Direct QR factorizations for tall-and-skinny matrices in MapReduce architectures

The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis. For matrices with many more rows than columns, so-called "tall-and-skinny matrices," there is a numerically stable, efficient, communication-avoiding algorithm for computing the QR factorization. It has been used in traditional high performance computing and grid computing environments. For MapReduce environments, existing methods to compute the QR decomposition use a numerically unstable approach that relies on indirectly computing the Q factor. In the best case, these methods require only two passes over the data. In this paper, we describe how to compute a stable tall-and-skinny QR factorization on a MapReduce architecture in only slightly more than 2 passes over the data. We can compute the SVD with only a small change and no difference in performance. We present a performance comparison between our new direct TSQR method, a standard unstable implementation for MapReduce (Cholesky QR), and the classic stable algorithm implemented for MapReduce (Householder QR). We find that our new stable method has a large performance advantage over the Householder QR method. This holds both in a theoretical performance model as well as in an actual implementation

Frequency domain laser velocimeter signal processor

A new scheme for processing signals from laser velocimeter systems is described. The technique utilizes the capabilities of advanced digital electronics to yield a signal processor capable of operating in the frequency domain maximizing the information obtainable from each signal burst. This allows a sophisticated approach to signal detection and processing, with a more accurate measurement of the chirp frequency resulting in an eight-fold increase in measurable signals over the present high-speed burst counter technology. Further, the required signal-to-noise ratio is reduced by a factor of 32, allowing measurements within boundary layers of wind tunnel models. Measurement accuracy is also increased up to a factor of five

Procedures for characterizing an alloy and predicting cyclic life with the total strain version of Strainrange Partitioning

Procedures are presented for characterizing an alloy and predicting cyclic life for isothermal and thermomechanical fatigue conditions by using the total strain version of strainrange partitioning (TS-SRP). Numerical examples are given. Two independent alloy characteristics are deemed important: failure behavior, as reflected by the inelastic strainrange versus cyclic life relations; and flow behavior, as indicated by the cyclic stress-strain-time response (i.e., the constitutive behavior). Failure behavior is characterized by conducting creep-fatigue tests in the strain regime, wherein the testing times are reasonably short and the inelastic strains are large enough to be determined accurately. At large strainranges, stress-hold, strain-limited tests are preferred because a high rate of creep damage per cycle is inherent in this type of test. At small strainranges, strain-hold cycles are more appropriate. Flow behavior is characterized by conducting tests wherein the specimen is usually cycled far short of failure and the wave shape is appropriate for the duty cycle of interest. In characterizing an alloy pure fatigue, or PP, failure tests are conducted first. Then depending on the needs of the analyst a series of creep-fatigue tests are conducted. As many of the three generic SRP cycles are featured as are required to characterize the influence of creep on fatigue life (i.e., CP, PC, and CC cycles, respectively, for tensile creep only, compressive creep only, and both tensile and compressive creep). Any mean stress effects on life also must be determined and accounted for when determining the SRP inelastic strainrange versus life relations for cycles featuring creep. This is particularly true for small strainranges. The life relations thus are established for a theoretical zero mean stress condition

Calculation of thermomechanical fatigue life based on isothermal behavior

The isothermal and thermomechanical fatigue (TMF) crack initiation response of a hypothetical material was analyzed. Expected thermomechanical behavior was evaluated numerically based on simple, isothermal, cyclic stress-strain - time characteristics and on strainrange versus cyclic life relations that have been assigned to the material. The attempt was made to establish basic minimum requirements for the development of a physically accurate TMF life-prediction model. A worthy method must be able to deal with the simplest of conditions: that is, those for which thermal cycling, per se, introduces no damage mechanisms other than those found in isothermal behavior. Under these assumed conditions, the TMF life should be obtained uniquely from known isothermal behavior. The ramifications of making more complex assumptions will be dealt with in future studies. Although analyses are only in their early stages, considerable insight has been gained in understanding the characteristics of several existing high-temperature life-prediction methods. The present work indicates that the most viable damage parameter is based on the inelastic strainrange

Learning on the quick and cheap: gains from trade through imported expertise

Gains from productivity and knowledge transmission arising from the presence of foreign firms has received a good deal of empirical attention, but micro-foundations for this mechanism are weak . Here we focus on production by foreign experts who may train domestic unskilled workers who work with them. Gains from training can in turn be decomposed into two types: (a) obtaining knowledge and skills at a lower cost than if they are self-taught at home, (b) producing domestic skilled workers earlier in time than if they the domestic economy had to rediscover the relevant knowledge through "reinventing the wheel". We develop a three-period model in which the economy initially has no skilled workers. Workers can withdraw from the labor force for two periods of self study and then produce as skilled workers in the third period. Alternatively, foreign experts can be hired in period 1 and domestic unskilled labor working with the experts become skilled in the second period. We analyze how production, training, and welfare depend on two important parameters: the cost of foreign experts and the learning (or "absorptive") capacity of the domestic economy. --learning,transmission mechanism,multinationals,imported

Life prediction of thermomechanical fatigue using total strain version of strainrange partitioning (SRP): A proposal

A method is proposed (without experimental verification) for extending the total strain version of Strainrange Partitioning (TS-SRP) to predict the lives of thermomechanical fatigue (TMF) cycles. The principal feature of TS SRP is the determination of the time-temperature-waveshape dependent elastic strainrange versus life lines that are added subsequently to the classical inelastic strainrange versus life lines to form the total strainrange versus life relations. The procedure is based on a derived relation between failure and flow behavior. Failure behavior is represented by conventional SRP inelastic strainrange versus cyclic life relations, while flow behavior is captured in terms of the cyclic stress-strain response characteristics. Stress-strain response is calculated from simple equations developed from approximations to more complex cyclic constitutive models. For applications to TMF life prediction, a new testing technique, bithermal cycling, is proposed as a means for generating the inelastic strainrange versus life relations. Flow relations for use in predicting TMF lives would normally be obtained from approximations to complex thermomechanical constitutive models. Bithermal flow testing is also proposed as an alternative to thermomechanical flow testing at low strainranges where the hysteresis loop is difficult to analyze

Learning on the Quick and Cheap: Gains from Trade Through Imported Expertise

Gains from productivity and knowledge transmission arising from the presence of foreign firms has received a good deal of empirical attention, but micro-foundations for this mechanism are weak . Here we focus on production by foreign experts who may train domestic unskilled workers who work with them. Gains from training can in turn be decomposed into two types: (a) obtaining knowledge and skills at a lower cost than if they are self-taught at home, (b) producing domestic skilled workers earlier in time than if they the domestic economy had to rediscover the relevant knowledge through reinventing the wheel'. We develop a three-period model in which the economy initially has no skilled workers. Workers can withdraw from the labor force for two periods of self study and then produce as skilled workers in the third period. Alternatively, foreign experts can be hired in period 1 and domestic unskilled labor working with the experts become skilled in the second period. We analyze how production, training, and welfare depend on two important parameters: the cost of foreign experts and the learning (or absorptive') capacity of the domestic economy.

Financial Barriers to International Trade in North Dakota

International Relations/Trade,

Stability of optically-active charged excitons in quasi-two dimensional systems

A negatively charged quasi-two dimensional exciton ($X^-$) is solved exactly numerically in the presence of a uniform perpendicular B-field. Various quasi-two dimensional geometries are studied. The charge distribution of the $X^-$ parallel to the B-field is found to be crucial in determining the stability of the optically-active $X^-$ and hence its photoluminescence (PL) signature. The theory provides a quantitative explanation of recent experimental results obtained for a GaAs quantum well. Effects are found which cannot be described within a lowest Landau level approximation. PACS: 78.20.Ls 78.66.-w 73.20.DxComment: Minor revisions, mainly removal of the term trion in favour of the term charged-exciton to comply with Physical Review B. To be published as a Rapid Communication in Physical Review