A scalable architecture for volume rendering

Image-space reconstruction of continuous surfaces from scattered one-pixel projections of points is known to potentially offer an advantageous time complexity compared to surface splatting techniques. We propose a new algorithm for hardware-accelerated image-space reconstruction using pull-push interpolation and present an efficient GPU implementation. Compared to published image-space reconstruction approaches employing the pull-push interpolation, our method offers a significantly improved image quality because of the integration of elliptic boxfilters and support for deferred Phong shading. For large point-based models, our GPU implementation is capable of rendering more than 50M points per second—including image-space reconstruction and deferred shading.

Since 2006, the government of Alberta has tried to increase the volume of raw bitumen upgraded and refined in the province. More specifically, the Alberta Petroleum Marketing Commission (APMC) and Canadian Natural Resources Ltd. (CNRL) have entered into agreements with a facility northeast of Edmonton called the North West Redwater (NWR) Sturgeon Refinery. The NWR Sturgeon Refinery is designed to process 79,000 barrels per day (bpd) of feedstock, consisting of 50,000 bpd of bitumen and 29,000 bpd of diluent (referred to as dilbit). The refinery will produce petroleum products consisting of approximately 40,000 bpd of low sulphur diesel, 28,000 bpd of diluent and 13,000 bpd of other lighter petroleum products. It will also be able to capture 1.2 million tonnes per year of carbon dioxide emitted from the refinery’s operations. This captured carbon dioxide will be compressed, put into a pipeline and then injected into an existing oil field in order to achieve increased production of crude oil (referred to as enhanced oil recovery or EOR). It is the first refinery built in Canada since 1984, and the first one in Canada to refine bitumen into petroleum products such as diesel fuel. It differs from the upgrader built in Lloydminster which only upgrades bitumen into synthetic crude oil that requires further refining at a conventional refinery in order to produce petroleum products. This paper gives a description of the structure of this support by APMC and CNRL using a mechanism whereby those two parties agree to enter into tolling agreements to process the diluted bitumen feedstock into refined petroleum products for sale. Under the tolling agreement, APMC and CNRL retain ownership of the diluted bitumen as it is refined into petroleum products. APMC and CNRL then sell such petroleum products, and pay a tolling fee to the NWR Sturgeon Refinery for the refining service provided. The paper also uses an economic model in Excel to give a projection of the economics of this facility for the first full year of operation. The objective is to put numbers to a project that has been the subject of much qualitative discussion. The Excel economic model contains base case assumptions for a number of variables such as the capital cost of the refinery, the financing costs associated with such capital costs, the operating costs of the refinery, the cost of the diluted bitumen feedstock and the price of the petroleum products produced by and sold from the refinery. Based on these base case assumptions, the Excel economic model shows that in the first full year of operation of the NWR Sturgeon Refinery in 2019, the two toll-paying entities, APMC and CNRL, are projected to lose a cash amount of about $24 million (about $1 per barrel of diluted bitumen supplied). This loss is based on a comparison to the toll payers’ alternative of just selling the diluted bitumen feedstock at market prices. The paper then uses the economic model to do a sensitivity analysis to show the effect of a lower or higher price of diluted bitumen feedstock, as well as the effect of a lower or higher price of the produced petroleum products. If the cost of the diluted bitumen feedstock were lower, or the price of the petroleum products were higher, then APMC and CNRL would earn a profit. If the converse occurred (feedstock costs higher or petroleum product price lower), then the loss to APMC and CNRL would be greater than $24 million. Finally, the paper attempts to create a template for governments to use when they consider whether or not to provide financial assistance to various projects.

ALICE is a dedicated heavy-ion experiment at CERN LHC aiming to study the properties of the quark–gluon plasma. A lead– lead collision might produce several ten thousand new particles. Detailed study of the event requires precise measurements of the particle tracks. A 90 m Time Projection Chamber (TPC) with more than 500 000 read-out pads was built as the main central barrel tracker. Collisions can be recorded at a rate of up to about 1 kHz. The front-end electronics, designed from FPGAs and custom ASICs, performs shaping, amplification, digitisation and digital filtering of the signals. The data is forwarded to DAQ via 216 1.25 Gb/s fibre-optical links. Configuration, control and monitoring is done by an embedded Linux system on the front-end electronics. First results on the performance of the front-end electronics and the distributed detector control system are presented. I. TIME PROJECTION CHAMBER (TPC) The A Large Ion Collider Experiment (ALICE) [1] is using a TPC [2] as the main track-finding detector. A TPC is a gaseous detector. It is shaped like an horizontal barrel and positioned in the same direction as the beam pipe, which is passing through the centre of the barrel. The overall length is 500 cm, divided by a 100 kV Central Electrode (CE) into two identical drift volume. The diameter is 494 cm, though the innermost 170 cm is not part of the TPC to make room for the beam pipe and inner tracking detectors. A schematic view of the TPC can be seen in Figure 1. Collisions will take place in the beam pipe in the centre of the TPC, allowing the particles produced to traverse the TPC and leave tracks of ionised gas along their paths. A strong electric field of from the CE will make the electrons drift towards the end planes, where data read-out is performed. Each end plane is divided into 18 azimuthal sectors, which again are divided into two Multi-Wire Proportional Chambers (MWPC), the Outer and Inner Read-Out Chamber (OROC/IROC). The OROC has four Read-out Partitions (RPs); the IROC two. A RP is an electronic entity for reading out data from read-out pads. The ionistic signal will be amplified by the space charge around the wires of the MWPC. The induced charge on the read-out pads is forwarded to the read-out electronics. In total for both sides there are 557568 pads. The drift volume is filled with counting gas composed of 85.7 % Ne, 9.5 % CO2 and 4.8 % N2. A cold, light gas is used to assure low diffusion and low multiple scattering. Field distortions are minimised because of the high ion mobility and few ionisation electrons per unit length. The electronics design noise figure is 1000 RMS e− (700 actually achieved); not limiting the position resolution will require a signal/noise ratio of at least 20. Apart from tracking—measuring the charged particle momentum and having a good two-track separation—it also provides Particle IDentification (PID). The TPC is expected to perform well at multiplicities as high as dNch/dη=8000 in the particle momentum range [0.1, 100] GeV/c and within |η| 90 %, and the dE/dx resolution better than 10 %. Further, the TPC alone will have a momentum resolution of about 1 % at 2 GeV/c and 10 % at 50 GeV/c. For p–p collisions a read-out rate of ≈1 kHz is expected, while for central Pb–Pb collisions ≈0.2 kHz. Figure 1: Schematic view of the TPC. To the left a singe Read-out Partition (RP) is enlarged for visibility. The support for the sectors is shown on the two end planes. Between them is the Central Electrode (CE). The TPC allows space around the centre of the length axis for beam pipe and inner silicon detectors. II. DATA READ-OUT DESIGN As already mentioned, each sector has six RPs. A RP consists of a Read-out Control Unit (RCU) with up to 25 Front-End Cards (FEC), depending on the radial location. The innermost RPs have the highest number of FECs, as a smaller size for the readout-pads is used to increase the resolution to take into account the higher track density close to the collisions. The electronics for one RP, as well as its connection to the central systems is shown as a block diagram in Figure 2. Eight ALICE TPC Read-Out (ALTRO) [3] chips are mounted on a FEC, each capable of reading out 16 read-out pads. The FECs are attached to the RCU via buses; one for data transfer and one for control/monitoring. Once on the RCU, the data is forwarded to Data Acquisition system (DAQ) and the High Level Trigger (HLT) via a 1.25 Gb/s optical fibre. A Detector Control System (DCS) board equipped with an embedded

We present a distributed active subspace method for training surrogate models of complex physical processes with high-dimensional inputs and function valued outputs. Specifically, we represent the model output with a truncated Karhunen-Lo\`eve (KL) expansion, screen the structure of the input space with respect to each KL mode via the active subspace method, and finally form an overall surrogate model of the output by combining surrogates of individual output KL modes. To ensure scalable computation of the gradients of the output KL modes, needed in active subspace discovery, we rely on adjoint-based gradient computation. The proposed method combines benefits of active subspace methods for input dimension reduction and KL expansions used for spectral representation of the output field. We provide a mathematical framework for the proposed method and conduct an error analysis of the mixed KL active subspace approach. Specifically, we provide an error estimate that quantifies errors due to active subspace projection and truncated KL expansion of the output. We demonstrate the numerical performance of the surrogate modeling approach with an application example from biotransport.

Knee osteoarthritis is highly prevalent in our country. An early diagnosis is very important to provide an accurate and early treatment, and eventually delay its progression. To compare the diagnostic yield for osteoarthritis of two projections in knee X ray examination. We evaluated 44 knees with conventional (AP weight-bearing, in full extension) and Rosenberg (PA weight-bearing in 45 degrees of flexion) X ray projections in 32 patients (24 women and 8 men), aged 26 to 78 years. All patients were symptomatic at the time of evaluation, with a suspicion of knee osteoarthritis. Both projections were analyzed and compared. Joint space in the lateral compartment with conventional AP weight-bearing and Rosenberg projections were 8.6+/-11.5 mm and 7.8+/-10.9 mm, respectively (NS). The joint space for the medial compartment were 8.2+/-10.9 mm and 6.7+/-8.6 mm, respectively (p <0.05). Rosenberg projection is more sensitive to detect knee joint space narrowing as compared with conventional AP weight-bearing projection, at least in the medial compartment of the knee. Therefore, Rosenberg projection should be included in the initial study of any patient with suspicion of knee osteoarthritis.

Most of the models for identifying required returns are based on the past performance of profitability, company share prices and market returns. The future expectations seldom get incorporated therein. Govt. expectations are based on different considerations altogether. Lenders also view this aspect differently. Infrastructure projects carried out with or without forming special purpose company pose another set of issues. Practitioners follow different methods & considerations for identifying project required return. These are WACC, CAPM, Risk Adjusted Discount rate, Gordon model, Asset Beta, industry averages, opportunity costs, strategic considerations etc. For a given cost and future projections of project a small upward or downward change in the project required return can make the project financially unattractive or attractive. This is a very grey area of project appraisal. The purpose of this article is to examine the spectrum of issues involved around deciding the hurdle ‘project required return’ and bring out comprehensive view on the same

This paper briefly discusses the ALICE machine background concerns and the background monitoring system. ALICE RUNNING STRATEGY ALICE (A Large Ion Collider Experiment) [1] is a general purpose detector designed to address the physics of strongly interacting matter and the quark-gluon plasma in nucleus-nucleus collisions at the LHC. It will allow a comprehensive study of particles produced in Pb–Pb collisions, up to the highest multiplicities anticipated at the LHC. The physics program also includes collisions with lighter ions as well as dedicated proton-nucleus runs. Regular data taking during pp runs will provide reference data for the heavy ion program and address a number of specific pp topics. The pp runs will be in parallel with the other experiments but at a reduced luminosity in IP2. In order to keep the pile-up in the Time Projection Chamber (TPC) and Silicon Drift Detectors (SDD) at an acceptable level, the luminosity during pp runs has to be limited to 3 × 10 cm−2s−1, corresponding to an interaction rate of 200 kHz. At this rate we record on average 20 overlapping events. The optimal detector operation and physics performance with the TPC, i.e. no pile-up, is at 10 cm−2s−1. IMPACT OF MACHINE BACKGROUND General considerations Due to the running at reduced luminosity ALICE has the most unfavorable interaction rate over background rate ratio (at least a factor of 10 less than the high luminosity experiments). Machine background effects are alleviated by the fact that ALICE has been designed to perform tracking for up to 1000 times the pp multiplicity and the trigger reduction factors are relatively small (typically 10). So far the expected effects of the background are mainly of cumulative nature, such as radiation damage (integral dose and neutron fluences). Also the increase of the data volume has obvious negative consequences in terms of data storage and offline computing requirements. To simulate these effects ALICE has so far considered beam gas events in the experimental region IP ±20 m and beam-halo from beam-gas scattering outside the experimental regions. Input for the quartiary background caused by tertiary collimators (TCT) close to the experimental region is not yet available for IP2. In case the collimators are at the nominal settings this contribution could well be the dominant source of machine background. However, since at full beam intensity ALICE will run at high β∗ (10 m), the inner triplet will not limit the aperture of the machine. ALICE requires that for stable beams the TCTs will be put at a position at which they protect the inner triplets against accidental losses but do not produce extra losses for stable beams. Dose in central detectors The radiation environment in the experimental cavern has been simulated for the planned running scenario of the ALICE experiment (Table 1) [2]. Running with p-p, low and high mass ion–ion collisions over a ten year period has been assumed. Beam-beam and beam-gas interactions have been considered as potential radiation sources. The highest doses, up to 2.8 kGy, are expected at the location of the inner tracking system (ITS) (Table 2). The contribution from beam halo [3] amounts to ≈ 20% of the total dose. The contribution from beam-gas collisions within the experimental region has been calculated assuming a very conservative residual gas pressure of 2× 10 molecules/m. Only under these conditions a sizeable contribution of about 10% of the total dose is expected. Charged particle rates on RPCs Among the ALICE detectors, the muon trigger system is one of the most sensitive to the machine induced background. As a matter of fact, the Resistive Plate Chambers (RPC) rate capability (50 − 100 Hz/cm) might be saturated by a too high background level, which might also have an impact on the detector lifetime. The fluxes of secondary charged particles through muon trigger system originating from machine induced background has been simulated [4]. The trigger background consists mainly of electrons from hadronic showers resulting in a hot spot of ≈ 60 Hz/cm located at x = 1.5 m and |y| < 1.5 m. BACKGROUND MONITORING For machine background monitoring during injection ALICE will use the beam condition monitor (BCM) and the V0 forward scintillator detectors at safe photomultiplier settings. Due to the different acceptance of the two detectors an OR of the two signals will be used. With circulating stable beams a combination of signals from BCM, V0, SPD, TPC and forward muon spectrometer will be used to obtain a normalized machine background signal. Beam condition monitors The purpose of the Beam Condition Monitor (BCM) is to detect adverse beam conditions within the ALICE experLHC Workshop on Experimental Conditions and Beam-Induced Detector Backgrounds

Background: Reduction mammoplasty is a challenging combination of aesthetic and functional plastic surgery. It is a technique that provides a safe and predictable result with NAC preservation. The end result should be judged on volume, scar pattern, shape, symmetry, and nipple position with projection. Though the ideal normal breast does not exist, the ideal operated breast should satisfy certain morphologic criteria. Despite the diversity of procedures, there is no consensus about the ideal technique for reduction mammoplasty. Aim: To compare the clinical and the aesthetic outcome of the superomedial pedicle and the inferior pedicle techniques in reduction mammoplasty for females complaining of symptomatic breast hypertrophy. Methods: 24 patients with huge symptomatic breasts at the department of General Surgery, Ain-shams University hospitals from Jan 2017 to September 2018 were divided into two groups; Group (A) Patients underwent reduction mammoplasty using superomedial pedicle technique and Group (B) Patients offered inferior pedicle technique. Both groups were compared as regards aesthetic, surgical outcome and relief of complaint. Results: 10 patients in group A suffered from pain and pra-srap groove opposite to 9 in group B. In group A and B 11 patients out of 12 in each group had the unaccepted body shape with social embarrassment. Mean BMI was 38.72 and 36.96 in group A and B respectively. The mean weight of excised tissue in our study was 1151.6 grams in group A and 1167.1 grams in group B. There was relief of pain in 100% of group A, 83.3% of group B. Pra strap groove diminished in 100% patients. optimum patient satisfaction occurred in 100% of group A and 83.3% of group B. Regarding the Desired size and shape of the breast, in group A; 11 patients (91.7%) gave Very good, 1 patient (8.3%) gave good while no patient gave poor (0%), on the other hand, 3 patients (25%) in group B gave very good, 7 (58.3%) good and 2 (16.7) poor. 4 patients in group B (33.3%) had boxy breast deformity, while no patient (0%) in group A had such complication. Conclusion: Both superomedial and inferior pedicle techniques in reduction mammoplasty are safe, feasible and effective however boxy breast deformity.

The objective of this research project is to develop a user-friendly and cost-effective interactive input device that allows intuitive and efficient manipulation of 3D objects (6 DoF) in virtual reality (VR) visualization environments with flat projections walls. During this project, it was planned to develop an extended version of a laser pointer with multiple laser beams arranged in specific patterns. Using stationary cameras observing projections of these patterns from behind the screens, it is planned to develop an algorithm for reconstruction of the emitter’s absolute position and orientation in space. Laser pointer concept is an intuitive way of interaction that would provide user with a familiar, mobile and efficient navigation though a 3D environment. In order to navigate in a 3D world, it is required to know the absolute position (x, y and z position) and orientation (roll, pitch and yaw angles) of the device, a total of 6 degrees of freedom (DoF). Ordinary laser-based pointers when captured on a flat surface with a video camera system and then processed, will only provide x and y coordinates effectively reducing available input to 2 DoF only. In order to overcome this problem, an additional set of multiple (invisible) laser pointers should be used in the pointing device. These laser pointers should be arranged in a way that the projection of their rays will form one fixed dot pattern when intersected with the flat surface of projection screens. Images of such a pattern will be captured via a real-time camera-based system and then processed using mathematical re-projection algorithms. This would allow the reconstruction of the full absolute 3D pose (6 DoF) of the input device. Additionally, multi-user or collaborative work should be supported by the system, would allow several users to interact with a virtual environment at the same time. Possibilities to port processing algorithms into embedded processors or FPGAs will be investigated during this project as well.

This paper results from the initiative taken by the Institute of Hygiene and Tropical Medicine of Lisbon, IHMT (institution representing today the first school of Portuguese Tropical Medicine, founded in Lisbon in 1902) in 2013, promoting the 2nd National Congress of Tropical Medicine, in memory of the 1st congress occurred 61 years before. It aims to analyse the motivations which conducted to the 1st National Congress of the History of Medicine held in Lisbon in 1952, in memory of the first 50 years of Portuguese tropical medicine under the imperialist project of the Portuguese State, as well as its projection throughout the following years, and which was the motto for an exhibition, opened to the public between the months of April and July (2013) in the Institute of Hygiene and Tropical Medicine , entitled “Portugal in the world – the 1st National Congress of Tropical Medicine, 1952.” The 1st National Congress of Tropical Medicine led by its director, Joao Fraga de Azevedo (1906-1977), represents an important landmark for the Portuguese history of science and medicine, in what concerns understanding the rhetoric and the Portuguese colonial discourse, for which tropical medicine, its actors and institutions contributed significantly to the imperialist project, in respect to the consolidation and the projection of Portugal’s image in the world. The Congress was organized around two axes of analysis: a commemorative documentary exhibition of overseas sanitary activities by the occasion of the fiftieth anniversary of the Portuguese tropical medicine, and the scientific congress itself, which brought together the main stakeholders of the medical network in the metropolis and in the colonies of the national context, as well as the participation of some international figures of relevance in tropical medicine. As methodology, we will analyse the iconographic and documentary material existing in the museum of the IHMT, such as the correspondence related to the organisation of this congress, the scientific and social programme, the scientific communications, some iconography related with the exhibition on the overseas sanitary activities, and the movies produced for the event. Amongst the multiplicity of papers presented at this conference, later published in the Anais do Instituto de Medicina Tropical (Annals of the Institute of Tropical Medicine) we will particularly focus on the analysis of communications on trypanosomiasis and malaria, as well as on some elements of the exhibition of Overseas Sanitary Activities, held at the National Palace of Junqueira (Palace Burnay), crucial elements to understand the importance of this congress to the consolidation and projection of the Portugal image around the world. Should this paper contribute to explore new and different lines of research on Portuguese tropical medicine providing continuity to this piece of our history always unfinished.

This thesis work presents the implementation and validation of image processing problems in hardware to estimate the performance and precision gain. It compares the implementation for the addressed problem on a Field Programmable Gate Array (FPGA) with a software implementation for a General Purpose Processor (GPP) architecture. For both solutions the implementation costs for their development is an important aspect in the validation. The analysis of the flexibility and extendability that can be achieved by a modular implementation for the FPGA design was another major aspect. This work is based upon approaches from previous work, which included the detection of Binary Large OBjects (BLOBs) in static images and continuous video streams [13, 15]. One addressed problem of this work is the tracking of the detected BLOBs in continuous image material. This has been implemented for the FPGA platform and the GPP architecture. Both approaches have been compared with respect to performance and precision. This research project is motivated by the MI6 project of the Computer Vision research group, which is located at the Bonn-Rhein-Sieg University of Applied Sciences. The intent of the MI6 project is the tracking of a user in an immersive environment. The proposed solution is to attach a light emitting device to the user for tracking the created light dots on the projection surface of the immersive environment. Having the center points of those light dots would allow the estimation of the user’s position and orientation. One major issue that makes Computer Vision problems computationally expensive is the high amount of data that has to be processed in real-time. Therefore, one major target for the implementation was to get a processing speed of more than 30 frames per second. This would allow the system to realize feedback to the user in a response time which is faster than the human visual perception. One problem that comes with the idea of using a light emitting device to represent the user, is the precision error. Dependent on the resolution of the tracked projection surface of the immersive environment, a pixel might have a size in cm2. Having a precision error of only a few pixels, might lead to an offset in the estimated user’s position of several cm. In this research work the development and validation of a detection and tracking system for BLOBs on a Cyclone II FPGA from Altera has been realized. The system supports different input devices for the image acquisition and can perform detection and tracking for five to eight BLOBs. A further extension of the design has been evaluated and is possible with some constraints. Additional modules for compressing the image data based on run-length encoding and sub-pixel precision for the computed BLOB center-points have been designed. For the comparison of the FPGA approach for BLOB tracking a similar implementation in software using a multi-threaded approach has been realized. The system can transmit the detection or tracking results on two available communication interfaces, USB and RS232. The analysis of the hardware solution showed a similar precision for the BLOB detection and tracking as the software approach. One problem is the strong increase of the allocated resources when extending the system to process more BLOBs. With one of the applied target platforms, the DE2-70 board from Altera, the BLOB detection could be extended to process up to thirty BLOBs. The implementation of the tracking approach in hardware required much more effort than the software solution. The design of high level problems in hardware for this case are more expensive than the software implementation. The search and match steps in the tracking approach could be realized more efficiently and reliably in software. The additional pre-processing modules for sub-pixel precision and run-length-encoding helped to increase the system’s performance and precision.

To fill the vacancy of domestic short focal range digital movie zoom projection lens and to meet the requirement of the market,a digital movie zoom projection lens for 0.65 inch DLP 1.3 K digital movie projector was designed by the mechanical compensation method.It includes the former fixed group,the zoom group,the compensation group and the last fixed group.It is composed of ten glass sphere lenses,and the zoom group is composed of one negative lens,the compensation group is composed of two doublet lenses.The total length of the digital movie zoom projection lens is 170 mm,the full aperture is 70 mm.Its focal length range is 14.5~18.2 mm,F-number is 2,projection ratio range is 0.99∶1~1.23∶1,and the BFL is 32.6 mm.The cam curves were designed with the method of equal interval zoom.The image quality in each focal length is excellent with advantages of simple structure,small size,and low cost,and its cam curves are smooth without cam inflexions and processed easily.

Mask Projection Microstereolithography is capable for fabricating true three-dimensional microparts and hence, holds promise as a potential micro-fabrication process for micro-machine components. In this paper, the Mask Projection Micro-Stereolithography (MPµSLA) system developed at the Rapid Prototyping and Manufacturing Institute at Georgia Institute of Technology is presented. The dimensional accuracy of the system is improved by reducing its process planning errors. To this effect, the MPµSLA process is mathematically modeled. In this paper, the irradiance received by the resin surface is modeled as a function of the imaging system parameters and the pattern displayed on the dynamic mask. The resin used in the system is characterized to experimentally determine its working curve. This work enables us to compute the dimensions of a single layer cured using our system. The analytical model is validated by curing test layers on the system. The model computes layer dimensions within 5% error.

The optimal design of information technology systems is a multi-objective problem requiring accurate prediction of both normal and peak loading conditions. The calculation of future peak loading requires the projection of average loading as well as a detailed understanding of parameter interactions. The failure to properly account for cross-source correlations for many component systems can lead to a significant underestimation of the total system variability. We present an IT network model that projects both average and peak loading for a system that is expanding traffic at multiple data sources. The average loading is modeled by independently calculating the traffic growth for all data sources. The future cumulative load distribution is calculated by taking into account historical sources of parameter correlations and scaling to account for future average growth. Finally, the duration of the peak states is calculated by simulating a vector Fractional ARIMA time series model.

We derive an adaptive solver for random elliptic boundary value problems, using techniques from adaptive wavelet methods. Substituting wavelets by polynomials of the random parameters leads to a modular solver for the parameter dependence, which combines with any discretization on the spatial domain. We show optimality properties of this solver, and present numerical computations. Introduction Stochastic Galerkin methods have emerged in the past decade as an efficient solution procedure for boundary value problems depending on random data, see [DBO01, XK02, BTZ04, WK05, MK05, FST05, WK06, TS07, BS09, BAS10]. These methods approximate the random solution by a Galerkin projection onto a finite dimensional space of random fields. This requires the solution of a single coupled system of deterministic equations for the coefficients of the Galerkin projection with respect to a predefined set of basis functions on the parameter domain. A major remaining obstacle is the construction of suitable spaces in which to compute approximate solutions. These should be adapted to the stochastic structure of the equation. Simple tensor product constructions are infeasible due to the high dimensionality of the parameter domain in case of input random fields with low regularity. Parallel to but independently from the development of stochastic Galerkin methods, a new class of adaptive methods has emerged, which are set not in the continuous framework of a boundary value problem, but rather on the level of coefficients with respect to a hierarchic Riesz basis, such as a wavelet basis. Due to the norm equivalences constitutive of Riesz bases, errors and residuals in appropriate sequence spaces are equivalent to those in physically meaningful function spaces. This permits adaptive wavelet methods to be applied directly to a large class of equations, provided that a suitable Riesz basis is available. For symmetric elliptic problems, the error of the Galerkin projection onto the span of a set of coefficients can be estimated using a sufficiently accurate approximation of the ∗Research supported in part by the Swiss National Science Foundation grant No. 200021-120290/1.