Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set

Stepwise uncertainty reduction (SUR) strategies aim at constructing a sequence of points for evaluating a function  f in such a way that the residual uncertainty about a quantity of interest progressively decreases to zero. Using such strategies in the framework of Gaussian process modeling has been shown to be efficient for estimating the volume of excursion of f above a fixed threshold. However, SUR strategies remain cumbersome to use in practice because of their high computational complexity, and the fact that they deliver a single point at each iteration. In this article we introduce several multipoint sampling criteria, allowing the selection of batches of points at which f can be evaluated in parallel. Such criteria are of particular interest when f is costly to evaluate and several CPUs are simultaneously available. We also manage to drastically reduce the computational cost of these strategies through the use of closed form formulas. We illustrate their performances in various numerical experiments, including a nuclear safety test case. Basic notions about kriging, auxiliary problems, complexity calculations, R code, and data are available online as supplementary materials.

Logical omniscience as infeasibility

Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that are simple enough. This contradiction points to the fruitlessness of trying to solve the Logical Omniscience Problem qualitatively if the rationality of agents is to be maintained. We provide a quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness. More precisely, we provide a test for the logical omniscience problem in a given formal theory of knowledge. The quantitative measures we use are inspired by the complexity theory. We illustrate our framework with a number of examples ranging from the traditional implicit representation of knowledge in modal logic to the language of justification logic, which is capable of spelling out the internal inference process. We use these examples to divide representations of knowledge into logically omniscient and not logically omniscient, thus trying to determine how much information about the reasoning process needs to be present in a theory to avoid logical omniscience.

Diagenesis of a light, tight-oil chert reservoir at the Ediacaran/Cambrian boundary, Sultanate of Oman

The Al Shomou Silicilyte Member (Athel Formation) in the South Oman Salt Basin shares many of the characteristics of a light, tight-oil (LTO) reservoir: it is a prolifi c source rock mature for light oil, it produces light oil from a very tight matrix and reservoir, and hydraulic fracking technology is required to produce the oil. What is intriguing about the Al Shomou Silicilyte, and different from other LTO reservoirs, is its position related to the Precambrian/Cambrian Boundary (PCB) and the fact that it is a ‘laminated chert‘ rather than a shale. In an integrated diagenetic study we applied microstructural analyses (SEM, BSE) combined with state-of-the-art stable isotope and trace element analysis of the silicilyte matrix and fractures. Fluid inclusion microthermometry was applied to record the salinity and minimum trapping temperatures. The microstructural investigations reveal a fi ne lamination of the silicilyte matrix with a mean lamina thickness of ca. 20 μm consisting of predominantly organic matter-rich and fi nely crystalline quartz-rich layers, respectively. Authigenic, micron-sized idiomorphic quartz crystals are the main matrix components of the silicilyte. Other diagenetic phases are pyrite, apatite, dolomite, magnesite and barite cements. Porosity values based on neutron density logs and core plug data indicate porosity in the silicilyte ranges from less than 2% to almost to 40%. The majority of the pore space in the silicilyte is related to (primary) inter-crystalline pores, with locally important oversized secondary pores. Pore casts of the silica matrix show that pores are extremely irregular in three dimensions, and are generally interconnected by a complex web or meshwork of fi ne elongate pore throats. Mercury injection capillary data are in line with the microstructural observations suggesting two populations of pore throats, with an effective average modal diameter of 0.4 μm. The acquired geochemical data support the interpretation that the primary source of the silica is the ambient seawater rather than hydrothermal or biogenic. A maximum temperature of ca. 45°C for the formation of microcrystalline quartz in the silicilyte is good evidence that the lithifi cation and crystallization of quartz occurred in the fi rst 5 Ma after deposition. Several phases of brittle fracturing and mineralization occurred in response to salt tectonics during burial. The sequences of fracture-fi lling mineral phases (dolomite - layered chalcedony – quartz – apatite - magnesite I+II - barite – halite) indicates a complex fl uid evolution after silicilyte lithifi cation. Primary, all-liquid fl uid inclusions in the fracturefi lling quartz are good evidence of growth beginning at low temperatures, i.e. ≤ 50ºC. Continuous precipitation during increasing temperature and burial is documented by primary two-phase fl uid inclusions in quartz cements that show brines at 50°C and fi rst hydrocarbons at ca. 70°C. The absolute timing of each mineral phase can be constrained based on U-Pb geochronometry, and basin modelling. Secondary fl uid inclusions in quartz, magnesite and barite indicate reactivation of the fracture system after peak burial temperature during the major cooling event, i.e. uplift, between 450 and 310 Ma. A number of fi rst-order trends in porosity and reservoir-quality distribution are observed which are strongly related to the diagenetic and fl uid history of the reservoir: the early in-situ generation of hydrocarbons and overpressure development arrests diagenesis and preserves matrix porosity. Chemical compaction by pressure dissolution in the fl ank areas could be a valid hypothesis to explain the porosity variations in the silicilitye slabs resulting in lower porosity and poorer connectivity on the fl anks of the reservoir. Most of the hydrocarbon storage and production comes from intervals characterized by Amthor et al. 114488 preserved micropores, not hydrocarbon storage in a fracture system. The absence of oil expulsion results in present-day high oil saturations. The main diagenetic modifi cations of the silicilyte occurred and were completed relatively early in its history, i.e. before 300 Ma. An instrumental factor for preserving matrix porosity is the diffi culty for a given slab to evacuate all the fl uids (water and hydrocarbons), or in other words, the very good sealing capacity of the salt embedding the slab.

Experimenter effects on behavioral test scores of eight inbred mouse strains under the influence of ethanol.

ight standard inbred mouse strains were evaluated for ethanol effects on a refined battery of behavioral tests in a study that was originally designed to assess the influence of rat odors in the colony on mouse behaviors. As part of the design of the study, two experimenters conducted the tests, and the study was carefully balanced so that equal numbers of mice in all groups and times of day were tested by each experimenter. A defect in airflow in the facility compromised the odor manipulation, and in fact the different odor exposure groups did not differ in their behaviors. The two experimenters, however, obtained markedly different results for three of the tests. Certain of the experimenter effects arose from the way they judged behaviors that were not automated and had to be rated by the experimenter, such as slips on the balance beam. Others were not evident prior to ethanol injection but had a major influence after the injection. For several measures, the experimenter effects were notably different for different inbred strains. Methods to evaluate and reduce the impact of experimenter effects in future research are discussed.