Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.Comment: 42 pages, 35 figure

On positivity of Ehrhart polynomials

Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if all Ehrhart coefficients are positive (which is not true for all integral polytopes). The main purpose of this article is to survey interesting families of polytopes that are known to be Ehrhart positive and discuss the reasons from which their Ehrhart positivity follows. We also include examples of polytopes that have negative Ehrhart coefficients and polytopes that are conjectured to be Ehrhart positive, as well as pose a few relevant questions.Comment: 40 pages, 7 figures. To appear in in Recent Trends in Algebraic Combinatorics, a volume of the Association for Women in Mathematics Series, Springer International Publishin

A behavioral comparison of male and female adults with high functioning autism spectrum conditions

Autism spectrum conditions (ASC) affect more males than females in the general population. However, within ASC it is unclear if there are phenotypic sex differences. Testing for similarities and differences between the sexes is important not only for clinical assessment but also has implications for theories of typical sex differences and of autism. Using cognitive and behavioral measures, we investigated similarities and differences between the sexes in age- and IQ-matched adults with ASC (high-functioning autism or Asperger syndrome). Of the 83 (45 males and 38 females) participants, 62 (33 males and 29 females) met Autism Diagnostic Interview-Revised (ADI-R) cut-off criteria for autism in childhood and were included in all subsequent analyses. The severity of childhood core autism symptoms did not differ between the sexes. Males and females also did not differ in self-reported empathy, systemizing, anxiety, depression, and obsessive-compulsive traits/symptoms or mentalizing performance. However, adult females with ASC showed more lifetime sensory symptoms (p = 0.036), fewer current socio-communication difficulties (p = 0.001), and more self-reported autistic traits (p = 0.012) than males. In addition, females with ASC who also had developmental language delay had lower current performance IQ than those without developmental language delay (p<0.001), a pattern not seen in males. The absence of typical sex differences in empathizing-systemizing profiles within the autism spectrum confirms a prediction from the extreme male brain theory. Behavioral sex differences within ASC may also reflect different developmental mechanisms between males and females with ASC. We discuss the importance of the superficially better socio-communication ability in adult females with ASC in terms of why females with ASC may more often go under-recognized, and receive their diagnosis later, than males

nIFTY galaxy cluster simulations - III. The similarity and diversity of galaxies and subhaloes

We examine subhaloes and galaxies residing in a simulated $\Lambda$ cold dark matter galaxy cluster ($M^{crit} _{200}$ = 1.1 × 10$^{15}$ $h^{−1}$ M$_\odot$) produced by hydrodynamical codes ranging from classic smooth particle hydrodynamics (SPH), newer SPH codes, adaptive and moving mesh codes. These codes use subgrid models to capture galaxy formation physics. We compare how well these codes reproduce the same subhaloes/galaxies in gravity-only, non-radiative hydrodynamics and $\textit{full feedback physics}$ runs by looking at the overall subhalo/galaxy distribution and on an individual object basis. We find that the subhalo population is reproduced to within $\lesssim$10 per cent for both dark matter only and non-radiative runs, with individual objects showing code-to-code scatter of $\lesssim$0.1 dex, although the gas in non-radiative simulations shows significant scatter. Including feedback physics significantly increases the diversity. Subhalo mass and $V_{max}$ distributions vary by ≈20 per cent. The galaxy populations also show striking code-to-code variations. Although the Tully–Fisher relation is similar in almost all codes, the number of galaxies with 10$^9$ $h^{−1}$ M$_\odot$ $\lesssim$ $M_∗$ $\lesssim$ 10$^{12}$ $h^{−1}$ M$_\odot$ can differ by a factor of 4. Individual galaxies show code-to-code scatter of ~0.5 dex in stellar mass. Moreover, systematic differences exist, with some codes producing galaxies 70 per cent smaller than others. The diversity partially arises from the inclusion/absence of active galactic nucleus feedback. Our results combined with our companion papers demonstrate that subgrid physics is not just subject to fine-tuning, but the complexity of building galaxies $\textit{in all environments}$ remains a challenge. We argue that even basic galaxy properties, such as stellar mass to halo mass, should be treated with errors bars of ~0.2–0.4 dex

nIFTY galaxy cluster simulations - III. The similarity and diversity of galaxies and subhaloes

We examine subhaloes and galaxies residing in a simulated $\Lambda$ cold dark matter galaxy cluster ($M^{crit} _{200}$ = 1.1 × 10$^{15}$ $h^{−1}$ M$_\odot$) produced by hydrodynamical codes ranging from classic smooth particle hydrodynamics (SPH), newer SPH codes, adaptive and moving mesh codes. These codes use subgrid models to capture galaxy formation physics. We compare how well these codes reproduce the same subhaloes/galaxies in gravity-only, non-radiative hydrodynamics and $\textit{full feedback physics}$ runs by looking at the overall subhalo/galaxy distribution and on an individual object basis. We find that the subhalo population is reproduced to within $\lesssim$10 per cent for both dark matter only and non-radiative runs, with individual objects showing code-to-code scatter of $\lesssim$0.1 dex, although the gas in non-radiative simulations shows significant scatter. Including feedback physics significantly increases the diversity. Subhalo mass and $V_{max}$ distributions vary by ≈20 per cent. The galaxy populations also show striking code-to-code variations. Although the Tully–Fisher relation is similar in almost all codes, the number of galaxies with 10$^9$ $h^{−1}$ M$_\odot$ $\lesssim$ $M_∗$ $\lesssim$ 10$^{12}$ $h^{−1}$ M$_\odot$ can differ by a factor of 4. Individual galaxies show code-to-code scatter of ~0.5 dex in stellar mass. Moreover, systematic differences exist, with some codes producing galaxies 70 per cent smaller than others. The diversity partially arises from the inclusion/absence of active galactic nucleus feedback. Our results combined with our companion papers demonstrate that subgrid physics is not just subject to fine-tuning, but the complexity of building galaxies $\textit{in all environments}$ remains a challenge. We argue that even basic galaxy properties, such as stellar mass to halo mass, should be treated with errors bars of ~0.2–0.4 dex

nIFTy galaxy cluster simulations – V. Investigation of the cluster infall region

We examine the properties of the galaxies and dark matter haloes residing in the cluster infall region surrounding the simulated $\Lambda$ cold dark matter galaxy cluster studied by Elahi et al. at $z$ = 0. The 1.1 × 10$^{15}$ $h^{−1}$ M$_\odot$ galaxy cluster has been simulated with eight different hydrodynamical codes containing a variety of hydrodynamic solvers and sub-grid schemes. All models completed a dark-matter-only, non-radiative and full-physics run from the same initial conditions. The simulations contain dark matter and gas with mass resolution $m_\text{DM}$ = 9.01 × 10$^8$ $h^{−1}$ M$_\odot$ and $m_\text{gas}$ = 1.9 × 10$^8$ $h^{−1}$ M$_\odot$, respectively. We find that the synthetic cluster is surrounded by clear filamentary structures that contain ~60 per cent of haloes in the infall region with mass ~10$^{12.5}$–10$^{14}$ $h^{−1}$ M$_\odot$, including 2–3 group-sized haloes (>10$^{13}$ $h^{−1}$ M$_\odot$). However, we find that only ~10 per cent of objects in the infall region are sub-haloes residing in haloes, which may suggest that there is not much ongoing pre-processing occurring in the infall region at $z$ = 0. By examining the baryonic content contained within the haloes, we also show that the code-to-code scatter in stellar fraction across all halo masses is typically ~2 orders of magnitude between the two most extreme cases, and this is predominantly due to the differences in sub-grid schemes and calibration procedures that each model uses. Models that do not include active galactic nucleus feedback typically produce too high stellar fractions compared to observations by at least ~1 order of magnitude.The authors would like the acknowledge the Centre for High Performance Computing in Rosebank, Cape Town, for financial support and for hosting the ‘Comparison Cape Town’ workshop in 2016, July. The authors would further like to acknowledge the support of the International Centre for Radio Astronomy Research (ICRAR) node at the University of Western Australia (UWA) in hosting the precursor workshop ‘Perth Simulated Cluster Comparison’ in 2015, March; the financial support of the UWA Research Collaboration Award 2014 and 2015 schemes; the financial support of the ARC Centre of Excellence for All Sky Astrophysics (CAASTRO) CE110001020 and ARC Discovery Projects DP130100117 and DP140100198. We would also like to thank the Instituto de Fisica Teorica (IFT-UAM/CSIC in Madrid) for its support, via the Centro de Excelencia Severo Ochoa Program under Grant No. SEV- 2012-0249, during the three-week workshop ‘nIFTy Cosmology’ in 2014, where the foundation for the whole comparison project was established. JA acknowledges support from a post-graduate award from STFC. PJE is supported by the SSimPL programme and the Sydney Institute for Astronomy (SIfA) and Australian Research Council (ARC) grants DP130100117 and DP140100198. AK is supported by the Ministerio de Econom´ıa y Competitividad (MINECO) in Spain through grant AYA2012-31101 as well as the ConsoliderIngenio 2010 Programme of the Spanish Ministerio de Ciencia e Innovacion (MICINN) under grant MultiDark CSD2009-00064. ´ He also acknowledges support from the ARC grant DP140100198. He further thanks Noonday Underground for surface noise. STK acknowledges support from STFC through grant ST/L000768/1. CP acknowledges the support of the ARC through Future Fellowship FT130100041 and Discovery Project DP140100198. WC and CP acknowledge the support of ARC DP130100117. GY and FS acknowledge support from MINECO (Spain) through the grant AYA 2012-31101. GY thanks also the Red Espanola de Supercomputa- ˜ cion for granting the computing time in the Marenostrum Supercomputer at BSC, where all the MUSIC simulations have been performed. AMB is supported by the DFG Research Unit 1254 ‘Magnetisation of interstellar and intergalactic media’ and by the DFG Cluster of Excellence ‘Universe’. GM acknowledge support from the PRIN-MIUR 2012 Grant ‘The Evolution of Cosmic Baryons’ funded by the Italian Minister of University and Research, by the PRIN-INAF 2012 Grant ‘Multi-scale Simulations of Cosmic Structures’, by the INFN INDARK Grant and by the ‘Consorzio per la Fisica di Trieste’. IGM acknowledges support from an STFC Advanced Fellowship. EP acknowledges support by the ERC grant ‘The Emergence of Structure During the Epoch of Reionization’

nIFTy galaxy cluster simulations II: radiative models

We have simulated the formation of a massive galaxy cluster (M$_{200}^{\rm crit}$ = 1.1$\times$10$^{15}h^{-1}M_{\odot}$) in a $\Lambda$CDM universe using 10 different codes (RAMSES, 2 incarnations of AREPO and 7 of GADGET), modeling hydrodynamics with full radiative subgrid physics. These codes include Smoothed-Particle Hydrodynamics (SPH), spanning traditional and advanced SPH schemes, adaptive mesh and moving mesh codes. Our goal is to study the consistency between simulated clusters modeled with different radiative physical implementations - such as cooling, star formation and AGN feedback. We compare images of the cluster at $z=0$, global properties such as mass, and radial profiles of various dynamical and thermodynamical quantities. We find that, with respect to non-radiative simulations, dark matter is more centrally concentrated, the extent not simply depending on the presence/absence of AGN feedback. The scatter in global quantities is substantially higher than for non-radiative runs. Intriguingly, adding radiative physics seems to have washed away the marked code-based differences present in the entropy profile seen for non-radiative simulations in Sembolini et al. (2015): radiative physics + classic SPH can produce entropy cores. Furthermore, the inclusion/absence of AGN feedback is not the dividing line -as in the case of describing the stellar content- for whether a code produces an unrealistic temperature inversion and a falling central entropy profile. However, AGN feedback does strongly affect the overall stellar distribution, limiting the effect of overcooling and reducing sensibly the stellar fraction

Visual motion with pink noise induces predation behaviour

Visual motion cues are one of the most important factors for eliciting animal behaviour, including predator-prey interactions in aquatic environments. To understand the elements of motion that cause such selective predation behaviour, we used a virtual plankton system where the predation behaviour in response to computer-generated prey was analysed. First, we performed motion analysis of zooplankton (Daphnia magna) to extract mathematical functions for biologically relevant motions of prey. Next, virtual prey models were programmed on a computer and presented to medaka (Oryzias latipes), which served as predatory fish. Medaka exhibited predation behaviour against several characteristic virtual plankton movements, particularly against a swimming pattern that could be characterised as pink noise motion. Analysing prey-predator interactions via pink noise motion will be an interesting research field in the future

Response of foundation macrophytes to near‐natural simulated marine heatwaves

Marine heatwaves have been observed worldwide and are expected to increase in both frequency and intensity due to climate change. Such events may cause ecosystem reconfigurations arising from species range contraction or redistribution, with ecological, economic and social implications. Macrophytes such as the brown seaweed Fucus vesiculosus and the seagrass Zostera marina are foundation species in many coastal ecosystems of the temperate northern hemisphere. Hence, their response to extreme events can potentially determine the fate of associated ecosystems. Macrophyte functioning is intimately linked to the maintenance of photosynthesis, growth and reproduction, and resistance against pathogens, epibionts and grazers. We investigated morphological, physiological, pathological and chemical defence responses of western Baltic Sea F. vesiculosus and Z. marina populations to simulated near‐natural marine heatwaves. Along with (a) the control, which constituted no heatwave but natural stochastic temperature variability (0HW), two treatments were applied: (b) two late‐spring heatwaves (June, July) followed by a summer heatwave (August; 3HW) and (c) a summer heatwave only (1HW). The 3HW treatment was applied to test whether preconditioning events can modulate the potential sensitivity to the summer heatwave. Despite the variety of responses measured in both species, only Z. marina growth was impaired by the accumulative heat stress imposed by the 3HW treatment. Photosynthetic rate, however, remained high after the last heatwave indicating potential for recovery. Only epibacterial abundance was significantly affected in F. vesiculosus. Hence both macrophytes, and in particular F. vesiculosus, seem to be fairly tolerant to short‐term marine heatwaves at least at the intensities applied in this experiment (up to 5°C above mean temperature over a period of 9 days). This may partly be due to the fact that F. vesiculosus grows in a highly variable environment, and may have a high phenotypic plasticit

nIFTy galaxy cluster simulations I: dark matter & non-radiative models

We have simulated the formation of a galaxy cluster in a $\Lambda$CDM universe using twelve different codes modeling only gravity and non-radiative hydrodynamics (\art, \arepo, \hydra\ and 9 incarnations of GADGET). This range of codes includes particle based, moving and fixed mesh codes as well as both Eulerian and Lagrangian fluid schemes. The various GADGET implementations span traditional and advanced smoothed-particle hydrodynamics (SPH) schemes. The goal of this comparison is to assess the reliability of cosmological hydrodynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be non-radiative. We compare images of the cluster at $z=0$, global properties such as mass, and radial profiles of various dynamical and thermodynamical quantities. The underlying gravitational framework can be aligned very accurately for all the codes allowing a detailed investigation of the differences that develop due to the various gas physics implementations employed. As expected, the mesh-based codes ART and AREPO form extended entropy cores in the gas with rising central gas temperatures. Those codes employing traditional SPH schemes show falling entropy profiles all the way into the very centre with correspondingly rising density profiles and central temperature inversions. We show that methods with modern SPH schemes that allow entropy mixing span the range between these two extremes and the latest SPH variants produce gas entropy profiles that are essentially indistinguishable from those obtained with grid based methods