Dehn functionsRight-angled Artin groupsLet \\(\\Gamma \\) be a finite simplicial graph such that the flag complex on \\(\\Gamma \\) is a 2-dimensional triangulated disk. We show that with some assumptions, the Dehn function of the associated Bestvina–Brady group is either quadratic, ...
Learn more about this mathematical subject with the help of the lesson titled Discontinuities in Functions and Graphs. The lesson will discuss the following: Distinguishing discontinuous and continuous functions Exploring point discontinuities and their examples ...
2. Use thismethod to determinethe complex zeros of f(x) = −2x^2 – 12x – 20. Show at least 5 points on both of your graphs. 3. Prove that this method works for any quadratic function whose graph does not intersect the x-axis. The followingsteps willhelp you organize your proof...
Functions are a specific type of relation in which each input value has one and only one output value. Polynomial functions have all of these characteristics as well as a domain and range, and corresponding graphs. In this section, we will identify and evaluate polynomial functions. Because ...
et al. De novo assembly of the Aedes aegypti genome using Hi-C yields chromosome-length scaffolds. Science 356, 92–95 (2017). Article CAS PubMed PubMed Central Google Scholar Ghurye, J. et al. Integrating Hi-C links with assembly graphs for chromosome-scale assembly. PLoS Comput. Biol...
Identifying such text segments is challenging because they require a fine-grained level of analysis even within a single sentence. At the same time, accessing them facilitates the analysis of the communicative functions of a text as well as the identification of relevant information. We propose an...
Protein ubiquitination regulates a wide range of cellular processes. The degree of protein ubiquitination is determined by the delicate balance between ubiquitin ligase (E3)-mediated ubiquitination and deubiquitinase (DUB)-mediated deubiquitination. In c
Shpitser and Pearl (2006b) constructed an algorithm for identifying joint interventional distributions in causal models, which contain unobserved variables and induce directed acyclic graphs. This algorithm can be seen as a repeated application of the rules of do-calculus and known properties of proba...
Perfect Crystals for Quantum Affine Algebras and Combinatorics of Young Walls 55:44 Regular Permutation Groups and Cayley Graphs 01:00:03 The Broughton Archipeligo Monitoring Program 13:53 The Mathematics of Doodling 01:10:14 A New Approach to the Bar-Cobar Duality 01:01:36 Brains and ...
We find that directed modules of real-world graphs inherently overlap and the investigated networks can be classified into two major groups in terms of the overlaps between the modules. Accordingly, in the word-association network and among Google's webpages the overlaps are likely to contain in...