Computation of conditional expectations with guarantees

Theoretically, the conditional expectation of a square-integrable random variable $Y$ given a $d$-dimensional random vector $X$ can be obtained by minimizing the mean squared distance between $Y$ and $f(X)$ over all Borel measurable functions $f \colon \mathbb{R}^d \to \mathbb{R}$. However, in many applications this minimization problem cannot be solved exactly, and instead, a numerical method that computes an approximate minimum over a suitable subfamily of Borel functions has to be used. The quality of the result depends on the adequacy of the subfamily and the performance of the numerical method. In this paper, we derive an expected value representation of the minimal mean square distance which in many applications can efficiently be approximated with a standard Monte Carlo average. This enables us to provide guarantees for the accuracy of any numerical approximation of a given conditional expectation. We illustrate the method by assessing the quality of approximate conditional expectations obtained by linear, polynomial as well as neural network regression in different concrete examples

Radiation Shielding of Lunar Regolith/Polyethylene Composites and Lunar Regolith/Water Mixtures

Space radiation is a complex mixed field of ionizing radiation that can pose hazardous risks to sophisticated electronics and humans. Mission planning for lunar exploration and long duration habitat construction will face tremendous challenges of shielding against various types of space radiation in an attempt to minimize the detrimental effects it may have on materials, electronics, and humans. In late 2009, the Lunar Crater Observation and Sensing Satellite (LCROSS) discovered that water content in lunar regolith found in certain areas on the moon can be up to 5.6 +/-2.8 weight percent (wt%) [A. Colaprete, et. al., Science, Vol. 330, 463 (2010). ]. In this work, shielding studies were performed utilizing ultra high molecular weight polyethylene (UHMWPE) and aluminum, both being standard space shielding materials, simulated lunar regolith/ polyethylene composites, and simulated lunar regolith mixed with UHMWPE particles and water. Based on the LCROSS findings, radiation shielding experiments were conducted to test for shielding efficiency of regolith/UHMWPE/water mixtures with various percentages of water to compare relative shielding characteristics of these materials. One set of radiation studies were performed using the proton synchrotron at the Loma Linda Medical University where high energy protons similar to those found on the surface of the moon can be generated. A similar experimental protocol was also used at a high energy spalation neutron source at Los Alamos Neutron Science Center (LANSCE). These experiments studied the shielding efficiency against secondary neutrons, another major component of space radiation field. In both the proton and neutron studies, shielding efficiency was determined by utilizing a tissue equivalent proportional counter (TEPC) behind various thicknesses of shielding composite panels or mixture materials. Preliminary results from these studies indicated that adding 2 wt% water to regolith particles could increase shielding of the regolith materials by about 6%. The findings may be utilized to extend the possibilities of potential candidate materials for lunar habitat structures, will potentially impact the design criteria of future human bases on the moon, and provide some guidelines for future space mission planning with respect to radiation exposure and risks posed on astronauts

Tissue Equivalent Proportional Counter Microdosimetry Measurements Utilized Aboard Aircraft and in Accelerator Based Space Radiation Shielding Studies

This slide presentation reviews the Tissue Equivalent Proportional Counter (TEPC), a description of the spatially restricted LET Model, high energy proton TEPC and the results of modeling, the study of shielding and the results from the flight exposures with the TEPC

Las estrategias didácticas de lectura en el primer ciclo de la educación

Esta investigación se realiza en torno a las estrategias didácticas de lectura que llevan a cabo seis docentes de ciclo I para apoyar el proceso lector de los niños de la Institución Educativa Don Bosco II. Para llevarla a cabo se recurre a la Investigación-Acción, haciendo uso de instrumentos de recolección de la información, como las filmaciones de las clases, registros fotográficos, diarios de campo y pruebas diagnósticas. Por esta razón, se elaboraron unas categorías de análisis, como: Estrategias, metodología, recursos, lectura y evaluación, a partir de las cuales se presenta el proceso de análisis y reflexión, teniendo en cuenta que dichos elementos están directamente relacionados con las estrategias didácticas que utilizan las docentes e influyen directamente en el proceso lector de los niños

Las estrategias didácticas de lectura en el primer ciclo de la educación

Esta investigación se realiza en torno a las estrategias didácticas de lectura que llevan a cabo seis docentes de ciclo I para apoyar el proceso lector de los niños de la Institución Educativa Don Bosco II. Para llevarla a cabo se recurre a la Investigación-Acción, haciendo uso de instrumentos de recolección de la información, como las filmaciones de las clases, registros fotográficos, diarios de campo y pruebas diagnósticas. Por esta razón, se elaboraron unas categorías de análisis, como: Estrategias, metodología, recursos, lectura y evaluación, a partir de las cuales se presenta el proceso de análisis y reflexión, teniendo en cuenta que dichos elementos están directamente relacionados con las estrategias didácticas que utilizan las docentes e influyen directamente en el proceso lector de los niños

Evaluation of Multi-Functional Materials for Deep Space Radiation Shielding

Small scale trade study of materials for radiation shielding: a) High-hydrogen polymers; b) Z-graded materials; c) Fiber-reinforced polymer composites. Discussed multi-functionality of fiber-reinforced polymer composites. Preliminary results of ground testing data

Potential Use of In Situ Material Composites such as Regolith/Polyethylene for Shielding Space Radiation

NASA has an extensive program for studying materials and methods for the shielding of astronauts to reduce the effects of space radiation when on the surfaces of the Moon and Mars, especially in the use of in situ materials native to the destination reducing the expense of materials transport. The most studied material from the Moon is Lunar regolith and has been shown to be as efficient as aluminum for shielding purposes (1). The addition of hydrogenous materials such as polyethylene should increase shielding effectiveness and provide mechanical properties necessary of structural materials (2). The neutron radiation shielding effectiveness of polyethylene/regolith stimulant (JSC-1A) composites were studied using confluent human fibroblast cell cultures exposed to a beam of high-energy spallation neutrons at the 30deg-left beam line (ICE house) at the Los Alamos Neutron Science Center. At this angle, the radiation spectrum mimics the energy spectrum of secondary neutrons generated in the upper atmosphere and encountered when aboard spacecraft and high-altitude aircraft. Cell samples were exposed in series either directly to the neutron beam, within a habitat created using regolith composite blocks, or behind 25 g/sq cm of loose regolith bulk material. In another experiment, cells were also exposed in series directly to the neutron beam in T-25 flasks completely filled with either media or water up to a depth of 20 cm to test shielding effectiveness versus depth and investigate the possible influence of secondary particle generation. All samples were sent directly back to JSC for sub-culturing and micronucleus analysis. This presentation is of work performed in collaboration with the NASA sponsored Center for Radiation Engineering and Science for Space Exploration (CRESSE) at Prairie View A&M

Analytical Representations for Characterizing the Global Aviation Radiation Environment Based on Model and Measurement Databases

The Nowcast of Atmospheric Ionizing Radiation for Aviation Safety climatological model and the Automated Radiation Measurements for Aerospace Safety (ARMAS) statistical database are presented as polynomial fit equations. Using equations based on altitude, L shell, and geomagnetic conditions an effective dose rate for any location from a galactic cosmic ray (GCR) environment can be calculated. A subset of the ARMAS database is represented by a second polynomial fit equation for the GCR plus probable relativistic energetic particle (REP; Van Allen belt REP) effective dose rates within a narrow band of L shells with altitudinal and geomagnetic dependency. Solar energetic particle events are not considered in this study since our databases do not contain these events. This work supports a suggestion that there may be a REP contribution having an effect at aviation altitudes. The ARMAS database is rich in Western Hemisphere observations for L shells between 1.5 and 5; there have been many cases of enhanced radiation events possibly related to effects from radiation belt particles. Our work identifies that the combined effects of an enhanced radiation environment in this L shell range are typically 15% higher than the GCR background. We also identify applications for the equations representing the Nowcast of Atmospheric Ionizing Radiation for Aviation Safety and ARMAS databases. They include (i) effective dose rate climatology in comparison with measured weather variability and (ii) climatological and statistical weather nowcasting and forecasting. These databases may especially help predict the radiation environment for regional air traffic management, for airport overflight operations, and for air carrier route operations of individual aircraft

Effects of orientation and heater length on critical heat flux from discrete and continuous heaters

The effects of flow orientation on critical heat flux (CHF) on a series of nine in-line simulated microelectronic chips in Fluorinert FC-72 were investigated. The chips were subjected to coolant in upflow, downflow, or horizontal flow with the chips on the top or bottom walls of the channel with respect to gravity. Changes in angle of orientation affected CHF for velocities below 200 cm/s, with some chips reaching CHF at heat fluxes below the pool boiling and flooding-induced CHF values. Increased subcooling was found to slightly dampen this adverse effect of orientation. Critical heat flux was overwhelmingly caused by localized dryout of the chip surface. However, during the low velocity downflow tests, low CHF values were measured because of liquid blockage by vapor counterflow and vapor stagnation in the channel. At the horizontal orientation with downward-facing chips, vapor/liquid stratification also yielded low CHF values. Previously derived correlations for water and long, continuous heaters had limited success in predicting CHF for the present discontinuous heater configuration. Because orientation has a profound effect on the hydrodynamics of two-phase flow and, consequently, on CHF for small inlet velocities, it is shown that downflow angles should be avoided, or when other constraints force the usage of downflow angles, the inlet liquid velocity should be sufficiently large. A critical heat flux model is presented that accounts for both heater length and orientation effects in near-saturated flow. Formulation of the model was based on flow visualization and photomicrography of the vapor-liquid interface on 10, 30, and 110-mm long heaters subjected to vertical, inclined, and horizontal flow. The photographs revealed the formation of a wavy vapor layer on the heater prior to CHF with surface wetting occurring at the wave troughs. The distance between these troughs increased in the stream-wise direction causing a reduction in the number of wetting fronts available for liquid replenishment of the heated surface. Lift off of the most upstream wetting front was found to catastrophically cause CHF. The model predicts the CHF data with a mean absolute error of 14.6%