Theoretical models of planetary system formation: mass vs. semi-major axis

Context. Planet formation models have been developed during the past years to try to reproduce what has been observed of both the solar system and the extrasolar planets. Some of these models have partially succeeded, but they focus on massive planets and, for the sake of simplicity, exclude planets belonging to planetary systems. However, more and more planets are now found in planetary systems. This tendency, which is a result of radial velocity, transit, and direct imaging surveys, seems to be even more pronounced for low-mass planets. These new observations require improving planet formation models, including new physics, and considering the formation of systems. Aims: In a recent series of papers, we have presented some improvements in the physics of our models, focussing in particular on the internal structure of forming planets, and on the computation of the excitation state of planetesimals and their resulting accretion rate. In this paper, we focus on the concurrent effect of the formation of more than one planet in the same protoplanetary disc and show the effect, in terms of architecture and composition of this multiplicity. Methods: We used an N-body calculation including collision detection to compute the orbital evolution of a planetary system. Moreover, we describe the effect of competition for accretion of gas and solids, as well as the effect of gravitational interactions between planets. Results: We show that the masses and semi-major axes of planets are modified by both the effect of competition and gravitational interactions. We also present the effect of the assumed number of forming planets in the same system (a free parameter of the model), as well as the effect of the inclination and eccentricity damping. We find that the fraction of ejected planets increases from nearly 0 to 8% as we change the number of embryos we seed the system with from 2 to 20 planetary embryos. Moreover, our calculations show that, when considering planets more massive than ~5 M⊕, simulations with 10 or 20 planetary embryos statistically give the same results in terms of mass function and period distribution.

Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease.

BACKGROUND The success of an intervention to prevent the complications of an infection is influenced by the natural history of the infection. Assumptions about the temporal relationship between infection and the development of sequelae can affect the predicted effect size of an intervention and the sample size calculation. This study investigates how a mathematical model can be used to inform sample size calculations for a randomised controlled trial (RCT) using the example of Chlamydia trachomatis infection and pelvic inflammatory disease (PID). METHODS We used a compartmental model to imitate the structure of a published RCT. We considered three different processes for the timing of PID development, in relation to the initial C. trachomatis infection: immediate, constant throughout, or at the end of the infectious period. For each process we assumed that, of all women infected, the same fraction would develop PID in the absence of an intervention. We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence. We also investigated the influence of the natural history parameters of chlamydia on the required sample size. RESULTS The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model. Even small changes in the assumed PID incidence and relative risk (RR) led to considerable differences in the hypothesised mechanism of PID development. The RR and the sample size needed per group also depend on the natural history parameters of chlamydia. CONCLUSIONS Mathematical modelling helps to understand the temporal relationship between an infection and its sequelae and can show how uncertainties about natural history parameters affect sample size calculations when planning a RCT.

Replications of fundamental research models in ultra high dilutions 1994 and 2015 - update on a bibliometric study

INTRODUCTION This paper focuses exclusively on experimental models with ultra high dilutions (i.e. beyond 10(-23)) that have been submitted to replication scrutiny. It updates previous surveys, considers suggestions made by the research community and compares the state of replication in 1994 with that in 2015. METHODS Following literature research, biochemical, immunological, botanical, cell biological and zoological studies on ultra high dilutions (potencies) were included. Reports were grouped into initial studies, laboratory-internal, multicentre and external replications. Repetition could yield either comparable, or zero, or opposite results. The null-hypothesis was that test and control groups would not be distinguishable (zero effect). RESULTS A total of 126 studies were found. From these, 28 were initial studies. When all 98 replicative studies were considered, 70.4% (i.e. 69) reported a result comparable to that of the initial study, 20.4% (20) zero effect and 9.2% (9) an opposite result. Both for the studies until 1994 and the studies 1995-2015 the null-hypothesis (dominance of zero results) should be rejected. Furthermore, the odds of finding a comparable result are generally higher than of finding an opposite result. Although this is true for all three types of replication studies, the fraction of comparable studies diminishes from laboratory-internal (total 82.9%) to multicentre (total 75%) to external (total 48.3%), while the fraction of opposite results was 4.9%, 10.7% and 13.8%. Furthermore, it became obvious that the probability of an external replication producing comparable results is bigger for models that had already been further scrutinized by the initial researchers. CONCLUSIONS We found 28 experimental models which underwent replication. In total, 24 models were replicated with comparable results, 12 models with zero effect, and 6 models with opposite results. Five models were externally reproduced with comparable results. We encourage further replications of studies in order to learn more about the model systems used.

Secondary left ventricular ejection fraction response to beta blocker therapy in heart failure patients

Chronic β-blocker treatment improves survival and left ventricular ejection fraction (LVEF) in patients with systolic heart failure (HF). Data on whether the improvement in LVEF after β-blocker therapy is sustained for a long term or whether there is a loss in LVEF after an initial gain is not known. Our study sought to determine the prevalence and prognostic role of secondary decline in LVEF in chronic systolic HF patients on β-blocker therapy and characterize these patients. Retrospective chart review of HF hospitalizations fulfilling Framingham Criteria was performed at the MEDVAMC between April 2000 and June 2006. Follow up vital status and recurrent hospitalizations were ascertained until May 2010. Three groups of patients were identified based on LVEF response to beta blockers; group A with secondary decline in LVEF following an initial increase, group B with progressive increase in LVEF and group C with progressive decline in LVEF. Covariate adjusted Cox proportional hazard models were used to examine differences in heart failure re-hospitalizations and all cause mortality between the groups. Twenty five percent (n=27) of patients had a secondary decline in LVEF following an initial gain. The baseline, peak and final LVEF in this group were 27.6±12%, 40.1±14% and 27.4±13% respectively. The mean nadir LVEF after decline was 27.4±13% and this decline occurred at a mean interval of 2.8±1.9 years from the day of beta blocker initiation. These patients were older, more likely to be whites, had advanced heart failure (NYHA class III/IV) more due to a non ischemic etiology compared to groups B & C. They were also more likely to be treated with metoprolol (p=0.03) compared to the other two groups. No significant differences were observed in combined risk of all cause mortality and HF re-hospitalization [hazard ratio 0.80, 95% CI 0.47 to 1.38, p=0.42]. No significant difference was observed in survival estimates between the groups. In conclusion, a late decline in LVEF does occur in a significant proportion of heart failure patients treated with beta blockers, more so in patients treated with metoprolol.^

Racial differences in heart failure with preserved ejection fraction in the ambulatory heart failure population

Racial differences in heart failure with preserved ejection fraction (HFpEF) have rarely been studied in an ambulatory, financially "equal access" cohort, although the majority of such patients are treated as outpatients. ^ Retrospective data was collected from 2,526 patients (2,240 Whites, 286 African American) with HFpEF treated at 153 VA clinics, as part of the VA External Peer Review Program (EPRP) between October 2000 and September 2002. Kaplan Meier curves (stratified by race) were created for time to first heart failure (HF) hospitalization, all cause hospitalization and death and Cox proportional multivariate regression models were constructed to evaluate the effect of race on these outcomes. ^ African American patients were younger (67.7 ± 11.3 vs. 71.2 ± 9.8 years; p < 0.001), had lower prevalence of atrial fibrillation (24.5 % vs. 37%; p <0.001), chronic obstructive pulmonary disease (23.4 % vs. 36.9%, p <0.001), but had higher blood pressure (systolic blood pressure > 120 mm Hg 77.6% vs. 67.8%; p < 0.01), glomerular filtration rate (67.9 ± 31.0 vs. 61.6 ± 22.6 mL/min/1.73 m2; p < 0.001), anemia (56.6% vs. 41.7%; p <0.001) as compared to whites. African Americans were found to have higher risk adjusted rate of HF hospitalization (HR 1.52, 95% CI 1.1 - 2.11; p = 0.01), with no difference in risk-adjusted all cause hospitalization (p = 0.80) and death (p= 0.21). ^ In a financially "equal access" setting of the VA, among ambulatory patients with HFpEF, African Americans have similar rates of mortality and all cause hospitalization but have an increased risk of HF hospitalizations compared to whites.^

Age models, accumulation rates, sand and carbonates at DSDP Leg 74 holes

Accumulation rates for the five sites drilled during Leg 74 of the Glomar Challenger are presented on a common timescale based on calibration of datum levels to paleomagnetic records in Leg 74 sediments for the Paleogene, and a new compilation by Berggren et al. (1985), for the Neogene, and using the seafloor-spreading magnetic anomaly timescale of Kent (1985). We present data on accumulation of total sediment, of foraminifers, of the noncarbonate portion, and of fish teeth that give a history of productivity, winnowing, carbonate dissolution, and nonbiogenic input to what was then a part of the South Atlantic at about 30 deg S.

Age models and foraminifer isotopes of four ODP Leg 202 sites

We present benthic isotope stratigraphies for Sites 1236, 1237, 1239, and 1241 that span the late Miocene-Pliocene time interval from 6 to 2.4 Ma. Orbitally tuned timescales were generated for Sites 1237 and 1241 by correlating the high-frequency variations in gamma ray attenuation density, percent sand of the carbonate fraction, and benthic d13C to variations in Earth's orbital parameters. The astronomical timescales for Sites 1237 and 1241 are in agreement with the one from Atlantic Site 925/926 (Ocean Drilling Program Leg 154). The comparison of benthic d18O and d13C records from the east Pacific sites and Atlantic Site 925/926 revealed a surprising clarity of the "41-k.y. signal" in d13C records and a remarkably good correlation between their d13C records. This suggests that the late Miocene-Pliocene amplitudes of obliquity-related d13C cycles reflect a magnitude of global response often larger than that provided by obliquity-related d18O cycles. At Site 1237, the orbitally derived ages of Pliocene magnetic reversal boundaries between the base of Réunion and the top of Thvera confirm astronomical datings of the generally accepted ATNTS2004 timescale, except for the top of Kaena and the base of Sidufjall. Our astronomical age for the top of Kaena is about one obliquity cycle older. The base of Sidufjall appears to be about one precession cycle younger. The age models of Sites 1236 and 1239 were established by correlating their benthic d18O and d13C records directly to the orbitally tuned isotope record of Site 1241.

Sediment organic matter, grain size, and results of prediction models from northern North Atlantic and Arctic Seas

Sediment samples and hydrographic conditions were studied at 28 stations around Iceland. At these sites, Conductivity-Temperature-Depth (CTD) casts were conducted to collect hydrographic data and multicorer casts were conductd to collect data on sediment characteristics including grain size distribution, carbon and nitrogen concentration, and chloroplastic pigment concentration. A total of 14 environmental predictors were used to model sediment characteristics around Iceland on regional geographic space. For these, two approaches were used: Multivariate Adaptation Regression Splines (MARS) and randomForest regression models. RandomForest outperformed MARS in predicting grain size distribution. MARS models had a greater tendency to over- and underpredict sediment values in areas outside the environmental envelope defined by the training dataset. We provide first GIS layers on sediment characteristics around Iceland, that can be used as predictors in future models. Although models performed well, more samples, especially from the shelf areas, will be needed to improve the models in future.

Helium isotope ratios and sedimentation rate models of ODP holes

A continuous age model for the brief climate excursion at the Paleocene-Eocene boundary has been constructed by assuming a constant flux of extraterrestrial 3He (3He[ET]) to the seafloor. 3He[ET] measurements from ODP Site 690 provide quantitative evidence for the rapid onset (models indicating extremely rapid release of isotopically light carbon, possibly from seafloor methane hydrate, as the proximal cause of the event. However, the 3He[ET] technique indicates a previously unrecognized and extreme increase in sedimentation rate coincident with the return of climate proxies to pre-event values. The 3He[ET]-based age model thus suggests a far more rapid recovery from the climatic perturbation than previously proposed or predicted on the basis of the modern carbon cycle, and so may indicate additional or accelerated mechanisms of carbon removal from the ocean-atmosphere system during this period. 3He[ET] was also measured at ODP Site 1051 to test the validity of the Site 690 chronology. Comparison of these data sets seems to require removal of several tens of kyr of sediment within the climatic excursion at Site 1051, an observation consistent with sediment structures and previous age modeling efforts. The Site 1051 age model shows a ~30 kyr period in which climate proxies return toward pre-event values, after which they remain invariant for ~80 kyr. If this rise represents the recovery interval identified at Site 690, then the 3HeET-based age models of the two sites are in good agreement. However, alternative interpretations are possible, and work on less disrupted sites is required to evaluate the reliability of the proposed new chronology of the climate excursion. Regardless of these details, this work shows that the 3HeET technique can provide useful independent evidence for the development and testing of astronomically calibrated age models.

Age models, sedimentology and geochemistry from sediment cores in Drake Passage throughflow

The Drake Passage (DP) is the major geographic constriction for the Antarctic Circumpolar Current (ACC) and exerts a strong control on the exchange of physical, chemical, and biological properties between the Atlantic, Pacific, and Indian Ocean basins. Resolving changes in the flow of circumpolar water masses through this gateway is, therefore, crucial for advancing our understanding of the Southern Ocean's role in global ocean and climate variability. Here, we reconstruct changes in DP throughflow dynamics over the past 65,000 y based on grain size and geochemical properties of sediment records from the southernmost continental margin of South America. Combined with published sediment records from the Scotia Sea, we argue for a considerable total reduction of DP transport and reveal an up to ~40% decrease in flow speed along the northernmost ACC pathway entering the DP during glacial times. Superimposed on this long-term decrease are high-amplitude, millennial-scale variations, which parallel Southern Ocean and Antarctic temperature patterns. The glacial intervals of strong weakening of the ACC entering the DP imply an enhanced export of northern ACC surface and intermediate waters into the South Pacific Gyre and reduced Pacific-Atlantic exchange through the DP ("cold water route"). We conclude that changes in DP throughflow play a critical role for the global meridional overturning circulation and interbasin exchange in the Southern Ocean, most likely regulated by variations in the westerly wind field and changes in Antarctic sea ice extent.

The Business Models and Economics of Peer-to-Peer lending. ECRI Research Report No 17, May 2016

This paper reviews peer-to-peer (P2P) lending, its development in the UK and other countries, and assesses the business and economic policy issues surrounding this new form of intermediation. P2P platform technology allows direct matching of borrowers’ and lenders’ diversification over a large number of borrowers without the loans having to be held on an intermediary balance sheet. P2P lending has developed rapidly in both the US and the UK, but it still represents a small fraction, less than 1%, of the stock of bank lending. In the UK – but not elsewhere – it is an important source of loans for smaller companies. We argue that P2P lending is fundamentally complementary to, and not competitive with, conventional banking. We therefore expect banks to adapt to the emergence of P2P lending, either by cooperating closely with third-party P2P lending platforms or offering their own proprietary platforms. We also argue that the full development of the sector requires much further work addressing the risks and business and regulatory issues in P2P lending, including risk communication, orderly resolution of platform failure, control of liquidity risks and minimisation of fraud, security and operational risks. This will depend on developing reliable business processes, the promotion to the full extent possible of transparency and standardisation and appropriate regulation that serves the needs of customers.

Physical models of dilatant normal faulting in jointed cohesive rocks

Dilatant faults often form in rocks containing pre-existing joints, but the effects of joints on fault segment linkage and fracture connectivity is not well understood. We present an analogue modeling study using cohesive powder with pre-formed joint sets in the upper layer, varying the angle between joints and a rigid basement fault. We analyze interpreted map-view photographs at maximum displacement for damage zone width, number of connected joints, number of secondary fractures, degree of segmentation and area fraction of massively dilatant fractures. Particle imaging velocimetry helps provide insights on deformation history of the experiments and illustrate the localization pattern of fault segments. Results show that with increasing angle between joint-set and basement-fault strike the number of secondary fractures and the number of connected joints increases, while the area fraction of massively dilatant fractures shows only a minor increase. Models without pre-existing joints show far lower area fractions of massively dilatant fractures while forming distinctly more secondary fractures.