Multiprocessing the Sieve of Eratosthenes

The Sieve of Eratosthenes for finding prime numbers in recent years has seen much use as a benchmark algorithm for serial computers while its intrinsically parallel nature has gone largely unnoticed. The implementation of a parallel version of this algorithm for a real parallel computer, the Flex/32, is described and its performance discussed. It is shown that the algorithm is sensitive to several fundamental performance parameters of parallel machines, such as spawning time, signaling time, memory access, and overhead of process switching. Because of the nature of the algorithm, it is impossible to get any speedup beyond 4 or 5 processors unless some form of dynamic load balancing is employed. We describe the performance of our algorithm with and without load balancing and compare it with theoretical lower bounds and simulated results. It is straightforward to understand this algorithm and to check the final results. However, its efficient implementation on a real parallel machine requires thoughtful design, especially if dynamic load balancing is desired. The fundamental operations required by the algorithm are very simple: this means that the slightest overhead appears prominently in performance data. The Sieve thus serves not only as a very severe test of the capabilities of a parallel processor but is also an interesting challenge for the programmer

Partitioning problems in parallel, pipelined and distributed computing

The problem of optimally assigning the modules of a parallel program over the processors of a multiple computer system is addressed. A Sum-Bottleneck path algorithm is developed that permits the efficient solution of many variants of this problem under some constraints on the structure of the partitions. In particular, the following problems are solved optimally for a single-host, multiple satellite system: partitioning multiple chain structured parallel programs, multiple arbitrarily structured serial programs and single tree structured parallel programs. In addition, the problems of partitioning chain structured parallel programs across chain connected systems and across shared memory (or shared bus) systems are also solved under certain constraints. All solutions for parallel programs are equally applicable to pipelined programs. These results extend prior research in this area by explicitly taking concurrency into account and permit the efficient utilization of multiple computer architectures for a wide range of problems of practical interest

A partitioning strategy for nonuniform problems on multiprocessors

The partitioning of a problem on a domain with unequal work estimates in different subddomains is considered in a way that balances the work load across multiple processors. Such a problem arises for example in solving partial differential equations using an adaptive method that places extra grid points in certain subregions of the domain. A binary decomposition of the domain is used to partition it into rectangles requiring equal computational effort. The communication costs of mapping this partitioning onto different microprocessors: a mesh-connected array, a tree machine and a hypercube is then studied. The communication cost expressions can be used to determine the optimal depth of the above partitioning

Shuffle-exchanges on augmented meshes

A mesh connected array of size N = two to the Kth power, K an integer, can be augmented by adding at most one edge per node such that it can perform a shuffle-exchange of size N/2 in constant time. A shuffle-exchange of size N is performed on this augmented array in constant time. This is done by combining the available perfect shuffle of size N/2 with the existing nearest neighbor connections of the mesh. By carefully scheduling the different permutations that are composed in order to achieve the shuffle, the time required is reduced to 5 steps, which is optimal for this network

Forecasting Inflation Through Econometric Models : an Empirical Study on Pakistani Data

Bu makale Pakistan’daki enflasyonu modellemeyi ve tahmin etmeyi amaçlamaktadır. Bunun için bir takım ekonometrik yaklaşımlar uygulanmış ve sonuçları karşılaştırılmıştır. ARIMA modellerinde p ve/veya q için fazladan gecikme eklenmesi, hesaplanan hata terimlerinin karelerinin toplamını her zaman azaltmadığı görülmüştür. Gecikmeli değerlerle bir model oluşturulduğunda ise bazı gözlemlerin kaybedildiği ortaya çıkmıştır. Sonuçlar ayrıca şunu göstermiştir ki VAR modelleri ARIMA (2,1,2) modellerinden daha iyi performans sergilememekte ve iki faktörlü ARIMA (2,1,2) modeli ARIMA (2,1,2) modelinden az da olsa daha iyi sonuçlar ortaya koymaktadır. Bu çalışma makroekonomik tahmin sorunu üzerine odaklanmasına rağmen elde edilen ampirik sonuçlar küçük ölçekli makro-ekonometrik modeller için daha genel implikasyonlar taşımaktadır.This article aims at modeling and forecasting inflation in Pakistan. For this purpose a number of econometric approaches are implemented and their results are compared. In ARIMA models, adding additional lags for p and/or q necessarily reduced the sum of squares of the estimated residuals. When a model is estimated using lagged variables, some observations are lost. Results further indicate that the VAR models do not perform better than the ARIMA (2, 1, 2) models and, the two factor model with ARIMA (2, 1, 2) slightly performs better than the ARIMA (2, 1, 2). Although the study focuses on the problem of macroeconomic forecasting, the empirical results have more general implications for small scale macroeconometric models

Demand estimation and merger simulations for drugs: Logits v. AIDS

We use ADHD drugs sales data from 2000-2003 and compare estimates of elasticities and merger simulations from three different demand models. Models include logit, random coefficients logit, and conditional AIDS demand model with multistage budgeting. The magnitude of cross-price elasticities is larger in the third model in comparison to the first two, and some of the cross-price elasticities are estimated to be negative. Hypothetical merger simulations show larger price effects for the multistage AIDS model in comparison to the discrete choice models

Forecasting Inflation Through Econometric Models : an Empirical Study on Pakistani Data

Bu makale Pakistan’daki enflasyonu modellemeyi ve tahmin etmeyi amaçlamaktadır. Bunun için bir takım ekonometrik yaklaşımlar uygulanmış ve sonuçları karşılaştırılmıştır. ARIMA modellerinde p ve/veya q için fazladan gecikme eklenmesi, hesaplanan hata terimlerinin karelerinin toplamını her zaman azaltmadığı görülmüştür. Gecikmeli değerlerle bir model oluşturulduğunda ise bazı gözlemlerin kaybedildiği ortaya çıkmıştır. Sonuçlar ayrıca şunu göstermiştir ki VAR modelleri ARIMA (2,1,2) modellerinden daha iyi performans sergilememekte ve iki faktörlü ARIMA (2,1,2) modeli ARIMA (2,1,2) modelinden az da olsa daha iyi sonuçlar ortaya koymaktadır. Bu çalışma makroekonomik tahmin sorunu üzerine odaklanmasına rağmen elde edilen ampirik sonuçlar küçük ölçekli makro-ekonometrik modeller için daha genel implikasyonlar taşımaktadır.This article aims at modeling and forecasting inflation in Pakistan. For this purpose a number of econometric approaches are implemented and their results are compared. In ARIMA models, adding additional lags for p and/or q necessarily reduced the sum of squares of the estimated residuals. When a model is estimated using lagged variables, some observations are lost. Results further indicate that the VAR models do not perform better than the ARIMA (2, 1, 2) models and, the two factor model with ARIMA (2, 1, 2) slightly performs better than the ARIMA (2, 1, 2). Although the study focuses on the problem of macroeconomic forecasting, the empirical results have more general implications for small scale macroeconometric models

Augmenting computer networks

Three methods of augmenting computer networks by adding at most one link per processor are discussed: (1) A tree of N nodes may be augmented such that the resulting graph has diameter no greater than 4log sub 2((N+2)/3)-2. Thi O(N(3)) algorithm can be applied to any spanning tree of a connected graph to reduce the diameter of that graph to O(log N); (2) Given a binary tree T and a chain C of N nodes each, C may be augmented to produce C so that T is a subgraph of C. This algorithm is O(N) and may be used to produce augmented chains or rings that have diameter no greater than 2log sub 2((N+2)/3) and are planar; (3) Any rectangular two-dimensional 4 (8) nearest neighbor array of size N = 2(k) may be augmented so that it can emulate a single step shuffle-exchange network of size N/2 in 3(t) time steps

Antimicrobial and phytotoxic screening of various fractions of Sonchus asper

Sonchus asper is used in the treatment of many diseases ethnopharmacologically in Pakistan. In the present manuscript we demonstrate the antimicrobial and phytotoxic effects of various fractions of S.asper. Six (6) different bacteria (Escherichia coli, Bacillus subtilis, Micrococcus luteus, klebsiella pneumoniae, Staphylococcus aureus and Pseudomonas aeruginosa) are used in the screening of extract as well as 4 strains of fungi are characterized. Raddish root inhibition assay was used for phytotoxic screening. Methanolic fraction of S. asper showed best activities in all of assays, in inhibition of microbes and phytotoxic activities. The potency of these activities is due to the presence of bioactive flavonoids, saponins and phenolic compounds