On vertex coloring without monochromatic triangles

We study a certain relaxation of the classic vertex coloring problem, namely, a coloring of vertices of undirected, simple graphs, such that there are no monochromatic triangles. We give the first classification of the problem in terms of classic and parametrized algorithms. Several computational complexity results are also presented, which improve on the previous results found in the literature. We propose the new structural parameter for undirected, simple graphs -- the triangle-free chromatic number $\chi_3$. We bound $\chi_3$ by other known structural parameters. We also present two classes of graphs with interesting coloring properties, that play pivotal role in proving useful observation about our problem. We give/ask several conjectures/questions throughout this paper to encourage new research in the area of graph coloring.Comment: Extended abstrac

Hepatitis C virus quasispecies in chronically infected children subjected to interferon–ribavirin therapy

Accumulating evidence suggests that certain features of hepatitis C virus (HCV), especially its high genetic variability, might be responsible for the low efficiency of anti-HCV treatment. Here, we present a bioinformatic analysis of HCV-1a populations isolated from 23 children with chronic hepatitis C (CHC) subjected to interferon–ribavirin therapy. The structures of the viral quasispecies were established based on a 132-amino-acid sequence derived from E1/E2 protein, including hypervariable region 1 (HVR1). Two types of HCV populations were identified. The first type, found in non-responders, contained a small number of closely related variants. The second type, characteristic for sustained responders, was composed of a large number of distantly associated equal-rank variants. Comparison of 445 HVR1 sequences showed that a significant number of variants present in non-responding patients are closely related, suggesting that certain, still unidentified properties of the pathogen may be key factors determining the result of CHC treatment

Impact of Tail Loss on the Behaviour and Locomotor Performance of Two Sympatric Lampropholis Skink Species

Caudal autotomy is an anti-predator behaviour that is used by many lizard species. Although there is an immediate survival benefit, the subsequent absence of the tail may inhibit locomotor performance, alter activity and habitat use, and increase the individuals' susceptibility to future predation attempts. We used laboratory experiments to examine the impact of tail autotomy on locomotor performance, activity and basking site selection in two lizard species, the delicate skink (Lampropholis delicata) and garden skink (L. guichenoti), that occur sympatrically throughout southeastern Australia and are exposed to an identical suite of potential predators. Post-autotomy tail movement did not differ between the two Lampropholis species, although a positive relationship between the shed tail length and distance moved, but not the duration of movement, was observed. Tail autotomy resulted in a substantial decrease in sprint speed in both species (28–39%), although this impact was limited to the optimal performance temperature (30°C). Although L. delicata was more active than L. guichenoti, tail autotomy resulted in decreased activity in both species. Sheltered basking sites were preferred over open sites by both Lampropholis species, although this preference was stronger in L. delicata. Caudal autotomy did not alter the basking site preferences of either species. Thus, both Lampropholis species had similar behavioural responses to autotomy. Our study also indicates that the impact of tail loss on locomotor performance may be temperature-dependent and highlights that future studies should be conducted over a broad thermal range

Naturally occurring variation in tadpole morphology and performance linked to predator regime

Divergent natural selection drives a considerable amount of the phenotypic and genetic variation observed in natural populations. For example, variation in the predator community can generate conflicting selection on behavioral, life-history, morphological, and performance traits. Differences in predator regime can subsequently increase phenotypic and genetic variations in the population and result in the evolution of reproductive barriers (ecological speciation) or phenotypic plasticity. We evaluated morphology and swimming performance in field collected Bronze Frog larvae (Lithobates clamitans) in ponds dominated by predatory fish and those dominated by invertebrate predators. Based on previous experimental findings, we hypothesized that tadpoles from fish-dominated ponds would have small bodies, long tails, and large tail muscles and that these features would facilitate fast-start speed. We also expected to see increased tail fin depth (i.e., the tail-lure morphology) in tadpoles from invertebrate-dominated ponds. Our results support our expectations with respect to morphology in affecting swimming performance of tadpoles in fish-dominated ponds. Furthermore, it is likely that divergent natural selection is playing a role in the diversification on morphology and locomotor performance in this system

The study of the influence of micro-environmental signals on macrophage differentiation using a quantitative Petri net based model

The complexity of many biological processes, which, thanks to the development of many fields of science, becomes for us more and more obvious, makes these processes extremely interesting for further analysis. In this paper a quantitative model of the process of macrophage differentiation, which is essential for many phenomena occurring in the human body, is proposed and analyzed. The model is expressed in the language of Petri net theory on the basis of one of the three hypotheses concerning macrophage differentiation existing in the literature. The performed analysis allowed to find an importance of individual factors in the studied phenomenon

The effect of cigarette smoking on endothelial damage and atherosclerosis development – modeled and analyzed using Petri nets

Atherosclerosis as one of the crucial causes of cardiovascular diseases (CVD) is the leading reason of death worldwide. One of the contributing factors to this phenomenon is endothelial dysfunction, which is associated with the impact of various agents and their interactions. Tobacco smoke is one of the well known factors here. For better understanding of its significance a model of its impact on atherosclerotic plaque formation has been proposed. The model contains selected aspects of the influence of tobacco smoke, dual function of nitric oxide (NO) (influence of various mechanisms on NO bioavailability), oxidative stress which promotes low density lipoproteins oxidation, macrophages significance and other mechanisms leading to an aggravation of the endothelial disturbances. The model has been built using Petri nets theory and the analysis has been based on t-invariants. This approach allowed to confirm the important role of inflammation and oxidative stress in atherosclerosis development and moreover it has shown the considerable influence of the cigarette smoke