Bipartite Structures Research Articles

Vertebrate centromeres in mitosis are functionally bipartite structures stabilized by cohesin

Centromeres are scaffolds for the assembly of kinetochores that ensure chromosome segregation during cell division. How vertebrate centromeres obtain a three-dimensional structure to accomplish their primary function is unclear. Using super-resolution imaging, capture-C, and polymer modeling, we show that vertebrate centromeres are partitioned by condensins into two subdomains during mitosis. The bipartite structure is found in human, mouse, and chicken cells and is therefore a fundamental feature of vertebrate centromeres. Super-resolution imaging and electron tomography reveal that bipartite centromeres assemble bipartite kinetochores, with each subdomain binding a distinct microtubule bundle. Cohesin links the centromere subdomains, limiting their separation in response to spindle forces and avoiding merotelic kinetochore-spindle attachments. Lagging chromosomes during cancer cell divisions frequently have merotelic attachments in which the centromere subdomains are separated and bioriented. Our work reveals a fundamental aspect of vertebrate centromere biology with implications for understanding the mechanisms that guarantee faithful chromosome segregation.

The ABJM Amplituhedron

In this paper, we take a major step towards the construction and applications of an all-loop, all-multiplicity amplituhedron for three-dimensional planar N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 6 Chern-Simons matter theory, or the ABJM amplituhedron. We show that by simply changing the overall sign of the positive region of the original amplituhedron for four-dimensional planar N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 super-Yang-Mills (sYM) and performing a symplectic reduction, only three-dimensional kinematics in the middle sector of even-multiplicity survive. The resulting form of the geometry, combined with its parity images, gives the full loop integrand. This simple modification geometrically enforces the vanishing of odd-multiplicity cuts, and manifests the correct soft cuts as well as two-particle unitarity cuts. Furthermore, the so-called “bipartite structures” of four-point all-loop negative geometries also directly generalize to all multiplicities. We introduce a novel approach for triangulating loop amplituhedra based on the kinematics of the tree region, resulting in local integrands tailored to “prescriptive unitarity”. This construction sheds fascinating new light on the interplay between loop and tree amplituhedra for both ABJM and N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 sYM: the loop geometry demands that the tree region must be dissected into chambers, defined by the simultaneous positivity of maximal cuts. The loop geometry is then the “fibration” of the tree region. Using the new construction, we give explicit results of one-loop integrands up to ten points and two-loop integrands up to eight points by computing the canonical form of ABJM loop amplituhedron.

Secret sharing on regular bipartite access structures

Bipartite secret sharing schemes realize access structures in which the participants are divided into two parts, and all the participants in the same part play an equivalent role. Such a bipartite structure can be described by the collection of its minimal points. The complexity of a scheme is the ratio between the maximum share size given to the participants and the secret size, and the Shannon complexity of a structure is the best lower bound provided by the entropy method. Within this work, we compute the Shannon complexity of regular bipartite structures and provide optimal constructions for some bipartite structures defined by 2 and 3 points.

Automating Terror: The Role and Impact of Telegram Bots in the Islamic State’s Online Ecosystem

ABSTRACT In this article, we use network science to explore the topology of the Islamic State’s “terrorist bot” network on the online social media platform Telegram, empirically identifying its connections to the Islamic State supporter-run groups and channels that operate across the platform, with which these bots form bipartite structures. As part of this, we examine the diverse activities of the bots to determine the extent to which they operate in synchrony with one another as well as explore their impacts. We show that these bots are mainly clustered around two communities of Islamic State supporters, or “munasirun,” with one community focusing on facilitating discussion and exchange, and the other one augmenting content distribution efforts. Operating as such, this network of bots is used to lubricate and augment the Islamic State’s influence activities, including facilitating content amplification and community cultivation efforts, and connecting people with the movement based on common behaviors, shared interests, and/or ideological proximity while minimizing risk for the broader organization.

Exact SDP relaxations for quadratic programs with bipartite graph structures

For nonconvex quadratically constrained quadratic programs (QCQPs), we first show that, under certain feasibility conditions, the standard semidefinite programming (SDP) relaxation is exact for QCQPs with bipartite graph structures. The exact optimal solutions are obtained by examining the dual SDP relaxation and the rank of the optimal solution of this dual SDP relaxation under strong duality. Our results generalize the previous results on QCQPs with sign-definite bipartite graph structures, QCQPs with forest structures, and QCQPs with nonpositive off-diagonal data elements. Second, we propose a conversion method from QCQPs with no particular structure to the ones with bipartite graph structures. As a result, we demonstrate that a wider class of QCQPs can be exactly solved by the SDP relaxation. Numerical instances are presented for illustration.

Diversity and evolution of optically complex eyes in a family of deep-sea fish: Ocular diverticula in barreleye spookfish (Opisthoproctidae)

Several families of mesopelagic fish have tubular eyes that are usually upwardly directed. These maximise sensitivity to dim downwelling sunlight and dorsal bioluminescence, as well as facilitating the detection of dark silhouettes above the animal. Such eyes, however, have a much-reduced field of view and will not be sensitive to, for example, lateral and ventral bioluminescent stimuli. All mesopelagic Opisthoproctidae so far examined have evolved mechanisms for extending the limited visual field of their eyes using approximately ventrolaterally directed, light-sensitive, diverticula. Some genera have small rudimentary lateral retinal areas capable of detecting only unfocussed illumination. Others have more extensive structures resulting in eyes that simultaneously focus light from above onto the main retina of the tubular eye using a lens, while diverticula produce focussed images of ventrolateral illumination using either reflection or possibly refraction. These bipartite structures represent perhaps the most optically complex of all vertebrate eyes. Here we extend the limited previous data on the ocular morphology of five Opisthoproctidae (Opisthoproctus soleatus, Winteria telescopa, Dolichopteryx longipes, Rhynchohyalus natalensis, and Bathylychnops exilis) using a combination of histology and magnetic resonance imaging and provide a preliminary description of the eyes of Macropinna microstoma. We note an increase in diverticular complexity over the life span of some species and quantify the contribution of the diverticulum to the eye’s total neural output in D. longipes and R. natalensis (25 and 20%, respectively). To help understand the evolution of Opisthoproctidae ocular diversity, a phylogeny, including all the species whose eye types are known, was reconstructed using DNA sequences from 15 mitochondrial and four nuclear genes. Mapping the different types of diverticula onto this phylogeny suggests a process of repeated evolution of complex ocular morphology from more rudimentary diverticula.

General Community Detection in Attributed Networks with Consistent-Module Constrained Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) model has been successfully applied to discover latent community structures due to its good performance and interpretability advantages in extracting hidden patterns. However, most previous studies explore only the structural information of the network while ignoring the rich attributes. Besides, they aim at detecting densely connected communities (also called community structures) and fail to identify general structures, such as bipartite structures and mixture structures. In this paper, we research on general structure discovery and propose a new method GCDNMF (General Community Detection based on Nonnegative Matrix Factorization), which integrates structural information and node attributes through consistency module constraint to capture the community interactions. It can discover the general community structures of nodes by iteratively updating the community-interaction matrix and the node-membership matrix. We also introduce matrix initialization based on centrality and dispersion of nodes for center selection to reduce the sensitivity of random initialization. Experimental results on real-world networks with a variety of characteristics validate the performance of our approach, especially on networks with general structures. In addition, the associated initialization evaluations demonstrate the effectiveness of our method in obtaining stable results.

SSBM: A signed stochastic block model for multiple structure discovery in large-scale exploratory signed networks

Signed network structure discovery has received extensive attention and has become a research focus in the field of network science. However, most of the existing studies are focused on the networks with a single structure, e.g., community or bipartite, while ignoring multiple structures, e.g., the coexistence of community and bipartite structures. Furthermore, existing studies were faced with challenge regarding large-scale signed networks due to their high time complexity, especially when determining the number of clusters in the observed network without any prior knowledge. In view of this, we propose a mathematically principled method for signed network multiple structure discovery named the Signed Stochastic Block Model (SSBM). The SSBM can capture the multiple structures contained in signed networks, e.g., community, bipartite, and coexistence of them, by adopting a probabilistic model. Moreover, by integrating the minimum message length (MML) criterion and component-wise EM (CEM) algorithm, a scalable learning algorithm that has the ability of model selection is proposed to handle large-scale signed networks. By comparing state-of-the-art methods on synthetic and real-world signed networks, extensive experimental results demonstrate the effectiveness and efficiency of SSBM in discovering large-scale exploratory signed networks with multiple structures.

On Characterization of Graphs Structures Connected with Some Algebraic Properties

In this paper, we have characterized graph structures connected with some algebraic properties. Also, this paper is actually the concatenation of graph theory and algebra. We have introduced left and right inverse graphs of antiautomorphic inverse property loops. Also, there is a connection between bipartite graphs and mathematical structures, commutator subloop, associator subloop, and associative part, the nucleus of the loop, through edge labeling.

Depositional elements and evolution of gravity-flow deposits on Lingshan Island (Eastern China): An integrated outcrop-subsurface study

Understanding how subaqueous sediment gravity flows (SSGF) evolve in time and space, and how their deposits vary spatially, is a key research focus for gravity flow sedimentology. This study investigates depositional facies, depositional elements, and sediment transport processes of supercritical flows and hybrid event beds (HEBs) of the Lingshandao Formation in Lingshan Island, Eastern China. Three kinds of depositional elements were recognized: mass transport deposits (MTDs), channel-lobe transition zone (CLTZs), and lobe complexes. MTDs can be sub-divided into proximal and distal deposits. CLTZs are characterized by facies changes from massive coarse-grained pebbly sandstone to backset bedding sandstone in a down-slope direction, which are the deposits of supercritical turbidity currents. HEBs are common in both proximal and distal lobe settings. Tripartite structure in HEBs, which may be caused by up-slope substrate erosion, implies a relatively proximal origin compared with bipartite HEBs, perhaps caused by fluid fractionation in the research area. The succession is formed by a prograding lobe unit, followed by MTDs which are themselves overlain by deposits from a CLTZ. This vertical stacking pattern implies the potential longitudinal facies tract from CLTZ; to lobe complex deposits, is accompanied by emplacement of MTDs at the slope break. The flow types accompanied by sediment transport processes imply that erosion by supercritical turbidity currents associated with a hydraulic jump in the channel-lobe transition zone may be the main reason for mud-clasts and matrix addition to the flow. The large-scale addition of mud-clasts and suspended mud may dampen turbulence in proximal to medial lobe settings, and result in medium-to thick-bedded HEBs with common erosional features and tripartite structures. The remaining suspension flow (with abundant mud) may further transport down-dip and form medium-to thin-bedded HEBs with bipartite structures and rare mud-clasts. These findings may be applicable to other SSGF systems with supercritical flow deposits and hybrid event beds, emphasizing the downdip and lateral variation in depositional elements associated with gravity flow evolution.

Relation Matters: Foreground-Aware Graph-Based Relational Reasoning for Domain Adaptive Object Detection.

Domain Adaptive Object Detection (DAOD) focuses on improving the generalization ability of object detectors via knowledge transfer. Recent advances in DAOD strive to change the emphasis of the adaptation process from global to local in virtue of fine-grained feature alignment methods. However, both the global and local alignment approaches fail to capture the topological relations among different foreground objects as the explicit dependencies and interactions between and within domains are neglected. In this case, only seeking one-vs-one alignment does not necessarily ensure the precise knowledge transfer. Moreover, conventional alignment-based approaches may be vulnerable to catastrophic overfitting regarding those less transferable regions (e.g., backgrounds) due to the accumulation of inaccurate localization results in the target domain. To remedy these issues, we first formulate DAOD as an open-set domain adaptation problem, in which the foregrounds and backgrounds are seen as the "known classes" and "unknown class" respectively. Accordingly, we propose a new and general framework for DAOD, named Foreground-aware Graph-based Relational Reasoning (FGRR), which incorporates graph structures into the detection pipeline to explicitly model the intra- and inter-domain foreground object relations on both pixel and semantic spaces, thereby endowing the DAOD model with the capability of relational reasoning beyond the popular alignment-based paradigm. FGRR first identifies the foreground pixels and regions by searching reliable correspondence and cross-domain similarity regularization respectively. The inter-domain visual and semantic correlations are hierarchically modeled via bipartite graph structures, and the intra-domain relations are encoded via graph attention mechanisms. Through message-passing, each node aggregates semantic and contextual information from the same and opposite domain to substantially enhance its expressive power. Empirical results demonstrate that the proposed FGRR exceeds the state-of-the-art performance on four DAOD benchmarks.

Beyond base and collocate

Abstract Support verb constructions figure among the most frequently investigated topics in the literature on collocation. So far, most studies of this kind have focused on bipartite structures, consisting of a verbal collocate and a nominal base. Accordingly, the analysis of how support verbs are distributed has concentrated almost exclusively on the lexical control exerted by the base. In this article, we draw attention towards the influence exerted by the participation of verb and noun in more complex patterns of lexical co-occurrence. We contend that the distribution of the support verb collocate is contingent not only on the base noun but also on other elements of the lexical context. This highlights the need to enrich the theoretical framework of collocation analysis with the additional descriptive category of ‘second-order collocate’. The proposal is illustrated with two case studies using a large-scale web corpus of English.

Angular momentum anisotropy of Dirac carriers: A new twist in graphene

Dirac carriers in graphene are commonly characterized by a pseudospin degree of freedom, arising from the degeneracy of the two inequivalent sublattices. The inherent chirality of the quasiparticles leads to a topologically nontrivial band structure, where the in-plane components of sublattice spin and momentum are intertwined. Equivalently, sublattice imbalance is intimately connected with angular momentum, inducing a torque of opposite sign at each Dirac point. In this work we develop an intuitive picture that associates sublattice spin and winding number with angular momentum. We develop a microscopic perturbative model to obtain the finite angular momentum contributions along the main crystallographic directions. Our results can be employed to determine the angular dependence of the $g$ factor and of light absorption in honeycomb bipartite structures.

A generative model for exploring structure regularities in attributed networks

Many real-world networks known as attributed networks contain two types of information: topology information and node attributes. It is a challenging task on how to use these two types of information to explore structural regularities. In this paper, by characterizing the potential relationship between communities of links and node attributes, a principled statistical model named PSB_PG that generates link topology and node attributes is proposed. This model for generating links is based on the stochastic blockmodels following a Poisson distribution. Therefore, it is capable of detecting a wide range of network structures including community structures, bipartite structures, and other mixture structures. The model for generating node attributes assumes that node attributes are high-dimensional, sparse, and also follow a Poisson distribution. This makes the model be uniform, and the model parameters can be directly estimated by the expectation-maximization (EM) algorithm. Experimental results on artificial networks and real networks containing various structures have shown that the proposed model PSB_PG is not only competitive with the state-of-the-art models, but also provides a good semantic interpretation for each community via the learned relationship between the community and its related attributes.

On Certain Counting Polynomial of Titanium Dioxide Nanotubes

Background: In 1936, Polya introduced the concept of a counting polynomial in chemistry. However, the subject established little attention from chemists for some decades even though the spectra of the characteristic polynomial of graphs were considered extensively by numerical means in order to obtain the molecular orbitals of unsaturated hydrocarbons. Counting polynomial is a sequence representation of a topological stuff so that the exponents precise the magnitude of its partitions while the coefficients are correlated to the occurrence of these partitions. Counting polynomials play a vital role in topological description of bipartite structures as well as counts of equidistant and non-equidistant edges in graphs. Omega, Sadhana, PI polynomials are wide examples of counting polynomials. Methods: Mathematical chemistry is a division of abstract chemistry in which we debate and forecast the chemical structure by using mathematical models. Chemical graph theory is a subdivision of mathematical chemistry in which the structure of a chemical compound can be embodied by a labelled graph whose vertices are atoms and edges are covalent bonds between the atoms. We use graph theoretic technique in finding the counting polynomials of TiO2 nanotubes. : Let ! be the molecular graph of TiO2. Then (!, !) = !!10!!+8!−2!−2 + (2! +1) !10!!+8!−2! + 2(! + 1)10!!+8!−2 Results: In this paper, the omega, Sadhana and PI counting polynomials are studied. These polynomials are useful in determining the omega, Sadhana and PI topological indices which play an important role in studies of Quantitative structure-activity relationship (QSAR) and Quantitative structure-property relationship (QSPR) which are used to predict the biological activities and properties of chemical compounds. Conclusion: These counting polynomials play an important role in topological description of bipartite structures as well as counts equidistance and non-equidistance edges in graphs. Computing distancecounting polynomial is under investigation.

Bipartite network structures and individual differences in sound change

This paper assesses the influence of social network structure, and the role of the individual, in shaping the loss of the regional vowel system in the Southern U.S. city of Raleigh, North Carolina. The entire front vowel system, including monophthongal /aɪ/ as in ride, is shifting toward the national standard. Previous network studies in sociolinguistics have focused on individual-level network characteristics, such as integration in dense local networks or contact with speakers from different neighborhoods or ethnic groups. By contrast, the Raleigh study focuses on individuals’ positions in the community network structure as represented by a bipartite network of people and the schools they attended. Bipartite networks indicate social proximity between people via their shared participation in an event or organization.With a 189-speaker sample of Raleigh natives, the network measure of structural equivalence offers a view of Raleigh’s community network structure and of the individual’s role in advancing the shift away from the Southern vowel system. Structural equivalence is the extent to which nodes inhabit similar positions within a social network. In this case, it describes the extent to which pairs of speakers attended the same schools. A distance matrix containing each pair’s network proximity is used to predict speakers’ linguistic similarity. The role of the individual and of the social indexicality of Southern variants is considered in the context of aggregate patterns of variation.

Detecting core-periphery structures by surprise

Detecting the presence of mesoscale structures in complex networks is of primary importance. This is especially true for financial networks, whose structural organization deeply affects their resilience to events like default cascades, shocks propagation, etc. Several methods have been proposed, so far, to detect communities, i.e., groups of nodes whose internal connectivity is significantly large. Communities, however do not represent the only kind of mesoscale structures characterizing real-world networks: other examples are provided by bow-tie structures, core-periphery structures and bipartite structures. Here we propose a novel method to detect statistically significant bimodular structures, i.e., either bipartite or core-periphery ones. It is based on a modification of the surprise, recently proposed for detecting communities. Our variant allows for bimodular nodes partitions to be revealed, by letting links to be placed either 1) within the core part and between the core and the periphery parts or 2) between the layers of a bipartite network. From a technical point of view, this is achieved by employing a multinomial hypergeometric distribution instead of the traditional, binomial hypergeometric one; as in the latter case, this allows a p-value to be assigned to any given (bi)partition of the nodes. To illustrate the performance of our method, we report the results of its application to several real-world networks, including social, economic and financial ones.

Origin and evolution processes of hybrid event beds in the Lower Cretaceous of the Lingshan Island, Eastern China

ABSTRACTOn the basis of detailed sedimentological investigation, three types of hybrid event beds (HEBs) together with debrites and turbidites were distinguished in the Lower Cretaceous sedimentary sequence on the Lingshan Island in the Yellow Sea, China. HEB 1, with a total thickness of 63–80 cm and internal bipartite structures, is characterised by a basal massive sandstone sharply overlain by a muddy sandstone interval. It is interpreted to have been formed by particle rearrangement at the base of cohesive debris flows. HEB 2, with a total thickness of 10–71 cm and an internal tripartite structure, is characterised by a normal grading sandstone base, followed by muddy siltstone middle unit and capped with siltstones; the top unit of HEB 2 may in places be partly or completely eroded. The boundary between the lowest unit and the middle unit is gradual, whereas that between the middle unit and the top unit is sharp. HEB 2 may be developed by up-dip muddy substrate erosion. HEB 3, with a total thickness up to 10 cm and an internal bipartite structure, is characterised by a basal massive sandstone sharply overlain by a muddy siltstone interval. The upper unit was probably deposited by cohesive debris flow with some plant fragments and rare mud clasts. HEB 3 may be formed by the deceleration of low-density turbidity currents. The distribution of HEBs together with debrites and turbidites implies a continuous evolution process of sediment gravity flows: debris flow → hybrid flow caused by particle rearrangement → high-density turbidity current → hybrid flow caused by muddy substrate erosion → low-density turbidity current → hybrid flow caused by deceleration.

Network modelling and variational Bayesian inference for structure analysis of signed networks

Abstract Currently, structure analysis of signed networks with positive and negative links has received wide attention and is becoming a research focus in the area of network science. In recent years, many community detection methods for signed networks have been proposed to analyze the structure of signed networks. However, current methods can only efficiently analyze the signed networks with the single community structure and unable to analyze the signed networks with the coexisting structure of communities and peripheral nodes, bipartite, or other structures. To address this problem, in this study, we present a mathematically principled method for the structure analysis of signed networks with positive and negative links, in which a probabilistic model firstly is proposed to model the signed networks with the single community or the coexisting structure, and a variational Bayesian approach is deduced to learn the approximate distribution of model parameters. For determining the optimal model, we also deduce a model selection criterion based on the evidence theory. In addition, to efficiently analyze the large signed networks, we propose a fast learning version of our algorithm with the time complexity O(k2E) where k is the number of groups and E is the number of links. In our experiments, the proposed method is validated in the synthetic and real-world signed networks, and is compared with the state-of-the-art methods. The experimental results demonstrate that the proposed method can more efficiently and accurately analyze to the structure of signed networks than the state-of-the-art methods.

Structural changes in the interbank market across the financial crisis from multiple core–periphery analysis

Interbank markets are often characterised in terms of a core-periphery network structure, with a highly interconnected core of banks holding the market together, and a periphery of banks connected mostly to the core but not internally. This paradigm has recently been challenged for short time scales, where interbank markets seem better characterised by a bipartite structure with more core-periphery connections than inside the core. Using a novel core-periphery detection method on the eMID interbank market, we enrich this picture by showing that the network is actually characterised by multiple core-periphery pairs. Moreover, a transition from core-periphery to bipartite structures occurs by shortening the temporal scale of data aggregation. We further show how the global financial crisis transformed the market, in terms of composition, multiplicity and internal organisation of core-periphery pairs. By unveiling such a fine-grained organisation and transformation of the interbank market, our method can find important applications in the understanding of how distress can propagate over financial networks.