@article{5680, abstract = {Pollinators display a remarkable diversity of foraging strategies with flowering plants, from primarily mutualistic interactions to cheating through nectar robbery. Despite numerous studies on the effect of nectar robbing on components of plant fitness, its contribution to reproductive isolation is unclear. We experimentally tested the impact of different pollinator strategies in a natural hybrid zone between two subspecies of Antirrhinum majus with alternate flower colour guides. On either side of a steep cline in flower colour between Antirrhinum majus pseudomajus (magenta) and A. m. striatum (yellow), we quantified the behaviour of all floral visitors at different time points during the flowering season. Using long-run camera surveys, we quantify the impact of nectar robbing on the number of flowers visited per inflorescence and the flower probing time. We further experimentally tested the effect of nectar robbing on female reproductive success by manipulating the intensity of robbing. While robbing increased over time the number of legitimate visitors tended to decrease concomitantly. We found that the number of flowers pollinated on a focal inflorescence decreased with the number of prior robbing events. However, in the manipulative experiment, fruit set and fruit volume did not vary significantly between low robbing and control treatments. Our findings challenge the idea that robbers have a negative impact on plant fitness through female function. This study also adds to our understanding of the components of pollinator-mediated reproductive isolation and the maintenance of Antirrhinum hybrid zones.}, author = {Andalo, Christophe and Burrus, Monique and Paute, Sandrine and Lauzeral, Christine and Field, David}, issn = {23818115}, journal = {Botany Letters}, number = {1}, pages = {80--92}, publisher = {Taylor and Francis}, title = {{Prevalence of legitimate pollinators and nectar robbers and the consequences for fruit set in an Antirrhinum majus hybrid zone}}, doi = {10.1080/23818107.2018.1545142}, volume = {166}, year = {2019}, } @article{5790, abstract = {The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation R′ giving some predrawn chords that represent an induced subgraph of G. The question is whether one can extend R′ to a representation R of the entire graph G, that is, whether one can draw the remaining chords into a partially predrawn representation to obtain a representation of G. Our main result is an O(n3) time algorithm for partial representation extension of circle graphs, where n is the number of vertices. To show this, we describe the structure of all representations of a circle graph using split decomposition. This can be of independent interest.}, author = {Chaplick, Steven and Fulek, Radoslav and Klavík, Pavel}, issn = {03649024}, journal = {Journal of Graph Theory}, number = {4}, pages = {365--394}, publisher = {Wiley}, title = {{Extending partial representations of circle graphs}}, doi = {10.1002/jgt.22436}, volume = {91}, year = {2019}, } @article{405, abstract = {We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy Class which has been introduced by Chen and Tropp quite recently.}, author = {Virosztek, Daniel}, journal = {Linear Algebra and Its Applications}, pages = {67--78}, publisher = {Elsevier}, title = {{Jointly convex quantum Jensen divergences}}, doi = {10.1016/j.laa.2018.03.002}, volume = {576}, year = {2019}, } @article{175, abstract = {An upper bound sieve for rational points on suitable varieties isdeveloped, together with applications tocounting rational points in thin sets,to local solubility in families, and to the notion of “friable” rational pointswith respect to divisors. In the special case of quadrics, sharper estimates areobtained by developing a version of the Selberg sieve for rational points.}, author = {Browning, Timothy D and Loughran, Daniel}, issn = {10886850}, journal = {Transactions of the American Mathematical Society}, number = {8}, pages = {5757--5785}, publisher = {American Mathematical Society}, title = {{Sieving rational points on varieties}}, doi = {10.1090/tran/7514}, volume = {371}, year = {2019}, } @article{319, abstract = {We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with boundary conditions. The calculus of modelled distributions established in Hairer (Invent Math 198(2):269–504, 2014. https://doi.org/10.1007/s00222-014-0505-4) is extended to this setting. We formulate and solve fixed point problems in these spaces with a class of kernels that is sufficiently large to cover in particular the Dirichlet and Neumann heat kernels. These results are then used to provide solution theories for the KPZ equation with Dirichlet and Neumann boundary conditions and for the 2D generalised parabolic Anderson model with Dirichlet boundary conditions. In the case of the KPZ equation with Neumann boundary conditions, we show that, depending on the class of mollifiers one considers, a “boundary renormalisation” takes place. In other words, there are situations in which a certain boundary condition is applied to an approximation to the KPZ equation, but the limiting process is the Hopf–Cole solution to the KPZ equation with a different boundary condition.}, author = {Gerencser, Mate and Hairer, Martin}, issn = {14322064}, journal = {Probability Theory and Related Fields}, number = {3-4}, pages = {697–758}, publisher = {Springer}, title = {{Singular SPDEs in domains with boundaries}}, doi = {10.1007/s00440-018-0841-1}, volume = {173}, year = {2019}, }