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At least 1,261 records · Page 70Linked to original sources
PubMed1995

A pedigree-based algorithm for finding efficient peeling sequences.

The computational cost, in terms of both storage requirements and calculation required, of performing an elimination ordering on a graph is considered as a function of the order in which the vertices of the moral graph are eliminated. Useful properties of the moral graph of a pedigree with respect to vertex elimination are observed and these properties extended to define a k-pedigree as a graph permitting allocation of one of k sexes to each vertex of the graph, such that the subgraph induced by vertices of a single six contains no cycles. Properties of k-pedigrees include an upper bound of 2k on clique size. A novel algorithm, SEXY, based upon these properties is proposed and its performance compared with other algorithms used to generate elimination sequences. It is found to give a widely dispersed range of of sequences, including some sequences requiring under a quarter of the storage and under a half of the computational time than had previously been found using standard methods.

ABO Blood-Group System↗
PubMed1994

The statistical analysis of single-subject data: a comparative examination.

BACKGROUND AND PURPOSE: The purposes of this study were to examine whether the use of three different statistical methods for analyzing single-subject data led to similar results and to identify components of graphed data that influence agreement (or disagreement) among the statistical procedures. METHODS: Forty-two graphs containing single-subject data were examined. Twenty-one were AB charts of hypothetical data. The other 21 graphs appeared in Journal of Applied Behavioral Analysis, Physical Therapy, Journal of the Association for Persons With Severe Handicaps, and Journal of Behavior Therapy and Experimental Psychiatry. Three different statistical tests--the C statistic, the two-standard deviation band method, and the split-middle method of trend estimation--were used to analyze the 42 graphs. RESULTS: A relatively low degree of agreement (38%) was found among the three statistical tests. The highest rate of agreement for any two statistical procedures (71%) was found for the two-standard deviation band method and the C statistic. A logistic regression analysis revealed that overlap in single-subject graphed data was the best predictor of disagreement among the three statistical tests (beta = .49, P < .03). CONCLUSION AND DISCUSSION: The results indicate that interpretation of data from single-subject research designs is directly influenced by the method of data analysis selected. Variation exists across both visual and statistical methods of data reduction. The advantages and disadvantages of statistical and visual analysis are described.

Data Interpretation, Statistical↗
PubMedDate not supplied

Comparison of visual inspection and statistical analysis of single-subject data in rehabilitation research.

Single-subject designs are being advocated to conduct outcome research in rehabilitation environments. The methods provide an alternative to traditional designs based on statistical comparisons across groups. Data analysis in single subject research does not rely on statistical hypothesis testing of responses collected from a sample of subjects. Instead, visual inspection of patient responses graphed over time is the usual method of data analysis in single-subject research. This study examined the agreement between visual analysis and statistical tests of single-subject data for 42 hypothetical single-subject graphs. Specially constructed graphs allowed the systematic manipulation of different treatment effect sizes across a commonly used single-subject design. Thirty-two rehabilitation and health care providers rated each of the 42 graphs to determine whether a clinically significant treatment effect existed across the phases of the designs. Data analysis focused on two questions: (1) How much agreement was there between visual judgments and the results of statistical tests? and (2) What level of treatment effect was required to produce a finding of visual versus statistical significance? The agreement between visual analysis and statistical significance was high (86%). The sensitivity of visual inferences compared with statistical test results was 0.84, specificity was 0.88, and positive predictive value was 0.91. Both visual and statistical procedures were sensitive to medium and large treatment effects in the 42 single-subject graphs examined in this study.

Audiovisual Aids↗
PubMed2005

Investigations for the diagnostic recording of nasal wing collapse.

BACKGROUND: The inspiratory medial movement of the nasal wing at high flow velocities is a protective physiologic mechanism. If this collapse of the nasal wing occurs at lower flow velocities, it may result in nasal obstruction. "Nasal wing collapse" is generally a clinical diagnosis. However, in the pressure-flow relationship of rhinomanometry, the medial movement of the nasal wing can be documented in the inspiratory arm of the graph. The diagnostic impact of this hysteresis was investigated. METHODS: The pressure-flow curves of three box models and three nasal models with a moveable valve (analogous to the nasal wing) in the entrance area as well as three volunteers with unstable nasal wings were investigated. We recorded synchronously the pressure-flow relationship and by endoscopy the movement of the valve in the box models and the nasal wing in the volunteers on video. For evaluation, we used the frame by frame analysis of the tape. RESULTS AND CONCLUSIONS: The medial movement of the nasal wing causes a hysteresis in the inspiratory arm of the pressure-flow curve. At this point, the graph runs on or between two border curves, termed the "no collapse curve" (for the maximally opened valve or a stable nasal wing) and the "collapse curve" (for the subtotally closed valve or a collapsed nasal wing), respectively. Analogous to the nasal wing motion, the descending course of hysteresis runs in two phases, and the ascending course runs in three phases. The medial movement of the nasal wing is expressed by a deviation of the graph from the "no collapse curve." The flow, at which the graph leaves this curve, depends on the elasticity module of the nasal wing. The extent of nasal wing collapse is reflected by the approximation of the pressure-flow curve to the "collapse curve" of the graph. The hysteresis appears because of a late opening of the collapsed nasal wing.

Adult↗
PubMed2006

Evolutionary games on cycles.

Traditional evolutionary game theory explores frequency-dependent selection in well-mixed populations without spatial or stochastic effects. But recently there has been much interest in studying the evolutionary game dynamics in spatial settings, on lattices and other graphs. Here, we present an analytic approach for the stochastic evolutionary game dynamics on the simplest possible graph, the cycle. For three different update rules, called 'birth-death' (BD), 'death-birth' (DB) and 'imitation' (IM), we derive exact conditions for natural selection to favour one strategy over another. As specific examples, we consider a coordination game and Prisoner's Dilemma. In the latter case, selection can favour cooperators over defectors for DB and IM updating. We also study the case where the replacement graph of evolutionary updating remains a cycle, but the interaction graph for playing the game is a complete graph. In this setting, all three update rules lead to identical conditions in the limit of weak selection, where we find the '1/3-law' of well-mixed populations.

Biological Evolution↗
PubMed2004

Comparative analysis of protein domain organization.

We have developed a set of graph theory-based tools, which we call Comparative Analysis of Protein Domain Organization (CADO), to survey and compare protein domain organizations of different organisms. In the language of CADO, the organization of protein domains in a given organism is shown as a domain graph in which protein domains are represented as vertices, and domain combinations, defined as instances of two domains found in one protein, are represented as edges. CADO provides a new way to analyze and compare whole proteomes, including identifying the consensus and difference of domain organization between organisms. CADO was used to analyze and compare >50 bacterial, archaeal, and eukaryotic genomes. Examples and overviews presented here include the analysis of the modularity of domain graphs and the functional study of domains based on the graph topology. We also report on the results of comparing domain graphs of two organisms, Pyrococcus horikoshii (an extremophile) and Haemophilus influenzae (a parasite with reduced genome) with other organisms. Our comparison provides new insights into the genome organization of these organisms. Finally, we report on the specific domain combinations characterizing the three kingdoms of life, and the kingdom "signature" domain organizations derived from those specific domain combinations.

Animals↗
PubMed2000

Recursive graphical construction of feynman diagrams in straight phi(4) theory: asymmetric case and effective energy

The free energy of a multicomponent scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys nonlinear functional differential equations which are turned into recursion relations for the connected Green's functions in a loop expansion. These relations amount to a simple proof that W[G,J] generates only connected graphs and can be used to find all such graphs with their combinatoric weights. A Legendre transformation with respect to the external current converts the functional differential equations for the free energy into those for the effective energy Gamma[G,Phi], which is considered as a functional of the free correlation function G and the field expectation Phi. These equations are turned into recursion relations for the one-particle irreducible Green's functions. These relations amount to a simple proof that Gamma[G,J] generates only one-particle irreducible graphs and can be used to find all such graphs with their combinatoric weights. The techniques used also allow for a systematic investigation into resummations of classes of graphs. Examples are given for resumming one-loop and multiloop tadpoles, both through all orders of perturbation theory. Since the functional differential equations derived are nonperturbative, they constitute also a convenient starting point for other expansions than those in numbers of loops or powers of coupling constants. We work with general interactions through four powers in the field.

Journal Article↗
PubMed2002

Evolutionary reconstruction of networks.

Can a graph specifying the pattern of connections of a dynamical network be reconstructed from statistical properties of a signal generated by such a system? In this model study, we present a Metropolis algorithm for reconstruction of graphs from their Laplacian spectra. Through a stochastic process of mutations and selection, evolving test networks converge to a reference graph. Applying the method to several examples of random graphs, clustered graphs, and small-world networks, we show that the proposed stochastic evolution allows exact reconstruction of relatively small networks and yields good approximations in the case of large sizes.

Journal Article↗
PubMed2003

Patterns in randomly evolving networks: idiotypic networks.

We present a model for the evolution of networks of occupied sites on undirected regular graphs. At every iteration step in a parallel update, I randomly chosen empty sites are occupied and occupied sites having occupied neighbor degree outside of a given interval (t(l),t(u)) are set empty. Depending on the influx I and the values of both lower threshold and upper threshold of the occupied neighbor degree, different kinds of behavior can be observed. In certain regimes stable long-living patterns appear. We distinguish two types of patterns: static patterns arising on graphs with low connectivity and dynamic patterns found on high connectivity graphs. Increasing I patterns become unstable and transitions between almost stable patterns, interrupted by disordered phases, occur. For still larger I the lifetime of occupied sites becomes very small and network structures are dominated by randomness. We develop methods to analyze the nature and dynamics of these network patterns, give a statistical description of defects and fluctuations around them, and elucidate the transitions between different patterns. Results and methods presented can be applied to a variety of problems in different fields and a broad class of graphs. Aiming chiefly at the modeling of functional networks of interacting antibodies and B cells of the immune system (idiotypic networks), we focus on a class of graphs constructed by bit chains. The biological relevance of the patterns and possible operational modes of idiotypic networks are discussed.

Journal Article↗
PubMed2003

Generating correlated networks from uncorrelated ones.

Given an ensemble of random graphs with a specific degree distribution, we show that the transformation which converts these graphs to their line (edge-dual) graphs produces an ensemble of graphs with nearly the same degree distribution, but with degree correlations and a much higher clustering coefficient. We also study the percolation properties of these new graphs.

Journal Article↗
PubMed2003

Uncorrelated random networks.

We define a statistical ensemble of nondegenerate graphs, i.e., graphs without multiple-connections and self-connections between nodes. The node degree distribution is arbitrary, but the nodes are assumed to be uncorrelated. This completes our earlier publication [Phys. Rev. 64, 046118 (2001)] where trees and degenerate graphs were considered. An efficient algorithm generating nondegenerate graphs is constructed. The corresponding computer code is available on request. Finite-size effects in scale-free graphs, i.e., those where the tail of the degree distribution falls like n(-beta), are carefully studied. We find that in the absence of dynamical internode correlations the degree distribution is cut at a degree value scaling like N(gamma), with gamma=min[1/2,1/(beta-1)], where N is the total number of nodes. The consequence is that, independently of any specific model, the internode correlations seem to be a necessary ingredient of the physics of scale-free networks observed in nature.

Journal Article↗
PubMed2005

Statistical mechanical load balancer for the web.

The maximum entropy principle from statistical mechanics states that a closed system attains an equilibrium distribution that maximizes its entropy. We first show that for graphs with fixed number of edges one can define a stochastic edge dynamic that can serve as an effective thermalization scheme, and hence, the underlying graphs are expected to attain their maximum-entropy states, which turn out to be Erdös-Rényi (ER) random graphs. We next show that (i) a rate-equation-based analysis of node degree distribution does indeed confirm the maximum-entropy principle, and (ii) the edge dynamic can be effectively implemented using short random walks on the underlying graphs, leading to a local algorithm for the generation of ER random graphs. The resulting statistical mechanical system can be adapted to provide a distributed and local (i.e., without any centralized monitoring) mechanism for load balancing, which can have a significant impact in increasing the efficiency and utilization of both the Internet (e.g., efficient web mirroring), and large-scale computing infrastructure (e.g., cluster and grid computing).

Journal Article↗
PubMed2005

Finding local community structure in networks.

Although the inference of global community structure in networks has recently become a topic of great interest in the physics community, all such algorithms require that the graph be completely known. Here, we define both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time. This algorithm runs in time O(k2d) for general graphs when d is the mean degree and k is the number of vertices to be explored. For graphs where exploring a new vertex is time consuming, the running time is linear, O(k). We show that on computer-generated graphs the average behavior of this technique approximates that of algorithms that require global knowledge. As an application, we use this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer.

Journal Article↗
PubMed2001

A new 3-D display method for 12-lead ECG.

A new three-dimensional (3-D) 12-lead electrocardiogram (ECG) display method is presented which employs a 3-D rectangular coordinate system to display the 12-lead cardiac electric signals in two 3-D graphs. The 3-D graph consists of a temporal axis representing the time domain of the cardiac signals, a spatial axis representing the lead positions, and an amplitude axis representing the voltages of the cardiac signals. The six horizontal plane leads and the other six frontal plane leads were displayed in two 3-D graphs, respectively. The voltages of the cardiac signals were represented in rainbow-like colors. Cubic interpolation was employed to insert interconnecting points between neighboring leads on each plane and to smooth the surface of the 3-D ECG graphs. The 3-D ECG graphs of a normal subject, a patient with myocardial infarction, and a patient with left bundle branch block were presented in this paper. This new display method could not only be used as a complementary display method to the 12-lead ECG, but also provide physicians with an overall integral view about the spatial distribution of the cardiac signals.

Color↗
PubMed2006

An improved neural network model for the two-page crossing number problem.

The simplest graph drawing method is that of putting the vertices of a graph on a line and drawing the edges as half-circles either above or below the line. Such drawings are called two-page book drawings. The smallest number of crossings over all two-page drawings of a graph G is called the two-page crossing number of G. Cimikowski and Shope have solved the two-page crossing number problem for an n-vertex and m-edge graph by using a Hopfield network with 2 m neurons. We present here an improved Hopfield model with m neurons. The new model achieves much better performance in the quality of solutions and is more efficient than the model of Cimikowski and Shope for all graphs tested. The parallel time complexity of the algorithm, without considering the crossing number calculations, is O(m) for the new Hopfield model with m processors clearly outperforming the previous algorithm.

Algorithms↗
PubMed2005

Dynamic algorithms for the shortest path routing problem: learning automata-based solutions.

This paper presents the first Learning Automaton-based solution to the dynamic single source shortest path problem. It involves finding the shortest path in a single-source stochastic graph topology where there are continuous probabilistic updates in the edge-weights. The algorithm is significantly more efficient than the existing solutions, and can be used to find the "statistical" shortest path tree in the "average" graph topology. It converges to this solution irrespective of whether there are new changes in edge-weights taking place or not. In such random settings, the proposed learning automata solution converges to the set of shortest paths. On the other hand, the existing algorithms will fail to exhibit such a behavior, and would recalculate the affected shortest paths after each weight-change. The important contribution of the proposed algorithm is that all the edges in a stochastic graph are not probed, and even if they are, they are not all probed equally often. Indeed, the algorithm attempts to almost always probe only those edges that will be included in the shortest path graph, while probing the other edges minimally. This increases the performance of the proposed algorithm. All the algorithms were tested in environments where edge-weights change stochastically, and where the graph topologies undergo multiple simultaneous edge-weight updates. Its superiority in terms of the average number of processed nodes, scanned edges and the time per update operation, when compared with the existing algorithms, was experimentally established. The algorithm can be applicable in domains ranging from ground transportation to aerospace, from civilian applications to military, from spatial database applications to telecommunications networking.

Algorithms↗
PubMedDate not supplied

TreePlus: interactive exploration of networks with enhanced tree layouts.

Despite extensive research, it is still difficult to produce effective interactive layouts for large graphs. Dense layout and occlusion make food webs, ontologies, and social networks difficult to understand and interact with. We propose a new interactive Visual Analytics component called TreePlus that is based on a tree-style layout. TreePlus reveals the missing graph structure with visualization and interaction while maintaining good readability. To support exploration of the local structure of the graph and gathering of information from the extensive reading of labels, we use a guiding metaphor of "Plant a seed and watch it grow." It allows users to start with a node and expand the graph as needed, which complements the classic overview techniques that can be effective at (but often limited to) revealing clusters. We describe our design goals, describe the interface, and report on a controlled user study with 28 participants comparing TreePlus with a traditional graph interface for six tasks. In general, the advantage of TreePlus over the traditional interface increased as the density of the displayed data increased. Participants also reported higher levels of confidence in their answers with TreePlus and most of them preferred TreePlus.

Algorithms↗
PubMed1998

Methodology of fever research: why are polyphasic fevers often thought to be biphasic?

This study explains why the recently described triphasic lipopolysaccharide (LPS) fevers have been repeatedly mistaken for biphasic fevers. Experiments were performed in loosely restrained male Wistar rats with a catheter implanted into the right jugular vein. Each animal was injected with Escherichia coli LPS, and its colonic (Tc) and tail skin temperatures were monitored. The results are presented as time graphs and phase-plane plots; in the latter case the rate of change of Tc is plotted against Tc. At an ambient temperature (Ta) of 30.0 degrees C, the response to the 10 microg/kg dose of LPS was triphasic, as is obvious from time graphs of Tc (3 peaks), time graphs of effector activity (3 waves of tail skin vasoconstriction), and phase-plane plots (3 complete loops). When the Ta was below neutral (22.0 degrees C) or the LPS dose was higher (100 or 1,000 microg/kg), the time graph of Tc did not allow for the reliable detection of all three febrile phases, but the phase-plane plot and time graph of effector activity clearly revealed the triphasic pattern. In a separate experiment, LPS (10 microg/kg) or saline was injected via one of two different procedures: in the first group the injection was performed through the jugular catheter, from outside the experimental chamber; in the second group the same nonstressing injection was combined with opening the chamber and pricking the animal in its lower abdomen with a needle. In the first group the febrile response was obviously triphasic, and none of the phases was due to the procedure of injection per se (injection of saline did not affect Tc). In the second group the fever similarly consisted of three Tc rises, but it might have been readily mistaken for biphasic because the first rise was indistinguishable from stress hyperthermia occurring in the saline-injected (and needle-pricked) controls. We conclude that several methodological factors (dose of LPS, procedure of its injection, and Ta) have contributed, although each in a different way, to the common misbelief that there are only two febrile phases.

Activity Cycles↗