Formal group laws and hypergraph colorings

Thesis (Ph.D.)--University of Washington, 2016-06

Computing hypergraph width measures exactly

Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A connection between these and tree decompositions is established. This enables us to almost seamlessly adapt the combinatorial and algorithmic results known for tree decompositions of graphs to the case of hypergraphs and obtain fast exact algorithms. As a consequence, we provide algorithms which, given a hypergraph H on n vertices and m hyperedges, compute the generalized hypertree-width of H in time O*(2n) and compute the fractional hypertree-width of H in time O(1.734601n.m).1

State Fair 2008 Coloring Book, 2008

The Secretary of the State Office produced a coloring book all any or all children that go to the State Fair of Iowa.

Abduction Prevention Coloring Book

Coloring book for the prevention of abduction made by Division of Criminal Investigation

Weak hypergraph regularity and linear hypergraphs

We consider conditions which allow the embedding of linear hypergraphs of fixed size. In particular, we prove that any k-uniform hypergraph H of positive uniform density contains all linear k-uniform hypergraphs of a given size. More precisely, we show that for all integers l >= k >= 2 and every d > 0 there exists Q > 0 for which the following holds: if His a sufficiently large k-uniform hypergraph with the property that the density of H induced on every vertex subset of size on is at least d, then H contains every linear k-uniform hypergraph F with l vertices. The main ingredient in the proof of this result is a counting lemma for linear hypergraphs, which establishes that the straightforward extension of graph epsilon-regularity to hypergraphs suffices for counting linear hypergraphs. We also consider some related problems. (C) 2009 Elsevier Inc. All rights reserved.

Coloring ionic trapping states in WO3 and Nb2O5 electrochromic materials

Complex electro-optical analysis is a very useful approach to separate different kinetic processes that occur during ionic insertion reactions in electrochromic oxide materials. In this paper, we use this type of combined technique to investigate ionic and optical changes in different oxide host systems, i.e., in two oxide hosts, specifically WO3 and Nb2O5. A comparison of their electro-optical responses revealed the presence of an ionic trapping contribution to the kinetics of the coloring sites, which was named here as coloring ionic trapping state. As expected, this coloring trapping process is slower in Nb2O5 since the reduction potential of Nb2O5 is more negative (more energy is needed for a higher degree of coloration). A phenomenological solid-state model that encompasses homogeneous charge transfer and valence trapping was proposed to explain the coloring ionic trapping process. Basically the model is able to explain how ionic dynamics at low frequency region, i.e., the slower kinetic step, controls the coloring kinetics, i.e., how it is capable to regulate the coloring rates.Optical transient analyses demonstrated the possibility of the presence of more than one coloring ionic trap, indicating the complexity of the processes involved in coloration phenomenon in metal oxide host systems. (C) 2008 Published by Elsevier Ltd.

Influence of the coloring agent concentration on bleaching gel and pulp chamber temperatures during dental bleaching

This study evaluated the Influence of the coloring agent concentration on the temperature of the gel layer and pulp chamber during dental bleaching with an LED/laser light source. Ten human incisors and a digital thermometer with K-type thermocouples were used. Using a high-speed spherical diamond bur, endodontic access was gained through openings on the lingual faces until pulp chamber was exposed. One end of the thermocouple was placed on the labial surface (immersed in bleaching gel) and the other end in the pulp chamber. The same 10 specimens were used in the 12 groups, according to the type and concentration of bleaching gel. Each bleaching gel was used in four different concentrations: manipulated without coloring, with normal quantity recommended by the manufacturer, with double the recommended amount of coloring, and with triple the recommended amount of coloring. The temperature rise was measured every 30 seconds for three minutes with a K-type thermocouple. The data were analyzed by ANOVA to examine the concentration and type of bleaching gel. This test was followed by Tukey's test, which was performed Independently for the gel at the labial surface and the pulp chamber (a = 5%). For both surfaces, values of p = 0.00 were obtained for all factors and for the Interaction between them. The varying concentrations of coloring agent produced statistically significant differences in terms of temperature increase for both the gel layer and the pulp chamber during activation.

Development of a Yellow Pigment Based on Bismuth and Molybdenum-Doped TiO2 for Coloring Polymers

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influence of the quantity of coloring agent in bleaching gels activated with LED/laser appliances on bleaching efficiency

The aim of this study was to assess the influence of the quantity of coloring agent on the bleaching efficiency of gels containing 35% H2O2. Sixty human third molars were sectioned mesiodistally, darkened in a coffee solution and sectioned in the occlusal-cervical direction, resulting in mesial (not bleached) and distal halves (bleached). They were distributed into three groups: Whiteness HP, Total Bleach, and Whiteform Perox Red Gel; and subdivided into four sub-groups: no coloring agent, manufacturer's standard, double the standard, and triple the standard. The gels were activated with light-ermitting diode/laser appliances. The images were analyzed with the Adobe Photoshop program (deltaEL*a*b*). The variation was submitted to the ANOVA test (two factors: type of gel and quantity of coloring agent) and Tukey test. Differences were observed for the quantity of coloring agent. The mean (+/-SD) was determined for each quantity of coloring used: no coloring agent -6.85 (+/-2.26)a, manufacturer's standard -794 (+/-2.55)ab, double the standard -8.65 (+/-2.47)b, triple the standard -9.05 (+/-2.72)b. In conclusion, the standard quantity of coloring agent did not provide significantly more intense bleaching than when it was completely absent. The use of double and triple the amount provided greater bleaching than that observed for the gel without coloring agent. No significant differences were observed between the tested gels.

Hypergraph Mining for Social Networks

Nowadays, more and more data is collected in large amounts, such that the need of studying it both efficiently and profitably is arising; we want to acheive new and significant informations that weren't known before the analysis. At this time many graph mining algorithms have been developed, but an algebra that could systematically define how to generalize such operations is missing. In order to propel the development of a such automatic analysis of an algebra, We propose for the first time (to the best of my knowledge) some primitive operators that may be the prelude to the systematical definition of a hypergraph algebra in this regard.

Edge coloring BIBDS and constructing MOELRs

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Some historical uses and background are touched upon as well. The majority of the definitions are contained within this chapter as well. In Chapter 2 we consider the question whether one can decompose λ copies of monochromatic Kv into copies of Kk such that each copy of the Kk contains at most one edge from each Kv. This is called a proper edge coloring (Hurd, Sarvate, [29]). The majority of the content in this section is a wide variety of examples to explain the constructions used in Chapters 3 and 4. In Chapters 3 and 4 we investigate how to properly color BIBD(v, k, λ) for k = 4, and 5. Not only will there be direct constructions of relatively small BIBDs, we also prove some generalized constructions used within. In Chapter 5 we talk about an alternate solution to Chapters 3 and 4. A purely graph theoretical solution using matchings, augmenting paths, and theorems about the edgechromatic number is used to develop a theorem that than covers all possible cases. We also discuss how this method performed compared to the methods in Chapters 3 and 4. In Chapter 6, we switch topics to Latin rectangles that have the same number of symbols and an equivalent sized matrix to Latin squares. Suppose ab = n2. We define an equitable Latin rectangle as an a × b matrix on a set of n symbols where each symbol appears either [b/n] or [b/n] times in each row of the matrix and either [a/n] or [a/n] times in each column of the matrix. Two equitable Latin rectangles are orthogonal in the usual way. Denote a set of ka × b mutually orthogonal equitable Latin rectangles as a k–MOELR(a, b; n). We show that there exists a k–MOELR(a, b; n) for all a, b, n where k is at least 3 with some exceptions.

A new DSATUR-based algorithm for exact vertex coloring

This paper describes a new exact algorithm PASS for the vertex coloring problem based on the well known DSATUR algorithm. At each step DSATUR maximizes saturation degree to select a new candidate vertex to color, breaking ties by maximum degree w.r.t. uncolored vertices. Later Sewell introduced a new tiebreaking strategy, which evaluated available colors for each vertex explicitly. PASS differs from Sewell in that it restricts its application to a particular set of vertices. Overall performance is improved when the new strategy is applied selectively instead of at every step. The paper also reports systematic experiments over 1500 random graphs and a subset of the DIMACS color benchmark.