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At least 343 records · Page 19Linked to original sources
PubMedDate not supplied

Group graph of the genetic code.

The genetic code doublets can be divided into two octets of completely degenerate and ambiguous coding dinucleotides. These two octets have the algebraic property of lying on continuously connected planes on the group graph (a tesseract) of the Cartesian product of two Klein 4-groups of nucleotide exchange operators. The K X K group can also be broken into four cosets, one of which has completely degenerate coding elements, and another that has completely ambiguous coding elements. The two octets of coding doublets have the further algebraic property that the product of their internal exchange operators naturally divide into two exactly equivalent sets. These properties of the genetic code are relevant to unraveling error-detecting and error-correcting (proof-reading) aspects of the genetic code and may be helpful in understanding the context-sensitive grammar of genetic language.

Genetic Code↗
PubMed1990

Structural resemblance between the families of bacterial signal-transduction proteins and of G proteins revealed by graph theoretical techniques.

The first application of a novel technique for the identification of common folding motifs in proteins is presented. Using techniques derived from graph theory, developed in order to compare secondary structure motifs in proteins, we have established that there is a striking resemblance in the tertiary fold of the Salmonella typhimurium Che Y chemotaxis protein and that of the GDP-binding domain of Escherichia coli elongation factor Tu (EF Tu). These two protein structures are representatives of two major macromolecular classes: CheY is a signal-transduction protein with sequence homologies to a wide range of bacterial proteins involved in regulation of chemotaxis, membrane synthesis and sporulation; whilst EF Tu is one of a family of guanosine-nucleotide-binding proteins which include the ras oncogene proteins and signal-transducing G proteins. The similarity we have found extends far beyond the previously recognized resemblances of each protein's fold to that of a generic nucleotide-binding domain. The lack of significant sequence homology between the two classes of proteins may mean that the common fold of the two proteins constitutes a particularly stable folding motif. However, an alternative possibility is that the strong three-dimensional structural resemblance may be indicative of a remote shared common ancestry between the bacterial signal-transduction proteins and the GDP-binding proteins.

Algorithms↗
PubMedDate not supplied

Three-dimensional vector graphing of the H reflex.

Comparison of latencies of the H reflex from side-to-side is considered a valid indicator of pathology, but amplitudes are too variable to allow similar comparison. Three pairs of electrodes were placed circumferentially and longitudinally along the calf to record the H reflex in three axes simultaneously. An H reflex with the greatest amplitude was produced by incrementally increasing submaximal stimulation to the tibial nerve. Three-dimensional vector graphs were constructed at three levels in each calf in ten normal individuals. Best fit curve Procrustes statistical analysis showed an average of 82.2 to 90.6% agreement of 3-D shape left-to-right with greater agreement at distal levels. Standard deviation ranged from 11.3% proximally to 8.2% distally. This represents much closer agreement than established norms for amplitude, which can vary from two to four times side-to-side. Three-dimensional vector analysis holds promise to further understanding of peripheral and central electrophysiologic phenomena.

Adult↗
PubMed1979

A dynamic graph for documentation of gestational age.

A graphic format is presented for the display and storage of data relating to gestational age. The graph permits rapid retrieval and synthesis of often confusion information and is thereby useful in the management of complicated pregnancies.

Female↗
PubMed1996

A graph theoretic approach to the analysis of DNA sequencing data.

The analysis of data from automated DNA sequencing instruments has been a limiting factor in the development of new sequencing technology. A new base-calling algorithm that is intended to be independent of any particular sequencing technology has been developed and shown to be effective with data from the Applied Biosystems 373 sequencing system. This algorithm makes use of a nonlinear deconvolution filter to detect likely oligomer events and a graph theoretic editing strategy to find the subset of those events that is most likely to correspond to the correct sequence. Metrics evaluating the quality and accuracy of the resulting sequence are also generated and have been shown to be predictive of measured error rates. Compared to the Applied Biosystems Analysis software, this algorithm generates 18% fewer insertion errors, 80% more deletion errors, and 4% fewer mismatches. The tradeoff between different types of errors can be controlled through a secondary editing step that inserts or deletes base calls depending on their associated confidence values.

Algorithms↗
PubMed2000

Noise in hysteretic systems and stochastic processes on graphs

It is shown that the theory of stochastic diffusion processes on graphs is a natural tool for the analysis of noise in hysteretic systems. In particular, by using this theory, analytical expressions for stationary characteristics of random outputs of some hysteretic systems are derived.

Journal Article↗
PubMed2001

Minimal vertex covers on finite-connectivity random graphs: a hard-sphere lattice-gas picture.

The minimal vertex-cover (or maximal independent-set) problem is studied on random graphs of finite connectivity. Analytical results are obtained by a mapping to a lattice gas of hard spheres of (chemical) radius 1, and they are found to be in excellent agreement with numerical simulations. We give a detailed description of the replica-symmetric phase, including the size and entropy of the minimal vertex covers, and the structure of the unfrozen component which is found to percolate at a connectivity c approximately 1.43. The replica-symmetric solution breaks down at c=e approximately 2.72. We give a simple one-step replica-symmetry-broken solution, and discuss the problems in the interpretation and generalization of this solution.

Journal Article↗
PubMed2001

Eigenstate structure in graphs and disordered lattices.

We study wave function structure for quantum graphs in the chaotic and disordered regime, using measures such as the wave function intensity distribution and the inverse participation ratio. The result is much less ergodicity than expected from random matrix theory, even though the spectral statistics are in agreement with random matrix predictions. Instead, analytical calculations based on short-time semiclassical behavior correctly describe the eigenstate structure.

Journal Article↗
PubMed2001

Topology of technology graphs: small world patterns in electronic circuits.

Recent theoretical studies and extensive data analyses have revealed a common feature displayed by biological, social, and technological networks: the presence of small world patterns. Here we analyze this problem by using several graphs obtained from one of the most common technological systems: electronic circuits. It is shown that both analogic and digital circuits exhibit small world behavior. We conjecture that the small world pattern arises from the compact design in which many elements share a small, close physical neighborhood plus the fact that the system must define a single connected component (which requires shortcuts connecting different integrated clusters). The degree distributions displayed are consistent with a conjecture concerning the sharp cutoffs associated to the presence of costly connections [Amaral et al., Proc. Natl. Acad. Sci. USA 97, 11 149 (2000)], thus providing a limit case for the classes of universality of small world patterns from real, artificial networks. The consequences for circuit design are outlined.

Journal Article↗
PubMed2001

Complex-temperature phase diagrams for the q-state Potts model on self-dual families of graphs and the nature of the q-->infinity limit.

Exact calculations of the Potts model partition function Z(G,q,v) have been presented for arbitrary q and temperature-like variable v on self-dual strip graphs G of the square lattice with fixed width L(y) and arbitrarily great length Lx with two types of boundary conditions. Letting Lx-->infinity, the resultant free energy and complex-temperature phase diagram have been computed, including the locus B where the free energy is nonanalytic. Results are analyzed for widths L(y)=1,2,3. These results have been used to study the approach to the large-q limit of B.

Journal Article↗
PubMed2001

Metastable configurations of spin models on random graphs.

One-flip stable configurations of an Ising model on a random graph with fluctuating connectivity are examined. In order to perform the quenched average of the number of stable configurations we introduce a global order-parameter function with two arguments. The analytical results are compared with numerical simulations.

Journal Article↗
PubMed2002

Glassy dynamics in granular compaction: sand on random graphs.

We discuss the use of a ferromagnetic spin model on a random graph to model granular compaction. A multispin interaction is used to capture the competition between local and global satisfaction of constraints characteristic for geometric frustration. We define an athermal dynamics designed to model repeated taps of a given strength. Amplitude cycling and the effect of permanently constraining a subset of the spins at a given amplitude is discussed. Finally we check the validity of Edwards's hypothesis for the athermal tapping dynamics.

Journal Article↗
PubMed2002

Exact, convergent periodic-orbit expansions of individual energy eigenvalues of regular quantum graphs.

We present exact, explicit, convergent periodic-orbit expansions for individual energy levels of regular quantum graphs in the paper. One simple application is the energy levels of a particle in a piecewise constant potential. Since the classical ray trajectories (including ray splitting) in such systems are strongly chaotic, this result provides an explicit quantization of a classically chaotic system.

Journal Article↗
PubMed2000

Periodic-orbit theory of anderson localization on graphs

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an aperiodic Kronig-Penney model in one dimension. The exact expression for the probability to return to an initially localized state is computed in terms of classical trajectories. It saturates to a finite value due to localization, while the diagonal approximation decays diffusively. Our theory is based on the identification of families of isometric orbits. The coherent periodic-orbit sums within these families, and the summation over all families, are performed analytically using advanced combinatorial methods.

Journal Article↗
PubMed2000

Number of guards needed by a museum: a phase transition in vertex covering of random graphs.

In this Letter we study the NP-complete vertex cover problem on finite connectivity random graphs. When the allowed size of the cover set is decreased, a discontinuous transition in solvability and typical-case complexity occurs. This transition is characterized by means of exact numerical simulations as well as by analytical replica calculations. The replica symmetric phase diagram is in excellent agreement with numerical findings up to average connectivity e, where replica symmetry becomes locally unstable.

Journal Article↗
PubMed2000

Chaotic scattering on graphs

Quantized, compact graphs are excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity, we show that they display all the features which characterize quantum chaotic scattering. We derive exact expressions for the scattering matrix, and an exact trace formula for the density of resonances, in terms of classical orbits, analogous to the semiclassical theory of chaotic scattering. A statistical analysis of the cross sections and resonance parameters compares well with the predictions of random matrix theory. Hence, this system is proposed as a convenient tool to study the generic behavior of chaotic scattering systems and their semiclassical description.

Journal Article↗
PubMed2001

Typical solution time for a vertex-covering algorithm on finite-connectivity random graphs.

We analytically describe the typical solution time needed by a backtracking algorithm to solve the vertex-cover problem on finite-connectivity random graphs. We find two different transitions: The first one is algorithm dependent and marks the dynamical transition from linear to exponential solution times. The second one gives the maximum computational complexity, and is found exactly at the threshold where the system undergoes an algorithm-independent phase transition in its solvability. Analytical results are corroborated by numerical simulations.

Journal Article↗
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↗