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Full-Text Articles in Discrete Mathematics and Combinatorics
Rainbow Perfect And Near-Perfect Matchings In Complete Graphs With Edges Colored By Circular Distance, Shuhei Saitoh, Naoki Matsumoto, Wei Wu
Rainbow Perfect And Near-Perfect Matchings In Complete Graphs With Edges Colored By Circular Distance, Shuhei Saitoh, Naoki Matsumoto, Wei Wu
Theory and Applications of Graphs
Given an edge-colored complete graph Kn on n vertices, a perfect (respectively, near-perfect) matching M in Kn with an even (respectively, odd) number of vertices is rainbow if all edges have distinct colors. In this paper, we consider an edge coloring of Kn by circular distance, and we denote the resulting complete graph by K●n. We show that when K●n has an even number of vertices, it contains a rainbow perfect matching if and only if n=8k or n=8k+2, where k is a nonnegative integer. In the case of an odd …
An Implementation Of Integrated Information Theory In Resting-State Fmri, Idan E. Nemirovsky
An Implementation Of Integrated Information Theory In Resting-State Fmri, Idan E. Nemirovsky
Electronic Thesis and Dissertation Repository
Integrated Information Theory (IIT) is a framework developed to explain consciousness, arguing that conscious systems consist of interacting elements that are integrated through their causal properties. In this study, we present the first application of IIT to functional magnetic resonance imaging (fMRI) data and investigate whether its principal metric, Phi, can meaningfully quantify resting-state cortical activity patterns. Data was acquired from 17 healthy subjects who underwent sedation with propofol, a short acting anesthetic. Using PyPhi, a software package developed for IIT, we thoroughly analyze how Phi varies across different networks and throughout sedation. Our findings indicate that variations in Phi …