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At least 343 records · Page 19Linked to original sources
PubMed2005

Backward simulation of ancestors of sampled individuals.

If the population is large and the sampling mechanism is random, the coalescent is commonly used to model the haplotypes in the sample. Ordered genotypes can then be formed by random matching of the derived haplotypes. However, this approach is not realistic when (1) there is departure from random mating (e.g., dominant individuals in breeding populations or monogamy in humans), or (2) the population is small and/or the individuals in the sample are ascertained by applying some particular non-random sampling scheme, as is usually the case when considering the statistical modeling and analysis of pedigree data. For such situations, we present here a data generation method where an ancestral graph with non-overlapping generations is first generated backwards in time, using ideas from coalescent theory. Alleles are randomly assigned to the founders, and subsequently the gene flow over the entire genome is simulated forwards in time by dropping alleles down the graph according to recombination model without interference. The parameters controlling the mating behavior of generated individuals in the graph (degree of monogamy) can be tuned in order to match a particular demographic situation, without restriction to simple random mating. The performance of the approach is illustrated with a simulation example. The software (written in C-language) is freely available for research purposes at http://www.rni.helsinki.fi/~dag/.

Female↗
PubMed1977

[The time-structure of a manic-depressive psychosis (author's transl)].

Some ideas about the desynchronisation and the restabilisation of the diurnal time-structure in the mood-and-drive system are the background for some hypotheses about the determination of the course and the theory of mixed states of manic-depressive psychoses. A model given in graphs is compared with empiric material from a typical casus, which could be shown with its prodrom and some weeks of its course. The structure of dimensionality was studied by factor-analysis, the time structure was studied by autocorrelation technique. A development of the chronobiological theory seems to be of interest.

Bipolar Disorder↗
PubMed2005

Quantum pumping: the charge transported due to a translation of a scatterer.

The amount of charge that is pushed by a moving scatterer is dQ= -GdX , where dX is the displacement of the scatterer. The question is: what is G ?. Does it depend on the transmission g(0) of the scatterer? Does the answer depend on whether the system is open (with leads attached to reservoirs) or closed? In the latter case what are the implications of having "quantum chaos" and/or coupling to the environment? The answers to these questions illuminate some fundamental aspects of the theory of quantum pumping. For the analysis we take a network (graph) as a model system, and use the Kubo formula approach.

Journal Article↗
PubMed2000

Bounds for cell entries in contingency tables given marginal totals and decomposable graphs.

Upper and lower bounds on cell counts in cross-classifications of nonnegative counts play important roles in a number of practical problems, including statistical disclosure limitation, computer tomography, mass transportation, cell suppression, and data swapping. Some features of the Frechet bounds are well known, intuitive, and regularly used by those working on disclosure limitation methods, especially those for two-dimensional tables. We previously have described a series of results relating these bounds to theory on loglinear models for cross-classified counts. This paper provides the actual theory and proofs for the special case of decomposable loglinear models and their related independence graphs. It also includes an extension linked to the structure of reducible graphs and a discussion of the relevance of other results linked to nongraphical loglinear models.

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↗
PubMed2002

The use of information graphs to evaluate and compare diagnostic tests.

OBJECTIVES: The purpose of this communication is to demonstrate the use of "information graphs" as a means of characterizing diagnostic test performance. METHODS: Basic concepts in information theory allow us to quantify diagnostic uncertainty and diagnostic information. Given the probabilities of the diagnoses that can explain a patient's condition, the entropy of that distribution is a measure of our uncertainty about the diagnosis. The relative entropy of the posttest probabilities with respect to the pretest probabilities quantifies the amount of information gained by diagnostic testing. Mutual information is the expected value of relative entropy and, hence, provides a measure of expected diagnostic information. These concepts are used to derive formulas for calculating diagnostic information as a function of pretest probability for a given pair of test operating characteristics. RESULTS: Plots of diagnostic information as a function of pretest probability are constructed to evaluate and compare the performance of three tests commonly used in the diagnosis of coronary artery disease. The graphs illustrate the critical role that the pretest probability plays in determining diagnostic test information. CONCLUSIONS: Information graphs summarize diagnostic test performance and offer a way to evaluate and compare diagnostic tests.

Computer Simulation↗
PubMed2001

What defines a view?

At a given instant we see only visible surfaces, not an object's complete 3D appearance. Thus, objects may be represented as discrete 'views' showing only those features visible from a limited range of viewpoints. We address how to define a view using Koenderink's (Koenderink & Van Doorn, Biol. Cybernet. 32 (1979) 211.) geometric method for enumerating complete sets of stable views as aspect graphs. Using objects with known aspect graphs, five experiments examined whether the perception of orientation is sensitive to the qualitative features that define aspect graphs. Highest sensitivity to viewpoint changes was observed at locations where the theory predicts qualitative transitions, although some transitions did not affect performance. Hypotheses about why humans ignore some transitions offer insights into mechanisms for object representation.

Discrimination, Psychological↗
PubMed2005

Spectral correlations of individual quantum graphs.

We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the energy-average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric nonlinear -model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner-Dyson random matrix theory. We explore the stability of the universal random matrix behavior with regard to perturbations, and discuss the crossover between different types of symmetries.

Journal Article↗
PubMed2007

Graph embedding and extensions: a general framework for dimensionality reduction.

Over the past few decades, a large family of algorithms - supervised or unsupervised; stemming from statistics or geometry theory - has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called Marginal Fisher Analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional Linear Discriminant Analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions.

Algorithms↗
PubMed2002

Improved QSPR analysis of standard entropy of acyclic and aromatic compounds using optimized correlation weights of linear graph invariants.

Entropy is calculated for a representative set of acyclic and aromatic compounds within the realm of QSAR/QSPR theory. Flexible topological molecular indices are chosen as independent variables in the fitting equations. The comparison with results derived from quantum mechanical calculations shows that the present approach gives better predictions. Some possible future extensions are pointed out.

Journal Article↗
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↗
PubMed2006

A reexamination of the ice III/IX hydrogen bond ordering phase transition.

Ice III is a hydrogen bond disordered crystal which when cooled 1 K / min or faster transforms to an antiferroelectric hydrogen bond ordered structure, ice IX. Throughout its region of stability, experiments indicate that the H bonds in ice III are, in fact, partially ordered, i.e., some proton arrangements are preferred. In addition, there has been evidence that the structure of ice IX retains some residual disorder after the transition. Diffraction experiments and calorimetry apparently conflict with regard to the degree of ordering at the ice III/IX transition. Mean field statistical mechanical theories have been used to link partial occupations from diffraction data with thermodynamics. In this work, we investigate the ice III/IX proton ordering phase transition using electronic density functional theory calculations for small unit cells, extended to simulate the phase transition in a large unit cell using graph invariants. In agreement with experiment, we observe partial ordering over a wide range of temperatures as ice III transforms to partially disordered ice IX, near 126 K, which becomes fully ordered at lower temperatures. We compare our results from full statistical mechanical simulations with mean field models, finding small errors for the low-temperature ice IX phase and much larger errors for the high-temperature ice III phase. The failure of mean field theories may explain the apparent conflict between diffraction experiments and calorimetry.

Journal Article↗
PubMed1993

Hierarchical functional organization of formal biological systems: a dynamical approach. III. The concept of non-locality leads to a field theory describing the dynamics at each level of organization of the (D-FBS) sub-system.

In paper I, the construction of the graph of interactions, called (O-FBS), was deduced from the 'self-association hypothesis'. In paper II, a criterion of evolution during development for the (O-FBS), which represents the topology of the biological system, was deduced from an optimum principle leading to specific dynamics. Experimental verification of the proposed extremum hypothesis is possible because precise knowledge of the dynamics is not necessary; only knowledge of the monotonic variation of the number of sinks is required for given initial conditions. Essentially, the properties of the (O-FBS) are based on the concept of non-symmetry of functional interactions, as shown by the 'orgatropy' function (paper II). In this paper, a field theory is proposed to describe the (D-FBS), i.e. the physiological processes expressed by functional interactions: (i) physiological processes are conceived as the transport of a field variable submitted to the action of a field operator; (ii) because of hierarchy, this field theory is based on the concept of non-locality, and includes a non-local and non-symmetric interaction operator; (iii) the geometry of the structure contributes to the dynamics via the densities of structural units; and (iv) because a physiological process evolves on a particular timescale, it is possible to classify the levels of organization according to distinct timescales, and, therefore, to obtain a 'decoupling' of dynamics at each level. Thus, a property of structurality for a biological system is proposed, which is based on the finiteness of the velocity of the interaction, thus, with distinct values of timescales for the construction of the hierarchy of the system. Three axioms are introduced to define the fields associated with the topology of the system: (i) the existence of the fields; (ii) the decoupling of the dynamics; and (iii) the ability of activation-inhibition. This formulation leads to a self-coherent definition of auto-organization: an FBS is self-organized if it goes from one stable state for the (D-FBS) to another under the influence of certain modifications of its topology, i.e. a modification of the (O-FBS). It is shown that properties deduced with this formalism give the relationship between topology and geometry in an FBS, and particularly, the geometrical re-distribution of units.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed1995

A shape representation for computer vision based on differential topology.

We describe a shape representation for use in computer vision, after a brief review of shape representation and object recognition in general. Our shape representation is based on graph structures derived from level sets whose characteristics are understood from differential topology, particularly singularity theory. This leads to a representation which is both stable and whose changes under deformation are simple. The latter allows smoothing in the representation domain ('symbolic smoothing'), which in turn can be used for coarse-to-fine strategies, or as a discrete analog of scale space. Essentially the same representation applies to an object embedded in 3-dimensional space as to one in the plane, and likewise for a 3D object and its silhouette. We suggest how this can be used for recognition.

Artificial Intelligence↗
PubMed2006

Vinylcyclobutane-cyclohexene rearrangement: theoretical exploration of mechanism and relationship to the Diels-Alder potential surface.

[graph: see text] The vinylcyclobutane-cyclohexene rearrangement has been studied computationally with density functional theory and complete active space SCF calculations. The rearrangement proceeds through a diradical that exists on a very flat potential energy surface. Transition structures for conformational processes, only slightly higher in energy than the minimum energy reaction path, account for the stereochemistries of products observed in the thermal rearrangements of vinylcyclobutane derivatives. The connection of this rearrangement to the Diels-Alder reaction of butadiene with ethylene is discussed.

Journal Article↗
PubMed2005

Fractal structure of high-temperature graphs of O(N) models in two dimensions.

The critical behavior of the two-dimensional O(N) model close to criticality is shown to be encoded in the fractal structure of the high-temperature graphs of the model. Based on Monte Carlo simulations and with the help of percolation theory, de Gennes' results for polymer rings, corresponding to the limit N-->0, are generalized to random loops for arbitrary -2<or=N<or=2. The loops are studied also close to their tricritical point, known as the Theta point in the context of polymers, where they collapse. The corresponding fractal dimensions are argued to be in one-to-one correspondence with those at the critical point, leading to an analytic prediction for the magnetic scaling dimension at the O(N) tricritical point.

Journal Article↗
PubMed2004

Experimental simulation of quantum graphs by microwave networks.

We present the results of experimental and theoretical study of irregular, tetrahedral microwave networks consisting of coaxial cables (annular waveguides) connected by T joints. The spectra of the networks were measured in the frequency range 0.0001-16 GHz in order to obtain their statistical properties such as the integrated nearest neighbor spacing distribution and the spectral rigidity Delta(3) (L). The comparison of our experimental and theoretical results shows that microwave networks can simulate quantum graphs with time reversal symmetry. In particular, we use the spectra of the microwave networks to study the periodic orbits of the simulated quantum graphs. We also present experimental study of directional microwave networks consisting of coaxial cables and Faraday isolators for which the time reversal symmetry is broken. In this case our experimental results indicate that spectral statistics of directional microwave networks deviate from predictions of Gaussian orthogonal ensembles in random matrix theory approaching, especially for small eigenfrequency spacing s, results for Gaussian unitary ensembles. Experimental results are supported by the theoretical analysis of directional graphs.

Journal Article↗
PubMed2002

Hadronic light-by-light scattering contribution to the muon g - 2: an effective field theory approach.

The hadronic light-by-light contribution to a(mu), the anomalous magnetic moment of the muon, is discussed from the point of view of an effective low-energy theory. As an application, the coefficient of the leading logarithm arising from the two-loop graphs involving two anomalous vertices is computed, and found to be positive. This corresponds to a positive sign for the pion-pole contribution to the hadronic light-by-light correction to a(mu), and to a sizable reduction of the discrepancy between the present experimental value of a(mu) and its theoretical counterpart in the standard model.

Journal Article↗