Участник:Valerie Kovaleva
Материал из MachineLearning.
(→Весна 2016, 6-й семестр) |
(→Осень 2016, 7-й семестр) |
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Abstract | Abstract | ||
| - | The spectral statistics of ensembles of exponentially weighted full binary trees and p-branching star graphs is investigated. It is shown that spectral densities demonstrate peculiar ultrametric structure typical for sparse graphs. In particular, the tails of the distribution for binary trees share the "Lifshitz behavior" | + | The spectral statistics of ensembles of exponentially weighted full binary trees and p-branching star graphs is investigated. It is shown that spectral densities demonstrate peculiar ultrametric structure typical for sparse graphs. In particular, the tails of the distribution for binary trees share the "Lifshitz behavior" ρ(λ) ~ exp(−c/√(λmax−λ)) typical for the one-dimensional Anderson localization, while the spectral statistics of p-branching star graphs strongly depends on p. Our analysis is applicable to polydisperse diluted solutions of fully branched tree-like and star-like macromolecules known as dendrimers. |
Статья загружена на arXiv [https://arxiv.org/abs/1612.01002]. | Статья загружена на arXiv [https://arxiv.org/abs/1612.01002]. | ||
Версия 15:05, 13 декабря 2016
МФТИ, ФУПМ
Кафедра "Интеллектуальные системы"
Направление "Интеллектуальный анализ данных"
valeriya.kovaleva@phystech.edu
Научно-исследовательская работа
Весна 2016, 6-й семестр
"Spectra of tree ensembles", V. Kovaleva, O. Valba
Abstract
This paper is devoted to spectra of sparse macromolecular clusters. We suggest such clusters to be modeled by unweighed undirected tree ensembles with size distributed in a certain known way. The goal of this work is to compute spectra of such ensembles analytically as spectra of their adjacency matrices. The motivation to the problem investigated is computing spectra of Bernoulli noise in sparse matrices which is essential in cases when the scale of the data and the noise is the same. We solve the special cases of star trees and full binary trees interpreting them as generalized Bethe trees. The target function of an individual tree is supposed to depend on the size of the tree and of an ensemble - on size distribution.
Keywords: binary trees; star trees; spectrum
Статья опубликована в трудах конференции ИТИС 2016.
Осень 2016, 7-й семестр
"Peculiar spectral statistics of ensembles of branched polymers", V. Kovaleva, Yu. Maximov, S. Nechaev, O. Valba
Abstract
The spectral statistics of ensembles of exponentially weighted full binary trees and p-branching star graphs is investigated. It is shown that spectral densities demonstrate peculiar ultrametric structure typical for sparse graphs. In particular, the tails of the distribution for binary trees share the "Lifshitz behavior" ρ(λ) ~ exp(−c/√(λmax−λ)) typical for the one-dimensional Anderson localization, while the spectral statistics of p-branching star graphs strongly depends on p. Our analysis is applicable to polydisperse diluted solutions of fully branched tree-like and star-like macromolecules known as dendrimers.
Статья загружена на arXiv [1].
