Characterizations in Domination Theory

Let G = (V,E) be a graph. A set R is a restrained dominating set (total restrained dominating set, resp.) if every vertex in V − R (V) is adjacent to a vertex in R and (every vertex in V −R) to a vertex in V −R. The restrained domination number of G (total restrained domination number of G), denoted by gamma_r(G) (gamma_tr(G)), is the smallest cardinality of a restrained dominating set (total restrained dominating set) of G. If T is a tree of order n, then gamma_r(T) is greater than or equal to (n+2)/3. We show that gamma_tr(T) is greater than or equal to (n+2)/2. Moreover, we show that if n is congruent to 0 mod 4, then gamma_tr(T) is greater than or equal to (n+2)/2 + 1. We then constructively characterize the extremal trees achieving these lower bounds. Finally, if G is a graph of order n greater than or equal to 2, such that both G and G\u27 are not isomorphic to P_3, then gamma_r(G) + gamma_r(G\u27) is greater than or equal to 4 and less than or equal to n +2. We provide a similar result for total restrained domination and characterize the extremal graphs G of order n achieving these bounds

Characterizing Information Propagation in Plants

This paper considers an electro-chemical based communication model for intercellular communication in plants. Many plants, such as Mimosa pudica (the "sensitive plant"), employ electrochemical signals known as action potentials (APs) for communication purposes. In this paper we present a simple model for action potential generation. We make use of the concepts from molecular communication to explain the underlying process of information transfer in a plant. Using the information-theoretic analysis, we compute the mutual information between the input and output in this work. The key aim is to study the variations in the information propagation speed for varying number of plant cells for one simple case. Furthermore we study the impact of the AP signal on the mutual information and information propagation speed. We aim to explore further that how the growth rate in plants can impact the information transfer rate and vice versa.Comment: 6 pages, 5 Figures, Submitted to IEEE Conference, 201

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Vowel normalization is a computation that is meant to account for the differences in the absolute direct (physical or psychophysical) representations of qualitatively equivalent vowel productions that arise due to differences in speaker properties such as body size types, age, gender, and other socially interpreted categories that are based on natural variation in vocal tract size and shape. In this dissertation, we address the metaphysical and epistemological aspects of vowel normalization pertaining to spoken language acquisition during early infancy. We begin by reviewing approaches to conceptualizing and modeling the phonetic components of early spoken language acquisition, forming a catalog of phenomena that serves as the basis for our discourse. We then establish the existence of a vowel normalization computation carried out by infants early in their spoken language acquisition, and put forward a conceptual and technical framework for its investigation which focuses attention on the generative nature of the computation. We then situate the acquisition of vowel normalization within a broader developmental framework encompassing a suite of vocal learning phenomena, including language-specific caretaker vocal exchanges