Decompositions of edge-colored infinite complete graphs into monochromatic paths

An $r$-edge coloring of a graph or hypergraph $G=(V,E)$ is a map $c:E\to \{0, \dots, r-1\}$. Extending results of Rado and answering questions of Rado, Gy\'arf\'as and S\'ark\"ozy we prove that (1.) the vertex set of every $r$-edge colored countably infinite complete $k$-uniform hypergraph can be partitioned into $r$ monochromatic tight paths with distinct colors (a tight path in a $k$-uniform hypergraph is a sequence of distinct vertices such that every set of $k$ consecutive vertices forms an edge), (2.) for all natural numbers $r$ and $k$ there is a natural number $M$ such that the vertex set of every $r$-edge colored countably infinite complete graph can be partitioned into $M$ monochromatic $k^{th}$ powers of paths apart from a finite set (a $k^{th}$ power of a path is a sequence $v_0, v_1, \dots$ of distinct vertices such that $1\le|i-j| \le k$ implies that $v_iv_j$ is an edge), (3.) the vertex set of every $2$-edge colored countably infinite complete graph can be partitioned into $4$ monochromatic squares of paths, but not necessarily into $3$, (4.) the vertex set of every $2$-edge colored complete graph on $\omega_1$ can be partitioned into $2$ monochromatic paths with distinct colors

Comparing weak versions of separability

Our aim is to investigate spaces with sigma-discrete and meager dense sets, as well as selective versions of these properties. We construct numerous examples to point out the differences between these classes while answering questions of Tkachuk [30], Hutchinson [17] and the authors of [8]

The Excitement of Life

These recent paintings explore the presence of excitement, energy and adrenaline rush one can capture in a moment. Oil paints have a quality that can make a painting come to life. This lifelike quality is exactly what I strive to capture in a way that allows the viewers to put themselves inside the painting. The inspiration for these paintings came from my own experiences of adventure and risk-taking. The use of foreshortening and distortion helps give the figures a sense of energy and create movement throughout the composition. By portraying the various situations through a warped lens, I believe that it draws the viewer in to question what is going on in the painting. As a result from viewing my paintings, I hope to inspire the viewer to feel the urge to go out and try something new and exciting. If they are not the type of people to partake in activities like these, then I wish to have them feel a sense of anxiety or unease. This sensation is desired because as a result the viewers are fully interested and engaged with the work to a point that it triggers their emotions. I feel that if you are touched on that level, then my work has truly come to life

MicroRNAs sound off

The message is loud and clear. MicroRNA-96, one in a cluster of three related neurosensory microRNAs, is crucial to the development and maintenance of inner ear hair cells and hearing in mice and humans. Two recent studies show that mutations in the critical seed region of the microRNA underlie the cause of hair cell degeneration and progressive hearing loss. Other recent reports reveal the general requirement of microRNAs for sensory epithelial development and maintenance in Dicer knockout mouse ear. The challenge begins to determine whether microRNAs will resonate as therapeutic agents or target molecules to preserve or restore hearing

The cellular magnetic response and biocompatibility of biogenic zinc- and cobalt-doped magnetite nanoparticles.

The magnetic moment and anisotropy of magnetite nanoparticles can be optimised by doping with transition metal cations, enabling their properties to be tuned for different biomedical applications. In this study, we assessed the suitability of bacterially synthesized zinc- and cobalt-doped magnetite nanoparticles for biomedical applications. To do this we measured cellular viability and activity in primary human bone marrow-derived mesenchymal stem cells and human osteosarcoma-derived cells. Using AC susceptibility we studied doping induced changes in the magnetic response of the nanoparticles both as stable aqueous suspensions and when associated with cells. Our findings show that the magnetic response of the particles was altered after cellular interaction with a reduction in their mobility. In particular, the strongest AC susceptibility signal measured in vitro was from cells containing high-moment zinc-doped particles, whilst no signal was observed in cells containing the high-anisotropy cobalt-doped particles. For both particle types we found that the moderate dopant levels required for optimum magnetic properties did not alter their cytotoxicity or affect osteogenic differentiation of the stem cells. Thus, despite the known cytotoxicity of cobalt and zinc ions, these results suggest that iron oxide nanoparticles can be doped to sufficiently tailor their magnetic properties without compromising cellular biocompatibility

The role of the testa during development and in establishment of dormancy of the legume seed

Timing of seed germination is one of the key steps in plant life cycles. It determines the beginning of plant growth in natural or agricultural ecosystems. In the wild, many seeds exhibit dormancy and will only germinate after exposure to certain environmental conditions. In contrast, crop seeds germinate as soon as they are imbibed usually at planting time. These domestication-triggered changes represent adaptations to cultivation and human harvesting. Germination is one of the common sets of traits recorded in different crops and termed the “domestication syndrome.” Moreover, legume seed imbibition has a crucial role in cooking properties. Different seed dormancy classes exist among plant species. Physical dormancy (often called hardseededness), as found in legumes, involves the development of a water-impermeable seed coat, caused by the presence of phenolics- and suberin-impregnated layers of palisade cells. The dormancy release mechanism primarily involves seed responses to temperature changes in the habitat, resulting in testa permeability to water. The underlying genetic controls in legumes have not been identified yet. However, positive correlation was shown between phenolics content (e.g., pigmentation), the requirement for oxidation and the activity of catechol oxidase in relation to pea seed dormancy, while epicatechin levels showed a significant positive correlation with soybean hardseededness. myeloblastosis family of transcription factors, WD40 proteins and enzymes of the anthocyanin biosynthesis pathway were involved in seed testa color in soybean, pea and Medicago, but were not tested directly in relation to seed dormancy. These phenolic compounds play important roles in defense against pathogens, as well as affecting the nutritional quality of products, and because of their health benefits, they are of industrial and medicinal interest. In this review, we discuss the role of the testa in mediating legume seed germination, with a focus on structural and chemical aspects

“Becoming a Family”: Developmental Processes Represented in Blended Family Discourse

We adopted a process-focus in order to gain a deeper understanding of how (step) blended family members experiencing different developmental pathways discursively represented their processes of becoming a family. Using a qualitative/interpretive method, we analyzed 980 pages of interview transcripts with stepparents and stepchildren. We studied the first four years of family development, using the five developmental pathways developed by Baxter, Braithwaite, and Nicholson (1999). Three salient issues identified in the family experiences were boundary management, solidarity, and adaptation. While the negotiation of these issues varied across the five trajectories, there were commonalities across family experiences that helped determine whether families had a successful experience of becoming a family. Implications for blended family researchers and practitioners are also discussed