MEXIT: Maximal un-coupling times for stochastic processes

Classical coupling constructions arrange for copies of the \emph{same} Markov process started at two \emph{different} initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two \emph{different} Markov (or other stochastic) processes to remain equal for as long as possible, when started in the \emph{same} state. We refer to this "un-coupling" or "maximal agreement" construction as \emph{MEXIT}, standing for "maximal exit". After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit \MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of \MEXIT for Brownian motions with two different constant drifts.Comment: 28 page

On the Impact of Fair Best Response Dynamics

In this work we completely characterize how the frequency with which each player participates in the game dynamics affects the possibility of reaching efficient states, i.e., states with an approximation ratio within a constant factor from the price of anarchy, within a polynomially bounded number of best responses. We focus on the well known class of congestion games and we show that, if each player is allowed to play at least once and at most $\beta$ times any $T$ best responses, states with approximation ratio $O(\beta)$ times the price of anarchy are reached after $T \lceil \log \log n \rceil$ best responses, and that such a bound is essentially tight also after exponentially many ones. One important consequence of our result is that the fairness among players is a necessary and sufficient condition for guaranteeing a fast convergence to efficient states. This answers the important question of the maximum order of $\beta$ needed to fast obtain efficient states, left open by [9,10] and [3], in which fast convergence for constant $\beta$ and very slow convergence for $\beta=O(n)$ have been shown, respectively. Finally, we show that the structure of the game implicitly affects its performances. In particular, we show that in the symmetric setting, in which all players share the same set of strategies, the game always converges to an efficient state after a polynomial number of best responses, regardless of the frequency each player moves with

Utilizing remote sensing of Thematic Mapper data to improve our understanding of estuarine processes and their influence on the productivity of estuarine-dependent fisheries

LANDSAT thematic mapper (TM) data are being used to refine and validate a stochastic spatial computer model to be applied to coastal resource management problems in Louisiana. Two major aspects of the research are: (1) the measurement of area of land (or emergent vegetation) and water and the length of the interface between land and water in TM imagery of selected coastal wetlands (sample marshes); and (2) the comparison of spatial patterns of land and water in the sample marshes of the imagery to that in marshes simulated by a computer model. In addition to activities in these two areas, the potential use of a published autocorrelation statistic is analyzed

Utilizing remote sensing of thematic mapper data to improve our understanding of estuarine processes and their influence on the productivity of estuarine-dependent fisheries

The land-water interface of coastal marshes may influence the production of estuarine-dependent fisheries more than the area of these marshes. To test this hypothesis, a spatial model was created to explore the dynamic relationship between marshland-water interface and level of disintegration in the decaying coastal marshes of Louisiana's Barataria, Terrebonne, and Timbalier basins. Calibrating the model with Landsat Thematic Mapper satellite imagery, a parabolic relationship was found between land-water interface and marsh disintegration. Aggregated simulation data suggest that interface in the study area will soon reach its maximum and then decline. A statistically significant positive linear relationship was found between brown shrimp catch and total interface length over the past 28 years. This relationship suggests that shrimp yields will decline when interface declines, possibly beginning about 1995

CLTs and asymptotic variance of time-sampled Markov chains

For a Markov transition kernel P and a probability distribution μ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel Pμ = Σkμ(k)Pk. In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker's and Metropolis algorithms in terms of asymptotic variance

Utilizing remote sensing of Thematic Mapper data to improve our understanding of estuarine processes and their influence on the productivity of estuarine-dependent fisheries

The purpose of the project is to refine and validate a probabilistic spatial computer model through the analyses of thematic mapper imagery. The model is designed to determine how the interface between marshland and water changes as marshland is converted to water in a disintegrating marsh. Coastal marshland in Louisiana is disintegrating at the rate of approximately 40 sq mi a year, and an evaluation of the potential impact of this loss on the landings of estuarine-dependent fisheries is needed by fisheries managers. Understanding how marshland-water interface changes as coastal marshland is lost is essential to the process of evaluating fisheries effects, because several studies suggest that the production of estuarine-dependent fish and shellfish may be more closely related to the interface between marshland and water than to acreage of marshland. The need to address this practical problem has provided an opportunity to apply some scientifically interesting new techniques to the analyses of satellite imagery. Progress with the development of these techniques is the subject of this report

NEAR-SURFACE EFFECTS IN MODELLING OSCILLATIONS OF ETA BOO

Following the report of solar-like oscillations in the G0 V star eta Boo (Kjeldsen et al. 1995, AJ 109, 1313), a first attempt to model the observed frequencies was made by Christensen-Dalsgaard et al. (1995, ApJ Letters, in press). This attempt succeeded in reproducing the observed frequency separations, although there remained a difference of about 10 microHz between observed and computed frequencies. In those models, the near-surface region of the star was treated rather crudely. Here we consider more sophisticated models that include non-local mixing-length theory, turbulent pressure and nonadiabatic oscillations.Comment: uuencoded and compressed Postscript (2 pages, including figure); To appear in Proceedings of IAU Colloquium 155, "Astrophysical Applications of Stellar Pulsation", Cape Town, South Afric

Second-order gravitational self-force

We derive an expression for the second-order gravitational self-force that acts on a self-gravitating compact-object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the first-order gravitational self-force. Here we find that our result conforms with the previously derived expression. Next we generalize our method and derive a new expression for the second-order gravitational self-force. This study also has a practical motivation: The data analysis for the planned gravitational wave detector LISA requires construction of waveforms templates for the expected gravitational waves. Calculation of the two leading orders of the gravitational self-force will enable one to construct highly accurate waveform templates, which are needed for the data analysis of gravitational-waves that are emitted from extreme mass-ratio binaries.Comment: 35 page

Экспериментальные исследования повышения безопасности подсистемы "оператор"

Приводится анализ условий и безопасности труда операторов мобильных машин при выполнении транспортных работ, влияющих на безопасность. Рассмотрена методика экспериментальных исследований условий труда операторов мобильных машин при транспортных работах. Представлены экспериментальные исследования влияния функциональных возможностей человека-оператора на безопасность транспортных работ. Особенностью выполнения транспортных работ является постоянно изменяющиеся условия производственной среды, которые влияют как на физиологические возможности адаптации оператора, так и на транспортное средство, что вызывает рассогласование между элементами системы оператор-машина-среда и приводит к резкому снижению уровня ее безопасности. Как следствие, требуется поэтапное изучение показателей профессиональной квалификации. Обработка статистического материала и экспериментальных данных позволяет установить взаимосвязь первичного коэффициента квалификации с дискретными значениями стажа работы. Анализ зависимостей тренажа показал, что после пятой повторности эффективность последующих циклов тренажа дает меньший прирост показателя квалификации, чем предыдущий. Имея математическую модель процесса тренажирования, полученную в результате проведения бальной экспертной оценки показателя квалификации, можно определить необходимое число повторности цикла тренажирования для человека-оператора.The article presents the analysis of conditions and labour safety of operators of mobile machines in the fulfillment of transportation work affecting safety. The technique of experimental researches of working conditions of operators of mobile machines in transport operations. Experimental research of the interaction between functional capabilities of the human operator and the security of transport operations. Transport operations are always associated with changing environmental conditions. They affect the physiological capabilities of adaptation of the operator and the reliability of the vehicle. This causes a misalignment between elements of the system operator-machine-environment and leads to a sharp decrease of its security level. This requires a phased study of the indicators of professional qualifications. Processing statistical material and experimental data allows to establish the relationship of initial qualification and level of experience. Dependency analysis when working on the simulator showed that after the fifth repetition, the effectiveness of a subsequent cycle gives a smaller increase of the indicator of skills than the previous cycle. Having a mathematical model of the process of working on the simulator received as a result of the ballroom expert assessment of qualifications, it is possible to define necessary number of repetition of the cycle on the simulator for the human operator