let $g$ be a graph and let $m_{ij}(g)$, $i,jge 1$, be the number of edges $uv$ of $g$ such that ${d_v(g), d_u(g)} = {i,j}$. the {em $m$-polynomial} of $g$ is introduced with $displaystyle{m(g;x,y) = sum_{ile j} m_{ij}(g)x^iy^j}$. it is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular ca...

This article focuses on a mass medial text genre scarcely found today, but which might assume considerable importance within a few years. It looks at hypernews, ie news written, structured and distributed as hypertexts. Over the past few years, the Internet-based hypertext system World Wide Web has become a news channel of great significance, in Norway as in other parts of the world. Despite th...

We present a system to procedurally generate complex models with interdependent elements. Our system relies on the concept of components to spatially and semantically define various elements. Through a series of successive statements executed on a subset of components selected with queries, we grow a tree of components ultimately defining a model. We apply our concept and representation of comp...

Studies of the graph of dictionary definitions (DD) (Picard et al., 2009; Levary et al., 2012) have revealed strong semantic coherence of local topological structures. The techniques used in these papers are simple and the main results are found by understanding the structure of cycles in the directed graph (where words point to definitions). Based on our earlier work (Levary et al., 2012), we ...

Abstract We present a memory-augmented approach to condition an autoregressive language model on knowledge graph. represent the graph as collection of relation triples and retrieve relevant relations for given context improve text generation. Experiments WikiText-103, WMT19, enwik8 English datasets demonstrate that our produces better in terms perplexity bits per character. also show relational...

Categories with algebraic structure—the most prominent example being monoidal categories—satisfy equational axioms only up-to coherent isomorphisms. Therefore they are pseudo algebras. We extend Lawvere’s functorial semantics to such pseudo structure: in contrast to standard strict algebras which are identified with productpreserving functors, pseudo algebras are product-preserving pseudo funct...

This paper presents a graph-based segmentation method using multiple criteria in successive stages to segment thoracoscopic images acquired during a diskectomy procedure commonly used for thoracoscopic anterior release and fusion for scoliosis treatment. Starting with image pre-processing, including Gaussian smoothing, brightness and contrast enhancement, and histogram thresholding, a standard ...

We describe a method for extractive summarization of legal judgments using our own graph-based summarization algorithm. In contrast to the connected and undirected graphs of previous work, we construct directed and disconnected graphs (a set of connected graphs) for each document, where each connected graph indicates a cluster that shares one topic in a document. Our method automatically choose...