Effect of migration in a diffusion model for template coexistence in protocells

The compartmentalization of distinct templates in protocells and the exchange of templates between them (migration) are key elements of a modern scenario for prebiotic evolution. Here we use the diffusion approximation of population genetics to study analytically the steady-state properties of such prebiotic scenario. The coexistence of distinct template types inside a protocell is achieved by a selective pressure at the protocell level (group selection) favoring protocells with a mixed template composition. In the degenerate case, where the templates have the same replication rate, we find that a vanishingly small migration rate suffices to eliminate the segregation effect of random drift and so to promote coexistence. In the non-degenerate case, a small migration rate greatly boosts coexistence as compared with the situation where there is no migration. However, increase of the migration rate beyond a critical value leads to the complete dominance of the more efficient template type (homogeneous regime). In this case, we find a continuous phase transition separating the homogeneous and the coexistence regimes, with the order parameter vanishing linearly with the distance to the transition point

Primitive abundant and weird numbers with many prime factors

We give an algorithm to enumerate all primitive abundant numbers (briefly, PANs) with a fixed $\Omega$ (the number of prime factors counted with their multiplicity), and explicitly find all PANs up to $\Omega=6$, count all PANs and square-free PANs up to $\Omega=7$ and count all odd PANs and odd square-free PANs up to $\Omega=8$. We find primitive weird numbers (briefly, PWNs) with up to 16 prime factors, improving the previous results of [Amato-Hasler-Melfi-Parton] where PWNs with up to 6 prime factors have been given. The largest PWN we find has 14712 digits: as far as we know, this is the largest example existing, the previous one being 5328 digits long [Melfi]. We find hundreds of PWNs with exactly one square odd prime factor: as far as we know, only five were known before. We find all PWNs with at least one odd prime factor with multiplicity greater than one and $\Omega = 7$ and prove that there are none with $\Omega < 7$. Regarding PWNs with a cubic (or higher) odd prime factor, we prove that there are none with $\Omega\le 7$, and we did not find any with larger $\Omega$. Finally, we find several PWNs with 2 square odd prime factors, and one with 3 square odd prime factors. These are the first such examples.Comment: New section on open problems. A mistake in table 2 corrected (# odd PAN with Omega=8). New PWN in table 5, last line, 2 squared prime factors, Omega=15. Updated bibliograph

Discontinuous Galerkin approximation of linear parabolic problems with dynamic boundary conditions

In this paper we propose and analyze a Discontinuous Galerkin method for a linear parabolic problem with dynamic boundary conditions. We present the formulation and prove stability and optimal a priori error estimates for the fully discrete scheme. More precisely, using polynomials of degree $p\geq 1$ on meshes with granularity $h$ along with a backward Euler time-stepping scheme with time-step $\Delta t$, we prove that the fully-discrete solution is bounded by the data and it converges, in a suitable (mesh-dependent) energy norm, to the exact solution with optimal order $h^p + \Delta t$. The sharpness of the theoretical estimates are verified through several numerical experiments

Upper body balance control strategy during continuous 3D postural perturbation in young adults

We explored how changes in vision and perturbation frequency impacted upright postural control in healthy adults exposed to continuous multiaxial support-surface perturbation. Ten subjects were asked to maintain equilibrium in standing stance with eyes open (EO) and eyes closed (EC) during sinusoidal 3D rotations at 0.25 (L) and 0.50 Hz (H). We measured upper-body kinematics – head, trunk, and pelvis – and analyzed differences in horizontal displacements and roll, pitch, and yaw sways. The presence of vision significantly decreased upper-body displacements in the horizontal plane, especially at the head level, while in EC the head was the most unstable segment. H trials produced a greater segment stabilization compared to L ones in EO and EC. Analysis of sways showed that in EO participants stabilized their posture by reducing the variability of trunk angles; in H trials a sway decrease for the examined segments was observed in the yaw plane and, for the pelvis only, in the pitch plane. Our results suggest that, during continuous multiaxial perturbations, visual information induced: (i) in L condition, a continuous reconfiguration of multi-body-segments orientation to follow the perturbation; (ii) in H condition, a compensation for the ongoing perturbation. These findings were not confirmed in EC where the same strategy – that is, the use of the pelvis as a reference frame for the body balance was adopted both in L and H

The light stop window

We show that a right-handed stop in the 200-400 GeV mass range, together with a nearly degenerate neutralino and, possibly, a gluino below 1.5 TeV, follows from reasonable assumptions, is consistent with present data, and offers interesting discovery prospects at the LHC. Triggering on an extra jet produced in association with stops allows the experimental search for stops even when their mass difference with neutralinos is very small and the decay products are too soft for direct observation. Using a razor analysis, we are able to set stop bounds that are stronger than those published by ATLAS and CMS.Comment: 21 pages, 9 figures. v2: fig. 9b has been updated and revised at large values of the stop/neutralino mass splitting. The discussion of stop co-annihilations has been upgraded including Sommerfeld enhancement

Ground Beetles From a Remnant Oak-Maple-Beech Forest and Its Surroundings in Northeastern Ohio (Coleoptera: Carabidae)

We report 66 ground beetle species in 14 tribes from a natural preserve in northeastern Ohio (Stark County). Six species are new state records. Data from pitfall trap transects across adjoining habitats suggest narrow habitat preferences in some species and broad tolerances in others. Trends toward flightlessness in forest species and macroptery in the fauna of disturbed agricultural sites are apparent