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

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

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

Weyl collineations that are not curvature collineations

Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel". Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality".Comment: 9 page

Fibroblast Growth Factor 23 in Long-Duration Spaceflight

Many nutritional factors influence bone, from the basics of calcium and vitamin D, to factors which influence bone through acid/base balance, including protein, sodium, and more. Fibroblast growth factor 23 (FGF23) is a recently identified factor, secreted from osteocytes, which is involved in classic (albeit complex) feedback loops controlling phosphorus homeostasis through both vitamin D and parathyroid hormone (PTH) (1, 2). As osteocytes are gravity sensing cells, it is important to determine if there are changes in FGF23 during spaceflight. In extreme cases, such as chronic kidney disease, FGF23 levels are highly elevated. FGF23 imbalances, secondary to dietary influences, may contribute to skeletal demineralization and kidney stone risk during spaceflight

Fibroblast Growth Factor-23 in Bed Rest and Spaceflight

Many nutritional factors influence bone, from the basics of calcium and vitamin D, to factors which influence bone through acid/base balance, including protein, sodium, and more. Fibroblast growth factor 23 (FGF23) is a recently identified factor, secreted from osteocytes, which is involved in classic (albeit complex) feedback loops controlling phosphorus homeostasis through both vitamin D and parathyroid hormone (PTH) (1, 2). As osteocytes are gravity sensing cells, it is important to determine if there are changes in FGF23 during spaceflight. In extreme cases, such as chronic kidney disease, FGF23 levels are highly elevated. FGF23 imbalances, secondary to dietary influences, may contribute to skeletal demineralization and kidney stone risk during spaceflight. Presented with an imbalanced dietary phosphorus to calcium ratio, increased secretion of FGF23 will inhibit renal phosphorus reabsorption, resulting in increased excretion and reduced circulating phosphorus. Increased intake and excretion of phosphorus is associated with increased kidney stone risk in both the terrestrial and microgravity environments. Highly processed foods and carbonated beverages are associated with higher phosphorus content. Ideally, the dietary calcium to phosphorus ratio should be at minimum 1:1. Nutritional requirements for spaceflight suggest that this ratio not be less than 0.67 (3), while the International Space Station (ISS) menu provides 1020 mg Ca and 1856 mg P, for a ratio of 0.55 (3). Subjects in NASA's bed rest studies, by design, have consumed intake ratios much closer to 1.0 (4). FGF23 also has an inhibitory influence on PTH secretion and 1(alpha)-hydroxylase, both of which are required for activating vitamin D with the conversion of 25-hydroxyvitamin D to 1,25-dihydroxyvitamin D. Decreased 1,25-dihydroxyvitamin D will result in decreased intestinal phosphorus absorption, and increased urinary phosphorus excretion (via decreased renal reabsorption). Should a decrease in 1,25- dihydroxyvitamin D be necessary to reduce intestinal phosphorus absorption, calcium absorption will also proportionally be reduced, potentially leading to skeletal demineralization. Demineralization of bone can increase kidney stone risk, a medical issue that could prove detrimental to mission success. Given the interrelationships described above, we sought to determine circulating FGF23 concentrations in spaceflight and ground analog studies to better understand the potential effects of dietary phosphorus on bone and calcium metabolism. We analyzed serum from ISS astronauts participating in studies of bone biochemistry, including the Nutrition SMO and Pro K experiments, and we also evaluated FGF23 during extended-duration bed rest. Serum intact FGF23 levels were determined using an ELISA kit from Kainos laboratories in Japan. While initial evaluation of the data showed no changes over time during flight or bed rest, evaluation continues of FGF23 data in light of dietary factors, PTH, vitamin D status, and other biochemical and endocrine factors

Inflating Lorentzian Wormholes

It has been speculated that Lorentzian wormholes of the Morris- Thorne type might be allowed by the laws of physics at submicroscopic, e.g. Planck, scales and that a sufficiently advanced civilization might be able to enlarge them to classical size. The purpose of this paper is to explore the possibility that inflation might provide a natural mechanism for the enlargement of such wormholes to macroscopic size. A new classical metric is presented for a Lorentzian wormhole which is imbedded in a flat deSitter space. It is shown that the throat and proper length of the wormhole inflate. The resulting properties and stress-energy tensor associated with this metric are discussed.Comment: 24 pg

Energy Content of Colliding Plane Waves using Approximate Noether Symmetries

This paper is devoted to study the energy content of colliding plane waves using approximate Noether symmetries. For this purpose, we use approximate Lie symmetry method of Lagrangian for differential equations. We formulate the first-order perturbed Lagrangian for colliding plane electromagnetic and gravitational waves. It is shown that in both cases, there does not existComment: 18 pages, accepted for publication in Brazilian J Physic

Proper Weyl Collineations in Kantowski-Sachs and Bianchi Type III Space-Times

A study of proper Weyl collineations in Kantowski-Sachs and Bianchi type III space-times is given by using the rank of the 6X6 Weyl matrix and direct integration techniques. Studying proper Weyl collineations in each of the above space-times, it is shown that there exists no such possibility when the above space-times admit proper Weyl collineations.Comment: 5 page