Chord Diagrams Research Articles

Multidrug resistance analysis method for pathogens of cow mastitis based on weighted-association rule mining and similarity comparison

Mastitis is one of the most common diseases and causes the greatest economic loss in dairy farming. Antibiotics are the most effective drugs to prevent and treat bacterial infection of mastitis. However, yet the growing problem of drug resistance, especially multidrug resistance (MDR), poses a great threat to disease control. To understand the MDR rules in bacteria of cow mastitis from national level, the main bacteria from cows with mastitis in large-scale farms were isolated and identified in China, and then drug sensitivity tests were conducted to establish a drug resistance data set. Aiming at the problem of numerous and disordered drug resistance data and lack of extensive correlations, a weighted Apriori association rule mining algorithm in conjunction with the bacterial drug resistance prevalence is proposed. We analyzed the associations between different antibiotics of key bacteria, extracted and visualized the key trends of high resistance prevalence and frequent occurrence, and discovered MDR patterns. Finally, a similarity comparison method based on Euclidean measurement was proposed to compare the relative MDR rules of different bacteria from the overall level with support, confidence, and promotion as characteristic parameters. The drug resistance data set showed that staphylococcus were the main bacteria isolated from dairy cow mastitis in China. Then based on the association rule algorithm, the important rules between different antibiotics resistance in this dataset were identified. In addition, the MDR patterns of different bacteria were visualized and analyzed by using the chord diagram. The results showed the bacteria are highly resistant to penicillin, gentamicin, and ampicillin, and most other antibiotics were linked with these three antibiotics. Finally, the high correlations and main rules in different bacteria were confirmed by a similarity comparison method. The assessment model and conclusions of this study are potentially valuable for assessing the evolution of MDR patterns, providing a scientific basis for relevant authorities to guide the rational use of antibiotics in the farming industry.

Finite type invariants for knotoids

We extend the theory of Vassiliev (or finite type) invariants for knots to knotoids using two different approaches. Firstly, we take closures on knotoids to obtain knots and we use the Vassiliev invariants for knots, proving that these are knotoid isotopy invariant. Secondly, we define finite type invariants directly on knotoids, by extending knotoid invariants to singular knotoid invariants via the Vassiliev skein relation. Then, for spherical knotoids we show that there are non-trivial type-1 invariants, in contrast with classical knot theory where type-1 invariants vanish. We give a complete theory of type-1 invariants for spherical knotoids, by classifying linear chord diagrams of order one, and we present examples arising from the affine index polynomial and the extended bracket polynomial.

Sponge-dwelling fauna: a review of known species from the Northwest Tropical Atlantic coral reefs.

BackgroundWithin tropical shallow-water coral reefs, marine sponges provide microhabitats for a wide range of fauna. Although there have been numerous studies and reports of symbiotic relationships amongst sponges and their associated fauna, those pieces of information are isolated and disconnected. For this reason, based on the available literature, we compiled a species-interaction dataset of coral reef marine sponge-associated fauna known to date.New informationWe introduce a dataset that includes 67 literature items that report 101 species of sponge hosts clustered in 12 Orders having a host/guest interaction with 284 guest species from six Phyla present in the Northwestern Tropical Atlantic coral reefs. This dataset consists of two types of information: 1. Machine-readable data and 2. Human-readable data. These two types of coding improve the scope of the dataset and facilitate the link between machine platforms and human-friendly displays. We also created an interactive visualisation of the species-interactions dataset and of a dynamic Chord Diagram of the host-guest species connections to generate a user-friendly link between the user and the dataset.

Songwriting with Iconic Notation in a Music Technology Classroom

Recognizing that music teachers may struggle to implement songwriting activities in a classroom, and that iconic notation provides an opportunity to increase access to school music for all students, the purpose of this article is to share one model of songwriting activities in a music technology class using chord diagrams, beat grids, and keyboard charts. The article outlines specific steps to the creation of drum grooves, simple chord progressions, bass lines, and melodies, using forms of notation that are appropriate for popular music instruments and styles.

“Neural differences in expert guitarists during over-learned non-standard visuomotor mapping of abstract versus concrete information”

Using visual information to perform actions is a fundamental aspect of human behavior. Musicians commonly translate visual information into action using both concrete and abstract visual information. We exposed expert guitarists to four types of familiar visual depictions of action instruction including musical notation (very abstract), tablature (abstract), chord diagrams (more concrete), and actual pictures of guitars chords being formed (very concrete). These were shown during fMRI scanning as the guitarists formed the appropriate chords (as visually depicted) on a magnet safe guitar fret board with strings, or where they simply viewed the visual stimuli without an action. Whole brain contrasts revealed that the right precuneus was more active for abstract instruction while an occipito-insular circuit was more active for concrete instruction. The current findings highlight that the degree of over-learned visual abstraction is an important factor modulating visual-motor processing.

Perturbative analysis of the colored Alexander polynomial and KP soliton τ-functions

In this paper we study the group theoretic structures of colored HOMFLY polynomials in a specific limit. The group structures arise in the perturbative expansion of SU(N) Chern-Simons Wilson loops, while the limit is N→0. The result of the paper is twofold. First, we explain the emergence of Kadomsev-Petviashvily (KP) τ-functions. This result is an extension of what we did in [1], where a symbolic correspondence between KP equations and group factors was established. In this paper we prove that integrability of the colored Alexander polynomial is due to it's relation to soliton τ-functions. Mainly, the colored Alexander polynomial is embedded in the action of the KP generating function on the soliton τ-function. Secondly, we use this correspondence to provide a rather simple combinatoric description of the group factors in term of Young diagrams, which is otherwise described in terms of chord diagrams, where no simple description is known. This is a first step providing an explicit description of the group theoretic data of Wilson loops, which would effectively reduce them to a purely topological quantity, mainly to a collection of Vassiliev invariants.

Finding the Shape of the Profile of Aero-Hydrodynamical Lattice by Given Chord Diagram of Velocity Distrubution

We consider the inverse boundary value problem of aero-hydrodynamical lattices. It is necessary to find the shape of the profile of a lattice streamlined by a potential flow of an incompressible non-viscous liquid, when the distribution of the velocity value on the profile is given as a function of the abscissa of the profile point (chord diagram); the lattice period and the ratio of complex liquid flow rates before and after the lattice are known.

Carbon Storage Change Analysis and Emission Reduction Suggestions under Land Use Transition: A Case Study of Henan Province, China.

The significant spatial heterogeneity among river basin ecosystems makes it difficult for local governments to carry out comprehensive governance for different river basins in a special administrative region spanning multi-river basins. However, there are few studies on the construction of a comprehensive governance mechanism for multi-river basins at the provincial level. To fill this gap, this paper took Henan Province of China, which straddles four river basins, as the study region. The chord diagram, overlay analysis, and carbon emission models were applied to the remote sensing data of land use to analyze the temporal and spatial patterns of carbon storage caused by land-use changes in Henan Province from 1990 to 2018 to reflect the heterogeneity of the contribution of the four basins to human activities and economic development. The results revealed that food security land in the four basins decreased, while production and living land increased. Ecological conservation land was increased over time in the Yangtze River Basin. In addition, the conversion from food security land to production and living land was the common characteristic for the four basins. Carbon emission in Henan increased from 134.46 million tons in 1990 to 553.58 million tons in 2018, while its carbon absorption was relatively stable (1.67–1.69 million tons between 1990 and 2018). The carbon emitted in the Huai River Basin was the main contributor to Henan Province’s total carbon emission. The carbon absorption in Yellow River Basin and Yangtze River Basin had an obvious spatial agglomeration effect. Finally, considering the current need of land spatial planning in China and the goal of carbon neutrality by 2060 set by the Chinese government, we suggested that carbon sequestration capacity should be further strengthened in Yellow River Basin and Yangtze River Basin based on their respective ecological resource advantages. For future development in Hai River Basin and Huai River Basin, coordinating the spatial allocation of urban scale and urban green space to build an ecological city is a key direction to embark upon.

Complex Sachdev-Ye-Kitaev model in the double scaling limit

We solve for the exact energy spectrum, 2-point and 4-point functions of the complex SYK model, in the double scaling limit at all energy scales. This model has a U(1) global symmetry. The analysis shows how to incorporate a chemical potential in the chord diagram picture, and we present results for the various observables also at a given fixed charge sector. In addition to matching to the spectral asymmetry, we consider an analogous asymmetry measure of the 2-point function obeying a non-trivial dependence on the operator’s dimension. We also provide the chord diagram structure for an SYK-like model that has a U(M) global symmetry at any disorder realization. We then show how to exactly compute the effect of inserting very heavy operators, with formally infinite conformal dimension. The latter separate the gravitational spacetime into several parts connected by an interface, whose properties are exactly computable at all scales. In particular, light enough states can still go between the spaces. This behavior has a simple description in the chord diagram picture.

DISTEVAL: a web server for evaluating predicted protein distances

BackgroundProtein inter-residue contact and distance prediction are two key intermediate steps essential to accurate protein structure prediction. Distance prediction comes in two forms: real-valued distances and ‘binned’ distograms, which are a more finely grained variant of the binary contact prediction problem. The latter has been introduced as a new challenge in the 14th Critical Assessment of Techniques for Protein Structure Prediction (CASP14) 2020 experiment. Despite the recent proliferation of methods for predicting distances, few methods exist for evaluating these predictions. Currently only numerical metrics, which evaluate the entire prediction at once, are used. These give no insight into the structural details of a prediction. For this reason, new methods and tools are needed.ResultsWe have developed a web server for evaluating predicted inter-residue distances. Our server, DISTEVAL, accepts predicted contacts, distances, and a true structure as optional inputs to generate informative heatmaps, chord diagrams, and 3D models. All of these outputs facilitate visual and qualitative assessment. The server also evaluates predictions using other metrics such as mean absolute error, root mean squared error, and contact precision.ConclusionsThe visualizations generated by DISTEVAL complement each other and collectively serve as a powerful tool for both quantitative and qualitative assessments of predicted contacts and distances, even in the absence of a true 3D structure.

Гафниан некоторых трехпараметрических теплицевых матриц и совершенные паросочетания дуговых и хордовых диаграмм

We obtain an explicit formula for exact calculatingthe hafnian of 3-parameter Toeplitz matrices of aspecial type in polynomial time. We also give anasymptotic estimate for the hafnian of this type ofmatrices. Separately, we consider a case of non-negativeinteger parameters, when calculating the hafnianis equivalent to enumerating perfect matchings of arc and chord diagrams.

Определение формы профиля гидродинамической решетки по заданной хордовой диаграмме распределения скорости

Определение формы профиля гидродинамической решетки по заданной хордовой диаграмме распределения скорости

The importance of MLH1, MSH2, MSH6 and PMS2 in determining DNA damage response in digestive cancers

Introduction: Genomic instability is a common feature across human cancers, but presents variation across different types of cancer, patients and cells of from the same tumor.This can be caused either by changes in the DNA damage repair pathways, aberrant histone modifications or methylation. The aim of this study was to determine the common mutated genes between digestive cancers that present genomic instability and to determine the biological processes in which these are implicated. Material and Methods: Mutational profiles for patients presenting digestive cancers and mutations in MLH1, MSH2, MSH6 and PMS2 were downloaded from the MSK impact cohort via cBioPortal. PANTHER was used to determine the GO SLIM processes in which the mutated genes are involved. R 3.5.3 and the R package circlize were used to generate chord diagrams. Results and Discussions: Considering the number of mutated genes from different digestive cancers it could be observed that the deregulated processes are general cellular processes, while when taking into consideration the fold change in overrepresentation of certain processes, the main deregulated processes are represented by DNA damage repair pathways, showing their overrepresentation in the selected cohort based on a few mutated genes. Conclusion: MLH1,MSH2,MSH6 and PMS2 mutations dictate the alterations in DNA damage repair pathways in digestive cancers.

Identifying Driver Genes Mutations with Clinical Significance in Thyroid Cancer

Advances in technology are enabling gene mutations in papillary thyroid carcinoma (PTC) to be analyzed and clinical outcomes, such as recurrence, to be predicted. To date, the most common genetic mutation in PTC is in BRAF kinase (BRAF). However, whether mutations in other genes coincide with those in BRAF remains to be clarified. The aim of this study was to find mutations in other genes that co-exist with mutated BRAF, and to analyze their frequency and clinical relevance in PTC. Clinical and genetic data were collected from 213 PTC patients with a total of 36,572 mutation sites in 735 genes. After matching with genes from PTC entries in a global database (NCBI Gene), 69 genes with mutations in coding regions were chosen for further study. Through frequency-based analysis, we identified commonly mutated genes co-existing with mutated BRAF and, using the mutation count correlation matrix (MCCM) method, analyzed their incidence according to age and gender. We designed Chord diagrams to reveal gene relationships concerning age and gender, and found that mutations in ALK, ATM, COL1A1, MSTIR, PRKCA, and WNK1 most commonly coincide with mutated BRAF, followed by APC, AURKA, and AURKB. These findings provide further insight into the genetic profile of PTC.

Unfolding Cubes: Nets, Packings, Partitions, Chords

We show that every ridge unfolding of an $n$-cube is without self-overlap, yielding a valid net. The results are obtained by developing machinery that translates cube unfolding into combinatorial frameworks. Moreover, the geometry of the bounding boxes of these cube nets are classified using integer partitions, as well as the combinatorics of path unfoldings seen through the lens of chord diagrams.

The double scaled limit of super-symmetric SYK models

We compute the exact density of states and 2-point function of the mathcal{N} = 2 super-symmetric SYK model in the large N double-scaled limit, by using combinatorial tools that relate the moments of the distribution to sums over oriented chord diagrams. In particular we show how SUSY is realized on the (highly degenerate) Hilbert space of chords. We further calculate analytically the number of ground states of the model in each charge sector at finite N, and compare it to the results from the double-scaled limit. Our results reduce to the super-Schwarzian action in the low energy short interaction length limit. They imply that the conformal ansatz of the 2-point function is inconsistent due to the large number of ground states, and we show how to add this contribution. We also discuss the relation of the model to SLq(2|1). For completeness we present an overview of the mathcal{N} = 1 super-symmetric SYK model in the large N double-scaled limit.

Crosscap number of knots and volume bounds

In this paper, we obtain the crosscap number of any alternating knots by using our recently-introduced diagrammatic knot invariant (Theorem 1). The proof is given by properties of chord diagrams (Kindred proved Theorem 1 independently via other techniques). For non-alternating knots, we give Theorem 2 that generalizes Theorem 1. We also improve known formulas to obtain upper bounds of the crosscap number of knots (alternating or non-alternating) (Theorem 3). As a corollary, this paper connects crosscap numbers and our invariant with other knot invariants such as the Jones polynomial, twist number, crossing number, and hyperbolic volume (Corollaries 1–7). In Appendix A, using Theorem 1, we complete giving the crosscap numbers of the alternating knots with up to 11 crossings including those of the previously unknown values for [Formula: see text] knots (Tables A.1).

Standard trees versus underwood: Historical patterns of tree taxon occurrence in coppice forests

AbstractQuestionsCoppice woods were once widespread in Europe. It is usually assumed that underwood tree taxon composition was not directly influenced by people, whereas especially Quercus was promoted among standard trees. However, no work has quantitatively tested these assumptions. Our main question was whether there were any patterns in our data to suggest that certain trees occurred more frequently as standards than as underwood, possibly as a result of management decisions.LocationCzech Republic.MethodsWe constructed a database covering 12,000 hectares of forests around AD 1900. We recorded the occurrence of tree taxa for standards and underwood in 1,507 compartments in 21 forest units. We visualised patterns in these data by bar graphs and chord diagrams. We analysed correlation patterns through association analysis and co‐correspondence analysis.ResultsThere was a statistically significant association between the occurrences of standards and underwood in individual compartments for Quercus, Alnus, Carpinus, Fagus, Larix, Populus tremula and Tilia. Only Quercus standards and underwood showed a positive association. The taxon composition of standards and underwood in forest compartments was statistically significantly correlated.ConclusionsNo simple answer can be given to the question whether or not the taxon composition of standards and underwood in coppice woods differed as a result of management. At the level of individual tree taxa, some trees were more common as standards while others, as underwood. However, the prevalence of Quercus among standards was not confirmed because in our study area Quercus was a common underwood tree as well. At the same time, no significant differences were apparent in the taxon composition of standards and underwood in individual forest compartments. It seems difficult to differentiate between the effects of human selection and indirect selection through natural properties and environmental factors. Our results also highlight the need to carefully consider the properties of written historical sources.

Chaos on the hypercube

We analyze the spectral properties of a d-dimensional HyperCubic (HC) lattice model originally introduced by Parisi. The U(1) gauge links of this model give rise to a magnetic flux of constant magnitude ϕ but random orientation through the faces of the hypercube. The HC model, which also can be written as a model of 2d interacting Majorana fermions, has a spectral flow that is reminiscent of Maldacena-Qi (MQ) model, and its spectrum at ϕ = 0, actually coincides with the coupling term of the MQ model. As was already shown by Parisi, at leading order in 1/d, the spectral density of this model is given by the density function of the Q-Hermite polynomials, which is also the spectral density of the double-scaled Sachdev-Ye-Kitaev model. Parisi demonstrated this by mapping the moments of the HC model to Q-weighted sums on chord diagrams. We point out that the subleading moments of the HC model can also be mapped to weighted sums on chord diagrams, in a manner that descends from the leading moments. The HC model has a magnetic inversion symmetry that depends on both the magnitude and the orientation of the magnetic flux through the faces of the hypercube. The spectrum for fixed quantum number of this symmetry exhibits a transition from regular spectra at ϕ = 0 to chaotic spectra with spectral statistics given by the Gaussian Unitary Ensembles (GUE) for larger values of ϕ. For small magnetic flux, the ground state is gapped and is close to a Thermofield Double (TFD) state.

Circular visualisation of historical migration in England in the long eighteenth-century

Migration is a central component of both individual life-courses and macro-level demographic systems. In the absence of population registers and other surveillance systems, however, it is often difficult to measure. This is especially the case in historical populations. Compared to measures of fertility, nuptiality and mortality, then, migration processes are rather less studied. Recent studies in the English historical context have challenged long standing theoretical constructs concerning the relationship between migration and modernisation; gender and distance travelled; motivation for movement and the very nature of the movers themselves. Using a set of marriage registers for a large, agricultural county, this study explores intra-county migration among a predominantly young population over the period 1700 to 1836. The proportion of migrants is explored as well as the distance between ‘home’ and ‘marriage’ parishes. For perhaps the first time, chord diagrams are deployed for historical English migration data to visualise inter- and intra- regional/district migration. Although there are numerous limitations concerning the scope of the sample and the study, the evidence presented here broadly accords with recent studies of migration in pre-industrial England; and shows the potential to both use circular visualisation and exploit large scale samples of marriage registers to gain a further insight into a particular type of historical migration.