Size-structured populations: immigration, (bi)stability and the net growth rate

We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the linearised system is governed by a quasicontraction semigroup. We also establish that linear stability of equilibrium solutions is governed by a generalized net reproduction function. In a special case of the model ingredients we discuss the nonlinear dynamics of the system when the spectral bound of the linearised operator equals zero, i.e. when linearisation does not decide stability. This allows us to demonstrate, through a concrete example, how immigration might be beneficial to the population. In particular, we show that from a nonlinearly unstable positive equilibrium a linearly stable and unstable pair of equilibria bifurcates. In fact, the linearised system exhibits bistability, for a certain range of values of the external inflow, induced potentially by All\'{e}e-effect.Comment: to appear in Journal of Applied Mathematics and Computin

Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

Problematic Internet Use and Problematic Online Gaming Are Not the Same: Findings from a Large Nationally Representative Adolescent Sample

There is an ongoing debate in the literature whether problematic internet use (PIU) and problematic online gaming (POG) are two distinct conceptual and nosological entities or whether they are the same. The present study contributes to this question by examining the interrelationship and the overlap between PIU and POG in terms of gender, school achievement, time spent using the internet and/or online gaming, psychological wellbeing, and preferred online activities. Questionnaires assessing these variables were administered to a nationally representative sample of adolescent gamers (N=2,073; mean age 16.4 years, SD=0.87, 68.4% male). Data showed that internet use was a common activity among adolescents while online gaming was engaged in by a considerably smaller group. Similarly, more adolescents met the criteria for PIU than for POG and a small group of adolescents showed symptoms of both problem behaviors. The most notable difference between the two problem behaviors was in terms of gender. POG was much more strongly associated with being male. Self-esteem had low effect sizes on both behaviors, while depressive symptoms were associated with both PIU and POG, affecting PIU slightly more. In terms of preferred online activities, PIU was positively associated with online gaming, online chatting, and social networking while POG was only associated with online gaming. Based on our findings POG appears to be a conceptually different behavior than PIU and therefore data support the notion that Internet Addiction Disorder and Internet Gaming Disorder are separate nosological entities

Segregation of granular binary mixtures by a ratchet mechanism

We report on a segregation scheme for granular binary mixtures, where the segregation is performed by a ratchet mechanism realized by a vertically shaken asymmetric sawtooth-shaped base in a quasi-two-dimensional box. We have studied this system by computer simulations and found that most binary mixtures can be segregated using an appropriately chosen ratchet, even when the particles in the two components have the same size, and differ only in their normal restitution coefficient or friction coefficient. These results suggest that the components of otherwise non-segregating granular mixtures may be separated using our method.Comment: revtex, 4 pages, 4 figures, submitte

Linear stability and positivity results for a generalized size-structured Daphnia model with inflow§

We employ semigroup and spectral methods to analyze the linear stability of positive stationary solutions of a generalized size-structured Daphnia model. Using the regularity properties of the governing semigroup, we are able to formulate a general stability condition which permits an intuitively clear interpretation in a special case of model ingredients. Moreover, we derive a comprehensive instability criterion that reduces to an elegant instability condition for the classical Daphnia population model in terms of the inherent net reproduction rate of Daphnia individuals

Vortices on Hyperbolic Surfaces

It is shown that abelian Higgs vortices on a hyperbolic surface $M$ can be constructed geometrically from holomorphic maps $f:M \to N$, where $N$ is also a hyperbolic surface. The fields depend on $f$ and on the metrics of $M$ and $N$. The vortex centres are the ramification points, where the derivative of $f$ vanishes. The magnitude of the Higgs field measures the extent to which $f$ is locally an isometry. Witten's construction of vortices on the hyperbolic plane is rederived, and new examples of vortices on compact surfaces and on hyperbolic surfaces of revolution are obtained. The interpretation of these solutions as SO(3)-invariant, self-dual SU(2) Yang--Mills fields on $\R^4$ is also given.Comment: Revised version: new section on four-dimensional interpretation of hyperbolic vortices added

Assessing the validity of subjective reports in the auditory streaming paradigm

Here, we tested three possible biasing effects on perceptual reports in the auditory streaming paradigm: errors due to imperfect understanding of the instructions, voluntary perceptual biasing, and susceptibility to implicit expectations. 1) Analysis of the responses to catch trials separately promoting each of the possible percepts allowed us to exclude participants who likely have not fully understood the instructions. 2) Explicit biasing instructions led to markedly different behavior than the conventional neutral-instruction condition, suggesting that listeners did not voluntarily bias their perception in a systematic way under the neutral instructions. Comparison with a random response condition further supported this conclusion. 3) No significant relationship was found between social desirability, a scale-based measure of susceptibility to implicit social expectations, and any of the perceptual measures extracted from the subjective reports. This suggests that listeners did not significantly bias their perceptual reports due to possible implicit expectations present in the experimental context. In sum, these results suggest that valid perceptual data can be obtained from subjective reports in the auditory streaming paradigm

Zassenhaus conjecture for central extensions of S5

We confirm a conjecture of Zassenhaus about rational conjugacy of torsion units in integral group rings for a covering group of the symmetric group S5 and for the general linear group GLð2; 5Þ. The first result, together with others from the literature, settles the conjugacy question for units of prime-power order in the integral group ring of a finite Frobenius group