Matroidal structure of generalized rough sets based on symmetric and transitive relations

Rough sets are efficient for data pre-process in data mining. Lower and upper approximations are two core concepts of rough sets. This paper studies generalized rough sets based on symmetric and transitive relations from the operator-oriented view by matroidal approaches. We firstly construct a matroidal structure of generalized rough sets based on symmetric and transitive relations, and provide an approach to study the matroid induced by a symmetric and transitive relation. Secondly, this paper establishes a close relationship between matroids and generalized rough sets. Approximation quality and roughness of generalized rough sets can be computed by the circuit of matroid theory. At last, a symmetric and transitive relation can be constructed by a matroid with some special properties.Comment: 5 page

Rough matroids based on coverings

The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving them are usually greedy. Matroid, as a generalization of linear independence in vector spaces, it has a variety of applications in many fields such as algorithm design and combinatorial optimization. An excellent introduction to the topic of rough matroids is due to Zhu and Wang. On the basis of their work, we study the rough matroids based on coverings in this paper. First, we investigate some properties of the definable sets with respect to a covering. Specifically, it is interesting that the set of all definable sets with respect to a covering, equipped with the binary relation of inclusion $\subseteq$, constructs a lattice. Second, we propose the rough matroids based on coverings, which are a generalization of the rough matroids based on relations. Finally, some properties of rough matroids based on coverings are explored. Moreover, an equivalent formulation of rough matroids based on coverings is presented. These interesting and important results exhibit many potential connections between rough sets and matroids.Comment: 15page

Improved Ductility of Boron Carbide by Microalloying with Boron Suboxide

Boron carbide (B_4C) is the third hardest material in nature, but applications are hindered by its brittle failure under impact. We found that this brittle failure of B_4C arises from amorphous shear band formation due to deconstruction of icosahedral clusters, and on the basis of this model we suggest and validate with quantum mechanics (QM, PBE flavor of density function theory) that a laminated B_4C–B_6O composite structure will eliminate this brittle failure. Using QM to apply shear deformations along various slip systems, we find that the (001)/[100] slip system has the lowest maximum shear strength, indicating it to be the most plausible slip system. We find that this composite structure has a shear strength of 38.33 GPa, essentially the same as that of B_4C (38.97 GPa), indicating the same intrinsic hardness as B4C. However, the critical failure strain for (001)/[100] slip in the composite is 0.465, which is 41% higher than B_4C, indicating a dramatically improvement on ductility. This arises because incorporation of B_6O prevents the failure mechanism of B_4C in which the carbene formed during shear deformation reacts with the C–B–C chains. This suggests a new strategy for designing ductile superhard ceramics

The angular spectrum of the scattering coefficient map reveals subsurface colorectal cancer

Abstract Colorectal cancer diagnosis currently relies on histological detection of endoluminal neoplasia in biopsy specimens. However, clinical visual endoscopy provides no quantitative subsurface cancer information. In this ex vivo study of nine fresh human colon specimens, we report the first use of quantified subsurface scattering coefficient maps acquired by swept-source optical coherence tomography to reveal subsurface abnormities. We generate subsurface scattering coefficient maps with a novel wavelet-based-curve-fitting method that provides significantly improved accuracy. The angular spectra of scattering coefficient maps of normal tissues exhibit a spatial feature distinct from those of abnormal tissues. An angular spectrum index to quantify the differences between the normal and abnormal tissues is derived, and its strength in revealing subsurface cancer in ex vivo samples is statistically analyzed. The study demonstrates that the angular spectrum of the scattering coefficient map can effectively reveal subsurface colorectal cancer and potentially provide a fast and more accurate diagnosis

Hierarchical graphs for rule-based modeling of biochemical systems

<p>Abstract</p> <p>Background</p> <p>In rule-based modeling, graphs are used to represent molecules: a colored vertex represents a component of a molecule, a vertex attribute represents the internal state of a component, and an edge represents a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions. A rule that specifies addition (removal) of an edge represents a class of association (dissociation) reactions, and a rule that specifies a change of a vertex attribute represents a class of reactions that affect the internal state of a molecular component. A set of rules comprises an executable model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system.</p> <p>Results</p> <p>For purposes of model annotation, we propose the use of hierarchical graphs to represent structural relationships among components and subcomponents of molecules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR) complex. We also show that computational methods developed for regular graphs can be applied to hierarchical graphs. In particular, we describe a generalization of Nauty, a graph isomorphism and canonical labeling algorithm. The generalized version of the Nauty procedure, which we call HNauty, can be used to assign canonical labels to hierarchical graphs or more generally to graphs with multiple edge types. The difference between the Nauty and HNauty procedures is minor, but for completeness, we provide an explanation of the entire HNauty algorithm.</p> <p>Conclusions</p> <p>Hierarchical graphs provide more intuitive formal representations of proteins and other structured molecules with multiple functional components than do the regular graphs of current languages for specifying rule-based models, such as the BioNetGen language (BNGL). Thus, the proposed use of hierarchical graphs should promote clarity and better understanding of rule-based models.</p

Multiple conserved regulatory domains promote Fezf2 expression in the developing cerebral cortex.

BackgroundThe genetic programs required for development of the cerebral cortex are under intense investigation. However, non-coding DNA elements that control the expression of developmentally important genes remain poorly defined. Here we investigate the regulation of Fezf2, a transcription factor that is necessary for the generation of deep-layer cortical projection neurons.ResultsUsing a combination of chromatin immunoprecipitation followed by high throughput sequencing (ChIP-seq) we mapped the binding of four deep-layer-enriched transcription factors previously shown to be important for cortical development. Building upon this we characterized the activity of three regulatory regions around the Fezf2 locus at multiple stages throughout corticogenesis. We identified a promoter that was sufficient for expression in the cerebral cortex, and enhancers that drove reporter gene expression in distinct forebrain domains, including progenitor cells and cortical projection neurons.ConclusionsThese results provide insight into the regulatory logic controlling Fezf2 expression and further the understanding of how multiple non-coding regulatory domains can collaborate to control gene expression in vivo