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

Magnon Planar Hall Effect and Anisotropic Magnetoresistance in a Magnetic Insulator

Electrical resistivities can be different for charge currents travelling parallel or perpendicular to the magnetization in magnetically ordered conductors or semiconductors, resulting in the well-known planar Hall effect and anisotropic magnetoresistance. Here, we study the analogous anisotropic magnetotransport behavior for magnons in a magnetic insulator Y$_{3}$Fe$_{5}$O$_{12}$. Electrical and thermal magnon injection, and electrical detection methods are used at room temperature with transverse and longitudinal geometries to measure the magnon planar Hall effect and anisotropic magnetoresistance, respectively. We observe that the relative difference between magnon current conductivities parallel and perpendicular to the magnetization, with respect to the average magnon conductivity, i.e. $|(\sigma_{\parallel}^{\textrm{m}}-\sigma_{\perp}^{\textrm{m}})/\sigma_{0}^{\textrm{m}}|$ , is approximately 5% with the majority of the measured devices showing $\sigma_{\perp}^{\textrm{m}}>\sigma_{\parallel}^{\textrm{m}}$.Comment: 18 pages, 16 figure

On the occurrence of bryophytes and macrolichens in different lowland rain forest types at Mabura Hill, Guyana

A floristic and ecological study of bryophytes and macrolichens in different lowland rain forest types around Mabura Hill, Guyana, South America, yielded 170 species: 52 mosses, 82 liverworts and 36 macrolichens. Lejeuneaceae account for about 30% of the species and are the dominant cryptogamic family of the lowland rain forest. Special attention was paid to the flora of the forest canopy, by using mountaineering techniques. It appeared that 50% of the bryophyte species and 86% of the macrolichens occurred exclusively in the canopy. Dry evergreen 'walaba' forest on white sand is particularly rich in lichens whereas the more humid 'mixed' forest on loamy soil is characterized by a rather rich liverwort flora. More species are exclusive to the mixed forest than to dry evergreen forest due to the 'canopy effect', i.e. the occurrence of xerophytic species in the outer canopy of both dry and humid forests. Furthermore, canopy species have wider vertical distributions on trees in the dry evergreen forest than in the mixed forest, due to the more open canopy foliage of the dry evergreen forest

Criteria for accurate determination of the magnon relaxation length from the nonlocal spin Seebeck effect

The nonlocal transport of thermally generated magnons not only unveils the underlying mechanism of the spin Seebeck effect, but also allows for the extraction of the magnon relaxation length ($\lambda_m$) in a magnetic material, the average distance over which thermal magnons can propagate. In this study, we experimentally explore in yttrium iron garnet (YIG)/platinum systems much further ranges compared with previous investigations. We observe that the nonlocal SSE signals at long distances ($d$) clearly deviate from a typical exponential decay. Instead, they can be dominated by the nonlocal generation of magnon accumulation as a result of the temperature gradient present away from the heater, and decay geometrically as $1/d^2$. We emphasize the importance of looking only into the exponential regime (i.e., the intermediate distance regime) to extract $\lambda_m$. With this principle, we study $\lambda_m$ as a function of temperature in two YIG films which are 2.7 and 50 $\mu$m in thickness, respectively. We find $\lambda_m$ to be around 15 $\mu$m at room temperature and it increases to 40 $\mu$m at $T=$ 3.5 K. Finite element modeling results agree with experimental studies qualitatively, showing also a geometrical decay beyond the exponential regime. Based on both experimental and modeling results we put forward a general guideline for extracting $\lambda_m$ from the nonlocal spin Seebeck effect.Comment: 9 pages, 7 figure

Pitching a business idea to investors: How new venture founders use micro-level rhetoric to achieve narrative plausibility and resonance

For entrepreneurial narratives to be effective, they need to be judged as plausible and have to resonate with an audience. Prior research has, however, not examined or explained how entrepreneurs try to meet these criteria. In this paper, we addressed this question by analysing the micro-level arguments underpinning the pitch narratives of entrepreneurs who joined a business incubator. We discerned four previously unidentified rhetorical strategies that these entrepreneurs used to achieve narrative plausibility and resonance. Our findings further suggest that temporality and product development status may shape how entrepreneurs use these strategies. By outlining these aspects of entrepreneurial rhetoric, we contribute to opening up the black box of narrative resonance and plausibility and advance work on the role of rhetoric in entrepreneurship

A Socio-Informatic Approach to Automated Account Classification on Social Media

Automated accounts on social media have become increasingly problematic. We propose a key feature in combination with existing methods to improve machine learning algorithms for bot detection. We successfully improve classification performance through including the proposed feature.Comment: International Conference on Social Media and Societ

Nonlocal magnon spin transport in yttrium iron garnet with tantalum and platinum spin injection/detection electrodes

We study the magnon spin transport in the magnetic insulator yttrium iron garnet (YIG) in a nonlocal experiment and compare the magnon spin excitation and detection for the heavy metal paramagnetic electrodes platinum (Pt|YIG|Pt) and tantalum (Ta|YIG|Ta). The electrical injection and detection processes rely on the (inverse) spin Hall effect in the heavy metals and the conversion between the electron spin and magnon spin at the heavy metal|YIG interface. Pt and Ta possess opposite signs of the spin Hall angle. Furthermore, their heterostructures with YIG have different interface properties, i.e. spin mixing conductances. By varying the distance between injector and detector, the magnon spin transport is studied. Using a circuit model based on the diffusion-relaxation transport theory, a similar magnon relaxation length of ~ 10 \mu m was extracted from both Pt and Ta devices. By changing the injector and detector material from Pt to Ta, the influence of interface properties on the magnon spin transport has been observed. For Ta devices on YIG the spin mixing conductance is reduced compared with Pt devices, which is quantitatively consistent when comparing the dependence of the nonlocal signal on the injector-detector distance with the prediction from the circuit model.Comment: 7 pages, 4 figure

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