A combinatorial Li-Yau inequality and rational points on curves

We present a method to control gonality of nonarchimedean curves based on graph theory. Let k denote a complete nonarchimedean valued field.We first prove a lower bound for the gonality of a curve over the algebraic closure of k in terms of the minimal degree of a class of graph maps, namely: one should minimize over all so-called finite harmonic graph morphisms to trees, that originate from any refinement of the dual graph of the stable model of the curve. Next comes our main result: we prove a lower bound for the degree of such a graph morphism in terms of the first eigenvalue of the Laplacian and some “volume” of the original graph; this can be seen as a substitute for graphs of the Li–Yau inequality from differential geometry, although we also prove that the strict analogue of the original inequality fails for general graphs. Finally,we apply the results to give a lower bound for the gonality of arbitraryDrinfeld modular curves over finite fields and for general congruence subgroups Γ of Γ (1) that is linear in the index [Γ (1) : Γ ], with a constant that only depends on the residue field degree and the degree of the chosen “infinite” place. This is a function field analogue of a theorem of Abramovich for classical modular curves. We present applications to uniform boundedness of torsion of rank two Drinfeld modules that improve upon existing results, and to lower bounds on the modular degree of certain elliptic curves over function fields that solve a problem of Papikian

Track Fitting in the ATLAS Experiment

ATLAS is one of the four experiments that will analyze the proton-proton collisions that the LHC will produce. ATLAS consists of several subsystems: the inner detector, the calorimeters, and the muon spectrometer. In this thesis, emphasis is placed on the analysis of the data from the inner tracker and the muon spectrometer. For each particle, the detector performs a number of position measurements. From this set of three-dimensional points, the trajectory of the particle can be reconstructed using computer calculations. In this thesis an algorithm is described that is based on the minimization of a global $\chi^2$ function. The algorithm corrects for energy loss and scattering in the detector material, by introducing extra fit parameters for these material effects. The propagation of the tracks through the magnetic field in the detector is performed using a fourth order Runge-Kutta procedure. This procedure is numerical, therefore it requires a significant amount of computation time. It turns out that the derivatives of the measurements with respect to the track parameters can be evaluated analytically, which reduces the amount of computation time required. The algorithm has been used to study data from the Combined Testbeam in 2004, as well as cosmic ray data recorded by the inner detector in 2006. In addition, the algorithm has been tested using simulated collision events in ATLAS. The performance of the algorithm is competitive with other solutions

Rigidity and reconstruction for graphs

The edge reconstruction conjecture of Harary (1964) states that a finite graph G can be reconstructed up to isomorphism from the multiset of its edge-deleted subgraphs G–e (with e running over the edges of G). We put this conjecture in the framework of measure-theoretic rigidity, revealing the importance of the lengths of labeled closed walks for the problem

Aansluiting van de kernkwaliteiten Rivierenland bij Farm & Fun : een quickscan van beleidsdocumenten

Deze rapportage doet verslag van een verkenning naar de kernkwaliteiten van en beleid in het werkgebied van Farm & Fun. Hoe sluit het concept aan bij de diverse waarden die centraal staan in het beleid (zoals groen/gezondheid, kinderen, duurzaamheid, vitale lokale plattelandseconomie). En hoe kunnen deze waarden worden vertaald naar een Maatschappelijke Effect Rapportage (MAER) per type activiteit binnen het concept Farm & Fun. Er is in dit project gekeken naar de beleidsdocumenten van de regio Rivierenland. Het samenspel van uiterwaarden, dijken, oeverwallen, stroomruggen, rivierduinen en kommen zijn in sterke mate beeld-en sfeerbepalend. Dijk-en kerkdorpen bevinden zich in slingerende linten door het landschap, met op veel plaatsen schilderachtige doorzichten naar de weidse en open gebieden die zich tussen de nederzettingen bevinden. Het gebied heeft veel natuurwaarde, zoals natuurlijke bossen, stroomdalgraslanden, natte en vochtige schrale graslanden, moerassen en wateren met uitzonderlijke, ecologisch waardevolle, waterkwaliteit. Slingerende landweggetjes en authentieke pontverbindingen over de traag meanderende rivieren bieden toegevoegde waarde voor het concept. Waardevolle monumentale bouwwerken, zoals kastelen, forten, burchten, landhuizen en boerderijen, kunnen het decor van activiteiten vormen of wellicht zelfs de plaats van handelin

Wat ben ik toch een groene jongen (m/v)!

A

Stable divisorial gonality is in NP

Divisorial gonality and stable divisorial gonality are graph parameters, which have an origin in algebraic geometry. Divisorial gonality of a connected graph $G$ can be defined with help of a chip firing game on $G$. The stable divisorial gonality of $G$ is the minimum divisorial gonality over all subdivisions of edges of $G$. In this paper we prove that deciding whether a given connected graph has stable divisorial gonality at most a given integer $k$ belongs to the class NP. Combined with the result that (stable) divisorial gonality is NP-hard by Gijswijt, we obtain that stable divisorial gonality is NP-complete. The proof consist of a partial certificate that can be verified by solving an Integer Linear Programming instance. As a corollary, we have that the number of subdivisions needed for minimum stable divisorial gonality of a graph with $n$ vertices is bounded by $2^{p(n)}$ for a polynomial $p$

Nonlocal magnon-polaron transport in yttrium iron garnet

The spin Seebeck effect (SSE) is observed in magnetic insulator|heavy metal bilayers as an inverse spin Hall effect voltage under a temperature gradient. The SSE can be detected nonlocally as well, viz. in terms of the voltage in a second metallic contact (detector) on the magnetic film, spatially separated from the first contact that is used to apply the temperature bias (injector). Magnon-polarons are hybridized lattice and spin waves in magnetic materials, generated by the magnetoelastic interaction. Kikkawa et al. [Phys. Rev. Lett. \textbf{117}, 207203 (2016)] interpreted a resonant enhancement of the local SSE in yttrium iron garnet (YIG) as a function of the magnetic field in terms of magnon-polaron formation. Here we report the observation of magnon-polarons in \emph{nonlocal} magnon spin injection/detection devices for various injector-detector spacings and sample temperatures. Unexpectedly, we find that the magnon-polaron resonances can suppress rather than enhance the nonlocal SSE. Using finite element modelling we explain our observations as a competition between the SSE and spin diffusion in YIG. These results give unprecedented insights into the magnon-phonon interaction in a key magnetic material.Comment: 5 pages, 6 figure

Auto-oscillation threshold and line narrowing in MgO-based spin-torque oscillators

We present an experimental study of the power spectrum of current-driven magnetization oscillations in MgO tunnel junctions under low bias. We find the existence of narrow spectral lines, down to 8 MHz in width at a frequency of 10.7 GHz, for small applied fields with clear evidence of an auto-oscillation threshold. Micromagnetics simulations indicate that the excited mode corresponds to an edge mode of the synthetic antiferromagnet