The Finite Field Kakeya Problem

A Besicovitch set in AG(n,q) is a set of points containing a line in every direction. The Kakeya problem is to determine the minimal size of such a set. We solve the Kakeya problem in the plane, and substantially improve the known bounds for n greater than 4.Comment: 13 page

Effects of environmental enrichment on behavioral responses to novelty, learning, and memory, and the circadian rhythm in cortisol in growing pigs

Previously we showed that pigs reared in an enriched environment had higher baseline salivary cortisol concentrations during the light period than pigs reared under barren conditions. In the present experiment, it was investigated whether these higher baseline salivary cortisol concentrations were a real difference in cortisol concentration or merely represented a phase difference in circadian rhythm. The effects of different cortisol concentrations on the behavioral responses to novelty and learning and long-term memory in a maze test were also studied in enriched and barren housed pigs. At 9 weeks of age enriched and barren housed pigs did not differ in baseline salivary cortisol concentrations nor in circadian rhythm, but at 22 weeks of age barren housed pigs had a blunted circadian rhythm in salivary cortisol as compared to enriched housed pigs. The differences in baseline salivary cortisol concentrations between enriched- and barren-housed pigs are age-dependent, and become visible after 15 weeks of age. Enriched- and barren-housed piglets did not differ in time spent on exploration in the novel environment test. Barren-housed pigs had an impaired long-term memory in the maze test compared to enriched-housed pigs; however, no differences in learning abilities between enriched- and barren-housed pigs were found. Because blunted circadian cortisol rhythms are often recorded during states of chronic stress in pigs and rats or during depression in humans, it is suggested that the blunted circadian rhythm in cortisol in barren-housed pigs similarily may reflect decreased welfare.

Good Random Matrices over Finite Fields

The random matrix uniformly distributed over the set of all m-by-n matrices over a finite field plays an important role in many branches of information theory. In this paper a generalization of this random matrix, called k-good random matrices, is studied. It is shown that a k-good random m-by-n matrix with a distribution of minimum support size is uniformly distributed over a maximum-rank-distance (MRD) code of minimum rank distance min{m,n}-k+1, and vice versa. Further examples of k-good random matrices are derived from homogeneous weights on matrix modules. Several applications of k-good random matrices are given, establishing links with some well-known combinatorial problems. Finally, the related combinatorial concept of a k-dense set of m-by-n matrices is studied, identifying such sets as blocking sets with respect to (m-k)-dimensional flats in a certain m-by-n matrix geometry and determining their minimum size in special cases.Comment: 25 pages, publishe

Single Molecule Statistics and the Polynucleotide Unzipping Transition

We present an extensive theoretical investigation of the mechanical unzipping of double-stranded DNA under the influence of an applied force. In the limit of long polymers, there is a thermodynamic unzipping transition at a critical force value of order 10 pN, with different critical behavior for homopolymers and for random heteropolymers. We extend results on the disorder-averaged behavior of DNA's with random sequences to the more experimentally accessible problem of unzipping a single DNA molecule. As the applied force approaches the critical value, the double-stranded DNA unravels in a series of discrete, sequence-dependent steps that allow it to reach successively deeper energy minima. Plots of extension versus force thus take the striking form of a series of plateaus separated by sharp jumps. Similar qualitative features should reappear in micromanipulation experiments on proteins and on folded RNA molecules. Despite their unusual form, the extension versus force curves for single molecules still reveal remnants of the disorder-averaged critical behavior. Above the transition, the dynamics of the unzipping fork is related to that of a particle diffusing in a random force field; anomalous, disorder-dominated behavior is expected until the applied force exceeds the critical value for unzipping by roughly 5 pN.Comment: 40 pages, 18 figure

Грунти як об’єкт науки

Висвітлюються деякі аспекти розвитку наших уявлень про ґрунтознавство як науковий напрямок природознавства та про ґрунти як об’єкт науки.Освещаются некоторые аспекты развития наших представлений о почвоведении как научном направлении природоведения и о почвах как объекте науки.The author highlights several aspects of human knowledge about soil research as a field of natural science, and about soils as a research object

Butyrate inhibits human mast cell activation via epigenetic regulation of FcεRI-mediated signaling

Background: Short-chain fatty acids (SCFAs) are fermented dietary components that regulate immune responses, promote colonic health, and suppress mast cell–mediated diseases. However, the effects of SCFAs on human mast cell function, including the underlying mechanisms, remain unclear. Here, we investigated the effects of the SCFAs (acetate, propionate, and butyrate) on mast cell–mediated pathology and human mast cell activation, including the molecular mechanisms involved. Method: Precision-cut lung slices (PCLS) of allergen-exposed guinea pigs were used to assess the effects of butyrate on allergic airway contraction. Human and mouse mast cells were co-cultured with SCFAs and assessed for degranulation after IgE- or non–IgE-mediated stimulation. The underlying mechanisms involved were investigated using knockout mice, small molecule inhibitors/agonists, and genomics assays. Results: Butyrate treatment inhibited allergen-induced histamine release and airway contraction in guinea pig PCLS. Propionate and butyrate, but not acetate, inhibited IgE- and non–IgE-mediated human or mouse mast cell degranulation in a concentration-dependent manner. Notably, these effects were independent of the stimulation of SCFA receptors GPR41, GPR43, or PPAR, but instead were associated with inhibition of histone deacetylases. Transcriptome analyses revealed butyrate-induced downregulation of the tyrosine kinases BTK, SYK, and LAT, critical transducers of FcεRI-mediated signals that are essential for mast cell activation. Epigenome analyses indicated that butyrate redistributed global histone acetylation in human mast cells, including significantly decreased acetylation at the BTK, SYK, and LAT promoter regions. Conclusion: Known health benefits of SCFAs in allergic disease can, at least in part, be explained by epigenetic suppression of human mast cell activation