Karhunen-Loeve representation of stochastic ocean waves

A new stochastic representation of a seastate is developed based on the Karhunen–Loeve spectral decomposition of stochastic signals and the use of Slepian prolate spheroidal wave functions with a tunable bandwidth parameter. The new representation allows the description of stochastic ocean waves in terms of a few independent sources of uncertainty when the traditional representation of a seastate in terms of Fourier series requires an order of magnitude more independent components. The new representation leads to parsimonious stochastic models of the ambient wave kinematics and of the nonlinear loads and responses of ships and offshore platforms. The use of the new representation is discussed for the derivation of critical wave episodes, the derivation of up-crossing rates of nonlinear loads and responses and the joint stochastic representation of correlated wave and wind profiles for use in the design of fixed or floating offshore wind turbines. The forecasting is also discussed of wave elevation records and vessel responses for use in energy yield enhancement of compliant floating wind turbines.ALSTOM (Firm)Ente nazionale per l'energia elettricab_TE

The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations

We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels $K(x,y)=2$, $x+y$ and $xy$. In another work, we classified all self-similar solutions and all universality classes (domains of attraction) for scaling limits under weak convergence (Comm. Pure Appl. Math 57 (2004)1197-1232). Here we add to this a complete description of the set of all limit points of solutions modulo scaling (the scaling attractor) and the dynamics on this limit set (the ultimate dynamics). The main tool is Bertoin's L\'{e}vy-Khintchine representation formula for eternal solutions of Smoluchowski's equation (Adv. Appl. Prob. 12 (2002) 547--64). This representation linearizes the dynamics on the scaling attractor, revealing these dynamics to be conjugate to a continuous dilation, and chaotic in a classical sense. Furthermore, our study of scaling limits explains how Smoluchowski dynamics ``compactifies'' in a natural way that accounts for clusters of zero and infinite size (dust and gel)

Выявление понятий и их взаимосвязей в рамках технологии контент-мониторинга

Приведены подходы к решению проблемы выявления фактографической информации из неструктурированных текстовых потоков. Описаны технологические решения, позволяющие извлекать из полнотекстовых документов такие понятия как фирмы, фамилии, географические названия и т.п., а также выявлять силу их взаимосвязей на основе применения двух алгоритмов. Первый из этих алгоритмов основывается на учете совместного вхождения понятий в одни и те же документы, а второй на учете общего для рассматриваемых понятий контекста.Наведено підходи до вирішення проблеми виявлення фактографічної інформації з неструктурованих текстових потоків. Описано технологічні рішення, що дозволяють добути з повнотекстових документів такі поняття як фірми, прізвища, географічні назви тощо, а також виявляти силу їхніх взаємозв’язків на базі застосування двох алгоритмів. Перший з цих алгоритмів базується на врахуванні спільного входження понять до одних і тих самих документів, а другий — на врахуванні загального для понять, що розглядаються, контексту.Approaches to the solution of a problem of revealing factual information from unstructured text flows are given. The technological solutions, allowing to take from text-through documents such concepts as a firm, a surname, place names, etc., and also to reveal force of their interrelations on the basis of application of two algorithms are described. The first of these algorithms is based on the account of joint concepts occurrence in the same documents, and the second one on the account of the context common for considered concepts