Continuous dual Hahn polynomials

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Weighted-based NC calculation in Phoenix

Phoenix is a decentralized network coordinate (NC) system based on the matrix factorization model.[1]

Background

  • Network coordinates (NC) system[2] is an efficient mechanism for Internet distance (round-trip latency) prediction with scalable measurements. For a network with N hosts, by performing O(N) measurements, all N*N distances can be predicted.
  • Use cases: Vuze BitTorrent, application layer multicast, PeerWise overlay, multi-player online gaming.
  • Triangle inequality violation (TIV) is widely exist on the Internet due to the current sub-optimal Internet routing.

Model

  • Most of the prior NC systems utilize the Euclidean distance model, i.e., embeds N hosts into a d-dimensional Euclidean space Rd. Due to the wide existence of TIV on the Internet, the prediction accuracy of such systems is limited. Phoenix chooses Matrix factorization (MF) model, which does not have the constraint of TIV.
  • The linear dependence among the rows motivates the factorization of Internet distance matrix, i.e., for a system with N Internet nodes, the N×N Internet distance matrix D can be factorized into two smaller matrices. DXYT where X and Y are N×d matrices (d << N). This matrix factorization is essentially a problem of linear dimensionality reduction, while Phoenix try to solve it via a distributed way.

Design choices in Phoenix

  • Different from the existing MF based NC systems such as IDES[3] and DMF,[4] Phoenix introduces a weight to each reference NC and trusts the NCs with higher weight values more than the others. The weight based mechanism can substantially reduce the impact of the error propagation.
  • For node discovery, Phoenix utilizes a distributed scheme, so-called Peer exchange (PEX), which is used in BitTorrent (protocol). The usage of PEX reduces the load of the tracker, while still ensuring the prediction accuracy under node churn.
  • Similar to DMF, for avoiding the potential drift of the NCs, Regularization (mathematics) is introduced in NC calculation.
  • NCShield[5] is a decentralized, goosip-based trust and reputation system to secure Phoenix and other matrix factorization-based NC systems.

See also

References

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    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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