Two-letter words and a fundamental homomorphism ruling geometric contextuality

It has recently been recognized by the author that the quantum contextuality paradigm may be formulated in terms of the properties of some subgroups of the two-letter free group $G$ and their corresponding point-line incidence geometry $\mathcal{G}$. I introduce a fundamental homomorphism $f$ mapping the (infinitely many) words of G to the permutations ruling the symmetries of $\mathcal{G}$. The substructure of $f$ is revealing the essence of geometric contextuality in a straightforward way.Comment: 18 pages, 11 figures, 2 tables to appear in "Symmetry: Culture and Science

Interval-valued intuitionistic fuzzy soft graphs with application

The concept of interval-valued intuitionistic fuzzy soft sets and fuzzy graphs structure together constitute a new structure called an interval-valued intuitionistic fuzzy soft graph. The definitions of interval-valued intuitionistic fuzzy soft subgraph and strong interval-valued intuitionistic fuzzy soft graph are introduced with suitable examples. The degree of the good influence of a parameter in a fuzzy network and there is no influence by an interval number in the same system. Similarly, the effectiveness and non-effectiveness of the other fuzzy system on other parameters is measured by the concept of soft graphs in this article. Also, several different types of operations, including Cartesian product, strong product and composition on interval-valued intuitionistic fuzzy soft graphs are presented. Some related properties of these operations are investigated. Finally, we give a real-life application of interval-valued intuitionistic fuzzy soft graphs on social media and find out the most affected person in social media.Publisher's Versio

Comprehensive prediction of chromosome dimer resolution sites in bacterial genomes

<p>Abstract</p> <p>Background</p> <p>During the replication process of bacteria with circular chromosomes, an odd number of homologous recombination events results in concatenated dimer chromosomes that cannot be partitioned into daughter cells. However, many bacteria harbor a conserved dimer resolution machinery consisting of one or two tyrosine recombinases, XerC and XerD, and their 28-bp target site, <it>dif</it>.</p> <p>Results</p> <p>To study the evolution of the <it>dif/</it>XerCD system and its relationship with replication termination, we report the comprehensive prediction of <it>dif </it>sequences <it>in silico </it>using a phylogenetic prediction approach based on iterated hidden Markov modeling. Using this method, <it>dif </it>sites were identified in 641 organisms among 16 phyla, with a 97.64% identification rate for single-chromosome strains. The <it>dif </it>sequence positions were shown to be strongly correlated with the GC skew shift-point that is induced by replicational mutation/selection pressures, but the difference in the positions of the predicted <it>dif </it>sites and the GC skew shift-points did not correlate with the degree of replicational mutation/selection pressures.</p> <p>Conclusions</p> <p>The sequence of <it>dif </it>sites is widely conserved among many bacterial phyla, and they can be computationally identified using our method. The lack of correlation between <it>dif </it>position and the degree of GC skew suggests that replication termination does not occur strictly at <it>dif </it>sites.</p

Anatomy and the type concept in biology show that ontologies must be adapted to the diagnostic needs of research

Background: In times of exponential data growth in the life sciences, machine-supported approaches are becoming increasingly important and with them the need for FAIR (Findable, Accessible, Interoperable, Reusable) and eScience-compliant data and metadata standards. Ontologies, with their queryable knowledge resources, play an essential role in providing these standards. Unfortunately, biomedical ontologies only provide ontological definitions that answer What is it? questions, but no method-dependent empirical recognition criteria that answer How does it look? questions. Consequently, biomedical ontologies contain knowledge of the underlying ontological nature of structural kinds, but often lack sufficient diagnostic knowledge to unambiguously determine the reference of a term. Results: We argue that this is because ontology terms are usually textually defined and conceived as essentialistic classes, while recognition criteria often require perception-based definitions because perception-based contents more efficiently document and communicate spatial and temporal information—a picture is worth a thousand words. Therefore, diagnostic knowledge often must be conceived as cluster classes or fuzzy sets. Using several examples from anatomy, we point out the importance of diagnostic knowledge in anatomical research and discuss the role of cluster classes and fuzzy sets as concepts of grouping needed in anatomy ontologies in addition to essentialistic classes. In this context, we evaluate the role of the biological type concept and discuss its function as a general container concept for groupings not covered by the essentialistic class concept. Conclusions: We conclude that many recognition criteria can be conceptualized as text-based cluster classes that use terms that are in turn based on perception-based fuzzy set concepts. Finally, we point out that only if biomedical ontologies model also relevant diagnostic knowledge in addition to ontological knowledge, they will fully realize their potential and contribute even more substantially to the establishment of FAIR and eScience-compliant data and metadata standards in the life sciences

Anatomy and the type concept in biology show that ontologies must be adapted to the diagnostic needs of research

Background: In times of exponential data growth in the life sciences, machine-supported approaches are becoming increasingly important and with them the need for FAIR (Findable, Accessible, Interoperable, Reusable) and eScience-compliant data and metadata standards. Ontologies, with their queryable knowledge resources, play an essential role in providing these standards. Unfortunately, biomedical ontologies only provide ontological definitions that answer What is it? questions, but no method-dependent empirical recognition criteria that answer How does it look? questions. Consequently, biomedical ontologies contain knowledge of the underlying ontological nature of structural kinds, but often lack sufficient diagnostic knowledge to unambiguously determine the reference of a term. Results: We argue that this is because ontology terms are usually textually defined and conceived as essentialistic classes, while recognition criteria often require perception-based definitions because perception-based contents more efficiently document and communicate spatial and temporal information—a picture is worth a thousand words. Therefore, diagnostic knowledge often must be conceived as cluster classes or fuzzy sets. Using several examples from anatomy, we point out the importance of diagnostic knowledge in anatomical research and discuss the role of cluster classes and fuzzy sets as concepts of grouping needed in anatomy ontologies in addition to essentialistic classes. In this context, we evaluate the role of the biological type concept and discuss its function as a general container concept for groupings not covered by the essentialistic class concept. Conclusions: We conclude that many recognition criteria can be conceptualized as text-based cluster classes that use terms that are in turn based on perception-based fuzzy set concepts. Finally, we point out that only if biomedical ontologies model also relevant diagnostic knowledge in addition to ontological knowledge, they will fully realize their potential and contribute even more substantially to the establishment of FAIR and eScience-compliant data and metadata standards in the life sciences

A ‘fuzzy clustering’ approach to conceptual confusion: how to classify natural ecological associations

The concept of the marine ecological community has recently experienced renewed attention, mainly owing to a shift in conservation policies from targeting single and specific objec- tives (e.g. species) towards more integrated approaches. Despite the value of communities as dis- tinct entities, e.g. for conservation purposes, there is still an ongoing debate on the nature of spe- cies associations. They are seen either as communities, cohesive units of non-randomly associated and interacting members, or as assemblages, groups of species that are randomly associated. We investigated such dualism using fuzzy logic applied to a large dataset in the German Bight (south- eastern North Sea). Fuzzy logic provides the flexibility needed to describe complex patterns of natural systems. Assigning objects to more than one class, it enables the depiction of transitions, avoiding the rigid division into communities or assemblages. Therefore we identified areas with either structured or random species associations and mapped boundaries between communities or assemblages in this more natural way. We then described the impact of the chosen sampling design on the community identification. Four communities, their core areas and probability of occurrence were identified in the German Bight: AMPHIURA-FILIFORMIS, BATHYPOREIA-TELLINA, GONIADELLA-SPISULA, and PHORONIS. They were assessed by estimating overlap and compactness and supported by analysis of beta-diversity. Overall, 62% of the study area was characterized by high species turnover and instability. These areas are very relevant for conservation issues, but become undetectable when studies choose sampling designs with little information or at small spatial scales

Comparing Features of Three-Dimensional Object Models Using Registration Based on Surface Curvature Signatures

This dissertation presents a technique for comparing local shape properties for similar three-dimensional objects represented by meshes. Our novel shape representation, the curvature map, describes shape as a function of surface curvature in the region around a point. A multi-pass approach is applied to the curvature map to detect features at different scales. The feature detection step does not require user input or parameter tuning. We use features ordered by strength, the similarity of pairs of features, and pruning based on geometric consistency to efficiently determine key corresponding locations on the objects. For genus zero objects, the corresponding locations are used to generate a consistent spherical parameterization that defines the point-to-point correspondence used for the final shape comparison

Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory

We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is applied to the perturbative dynamics of scalar field theory, to tachyon dynamics in string field theory, and to the Hamiltonian dynamics of noncommutative gauge theory in two dimensions. We also describe the adiabatic dynamics of solitons on the noncommutative torus and compare various classes of noncommutative solitons on the torus and the plane.Comment: 70 pages, 4 figures; v2: References added and update