A partially ordered (generalized) pattern (POP) is a generalized pattern some of whose letters are incomparable, an extension of generalized permutation patterns introduced by Babson and Steingŕımsson. POPs were introduced in the symmetric group by Kitaev [19, 21], and studied in the set of k-ary words by Kitaev and Mansour [22]. Moreover, Kitaev et al. [23] introduced segmented POPs in composi...

The main theorem establishes the generating function F which counts the number of times the staircase 1+2+3+ · · ·m+ fits inside an integer composition of n. F = km − qx my 1−x km−1 (1− q)x( 2 ) ( y 1−x )m + 1−x−xy 1−x ( km − qx my 1−x km−1 ) . where km = m−1 ∑ æ=0 xmj−( j 2) ( y 1− x )j . Here x and y respectively track the composition size and number of parts, whilst q tracks the number of su...

AUTHOR Cohen, Andrew D. TITLE Reformulating Second-Language Compositions: A Potential Source of Input for the Learner. PUB DATE Apr 83 NOTE 25p.; For related document, see ED 224 338. Revised version of a paper presented at the Annual Convention of Teachers of English to Speakers of Other Languages (17th, Toronto, O-ntario, March 15-20, 1983). PUB TYPE Reports Research/Technical (143) -Speeches...

A connected partition of a graph G is a partition of its vertex set such that each induced subgraph is connected. In earlier research it was called a connected composition of a graph. We find a polynomial, the defect polynomial of the graph, that decribes the number of connected partitions of complements of graphs with respect to any complete graph. The defect polynomial is calculated for sever...

This paper discusses an OWL ontology for specifying sensors. The ontology is intended as the basis for the semantic representation of sensors and as the formal description for reasoning about sensors and observations. The paper describes the ontology, presents two example sensor descriptions and shows how standard reasoning and querying techniques can be used to perform tasks including classifi...

Dota 2 is a multiplayer online game in which two teams of five players control “heroes” and compete to earn gold and destroy enemy structures. Teamwork is essential and heroes are chosen to create a balanced team that will counter the opponents’ selections. We studied how the win rate depends on hero selection by performing logistic regression with models that incorporate interactions between h...

The idea of graph compositions generalizes both ordinary compositions of positive integers and partitions of finite sets. In this paper we develop formulas, generating functions, and recurrence relations for composition counting functions for several families of graphs.

Lost Time Accident is a series of compositions exploring the creation of interactive real-time soundscapes and compositions for the new media opera, Ausländer und Staatenlose. This paper explores the background to these compositions including the systems they are based on and the possibilities for a generative sensorium for multimedia and virtual reality content. Author:...........................

We consider words over the alphabet [k] = {1, 2, . . . , k}, k ≥ 2. For a fixed nonnegative integer p, a p-succession in a word w1w2 · · ·wn consists of two consecutive letters of the form (wi, wi + p), i = 1, 2, . . . , n − 1. We analyze words with respect to a given number of contained p-successions. First we find the mean and variance of the number of p-successions. We then determine the dis...

The concept of a composition of a graph was introduced by Arnold Knopfmacher and M.E. Mays in [2] and denotes a partition of the vertices such that the induced subgraph on each part is connected. Alternatively, a partition can be viewed as the set of connected components of a subgraph including all the vertices of the graph but only a subset of the edges. Most attention hitherto has been devote...