Interconnection networks for parallel and distributed computing

Parallel computers are generally either shared-memory machines or distributed- memory machines. There are currently technological limitations on shared-memory architectures and so parallel computers utilizing a large number of processors tend tube distributed-memory machines. We are concerned solely with distributed-memory multiprocessors. In such machines, the dominant factor inhibiting faster global computations is inter-processor communication. Communication is dependent upon the topology of the interconnection network, the routing mechanism, the flow control policy, and the method of switching. We are concerned with issues relating to the topology of the interconnection network. The choice of how we connect processors in a distributed-memory multiprocessor is a fundamental design decision. There are numerous, often conflicting, considerations to bear in mind. However, there does not exist an interconnection network that is optimal on all counts and trade-offs have to be made. A multitude of interconnection networks have been proposed with each of these networks having some good (topological) properties and some not so good. Existing noteworthy networks include trees, fat-trees, meshes, cube-connected cycles, butterflies, Möbius cubes, hypercubes, augmented cubes, k-ary n-cubes, twisted cubes, n-star graphs, (n, k)-star graphs, alternating group graphs, de Bruijn networks, and bubble-sort graphs, to name but a few. We will mainly focus on k-ary n-cubes and (n, k)-star graphs in this thesis. Meanwhile, we propose a new interconnection network called augmented k-ary n- cubes. The following results are given in the thesis.1. Let k ≥ 4 be even and let n ≥ 2. Consider a faulty k-ary n-cube Q(^k_n) in which the number of node faults f(_n) and the number of link faults f(_e) are such that f(_n) + f(_e) ≤ 2n - 2. We prove that given any two healthy nodes s and e of Q(^k_n), there is a path from s to e of length at least k(^n) - 2f(_n) - 1 (resp. k(^n) - 2f(_n) - 2) if the nodes s and e have different (resp. the same) parities (the parity of a node Q(^k_n) in is the sum modulo 2 of the elements in the n-tuple over 0, 1, ∙∙∙ , k - 1 representing the node). Our result is optimal in the sense that there are pairs of nodes and fault configurations for which these bounds cannot be improved, and it answers questions recently posed by Yang, Tan and Hsu, and by Fu. Furthermore, we extend known results, obtained by Kim and Park, for the case when n = 2.2. We give precise solutions to problems posed by Wang, An, Pan, Wang and Qu and by Hsieh, Lin and Huang. In particular, we show that Q(^k_n) is bi-panconnected and edge-bipancyclic, when k ≥ 3 and n ≥ 2, and we also show that when k is odd, Q(^k_n) is m-panconnected, for m = (^n(k - 1) + 2k - 6’ / ‘_2), and (k -1) pancyclic (these bounds are optimal). We introduce a path-shortening technique, called progressive shortening, and strengthen existing results, showing that when paths are formed using progressive shortening then these paths can be efficiently constructed and used to solve a problem relating to the distributed simulation of linear arrays and cycles in a parallel machine whose interconnection network is Q(^k_n) even in the presence of a faulty processor.3. We define an interconnection network AQ(^k_n) which we call the augmented k-ary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube Q(^k_n) has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube Q(^k_n) - is a Cayley graph (and so is vertex-symmetric); has connectivity 4n - 2, and is such that we can build a set of 4n - 2 mutually disjoint paths joining any two distinct vertices so that the path of maximal length has length at most max{{n- l)k- (n-2), k + 7}; has diameter [(^k) / (_3)] + [(^k - 1) /( _3)], when n = 2; and has diameter at most (^k) / (_4) (n+ 1), for n ≥ 3 and k even, and at most [(^k)/ (_4) (n + 1) + (^n) / (_4), for n ^, for n ≥ 3 and k odd.4. We present an algorithm which given a source node and a set of n - 1 target nodes in the (n, k)-star graph S(_n,k) where all nodes are distinct, builds a collection of n - 1 node-disjoint paths, one from each target node to the source. The collection of paths output from the algorithm is such that each path has length at most 6k - 7, and the algorithm has time complexity O(k(^3)n(^4))

The p-widths of a surface

The $p$-widths of a closed Riemannian manifold are a nonlinear analogue of the spectrum of its Laplace--Beltrami operator, which corresponds to areas of a certain min-max sequence of minimal submanifolds. We show that the $p$-widths of any closed Riemannian two-manifold correspond to a union of closed immersed geodesics, rather than simply geodesic nets. We then prove optimality of the sweepouts of the round two-sphere constructed from the zero set of homogeneous polynomials, showing that the $p$-widths of the round sphere are attained by $\lfloor \sqrt p \rfloor$ great circles. As a result, we find the universal constant in the Liokumovich--Marques--Neves--Weyl law for surfaces to be $\sqrt \pi$. En route to calculating the $p$-widths of the round two-sphere, we prove two additional new results: a bumpy metrics theorem for stationary geodesic nets, and that, generically, stationary geodesic nets with bounded mass and bounded singular set have Lusternik--Schnirelmann category zero.Comment: All comments welcom

C-Band Airport Surface Communications System Standards Development. Phase II Final Report. Volume 1: Concepts of Use, Initial System Requirements, Architecture, and AeroMACS Design Considerations

This report is provided as part of ITT s NASA Glenn Research Center Aerospace Communication Systems Technical Support (ACSTS) contract NNC05CA85C, Task 7: New ATM Requirements-Future Communications, C-Band and L-Band Communications Standard Development and was based on direction provided by FAA project-level agreements for New ATM Requirements-Future Communications. Task 7 included two subtasks. Subtask 7-1 addressed C-band (5091- to 5150-MHz) airport surface data communications standards development, systems engineering, test bed and prototype development, and tests and demonstrations to establish operational capability for the Aeronautical Mobile Airport Communications System (AeroMACS). Subtask 7-2 focused on systems engineering and development support of the L-band digital aeronautical communications system (L-DACS). Subtask 7-1 consisted of two phases. Phase I included development of AeroMACS concepts of use, requirements, architecture, and initial high-level safety risk assessment. Phase II builds on Phase I results and is presented in two volumes. Volume I (this document) is devoted to concepts of use, system requirements, and architecture, including AeroMACS design considerations. Volume II describes an AeroMACS prototype evaluation and presents final AeroMACS recommendations. This report also describes airport categorization and channelization methodologies. The purposes of the airport categorization task were (1) to facilitate initial AeroMACS architecture designs and enable budgetary projections by creating a set of airport categories based on common airport characteristics and design objectives, and (2) to offer high-level guidance to potential AeroMACS technology and policy development sponsors and service providers. A channelization plan methodology was developed because a common global methodology is needed to assure seamless interoperability among diverse AeroMACS services potentially supplied by multiple service providers

Spatiotemporal network coding of physiological mossy fiber inputs by the cerebellar granular layer

The granular layer, which mainly consists of granule and Golgi cells, is the first stage of the cerebellar cortex and processes spatiotemporal information transmitted by mossy fiber inputs with a wide variety of firing patterns. To study its dynamics at multiple time scales in response to inputs approximating real spatiotemporal patterns, we constructed a large-scale 3D network model of the granular layer. Patterned mossy fiber activity induces rhythmic Golgi cell activity that is synchronized by shared parallel fiber input and by gap junctions. This leads to long distance synchrony of Golgi cells along the transverse axis, powerfully regulating granule cell firing by imposing inhibition during a specific time window. The essential network mechanisms, including tunable Golgi cell oscillations, on-beam inhibition and NMDA receptors causing first winner keeps winning of granule cells, illustrate how fundamental properties of the granule layer operate in tandem to produce (1) well timed and spatially bound output, (2) a wide dynamic range of granule cell firing and (3) transient and coherent gating oscillations. These results substantially enrich our understanding of granule cell layer processing, which seems to promote spatial group selection of granule cell activity as a function of timing of mossy fiber input

NASA earth science and applications division: The program and plans for FY 1988-1989-1990

Described here are the Division's research goals, priorities and emphases for the next several years and an outline of longer term plans. Included are highlights of recent accomplishments, current activities in FY 1988, research emphases in FY 1989, and longer term future plans. Data and information systems, the Geodynamics Program, the Land Processes Program, the Oceanic Processes Program, the Atmospheric Dynamics and Radiation Program, the Atmospheric Chemistry Program, and space flight programs are among the topic covered

Cargo Logistics Airlift Systems Study (CLASS). Volume 3: Cross impact between the 1990 market and the air physical distribution systems, book 1

The interrelations between the infrastructure and the forecast future market are discussed. Also, using forecasts of market growth for a base, future aircraft and air service concepts were evaluated

Problem solving in biology at university level

The preliminary study sought to identify the main areas of the first year biology curriculum where students tended to encounter difficulties. These areas were seen to encompass potential themes where open-ended problems might be devised: light and dark reactions in photosynthesis, phytochrome and germination, cell mediated immunity, antibodies, the immunological armoury and gene function and gene expression in plant growth. The main experiment had three stages. In each stage, a battery of tests (cognitive and attitudinal) was used and the outcomes related to students' performance on an open-ended problem. Four new open-ended problem-solving units were developed. The battery of tests in the first stage 9with 642 students) were True-False tests, a Word Association Test, a Structural Communication Grid test and assessments of attitudes to learning (using a Perry Position Questionnaire). Several open-ended problems were devised and used but the outcomes from the cognitive tests were related to one individual problem-solving unit on the topic: forests that Need Fires. This stage attempted to gain some kind of insight into the extent to which nodes and links in long term memory contribute to success in problem solving. The results indicated that problem-solving success might be related to factual knowledge, links between nodes of knowledge and understanding. However, generic ability in biology might offer an alternative explanation. To test the latter, stage two involved the same sample of students in a second battery of tests, most which were on a parallel but unrelated topic: Evolution. The outcomes showed that, while some kind of generic biological ability was a factor, this did not seem to explain all the correlations observed in the first stage. The third stage approached from a fresh perspective. Working with 525 students, this involved the same four problem based units but a new set of tests was applied: tests of Lateral Thinking, a test of Convergency / Divergency, another Ranking test and a Self-Report Questionnaire. The results suggested that the number of accessible nodes and links in long term memory (reflecting 'brain architecture' and, perhaps, aspects of cognitive styles) do seem to be related to success in a problem-solving task. However, it is recognised that the validity of the test battery is an important issue in drawing such conclusions. This study raised important questions: is the way of string the knowledge or the order of storage a factor? Is it something relating to the physical factors such as structure of the brain (architecture) in terms of neurons and synapses, psychological factors such as structure of information in terms of nodes and links or emotional factors such as desire and willingness to store specific ideas other than others (knowledge filtration)? While it is well known that working memory is a key factor in determining problem-solving success (and this was not explored further in this study), the study suggests that the following factors may be important in leading to success with open-ended problems in biology: Factual knowledge held in long term memory; Understanding of conceptual knowledge; Generic biological ability (skill); Number of accessible nodes and links in long term memory; Effect of 'brain architecture'; and Aspects of cognitive styles (divergency, creativity or lateral thinking)

Oceanus.

v. 34, no. 1 (1991