Investigating the efficiency of fitting Coxian phase-type distributions to health care data

Coxian phase-type distributions are becoming a popular means of representing survival times within a health care environment. They are favoured as they show a distribution as a system of phases and can allow for an easy visual representation of the rate of flow of patients through a system. Difficulties arise, however, in determining the parameter estimates of the Coxian phase-type distribution. This paper examines ways of making the fitting of the Coxian phase-type distribution less cumbersome by outlining different software packages and algorithms available to perform the fit and assessing their capabilities through a number of performance measures. The performance measures rate each of the methods and help in identifying the more efficient. Conclusions drawn from these performance measures suggest SAS to be the most robust package. It has a high rate of convergence in each of the four example model fits considered, short computational times, detailed output, convergence criteria options, along with a succinct ability to switch between different algorithms.

Dynamics of the Indonesian seas circulation. Part I – The influence of bottom topography on temperature and salinity distributions

The influence of bottom topography on the distribution of temperature and salinity in the Indonesian seas region has been studied with a high-resolution model based on the Princeton Ocean Model. One of the distinctive properties of the model is an adequate reproduction of all major topographic features in the region by the model bottom relief. The three major routes of flow of Pacific water through the region have been identified. The western route follows the flow of North Pacific Water through the Sulawesi Sea, Makassar Strait, Flores Sea, and Banda Sea. This is the main branch of the Indonesian Throughflow. The eastern routes follow the flow of South Pacific water through the eastern Indonesian seas. This water enters the region either through the Halmahera Sea or by flowing to the north around Halmahera Island into the Morotai Basin and then into the Maluku Sea. A deep southward flow of South Pacific Water fills the Seram Sea below 1200 m through the Lifamatola Passage. As it enters the Seram Sea, this overflow turns eastward at depths greater than 2000 m, then upwells in the eastern part of the Seram Sea before returning westward at ~1500-2000 m. The flow continues westward across the Seram Sea, spreading to greater depths before entering the Banda Sea at the Buru-Mangole passage. It is this water that shapes the temperature and salinity of the deep Banda Sea. Topographic elevations break the Indonesian seas region down into separate basins. The difference in the distributions of potential temperature, ?, and salinity, S, in adjacent basins is primarily due to specific properties of advection of ? and S across a topographic rise. By and large, the topographic rise blocks deep flow between basins whereas water shallower than the depth of the rise is free to flow between basins. To understand this process, the structure of simulated fields of temperature and salinity has been analyzed. To identify a range of advected ? or S, special sections over the sills with isotherms or isohalines and isotachs of normal velocity have been considered. Following this approach the impact of various topographic rises on the distribution of ? and S has been identified. There are no substantial structural changes of potential temperature and salinity distributions between seasons, though values of some parameters of temperature and salinity distributions, e.g., magnitudes of maxima and minima, can change. It is shown that the main structure of the observed distributions of temperature and salinity is satisfactorily reproduced by the model throughout the entire domain.

Transient distributions of composition and temperature in a gas-solid packed bed reactor by near-infrared tomography

Near-infrared diffuse tomography was used in order to observe dynamic behaviour of flowing gases by measuring the 3D distributions of composition and temperature in a weakly scattering packed bed reactor, subject to wall effects and non-isothermal conditions. The technique was applied to the vapour phase hydrogen isotopic exchange reaction in a hydrophobic packing of low aspect ratio made of platinum on styrene divinyl benzene sulphonate copolymer resin. The results of tomography revealed uneven temperature and composition maps of water and deuterated water vapours in the core-packed bed and in the vicinity of the wall owing to flow maldistribution. The dynamic lag between the near-wall water vapour and deuterated water vapour compositions were observed suggesting that the convective transfer which was significant near the wall at the start, owing to high porosity, was also effective at large conversions. (C) 2012 Elsevier B.V. All rights reserved.

Analytical approximations to numerical solutions of theoretical emission measure distributions

Emission line fluxes from cool stars are widely used to establish an apparent emission measure distribution, EmdApp(Te), between temperatures characteristic of the low transition region and the low corona. The true emission measure distribution, EmdTrue(Te), is determined by the energy balance and geometry adopted and, with a numerical model, can be used to predict EmdApp(Te), to guide further modelling. The scaling laws that exist between coronal parameters arise from the dimensions of the terms in the energy balance equation. Here, analytical approximations to numerical solutions for EmdTrue(Te) are presented, which show how the constants in the coronal scaling laws are determined. The apparent emission measure distributions show a minimum value at some T0 and a maximum at the mean coronal temperature Tc (although in some stars, emission from active regions can contribute). It is shown that, for the energy balance and geometry adopted, the analytical values of the emission measure and electron pressure at T0 and Tc depend on only three parameters: the stellar surface gravity and the values of T0 and Tc. The results are tested against full numerical solutions for e Eri (K2 V) and are applied to Procyon (a CMi, F5 IV/V). The analytical approximations can be used to restrict the required range of full numerical solutions, to check the assumed geometry and to show where the adopted energy balance may not be appropriate. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.

Middle Stone Age (MSA) site distributions in eastern Africa and their relationship to Quaternary environmental change, refugia and the evolution of Homo sapiens

This paper considers the evolution of Homo sapiens in eastern Africa in relation to refugia and bottlenecks around ~200 ka BP, at a macro scale. Middle Stone Age (MSA) lithics, site distributions and locations are analysed in relation to palaeovegetation maps of the last glacial/interglacial cycle, which are used as a proxy for earlier climate cycles. A ‘‘push and pull’’ model is then postulated for the spread of Homo sapiens out of refugia in eastern Africa, involving both volcanism (push) and habitat availability (pull). A date within OIS 5 is suggested for this expansion to other parts of the continent, and potentially further a?eld, contrary to a frequently proposed expansion within OIS 3. ©2008 Elsevier Ltd. All rights reserved.

Ion-acoustic supersolitons in plasmas with two-temperature electrons: Boltzmann and kappa distributions

Acoustic supersolitons arise when a plasma model is able to support three consecutive local extrema of the Sagdeev pseudopotential between the undisturbed conditions and an accessible root. This leads to a characteristic electric field signature, where a simple bipolar shape is enriched by subsidiary maxima. Large-amplitude nonlinear acoustic modes are investigated, using a pseudopotential approach, for plasmas containing two-temperature electrons having Boltzmann or kappa distributions, in the presence of cold fluid ions. The existence domains for positive supersolitons are derived in a methodological way, both for structure velocities and amplitudes, in terms of plasma compositional parameters. In addition, typical pseudopotentials, soliton, and electric field profiles have been given to illustrate that positive supersolitons can be found in the whole range of electron distributions from Maxwellian to a very hard nonthermal spectrum in kappa. However, it is found that the parameter ranges that support supersolitons vary significantly over the wide range of kappa considered. VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4818888]

Phylogeographical analysis of two cold-tolerant plants with disjunct Lusitanian distributions does not support in situ survival during the last glaciation

Aim: We used a combination of modelling and genetic approaches to investigate whether Pinguicula grandiflora and Saxifraga spathularis, two species that exhibit disjunct Lusitanian distributions, may have persisted through the Last Glacial Maximum (LGM, c. 21 ka) in separate northern and southern refugia.

Location: Northern and eastern Spain and south-western Ireland.

Methods: Palaeodistribution modelling using maxent was used to identify putative refugial areas for both species at the LGM, as well as to estimate their distributions during the Last Interglacial (LIG, c. 120 ka). Phylogeographical analysis of samples from across both species' ranges was carried out using one chloroplast and three nuclear loci for each species.

Results: The palaeodistribution models identified very limited suitable habitat for either species during the LIG, followed by expansion during the LGM. A single, large refugium across northern Spain and southern France was postulated for P. grandiflora. Two suitable regions were identified for S. spathularis: one in northern Spain, corresponding to the eastern part of the species' present-day distribution in Iberia, and the other on the continental shelf off the west coast of Brittany, south of the limit of the British–Irish ice sheet. Phylogeographical analyses indicated extremely reduced levels of genetic diversity in Irish populations of P. grandiflora relative to those in mainland Europe, but comparable levels of diversity between Irish and mainland European populations of S. spathularis, including the occurrence of private hapotypes in both regions.

Main conclusions: Modelling and phylogeographical analyses indicate that P. grandiflora persisted through the LGM in a southern refugium, and achieved its current Irish distribution via northward dispersal after the retreat of the ice sheets. Although the results for S. spathularis are more equivocal, a similar recolonization scenario also seems the most likely explanation for the species' current distribution.

Angular distributions in two-colour two-photon ionization of He

We present R-Matrix with time dependence (RMT) calculations for the photoionization of helium irradiated by an EUV laser pulse and an overlapping IR pulse with an emphasis on the anisotropy parameters of the sidebands generated by the dressing laser field. We investigate how these parameters depend on the amount of atomic structure included in the theoretical model for two-photon ionization. To verify the accuracy of the RMT approach, our theoretical results are compared with experiment.

Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.