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Torus-connected cycles: A simple and scalable topology for interconnection networks

Bossard A., Kaneko K.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 4

723--735

EN

Supercomputers are today made up of hundreds of thousands of nodes. The interconnection network is responsible for connecting all these nodes to each other. Different interconnection networks have been proposed; high performance topologies have been introduced as a replacement for the conventional topologies of recent decades. A high order, a low degree and a small diameter are the usual properties aimed for by such topologies. However, this is not sufficient to lead to actual hardware implementations. Network scalability and topology simplicity are two critical parameters, and they are two of the reasons why modern supercomputers are often based on torus interconnection networks (e.g., Fujitsu K, IBM Sequoia). In this paper we first describe a new topology, torus-connected cycles (TCCs), realizing a combination of a torus and a ring, thus retaining interesting properties of torus networks in addition to those of hierarchical interconnection networks (HINs). Then, we formally establish the diameter of a TCC, and deduce a point-to-point routing algorithm. Next, we propose routing algorithms solving the Hamiltonian cycle problem, and, in a two dimensional TCC, the Hamiltonian path one. Correctness and complexities are formally proved. The proposed algorithms are time-optimal.

2

A Hamiltonian approach to fault isolation in a planar vertical take-off and landing aircraft model

Rodriguez-Alfaro L. H., Alcorta-Garcia E., Lara D., Romero G.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 1

65--76

EN

The problem of fault detection and isolation in a class of nonlinear systems having a Hamiltonian representation is considered. In particular, a model of a planar vertical take-off and landing aircraft with sensor and actuator faults is studied. A Hamiltonian representation is derived from an Euler–Lagrange representation of the system model considered. In this form, nonlinear decoupling is applied in order to obtain subsystems with (as much as possible) specific fault sensitivity properties. The resulting decoupled subsystem is represented as a Hamiltonian system and observer-based residual generators are designed. The results are presented through simulations to show the effectiveness of the proposed approach.

3

Metody hamiltonowskie w mechanice płynów

Icha A.

Modelowanie Inżynierskie

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2011

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T. 10, nr 41

135-142

PL

Praca dotyczy hamiltonowskiego sformułowania wybranych zagadnień mechaniki płynów. Krótko przedstawiono podstawowe fakty z zakresu mechaniki układów o skończonej liczbie stopni swobody w ujęciu lagranżowskim, hamiltonowskim i symplektycznym. Następnie uogólniono ten formalizm na przypadek układów ciągłych (cieczy) i w charakterze przykładu, zaprezentowano hamiltonowskie ujęcie niejednorodnego, stratyfikowanego termicznie i zasoleniowo przepływu geofizycznego w przybliżeniu „płytkiej wody".

EN

The paper deals with hamiltonian formulation of selected problems of fluid mechanics. Some basie facts from finite dimensional mechanical systems in lagrangian, hamiltonian and symplectic approaches arę reviewed, Next, the transition from discrete to continuous is described and the hamiltonian form of thermally and saltly stratified flow in „shallow water" approximation, is presented.