Bayesian modelling of skewness and kurtosis with two-piece scale and shape distributions

We formalise and generalise the definition of the family of univariate double two--piece distributions, obtained by using a density--based transformation of unimodal symmetric continuous distributions with a shape parameter. The resulting distributions contain five interpretable parameters that control the mode, as well as the scale and shape in each direction. Four-parameter subfamilies of this class of distributions that capture different types of asymmetry are discussed. We propose interpretable scale and location-invariant benchmark priors and derive conditions for the propriety of the corresponding posterior distribution. The prior structures used allow for meaningful comparisons through Bayes factors within flexible families of distributions. These distributions are applied to data from finance, internet traffic and medicine, comparing them with appropriate competitors

A Simple Approach to Maximum Intractable Likelihood Estimation

Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits maximum-likelihood (or maximum-a-posteriori) inference to be conducted, approximately, using essentially the same techniques. An elementary approach to this problem which simply obtains a nonparametric approximation of the likelihood surface which is then used as a smooth proxy for the likelihood in a subsequent maximisation step is developed here and the convergence of this class of algorithms is characterised theoretically. The use of non-sufficient summary statistics in this context is considered. Applying the proposed method to four problems demonstrates good performance. The proposed approach provides an alternative for approximating the maximum likelihood estimator (MLE) in complex scenarios

Transient charge and energy flow in the wide-band limit

The wide-band limit is a commonly used approximation to analyze transport through nanoscale devices. In this work we investigate its applicability to the study of charge and heat transport through molecular break junctions exposed to voltage biases and temperature gradients. We find that while this approximation faithfully describes the long-time charge and heat transport, it fails to characterize the short-time behavior of the junction. In particular, we find that the charge current flowing through the device shows a discontinuity when a temperature gradient is applied, while the energy flow is discontinuous when a voltage bias is switched on and even diverges when the junction is exposed to both a temperature gradient and a voltage bias. We provide an explanation for this pathological behavior and propose two possible solutions to this problem.Comment: 11 pages, 9 figure

A linear acoustic model for multi-cylinder IC engine intake manifolds including the effects of the intake throttle

This paper presents a linear acoustic model of a multi-cylinder intake manifold that can be used as part of a hybrid time/frequency domain method to calculate the intake wave dynamics of practical naturally aspirated engines. The method allows the user to construct a model of almost any manifold of complex geometry. The model is constructed as an assemblage of sub-models: (i) A model for a straight pipe with both ends open and through-flow. (ii) A model for an expansion chamber consisting of three lengths of pipe laid end-to-end: a narrow bore pipe expanding into a wide bore pipe contracting into a narrower bore pipe once more. (iii) A model of a side-branch, which includes a model for a straight pipe with one end closed and a model for the three way junction that joins the side-branch to a length of flow pipe. (iv) A model for an expansion with two (or more) side-branches, which combines the sub-models (i, ii, iii) into a multi-way (n-way) junction model. (v) A model for an intake throttle. Good agreement with measurement has been found for each sub-model when bench-tested in isolation and encouraging agreement has been found when many sub-models are used together to model a complex intake manifold on a running engine

Stability of three-dimensional relativistic jets: implications for jet collimation

The stable propagation of jets in FRII sources is remarkable if one takes into account that large-scale jets are subjected to potentially highly disruptive three-dimensional (3D) Kelvin-Helmholtz instabilities. Numerical simulations can address this problem and help clarify the causes of this remarkable stability. Following previous studies of the stability of relativistic flows in two dimensions (2D), it is our aim to test and extend the conclusions of such works to three dimensions. We present numerical simulations for the study of the stability properties of 3D, sheared, relativistic flows. This work uses a fully parallelized code Ratpenat that solves equations of relativistic hydrodynamics in 3D. The results of the present simulations confirm those in 2D. We conclude that the growth of resonant modes in sheared relativistic flows could be important in explaining the long-term collimation of extragalactic jets.Comment: Accepted for publication in A&

Occurrence and persistence of magnetic elements in the quiet Sun

Turbulent convection efficiently transports energy up to the solar photosphere, but its multi-scale nature and dynamic properties are still not fully understood. Several works in the literature have investigated the emergence of patterns of convective and magnetic nature in the quiet Sun at spatial and temporal scales from granular to global. Aims. To shed light on the scales of organisation at which turbulent convection operates, and its relationship with the magnetic flux therein, we studied characteristic spatial and temporal scales of magnetic features in the quiet Sun. Methods. Thanks to an unprecedented data set entirely enclosing a supergranule, occurrence and persistence analysis of magnetogram time series were used to detect spatial and long-lived temporal correlations in the quiet Sun and to investigate their nature. Results. A relation between occurrence and persistence representative for the quiet Sun was found. In particular, highly recurrent and persistent patterns were detected especially in the boundary of the supergranular cell. These are due to moving magnetic elements undergoing motion that behaves like a random walk together with longer decorrelations ($\sim2$ h) with respect to regions inside the supergranule. In the vertices of the supegranular cell the maximum observed occurrence is not associated with the maximum persistence, suggesting that there are different dynamic regimes affecting the magnetic elements

Pair separation of magnetic elements in the quiet Sun

The dynamic properties of the quiet Sun photosphere can be investigated by analyzing the pair dispersion of small-scale magnetic fields (i.e., magnetic elements). By using $25$ hr-long Hinode magnetograms at high spatial resolution ($0".3$), we tracked $68,490$ magnetic element pairs within a supergranular cell near the disk center. The computed pair separation spectrum, calculated on the whole set of particle pairs independently of their initial separation, points out what is known as a super-diffusive regime with spectral index $\gamma=1.55\pm0.05$, in agreement with the most recent literature, but extended to unprecedented spatial and temporal scales (from granular to supergranular). Furthermore, for the first time, we investigated here the spectrum of the mean square displacement of pairs of magnetic elements, depending on their initial separation $r_0$. We found that there is a typical initial distance above (below) which the pair separation is faster (slower) than the average. A possible physical interpretation of such a typical spatial scale is also provided

High Excitation Molecular Gas in the Magellanic Clouds

We present the first survey of submillimeter CO 4-3 emission in the Magellanic Clouds. The survey is comprised of 15 6'x6' maps obtained using the AST/RO telescope toward the molecular peaks of the Large and Small Magellanic Clouds. We have used these data to constrain the physical conditions in these objects, in particular their molecular gas density and temperature. We find that there are significant amounts of molecular gas associated with most of these molecular peaks, and that high molecular gas temperatures are pervasive throughout our sample. We discuss whether this may be due to the low metallicities and the associated dearth of gas coolants in the Clouds, and conclude that the present sample is insufficient to assert this effect.Comment: 18 pages, 3 figures, 5 tables. To appear in Ap