Comparing compact binary parameter distributions I: Methods

Being able to measure each merger's sky location, distance, component masses, and conceivably spins, ground-based gravitational-wave detectors will provide a extensive and detailed sample of coalescing compact binaries (CCBs) in the local and, with third-generation detectors, distant universe. These measurements will distinguish between competing progenitor formation models. In this paper we develop practical tools to characterize the amount of experimentally accessible information available, to distinguish between two a priori progenitor models. Using a simple time-independent model, we demonstrate the information content scales strongly with the number of observations. The exact scaling depends on how significantly mass distributions change between similar models. We develop phenomenological diagnostics to estimate how many models can be distinguished, using first-generation and future instruments. Finally, we emphasize that multi-observable distributions can be fully exploited only with very precisely calibrated detectors, search pipelines, parameter estimation, and Bayesian model inference

Information criteria for efficient quantum state estimation

Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to be estimated is reduced by tentatively introducing certain simplifying assumptions on the form of the quantum state, and subsequently using the data to rigorously verify these assumptions. The simplifying assumptions considered so far were (i) the state can be well approximated to be of low rank, or (ii) the state can be well approximated as a matrix product state. We add one more method in that same spirit: we allow in principle any model for the state, using any (small) number of parameters (which can, e.g., be chosen to have a clear physical meaning), and the data are used to verify the model. The proof that this method is valid cannot be as strict as in above-mentioned cases, but is based on well-established statistical methods that go under the name of "information criteria." We exploit here, in particular, the Akaike Information Criterion (AIC). We illustrate the method by simulating experiments on (noisy) Dicke states

Ecological Effects of Fear: How Spatiotemporal Heterogeneity in Predation Risk Influences Mule Deer Access to Forage in a Sky‐Island System

Forage availability and predation risk interact to affect habitat use of ungulates across many biomes. Within sky‐island habitats of the Mojave Desert, increased availability of diverse forage and cover may provide ungulates with unique opportunities to extend nutrient uptake and/or to mitigate predation risk. We addressed whether habitat use and foraging patterns of female mule deer (Odocoileus hemionus) responded to normalized difference vegetation index (NDVI), NDVI rate of change (green‐up), or the occurrence of cougars (Puma concolor). Female mule deer used available green‐up primarily in spring, although growing vegetation was available during other seasons. Mule deer and cougar shared similar habitat all year, and our models indicated cougars had a consistent, negative effect on mule deer access to growing vegetation, particularly in summer when cougar occurrence became concentrated at higher elevations. A seemingly late parturition date coincided with diminishing NDVI during the lactation period. Sky‐island populations, rarely studied, provide the opportunity to determine how mule deer respond to growing foliage along steep elevation and vegetation gradients when trapped with their predators and seasonally limited by aridity. Our findings indicate that fear of predation may restrict access to the forage resources found in sky islands

Characterizing Entanglement Sources

We discuss how to characterize entanglement sources with finite sets of measurements. The measurements do not have to be tomographically complete, and may consist of POVMs rather than von Neumann measurements. Our method yields a probability that the source generates an entangled state as well as estimates of any desired calculable entanglement measures, including their error bars. We apply two criteria, namely Akaike's information criterion and the Bayesian information criterion, to compare and assess different models (with different numbers of parameters) describing entanglement-generating devices. We discuss differences between standard entanglement-verificaton methods and our present method of characterizing an entanglement source.Comment: This submission, together with the next one, supersedes arXiv:0806.416

The Axis of Evil revisited

In light of the three-year data release from WMAP we re-examine the evidence for the ``Axis of Evil'' (AOE). We discover that previous statistics are not robust with respect to the data-sets available and different treatments of the galactic plane. We identify the cause of the instability and implement an alternative ``model selection'' approach. A comparison to Gaussian isotropic simulations find the features significant at the 94-98% level, depending on the particular AOE model. The Bayesian evidence finds lower significance, ranging from ``substantial'' at $\Delta(\ln E)\sim 1.4$, to no evidence for the most general AOE model.Comment: 7 pages, accepted to MNRA

The complex network of global cargo ship movements

Transportation networks play a crucial role in human mobility, the exchange of goods, and the spread of invasive species. With 90% of world trade carried by sea, the global network of merchant ships provides one of the most important modes of transportation. Here we use information about the itineraries of 16,363 cargo ships during the year 2007 to construct a network of links between ports. We show that the network has several features which set it apart from other transportation networks. In particular, most ships can be classified in three categories: bulk dry carriers, container ships and oil tankers. These three categories do not only differ in the ships' physical characteristics, but also in their mobility patterns and networks. Container ships follow regularly repeating paths whereas bulk dry carriers and oil tankers move less predictably between ports. The network of all ship movements possesses a heavy-tailed distribution for the connectivity of ports and for the loads transported on the links with systematic differences between ship types. The data analyzed in this paper improve current assumptions based on gravity models of ship movements, an important step towards understanding patterns of global trade and bioinvasion.Comment: 7 figures Accepted for publication by Journal of the Royal Society Interface (2010) For supplementary information, see http://www.icbm.de/~blasius/publications.htm

Experimentally increased brood size accelerates actuarial senescence and increases subsequent reproductive effort in a wild bird population

The assumption that reproductive effort decreases somatic state, accelerating ageing, is central to our understanding of life-history variation. Maximal reproductive effort early in life is predicted to be maladaptive by accelerating ageing disproportionally, decreasing fitness. Optimality theory predicts that reproductive effort is restrained early in life to balance the fitness contribution of reproduction against the survival cost induced by the reproductive effort. When adaptive, the level of reproductive restraint is predicted to be inversely linked to the remaining life expectancy, potentially resulting in a terminal effort in the last period of reproduction. Experimental tests of the reproductive restraint hypothesis require manipulation of somatic state and subsequent investigation of reproductive effort and residual life span. To our knowledge the available evidence remains inconclusive, and hence reproductive restraint remains to be demonstrated. We modulated somatic state through a lifelong brood size manipulation in wild jackdaws and measured its consequences for age-dependent mortality and reproductive success. The assumption that lifelong increased brood size reduced somatic state was supported: Birds rearing enlarged broods showed subsequent increased rate of actuarial senescence, resulting in reduced residual life span. The treatment induced a reproductive response in later seasons: Egg volume and nestling survival were higher in subsequent seasons in the increased versus reduced broods' treatment group. We detected these increases in egg volume and nestling survival despite the expectation that in the absence of a change in reproductive effort, the reduced somatic state indicated by the increased mortality rate would result in lower reproductive output. This leads us to conclude that the higher reproductive success we observed was the result of higher reproductive effort. Our findings show that reproductive effort negatively covaries with remaining life expectancy, supporting optimality theory and confirming reproductive restraint as a key factor underpinning life-history variation