Visualization of interactive narrative structures remains a difficult problem: while authoring systems have developed robust ways to visually communicate narrative structures, comparatively little work has been done towards visualizing the output of playthroughs, namely story metrics and redundant content paths. This paper explores an interactive visualization that quickly helps authors spot re...

In the present paper, enumeration of a certain class directed lattice paths is based on analysis dynamical correlation functions exactly solvable XX0 model. This model zero anisotropy limit one basic models theory integrable systems, XXZ Heisenberg magnet. It demonstrated that considered under different boundary conditions are exponential generating various types paths, in particular, Dyck and ...

Online and offline hybrid teaching breaks the discontinuity of traditional teaching, provides teachers with a variety evaluation channels, students rich resources, expands enriches content Japanese courses, makes course colorful. The cultural nature determines feasibility developing ideology politics, internationality necessity which is conducive to cultivating students' patriotic feelings huma...

We study the following geometric hypergraph coloring problem: given a planar point set and an integer k, we wish to color the points with k colors so that any axis-aligned strip containing sufficiently many points contains all colors. We show that if the strip contains at least 2k−1 points, such a coloring can always be found. In dimension d, we show that the same holds provided the strip conta...

Nonlinearities provide a neverending challenge to systems and control. We savor linear systems since we have a good understanding of how they behave, and there is much we can do to analyze and predict their performance. As we move away from linearity, we need to scrutinize each nonlinearity that we encounter to assess its benefi t or detriment in terms of what we wish to achieve. The first issu...

In this paper we give recursive formulas for the number of colorful tilings of small rectangular arrays. We enumerate the tilings of a 2 × n board with painted squares, dominoes, and I-trominoes. We also provide a recursion formula for the number of tilings of a 3 × n board with colorful squares and dominoes. Finally, we describe a general method for calculating the number of colorful tilings o...

Let T be a symmetric directed tree, i.e., a tree with each edge viewed as two opposite directed links. We consider the problem of routing arbitrary sets of connection requests in T. In all-optical communication tree networks with WDM (wavelength-division multiplexing) this is equivalent to color (assign wavelengths to) a given set of directed paths so that no two directed paths of the same colo...

We describe the complex global structure of giant components in directed multiplex networks that generalizes the well-known bow-tie structure, generic for ordinary directed networks. By definition, a directed multiplex network contains vertices of one type and directed edges of m different types. In directed multiplex networks, we distinguish a set of different giant components based on the exi...

Finding disjoint paths in graphs is a problem that has attracted considerable attention from at least three perspectives: graph theory, VLSI design and network routing/flow. The corresponding literature is extensive. In this chapter we focus mostly on results on offline approximation algorithms for problems on general graphs as influenced from the network flow perspective. Surveys examining the...

A naı̈ve algorithm for the replacement paths problem runs in O(n(m+n logn)) time, executing the single-source shortest path algorithm up to n times. In our paper [3], we claimed that the replacement paths problem can be solved inO(m+n logn) time for both undirected and directed graphs. However, there is a flaw that invalidates the algorithm for directed graphs. (The algorithm for undirected grap...