SEARCH · PubMed Health

Results for “Graph”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 451 records · Page 25Linked to original sources

PubMed2004

Universal spectral statistics in Wigner-Dyson, chiral, and Andreev star graphs. II. Semiclassical approach.

A semiclassical approach to the universal ergodic spectral statistics in quantum star graphs is presented for all known ten symmetry classes of quantum systems. The approach is based on periodic orbit theory, the exact semiclassical trace formula for star graphs, and on diagrammatic techniques. The appropriate spectral form factors are calculated up to one order beyond the diagonal and self-dual approximations. The results are in accordance with the corresponding random-matrix theories which supports a properly generalized Bohigas-Giannoni-Schmit conjecture.

Journal Article↗

PubMed2004

Return times of random walk on generalized random graphs.

Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even broader classes of related stochastic models. Abundant results are obtained for random walk on simple graphs such as the regular lattices and the Cayley trees. However, random walks and related processes on more complex networks, which are often more relevant in the real world, are still open issues, possibly yielding different characteristics. In this paper, we investigate the return times of random walks on random graphs with arbitrary vertex degree distributions. We analytically derive the distributions of the return times. The results are applied to some types of networks and compared with numerical data.

Journal Article↗

PubMed2005

Majority-vote model on random graphs.

The majority-vote model with noise on Erdös-Rényi's random graphs has been studied. Monte Carlo simulations were performed to characterize the order-disorder phase transition appearing in the system. We found that the value of the critical noise parameter qc is an increasing function of the mean connectivity z of the random graph. The critical exponents beta/nu, gamma/nu, and 1/nu were calculated for several values of z, and our analysis yielded critical exponents satisfying the hyperscaling relation with effective dimensionality equal to unity.

Journal Article↗

PubMed2005

Sampling properties of random graphs: the degree distribution.

We discuss two sampling schemes for selecting random subnets from a network, random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling. Here we derive a necessary and sufficient condition that guarantees that the degree distributions of the subnet and the true network belong to the same family of probability distributions. For completely random sampling of nodes we find that this condition is satisfied by classical random graphs; for the vast majority of networks this condition will, however, not be met. We furthermore discuss the case where the probability of sampling a node depends on the degree of a node and we find that even classical random graphs are no longer closed under this sampling regime. We conclude by relating the results to real Eschericia coli protein interaction network data.

Journal Article↗

PubMed2006

Scale-free networks emerging from weighted random graphs.

We study Erdös-Rényi random graphs with random weights associated with each link. We generate a "supernode network" by merging all nodes connected by links having weights below the percolation threshold (percolation clusters) into a single node. We show that this network is scale-free, i.e., the degree distribution is P(k) approximately k(-lambda) with lambda=2.5. Our results imply that the minimum spanning tree in random graphs is composed of percolation clusters, which are interconnected by a set of links that create a scale-free tree with lambda=2.5. We suggest that optimization causes the percolation threshold to emerge spontaneously, thus creating naturally a scale-free supernode network. We discuss the possibility that this phenomenon is related to the evolution of several real world scale-free networks.

Journal Article↗

PubMed2006

Cooperation in the noisy case: Prisoner's dilemma game on two types of regular random graphs.

We have studied an evolutionary prisoner's dilemma game with players located on two types of random regular graphs with a degree of 4. The analysis is focused on the effects of payoffs and noise (temperature) on the maintenance of cooperation. When varying the noise level and/or the highest payoff, the system exhibits a second-order phase transition from a mixed state of cooperators and defectors to an absorbing state where only defectors remain alive. For the random regular graph (and Bethe lattice) the behavior of the system is similar to those found previously on the square lattice with nearest neighbor interactions, although the measure of cooperation is enhanced by the absence of loops in the connectivity structure. For low noise the optimal connectivity structure is built up from randomly connected triangles.

Journal Article↗

PubMed2000

New algorithm for the Ising problem: partition function for finite lattice graphs.

We present a new efficient method to find the Ising problem partition function for finite lattice graphs embeddable on an arbitrary orientable surface, with integral coupling constants bounded in the absolute value by a polynomial of the size of the lattice graph. The algorithm has been implemented for toroidal lattices using modular arithmetic and the generalized nested dissection method. The implementation has substantially better performance than any other as far as we know.

Journal Article↗

PubMed2002

Leading off-diagonal correction to the form factor of large graphs.

Using periodic-orbit theory beyond the diagonal approximation we investigate the form factor, K(tau), of a generic quantum graph with mixing classical dynamics and time-reversal symmetry. We calculate the contribution from pairs of self-intersecting orbits that differ from each other only in the orientation of a single loop. In the limit of large graphs, these pairs produce a contribution -2tau(2) to the form factor which agrees with random-matrix theory.

Journal Article↗

PubMed2004

Universal spectral statistics in quantum graphs.

We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random-matrix theory. The stability of these correlations with regard to nonuniversal corrections is analyzed in terms of the linear operator governing the classical dynamics on the graph.

Journal Article↗

PubMed2005

Dynamical replica analysis of disordered Ising spin systems on finitely connected random graphs.

We study the dynamics of macroscopic observables such as the magnetization and the energy per degree of freedom in Ising spin models on random graphs of finite connectivity, with random bonds and/or heterogeneous degree distributions. To do so, we generalize existing versions of dynamical replica theory and cavity field techniques to systems with strongly disordered and locally treelike interactions. We illustrate our results via application to, e.g., +/-J spin glasses on random graphs and of the overlap in finite connectivity Sourlas codes. All results are tested against Monte Carlo simulations.

Journal Article↗

PubMed2000

Application of graph theory to detect disconnected structures in a crystallographic database: copper oxide perovskites as a case study

Every crystal structure can be described as a graph with atoms as vertices and bonds as edges. Although such a graph loses the space arrangement of atoms and symmetry elements, it can mathematically represent the connectivity between atoms. This topological approach was used to develop a new method for detecting disconnected structures, in which individual atoms or structural fragments are located too far from each other, forming impossibly large gaps. Approximately 2300 perovskite-related crystal structures have been extracted from the Inorganic Crystal Structure Database (in 1999) and the maximum disconnecting distances, and the relations between them and the ionic radii of elements, have been analysed. Several disconnected structures, which are erroneous by our definition, have been revealed. Conventional tests for crystallographic data checking did not detect those entries.

Journal Article↗

PubMed2001

Automated graph-based analysis and correction of cortical volume topology.

The human cerebral cortex is topologically equivalent to a sheet and can be considered topologically spherical if it is closed at the brain stem. Low-level segmentation of magnetic resonance (MR) imagery typically produces cerebral volumes whose tessellations are not topologically spherical. We present a novel algorithm that analyzes and constrains the topology of a volumetric object. Graphs are formed that represent the connectivity of voxel segments in the foreground and background of the image. These graphs are analyzed and minimal corrections to the volume are made prior to tessellation. We apply the algorithm to a simple test object and to cerebral white matter masks generated by a low-level tissue identification sequence. We tessellate the resulting objects using the marching cubes algorithm and verify their topology by computing their Euler characteristics. A key benefit of the algorithm is that it localizes the change to a volume to the specific areas of its topological defects.

Algorithms↗

PubMedDate not supplied

Constructing splits graphs.

Phylogenetic trees correspond one-to-one to compatible systems of splits and so splits play an important role in theoretical and computational aspects of phylogeny. Whereas any tree reconstruction method can be thought of as producing a compatible system of splits, an increasing number of phylogenetic algorithms are available that compute split systems that are not necessarily compatible and, thus, cannot always be represented by a tree. Such methods include the split decomposition, Neighbor-Net, consensus networks, and the Z-closure method. A more general split system of this kind can be represented graphically by a so-called splits graph, which generalizes the concept of a phylogenetic tree. This paper addresses the problem of computing a splits graph for a given set of splits. We have implemented all presented algorithms in a new program called SplitsTree4.

Algorithms↗

PubMed2004

A graph-spectral approach to shape-from-shading.

In this paper, we explore how graph-spectral methods can be used to develop a new shape-from-shading algorithm. We characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large changes in surface normal direction. Modeling the blocks of the weight matrix as distinct surface patches, we use a graph seriation method to find a surface integration path that maximizes the sum of curvature-dependent weights and that can be used for the purposes of height reconstruction. To smooth the reconstructed surface, we fit quadrics to the height data for each patch. The smoothed surface normal directions are updated ensuring compliance with Lambert's law. The processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained. We provide results on synthetic and real-world imagery.

Algorithms↗

PubMed2005

Motion layer extraction in the presence of occlusion using graph cuts.

Extracting layers from video is very important for video representation, analysis, compression, and synthesis. Assuming that a scene can be approximately described by multiple planar regions, this paper describes a robust and novel approach to automatically extract a set of affine or projective transformations induced by these regions, detect the occlusion pixels over multiple consecutive frames, and segment the scene into several motion layers. First, after determining a number of seed regions using correspondences in two frames, we expand the seed regions and reject the outliers employing the graph cuts method integrated with level set representation. Next, these initial regions are merged into several initial layers according to the motion similarity. Third, an occlusion order constraint on multiple frames is explored, which enforces that the occlusion area increases with the temporal order in a short period and effectively maintains segmentation consistency over multiple consecutive frames. Then, the correct layer segmentation is obtained by using a graph cuts algorithm and the occlusions between the overlapping layers are explicitly determined. Several experimental results are demonstrated to show that our approach is effective and robust.

Algorithms↗

PubMed2005

How to complete performance graphs in content-based image retrieval: add generality and normalize scope.

The performance of a Content-Based Image Retrieval (CBIR) system, presented in the form of Precision-Recall or Precision-Scope graphs, offers an incomplete overview of the system under study: The influence of the irrelevant items (embedding) is obscured. In this paper, we propose a comprehensive and well-normalized description of the ranking performance compared to the performance of an Ideal Retrieval System defined by ground-truth for a large number of predefined queries. We advocate normalization with respect to relevant class size and restriction to specific normalized scope values (the number of retrieved items). We also propose new three and two-dimensional performance graphs for total recall studies in a range of embeddings.

Algorithms↗

PubMedDate not supplied

Interactive visual analysis of families of function graphs.

The analysis and exploration of multidimensional and multivariate data is still one of the most challenging areas in the field of visualization. In this paper, we describe an approach to visual analysis of an especially challenging set of problems that exhibit a complex internal data structure. We describe the interactive visual exploration and analysis of data that includes several (usually large) families of function graphs fi (x, t). We describe analysis procedures and practical aspects of the interactive visual analysis specific to this type of data (with emphasis on the function graph characteristic of the data). We adopted the well-proven approach of multiple, linked views with advanced interactive brushing to assess the data. Standard views such as histograms, scatterplots, and parallel coordinates are used to jointly visualize data. We support iterative visual analysis by providing means to create complex, composite brushes that span multiple views and that are constructed using different combination schemes. We demonstrate that engineering applications represent a challenging but very applicable area for visual analytics. As a case study, we describe the optimization of a fuel injection system in diesel engines of passenger cars.

Algorithms↗

PubMedDate not supplied

Graph visualization techniques for web clustering engines.

One of the most challenging issues in mining information from the World Wide Web is the design of systems that present the data to the end user by clustering them into meaningful semantic categories. We show that the analysis of the results of a clustering engine can significantly take advantage of enhanced graph drawing and visualization techniques. We propose a graph-based user interface for Web clustering engines that makes it possible for the user to explore and visualize the different semantic categories and their relationships at the desired level of detail.

Algorithms↗