![Self-polar Polytopes and Sequential Importance Sampling Algorithms için kapak resmi Self-polar Polytopes and Sequential Importance Sampling Algorithms için kapak resmi](/client/assets/d79c3e4af2b6d196/ctx/images/no_image.png)
Self-polar Polytopes and Sequential Importance Sampling Algorithms
Başlık:
Self-polar Polytopes and Sequential Importance Sampling Algorithms
Yazar:
Jensen, Alathea, author. (orcid)0000-0002-2399-0815
ISBN:
9780438114920
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (124 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: James F. Lawrence; Isabel M. Beichl Committee members: Walter D. Morris; Valeriu Soltan.
Özet:
The first part of this dissertation is on the topic of self-polar polytopes, which are polytopes that are orthogonal transformations of their polar sets. These polytopes were first studied by Lovasz as a means of establishing the chromatic number of distance graphs on spheres, and they can also be used to construct triangle-free graphs with arbitrarily high chromatic number. We investigate the existence, construction, facial structure, and practical applications of self-polar polytopes, as well as the place of these polytopes within the broader set of self-dual polytopes.
The second part of this dissertation is on the topic of sequential importance sampling algorithms. A great many varied problems in the computational sciences can be solved by counting the leaves of a decision tree, or, more generally, summing a cost function over the nodes of the tree. The main two classes of algorithms for summing a cost function over a tree are Markov chain Monte Carlo methods and sequential importance sampling. We explore in depth the application of our algorithm to counting linear extensions of a partially ordered set. We also provide a generalization of one of the newest sequential importance sampling algorithms, stochastic enumeration, and conduct rigorous analysis, both theoretical and numerical, to the resulting algorithm.
Notlar:
School code: 0883
Tüzel Kişi Ek Girişi:
Mevcut:*
Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(691975.1) | 691975-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
On Order
Liste seç
Bunu varsayılan liste yap.
Öğeler başarıyla eklendi
Öğeler eklenirken hata oldu. Lütfen tekrar deneyiniz.
:
Select An Item
Data usage warning: You will receive one text message for each title you selected.
Standard text messaging rates apply.