Change Point Testing for the Drift Parameters of a Periodic Mean Reversion Process

In this paper we investigate the problem of detecting a change in the drift parameters of a generalized Ornstein-Uhlenbeck process which is defined as the solution of $dX_t=(L(t)-\alpha X_t) dt + \sigma dB_t$, and which is observed in continuous time. We derive an explicit representation of the generalized likelihood ratio test statistic assuming that the mean reversion function $L(t)$ is a finite linear combination of known basis functions. In the case of a periodic mean reversion function, we determine the asymptotic distribution of the test statistic under the null hypothesis

The research of correlation between recycling plastic lubricants quality indicators

У статті наведено залежності між основними показниками якості пластичних мастил на прикладі рециклінгових мастила, яка отримана з відпрацьованого напівсинтетичного моторного масла SAE10W-40 API SL, яка загущена подрібненими твердими використаними поліетиленовими виробами. Вже згадана мастило є досить перспективною, оскільки її виробництво забезпечує утилізацію промислових і побутових відходів, значно знижуючи екологічне навантаження на навколишнє середовище. Отримана мастило має більш високі значення показників якості, в порівнянні з вітчизняними і зарубіжними аналогами. Встановлено, що між розглянутими стандартизованими показниками якості пластичного мастила спостерігається значущий ранговий кореляційний зв'язок. Отримані залежності між певними показниками якості мастила адекватно описуються квадратичними рівняннями регресії, про що свідчать дуже високі значення коефіцієнтів достовірності апроксимації R2. Отримані залежності можуть бути використані при прогнозуванні зміни якості пластичного мастила при експлуатації в вузлах механізмів і на стадії їх виробництва при розробці системи автоматичного керування технологічним процесом.The article shows the relationships between the main indicators of the quality of greases on the example of recycling lubrication, which is obtained from the used semi-synthetic motor oil SAE10W-40 API SL, which is thickened with crushed solid used polyethylene products. This lubricant is very promising, as its production provides utilization of industrial and domestic waste, significantly reducing the environmental burden on the environment. The resulting grease has higher quality values, compared to domestic and foreign counterparts. It is established that a significant rank correlation is observed between the standardized indicators of the quality of grease being considered. The obtained dependences between certain parameters of the lubricant quality are adequately described by the quadratic regression equations, as evidenced by very high values of the reliability coefficients of the approximation R². The obtained dependences can be used when predicting the change in the quality of grease during operation in the nodes of mechanisms and at the stage of their production when developing a system for automatic control of the technological process

Drift estimation for a periodic mean reversion process

In this paper we propose a periodic, mean-reverting Ornstein-Uhlenbeck process of the form dXt = (L(t) − alpha Xt) dt + sigma dBt, where L(t) is a periodic, parametric function. We apply maximum likelihood estimation for the drift parameters based on time-continuous observations. The estimator is given explicitly and we prove strong consistency and asymptotic normality as the observed number of periods tends to infinity. The essential idea of the asymptotic study is the interpretation of the stochastic process as a sequence of random variables that take values in some function space

Undersampling reconstruction in parallel and single coil imaging with COMPaS -- COnvolutional Magnetic Resonance Image Prior with Sparsity regularization

Purpose: To propose COMPaS, a learning-free Convolutional Network, that combines Deep Image Prior (DIP) with transform-domain sparsity constraints to reconstruct undersampled Magnetic Resonance Imaging (MRI) data without previous training of the network. Methods: COMPaS uses a U-Net as DIP for undersampledMRdata in the image domain. Reconstruction is constrained by data fidelity to k-space measurements and transform-domain sparsity, such as Total Variation (TV) or Wavelet transform sparsity. Two-dimensional MRI data from the public FastMRI dataset with Cartesian undersampling in phase-encoding direction were reconstructed for different acceleration rates (R) from R = 2 to R = 8 for single coil and multicoil data. Performance of the proposed architecture was compared to Parallel Imaging with Compressed Sensing (PICS). Results: COMPaS outperforms standard PICS algorithms by reducing ghosting artifacts and yielding higher quantitative reconstruction quality metrics in multicoil imaging settings and especially in single coil k-space reconstruction. Furthermore, COMPaS can reconstruct multicoil data without explicit knowledge of coil sensitivity profiles. Conclusion: COMPaS utilizes a training-free convolutional network as a DIP in MRI reconstruction and transforms it with transform-domain sparsity regularization. It is a competitive algorithm for parallel imaging and a novel tool for accelerating single coil MRI.Comment: 13 pages, 8 figures, 2 table

Asynchronous, distributed optimization for the coordinated planning of air and space assets

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 189-194).Recent decades have seen the development of more advanced sensor and communication systems, with the future certainly holding more innovation in these areas. However, current operations involve "stovepipe" systems in which inefficiencies are inherent. In this thesis, we examine how to increase the value of Earth observations made by coordinating across multiple collection systems. We consider both air and space assets in an asynchronous and distributed environment. We consider requests with time windows and priority levels, some of which require simultaneous observations by different sensors. We consider how these improvements could impact Earth observing sensors in two use areas; climate studies and intelligence collection operations. The primary contributions of this thesis include our approach to the asynchronous and distributed nature of the problem and the development of a value function to facilitate the coordination of the observations with multiple surveillance assets. We embed a carefully constructed value function in a simple optimization problem that we prove can be solved as a Linear Programming (LP) problem. We solve the optimization problem repeatedly over time to intelligently allocate requests to single-mission planners, or "sub-planners." We then show that the value function performs as we intend through empirical and statistical analysis. To test our methodologies, we integrate the coordination planner with two types of sub-planners, an Unmanned Aerial Vehicle (UAV) sub-planner, and a satellite sub-planner. We use the coordinator to generate observation plans for two notional operational Earth Science scenarios. Specifically, we show that coordination offers improvements in the priority of the requests serviced, the quality of those observations, and the ability to take dual collections. We conclude that a coordinated planning framework provides clear benefits.by Thomas Michael Herold.S.M

Poisson limits for U-statistics

AbstractWe study Poisson limits for U-statistics with non-negative kernels. The limit theory is derived from the Poisson convergence of suitable point processes of U-statistics structure. We apply these results to derive infinite variance stable limits for U-statistics with a regularly varying kernel and to determine the index of regular variation of the left tail of the kernel. The latter is known as correlation dimension. We use the point process convergence to study the asymptotic behavior of some standard estimators of this dimension

When local bookshops close, more people give up reading

Many consumers don't rush to buy books online; they simply choose other activities instead of reading, write Georg Götz, Daniel Herold, Jan Thomas Schäfer and Phil-Adrian Klot

Performance Analysis of MDPC and RS codes in Two-channel THz Communication Systems

We analyze whether a multidimensional parity check (MDPC) or a Reed-Solomon (RS) code in combination with an auxiliary channel can improve the throughput and extend the THz transmission distance. While channel quality is addressed by various coding approaches, and an effective THz system configuration is enabled by other approaches with additional channels, their combination is new with the potential for significant improvements in quality of the data transmission. Our specific solution is designed to correct data bits at the physical layer by using a low complexity erasure code (MDPC or RS), whereby original and parity data are transferred over two separate and parallel THz channels, including one main channel and one additional channel. The results are theoretically analyzed to see that our new solution can improve throughput, support higher modulation levels and transfer data over the longer distances with THz communications.Comment: This paper is uploaded here for research community, thus it is for non-commercial purpose