Exhaustive generation of kk-critical H\mathcal H-free graphs

We describe an algorithm for generating all $k$-critical $\mathcal H$-free graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove that there are only finitely many $4$-critical $(P_7,C_k)$-free graphs, for both $k=4$ and $k=5$. We also show that there are only finitely many $4$-critical graphs $(P_8,C_4)$-free graphs. For each case of these cases we also give the complete lists of critical graphs and vertex-critical graphs. These results generalize previous work by Hell and Huang, and yield certifying algorithms for the $3$-colorability problem in the respective classes. Moreover, we prove that for every $t$, the class of 4-critical planar $P_t$-free graphs is finite. We also determine all 27 4-critical planar $(P_7,C_6)$-free graphs. We also prove that every $P_{10}$-free graph of girth at least five is 3-colorable, and determine the smallest 4-chromatic $P_{12}$-free graph of girth five. Moreover, we show that every $P_{13}$-free graph of girth at least six and every $P_{16}$-free graph of girth at least seven is 3-colorable. This strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with arXiv:1504.0697

Rural men and mental health: their experiences and how they managed

There is a growing awareness that a primary source of information about mental health lies with the consumers. This article reports on a study that interviewed rural men with the aim of exploring their mental health experiences within a rural environment. The results of the interviews are a number of stories of resilience and survival that highlight not only the importance of exploring the individuals' perspective of their issues, but also of acknowledging and drawing on their inner strengths. Rural men face a number of challenges that not only increase the risk of mental illness but also decrease the likelihood of them seeking and/or finding professional support. These men's stories, while different from each other, have a common thread of coping. Despite some support from family and friends participants also acknowledged that seeking out professional support could have made the recovery phase easier. Mental health nurses need to be aware, not only of the barrier to professional support but also of the significant resilience that individuals have and how it can be utilised

Critical dynamics of self-gravitating Langevin particles and bacterial populations

We study the critical dynamics of the generalized Smoluchowski-Poisson system (for self-gravitating Langevin particles) or generalized Keller-Segel model (for the chemotaxis of bacterial populations). These models [Chavanis & Sire, PRE, 69, 016116 (2004)] are based on generalized stochastic processes leading to the Tsallis statistics. The equilibrium states correspond to polytropic configurations with index $n$ similar to polytropic stars in astrophysics. At the critical index $n_{3}=d/(d-2)$ (where $d\ge 2$ is the dimension of space), there exists a critical temperature $\Theta_{c}$ (for a given mass) or a critical mass $M_{c}$ (for a given temperature). For $\Theta>\Theta_{c}$ or $M<M_{c}$ the system tends to an incomplete polytrope confined by the box (in a bounded domain) or evaporates (in an unbounded domain). For $\Theta<\Theta_{c}$ or $M>M_{c}$ the system collapses and forms, in a finite time, a Dirac peak containing a finite fraction $M_c$ of the total mass surrounded by a halo. This study extends the critical dynamics of the ordinary Smoluchowski-Poisson system and Keller-Segel model in $d=2$ corresponding to isothermal configurations with $n_{3}\to +\infty$. We also stress the analogy between the limiting mass of white dwarf stars (Chandrasekhar's limit) and the critical mass of bacterial populations in the generalized Keller-Segel model of chemotaxis

All solutions of the n = 5 Lane-Emden equation

All real solutions of the Lane-Emden equation for n = 5 are obtained in terms of Jacobian and Weierstrass elliptic functions. A new family of solutions is found. It is expressed by remarkably simple formulae involving Jacobian elliptic functions only. The general properties and discrete scaling symmetries of these new solutions are discussed. We also comment on their possible applications.Comment: To appear in Journal of Mathematical Physic

The Complete Plastid Genome Sequence of the Secondarily Nonphotosynthetic Alga Cryptomonas paramecium: Reduction, Compaction, and Accelerated Evolutionary Rate

The cryptomonads are a group of unicellular algae that acquired photosynthesis through the engulfment of a red algal cell, a process called secondary endosymbiosis. Here, we present the complete plastid genome sequence of the secondarily nonphotosynthetic species Cryptomonas paramecium CCAP977/2a. The ∼78 kilobase pair (Kbp) C. paramecium genome contains 82 predicted protein genes, 29 transfer RNA genes, and a single pseudogene (atpF). The C. paramecium plastid genome is approximately 50 Kbp smaller than those of the photosynthetic cryptomonads Guillardia theta and Rhodomonas salina; 71 genes present in the G. theta and/or R. salina plastid genomes are missing in C. paramecium. The pet, psa, and psb photosynthetic gene families are almost entirely absent. Interestingly, the ribosomal RNA operon, present as inverted repeats in most plastid genomes (including G. theta and R. salina), exists as a single copy in C. paramecium. The G + C content (38%) is higher in C. paramecium than in other cryptomonad plastid genomes, and C. paramecium plastid genes are characterized by significantly different codon usage patterns and increased evolutionary rates. The content and structure of the C. paramecium plastid genome provides insight into the changes associated with recent loss of photosynthesis in a predominantly photosynthetic group of algae and reveals features shared with the plastid genomes of other secondarily nonphotosynthetic eukaryotes

Predictive tracking with improved motion models for optical belt sorting

Optical belt sorters are a versatile means to sort bulk materials. In previous work, we presented a novel design of an optical belt sorter, which includes an area scan camera instead of a line scan camera. Line scan cameras, which are well-established in optical belt sorting, only allow for a single observation of each particle. Using multitarget tracking, the data of the area scan camera can be used to derive a part of the trajectory of each particle. The knowledge of the trajectories can be used to generate accurate predictions as to when and where each particle passes the separation mechanism. Accurate predictions are key to achieve high quality sorting results. The accuracy of the trajectories and the predictions heavily depends on the motion model used. In an evaluation based on a simulation that provides us with ground truth trajectories, we previously identified a bias in the temporal component of the prediction. In this paper, we analyze the simulation-based ground truth data of the motion of different bulk materials and derive models specifically tailored to the generation of accurate predictions for particles traveling on a conveyor belt. The derived models are evaluated using simulation data involving three different bulk materials. The evaluation shows that the constant velocity model and constant acceleration model can be outperformed by utilizing the similarities in the motion behavior of particles of the same type

Identification of novel aphid-killing bacteria to protect plants.

Aphids, including the peach-potato aphid, Myzus persicae, are major insect pests of agriculture and horticulture, and aphid control measures are limited. There is therefore an urgent need to develop alternative and more sustainable means of control. Recent studies have shown that environmental microbes have varying abilities to kill insects. We screened a range of environmental bacteria isolates for their abilities to kill target aphid species. Tests demonstrated the killing aptitude of these bacteria against six aphid genera (including Myzus persicae). No single bacterial strain was identified that was consistently toxic to insecticide-resistant aphid clones than susceptible clones, suggesting resistance to chemicals is not strongly correlated with bacterial challenge. Pseudomonas fluorescens PpR24 proved the most toxic to almost all aphid clones whilst exhibiting the ability to survive for over three weeks on three plant species at populations of 5–6 log CFU cm−2 leaf. Application of PpR24 to plants immediately prior to introducing aphids onto the plants led to a 68%, 57% and 69% reduction in aphid populations, after 21 days, on Capsicum annuum, Arabidopsis thaliana and Beta vulgaris respectively. Together, these findings provide new insights into aphid susceptibility to bacterial infection with the aim of utilizing bacteria as effective biocontrol agents

Stability of oligosaccharides derived from lactulose during the processing of milk and apple juice

The scientific evidence on the bioactivity of oligosaccharides from lactulose has encouraged us to study their physicochemical modifications during the processing of milk and apple juice. The carbohydrate fraction with a degree of polymerization ≥3 was stable in milk heated at temperatures up to 100°C for 30 min and in apple juice heated up to 90°C for 15 min. An assessment of the Maillard reaction in heated milk pointed out a higher formation of furosine in milk with oligosaccharides from lactulose as compared to its counterpart without this ingredient, due to a higher presence of galactose. The organoleptic properties of juice with oligosaccharides from lactulose were acceptable and similar to those of apple juice with commercial galactooligosaccharides. The results presented herein demonstrate that oligosaccharides from lactulose can be used as prebiotic ingredients in a wide range of functional foods, including those intended for diabetics and lactose intolerant individuals.This work has been supported by project AGL2011-27884 from Spanish Ministerio de Economía y Competitividad.Peer Reviewe

Algorithms and Bounds for Drawing Directed Graphs

In this paper we present a new approach to visualize directed graphs and their hierarchies that completely departs from the classical four-phase framework of Sugiyama and computes readable hierarchical visualizations that contain the complete reachability information of a graph. Additionally, our approach has the advantage that only the necessary edges are drawn in the drawing, thus reducing the visual complexity of the resulting drawing. Furthermore, most problems involved in our framework require only polynomial time. Our framework offers a suite of solutions depending upon the requirements, and it consists of only two steps: (a) the cycle removal step (if the graph contains cycles) and (b) the channel decomposition and hierarchical drawing step. Our framework does not introduce any dummy vertices and it keeps the vertices of a channel vertically aligned. The time complexity of the main drawing algorithms of our framework is $O(kn)$, where $k$ is the number of channels, typically much smaller than $n$ (the number of vertices).Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018