Orthogonal Range Reporting and Rectangle Stabbing for Fat Rectangles

In this paper we study two geometric data structure problems in the special case when input objects or queries are fat rectangles. We show that in this case a significant improvement compared to the general case can be achieved. We describe data structures that answer two- and three-dimensional orthogonal range reporting queries in the case when the query range is a \emph{fat} rectangle. Our two-dimensional data structure uses $O(n)$ words and supports queries in $O(\log\log U +k)$ time, where $n$ is the number of points in the data structure, $U$ is the size of the universe and $k$ is the number of points in the query range. Our three-dimensional data structure needs $O(n\log^{\varepsilon}U)$ words of space and answers queries in $O(\log \log U + k)$ time. We also consider the rectangle stabbing problem on a set of three-dimensional fat rectangles. Our data structure uses $O(n)$ space and answers stabbing queries in $O(\log U\log\log U +k)$ time.Comment: extended version of a WADS'19 pape

Glueball masses in the large N limit

The lowest-lying glueball masses are computed in SU($N$) gauge theory on a spacetime lattice for constant value of the lattice spacing $a$ and for $N$ ranging from 3 to 8. The lattice spacing is fixed using the deconfinement temperature at temporal extension of the lattice $N_T = 6$. The calculation is conducted employing in each channel a variational ansatz performed on a large basis of operators that includes also torelon and (for the lightest states) scattering trial functions. This basis is constructed using an automatic algorithm that allows us to build operators of any size and shape in any irreducible representation of the cubic group. A good signal is extracted for the ground state and the first excitation in several symmetry channels. It is shown that all the observed states are well described by their large $N$ values, with modest ${\cal O}(1/N^2)$ corrections. In addition spurious states are identified that couple to torelon and scattering operators. As a byproduct of our calculation, the critical couplings for the deconfinement phase transition for N=5 and N=7 and temporal extension of the lattice $N_T=6$ are determined.Comment: 1+36 pages, 22 tables, 21 figures. Typos corrected, conclusions unchanged, matches the published versio

Superpotential de-sequestering in string models

Non-perturbative superpotential cross-couplings between visible sector matter and K\"ahler moduli can lead to significant flavour-changing neutral currents in compactifications of type IIB string theory. Here, we compute corrections to Yukawa couplings in orbifold models with chiral matter localised on D3-branes and non-perturbative effects on distant D7-branes. By evaluating a threshold correction to the D7-brane gauge coupling, we determine conditions under which the non-perturbative corrections to the Yukawa couplings appear. The flavour structure of the induced Yukawa coupling generically fails to be aligned with the tree-flavour structure. We check our results by also evaluating a correlation function of two D7-brane gauginos and a D3-brane Yukawa coupling. Finally, by calculating a string amplitude between n hidden scalars and visible matter we show how non-vanishing vacuum expectation values of distant D7-brane scalars, if present, may correct visible Yukawa couplings with a flavour structure that differs from the tree-level flavour structure.Comment: 37 pages + appendices, 8 figure

Chemotaxis When Bacteria Remember: Drift versus Diffusion

{\sl Escherichia coli} ({\sl E. coli}) bacteria govern their trajectories by switching between running and tumbling modes as a function of the nutrient concentration they experienced in the past. At short time one observes a drift of the bacterial population, while at long time one observes accumulation in high-nutrient regions. Recent work has viewed chemotaxis as a compromise between drift toward favorable regions and accumulation in favorable regions. A number of earlier studies assume that a bacterium resets its memory at tumbles -- a fact not borne out by experiment -- and make use of approximate coarse-grained descriptions. Here, we revisit the problem of chemotaxis without resorting to any memory resets. We find that when bacteria respond to the environment in a non-adaptive manner, chemotaxis is generally dominated by diffusion, whereas when bacteria respond in an adaptive manner, chemotaxis is dominated by a bias in the motion. In the adaptive case, favorable drift occurs together with favorable accumulation. We derive our results from detailed simulations and a variety of analytical arguments. In particular, we introduce a new coarse-grained description of chemotaxis as biased diffusion, and we discuss the way it departs from older coarse-grained descriptions.Comment: Revised version, journal reference adde

Anatomical and biomechanical evaluation of the tension band technique in patellar fractures

Tension band wiring for patellar fractures is common, but some recent reports refer to disadvantages of this approach. Our anatomical and biomechanical study focused on use of tension band techniques in patellar fractures. The anatomy of the patella and tendon insertion was examined with knee magnetic resonance imaging (MRI) and correlated with the technical requirements of the tension band. Tension band wiring over tendinous tissue was simulated and calculated with a cyclic biomechanical test on cow patellae. According to tension band templating on the MRI section, Kirschner wire insertion was needed for the tension band to turn over the tendinous tissue. The tension band became more stable while turning over less tendinous tissue and more adjacent bone surface. Nevertheless, cyclic loading tests indicate that all tension band applications in this study lose their initial stability. Excessive initial compression by the tension band resulted in bending of the Kirschner wire and thus reduction failure. For optimum stabilisation, tension force transfer should be done directly on bone or at least material that protects the tendon would be useful

AFLP analysis reveals a lack of phylogenetic structure within Solanum section Petota

<p>Abstract</p> <p>Background</p> <p>The secondary genepool of our modern cultivated potato (<it>Solanum tuberosum </it>L.) consists of a large number of tuber-bearing wild <it>Solanum </it>species under <it>Solanum </it>section <it>Petota</it>. One of the major taxonomic problems in section <it>Petota </it>is that the series classification (as put forward by Hawkes) is problematic and the boundaries of some series are unclear. In addition, the classification has received only partial cladistic support in all molecular studies carried out to date.</p> <p>The aim of the present study is to describe the structure present in section <it>Petota</it>. When possible, at least 5 accessions from each available species and 5 individual plants per accession (totally approx. 5000 plants) were genotyped using over 200 AFLP markers. This resulted in the largest dataset ever constructed for <it>Solanum </it>section <it>Petota</it>. The data obtained are used to evaluate the 21 series hypothesis put forward by Hawkes and the 4 clade hypothesis of Spooner and co-workers.</p> <p>Results</p> <p>We constructed a NJ tree for 4929 genotypes. For the other analyses, due to practical reasons, a condensed dataset was created consisting of one representative genotype from each available accession. We show a NJ jackknife and a MP jackknife tree. A large part of both trees consists of a polytomy. Some structure is still visible in both trees, supported by jackknife values above 69. We use these branches with >69 jackknife support in the NJ jackknife tree as a basis for informal species groups. The informal species groups recognized are: Mexican diploids, Acaulia, Iopetala, Longipedicellata, polyploid Conicibaccata, diploid Conicibaccata, Circaeifolia, diploid Piurana and tetraploid Piurana.</p> <p>Conclusion</p> <p>Most of the series that Hawkes and his predecessors designated can not be accepted as natural groups, based on our study. Neither do we find proof for the 4 clades proposed by Spooner and co-workers. A few species groups have high support and their inner structure displays also supported subdivisions, while a large part of the species cannot be structured at all. We believe that the lack of structure is not due to any methodological problem but represents the real biological situation within section <it>Petota</it>.</p