Evaluating Decision Trees under Different Criteria

Based on our earlier results in decision theory, we demonstrate how decision trees can be integrated into a general framework for analysing decision situations with respect to different criteria, and suggest an evaluation rule taking into account all strategies, criteria, probabilities and utilities involved in the situations under consideration. A significant property of the framework is that it admits the representation of imprecise information at all stages. This information is modelled in sets of measures constrained by interval estimates. The strategies are then evaluated relative to different decision rules, e.g., a set of generalisations of the principle of admissibility. Decision situations are evaluated using fast algorithms developed particularly for solving these kinds of problems. The presented framework has been developed and used within a large-scale evaluation project at the Swedish National Rail Administration

A robustness study of state-of-the-art surrogate weights for MCDM

A vast number of methods for solving multi-criteria decision problems have been suggested for assessing criteria weights requiring more exact input data than users normally are able to provide. In particular, the selection of adequate criteria weights is difficult and in order to be realistic, other methods must be introduced. One class of such methods is to introduce so called surrogate weights, where numerical weights are assigned to each criterion based on a cardinal or ordinal rank ordering, assumed to represent the information extracted from the user. One essential problem is the robustness of such methods. In this article, we compare state-of-the-art methods based on surrogate weights from the literature and, utilizing a simulation approach, discuss underlying assumptions and robustness properties. This results in a quantitative measurement of these weighting methods and a methodology applicable also to forthcoming methods

Trade-offs for Ordinal Ranking Methods in Multi-Criteria Decisions

Weight elicitation methods in multi-criteria decision analysis (MCDA) are often cognitively demanding, require too much precision and too much time and effort. Some of the issues may be remedied by connecting elicitation methods to an inference engine facilitating a quick and easy method for decision-makers to use weaker input statements, yet being able to utilize these statements in a method for decision evaluation. One important class of such methods ranks the criteria and converts the resulting ranking into numerical so called surrogate weights. We analyse the relevance of these methods and discuss how robust they are as candidates for modelling decision-makers and analysing multi-criteria decision problems under the perspectives of several stakeholders

Highly Siderophile Elements in Pallasites and Diogenites, Including the New Pallasite, CMS 04071

Pallasites are long thought to represent a metallic core-silicate mantle boundary, where the IIIAB irons are linked to the crystallization history of the metallic fraction, and the HED meteorites may be linked to the silicate fraction. However, measurement of trace elements in individual metallic and silicate phases is necessary in order to fully under-stand the petrogenetic history of pallasites, as well as any magmatic processes which may link pallasites to both IIIAB irons and HED meteorites. In order to achieve this objective, abundances of a suite of elements were measured, including the highly siderophile elements (HSEs), in kamacite, taenite, troilite, schreibersite, chromite and olivine for the pallasites Admire, Imilac, Springwater, CMS 04071. In the diogenites GRO 95555, LAP 91900, and MET 00436, metal, sulfide, spinel, pyroxene, and silica were individually measured

Partitioning of Pd Between Fe-S-C and Mantle Liquids at High Pressure and Temperature: Implications for Core Formation

One of the most elusive geochemical aspects of the early Earth has been explaining the near chondritic relative abundances of the highly siderophile elements (HSE; Au, Re and the platinum group elements) in Earth's primitive upper mantle (PUM). Perhaps they were delivered to the Earth after core formation, by late addition of carbonaceous chondrite material. However, the recognition that many moderately siderophile elements can be explained by high pressure and temperature (PT) metal-silicate equilibrium, leads to the question whether high PT equilibrium can also explain the HSE concentrations. Answers to this question have been slowed by experimental difficulties (nugget effect and very low solubilities). But two different perspectives have emerged from recent studies. One perspective is that D(M/S) for HSE at high PT are not low enough to explain terrestrial mantle depletions of these elements (for Pd and Pt). A second perspective is D(M/S) are reduced substantially at high PT and even low enough to explain terrestrial mantle depletions (for Au and Pt). Issues complicating interpretation of all experiments include use of MgO- and FeO-free silicate melts, and S-free and FeNi metal-free systems. In addition, conclusions for Pt rest on an interpretation that the tiny metallic nuggets plaguing many such experiments, were formed upon quench. There is not agreement on this issue, and the general question of HSE solubility at high PT remains unresolve

Killing Horizons Decohere Quantum Superpositions

We recently showed that if a massive (or charged) body is put in a quantum spatial superposition, the mere presence of a black hole in its vicinity will eventually decohere the superposition. In this paper we show that, more generally, decoherence of stationary superpositions will occur in any spacetime with a Killing horizon. This occurs because, in effect, the long-range field of the body is registered on the Killing horizon which, we show, necessitates a flux of "soft horizon gravitons/photons" through the horizon. The Killing horizon thereby harvests "which path" information of quantum superpositions and will decohere any quantum superposition in a finite time. It is particularly instructive to analyze the case of a uniformly accelerating body in a quantum superposition in flat spacetime. As we show, from the Rindler perspective the superposition is decohered by "soft gravitons/photons" that propagate through the Rindler horizon with negligible (Rindler) energy. We show that this decoherence effect is distinct from--and larger than--the decoherence resulting from the presence of Unruh radiation. We further show that from the inertial perspective, the decoherence is due to the radiation of high frequency (inertial) gravitons/photons to null infinity. (The notion of gravitons/photons that propagate through the Rindler horizon is the same notion as that of gravitons/photons that propagate to null infinity.) We also analyze the decoherence of a spatial superposition due to the presence of a cosmological horizon in de Sitter spacetime. We provide estimates of the decoherence time for such quantum superpositions in both the Rindler and cosmological cases. Although we explicitly treat the case of spacetime dimension $d=4$, our analysis applies to any dimension $d \geq 4$.Comment: 16 pages, 1 figure. Accepted for publication in Phys. Rev. D. v2: Added clarifying remarks and a figure, and pointed out that the effect arises for any d>=4; corrected equation (3.18

Experimental Crystallization of Yamato 980459

Currently, only two martian meteorites QUE 94201 (QUE) and Yamato 980459 (Y98) have been experimentally shown to me true melt compositions. Most martian meteorites are instead, cumulates or partial cumulates. We have performed experiments on a Y98 composition to assess whether QUE could be related to Y98 by some fractionation process [1]. Y98 is a basaltic shergottite from the SNC (Shergotty, Nakhla, Chassigny) meteorite group. Y98 is composed of 26% olivine, 48% pyroxene, 25% mesostasis, and no plagioclase [2]. The large size of the olivine megacrysts and absence of plagioclase suggest that the parental melt which formed this meteorite had begun cooling slowly until some mechanism, such as magma ascent, caused rapid cooling [3]. Y98 s olivines have the highest Mg content of all the shergottites suggesting that it is the most primitive [4]. Y98 has been determined to be a melt composition by comparing the composition of experimental liquidus olivines with the composition of the cores of Y98 olivines [4]. The liquidus of Y98 is predicted by MELTS [5] and by experimentation [6] to be ~1450 C. Analyses of Y98 show it to be very depleted in LREEs and it has similar depleted patterns as other shergottites such as QUE [7]

High Pressure and Temperature Core Formation as an Alternative to the "Late Veneer" Hypothesis

The highly siderophile elements (HSE; Re, Au and the Platinum Group Elements - Pd Pt, Rh, Ru, Ir, Os) are commonly utilized to constrain accretion processes in terrestrial differentiated bodies due to their affinity for FeNi metal [1]. These eight elements exhibit highly siderophile behavior, but nonetheless have highly diverse metal-silicate partition coefficients [2]. Therefore the near chondritic relative concentrations of HSEs in the terrestrial and lunar mantles, as well as some other bodies, are attributed to late accretion rather than core formation [1]. Evaluation of competing theories, such as high pressure metal-silicate partitioning or magma ocean hypotheses has been hindered by a lack of relevant partitioning data for this group of eight elements. In particular, systematic studies isolating the effect of one variable (e.g. temperature or melt compositions) are lacking. Here we undertake new experiments on all eight elements, using Fe metal and FeO-bearing silicate melts at fixed pressure, but variable temperatures. These experiments, as well as some additional planned experiments should allow partition coefficients to be more accurately calculated or estimated at the PT conditions and compositions at which core formation is thought to have occurred

The Combined Strength of Thermodynamics and Comparative Planetology: Application of Activity Models to Core Formation in Terrestrial Bodies

Recent models for accretion of terrestrial bodies involve metal-silicate equilibrium as the metallic core formed during growth. Most elements considered are either refractory or well studied elements for which effects of pressure, temperature, oxygen fugacity, and metallic liquid composition are well known. There are a large number of elements that are both siderophile and volatile, whose fate in such models is unknown, largely due to a lack of data at comparable conditions and com-positions (FeNi core with light elements such as S, C, Si, and O). We have focused on Ge, In, As, Sb and determined the effect of Si and C on metal-silicate partitioning, and developed a thermo-dynamic model that allows application of these new data to a wide range of planetary bodies. New experiments: We have previously carried out experiments with FeSi metallic liquid at C-saturated conditions at 1600 and 1800 C [4]. In a new series of experiments we investigate the effect of Si in carbon-free systems at 1600 C for comparison. Experiments were carried out at 1 GPa in MgO capsules using the same basaltic starting composition as in previous studies. The MgO capsule reacts with the silicate melt to form more MgO-rich liquids that have 22-26 wt% MgO. Experimental met-als and silicates were analyzed using a combination of electron microprobe analysis and laser ablation ICP-MS. Results: The new results can be interpreted by considering Ge as an example, in the simple exchange equilibrium Fe + GeO = FeO + Ge, where the equilibrium constant Kd can be examined as a function of Si content of the metal. The slope of lnKd vs. (1-XSi) for this new series allows derivation of the epsilon interaction parameter for each of these four elements and Si (both C-saturated and C-free).All four elements have positive epsilon values, indicating that Si causes a decrease in the partition coefficients; values are 6.6, 6.5, 27.8 and 25.2 for In, Ge, As, and Sb, respectively, at 1 GPa and 1600 C. As an example of how large the effect of Si can be, these epsilon values correspond to activity coefficients (gamma) for As of 0.01 when XSi = 0, and up to gamma = 23 when XSi = 0.2. Combining these new results with previous determinations [5,6] of epsilon parameters for S and C for these elements allows us calculate activity of Ge, In, As, and Sb in Fe-Ni-Si-S-C-O metallic liquids. We apply this new model to sever-al terrestrial bodies such as Earth (Si-rich core), Mars (S-rich core), Moon (S-, C-, and Si-poor core), and Vesta, and examine the resulting core and mantle concentrations of these elements. Mantle concentrations of these four elements are well explained for Earth and Mars in models that call for mid-mantle equilibration between Si-bearing and S-bearing FeNi cores, respectively. Modeling results for the Moon and Vesta will also be presented

V Xanes in Spinels as an Oxy-Barometer in Meteorites with Implications for Redox Variations in the Inner Solar System

The variation of oxygen fugacity within inner solar system materials spans a range of nearly 15 orders of magnitude. Igneous and metamorphic rocks commonly contain a mineral assemblage that allows oxygen fugacity to be calculated or con-strained such as FeTi oxides, olivine-opx-spinel, or some other oxy-barometer. Some rocks, however, contain a limited mineral assemblage and do not provide constraints on fO2 using mineral equilibria. Good examples of the latter are orthopyroxenites or dunites, such as diogenites, ALH 84001, chassignites, or brachinites. In fact it is no surprise that the fO2 of many of these achondrites is not well known, other than being "reduced" and below the metal saturation value. In order to bridge this gap in our understanding, we have initiated a study of V in chromites in achondrite. Because the V pre-edge peak intensity and energy in chromites varies with fO2, and this has been calibrated over a large fO2 range, we can apply this relation to rocks for which we otherwise have no fO2 constraints