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PubMed2004

Win-stay, lose-shift in language learning from peers.

Traditional language learning theory explores an idealized interaction between a teacher and a learner. The teacher provides sentences from a language, while the learner has to infer the underlying grammar. Here, we study a new approach by considering a population of individuals that learn from each other. There is no designated teacher. We are inspired by the observation that children grow up to speak the language of their peers, not of their parents. Our goal is to characterize learning strategies that generate "linguistic coherence," which means that most individuals use the same language. We model the resulting learning dynamics as a random walk of a population on a graph. Each vertex represents a candidate language. We find that a simple strategy using a certain aspiration level with the principle of win-stay, lose-shift does extremely well: stay with your current language, if at least three others use that language; otherwise, shift to an adjacent language on the graph. This strategy guarantees linguistic coherence on all nearly regular graphs, in the relevant limit where the number of candidate languages is much greater than the population size. Moreover, for many graphs, it is sufficient to have an aspiration level demanding only two other individuals to use the same language.

Algorithms↗
PubMed2005

A tool for filtering information in complex systems.

We introduce a technique to filter out complex data sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation-based graphs, giving filtered graphs that preserve the hierarchical organization of the minimum spanning tree but containing a larger amount of information in their internal structure. In particular in the case of planar filtered graphs (genus equal to 0), triangular loops and four-element cliques are formed. The application of this filtering procedure to 100 stocks in the U.S. equity markets shows that such loops and cliques have important and significant relationships with the market structure and properties.

Journal Article↗
PubMed2005

The hypergraph regularity method and its applications.

Szemeredi's regularity lemma asserts that every graph can be decomposed into relatively few random-like subgraphs. This random-like behavior enables one to find and enumerate subgraphs of a given isomorphism type, yielding the so-called counting lemma for graphs. The combined application of these two lemmas is known as the regularity method for graphs and has proved useful in graph theory, combinatorial geometry, combinatorial number theory, and theoretical computer science. Here, we report on recent advances in the regularity method for k-uniform hypergraphs, for arbitrary k > or = 2. This method, purely combinatorial in nature, gives alternative proofs of density theorems originally due to E. Szemeredi, H. Furstenberg, and Y. Katznelson. Further results in extremal combinatorics also have been obtained with this approach. The two main components of the regularity method for k-uniform hypergraphs, the regularity lemma and the counting lemma, have been obtained recently: Rodl and Skokan (based on earlier work of Frankl and Rodl) generalized Szemeredi's regularity lemma to k-uniform hypergraphs, and Nagle, Rodl, and Schacht succeeded in proving a counting lemma accompanying the Rodl-Skokan hypergraph regularity lemma. The counting lemma is proved by reducing the counting problem to a simpler one previously investigated by Kohayakawa, Rodl, and Skokan. Similar results were obtained independently by W. T. Gowers, following a different approach.

Journal Article↗
PubMed2003

Mixed Markov models.

Markov random fields can encode complex probabilistic relationships involving multiple variables and admit efficient procedures for probabilistic inference. However, from a knowledge engineering point of view, these models suffer from a serious limitation. The graph of a Markov field must connect all pairs of variables that are conditionally dependent even for a single choice of values of the other variables. This makes it hard to encode interactions that occur only in a certain context and are absent in all others. Furthermore, the requirement that two variables be connected unless always conditionally independent may lead to excessively dense graphs, obscuring the independencies present among the variables and leading to computationally prohibitive inference algorithms. Mumford [Mumford, D. (1996) in ICIAM 95, eds. Kirchgassner, K., Marenholtz, O. & Mennicken, R. (Akademie Verlag, Berlin), pp. -->233-256-->] proposed an alternative modeling framework where the graph need not be rigid and completely determined a priori. Mixed Markov models contain node-valued random variables that, when instantiated, augment the graph by a set of transient edges. A single joint probability distribution relates the values of regular and node-valued variables. In this article, we study the analytical and computational properties of mixed Markov models. In particular, we show that positive mixed models have a local Markov property that is equivalent to their global factorization. We also describe a computationally efficient procedure for answering probabilistic queries in mixed Markov models.

Journal Article↗
PubMed1978

Activation energy for RNA transport from isolated rat liver nuclei.

The temperature dependence of ATP-enhanced RNA delivery from rat liver nuclei to a surrogate cytoplasm was investigated. Examination of linear-rate data on Arrhenius graphs of 1/T vs. log (% RNA delivered per min) revealed an activation energy of 12.5--13 kcal/mol. When data derived from longer incubation periods was displayed on Arrhenius graphs, we observed a discontinuous graph--two distinct linear segments with slopes of differing sign which intersected near 20 degrees C. It was demonstrated that this discontinuity was not due to lipid phase transition in the nuclear membranes and that its position depended upon treatment of the nuclei and upon additives to the incubation mixtures. The decline in transport apparent in the upper-temperature domain on 20-min Arrhenius graphs was shown to be based on the diffusion of transported macromolecular RNA back into the nucleus--a process greatly amplified by the rapidity of transport in this domain. The large net inward diffusion, in concert with significantly differing activation energies for RNA transport and passive diffusion, suggests that the process of nucleocytoplasmic RNA transport is not diffusion driven. Our data have established that an integral parameter of RNA transport (namely, the activation energy) remains unchanged in various in vitro manipulations.

Animals↗
PubMed2001

Overall molecular descriptors. 3. Overall Zagreb indices.

This paper develops further the concept of overall characterization of molecular topology, which is based on calculation of a given graph-invariant for all subgraphs of molecular graph. The new approach defines a cumulative topological descriptor, and an ordered series of terms (eth-order descriptor), which present the sum of the graph-invariant values for all subgraphs having the same number of edges. Alternatively, the terms in the series may be further partitioned, in the manner of molecular connectivity concept of Randić, Kier, and Hall, into contributions of path, cluster, and path-cluster type of subgraphs. The previous publications on the novel approach were based on the simplest graph-invariants--the sum of entries of the adjacency matrix and the distance matrix. Overall connectivity and overall Wiener index were thus defined, along with their respective series of e-order terms. The present study makes use of two other simple functions of vertex degrees, the first and second Zagreb indices. The overall versions of these two indices, very recently constructed, are analyzed in detail. Their potential applicability is verified by deriving multilinear regression models of ten physicochemical properties of alkanes, and comparing them to the results obtained by molecular connectivity and overall connectivity indices.

Chemical Phenomena↗
PubMed2005

Evaluating intraspecific "network" construction methods using simulated sequence data: do existing algorithms outperform the global maximum parsimony approach?

In intraspecific studies, reticulated graphs are valuable tools for visualization, within a single figure, of alternative genealogical pathways among haplotypes. As available software packages implementing the global maximum parsimony (MP) approach only give the possibility to merge resulting topologies into less-resolved consensus trees, MP has often been neglected as an alternative approach to purely algorithmic (i.e., methods defined solely on the basis of an algorithm) "network" construction methods. Here, we propose to search tree space using the MP criterion and present a new algorithm for uniting all equally most parsimonious trees into a single (possibly reticulated) graph. Using simulated sequence data, we compare our method with three purely algorithmic and widely used graph construction approaches (minimum-spanning network, statistical parsimony, and median-joining network). We demonstrate that the combination of MP trees into a single graph provides a good estimate of the true genealogy. Moreover, our analyses indicate that, when internal node haplotypes are not sampled, the median-joining and MP methods provide the best estimate of the true genealogy whereas the minimum-spanning algorithm shows very poor performances.

Algorithms↗
PubMed1989

Protons resolve dual effects of calcium on miniature end-plate potential frequency at frog neuromuscular junctions.

Inhibition of transmitter release by protons (H+) was studied at the frog neuromuscular junction at various extracellular concentrations of calcium ([Ca++]o) and potassium ([K+]o) by recording miniature end-plate potential (MEPP) frequency with the intracellular microelectrode. H+ decreased K+ -stimulated MEPP frequency. A double logarithmic graph of MEPP frequency at 7.5 mM K+ vs. [H+]o yielded a straight line with negative slope. At 10 mM K+, there was a parallel shift to the right of the graph. According to the surface charge model, K+ acts solely to depolarize the prejunctional membrane in accordance with the Nernst equation. By decreasing the prejunctional negative surface charge, H+ decreases K+ -stimulated MEPP frequency by decreasing [Ca++]o at the Ca++ channel. An estimated pKa of 4.20 may represent an acidic site at the Ca++ channel associated with Ca++ influx. As [Ca++]o increased above 1 mM for pH 7.40 and 10 mM K+, MEPP frequency decreased, i.e., the inhibitory component of dual effects of Ca++ occurred. At pH 6.40, the inhibitory component was abolished, unmasking the stimulatory effect of Ca++ on MEPP frequency. Reversal of Ca++ action by H+ could not be explained by surface charge theory alone. A double logarithmic graph of MEPP frequency vs. [K+]o at 8.5-10.5 mM was linear with a slope of 4. There were parallel shifts to the right of this graph for changes in pH from 7.40 to 6.90 and in [Ca++]o from 1 to 2.5 mM. These results are explained on the hypothesis that K+ also acts at an acidic prejunctional site to increase Ca++ -dependent quantal transmitter release. This action of K+ was inhibited by H+ and raised Ca++. Based on kinetic theory, the estimated pKa of the acidic prejunctional K+ site was 6.31. Based on free energy calculations, its cation preference was H+ greater than K+ greater than Ca++.

Animals↗
PubMed2006

Algorithmic computation of knot polynomials of secondary structure elements of proteins.

The classification of protein structures is an important and still outstanding problem. The purpose of this paper is threefold. First, we utilize a relation between the Tutte and homfly polynomial to show that the Alexander-Conway polynomial can be algorithmically computed for a given planar graph. Second, as special cases of planar graphs, we use polymer graphs of protein structures. More precisely, we use three building blocks of the three-dimensional protein structure--alpha-helix, antiparallel beta-sheet, and parallel beta-sheet--and calculate, for their corresponding polymer graphs, the Tutte polynomials analytically by providing recurrence equations for all three secondary structure elements. Third, we present numerical results comparing the results from our analytical calculations with the numerical results of our algorithm-not only to test consistency, but also to demonstrate that all assigned polynomials are unique labels of the secondary structure elements. This paves the way for an automatic classification of protein structures.

Algorithms↗
PubMed2001

Clustering protein sequences--structure prediction by transitive homology.

MOTIVATION: It is widely believed that for two proteins Aand Ba sequence identity above some threshold implies structural similarity due to a common evolutionary ancestor. Since this is only a sufficient, but not a necessary condition for structural similarity, the question remains what other criteria can be used to identify remote homologues. Transitivity refers to the concept of deducing a structural similarity between proteins A and C from the existence of a third protein B, such that A and B as well as B and C are homologues, as ascertained if the sequence identity between A and B as well as that between B and C is above the aforementioned threshold. It is not fully understood if transitivity always holds and whether transitivity can be extended ad infinitum. RESULTS: We developed a graph-based clustering approach, where transitivity plays a crucial role. We determined all pair-wise similarities for the sequences in the SwissProt database using the Smith-Waterman local alignment algorithm. This data was transformed into a directed graph, where protein sequences constitute vertices. A directed edge was drawn from vertex A to vertex B if the sequences A and B showed similarity, scaled with respect to the self-similarity of A, above a fixed threshold. Transitivity was important in the clustering process, as intermediate sequences were used, limited though by the requirement of having directed paths in both directions between proteins linked over such sequences. The length dependency-implied by the self-similarity-of the scaling of the alignment scores appears to be an effective criterion to avoid clustering errors due to multi-domain proteins. To deal with the resulting large graphs we have developed an efficient library. Methods include the novel graph-based clustering algorithm capable of handling multi-domain proteins and cluster comparison algorithms. Structural Classification of Proteins (SCOP) was used as an evaluation data set for our method, yielding a 24% improvement over pair-wise comparisons in terms of detecting remote homologues. AVAILABILITY: The software is available to academic users on request from the authors. CONTACT: e.bolten@science-factory.com; schliep@zpr.uni-koeln.de; s.schneckener@science-factory.com; d.schomburg@uni-koeln.de; schrader@zpr.uni-koeln.de. SUPPLEMENTARY INFORMATION: http://www.zaik.uni-koeln.de/~schliep/ProtClust.html.

Algorithms↗
PubMed2003

Deriving phylogenetic trees from the similarity analysis of metabolic pathways.

MOTIVATION: Comparative analysis of metabolic pathways in different genomes can give insights into the understanding of evolutionary and organizational relationships among species. This type of analysis allows one to measure the evolution of complete processes (with different functional roles) rather than the individual elements of a conventional analysis. We present a new technique for the phylogenetic analysis of metabolic pathways based on the topology of the underlying graphs. A distance measure between graphs is defined using the similarity between nodes of the graphs and the structural relationship between them. This distance measure is applied to the enzyme-enzyme relational graphs derived from metabolic pathways. Using this approach, pathways and group of pathways of different organisms are compared to each other and the resulting distance matrix is used to obtain a phylogenetic tree. RESULTS: We apply the method to the Citric Acid Cycle and the Glycolysis pathways of different groups of organisms, as well as to the Carbohydrate metabolic networks. Phylogenetic trees obtained from the experiments were close to existing phylogenies and revealed interesting relationships among organisms.

Algorithms↗
PubMed2003

A fast layout algorithm for protein interaction networks.

MOTIVATION: Graph drawing algorithms are often used for visualizing relational information, but a naive implementation of a graph drawing algorithm encounters real difficulties when drawing large-scale graphs such as protein interaction networks. RESULTS: We have developed a new, extremely fast layout algorithm for visualizing large-scale protein interaction networks in the three-dimensional space. The algorithm (1) first finds a layout of connected components of an entire network, (2) finds a global layout of nodes with respect to pivot nodes within a connected component and (3) refines the local layout of each connected component by first relocating midnodes with respect to their cutvertices and direct neighbors of the cutvertices and then by relocating all nodes with respect to their neighbors within distance 2. Advantages of this algorithm over classical graph drawing methods include: (1) it is an order of magnitude faster, (2) it can directly visualize data from protein interaction databases and (3) it provides several abstraction and comparison operations for effectively analyzing large-scale protein interaction networks. AVAILABILITY: http://wilab.inha.ac.kr/interviewer/

Algorithms↗
PubMed1997

The genealogy of samples in models with selection.

We introduce the genealogy of a random sample of genes taken from a large haploid population that evolves according to random reproduction with selection and mutation. Without selection, the genealogy is described by Kingman's well-known coalescent process. In the selective case, the genealogy of the sample is embedded in a graph with a coalescing and branching structure. We describe this graph, called the ancestral selection graph, and point out differences and similarities with Kingman's coalescent. We present simulations for a two-allele model with symmetric mutation in which one of the alleles has a selective advantage over the other. We find that when the allele frequencies in the population are already in equilibrium, then the genealogy does not differ much from the neutral case. This is supported by rigorous results. Furthermore, we describe the ancestral selection graph for other selective models with finitely many selection classes, such as the K-allele models, infinitely-many-alleles models. DNA sequence models, and infinitely-many-sites models, and briefly discuss the diploid case.

Genealogy and Heraldry↗
PubMed2002

The KEGG databases at GenomeNet.

The Kyoto Encyclopedia of Genes and Genomes (KEGG) is the primary database resource of the Japanese GenomeNet service (http://www.genome.ad.jp/) for understanding higher order functional meanings and utilities of the cell or the organism from its genome information. KEGG consists of the PATHWAY database for the computerized knowledge on molecular interaction networks such as pathways and complexes, the GENES database for the information about genes and proteins generated by genome sequencing projects, and the LIGAND database for the information about chemical compounds and chemical reactions that are relevant to cellular processes. In addition to these three main databases, limited amounts of experimental data for microarray gene expression profiles and yeast two-hybrid systems are stored in the EXPRESSION and BRITE databases, respectively. Furthermore, a new database, named SSDB, is available for exploring the universe of all protein coding genes in the complete genomes and for identifying functional links and ortholog groups. The data objects in the KEGG databases are all represented as graphs and various computational methods are developed to detect graph features that can be related to biological functions. For example, the correlated clusters are graph similarities which can be used to predict a set of genes coding for a pathway or a complex, as summarized in the ortholog group tables, and the cliques in the SSDB graph are used to annotate genes. The KEGG databases are updated daily and made freely available (http://www.genome.ad.jp/kegg/).

Animals↗
PubMed2004

The Alternative Splicing Gallery (ASG): bridging the gap between genome and transcriptome.

Alternative splicing essentially increases the diversity of the transcriptome and has important implications for physiology, development and the genesis of diseases. Conventionally, alternative splicing is investigated in a case-by-case fashion, but this becomes cumbersome and error prone if genes show a huge abundance of different splice variants. We use a different approach and integrate all transcripts derived from a gene into a single splicing graph. Each transcript corresponds to a path in the graph, and alternative splicing is displayed by bifurcations. This representation preserves the relationships between different splicing variants and allows us to investigate systematically all possible putative transcripts. We built a database of splicing graphs for human genes, using transcript information from various major sources (Ensembl, RefSeq, STACK, TIGR and UniGene). A Web interface allows users to display the splicing graphs, to interactively assemble transcripts and to access their sequences as well as neighboring genomic regions. We also provide for each gene an exhaustive pre-computed catalog of putative transcripts--in total more than 1.2 million sequences. We found that approximately 65% of the investigated genes show evidence for alternative splicing, and in 5% of the cases, a single gene might produce over 100 transcripts.

Alternative Splicing↗
PubMed1988

Empirical investigation of visual-inspection versus trend-line analysis of single-subject data.

We examined the inferential decisions made using either visual analysis alone or in combination with a trend line to evaluate data from single-subject research designs. Thirty-nine subjects were randomly assigned to either a Visual Group (n = 20) that used a visual-inspection approach to analyzing graphed data or a Quantitative Group (n = 19) that used a trend-line approach. After instruction in interpretation, we asked the subjects to analyze graphs containing data from five hypothetical AB single-subject designs. Results revealed a statistically significant difference in the decision made between the two groups for four of the five graphs. The group using the trend line to analyze graphed data exhibited more confidence in the decisions they made and also demonstrated greater within-group consistency as compared with the group using visual inspection. The implications of various methods of data analysis in establishing the scientific legitimacy of single-subject research methods are discussed, and the argument is made that quantitative procedures can assist in the analysis and interpretation of single-subject data.

Data Collection↗
PubMed1997

Vagaries in the delimitation of character states in quantitative variation--an experimental study.

An experimental study on the delimitation of character states in continuous variation indicates that (1) the way data are presented influences the assignment of character states and (2) states in the same data set are delimited in various ways by different individuals. Forty-nine individuals were given a set of graphs denoting variation of 10 characters in the genus Kalmia (Ericaceae) and outgroups, all identification having been removed from the graphs. The variation was represented in one of three ways: as 95% confidence intervals on a linear scale, as 95% confidence intervals on a log10 scale, or with bars showing SD x 2 on a linear scale. No two individuals scored a set of graphs in the same way, and only one character in one representation was scored identically by all individuals; the scoring for this character was completely different when the ordinate was changed from linear to logarithmic. Together, the 49 individuals delimited states within each character between 9 and 16 different ways. In general, variation represented by 2 x SD bars elicited the largest numbers of different scorings, yet with a relatively low number of states; the complexity of the patterns in the graphs in this representation was greatest. Expert knowledge appears to be of dubious value in delimiting states in such variation, and if such characters are to be used in phylogenetic analyses, states could be delimited by people who know nothing of the details of the study being scored; in any case, presentation of data and an explicit protocol to follow when delimiting states are essential. In converting data of this type into character states, psychological factors are particularly likely to come into play. Other implications of our experiments include the severe underdetermination of some phylogenetic hypotheses by observation and the heterogeneous nature of morphological data.

Data Interpretation, Statistical↗
PubMed1988

Pregnancy-induced hypertension without proteinuria: is it true preeclampsia?

A profile scoring system has recently been developed as a standardized method of early identification and severity assessment of pregnancy-induced hypertension (PIH). The purpose of this study is twofold: (1) to compare the PIH profile scores of patients demonstrating mild PIH without proteinuria with those of patients demonstrating mild PIH with proteinuria, and (2) to introduce the PIH profile graph as a standardized clinical assessment tool. Serial PIH profile data after 24 weeks' gestation from 46 term primigravid patients with mild PIH (group 1 = 19 patients without proteinuria; group 2 = 27 patients with proteinuria) were plotted on PIH profile graphs and compared. Profile scores from ten normotensive primigravidas at term served as controls. Serial profile scores for groups 1 and 2 showed similar patterns on the profile graph. Based on these data, we believe that PIH without proteinuria is clinically and biochemically a manifestation of true preeclampsia before the onset of proteinuria. Furthermore, the PIH profile graph allows one to identify subtle changes in the disorder and to anticipate the development of severe preeclampsia.

Adult↗