (Squared Deviations and NAD (Normalized Absolute Deviations are the three criteria that are mostly employed in practice. In the literature some assumptions have been made about the properties of each criterion. In this paper, we present statistical analyses performed to compare the three criteria from different perspectives. For this purpose, we employ the ℓkpθ-norm as the distance predicting function, and statistically compare the three criteria by using normalized absolute prediction error distributions in seventeen geographical regions. We find that there exist no significant differences between the criteria. However, since the criterion SD has desirable properties in terms of distance modelling procedures, we suggest its use in practice.
Multivariate Welch t-test on distances.
Alekseyenko, Alexander V
2016-12-01
Permutational non-Euclidean analysis of variance, PERMANOVA, is routinely used in exploratory analysis of multivariate datasets to draw conclusions about the significance of patterns visualized through dimension reduction. This method recognizes that pairwise distance matrix between observations is sufficient to compute within and between group sums of squares necessary to form the (pseudo) F statistic. Moreover, not only Euclidean, but arbitrary distances can be used. This method, however, suffers from loss of power and type I error inflation in the presence of heteroscedasticity and sample size imbalances. We develop a solution in the form of a distance-based Welch t-test, [Formula: see text], for two sample potentially unbalanced and heteroscedastic data. We demonstrate empirically the desirable type I error and power characteristics of the new test. We compare the performance of PERMANOVA and [Formula: see text] in reanalysis of two existing microbiome datasets, where the methodology has originated. The source code for methods and analysis of this article is available at https://github.com/alekseyenko/Tw2 Further guidance on application of these methods can be obtained from the author. alekseye@musc.edu. © The Author 2016. Published by Oxford University Press.
Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?
Mehmet Fatih Öçal
2017-01-01
Full Text Available Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students’ learning during graphing functions. However, the display of graphs of functions that students sketched by hand may be relatively different when compared to the correct forms sketched using graphing software. The possible misleading effects of this situation brought a discussion of a misconception (asymptote misconception on graphing functions. The purpose of this study is two- fold. First of all, this study investigated whether using graphing software (GeoGebra in this case helps students to determine and resolve this misconception in calculus classrooms. Second, the reasons for this misconception are sought. The multiple case study was utilized in this study. University students in two calculus classrooms who received instructions with (35 students or without GeoGebra assisted instructions (32 students were compared according to whether they fell into this misconception on graphing basic functions (1/x, lnx, ex. In addition, students were interviewed to reveal the reasons behind this misconception. Data were analyzed by means of descriptive and content analysis methods. The findings indicated that those who received GeoGebra assisted instruction were better in resolving it. In addition, the reasons behind this misconception were found to be teacher-based, exam-based and some other factors.
On the Convergence and Law of Large Numbers for the Non-Euclidean Lp -Means
George Livadiotis
2017-05-01
Full Text Available This paper describes and proves two important theorems that compose the Law of Large Numbers for the non-Euclidean L p -means, known to be true for the Euclidean L 2 -means: Let the L p -mean estimator, which constitutes the specific functional that estimates the L p -mean of N independent and identically distributed random variables; then, (i the expectation value of the L p -mean estimator equals the mean of the distributions of the random variables; and (ii the limit N → ∞ of the L p -mean estimator also equals the mean of the distributions.
Intrinsic Regularization in a Lorentz invariant non-orthogonal Euclidean Space
Tornow, Carmen
2006-01-01
It is shown that the Lorentz transformations can be derived for a non-orthogonal Euclidean space. In this geometry one finds the same relations of special relativity as the ones known from the orthogonal Minkowski space. In order to illustrate the advantage of a non-orthogonal Euclidean metric the two-point Green’s function at x = 0 for a self-interacting scalar field is calculated. In contrast to the Minkowski space the one loop mass correction derived from this function gives a convergent r...
Scalar Green's functions in an Euclidean space with a conical-type line singularity
Guimaraes, M.E.X.; Linet, B.
1994-01-01
In an Euclidean space with a conical-type line singularity, we determine the Green's function for a charged massive scalar field interacting with a magnetic flux running through the line singularity. We give an integral expression of the Green's function and a local form in the neighbourhood of the point source, where it is the sum of the usual Green's function in Euclidean space and a regular term. As an application, we derive the vacuum energy-momentum tensor in the massless case for an arbitrary magnetic flux. (orig.)
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
Said Broumi; Mohamed Talea; Assia Bakali; Florentin Smarandache
2016-01-01
In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.
Graph Theory. 2. Vertex Descriptors and Graph Coloring
Lorentz JÄNTSCHI
2002-12-01
Full Text Available This original work presents the construction of a set of ten sequence matrices and their applications for ordering vertices in graphs. For every sequence matrix three ordering criteria are applied: lexicographic ordering, based on strings of numbers, corresponding to every vertex, extracted as rows from sequence matrices; ordering by the sum of path lengths from a given vertex; and ordering by the sum of paths, starting from a given vertex. We also examine a graph that has different orderings for the above criteria. We then proceed to demonstrate that every criterion induced its own partition of graph vertex. We propose the following theoretical result: both LAVS and LVDS criteria generate identical partitioning of vertices in any graph. Finally, a coloring of graph vertices according to introduced ordering criteria was proposed.
GraMi: Generalized Frequent Pattern Mining in a Single Large Graph
Saeedy, Mohammed El
2011-11-01
Mining frequent subgraphs is an important operation on graphs. Most existing work assumes a database of many small graphs, but modern applications, such as social networks, citation graphs or protein-protein interaction in bioinformatics, are modeled as a single large graph. Interesting interactions in such applications may be transitive (e.g., friend of a friend). Existing methods, however, search for frequent isomorphic (i.e., exact match) subgraphs and cannot discover many useful patterns. In this paper the authors propose GRAMI, a framework that generalizes frequent subgraph mining in a large single graph. GRAMI discovers frequent patterns. A pattern is a graph where edges are generalized to distance-constrained paths. Depending on the definition of the distance function, many instantiations of the framework are possible. Both directed and undirected graphs, as well as multiple labels per vertex, are supported. The authors developed an efficient implementation of the framework that models the frequency resolution phase as a constraint satisfaction problem, in order to avoid the costly enumeration of all instances of each pattern in the graph. The authors also implemented CGRAMI, a version that supports structural and semantic constraints; and AGRAMI, an approximate version that supports very large graphs. The experiments on real data demonstrate that the authors framework is up to 3 orders of magnitude faster and discovers more interesting patterns than existing approaches.
Xu, Zhiqiang
2017-02-16
Attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.
Xu, Zhiqiang; Cheng, James; Xiao, Xiaokui; Fujimaki, Ryohei; Muraoka, Yusuke
2017-01-01
Attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.
The planar cubic Cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Groupies in random bipartite graphs
Yilun Shang
2010-01-01
A vertex $v$ of a graph $G$ is called a groupie if its degree is notless than the average of the degrees of its neighbors. In thispaper we study the influence of bipartition $(B_1,B_2)$ on groupiesin random bipartite graphs $G(B_1,B_2,p)$ with both fixed $p$ and$p$ tending to zero.
Nested Dynamic Condition Response Graphs
Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs
2012-01-01
We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner...
Bell inequalities for graph states
Toth, G.; Hyllus, P.; Briegel, H.J.; Guehne, O.
2005-01-01
Full text: In the last years graph states have attracted an increasing interest in the field of quantum information theory. Graph states form a family of multi-qubit states which comprises many popular states such as the GHZ states and the cluster states. They also play an important role in applications. For instance, measurement based quantum computation uses graph states as resources. From a theoretical point of view, it is remarkable that graph states allow for a simple description in terms of stabilizing operators. In this contribution, we investigate the non-local properties of graph states. We derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positively of the partial transpose or the geometric measure of entanglement. (author)
Graph Sampling for Covariance Estimation
Chepuri, Sundeep Prabhakar; Leus, Geert
2017-01-01
specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non
Network reconstruction via graph blending
Estrada, Rolando
2016-05-01
Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.
A cluster algorithm for graphs
S. van Dongen
2000-01-01
textabstractA cluster algorithm for graphs called the emph{Markov Cluster algorithm (MCL~algorithm) is introduced. The algorithm provides basically an interface to an algebraic process defined on stochastic matrices, called the MCL~process. The graphs may be both weighted (with nonnegative weight)
Planar graphs theory and algorithms
Nishizeki, T
1988-01-01
Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.
Quantum chaos on discrete graphs
Smilansky, Uzy
2007-01-01
Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of ζ functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)
RJSplot: Interactive Graphs with R.
Barrios, David; Prieto, Carlos
2018-03-01
Data visualization techniques provide new methods for the generation of interactive graphs. These graphs allow a better exploration and interpretation of data but their creation requires advanced knowledge of graphical libraries. Recent packages have enabled the integration of interactive graphs in R. However, R provides limited graphical packages that allow the generation of interactive graphs for computational biology applications. The present project has joined the analytical power of R with the interactive graphical features of JavaScript in a new R package (RJSplot). It enables the easy generation of interactive graphs in R, provides new visualization capabilities, and contributes to the advance of computational biology analytical methods. At present, 16 interactive graphics are available in RJSplot, such as the genome viewer, Manhattan plots, 3D plots, heatmaps, dendrograms, networks, and so on. The RJSplot package is freely available online at http://rjsplot.net. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Nichols, Jeri Ann
This study examined the relationship between mathematics background and performance on graph-related problems in physics before and after instruction on the graphical analysis of motion and several microcomputer-based laboratory experiences. Students identified as either having or not having a graphing technology enhanced precalculus mathematics background were further categorized into one of four groups according to mathematics placement at the university. The performances of these groups were compared to identity differences. Pre- and Post-test data were collected from 589 students and 312 students during Autumn Quarter 1990 and Winter Quarter 1991 respectively. Background information was collected from each student. Significant differences were found between students with the technology enhanced mathematics background and those without when considering the entire populations both quarters. The students with the technology background were favored Autumn quarter and students without the technology background were favored Winter quarter. However, the entire population included an underrepresentation of students at the highest and lowest placements; hence, these were eliminated from the analyses. No significant differences were found between the technology/no technology groups after the elimination of the underrepresented groups. All categories of students increased their mean scores from pretest to post-test; the average increase was 8.23 points Autumn Quarter and 11.41 points Winter Quarter. Males consistently outperformed females on both the pretest and the post-test Autumn 1990. All students found questions involving the concept of acceleration more difficult than questions involving velocity or distance. Questions requiring students to create graphs were more difficult than questions requiring students to interpret graphs. Further research involving a qualitative component is recommended to identify the specific skills students use when solving graph
L(2,1)-labelling of Circular-arc Graph
Paul, Satyabrata; Pal, Madhumangal; Pal, Anita
2014-01-01
An L(2,1)-labelling of a graph $G=(V, E)$ is $\\lambda_{2,1}(G)$ a function $f$ from the vertex set V (G) to the set of non-negative integers such that adjacent vertices get numbers at least two apart, and vertices at distance two get distinct numbers. The L(2,1)-labelling number denoted by $\\lambda_{2,1}(G)$ of $G$ is the minimum range of labels over all such labelling. In this article, it is shown that, for a circular-arc graph $G$, the upper bound of $\\lambda_{2,1}(G)$ is $\\Delta+3\\omega$, ...
On characterizing terrain visibility graphs
William Evans
2015-06-01
Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.
On Euclidean connections for su(1,1), suq(1,1) and the algebraic approach to scattering
Ionescu, R.A.
1994-11-01
We obtain a general Euclidean connection for su(1,1) and suq(1,1) algebras. Our Euclidean connection allows an algebraic derivation for the S matrix. These algebraic S matrices reduce to the known ones in suitable circumstances. Also, we obtain a map between su(1,1) and su q (1,1) representations. (author). 8 refs
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-11-12
Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most existing algorithms for graph embedding only rely on the topology information and fail to use the copious information in nodes as well as edges. As a result, their performance for many tasks may not be satisfactory. In this thesis, we proposed a novel and general framework for graph embedding with rich text information (GERI) through constructing a heterogeneous network, in which we integrate node and edge content information with graph topology. Specially, we designed a novel biased random walk to explore the constructed heterogeneous network with the notion of flexible neighborhood. Our sampling strategy can compromise between BFS and DFS local search on heterogeneous graph. To further improve our algorithm, we proposed semi-supervised GERI (SGERI), which learns graph embedding in an discriminative manner through heterogeneous network with label information. The efficacy of our method is demonstrated by extensive comparison experiments with 9 baselines over multi-label and multi-class classification on various datasets including Citeseer, Cora, DBLP and Wiki. It shows that GERI improves the Micro-F1 and Macro-F1 of node classification up to 10%, and SGERI improves GERI by 5% in Wiki.
CORECLUSTER: A Degeneracy Based Graph Clustering Framework
Giatsidis , Christos; Malliaros , Fragkiskos; Thilikos , Dimitrios M. ,; Vazirgiannis , Michalis
2014-01-01
International audience; Graph clustering or community detection constitutes an important task forinvestigating the internal structure of graphs, with a plethora of applications in several domains. Traditional tools for graph clustering, such asspectral methods, typically suffer from high time and space complexity. In thisarticle, we present \\textsc{CoreCluster}, an efficient graph clusteringframework based on the concept of graph degeneracy, that can be used along withany known graph clusteri...
The positive action conjecture and asymptotically euclidean metrics in quantum gravity
Gibbons, G.W.; Pope, C.N.
1979-01-01
The positive action conjecture requires that the action of any asymptotically Euclidean 4-dimensional Riemannian metric be positive, vanishing if and only if the space is flat. Because any Ricci flat, asymptotically Euclidean metric has zero action and is local extremum of the action which is a local minimum at flat space, the conjecture requires that there are no Ricci flat asymptotically Euclidean metrics other than flat space, which would establish that flat space is the only local minimum. We prove this for metrics on R 4 and a large class of more complicated topologies and for self-dual metrics. We show that if Rsupμsubμ >= 0 there are no bound states of the Dirac equation and discuss the relevance to possible baryon non-conserving processes mediated by gravitational instantons. We conclude that these are forbidden in the lowest stationary phase approximation. We give a detailed discussion of instantons invariant under an SU(2) or SO(3) isometry group. We find all regular solutions, none of which is asymptotically Euclidean and all of which possess a further Killing vector. In an appendix we construct an approximate self-dual metric on K3 - the only simply connected compact manifold which admits a self-dual metric. (orig.) [de
Usability Evaluation of an Augmented Reality System for Teaching Euclidean Vectors
Martin-Gonzalez, Anabel; Chi-Poot, Angel; Uc-Cetina, Victor
2016-01-01
Augmented reality (AR) is one of the emerging technologies that has demonstrated to be an efficient technological tool to enhance learning techniques. In this paper, we describe the development and evaluation of an AR system for teaching Euclidean vectors in physics and mathematics. The goal of this pedagogical tool is to facilitate user's…
Rooij, van I.; Stege, U.; Schactman, A.
2003-01-01
Recently there has been growing interest among psychologists in human performance on the Euclidean traveling salesperson problem (E-TSP). A debate has been initiated on what strategy people use in solving visually presented E-TSP instances. The most prominent hypothesis is the convex-hull
Pordt, A.
1985-10-01
The author describes the Mayer expansion in Euclidean lattice field theory by comparing it with the statistical mechanics of polymer systems. In this connection he discusses the Borel summability and the analyticity of the activities on the lattice. Furthermore the relations between renormalization and the Mayer expansion are considered. (HSI)
Loci of points in the Euclidean plane are deter- mined from ...
Loci of points in the Euclidean plane are deter- mined from prescribed relations of the points with given points, and/or, lines. The depen- dence of these relations on parameters lead to the differential equations representing the fam- ily of loci under concern. Incidentally most of the differential equations thus obtained are non ...
Faster exact algorithms for computing Steiner trees in higher dimensional Euclidean spaces
Fonseca, Rasmus; Brazil, Marcus; Winter, Pawel
The Euclidean Steiner tree problem asks for a network of minimum total length interconnecting a finite set of points in d-dimensional space. For d ≥ 3, only one practical algorithmic approach exists for this problem --- proposed by Smith in 1992. A number of refinements of Smith's algorithm have...
Non-Euclidean spacetime structure and the two-slit experiment
El Naschie, M.S.
2005-01-01
A simple mathematical model for the two-slit experiment is given to account for the wave-particle duality. Subsequently, the various solutions are interpreted via the experimental evidence as a property of the underlying non-Euclidean spacetime topology and geometry at the quantum level
Characterizations of Space Curves According to Bishop Darboux Vector in Euclidean 3-Space E3
Huseyin KOCAYIGIT; Ali OZDEMIR
2014-01-01
In this paper, we obtained some characterizations of space curves according to Bihop frame in Euclidean 3-space E3 by using Laplacian operator and Levi-Civita connection. Furthermore, we gave the general differential equations which characterize the space curves according to the Bishop Darboux vector and the normal Bishop Darboux vector.
Hierarchy of modular graph identities
D’Hoker, Eric; Kaidi, Justin
2016-01-01
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.
Semantic graphs and associative memories
Pomi, Andrés; Mizraji, Eduardo
2004-12-01
Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.
Hierarchy of modular graph identities
D’Hoker, Eric; Kaidi, Justin [Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy,University of California,Los Angeles, CA 90095 (United States)
2016-11-09
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.
XML Graphs in Program Analysis
Møller, Anders; Schwartzbach, Michael I.
2011-01-01
of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey the use of XML graphs for program analysis with four very different languages: XACT (XML in Java), Java Servlets (Web application programming), XSugar......XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...
Rabern, Landon
2007-01-01
We improve upper bounds on the chromatic number proven independently in \\cite{reedNote} and \\cite{ingo}. Our main lemma gives a sufficient condition for two paths in graph to be completely joined. Using this, we prove that if a graph has an optimal coloring with more than $\\frac{\\omega}{2}$ singleton color classes, then it satisfies $\\chi \\leq \\frac{\\omega + \\Delta + 1}{2}$. It follows that a graph satisfying $n - \\Delta < \\alpha + \\frac{\\omega - 1}{2}$ must also satisfy $\\chi \\leq \\frac{\\ome...
Graphs with Eulerian unit spheres
Knill, Oliver
2015-01-01
d-spheres in graph theory are inductively defined as graphs for which all unit spheres S(x) are (d-1)-spheres and that the removal of one vertex renders the graph contractible. Eulerian d-spheres are geometric d-spheres which are d+1 colorable. We prove here that G is an Eulerian sphere if and only if the degrees of all the (d-2)-dimensional sub-simplices in G are even. This generalizes a Kempe-Heawood result for d=2 and is work related to the conjecture that all d-spheres have chromatic numb...
Tailored graph ensembles as proxies or null models for real networks II: results on directed graphs
Roberts, E S; Coolen, A C C; Schlitt, T
2011-01-01
We generate new mathematical tools with which to quantify the macroscopic topological structure of large directed networks. This is achieved via a statistical mechanical analysis of constrained maximum entropy ensembles of directed random graphs with prescribed joint distributions for in- and out-degrees and prescribed degree-degree correlation functions. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies and complexities of these ensembles, and for information-theoretic distances. The results are applied to data on gene regulation networks.
Row—column visibility graph approach to two-dimensional landscapes
Xiao Qin; Pan Xue; Li Xin-Li; Stephen Mutua; Yang Hui-Jie; Jiang Yan; Wang Jian-Yong; Zhang Qing-Jun
2014-01-01
A new concept, called the row—column visibility graph, is proposed to map two-dimensional landscapes to complex networks. A cluster coverage is introduced to describe the extensive property of node clusters on a Euclidean lattice. Graphs mapped from fractals generated with the probability redistribution model behave scale-free. They have pattern-induced hierarchical organizations and comparatively much more extensive structures. The scale-free exponent has a negative correlation with the Hurst exponent, however, there is no deterministic relation between them. Graphs for fractals generated with the midpoint displacement model are exponential networks. When the Hurst exponent is large enough (e.g., H > 0.5), the degree distribution decays much more slowly, the average coverage becomes significant large, and the initially hierarchical structure at H < 0.5 is destroyed completely. Hence, the row—column visibility graph can be used to detect the pattern-related new characteristics of two-dimensional landscapes. (interdisciplinary physics and related areas of science and technology)
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.
Joh, C.H.; Arentze, T.A.; Timmermans, H.J.P.
2001-01-01
The application of a multidimensional sequence alignment method for classifying activity travel patterns is reported. The method was developed as an alternative to the existing classification methods suggested in the transportation literature. The relevance of the multidimensional sequence alignment
Pastore, J; Moler, E; Ballarin, V
2007-01-01
To quantify the efficiency of a segmentation method, it is necessary to do some validation experiments, consisting generally in comparing the result obtained against the expected result. The most direct method for validation is the comparison of a simple visual inspection between the automatic segmentation and a segmentation obtained manually by a specialist, but this method does not guarantee robustness. This work presents a new similarity parameter between a segmented object and a control object, that combines a measurement of spatial similarity through the Hausdorff metrics and the difference in the contour areas based on the symmetric difference between sets
Robust Point Matching for Non-Rigid Shapes: A Relaxation Labeling Based Approach
Zheng, Yefeng; Doermann, David S
2004-01-01
.... Based on this observation, we formulate point matching as a graph matching problem. Each point is a node in the graph, and two nodes are connected by an edge if their Euclidean distance is less...
Graph cut-based method for segmenting the left ventricle from MRI or echocardiographic images.
Bernier, Michael; Jodoin, Pierre-Marc; Humbert, Olivier; Lalande, Alain
2017-06-01
In this paper, we present a fast and interactive graph cut method for 3D segmentation of the endocardial wall of the left ventricle (LV) adapted to work on two of the most widely used modalities: magnetic resonance imaging (MRI) and echocardiography. Our method accounts for the fundamentally different nature of both modalities: 3D echocardiographic images have a low contrast, a poor signal-to-noise ratio and frequent signal drop, while MR images are more detailed but also cluttered and contain highly anisotropic voxels. The main characteristic of our method is to work in a 3D Bezier coordinate system instead of the original Euclidean space. This comes with several advantages, including an implicit shape prior and a result guarantied not to have any holes in it. The proposed method is made of 4 steps. First, a 3D sampling of the LV cavity is made based on a Bezier coordinate system. This allows to warp the input 3D image to a Bezier space in which a plane corresponds to an anatomically plausible 3D Euclidean bullet shape. Second, a 3D graph is built and an energy term (which is based on the image gradient and a 3D probability map) is assigned to each edge of the graph, some of which being given an infinite energy to ensure the resulting 3D structure passes through key anatomical points. Third, a max-flow min-cut procedure is executed on the energy graph to delineate the endocardial surface. And fourth, the resulting surface is projected back to the Euclidean space where a post-processing convex hull algorithm is applied on every short axis slice to remove local concavities. Results obtained on two datasets reveal that our method takes between 2 and 5s to segment a 3D volume, it has better results overall than most state-of-the-art methods on the CETUS echocardiographic dataset and is statistically as good as a human operator on MR images. Copyright © 2017 Elsevier Ltd. All rights reserved.
Properly colored connectivity of graphs
Li, Xueliang; Qin, Zhongmei
2018-01-01
A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references. Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introduction to proper connection of graphs for new and advanced researchers, a solid book for a graduate level topics course, or as a reference for those interested in expanding and further developing research in the area.
Graph anomalies in cyber communications
Vander Wiel, Scott A [Los Alamos National Laboratory; Storlie, Curtis B [Los Alamos National Laboratory; Sandine, Gary [Los Alamos National Laboratory; Hagberg, Aric A [Los Alamos National Laboratory; Fisk, Michael [Los Alamos National Laboratory
2011-01-11
Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail.
Open Graphs and Computational Reasoning
Lucas Dixon
2010-06-01
Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.
Woeginger, G.J.
1998-01-01
In this short note we argue that the toughness of split graphs can be computed in polynomial time. This solves an open problem from a recent paper by Kratsch et al. (Discrete Math. 150 (1996) 231–245).
Generating random networks and graphs
Coolen, Ton; Roberts, Ekaterina
2017-01-01
This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...
Graph theory and its applications
Gross, Jonathan L
2006-01-01
Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
Upper bound for the span of pencil graph
Parvathi, N.; Vimala Rani, A.
2018-04-01
An L(2,1)-Coloring or Radio Coloring or λ coloring of a graph is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x) ‑ f(y)| ≥ 2 if d(x,y) = 1 and |f(x) ‑ f(y)| ≥ 1 if d(x,y)=2, where d(x,y) denotes the distance between x and y in G. The L(2,1)-coloring number or span number λ(G) of G is the smallest number k such that G has an L(2,1)-coloring with max{f(v) : v ∈ V(G)} = k. [2]The minimum number of colors used in L(2,1)-coloring is called the radio number rn(G) of G (Positive integer). Griggs and yeh conjectured that λ(G) ≤ Δ2 for any simple graph with maximum degree Δ>2. In this article, we consider some special graphs like, n-sunlet graph, pencil graph families and derive its upper bound of (G) and rn(G).
Metrics for measuring distances in configuration spaces
Sadeghi, Ali; Ghasemi, S. Alireza; Schaefer, Bastian; Mohr, Stephan; Goedecker, Stefan; Lill, Markus A.
2013-01-01
In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint vectors satisfies the properties of a metric and can therefore safely be used to measure dissimilarities between configurations in the high dimensional configuration space. In particular we show that these metrics are a perfect and computationally cheap replacement for the root-mean-square distance (RMSD) when one has to decide whether two noise contaminated configurations are identical or not. We introduce a Monte Carlo approach to obtain the global minimum of the RMSD between configurations, which is obtained from a global minimization over all translations, rotations, and permutations of atomic indices
A faithful functor among algebras and graphs
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vigo Aguiar, Jesús (Coordinador)
2016-01-01
The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertex-colored graphs, we describe here a pair of graphs that enable us to find a faithful functor between finite-dimensional algebras over finite fields and these graphs.
Graphs with branchwidth at most three
Bodlaender, H.L.; Thilikos, D.M.
1997-01-01
In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three, if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph
A Modal-Logic Based Graph Abstraction
Bauer, J.; Boneva, I.B.; Kurban, M.E.; Rensink, Arend; Ehrig, H; Heckel, R.; Rozenberg, G.; Taentzer, G.
2008-01-01
Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract
Graphs whose complement and square are isomorphic
Pedersen, Anders Sune
2014-01-01
We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-compl...
Acyclicity in edge-colored graphs
Gutin, Gregory; Jones, Mark; Sheng, Bin
2017-01-01
A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type...
Building Scalable Knowledge Graphs for Earth Science
Ramachandran, Rahul; Maskey, Manil; Gatlin, Patrick; Zhang, Jia; Duan, Xiaoyi; Miller, J. J.; Bugbee, Kaylin; Christopher, Sundar; Freitag, Brian
2017-01-01
Knowledge Graphs link key entities in a specific domain with other entities via relationships. From these relationships, researchers can query knowledge graphs for probabilistic recommendations to infer new knowledge. Scientific papers are an untapped resource which knowledge graphs could leverage to accelerate research discovery. Goal: Develop an end-to-end (semi) automated methodology for constructing Knowledge Graphs for Earth Science.
Port-Hamiltonian Systems on Open Graphs
Schaft, A.J. van der; Maschke, B.M.
2010-01-01
In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
Skew-adjacency matrices of graphs
Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.
2012-01-01
The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic
Chromatic polynomials of random graphs
Van Bussel, Frank; Fliegner, Denny; Timme, Marc; Ehrlich, Christoph; Stolzenberg, Sebastian
2010-01-01
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.
Commuting graphs of matrix algebras
Akbari, S.; Bidkhori, H.; Mohammadian, A.
2006-08-01
The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all non- central elements of R and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this paper we investigate some graph theoretic properties of Γ(M n (F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GL n (F) and SL n (F). We show that Γ(M n (F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GL n (F)) and Γ(SL n (F)). Also we show that for two fields E and F and integers m, n ≥> 2, if Γ(M m (E)) ≅ Γ(M n (F)), then m = n and vertical bar E vertical bar = vertical bar F vertical bar. (author)
Generalizing a categorization of students’ interpretations of linear kinematics graphs
Laurens Bollen
2016-02-01
Full Text Available We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven and the Basque Country, Spain (University of the Basque Country. We discuss how we adapted the categorization to accommodate a much more diverse student cohort and explain how the prior knowledge of students may account for many differences in the prevalence of approaches and success rates. Although calculus-based physics students make fewer mistakes than algebra-based physics students, they encounter similar difficulties that are often related to incorrectly dividing two coordinates. We verified that a qualitative understanding of kinematics is an important but not sufficient condition for students to determine a correct value for the speed. When comparing responses to questions on linear distance-time graphs with responses to isomorphic questions on linear water level versus time graphs, we observed that the context of a question influences the approach students use. Neither qualitative understanding nor an ability to find the slope of a context-free graph proved to be a reliable predictor for the approach students use when they determine the instantaneous speed.
Generalizing a categorization of students' interpretations of linear kinematics graphs
Bollen, Laurens; De Cock, Mieke; Zuza, Kristina; Guisasola, Jenaro; van Kampen, Paul
2016-06-01
We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque Country, Spain (University of the Basque Country). We discuss how we adapted the categorization to accommodate a much more diverse student cohort and explain how the prior knowledge of students may account for many differences in the prevalence of approaches and success rates. Although calculus-based physics students make fewer mistakes than algebra-based physics students, they encounter similar difficulties that are often related to incorrectly dividing two coordinates. We verified that a qualitative understanding of kinematics is an important but not sufficient condition for students to determine a correct value for the speed. When comparing responses to questions on linear distance-time graphs with responses to isomorphic questions on linear water level versus time graphs, we observed that the context of a question influences the approach students use. Neither qualitative understanding nor an ability to find the slope of a context-free graph proved to be a reliable predictor for the approach students use when they determine the instantaneous speed.
Computing the Maximum Detour of a Plane Graph in Subquadratic Time
Wulff-Nilsen, Christian
2008-01-01
Let G be a plane graph where each edge is a line segment. We consider the problem of computing the maximum detour of G, defined as the maximum over all pairs of distinct points p and q of G of the ratio between the distance between p and q in G and the distance |pq|. The fastest known algorithm...
Graph Quasicontinuous Functions and Densely Continuous Forms
Lubica Hola
2017-07-01
Full Text Available Let $X, Y$ be topological spaces. A function $f: X \\to Y$ is said to be graph quasicontinuous if there is a quasicontinuous function $g: X \\to Y$ with the graph of $g$ contained in the closure of the graph of $f$. There is a close relation between the notions of graph quasicontinuous functions and minimal usco maps as well as the notions of graph quasicontinuous functions and densely continuous forms. Every function with values in a compact Hausdorff space is graph quasicontinuous; more generally every locally compact function is graph quasicontinuous.
Chain hexagonal cacti with the extremal eccentric distance sum.
Qu, Hui; Yu, Guihai
2014-01-01
Eccentric distance sum (EDS), which can predict biological and physical properties, is a topological index based on the eccentricity of a graph. In this paper we characterize the chain hexagonal cactus with the minimal and the maximal eccentric distance sum among all chain hexagonal cacti of length n, respectively. Moreover, we present exact formulas for EDS of two types of hexagonal cacti.
Katarina Pucelj
2006-12-01
Full Text Available I would like to underline the role and importance of knowledge, which is acquired by individuals as a result of a learning process and experience. I have established that a form of learning, such as distance learning definitely contributes to a higher learning quality and leads to innovative, dynamic and knowledgebased society. Knowledge and skills enable individuals to cope with and manage changes, solve problems and also create new knowledge. Traditional learning practices face new circumstances, new and modern technologies appear, which enable quick and quality-oriented knowledge implementation. The centre of learning process at distance learning is to increase the quality of life of citizens, their competitiveness on the workforce market and ensure higher economic growth. Intellectual capital is the one, which represents the biggest capital of each society and knowledge is the key factor for succes of everybody, who are fully aware of this. Flexibility, openness and willingness of people to follow new IT solutions form suitable environment for developing and deciding to take up distance learning.
Graph Design via Convex Optimization: Online and Distributed Perspectives
Meng, De
Network and graph have long been natural abstraction of relations in a variety of applications, e.g. transportation, power system, social network, communication, electrical circuit, etc. As a large number of computation and optimization problems are naturally defined on graphs, graph structures not only enable important properties of these problems, but also leads to highly efficient distributed and online algorithms. For example, graph separability enables the parallelism for computation and operation as well as limits the size of local problems. More interestingly, graphs can be defined and constructed in order to take best advantage of those problem properties. This dissertation focuses on graph structure and design in newly proposed optimization problems, which establish a bridge between graph properties and optimization problem properties. We first study a new optimization problem called Geodesic Distance Maximization Problem (GDMP). Given a graph with fixed edge weights, finding the shortest path, also known as the geodesic, between two nodes is a well-studied network flow problem. We introduce the Geodesic Distance Maximization Problem (GDMP): the problem of finding the edge weights that maximize the length of the geodesic subject to convex constraints on the weights. We show that GDMP is a convex optimization problem for a wide class of flow costs, and provide a physical interpretation using the dual. We present applications of the GDMP in various fields, including optical lens design, network interdiction, and resource allocation in the control of forest fires. We develop an Alternating Direction Method of Multipliers (ADMM) by exploiting specific problem structures to solve large-scale GDMP, and demonstrate its effectiveness in numerical examples. We then turn our attention to distributed optimization on graph with only local communication. Distributed optimization arises in a variety of applications, e.g. distributed tracking and localization, estimation
Interactive Graph Layout of a Million Nodes
Peng Mi; Maoyuan Sun; Moeti Masiane; Yong Cao; Chris North
2016-01-01
Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph to...
Khovanov homology of graph-links
Nikonov, Igor M [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2012-08-31
Graph-links arise as the intersection graphs of turning chord diagrams of links. Speaking informally, graph-links provide a combinatorial description of links up to mutations. Many link invariants can be reformulated in the language of graph-links. Khovanov homology, a well-known and useful knot invariant, is defined for graph-links in this paper (in the case of the ground field of characteristic two). Bibliography: 14 titles.
Singular Minkowski and Euclidean solutions for SU(2) Yang-Mills theory
Singleton, D.
1996-01-01
In this paper it is examined a solution to the SU(2) Yang-Mills-Higgs system, which is a trivial mathematical extension of recently discovered Schwarzschild- like solutions (Singleton D., Phys. Rev. D, 51 (1955) 5911). Physically, however, this new solution has drastically different properties from the Schwarzschild-like solutions. It is also studied a new classical solution for Euclidean SU(2) Yang-Mills theory. Again this new solution is a mathematically trivial extension of the Belavin-Polyakov-Schwartz-Tyupkin (BPST) (Belavin A. A. et al., Phys. Lett. B, 59 (1975) 85) instanton, but is physically very different. Unlike the usual instanton solution, the present solution is singular on a sphere of arbitrary radius in Euclidean space. Both of these solutions are infinite-energy solutions, so their practical value is somewhat unclear. However, they may be useful in exploring some of the mathematical aspects of classical Yang-Mills theory
Statistical 2D and 3D shape analysis using Non-Euclidean Metrics
Larsen, Rasmus; Hilger, Klaus Baggesen; Wrobel, Mark Christoph
2002-01-01
We address the problem of extracting meaningful, uncorrelated biological modes of variation from tangent space shape coordinates in 2D and 3D using non-Euclidean metrics. We adapt the maximum autocorrelation factor analysis and the minimum noise fraction transform to shape decomposition. Furtherm......We address the problem of extracting meaningful, uncorrelated biological modes of variation from tangent space shape coordinates in 2D and 3D using non-Euclidean metrics. We adapt the maximum autocorrelation factor analysis and the minimum noise fraction transform to shape decomposition....... Furthermore, we study metrics based on repated annotations of a training set. We define a way of assessing the correlation between landmarks contrary to landmark coordinates. Finally, we apply the proposed methods to a 2D data set consisting of outlines of lungs and a 3D/(4D) data set consisting of sets...
Membrane paradigm and entropy of black holes in the Euclidean action approach
Lemos, Jose P. S.; Zaslavskii, Oleg B.
2011-01-01
The membrane paradigm approach to black holes fixes in the vicinity of the event horizon a fictitious surface, the stretched horizon, so that the spacetime outside remains unchanged and the spacetime inside is vacuum. Using this powerful method, several black hole properties have been found and settled, such as the horizon's viscosity, electrical conductivity, resistivity, as well as other properties. On the other hand, the Euclidean action approach to black hole spacetimes has been very fruitful in understanding black hole entropy. Combining both the Euclidean action and membrane paradigm approaches, a direct derivation of the black hole entropy is given. In the derivation, it is considered that the only fields present are the gravitational and matter fields, with no electric field.
A Low-Complexity Euclidean Orthogonal LDPC Architecture for Low Power Applications
M. Revathy
2015-01-01
Full Text Available Low-density parity-check (LDPC codes have been implemented in latest digital video broadcasting, broadband wireless access (WiMax, and fourth generation of wireless standards. In this paper, we have proposed a high efficient low-density parity-check code (LDPC decoder architecture for low power applications. This study also considers the design and analysis of check node and variable node units and Euclidean orthogonal generator in LDPC decoder architecture. The Euclidean orthogonal generator is used to reduce the error rate of the proposed LDPC architecture, which can be incorporated between check and variable node architecture. This proposed decoder design is synthesized on Xilinx 9.2i platform and simulated using Modelsim, which is targeted to 45 nm devices. Synthesis report proves that the proposed architecture greatly reduces the power consumption and hardware utilizations on comparing with different conventional architectures.
A Low-Complexity Euclidean Orthogonal LDPC Architecture for Low Power Applications.
Revathy, M; Saravanan, R
2015-01-01
Low-density parity-check (LDPC) codes have been implemented in latest digital video broadcasting, broadband wireless access (WiMax), and fourth generation of wireless standards. In this paper, we have proposed a high efficient low-density parity-check code (LDPC) decoder architecture for low power applications. This study also considers the design and analysis of check node and variable node units and Euclidean orthogonal generator in LDPC decoder architecture. The Euclidean orthogonal generator is used to reduce the error rate of the proposed LDPC architecture, which can be incorporated between check and variable node architecture. This proposed decoder design is synthesized on Xilinx 9.2i platform and simulated using Modelsim, which is targeted to 45 nm devices. Synthesis report proves that the proposed architecture greatly reduces the power consumption and hardware utilizations on comparing with different conventional architectures.
Structure functions at small xBj in a Euclidean field theory approach
Hebecker, A.; Meggiolaro, E.; Nachtmann, O.
2000-01-01
The small-x Bj limit of deep inelastic scattering is related to the high-energy limit of the forward Compton amplitude in a familiar way. We show that the analytic continuation of this amplitude in the energy variable is calculable from a matrix element in Euclidean field theory. This matrix element can be written as a Euclidean functional integral in an effective field theory. Its effective Lagrangian has a simple expression in terms of the original Lagrangian. The functional integral expression obtained can, at least in principle, be evaluated using genuinely non-perturbative methods, e.g., on the lattice. Thus, a fundamentally new approach to the long-standing problem of structure functions at very small x Bj seems possible. We give arguments that the limit x Bj →0 corresponds to a critical point of the effective field theory where the correlation length becomes infinite in one direction
The non-Euclidean revolution with an introduction by H.S.M. Coxeter
Trudeau, Richard J
2001-01-01
How unique and definitive is Euclidean geometry in describing the "real" space in which we live? Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world. Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world. A portion of the book won the Pólya Prize, a distinguished award from the Mathematical Association of America.
From Euclidean to Minkowski space with the Cauchy-Riemann equations
Gimeno-Segovia, Mercedes; Llanes-Estrada, Felipe J.
2008-01-01
We present an elementary method to obtain Green's functions in non-perturbative quantum field theory in Minkowski space from Green's functions calculated in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes often is unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore, we suggest to use the Cauchy-Riemann equations, which perform the analytical continuation without assuming global information on the function in the entire complex plane, but only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge quantum chromodynamics, which is known from lattice and Dyson-Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy-Riemann equations against high-frequency noise,which makes it difficult to achieve good accuracy. We also point out a few curious details related to the Wick rotation. (orig.)
PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION
W. Dorner
2016-06-01
Full Text Available After the success of GNSS (Global Navigational Satellite Systems and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS – Real Time Locating Services (e.g. WIFI and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites, but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.
The Euclidean three-point function in loop and perturbative gravity
Rovelli, Carlo; Zhang Mingyi
2011-01-01
We compute the leading order of the three-point function in loop quantum gravity, using the vertex expansion of the Euclidean version of the new spin foam dynamics, in the region of γ < 1. We find results consistent with Regge calculus in the limit γ → 0, j → ∞. We also compute the tree-level three-point function of perturbative quantum general relativity in position space and discuss the possibility of directly comparing the two results.
Feynman graph derivation of Einstein quadrupole formula
Dass, N.D.H.; Soni, V.
1980-11-01
The one graviton transition operator, and consequently, the classical energy loss formula for gravitational radiation are derived from the Feynman graphs of helicity +- 2 theories of gravitation. The calculations are done both for the case of electromagnetic and gravitational scattering. The departure of the in and out states from plane waves owing to the long range nature of gravitation is taken into account to improve the Born approximation calculations. This also includes a long range modification of the graviton wave function which is shown to be equivalent to the classical problem of the true light cones deviating logarithmically at large distances from the flat space light cones. The transition from the S-matrix elements calculated graphically to the graviton transition operator is done by using complimentarity of space-time and momentum descriptions. The energy loss formula derived originally by Einstein is shown to be correct. (Auth.)
Generalizing a categorization of students' interpretations of linear kinematics graphs
Bollen, Laurens; De Cock, Mieke; Zuza, Kristina; Guisasola, Jenaro; van Kampen, Paul
2016-01-01
We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque Country, Spain (University of the Basque Country). We discuss how we adapted the categorization to accommodate a much more diverse student cohort and ...
Eigenfunction statistics on quantum graphs
Gnutzmann, S.; Keating, J.P.; Piotet, F.
2010-01-01
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.
Andreas P. Braun
2016-04-01
Full Text Available Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5 by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.
Degree-based graph construction
Kim, Hyunju; Toroczkai, Zoltan; Erdos, Peter L; Miklos, Istvan; Szekely, Laszlo A
2009-01-01
Degree-based graph construction is a ubiquitous problem in network modelling (Newman et al 2006 The Structure and Dynamics of Networks (Princeton Studies in Complexity) (Princeton, NJ: Princeton University Press), Boccaletti et al 2006 Phys. Rep. 424 175), ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive construction and sampling questions with aspects that are still open today. Here we give necessary and sufficient conditions for a sequence of nonnegative integers to be realized as a simple graph's degree sequence, such that a given (but otherwise arbitrary) set of connections from an arbitrarily given node is avoided. We then use this result to present a swap-free algorithm that builds all simple graphs realizing a given degree sequence. In a wider context, we show that our result provides a greedy construction method to build all the f-factor subgraphs (Tutte 1952 Can. J. Math. 4 314) embedded within K n setmn S k , where K n is the complete graph and S k is a star graph centred on one of the nodes. (fast track communication)
Hierarchical organisation of causal graphs
Dziopa, P.
1993-01-01
This paper deals with the design of a supervision system using a hierarchy of models formed by graphs, in which the variables are the nodes and the causal relations between the variables of the arcs. To obtain a representation of the variables evolutions which contains only the relevant features of their real evolutions, the causal relations are completed with qualitative transfer functions (QTFs) which produce roughly the behaviour of the classical transfer functions. Major improvements have been made in the building of the hierarchical organization. First, the basic variables of the uppermost level and the causal relations between them are chosen. The next graph is built by adding intermediary variables to the upper graph. When the undermost graph has been built, the transfer functions parameters corresponding to its causal relations are identified. The second task consists in the upwelling of the information from the undermost graph to the uppermost one. A fusion procedure of the causal relations has been designed to compute the QFTs relevant for each level. This procedure aims to reduce the number of parameters needed to represent an evolution at a high level of abstraction. These techniques have been applied to the hierarchical modelling of nuclear process. (authors). 8 refs., 12 figs
Integer Flows and Circuit Covers of Graphs and Signed Graphs
Cheng, Jian
The work in Chapter 2 is motivated by Tutte and Jaeger's pioneering work on converting modulo flows into integer-valued flows for ordinary graphs. For a signed graphs (G, sigma), we first prove that for each k ∈ {2, 3}, if (G, sigma) is (k - 1)-edge-connected and contains an even number of negative edges when k = 2, then every modulo k-flow of (G, sigma) can be converted into an integer-valued ( k + 1)-ow with a larger or the same support. We also prove that if (G, sigma) is odd-(2p+1)-edge-connected, then (G, sigma) admits a modulo circular (2 + 1/ p)-flows if and only if it admits an integer-valued circular (2 + 1/p)-flows, which improves all previous result by Xu and Zhang (DM2005), Schubert and Steffen (EJC2015), and Zhu (JCTB2015). Shortest circuit cover conjecture is one of the major open problems in graph theory. It states that every bridgeless graph G contains a set of circuits F such that each edge is contained in at least one member of F and the length of F is at most 7/5∥E(G)∥. This concept was recently generalized to signed graphs by Macajova et al. (JGT2015). In Chapter 3, we improve their upper bound from 11∥E( G)∥ to 14/3 ∥E(G)∥, and if G is 2-edgeconnected and has even negativeness, then it can be further reduced to 11/3 ∥E(G)∥. Tutte's 3-flow conjecture has been studied by many graph theorists in the last several decades. As a new approach to this conjecture, DeVos and Thomassen considered the vectors as ow values and found that there is a close relation between vector S1-flows and integer 3-NZFs. Motivated by their observation, in Chapter 4, we prove that if a graph G admits a vector S1-flow with rank at most two, then G admits an integer 3-NZF. The concept of even factors is highly related to the famous Four Color Theorem. We conclude this dissertation in Chapter 5 with an improvement of a recent result by Chen and Fan (JCTB2016) on the upperbound of even factors. We show that if a graph G contains an even factor, then it
Caddle, Mary C.; Brizuela, Barbara M.
2011-01-01
This paper looks at 21 fifth grade students as they discuss a linear graph in the Cartesian plane. The problem presented to students depicted a graph showing distance as a function of elapsed time for a person walking at a constant rate of 5 miles/h. The question asked students to consider how many more hours, after having already walked 4 h,…
Dasgupta, I.
1998-01-01
We discuss new bounce-like (but non-time-reversal-invariant) solutions to Euclidean equations of motion, which we dub boomerons. In the Euclidean path integral approach to quantum theories, boomerons make an imaginary contribution to the vacuum energy. The fake vacuum instability can be removed by cancelling boomeron contributions against contributions from time reversed boomerons (anti-boomerons). The cancellation rests on a sign choice whose significance is not completely understood in the path integral method. (orig.)
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.
Negation switching invariant signed graphs
Deepa Sinha
2014-04-01
Full Text Available A signed graph (or, $sigraph$ in short is a graph G in which each edge x carries a value $\\sigma(x \\in \\{-, +\\}$ called its sign. Given a sigraph S, the negation $\\eta(S$ of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs $S_{1}$ and $S_{2}$ on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus' or `-' (`minus' to vertices of $S_{1}$ such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains $S_{2}$. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and $\\eta (S$ are signed isomorphic.
Rosmanis, Ansis
2011-01-01
I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.
On Graph Rewriting, Reduction and Evaluation
Zerny, Ian
2010-01-01
We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter-derive a t......We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter...
The fascinating world of graph theory
Benjamin, Arthur; Zhang, Ping
2015-01-01
Graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducin
Graph-based modelling in engineering
Rysiński, Jacek
2017-01-01
This book presents versatile, modern and creative applications of graph theory in mechanical engineering, robotics and computer networks. Topics related to mechanical engineering include e.g. machine and mechanism science, mechatronics, robotics, gearing and transmissions, design theory and production processes. The graphs treated are simple graphs, weighted and mixed graphs, bond graphs, Petri nets, logical trees etc. The authors represent several countries in Europe and America, and their contributions show how different, elegant, useful and fruitful the utilization of graphs in modelling of engineering systems can be. .
XML Graphs in Program Analysis
Møller, Anders; Schwartzbach, Michael Ignatieff
2007-01-01
XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...... of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey four very different applications: XML in Java, Java Servlets and JSP, transformations between XML and non-XML data, and XSLT....
Graph topologies on closed multifunctions
Giuseppe Di Maio
2003-10-01
Full Text Available In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.
Cyclic graphs and Apery's theorem
Sorokin, V N
2002-01-01
This is a survey of results about the behaviour of Hermite-Pade approximants for graphs of Markov functions, and a survey of interpolation problems leading to Apery's result about the irrationality of the value ζ(3) of the Riemann zeta function. The first example is given of a cyclic graph for which the Hermite-Pade problem leads to Apery's theorem. Explicit formulae for solutions are obtained, namely, Rodrigues' formulae and integral representations. The asymptotic behaviour of the approximants is studied, and recurrence formulae are found
Interacting particle systems on graphs
Sood, Vishal
In this dissertation, the dynamics of socially or biologically interacting populations are investigated. The individual members of the population are treated as particles that interact via links on a social or biological network represented as a graph. The effect of the structure of the graph on the properties of the interacting particle system is studied using statistical physics techniques. In the first chapter, the central concepts of graph theory and social and biological networks are presented. Next, interacting particle systems that are drawn from physics, mathematics and biology are discussed in the second chapter. In the third chapter, the random walk on a graph is studied. The mean time for a random walk to traverse between two arbitrary sites of a random graph is evaluated. Using an effective medium approximation it is found that the mean first-passage time between pairs of sites, as well as all moments of this first-passage time, are insensitive to the density of links in the graph. The inverse of the mean-first passage time varies non-monotonically with the density of links near the percolation transition of the random graph. Much of the behavior can be understood by simple heuristic arguments. Evolutionary dynamics, by which mutants overspread an otherwise uniform population on heterogeneous graphs, are studied in the fourth chapter. Such a process underlies' epidemic propagation, emergence of fads, social cooperation or invasion of an ecological niche by a new species. The first part of this chapter is devoted to neutral dynamics, in which the mutant genotype does not have a selective advantage over the resident genotype. The time to extinction of one of the two genotypes is derived. In the second part of this chapter, selective advantage or fitness is introduced such that the mutant genotype has a higher birth rate or a lower death rate. This selective advantage leads to a dynamical competition in which selection dominates for large populations
Average geodesic distance of skeleton networks of Sierpinski tetrahedron
Yang, Jinjin; Wang, Songjing; Xi, Lifeng; Ye, Yongchao
2018-04-01
The average distance is concerned in the research of complex networks and is related to Wiener sum which is a topological invariant in chemical graph theory. In this paper, we study the skeleton networks of the Sierpinski tetrahedron, an important self-similar fractal, and obtain their asymptotic formula for average distances. To provide the formula, we develop some technique named finite patterns of integral of geodesic distance on self-similar measure for the Sierpinski tetrahedron.
Salonen, Maria; Maeda, Eduardo Eiji; Toivonen, Tuuli
2014-10-01
Land use and land cover change (LUCC) models frequently employ different accessibility measures as a proxy for human influence on land change processes. Here, we simulate deforestation in Peruvian Amazonia and evaluate different accessibility measures as LUCC model inputs. We demonstrate how the selection, and different combinations, of accessibility measures impact simulation results. Out of the individual measures, time distance to market center catches the essential aspects of accessibility in our study area. The most accurate simulation is achieved when time distance to market center is used in association with distance to transport network and additional landscape variables. Although traditional Euclidean measures result in clearly lower simulation accuracy when used separately, the combination of two complementary Euclidean measures enhances simulation accuracy significantly. Our results highlight the need for site and context sensitive selection of accessibility variables. More sophisticated accessibility measures can potentially improve LUCC models' spatial accuracy, which often remains low.
Multiple graph regularized protein domain ranking
Wang, Jim Jing-Yan
2012-11-19
Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.
Multiple graph regularized protein domain ranking
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
2012-01-01
Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.
Multiple graph regularized protein domain ranking.
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
2012-11-19
Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.
Multiple graph regularized protein domain ranking
Wang Jim
2012-11-01
Full Text Available Abstract Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.
Mining chemical reactions using neighborhood behavior and condensed graphs of reactions approaches.
de Luca, Aurélie; Horvath, Dragos; Marcou, Gilles; Solov'ev, Vitaly; Varnek, Alexandre
2012-09-24
This work addresses the problem of similarity search and classification of chemical reactions using Neighborhood Behavior (NB) and Condensed Graphs of Reaction (CGR) approaches. The CGR formalism represents chemical reactions as a classical molecular graph with dynamic bonds, enabling descriptor calculations on this graph. Different types of the ISIDA fragment descriptors generated for CGRs in combination with two metrics--Tanimoto and Euclidean--were considered as chemical spaces, to serve for reaction dissimilarity scoring. The NB method has been used to select an optimal combination of descriptors which distinguish different types of chemical reactions in a database containing 8544 reactions of 9 classes. Relevance of NB analysis has been validated in generic (multiclass) similarity search and in clustering with Self-Organizing Maps (SOM). NB-compliant sets of descriptors were shown to display enhanced mapping propensities, allowing the construction of better Self-Organizing Maps and similarity searches (NB and classical similarity search criteria--AUC ROC--correlate at a level of 0.7). The analysis of the SOM clusters proved chemically meaningful CGR substructures representing specific reaction signatures.
Constructing Knowledge Graphs of Depression
Huang, Zhisheng; Yang, Jie; van Harmelen, Frank; Hu, Qing
2017-01-01
Knowledge Graphs have been shown to be useful tools for integrating multiple medical knowledge sources, and to support such tasks as medical decision making, literature retrieval, determining healthcare quality indicators, co-morbodity analysis and many others. A large number of medical knowledge
Partitioning graphs into connected parts
Hof, van 't P.; Paulusma, D.; Woeginger, G.J.; Frid, A.; Morozov, A.S.; Rybalchenko, A.; Wagner, K.W.
2009-01-01
The 2-DISJOINT CONNECTED SUBGRAPHS problem asks if a given graph has two vertex-disjoint connected subgraphs containing pre-specified sets of vertices. We show that this problem is NP-complete even if one of the sets has cardinality 2. The LONGEST PATH CONTRACTIBILITY problem asks for the largest
Isoperimetric inequalities for minimal graphs
Pacelli Bessa, G.; Montenegro, J.F.
2007-09-01
Based on Markvorsen and Palmer's work on mean time exit and isoperimetric inequalities we establish slightly better isoperimetric inequalities and mean time exit estimates for minimal graphs in N x R. We also prove isoperimetric inequalities for submanifolds of Hadamard spaces with tamed second fundamental form. (author)
Ancestral Genres of Mathematical Graphs
Gerofsky, Susan
2011-01-01
Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…
Humidity Graphs for All Seasons.
Esmael, F.
1982-01-01
In a previous article in this journal (Vol. 17, p358, 1979), a wet-bulb depression table was recommended for two simple experiments to determine relative humidity. However, the use of a graph is suggested because it gives the relative humidity directly from the wet and dry bulb readings. (JN)
Contracting a planar graph efficiently
Holm, Jacob; Italiano, Giuseppe F.; Karczmarz, Adam
2017-01-01
the data structure, we can achieve optimal running times for decremental bridge detection, 2-edge connectivity, maximal 3-edge connected components, and the problem of finding a unique perfect matching for a static planar graph. Furthermore, we improve the running times of algorithms for several planar...
Graph Model Based Indoor Tracking
Jensen, Christian Søndergaard; Lu, Hua; Yang, Bin
2009-01-01
The tracking of the locations of moving objects in large indoor spaces is important, as it enables a range of applications related to, e.g., security and indoor navigation and guidance. This paper presents a graph model based approach to indoor tracking that offers a uniform data management...
A graph with fractional revival
Bernard, Pierre-Antoine; Chan, Ada; Loranger, Érika; Tamon, Christino; Vinet, Luc
2018-02-01
An example of a graph that admits balanced fractional revival between antipodes is presented. It is obtained by establishing the correspondence between the quantum walk on a hypercube where the opposite vertices across the diagonals of each face are connected and, the coherent transport of single excitations in the extension of the Krawtchouk spin chain with next-to-nearest neighbour interactions.
Fixation Time for Evolutionary Graphs
Nie, Pu-Yan; Zhang, Pei-Ai
Evolutionary graph theory (EGT) is recently proposed by Lieberman et al. in 2005. EGT is successful for explaining biological evolution and some social phenomena. It is extremely important to consider the time of fixation for EGT in many practical problems, including evolutionary theory and the evolution of cooperation. This study characterizes the time to asymptotically reach fixation.
Locating sources within a dense sensor array using graph clustering
Gerstoft, P.; Riahi, N.
2017-12-01
We develop a model-free technique to identify weak sources within dense sensor arrays using graph clustering. No knowledge about the propagation medium is needed except that signal strengths decay to insignificant levels within a scale that is shorter than the aperture. We then reinterpret the spatial coherence matrix of a wave field as a matrix whose support is a connectivity matrix of a graph with sensors as vertices. In a dense network, well-separated sources induce clusters in this graph. The geographic spread of these clusters can serve to localize the sources. The support of the covariance matrix is estimated from limited-time data using a hypothesis test with a robust phase-only coherence test statistic combined with a physical distance criterion. The latter criterion ensures graph sparsity and thus prevents clusters from forming by chance. We verify the approach and quantify its reliability on a simulated dataset. The method is then applied to data from a dense 5200 element geophone array that blanketed of the city of Long Beach (CA). The analysis exposes a helicopter traversing the array and oil production facilities.
Coloring sums of extensions of certain graphs
Johan Kok
2017-12-01
Full Text Available We recall that the minimum number of colors that allow a proper coloring of graph $G$ is called the chromatic number of $G$ and denoted $\\chi(G$. Motivated by the introduction of the concept of the $b$-chromatic sum of a graph the concept of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum are introduced in this paper. The extended graph $G^x$ of a graph $G$ was recently introduced for certain regular graphs. This paper furthers the concepts of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum to extended paths and cycles. Bipartite graphs also receive some attention. The paper concludes with patterned structured graphs. These last said graphs are typically found in chemical and biological structures.
Mathematical Minute: Rotating a Function Graph
Bravo, Daniel; Fera, Joseph
2013-01-01
Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.
Towards a theory of geometric graphs
Pach, Janos
2004-01-01
The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been su...
Bounds on Gromov hyperbolicity constant in graphs
Infinite graphs; Cartesian product graphs; independence number; domin- ation number; geodesics ... the secure transmission of information through the internet (see [15, 16]). In particular, ..... In particular, δ(G) is an integer multiple of 1/4.
Summary: beyond fault trees to fault graphs
Alesso, H.P.; Prassinos, P.; Smith, C.F.
1984-09-01
Fault Graphs are the natural evolutionary step over a traditional fault-tree model. A Fault Graph is a failure-oriented directed graph with logic connectives that allows cycles. We intentionally construct the Fault Graph to trace the piping and instrumentation drawing (P and ID) of the system, but with logical AND and OR conditions added. Then we evaluate the Fault Graph with computer codes based on graph-theoretic methods. Fault Graph computer codes are based on graph concepts, such as path set (a set of nodes traveled on a path from one node to another) and reachability (the complete set of all possible paths between any two nodes). These codes are used to find the cut-sets (any minimal set of component failures that will fail the system) and to evaluate the system reliability
Torsional rigidity, isospectrality and quantum graphs
Colladay, Don; McDonald, Patrick; Kaganovskiy, Leon
2017-01-01
We study torsional rigidity for graph and quantum graph analogs of well-known pairs of isospectral non-isometric planar domains. We prove that such isospectral pairs are distinguished by torsional rigidity. (paper)
SpectralNET – an application for spectral graph analysis and visualization
Schreiber Stuart L
2005-10-01
Full Text Available Abstract Background Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices and interactions (edges that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks. Results Available both as a standalone .NET executable and as an ASP.NET web application, SpectralNET was designed specifically with the analysis of graph-theoretic metrics in mind, a computational task not easily accessible using currently available applications. Users can choose either to upload a network for analysis using a variety of input formats, or to have SpectralNET generate an idealized random network for comparison to a real-world dataset. Whichever graph-generation method is used, SpectralNET displays detailed information about each connected component of the graph, including graphs of degree distribution, clustering coefficient by degree, and average distance by degree. In addition, extensive information about the selected vertex is shown, including degree, clustering coefficient, various distance metrics, and the corresponding components of the adjacency, Laplacian, and normalized Laplacian eigenvectors. SpectralNET also displays several graph visualizations, including a linear dimensionality reduction for uploaded datasets (Principal Components Analysis and a non-linear dimensionality reduction that provides an elegant view of global graph structure (Laplacian eigenvectors. Conclusion SpectralNET provides an easily accessible means of analyzing graph-theoretic metrics for data modeling and dimensionality reduction. SpectralNET is publicly available as both a .NET application and an ASP.NET web application from http://chembank.broad.harvard.edu/resources/. Source code is
Bond graph modeling of centrifugal compression systems
Uddin, Nur; Gravdahl, Jan Tommy
2015-01-01
A novel approach to model unsteady fluid dynamics in a compressor network by using a bond graph is presented. The model is intended in particular for compressor control system development. First, we develop a bond graph model of a single compression system. Bond graph modeling offers a different perspective to previous work by modeling the compression system based on energy flow instead of fluid dynamics. Analyzing the bond graph model explains the energy flow during compressor surge. Two pri...
A Graph Calculus for Predicate Logic
Paulo A. S. Veloso
2013-03-01
Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation.
Deep Learning with Dynamic Computation Graphs
Looks, Moshe; Herreshoff, Marcello; Hutchins, DeLesley; Norvig, Peter
2017-01-01
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different shape and size for every input, such networks do not directly support batched training or inference. They are also difficult to implement in popular deep learning libraries, which are based on static data-flow graphs. We introduce a technique called dynami...
Constructs for Programming with Graph Rewrites
Rodgers, Peter
2000-01-01
Graph rewriting is becoming increasingly popular as a method for programming with graph based data structures. We present several modifications to a basic serial graph rewriting paradigm and discuss how they improve coding programs in the Grrr graph rewriting programming language. The constructs we present are once only nodes, attractor nodes and single match rewrites. We illustrate the operation of the constructs by example. The advantages of adding these new rewrite modifiers is to reduce t...
Supersymmetry on a euclidean spacetime lattice 1. A target theory with four supercharges
Cohen, Andrew G.; Kaplan, David B.; Katz, Emanuel; Uensal, Mithat
2003-01-01
We formulate a euclidean spacetime lattice whose continuum limit is (2,2) supersymmetric Yang-Mills theory in two dimensions, a theory which possesses four supercharges and an anomalous global chiral symmetry. The lattice action respects one exact supersymmetry, which allows the target theory to emerge in the continuum limit without fine-tuning. Our method exploits an orbifold construction described previously for spatial lattices in Minkowski space, and can be generalized to more complicated theories with additional supersymmetry and more spacetime dimensions. (author)
The stochastic versus the Euclidean approach to quantum fields on a static space-time
De Angelis, G.F.; de Falco, D.
1986-01-01
Equations are presented which modify the definition of the Gaussian field in the Rindler chart in order to make contact with the Wightman state, the Hartle-Hawking state, and the Euclidean field. By taking Ornstein-Uhlenbeck processes the authors have chosen, in the sense of stochastic mechanics, to place precisely the Fulling modes in their harmonic oscillator ground state. In this respect, together with the periodicity of Minkowski space-time, the authors observe that the covariance of the Ornstein-Uhlenbeck process can be obtained by analytical continuation of the Wightman function of the harmonic oscillator at zero temperature
Constant curvature black holes in Einstein AdS gravity: Euclidean action and thermodynamics
Guilleminot, Pablo; Olea, Rodrigo; Petrov, Alexander N.
2018-03-01
We compute the Euclidean action for constant curvature black holes (CCBHs), as an attempt to associate thermodynamic quantities to these solutions of Einstein anti-de Sitter (AdS) gravity. CCBHs are gravitational configurations obtained by identifications along isometries of a D -dimensional globally AdS space, such that the Riemann tensor remains constant. Here, these solutions are interpreted as extended objects, which contain a (D -2 )-dimensional de-Sitter brane as a subspace. Nevertheless, the computation of the free energy for these solutions shows that they do not obey standard thermodynamic relations.
Absence of even-integer ζ-function values in Euclidean physical quantities in QCD
Jamin, Matthias; Miravitllas, Ramon
2018-04-01
At order αs4 in perturbative quantum chromodynamics, even-integer ζ-function values are present in Euclidean physical correlation functions like the scalar quark correlation function or the scalar gluonium correlator. We demonstrate that these contributions cancel when the perturbative expansion is expressed in terms of the so-called C-scheme coupling αˆs which has recently been introduced in Ref. [1]. It is furthermore conjectured that a ζ4 term should arise in the Adler function at order αs5 in the MS ‾-scheme, and that this term is expected to disappear in the C-scheme as well.
Exact Boson-Fermion Duality on a 3D Euclidean Lattice
Chen, Jing-Yuan; Son, Jun Ho; Wang, Chao; Raghu, S.
2018-01-01
The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless two-component Dirac fermion extends this notion to gapless systems. This duality sheds light on highly nontrivial problems such as the half-filled Landau level, the superconductor-insulator transition, and surface states of strongly coupled topological insulators. Although this boson-fermion duality has undergone many consistency checks, it has remained unproven. We describe the duality in a nonperturbative fashion using an exact UV mapping of partition functions on a 3D Euclidean lattice.
Green's functions in Bianchi type-I spaces. Relation between Minkowski and Euclidean approaches
Bukhbinder, I.L.; Kirillova, E.N.
1988-01-01
A theory is considered for a free scalar field with a conformal connection in a curved space-time with a Bianchi type-I metric. A representation is obtained for the Green's function G∼ in in in the form of an integral of a Schwinger-DeWitt kernel along a contour in a plane of complex-valued proper time. It is shown how as transition may be accomplished from Green's functions in space with the Euclidean signature to Green's functions in space with Minkowski signature and vice versa
McMillen, Sue; McMillen, Beth
2010-01-01
Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy. Even students who are able to "create" bar graphs may struggle to correctly "interpret" them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information…
The groupies of random multipartite graphs
Portmann, Marius; Wang, Hongyun
2012-01-01
If a vertex $v$ in a graph $G$ has degree larger than the average of the degrees of its neighbors, we call it a groupie in $G$. In the current work, we study the behavior of groupie in random multipartite graphs with the link probability between sets of nodes fixed. Our results extend the previous ones on random (bipartite) graphs.
Modeling Software Evolution using Algebraic Graph Rewriting
Ciraci, Selim; van den Broek, Pim
We show how evolution requests can be formalized using algebraic graph rewriting. In particular, we present a way to convert the UML class diagrams to colored graphs. Since changes in software may effect the relation between the methods of classes, our colored graph representation also employs the