Об Одной Задаче Распознавания Последовательности, Включающей Повторяющийся Вектор

* Работа поддержана грантами РФФИ 09-01-00032, 07-07-00022 и грантом АВЦП Рособразования 2.1.1/3235Рассматривается дискретная экстремальная задача, к которой сводится один из вариантов проблемы помехоустойчивого off-line распознавания векторных последовательностей, включающих в качестве элемента квазипериодически повторяющийся вектор евклидова пространства. Обоснован эффективный алгоритм решения задачи, гарантирующий оптимальность решения по критерию максимального правдоподобия в случае, когда помеха аддитивна и является гауссовской последовательностью независимых одинаково распределённых случайных величин

Kepler-36: A Pair of Planets with Neighboring Orbits and Dissimilar Densities

In the Solar system the planets' compositions vary with orbital distance, with rocky planets in close orbits and lower-density gas giants in wider orbits. The detection of close-in giant planets around other stars was the first clue that this pattern is not universal, and that planets' orbits can change substantially after their formation. Here we report another violation of the orbit-composition pattern: two planets orbiting the same star with orbital distances differing by only 10%, and densities differing by a factor of 8. One planet is likely a rocky `super-Earth', whereas the other is more akin to Neptune. These planets are thirty times more closely spaced--and have a larger density contrast--than any adjacent pair of planets in the Solar system.Comment: Accepted for publication in Science. Published online on June 21, 2012. Main Text and supplemental information included in a single merged file, 69 pages. Attachments to the supplemental material are available for free on Science websit

Kepler-36: A Pair of Planets with Neighboring Orbits and Dissimilar Densities

In the solar system, the planets’ compositions vary with orbital distance, with rocky planets in close orbits and lower-density gas giants in wider orbits. The detection of close-in giant planets around other stars was the first clue that this pattern is not universal and that planets’ orbits can change substantially after their formation. Here, we report another violation of the orbit-composition pattern: two planets orbiting the same star with orbital distances differing by only 10% and densities differing by a factor of 8. One planet is likely a rocky “super-Earth,” whereas the other is more akin to Neptune. These planets are 20 times more closely spaced and have a larger density contrast than any adjacent pair of planets in the solar system