Relative Consistency of Sample Entropy Is Not Preserved in MIX Processes

Relative consistency is a notion related to entropic parameters, most notably to Approximate Entropy and Sample Entropy. It is a central characteristic assumed for e.g., biomedical and economic time series, since it allows the comparison between different time series at a single value of the threshold parameter r. There is no formal proof for this property, yet it is generally accepted that it is true. Relative consistency in both Approximate Entropy and Sample entropy was first tested with the M I X process. In the seminal paper by Richman and Moorman, it was shown that Approximate Entropy lacked the property for cases in which Sample Entropy did not. In the present paper, we show that relative consistency is not preserved for M I X processes if enough noise is added, yet it is preserved for another process for which we define a sum of a sinusoidal and a stochastic element, no matter how much noise is present. The analysis presented in this paper is only possible because of the existence of the very fast NCM algorithm for calculating correlation sums and thus also Sample Entropy.

Sparse Deep Neural Network Optimization for Embedded Intelligence

Deep neural networks become more popular as its ability to solve very complex pattern recognition problems. However, deep neural networks often need massive computational and memory resources, which is main reason resulting them to be difficult efficiently and entirely running on embedded platforms. This work addresses this problem by saving the computational and memory requirements of deep neural networks by proposing a variance reduced (VR)-based optimization with regularization techniques to compress the requirements of memory of models within fast training process. It is shown theoretically and experimentally that sparsity-inducing regularization can be effectively worked with the VR-based optimization whereby in the optimizer the behaviors of the stochastic element is controlled by a hyper-parameter to solve non-convex problems.

Existence and Uniqueness of the Local Smooth Solution to 3D Stochastic MHD Equations without Diffusion

In this paper, we consider the existence of local smooth solution to stochastic magneto-hydrodynamic equations without diffusion forced by additive noise in R 3 . We first transform the system into a random system via a simple change of variable and borrow the result obtained for classical magneto-hydrodynamic equations, then we show that this random transformed system is measurable with respect to the stochastic element. Finally we extend the solution to the maximality solution. Due to the coupled construction of this system, we need more elaborate and complicated estimates with respect to stochastic Euler equation.

On the loading and unloading of metal-to-metal seals: A two-scale stochastic approach

During operation, the mating surfaces of a metal-to-metal seal typically undergo significant plastic deformation, which in turn can have beneficial effect on its performance. In previous studies, it has, for instance, been shown that plastic deformation can provide for better sealing during unloading. Those studies did, however, only consider flow through unrealistically small domains. Therefore, it is possible that this might be a size effect, which would not be apparent in a real situation with a much larger domain. In this paper, we develop a model which can handle real-sized seal domains at the same time as fine details of the surface topography. More precisely, we construct a two-scale model, in which the global scale represents the seal domain and where the influence of the fine details at the local scale are represented by a stochastic element. By means of this stochastic two-scale model, we show that the beneficial effect associated with the plastic deformation persists also when real-sized seal domains are considered.

Beberapa Metode pada Masalah Pemrograman Stokastik

Stochastic programming problem is mathematical problem (linear, integer, mixed integer, and nonlinier) with stochastic element lies data. To get reasonable solution and optimal with its stochastic data is needed several method. Applicable method in trouble stochastic programming are L-Shape decomposition and lagrange decomposition. Each method can determine optimal solution to troubleshoots stochastic programming

Yuliy Sannikov: Winner of the 2016 Clark Medal

Yuliy Sannikov is an extraordinary theorist who has developed methods that offer new insights in analyzing problems that had seemed well-studied and familiar: for example, decisions that might bring about cooperation and/or defection in a repeated-play prisoner's dilemma game, or that affect the balance of incentives and opportunism in a principal–agent relationship. His work has broken new ground in methodology, often through the application of stochastic calculus methods. The stochastic element means that his work naturally captures situations in which there is a random chance that monitoring, communication, or signaling between players is imperfect. Using calculus in the context of continuous-time games allows him to overcome tractability problems that had long hindered research in a number of areas. He has substantially altered the toolbox available for studying dynamic games. This essay offers an overview of Sannikov's research in several areas.

A stochastic two-scale model for pressure-driven flow between rough surfaces

Seal surface topography typically consists of global-scale geometric features as well as local-scale roughness details and homogenization-based approaches are, therefore, readily applied. These provide for resolving the global scale (large domain) with a relatively coarse mesh, while resolving the local scale (small domain) in high detail. As the total flow decreases, however, the flow pattern becomes tortuous and this requires a larger local-scale domain to obtain a converged solution. Therefore, a classical homogenization-based approach might not be feasible for simulation of very small flows. In order to study small flows, a model allowing feasibly-sized local domains, for really small flow rates, is developed. Realization was made possible by coupling the two scales with a stochastic element. Results from numerical experiments, show that the present model is in better agreement with the direct deterministic one than the conventional homogenization type of model, both quantitatively in terms of flow rate and qualitatively in reflecting the flow pattern.

Stochastic forecast of the population of Central Serbia based on empiric forecast errors

Based on the example of the forecast of the population of Central Serbia for the 2005-2032 period, the basic probabilistic concept in forecasting the trends of demographic components of population development have been presented. The stochastic element of forecast is based on the analysis of empirical forecast errors of corresponding indicators of demographic development. The analysis frameworks were forecasts of official bureaus of statistics published during the second half of the 20th century. The statistical distribution of probability for chosen forecast parameters were formed around so called middle variant of corresponding indicators in the current national forecast of population, published by the Statistical Office of the Republic of Serbia (SORS) for the period 2002-2032. The basic characteristics of the probabilistic approach of forecasting were presented through mutual comparison of the main methodological assumptions, namely though comparative demographic-statistical valorization of results with traditional deterministic concept, represented by forecasts of RSB. The stochastic forecast of the population of Serbia clearly indicated to the key advantages of this approach: methodological consistency in quantifying demographic indicators as well as the possibility of transparent usage of results in numerous aspects of social planning. In this way the significance of the necessity for the elaboration of a studious national forecast of the population of Serbia completely based on a stochastic basis has been stressed, regardless of the still-present restrictions in the development of the probabilistic approach.