The inverse problems for some topological indices in combinatorial chemistry.

In the original paper, Goldman et al. (2000) launched the study of the inverse problems in combinatorial chemistry, which is closely related to the design of combinatorial libraries for drug discovery. Following their ideas, we investigate four other topological indices, i.e., the sigma-index, the c-index, the Z-index, and the M(1)-index, with a special emphasis on the sigma-index. Like the Wiener index, these four indices are very popular in combinatorial chemistry and reflect many chemical and physical properties. We give algorithmic and analytical solutions for the inverse problems of the four indices. We also show that the SUBTREEVALUE reconstruction problem for the sigma-index is NP-hard.     

New concentration measures as kinds of the quadratic entropy

We introduced two new quadratic entropy indices and performed numerical experimentation on biological data sets to reveal their properties. The difference between two individuals was postulated in both cases on the basis of occurrence probabilities of the species concerned. The new measures summarize a different aspect of community properties than biodiversity indices. They may play a critical role among others in population dynamic models and in the analysis of dominance in ecology. The numerical experimentation was based in part on the characteristics of so-called sensitivity graphs. The graphs related to the new indices are very similar to the opposites of sensitivity graphs of diversity indices, generally used in statistical ecology. Further relations between the new indices and concentration indices were analysed on plot diagrams originating from simulated data. From these analyses, we conclude that the new quadratic entropies are close to concentration measures.     

A novel representation of RNA secondary structure based on element-contact graphs

Background  

Depending on their specific structures, noncoding RNAs (ncRNAs) play important roles in many biological processes. Interest in developing new topological indices based on RNA graphs has been revived in recent years, as such indices can be used to compare, identify and classify RNAs. Although the topological indices presented before characterize the main topological features of RNA secondary structures, information on RNA structural details is ignored to some degree. Therefore, it is necessity to identify topological features with low degeneracy based on complete and fine-grained RNA graphical representations.     

Laplacian Estrada and Normalized Laplacian Estrada Indices of Evolving Graphs

Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.     

Markov clustering versus affinity propagation for the partitioning of protein interaction graphs

Background  

Genome scale data on protein interactions are generally represented as large networks, or graphs, where hundreds or thousands of proteins are linked to one another. Since proteins tend to function in groups, or complexes, an important goal has been to reliably identify protein complexes from these graphs. This task is commonly executed using clustering procedures, which aim at detecting densely connected regions within the interaction graphs. There exists a wealth of clustering algorithms, some of which have been applied to this problem. One of the most successful clustering procedures in this context has been the Markov Cluster algorithm (MCL), which was recently shown to outperform a number of other procedures, some of which were specifically designed for partitioning protein interactions graphs. A novel promising clustering procedure termed Affinity Propagation (AP) was recently shown to be particularly effective, and much faster than other methods for a variety of problems, but has not yet been applied to partition protein interaction graphs.     

Graph theoretical methods for comparing phytosociological structures

This paper describes some methods that can be used to compare the phytosociological structure of plant communities using some graph theoretic properties of the directed graphs that represent them. In such a graph, the species are represented by points and the association of species A with species B is represented by a directed line segment going from B to A. Two communities can be compared using simple indices to measure the similarity of their species-lists (point similarity) and of the species associations in them (line similarity). A more sophisticated and informative measure of line similarity is the probability that, given the number of points shared by two graphs, they have at least as many lines in common as they are observed to have. A formula for calculating that probability is given here. The graphs of community structure can also be compared with respect to the homogeneity of the distribution of the lines among the points, a property related to the number of species that are important in determining the composition of the community. These techniques are illustrated using the graphs of the phytosociological structure of intertidal seaweed communities on the southeast coast of Nova Scotia.Nomenclature follows: South and Cardinal (1970)     

Electronic structures of bisnoradamantenyl and bisnoradamantanyl dications and related species

The highly pyramidalized molecule bisnoradamantene is extremely reactive toward nucleophiles and dienes. In this work, we studied the electronic structure of bisnoaradamantene, as well as those of its cation and dication, which are previously unreported carbonium ions. According to QTAIM and MO analysis, there is a 3c-2e bonding system in the bisnoradamantenyl cation and a 4c-2e bonding system in the bisnoradamantenyl dication. A topological study indicated that, on going from bisnoradamantene to its dication, π-bond interaction with the bridgehead carbon atom increases. Additional study of the bisnoradamantanyl dication also indicated that it has two multicenter bonding systems. Comparison of the D3BIA and NICS aromaticity indices of these molecules and other derivatives indicates that these indices are well correlated, and analysis of these indices shows that the cationic and dicationic bisnoradamantenyl species are homoaromatic.

Connection topology of proteins

One-dimensional amino acid sequences and three-dimensional foldedpolypeptide chains were modelled as non-directed graphs in whichnodes corresponded to amino acids and arcs repre sented connectionsbetween them. In the case of folded chains, non-backbone connectionswere assigned to amino acid pairs if their distance was lowerthan a threshold. Two topological indices, the connectednessnumber and the effective chain length were devised to comparefolding topologies. Loops created by non-backbone connectionsin the structure graphs were studied by simple graphical representations,revealing the hierarchy in native protein structures.     

农业生态经济系统生产力评价指标体系研究

本文着眼于如何把生态经济理论应用于生产实践,探讨了农业生态经济系统生产力评价指标体系的建立原则和方法,设计出一套包括6项综合指标在内的评价指标体系,并根据对北京留民营、窦店2个典型系统的计算,初步确定出京郊农业生态经济系统的参照指标,从而进一步对京郊渠头农场的系统生产力水平进行了评估分析,取得了比较满意的结果。     

Locomotion,posture, and the foramen magnum in primates: Reliability of indices and insights into hominin bipedalism

The position (FMP) and orientation (FMO) of the foramen magnum have been used as proxies for locomotion and posture in extant and extinct primates. Several indices have been designed to quantify FMP and FMO but their application has led to conflicting results. Here, we test six widely used indices and two approaches (univariate and multivariate) for their capability to discriminate between postural and locomotor types in extant primates and fossil hominins. We then look at the locomotion of australopithecines and Homo on the base of these new findings. The following measurements are used: the opisthocranion–prosthion (OP–PR) and the opisthocranion–glabella (OP–GL) indices, the basion–biporion (BA–BP) and basion–bicarotid chords, the foramen magnum angle (FMA), and the basion–sphenoccipital ratio. After exploring the indices variability using principal component analysis, pairwise comparisons are performed to test for the association between each index and the locomotor and postural habits. Cranial size and phylogeny are taken into account. Our analysis indicates that none of the indices or approaches provides complete discrimination across locomotor and postural categories, although some differences are highlighted. FMA and BA–BP distinguish respectively obligate and facultative bipeds from all other groups. For what concerns posture, orthogrades and pronogrades differ with respects to OP–PR, OP–GL, and FMA. Although the multivariate approach seems to have some discrimination power, the results are most likely driven by facial and neurocranial variability embedded in some of the indices. These results demonstrate that indices relying on the anteroposterior positioning of the foramen may not be appropriate proxies for locomotion among primates. The assumptions about locomotor and postural habits in fossil hominins based on foramen magnum indices should be revised in light of these new findings.     

Finding the Minimum Sample Richness (MSR) for multivariate analyses: implications for palaeoecology

Many techniques have been developed to estimate species richness and beta diversity. Those techniques, dependent on sampling, require abundance or presence/absence data. Palaeontological data is by nature incomplete, and presence/absence data is often the only type of data that can be used to provide an estimate of ancient biodiversity. We used a simulation approach to investigate the behaviour of commonly used similarity indices, and the reliability of classifications derived from these indices, when working with incomplete data. We drew samples, of varying number and richness, from artificial species lists, which represented original life assemblages, and calculated error rates for classifications of the parent lists and samples. Using these results, we estimated the Minimum Sample Richness (MSR) needed to achieve 95% classification accuracy. Results were compared for classifications derived from several commonly used similarity indexes (Dice, Jaccard, Simpson and Raup–Crick). MSR was similar for the Dice, Jaccard and Simpson indices. MSR for the Raup–Crick index was often much lower, suggesting that it is preferable for classifying patchy data, however the performance of this index was less stable than the other three in the simulations, which required an even lower MSR. MSR can be found for all presence/absence data from the contour graphs and equations as long as the absolute species richness and the beta diversity can be estimated.     

Graphical integrity issues in open access publications: Detection and patterns of proportional ink violations

Academic graphs are essential for communicating complex scientific ideas and results. To ensure that these graphs truthfully reflect underlying data and relationships, visualization researchers have proposed several principles to guide the graph creation process. However, the extent of violations of these principles in academic publications is unknown. In this work, we develop a deep learning-based method to accurately measure violations of the proportional ink principle (AUC = 0.917), which states that the size of shaded areas in graphs should be consistent with their corresponding quantities. We apply our method to analyze a large sample of bar charts contained in 300K figures from open access publications. Our results estimate that 5% of bar charts contain proportional ink violations. Further analysis reveals that these graphical integrity issues are significantly more prevalent in some research fields, such as psychology and computer science, and some regions of the globe. Additionally, we find no temporal and seniority trends in violations. Finally, apart from openly releasing our large annotated dataset and method, we discuss how computational research integrity could be part of peer-review and the publication processes.     

Overlap graphs and de Bruijn graphs: data structures for de novo genome assembly in the big data era

Background: De novo genome assembly relies on two kinds of graphs: de Bruijn graphs and overlap graphs. Overlap graphs are the basis for the Celera assembler, while de Bruijn graphs have become the dominant technical device in the last decade. Those two kinds of graphs are collectively called assembly graphs.Results: In this review, we discuss the most recent advances in the problem of constructing, representing and navigating assembly graphs, focusing on very large datasets. We will also explore some computational techniques, such as the Bloom filter, to compactly store graphs while keeping all functionalities intact. Conclusions: We complete our analysis with a discussion on the algorithmic issues of assembling from long reads (e.g., PacBio and Oxford Nanopore). Finally, we present some of the most relevant open problems in this field.     

New similarity indices for the assignment of relevés to the vegetation units of an existing phytosociological classification

Every proposed vegetation classification is sooner or later confronted with an accumulation of new data, which has to be assigned to existing vegetation units. Calculation of similarity indices between new relevés (vegetation plots) and constancy columns of established vegetation units is a suitable method for computerised assignment of relevés to these units. This paper compares several similarity indices using simulated data set where either randomly distributed or diagnostic species prevail in the species composition of the tested relevé. Traditional indices, based only on species composition, produce different results than similarity indices that consider species fidelity. However, both types of indices failed in some situations and thus cannot be widely accepted as suitable methods of additional relevé assignment. Therefore a combined Frequency-Positive Fidelity Index (FPFI) is proposed. This new index includes compositional similarity of an assigned relevé with vegetation unit and retains the advantages and lacks the disadvantages of tested indices. The calculation of all these indices is available in the JUICE program (http://www.sci.muni.cz/botany/juice.htm).     

Dynamic response of a cricadian pacemaker

The term cell assembly, first introduced by D. O. Hebb, is defined in the framework of graph theory. This definition leads to some beautiful problems concerning the number and size of cell assemblies in large graphs. Some approaches to solve these problems are presented. In particular, the graphs K _n xK _m are constructed that have n·m points, n+m-2 connections per point, and at least 2ⁿ+2^m-4 assemblies. Several new notions of connectivity in directed graphs are introduced and their relationships are investigated. The insight into these notions and their relationships will be helpful for further construction of graphs with many assemblies and/or high connectivity. The resulting graphs are not only important for the idea of cell assemblies in the context of neurodynamics, they may also find applications in the construction of communication networks and associative memories.