Automatic Text Summarization by Providing Coverage, Non-Redundancy, and Novelty Using Sentence Graph

The day-to-day growth of online information necessitates intensive research in automatic text summarization (ATS). The ATS software produces summary text by extracting important information from the original text. With the help of summaries, users can easily read and understand the documents of interest. Most of the approaches for ATS used only local properties of text. Moreover, the numerous properties make the sentence selection difficult and complicated. So this article uses a graph based summarization to utilize structural and global properties of text. It introduces maximal clique based sentence selection (MCBSS) algorithm to select important and non-redundant sentences that cover all concepts of the input text for summary. The MCBSS algorithm finds novel information using maximal cliques (MCs). The experimental results of recall oriented understudy for gisting evaluation (ROUGE) on Timeline dataset show that the proposed work outperforms the existing graph algorithms Bushy Path (BP), Aggregate Similarity (AS), and TextRank (TR).

Generalized Cell Mapping Method with Deep Learning for Global Analysis and Response Prediction of Dynamical Systems

A novel method that combines generalized cell mapping and deep learning is developed to analyze the global properties and predict the responses of dynamical systems. The proposed method only requires some prior knowledge of the system governing equations and obtains dynamical properties of the system from observed data. By combining the theoretical demonstration and empirical inference results, appropriate network structure and training hyperparameters are computed. Then a robust and efficient neural network approximation with the estimated mapping parameters is obtained. By using the approximate dynamical system model, we construct the one-step transition probability matrix and introduce the digraph analysis method to analyze the global properties. System responses at any time can be obtained with the trained model on the basis of the property of Markov chain. Several examples with periodic or chaotic attractors are presented to validate the proposed method. The influence of the number of hidden layers and the size of training data on calculated results is discussed, and an admissible architecture of the neural network is found. Numerical results indicate that the proposed method is quite effective for both global analysis and response prediction.

Emergent dimensions underlying human understanding of the reachable world

Near-scale, reach-relevant environments, like work desks, restaurant place settings or lab benches, are the interface of our hand-based interactions with the world. How are our conceptual representations of these environments organized? For navigable-scale scenes, global properties such as openness, depth or naturalness have been identified, but the analogous organizing principles for reach-scale environments are not known. To uncover such principles, we obtained 1.25 million odd-one-out behavioral judgments on image triplets assembled from 990 reachspace images. Images were selected to comprehensively sample the variation both between and within reachspace categories. Using data-driven modeling, we generated a 30-dimensional embedding which predicts human similarity judgments among the images. First, examination of the embedding dimensions revealed key properties that distinguish among reachspaces, relating to their structural layout, affordances, visual appearances and functional roles. Second, clustering analyses performed over the embedding revealed four distinct interpretable classes of reachspaces, with separate clusters for spaces related to food, electronics, analog activities, and storage or display. Finally, we found that the similarity structure among reachspace images was better predicted by the function of the spaces than their locations, suggesting that reachspaces are largely conceptualized in terms of the actions they are designed to support. Altogether, these results reveal the behaviorally-relevant principles that that structure our internal representations of reach-relevant environments.

The geometry of the Wigner caustic and a decomposition of a curve into parallel arcs

In this paper we study global properties of the Wigner caustic of parameterized closed planar curves. We find new results on its geometry and singular points. In particular, we consider the Wigner caustic of rosettes, i.e. regular closed parameterized curves with non-vanishing curvature. We present a decomposition of a curve into parallel arcs to describe smooth branches of the Wigner caustic. By this construction we can find the number of smooth branches, the rotation number, the number of inflexion points and the parity of the number of cusp singularities of each branch. We also study the global properties of the Wigner caustic on shell (the branch of the Wigner caustic connecting two inflexion points of a curve). We apply our results to whorls—the important object to study the dynamics of a quantum particle in the optical lattice potential.

Curvature

The mathematics of Riemannian curvature is presented. The Riemann curvature tensor and its role in parallel transport, in the metric, and in geodesic deviation are expounded at length. We begin by defining the curvature tensor and the torsion tensor by relating them to covariant derivatives. Then the local metric is obtained up to second order in terms of Minkowski metric and curvature tensor. Geometric issues such as the closure or non-closure of parallelograms are discussed. Next, the relation between curvature and parallel transport around a loop is derived. Then we proceed to geodesic deviation. The influence of global properties of the manifold on parallel transport is briefly expounded. The Lie derivative is then defined, and isometries of spacetime are discussed. Killing’s equation and properties of Killing vectors are obtained. Finally, the Weyl tensor (conformal tensor) is introduced.

SSIM can robustly identify changes in 3D genome conformation maps

We previously presented Comparison of Hi-C Experiments using Structural Similarity (CHESS), an approach that applies the concept of the structural similarity index (SSIM) to Hi-C matrices, and demonstrated that it could be used to identify both regions with similar 3D chromatin conformation across species, and regions with different chromatin conformation in different conditions. In contrast to the claim of Lee et al. that the SSIM output of CHESS is independent of the input data, here we confirm that SSIM depends on both local and global properties of the input Hi-C matrices. We provide two approaches for using CHESS to highlight regions of differential genome organisation for further investigation, and expanded guidelines for choosing appropriate parameters and controls for these analyses.

Global properties of regulatory sequences are predicted by transcription factor recognition mechanisms

Background Mammalian genomes contain millions of putative regulatory sequences, which are delineated by binding of multiple transcription factors. The degree to which spacing and orientation constraints among transcription factor binding sites contribute to the recognition and identity of regulatory sequence is an unresolved but important question that impacts our understanding of genome function and evolution. Global mechanisms that underlie phenomena including the size of regulatory sequences, their uniqueness, and their evolutionary turnover remain poorly described. Results Here, we ask whether models incorporating different degrees of spacing and orientation constraints among transcription factor binding sites are broadly consistent with several global properties of regulatory sequence. These properties include length, sequence diversity, turnover rate, and dominance of specific TFs in regulatory site identity and cell type specification. Models with and without spacing and orientation constraints are generally consistent with all observed properties of regulatory sequence, and with regulatory sequences being fundamentally small (~ 1 nucleosome). Uniqueness of regulatory regions and their rapid evolutionary turnover are expected under all models examined. An intriguing issue we identify is that the complexity of eukaryotic regulatory sites must scale with the number of active transcription factors, in order to accomplish observed specificity. Conclusions Models of transcription factor binding with or without spacing and orientation constraints predict that regulatory sequences should be fundamentally short, unique, and turn over rapidly. We posit that the existence of master regulators may be, in part, a consequence of evolutionary pressure to limit the complexity and increase evolvability of regulatory sites.