The Limits of Mathematics

This condensed version of chao-dyn/9509010 will be the main hand-out for a course on algorithmic information theory to be given 22-29 May 1996 at the Rovaniemi Institute of Technology, Rovaniemi, Finland (see announcement at http://www.rotol.fi/ ).Comment: LaTeX, 45 page

High-resolution imaging of KeplerKepler planet host candidates. A comprehensive comparison of different techniques

The Kepler mission has discovered thousands of planet candidates. Currently, some of them have already been discarded; more than 200 have been confirmed by follow-up observations, and several hundreds have been validated. However, most of them are still awaiting for confirmation. Thus, priorities (in terms of the probability of the candidate being a real planet) must be established for subsequent observations. The motivation of this work is to provide a set of isolated (good) host candidates to be further tested by other techniques. We identify close companions of the candidates that could have contaminated the light curve of the planet host. We used the AstraLux North instrument located at the 2.2 m telescope in the Calar Alto Observatory to obtain diffraction-limited images of 174 Kepler objects of interest. The lucky-imaging technique used in this work is compared to other AO and speckle imaging observations of Kepler planet host candidates. We define a new parameter, the blended source confidence level (BSC), to assess the probability of an object to have blended non-detected eclipsing binaries capable of producing the detected transit. We find that 67.2% of the observed Kepler hosts are isolated within our detectability limits, and 32.8% have at least one visual companion at angular separations below 6 arcsec. We find close companions (below 3 arcsec) for the 17.2% of the sample. The planet properties of this sample of non-isolated hosts are revised. We report one possible S-type binary (KOI-3158). We also report three possible false positives (KOIs 1230.01, 3649.01, and 3886.01) due to the presence of close companions. The BSC parameter is calculated for all the isolated targets and compared to both the value prior to any high-resolution image and, when possible, to observations from previous high-spatial resolution surveys in the Kepler sample.Comment: Accepted for publication in A&A on April 29, 2014; 32 pages, 11 figures, 11 table

Kepler-539: a young extrasolar system with two giant planets on wide orbits and in gravitational interaction

We confirm the planetary nature of Kepler-539b (aka Kepler object of interest K00372.01), a giant transiting exoplanet orbiting a solar-analogue G2 V star. The mass of Kepler-539b was accurately derived thanks to a series of precise radial velocity measurements obtained with the CAFE spectrograph mounted on the CAHA 2.2m telescope. A simultaneous fit of the radial-velocity data and Kepler photometry revealed that Kepler-539b is a dense Jupiter-like planet with a mass of Mp = 0.97 Mjup and a radius of Rp = 0.747 Rjup, making a complete circular revolution around its parent star in 125.6 days. The semi-major axis of the orbit is roughly 0.5 au, implying that the planet is at roughly 0.45 au from the habitable zone. By analysing the mid-transit times of the 12 transit events of Kepler-539b recorded by the Kepler spacecraft, we found a clear modulated transit time variation (TTV), which is attributable to the presence of a planet c in a wider orbit. The few timings available do not allow us to precisely estimate the properties of Kepler-539c and our analysis suggests that it has a mass between 1.2 and 3.6 Mjup, revolving on a very eccentric orbit (0.4<e<0.6) with a period larger than 1000 days. The high eccentricity of planet c is the probable cause of the TTV modulation of planet b. The analysis of the CAFE spectra revealed a relatively high photospheric lithium content, A(Li)=2.48 dex, which, together with both a gyrochronological and isochronal analysis, suggests that the parent star is relatively young.Comment: 11 pages, 14 figures, accepted for publication in Astronomy & Astrophysic

Genetic Basis for \u3cem\u3eRhizobium etli\u3c/em\u3e CE3 O-Antigen O-Methylated Residues That Vary According to Growth Conditions

The Rhizobium etli CE3 O antigen is a fixed-length heteropolymer with O methylation being the predominant type of sugar modification. There are two O-methylated residues that occur, on average, once per complete O antigen: a multiply O-methylated terminal fucose and 2-O methylation of a fucose residue within a repeating unit. The amount of the methylated terminal fucose decreases and the amount of 2-O-methylfucose increases when bacteria are grown in the presence of the host plant, Phaseolus vulgaris, or its seed exudates. Insertion mutagenesis was used to identify open reading frames required for the presence of these O-methylated residues. The presence of the methylated terminal fucose required genes wreA, wreB, wreC, wreD, and wreF, whereas 2-O methylation of internal fucoses required the methyltransferase domain of bifunctional gene wreM. Mutants lacking only the methylated terminal fucose, lacking only 2-O methylation, or lacking both the methylated terminal fucose and 2-O methylation exhibited no other lipopolysaccharide structural defects. Thus, neither of these decorations is required for normal O-antigen length, transport, or assembly into the final lipopolysaccharide. This is in contrast to certain enteric bacteria in which the absence of a terminal decoration severely affects O-antigen length and transport. R. etli mutants lacking only the methylated terminal fucose were not altered in symbiosis with host Phaseolus vulgaris, whereas mutants lacking only 2-O-methylfucose exhibited a delay in nodule development during symbiosis. These results support previous conclusions that the methylated terminal fucose is dispensable for symbiosis, whereas 2-O methylation of internal fucoses somehow facilitates early events in symbiosis

Joining Forces of Bayesian and Frequentist Methodology: A Study for Inference in the Presence of Non-Identifiability

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take advantage of both Bayesian and frequentist methods. The elegance of Bayesian methodology is founded in the propagation of information content provided by experimental data and prior assumptions to the posterior probability distribution of model predictions. However, for complex applications experimental data and prior assumptions potentially constrain the posterior probability distribution insufficiently. In these situations Bayesian Markov chain Monte Carlo sampling can be infeasible. From a frequentist point of view insufficient experimental data and prior assumptions can be interpreted as non-identifiability. The profile likelihood approach offers to detect and to resolve non-identifiability by experimental design iteratively. Therefore, it allows one to better constrain the posterior probability distribution until Markov chain Monte Carlo sampling can be used securely. Using an application from cell biology we compare both methods and show that a successive application of both methods facilitates a realistic assessment of uncertainty in model predictions.Comment: Article to appear in Phil. Trans. Roy. Soc.

Kepler-447b: a hot-Jupiter with an extremely grazing transit

We present the radial velocity confirmation of the extrasolar planet Kepler-447b, initially detected as a candidate by the Kepler mission. In this work, we analyze its transit signal and the radial velocity data obtained with the Calar Alto Fiber-fed Echelle spectrograph (CAFE). By simultaneously modeling both datasets, we obtain the orbital and physical properties of the system. According to our results, Kepler-447b is a Jupiter-mass planet ($M_p=1.37^{+0.48}_{-0.46}~M_{\rm Jup}$), with an estimated radius of $R_p=1.65^{+0.59}_{-0.56}~R_{\rm Jup}$ (uncertainties provided in this work are $3\sigma$ unless specified). This translates into a sub-Jupiter density. The planet revolves every $\sim7.8$ days in a slightly eccentric orbit ($e=0.123^{+0.037}_{-0.036}$) around a G8V star with detected activity in the Kepler light curve. Kepler-447b transits its host with a large impact parameter ($b=1.076^{+0.112}_{-0.086}$), being one of the few planetary grazing transits confirmed so far and the first in the Kepler large crop of exoplanets. We estimate that only around 20% of the projected planet disk occults the stellar disk. The relatively large uncertainties in the planet radius are due to the large impact parameter and short duration of the transit. Planets with such an extremely large impact parameter can be used to detect and analyze interesting configurations such as additional perturbing bodies, stellar pulsations, rotation of a non-spherical planet, or polar spot-crossing events. All these scenarios would periodically modify the transit properties (depth, duration, and time of mid-transit), what could be detectable with sufficient accurate photometry. Short-cadence photometric data (at the 1 minute level) would help in the search for these exotic configurations in grazing planetary transits like that of Kepler-447b.Comment: Accepted for publication in A&A. 13 pages, 8 figures, 4 tables. This version replaces an earlier version of the pape

Detection of the secondary eclipse of Qatar-1b in the Ks band

Qatar-1b is a close-orbiting hot Jupiter ($R_p\simeq 1.18$ $R_J$, $M_p\simeq 1.33$ $M_J$) around a metal-rich K-dwarf, with orbital separation and period of 0.023 AU and 1.42 days. We have observed the secondary eclipse of this exoplanet in the Ks band with the objective of deriving a brightness temperature for the planet and providing further constraints to the orbital configuration of the system. We obtained near-infrared photometric data from the ground by using the OMEGA2000 instrument at the 3.5 m telescope at Calar Alto (Spain) in staring mode, with the telescope defocused. We have used principal component analysis (PCA) to identify correlated systematic trends in the data. A Markov chain Monte Carlo analysis was performed to model the correlated systematics and fit for the secondary eclipse of Qatar-1b using a previously developed occultation model. We adopted the prayer bead method to assess the effect of red noise on the derived parameters. We measured a secondary eclipse depth of $0.196\%^{+0.071\%}_{-0.051\%}$, which indicates a brightness temperature in the Ks band for the planet of $1885^{+212}_{-168}$ K. We also measured a small deviation in the central phase of the secondary eclipse of $-0.0079^{+0.0162}_{-0.0043}$, which leads to a value for $e\cos{\omega}$ of $-0.0123^{+0.0252}_{-0.0067}$. However, this last result needs to be confirmed with more data.Comment: 6 pages, 6 figures, accepted for publication in A&

The lice (Insecta : phthiraptera) of short-tailed shearwaters, ardenna tenuirostris, in Bass Strait, Tasmania

There is a paucity of research into the louse fauna of Shorttailed Shearwaters, Ardenna tenuirostris (Temminck, 1835), despite this species being one of the world's most studied seabirds (Bradley et al. 1991 and references therein). Research has been undertaken on these shearwaters at their breeding grounds in Bass Strait, Tasmania, since 1947 (Bradley et al. 1991). As Short-tailed Shearwaters are long-lived, with an estimated average longevity of 38 years (Skira et al. 1985), they may offer a long-term host potential to host-dependent ectoparasites (i.e., lice) (Crompton 1997). Also, with approximately 23 million shearwaters breeding in burrows in dense rookeries on the islands and headlands of southern Australia, from southern New South Wales to Tasmania and from Victoria to Western Australia (Marchant & Higgins 1990), there may be the potential for increased transmission of ectoparasites between individual birds. Increased infestation rates by lice have been shown in colonial living birds. For instance, Rozsa et al. (1996) found an increase in louse infestation on Colonial Rooks, Corvus frugilegus Linnaeus, 1758, as compared to the territorial Hooded Crow, Corvus corone cornix Linnaeus, 1758. Short-tailed Shearwaters undertake an annual transequatorial migration to the Bering Sea for the austral winter (Serventy 1967), and so may act as vectors for the transmission of parasites across hemispheres (Lopez et al. 2005, Price et al. 2003). There are three publications that list the lice of Shorttailed Shearwaters. Green & Munday (1971) were the first to document the ectoparasites of Tasmanian fauna, albeit from personal communications- no published literature was cited. Twenty years later, Green & Palma (1991) listed the lice of Tasmania's vertebrates. They essentially used Green & Munday's (1971) list of lice on shearwaters and added Austromenopon paululum, listed as Austromenopon sp. in Green & Munday (1971). Price et al. (2003), in their checklist of the chewing lice (Phthiraptera) of the world, also listed the lice of Short -tailed Shearwaters. Included in this list were two louse species, Naubates harrisoni (Bedford, 1930) and Ancistrona vagelli (Fabricus, 1787), not mentioned in Green & Munday (1971). As part of the long-term research into Bass Strait's Short-tailed Shearwaters, this study aimed to confirm their current louse fauna, detailing the specific location, and collection method, to fill a gap in the primary literature

Application of Bayesian model averaging to measurements of the primordial power spectrum

Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for assessing parameter uncertainties in situations where there is also uncertainty in the underlying model. We apply model averaging to the estimation of the parameters associated with the primordial power spectra of curvature and tensor perturbations. We use CosmoNest and MultiNest to compute the model Evidences and posteriors, using cosmic microwave data from WMAP, ACBAR, BOOMERanG and CBI, plus large-scale structure data from the SDSS DR7. We find that the model-averaged 95% credible interval for the spectral index using all of the data is 0.940 < n_s < 1.000, where n_s is specified at a pivot scale 0.015 Mpc^{-1}. For the tensors model averaging can tighten the credible upper limit, depending on prior assumptions.Comment: 7 pages with 7 figures include

Conditions for the Optimality of Exponential Smoothing Forecast Procedures

Exponential smoothing procedures, in particular those recommended by Brown are used extensively in many areas of economics, business and engineering. It is shown in this paper that: (i) Brown's forecasting procedures are optimal in terms of achieving minimum mean square error forecasts only if the underlying stochastic process is included in a limited subclass of ARIMA (p,d,q) processes. Hence, it is shown what assumptions are made when using these procedures. (ii) The implication of point (i) is that the users of Brown's procedures tacitly assume that the stochastic processes which occur in the real world are from the particular restricted subclass of ARIMA (p,d,q) processes. No reason can be found why these particular models should occur more frequently than others. (iii) It is further shown that even if a stochastic process which would lead to Brown's model occurred, the actual methods used for making the forecasts are clumsy and much simpler procedures can be employed