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PubMed2001

Tapping spin glasses and ferromagnets on random graphs.

We consider a tapping dynamics, analogous to that in experiments on granular media, on spin glasses and ferromagnets on random thin graphs. Between taps, zero temperature single spin flip dynamics takes the system to a metastable state. Tapping corresponds to flipping simultaneously any spin with probability p. This dynamics leads to a stationary regime with a steady state energy E(p). We analytically solve this dynamics for the one-dimensional ferromagnet and +/-J spin glass. Numerical simulations for spin glasses and ferromagnets of higher connectivity are carried out; in particular, we find a novel first order transition for the ferromagnetic systems.

Journal Article↗
PubMed2002

Nonconservative earthquake model of self-organized criticality on a random graph.

We numerically investigate the Olami-Feder-Christensen model on a quenched random graph. Contrary to the case of annealed random neighbors, we find that the quenched model exhibits self-organized criticality deep within the nonconservative regime. The probability distribution for avalanche size obeys finite size scaling, with universal critical exponents. In addition, a power law relation between the size and the duration of an avalanche exists. We propose that this may represent the correct mean-field limit of the model rather than the annealed random neighbor version.

Journal Article↗
PubMed2000

Search for isotypism in crystal structures by means of the graph theory

A method for the classification of crystal structures of chemical compounds is proposed, which is based on the representation of the system of interatomic bonds in a crystal as a finite 'reduced' graph. The program IsoTest is described, allowing one to find automatically the topological similarity (isotypism) for large groups of stoichiometrically and structurally different compounds. The analysis of crystal structures of simple and double sulfates and binary inorganic compounds was carried out and numerous examples of topological isotypism of the representatives of these groups of substances were found. It is shown that in many cases the ionic sublattices, constructed according to one of the close packings, can be selected in the sulfate crystal structures.

Journal Article↗
PubMed2000

Automated assignment of graph-set descriptors for crystallographically symmetric molecules

Algorithms for the automatic assignment of graph-set notation for intermolecular networks have been extended to molecules having internal crystallographic symmetry, for patterns up to the second level. This provides a means of achieving systematic and consistent assignments for networks containing symmetric molecules. These methodologies have been implemented in the program RPLUTO. Examples are given of the application of the method to a number of molecules with hydrogen-bonded and other intermolecular networks, illustrating the diversity of the patterns that occur.

Journal Article↗
PubMed2000

Graph-set and packing analysis of hydrogen-bonded networks in polyamide structures in the Cambridge Structural Database.

The hydrogen-bond networks and crystal packing of 81 unique secondary di- and polyamides in the Cambridge Structural Database are investigated. Graph-set analysis, as implemented in the RPluto program, is used to classify network motifs. These have been rationalized in terms of the relative dispositions of the amide groups. Peptide and retropeptides exhibit significant conformational flexibility, which permits alternative hydrogen-bonding patterns. In peptides, dihedral angles of -psi approximately varphi approximately 105 degrees allow an antiparallel ladder arrangement, containing rings of either the same or alternating sizes. For retropeptides, and diamides with an odd number of CH(2) spacers, this conformation leads to a parallel ladder with rings of equal size. If varphi approaches -60 degrees and psi 180 degrees, ladders adopt a helical twist, and if the conformation is distorted further, a three-dimensional network is usually adopted. Diamides with aromatic or an even number of CH(2) spacers generally form either antiparallel ladders or sheets, although some exhibit both polymorphs. Symmetry relationships within and between hydrogen-bonded chains, ladders and sheets in the crystal packing have also been analysed. Polyamides form considerably more complex networks, although many of the structural motifs present in the diamides occur as components of these networks.

Journal Article↗
PubMed1990

Graph-set analysis of hydrogen-bond patterns in organic crystals.

A method is presented based on graph theory for categorizing hydrogen-bond motifs in such a way that complex hydrogen-bond patterns can be disentangled, or decoded, systematically and consistently. This method is based on viewing hydrogen-bond patterns topologically as if they were intertwined nets with molecules as the nodes and hydrogen bonds as the lines. Surprisingly, very few parameters are needed to define the hydrogen-bond motifs comprising these networks. The methods for making these assignments, and examples of their chemical utility are given.

Chemical Phenomena↗
PubMed1999

Visualization and characterization of non-covalent networks in molecular crystals: automated assignment of graph-set descriptors for asymmetric molecules.

A method of visualizing intermolecular networks (for example, hydrogen-bonded networks) in the crystalline state has been developed, based on the concept of link atoms, i.e. those atoms deemed to be in contact with each unique molecule or ion in the crystal chemical unit (CCU). Extension of a structure using each of these primary links can be achieved, enabling the generation and investigation of extended networks. Algorithms have been developed for the automatic assignment of graph-set notation for patterns up to second level, i.e. those involving one or two crystallographically independent non-covalent bonds, in the absence of internal crystallographic symmetry in the unique molecules of the CCU. The self, ring, chain and discrete motifs may be displayed by highlighting the atoms and bonds comprising the pattern. These methodologies have been implemented in the Cambridge Structural Database program PLUTO.

Journal Article↗
PubMed1991

The use of modified constellation graph method for computer-aided classification of congenital heart diseases.

This paper describes a new method of data reduction and classification in a multidimensional symptom space for diagnostic aid of congenital heart diseases. The algorithm developed here is to reduce interactively a multidimensional symptom space to sectorial regions representing each disease in a semicircle using the modified constellation graph method. This method enables us to classify patients using the angle in the semicircle as a single classifying parameter with an accuracy of about 90%, that is, with little overlapping between disease sectors. Comparing this method with conventional factor analysis, we have found the former far more effective than the latter for disease region separation.

Algorithms↗
PubMed2001

Stabilizing interactions in the dimer interface of alpha-subunit in Escherichia coli RNA polymerase: a graph spectral and point mutation study.

The formation of alpha(2) dimer in Escherichia coli core RNA polymerase (RNAP) is thought to be the first step toward the assembly of the functional enzyme. A large number of evidences indicate that the alpha-subunit dimerizes through its N-terminal domain (NTD). The crystal structures of the alpha-subunit NTD and that of a homologous Thermus aquaticus core RNAP are known. To identify the stabilizing interactions in the dimer interface of the alpha-NTD of E. coli RNAP, we identified side-chain clusters by using the crystal structure coordinates of E. coli alpha-NTD. A graph spectral algorithm was used to identify side-chain clusters. This algorithm considers the global nonbonded side-chain interactions of the residues for the clustering procedure and is unique in identifying residues that make the largest number of interactions among the residues that form clusters in a very quantitative way. By using this algorithm, a nine-residue cluster consisting of polar and hydrophobic residues was identified in the subunit interface adjacent to the hydrophobic core. The residues forming the cluster are relatively rigid regions of the interface, as measured by the thermal factors of the residues. Most of the cluster residues in the E. coli enzyme were topologically and sequentially conserved in the T. aquaticus RNAP crystal structure. Residues 35F and 46I were predicted to be important in the stability of the alpha-dimer interface, with 35F forming the center of the cluster. The predictions were tested by isolating single-point mutants alpha-F35A and alpha-I46S on the dimer interface, which were found to disrupt dimerization. Thus, the identified cluster at the edge of the dimer interface seems to be a vital component in stabilizing the alpha-NTD.

Algorithms↗
PubMedDate not supplied

Extension of Vedernikov's graph for seepage from canals.

In this investigation, using previously derived equations by Vedernikov and Morel-Seytoux, closed-form solutions have been obtained to compute the seepage from a slit and a strip. Also, a graphical solution as an extension of Vedernikov's graph has been presented for computing quantity of seepage from triangular, rectangular, and trapezoidal canals. The solution replaces approximately the cumbersome evaluation of improper integrals with unknown implicit transformation variables.

Agriculture↗
PubMed1983

Acoustic modeling of lung dynamics using bond graphs.

Bond graphs are used to model the acoustic behavior of the respiratory system. The model includes the distributed dynamics of the upper airways while the lower passage generations are represented by "lumping" of resistance and compliance effects. The lower airway representation is terminated with ten lung segments. The model is accurate for frequencies as high as 8500 Hz. The model is currently capable of predicting system eigenvalues as a function of system parameters and geometry for a "nonbreathing" lung. Future plans include modifying the model to include lung segment expansion and contraction as well as turbulence generation at airway bifurcations.

Acoustics↗
PubMed1969

Cell population kinetics: a modified interpretation of the graph of labeled mitoses.

Graphs of labeled mitoses, derived from autoradiographs of cell populations with (3)H-thymidine, show depressions in the curves at their midpoints. These depressions reflect interruption of DNA synthesis midway through S phase. Such interruptions revealed by the method of labeled mitoses should be considered when determining cell-cycle times.

Animals↗
PubMed1988

A graph-dynamic model of the power law of practice and the problem-solving fan-effect.

Numerous human learning phenomena have been observed and captured by individual laws, but no unified theory of learning has succeeded in accounting for these observations. A theory and model are proposed that account for two of these phenomena: the power law of practice and the problem-solving fan-effect. The power law of practice states that the speed of performance of a task will improve as a power of the number of times that the task is performed. The power law resulting from two sorts of problem-solving changes, addition of operators to the problem-space graph and alterations in the decision procedure used to decide which operator to apply at a particular state, is empirically demonstrated. The model provides an analytic account for both of these sources of the power law. The model also predicts a problem-solving fan-effect, slowdown during practice caused by an increase in the difficulty of making useful decisions between possible paths, which is also found empirically.

Decision Making↗
PubMed2000

Identifying amino acid residues in medium resolution critical point graphs using instance based query generation.

Instance Based Query Generation is defined and applied to the problem of recognising amino acid residues in medium resolution critical point graphs. The technique is an amalgamation of Relational Instance Based Learning and Frequent Query Discovery in First Order Logic. Instances are automatically constructed from a deductive database and first order association rules are derived from the instances. The initial investigations presented here indicate that the technique is able to discriminate some of the larger amino acid types as well as discriminating the protein from background solvent. Identification of the smaller amino acids remains difficult and requires further work.

Amino Acids↗
PubMed1999

Spatial analysis of the neuronal density of aminergic brainstem nuclei in primary neurodegenerative and vascular dementia: a comparative immunocytochemical and quantitative study using a graph method.

A graph method was employed to analyse spatial neuronal patterns of pontine nuclei with ascending aminergic projections to the forebrain (nucleus centralis superior (NCS), raphes dorsalis (NRD) and locus coeruleus (LC)), in Alzheimer disease (AD), Huntington disease (HD), and vascular (VD) as well as "mixed-type" (VA) dementia, compared with non-demented controls (CO) and a small sample of brains from schizophrenics ("dementia praecox" (DP)). The quantitative evaluations by the "minimal spanning tree (MST)" were complemented by rough neurofibrillary tangle (NFT) counts and by semiquantitative immunohistochemical assessment of amyloid deposition, neuritic plaque formation, and cellular gliosis. The AD cases showed a significant decline of neuronal density in all nuclei examined, as compared with controls and DP. Neuronal loss was not significant in VD, while the mixed cases with both vascular and Alzheimer-type pathology exhibited pronounced changes of neuronal density. Amyloid deposition occurred almost exclusively in AD and VA, as a rule, being of moderate degree, except for two presenile AD cases where it was marked. NFT were significantly increased in all nuclei in AD and in the VA cases, while they only occasionally appeared beyond age 55 in HD, DP and CO. The four HD cases showed in the NCS and NRD neuronal loss as severe as in AD. This neuronal loss implicates impairment of serotoninergic and noradrenergic neuromodulation as one basic mechanism promoting dementia in AD, VA and perhaps in HD.

Adult↗
PubMed2001

The Whitney reduction network: a method for computing autoassociative graphs.

This article introduces a new architecture and associated algorithms ideal for implementing the dimensionality reduction of an m-dimensional manifold initially residing in an n-dimensional Euclidean space where n >> m. Motivated by Whitney's embedding theorem, the network is capable of training the identity mapping employing the idea of the graph of a function. In theory, a reduction to a dimension d that retains the differential structure of the original data may be achieved for some d < or = 2m + 1. To implement this network, we propose the idea of a good-projection, which enhances the generalization capabilities of the network, and an adaptive secant basis algorithm to achieve it. The effect of noise on this procedure is also considered. The approach is illustrated with several examples.

Journal Article↗
PubMed1999

Replicator equations, maximal cliques, and graph isomorphism.

We present a new energy-minimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feature of this formulation is that a clear one-to-one correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem. To solve the program we use the so-called replicator equations--a class of straightforward continuous- and discrete-time dynamical systems developed in various branches of theoretical biology. We show how, despite their inherent inability to escape from local solutions, they nevertheless provide experimental results that are competitive with those obtained using more elaborate mean-field annealing heuristics.

Mathematics↗