Online choosability of graphs

We study several problems in graph coloring. In list coloring, each vertex $v$ has a set $L(v)$ of available colors and must be assigned a color from this set so that adjacent vertices receive distinct colors; such a coloring is an $L$-coloring, and we then say that $G$ is $L$-colorable. Given a graph $G$ and a function $f:V(G)\to\N$, we say that $G$ is $f$-choosable if $G$ is $L$-colorable for any list assignment $L$ such that $|L(v)|\ge f(v)$ for all $v\in V(G)$. When $f(v)=k$ for all $v$ and $G$ is $f$-choosable, we say that $G$ is $k$-choosable. The least $k$ such that $G$ is $k$-choosable is the choice number, denoted $\ch(G)$. We focus on an online version of this problem, which is modeled by the Lister/Painter game. The game is played on a graph in which every vertex has a positive number of tokens. In each round, Lister marks a nonempty subset $M$ of uncolored vertices, removing one token at each marked vertex. Painter responds by selecting a subset $D$ of $M$ that forms an independent set in $G$. A color distinct from those used on previous rounds is given to all vertices in $D$. Lister wins by marking a vertex that has no tokens, and Painter wins by coloring all vertices in $G$. When Painter has a winning strategy, we say that $G$ is $f$-paintable. If $f(v)=k$ for all $v$ and $G$ is $f$-paintable, then we say that $G$ is $k$-paintable. The least $k$ such that $G$ is $k$-paintable is the paint number, denoted \pa(G). In Chapter 2, we develop useful tools for studying the Lister/Painter game. We study the paintability of graph joins and of complete bipartite graphs. In particular, \pa(K_{k,r})\le k if and only if $r<k^k$. In Chapter 3, we study the Lister/Painter game with the added restriction that the proper coloring produced by Painter must also satisfy some property $\mathcal{P}$. The main result of Chapter 3 provides a general method to give a winning strategy for Painter when a strategy for the list coloring problem is already known. One example of a property $\mathcal{P}$ is that of having an $r$-dynamic coloring, where a proper coloring is $r$-dynamic if each vertex $v$ has at least $\min\set{r,d(v)}$ distinct colors in its neighborhood. For any graph $G$ and any $r$, we give upper bounds on how many tokens are necessary for Painter to produce an $r$-dynamic coloring of $G$. The upper bounds are in terms of $r$ and the genus of a surface on which $G$ embeds. In Chapter 4, we study a version of the Lister/Painter game in which Painter must assign $m$ colors to each vertex so that adjacent vertices receive disjoint color sets. We characterize the graphs in which $2m$ tokens is sufficient to produce such a coloring. We strengthen Brooks' Theorem as well as Thomassen's result that planar graphs are 5-choosable. In Chapter 5, we study sum-paintability. The sum-paint number of a graph $G$, denoted \spa(G), is the least $\sum f(v)$ over all $f$ such that $G$ is $f$-paintable. We prove the easy upper bound: \spa(G)\le|V(G)|+|E(G)|. When \spa(G)=|V(G)|+|E(G)|, we say that $G$ is sp-greedy. We determine the sum-paintability of generalized theta-graphs. The generalized theta-graph $\Theta_{\ell_1,\dots,\ell_k}$ consists of two vertices joined by $k$ paths of lengths \VEC \ell1k. We conjecture that outerplanar graphs are sp-greedy and prove several partial results toward this conjecture. In Chapter 6, we study what happens when Painter is allowed to allocate tokens as Lister marks vertices. The slow-coloring game is played by Lister and Painter on a graph $G$. Lister marks a nonempty set of uncolored vertices and scores 1 point for each marked vertex. Painter colors all vertices in an independent subset of the marked vertices with a color distinct from those used previously in the game. The game ends when all vertices have been colored. The sum-color cost of a graph $G$, denoted \scc(G), is the maximum score Lister can guarantee in the slow-coloring game on $G$. We prove several general lower and upper bounds for \scc(G). In more detail, we study trees and prove sharp upper and lower bounds over all trees with $n$ vertices. We give a formula to determine \scc(G) exactly when $\alpha(G)\le2$. Separately, we prove that \scc(G)=\spa(G) if and only if $G$ is a disjoint union of cliques. Lastly, we give lower and upper bounds on \scc(K_{r,s})

Surveying structural complexity in quantum many-body systems

Quantum many-body systems exhibit a rich and diverse range of exotic behaviours, owing to their underlying non-classical structure. These systems present a deep structure beyond those that can be captured by measures of correlation and entanglement alone. Using tools from complexity science, we characterise such structure. We investigate the structural complexities that can be found within the patterns that manifest from the observational data of these systems. In particular, using two prototypical quantum many-body systems as test cases - the one-dimensional quantum Ising and Bose-Hubbard models - we explore how different information-theoretic measures of complexity are able to identify different features of such patterns. This work furthers the understanding of fully-quantum notions of structure and complexity in quantum systems and dynamics.Comment: 9 pages, 5 figure

Sources of Nutrition Information in Recreational Ultra-marathon Runners: A Mixed Methods Analysis

Ultra-marathon events (i.e., .42.2-km) continue to grow in popularity; however, little is known regarding the sources of nutrition information which inform their beliefs and habits. The objective of this study was to characterize the acquisition of sport-specific nutrition information among ultra-endurance athletes using a mixed methods design. Qualitative data were collected through focus groups and analyzed using thematic analysis. Three primary higher order themes were identified: Optimal Diet for Ultra-Endurance Athletes, Common Sources of Information, and Barriers to Scientific Information. Then, a self-report inventory (Sources of Nutrition Information-SONI questionnaire) was developed to assess common sources of nutrition information and characterize their beliefs about those sources. Likert-type questions were used, and primary sources were scored out of 3, sub-questions out of 5. Differences between sources were assessed using RM-ANOVA. Participants (N = 224) accessed, responded to, and submitted the survey via a secure, study-specific web-based link. Peer reviewed literature was reported as the most frequently used (mean score = 1.64, p \u3c 0.001), credible (3.02, p \u3c 0.001), and interesting (2.62, p \u3c 0.002). Social media was the most accessible (2.81, p \u3c 0.001), but the least credible (1.87, p \u3c 0.001). While social media was perceived less credible than other sources, its accessibility could make it a promising tool to provide evidence-based nutrition information to this population

Noradrenergic α1 Receptor Antagonist Treatment Attenuates Positive Subjective Effects of Cocaine in Humans: A Randomized Trial

Preclinical research implicates dopaminergic and noradrenergic mechanisms in mediating the reinforcing effects of drugs of abuse, including cocaine. The objective of this study was to evaluate the impact of treatment with the noradrenergic α(1) receptor antagonist doxazosin on the positive subjective effects of cocaine.Thirteen non-treatment seeking, cocaine-dependent volunteers completed this single-site, randomized, placebo-controlled, within-subjects study. In one study phase volunteers received placebo and in the other they received doxazosin, with the order counterbalanced across participants. Study medication was masked by over-encapsulating doxazosin tablets and matched placebo lactose served as the control. Study medication treatment was initiated at 1 mg doxazosin or equivalent number of placebo capsules PO/day and increased every three days by 1 mg. After receiving 4 mg doxazosin or equivalent number of placebo capsules participants received masked doses of 20 and 40 mg cocaine IV in that order with placebo saline randomly interspersed to maintain the blind.Doxazosin treatment was well tolerated and doxazosin alone produced minimal changes in heart rate and blood pressure. During treatment with placebo, cocaine produced dose-dependent increases in subjective effect ratings of "high", "stimulated", "like cocaine", "desire cocaine", "any drug effect", and "likely to use cocaine if had access" (p<.001). Doxazosin treatment significantly attenuated the effects of 20 mg cocaine on ratings of "stimulated", "like cocaine", and "likely to use cocaine if had access" (p<.05). There were trends for doxazosin to reduce ratings of "stimulated", "desire cocaine", and "likely to use cocaine if had access" (p<.10).Medications that block noradrenergic α₁ receptors, such as doxazosin, may be useful as treatments for cocaine dependence, and should be evaluated further.Clinicaltrials.gov NCT01062945

on Performance

Abstract Ultra-marathons (footraces greater than 42.2 km) are increasing in popularity, however little is known about the habitual dietary intake of these runners. The aim of this investigation was to empirically describe the habitual training diet of ultra-marathon runners and determine if macronutrient intake was associated with 161-km race performance. To assess habitual diet, runners recruited from five 161-km ultra-marathons across the U.S. (N = 47) completed a diet and training questionnaire, and a web-based 24-hour dietary recall on three separate days within 1-4 weeks prior to a 161-km race. Multiple linear regression was used to predict finish time with covariates carbohydrate, fat and protein, expressed relative to body weight (g·kg -1 ) and total intake (% of diet). To determine differences in macronutrient intake between finishers and non-finishers, two-sample t-tests were used. Dietary intake was varied among participants; mean carbohydrate intake (5.19±2.62 g·kg ) predicted finish time (R 2 = 0.232, P =0.036), however fat was the only significant covariate (t = -2.90, P =0.007). Relative macronutrient intake (% of diet) did not predict finish time (R 2 =0.145, P =0.155). No significant differences were found in macronutrient intake between finishers (n=36) and non-finishers (n=11). Habitual dietary fat intake in ultra-marathon runners was a significant predictor of 161-km finish time, regardless of carbohydrate or protein intake. Further investigation is warranted to determine the optimal nutrient intake in ultra-marathon runners to maximize performance

Iceberg topography and volume classification using TanDEM-X interferometry

Icebergs in polar regions affect water salinity, alter marine habitats, and impose serious hazards on maritime operations and navigation. These impacts mainly depend on the iceberg volume, which remains an elusive parameter to measure. We investigate the capability of TanDEM-X bistatic single-pass synthetic aperture radar interferometry (InSAR) to derive iceberg subaerial morphology and infer total volume. We cross-verify InSAR results with Operation IceBridge (OIB) data acquired near Wordie Bay, Antarctica, as part of the OIB/TanDEM-X Antarctic Science Campaign (OTASC). While icebergs are typically classified according to size based on length or maximum height, we develop a new volumetric classification approach for applications where iceberg volume is relevant. For icebergs with heights exceeding 5 m, we find iceberg volumes derived from TanDEM-X and OIB data match within 7 %. We also derive a range of possible iceberg keel depths relevant to grounding and potential impacts on subsea installations. These results suggest that TanDEM-X could pave the way for future single-pass interferometric systems for scientific and operational iceberg mapping and classification based on iceberg volume and keel depth

A High Resolution Measurement of the 2.223 MeV Neutron Capture Line in a Solar Flare

An intense solar flare lasting 40 s was observed by the HEAO 3 γ-ray spectrometer on 1979 November 9 at 3:05 UT. The flare was observed in four high-resolution germanium detectors as well as in five CsI shield detectors over an energy range of 100 keV to above 5 MeV. Of particular interest is a line feature at 2.2248 ± 0.0010 MeV. The precise energy measurement provides unambiguous evidence that this is the ^1H(n,γ)^2H line resulting from neutron capture on hydrogen. An upper limit of 5 keV is found for the natural line width. The time dependence of the neutron capture line is discussed as well as the overall characteristics of the November 9 flare

Who says what to whom? Alignments and arguments in EU policy-making

In the EU multilevel polity, domestic interest groups seek to shape EU legislation by accessing both national and EU institutions. Previous studies indicated that institutional and issue contexts, as well as organizational characteristics shape their strategies of interest representation. However, we know much less about how alignments and arguments impact on their participation in EU and national policy consultations. Addressing this gap, we investigate the lobbying strategies of almost 2,900 national interest organizations from five member states (Germany, the Netherlands, Slovenia, Sweden, and the United Kingdom) on 20 EU directive proposals bringing also a new empirical scope to the study of multilevel interest representation. The findings indicate that alignments and arguments shape the participation of domestic interest groups in consultations on EU policies. We infer from our study that some general predictions of interest group behaviour are overstretched and outline four variations of interest representation routines

Applications of Direct Injection Soft Chemical Ionisation-Mass Spectrometry for the Detection of Pre-blast Smokeless Powder Organic Additives

Analysis of smokeless powders is of interest from forensics and security perspectives. This article reports the detection of smokeless powder organic additives (in their pre-detonation condition), namely the stabiliser diphenylamine and its derivatives 2-nitrodiphenylamine and 4-nitrodiphenylamine, and the additives (used both as stabilisers and plasticisers) methyl centralite and ethyl centralite, by means of swab sampling followed by thermal desorption and direct injection soft chemical ionisation-mass spectrometry. Investigations on the product ions resulting from the reactions of the reagent ions H3O+ and O2+ with additives as a function of reduced electric field are reported. The method was comprehensively evaluated in terms of linearity, sensitivity and precision. For H3O+, the limits of detection (LoD) are in the range of 41-88 pg of additive, for which the accuracy varied between 1.5 and 3.2%, precision varied between 3.7 and 7.3% and linearity showed R20.9991. For O2+, LoD are in the range of 72 to 1.4 ng, with an accuracy of between 2.8 and 4.9% and a precision between 4.5 and 8.6% and R20.9914. The validated methodology was applied to the analysis of commercial pre-blast gun powders from different manufacturers.(VLID)4826148Accepted versio