Ring Migration Topology Helps Bypassing Local Optima

Running several evolutionary algorithms in parallel and occasionally exchanging good solutions is referred to as island models. The idea is that the independence of the different islands leads to diversity, thus possibly exploring the search space better. Many theoretical analyses so far have found a complete (or sufficiently quickly expanding) topology as underlying migration graph most efficient for optimization, even though a quick dissemination of individuals leads to a loss of diversity. We suggest a simple fitness function FORK with two local optima parametrized by $r \geq 2$ and a scheme for composite fitness functions. We show that, while the (1+1) EA gets stuck in a bad local optimum and incurs a run time of $\Theta(n^{2r})$ fitness evaluations on FORK, island models with a complete topology can achieve a run time of $\Theta(n^{1.5r})$ by making use of rare migrations in order to explore the search space more effectively. Finally, the ring topology, making use of rare migrations and a large diameter, can achieve a run time of $\tilde{\Theta}(n^r)$, the black box complexity of FORK. This shows that the ring topology can be preferable over the complete topology in order to maintain diversity.Comment: 12 page

The early evolution of the H-free process

The H-free process, for some fixed graph H, is the random graph process defined by starting with an empty graph on n vertices and then adding edges one at a time, chosen uniformly at random subject to the constraint that no H subgraph is formed. Let G be the random maximal H-free graph obtained at the end of the process. When H is strictly 2-balanced, we show that for some c>0, with high probability as $n \to \infty$, the minimum degree in G is at least $cn^{1-(v_H-2)/(e_H-1)}(\log n)^{1/(e_H-1)}$. This gives new lower bounds for the Tur\'an numbers of certain bipartite graphs, such as the complete bipartite graphs $K_{r,r}$ with $r \ge 5$. When H is a complete graph $K_s$ with $s \ge 5$ we show that for some C>0, with high probability the independence number of G is at most $Cn^{2/(s+1)}(\log n)^{1-1/(e_H-1)}$. This gives new lower bounds for Ramsey numbers R(s,t) for fixed $s \ge 5$ and t large. We also obtain new bounds for the independence number of G for other graphs H, including the case when H is a cycle. Our proofs use the differential equations method for random graph processes to analyse the evolution of the process, and give further information about the structure of the graphs obtained, including asymptotic formulae for a broad class of subgraph extension variables.Comment: 36 page

Neutral H density at the termination shock: a consolidation of recent results

We discuss a consolidation of determinations of the density of neutral interstellar H at the nose of the termination shock carried out with the use of various data sets, techniques, and modeling approaches. In particular, we focus on the determination of this density based on observations of H pickup ions on Ulysses during its aphelion passage through the ecliptic plane. We discuss in greater detail a novel method of determination of the density from these measurements and review the results from its application to actual data. The H density at TS derived from this analysis is equal to 0.087 \pm 0.022 cm-3, and when all relevant determinations are taken into account, the consolidated density is obtained at 0.09 \pm 0.022 cm-3. The density of H in CHISM based on literature values of filtration factor is then calculated at 0.16 \pm 0.04 cm-3.Comment: Submitted to Space Science Review

Moderate deviations via cumulants

The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations probabilities due to Rudzkis, Saulis and Statulevicius. The examples of random objects we treat include dependency graphs, subgraph-counting statistics in Erd\H{o}s-R\'enyi random graphs and $U$-statistics. Moreover, we prove moderate deviation principles for certain statistics appearing in random matrix theory, namely characteristic polynomials of random unitary matrices as well as the number of particles in a growing box of random determinantal point processes like the number of eigenvalues in the GUE or the number of points in Airy, Bessel, and $\sin$ random point fields.Comment: 24 page

A model of AW UMa

The contact binary AW UMa has an extreme mass ratio, with the more massive component (the current primary) close to the main sequence, while the low mass star at q ~ 0.1 (the current secondary) has a much larger radius than a main sequence star of a comparable mass. We propose that the current secondary has almost exhausted hydrogen in its center and is much more advanced in its evolution, as suggested by Stepien. Presumably the current secondary lost most of its mass during its evolution with part of it transferred to the current primary. After losing a large fraction of its angular momentum, the binary may evolve into a system of FK Com type.Comment: 5 pages, 6 figures, Accepted to MNRAS, content change

An irradiated brown-dwarf companion to an accreting white dwarf

Interacting compact binary systems provide a natural laboratory in which to study irradiated substellar objects. As the mass-losing secondary (donor) in these systems makes a transition from the stellar to the substellar regime, it is also irradiated by the primary (compact accretor)1, 2. The internal and external energy fluxes are both expected to be comparable in these objects, providing access to an unexplored irradiation regime. The atmospheric properties of donors are largely unknown3, but could be modified by the irradiation. To constrain models of donor atmospheres, it is necessary to obtain accurate observational estimates of their physical properties (masses, radii, temperatures and albedos). Here we report the spectroscopic detection and characterization of an irradiated substellar donor in an accreting white-dwarf binary system. Our near-infrared observations allow us to determine a model-independent mass estimate for the donor of 0.055 ± 0.008 solar masses and an average spectral type of L1 ± 1, supporting both theoretical predictions and model-dependent observational constraints that suggest that the donor is a brown dwarf. Our time-resolved data also allow us to estimate the average irradiation-induced temperature difference between the dayside and nightside of the substellar donor (57 kelvin) and the maximum difference between the hottest and coolest parts of its surface (200 kelvin). The observations are well described by a simple geometric reprocessing model with a bolometric (Bond) albedo of less than 0.54 at the 2σ confidence level, consistent with high reprocessing efficiency, but poor lateral heat redistribution in the atmosphere of the brown-dwarf donor4, 5. These results add to our knowledge of binary evolution, in that the donor has survived the transition from the stellar to the substellar regime, and of substellar atmospheres, in that we have been able to test a regime in which the irradiation and the internal energy of a brown dwarf are comparable

Solar parameters for modeling interplanetary background

The goal of the Fully Online Datacenter of Ultraviolet Emissions (FONDUE) Working Team of the International Space Science Institute in Bern, Switzerland, was to establish a common calibration of various UV and EUV heliospheric observations, both spectroscopic and photometric. Realization of this goal required an up-to-date model of spatial distribution of neutral interstellar hydrogen in the heliosphere, and to that end, a credible model of the radiation pressure and ionization processes was needed. This chapter describes the solar factors shaping the distribution of neutral interstellar H in the heliosphere. Presented are the solar Lyman-alpha flux and the solar Lyman-alpha resonant radiation pressure force acting on neutral H atoms in the heliosphere, solar EUV radiation and the photoionization of heliospheric hydrogen, and their evolution in time and the still hypothetical variation with heliolatitude. Further, solar wind and its evolution with solar activity is presented in the context of the charge exchange ionization of heliospheric hydrogen, and in the context of dynamic pressure variations. Also the electron ionization and its variation with time, heliolatitude, and solar distance is presented. After a review of all of those topics, we present an interim model of solar wind and the other solar factors based on up-to-date in situ and remote sensing observations of solar wind. Results of this effort will further be utilised to improve on the model of solar wind evolution, which will be an invaluable asset in all heliospheric measurements, including, among others, the observations of Energetic Neutral Atoms by the Interstellar Boundary Explorer (IBEX).Comment: Chapter 2 in the planned "Cross-Calibration of Past and Present Far UV Spectra of Solar System Objects and the Heliosphere", ISSI Scientific Report No 12, ed. R.M. Bonnet, E. Quemerais, M. Snow, Springe