Nowhere differentiable functions constructed from probabilistic point of view

1994 ◽  
Vol 65 (3) ◽  
pp. 285-295
Author(s):  
N. Kôno
Keyword(s):  
Point Of View ◽  
Differentiable Functions ◽  
Nowhere Differentiable Functions ◽  
Probabilistic Point

Nonlinear Time-Series Prediction with Missing and Noisy Data

1998 ◽  
Vol 10 (3) ◽  
pp. 731-747 ◽  
Author(s):  
Volker Tresp ◽  
Reimar Hofmann
Keyword(s):  
Time Series ◽  
Stochastic Simulation ◽  
Time Series Prediction ◽  
Noisy Data ◽  
Nonlinear Time Series ◽  
Point Of View ◽  
Data Set ◽  
Sunspot Data ◽  
Error Bars ◽  
Probabilistic Point

We derive solutions for the problem of missing and noisy data in nonlinear time-series prediction from a probabilistic point of view. We discuss different approximations to the solutions—in particular, approximations that require either stochastic simulation or the substitution of a single estimate for the missing data. We show experimentally that commonly used heuristics can lead to suboptimal solutions. We show how error bars for the predictions can be derived and how our results can be applied to K-step prediction. We verify our solutions using two chaotic time series and the sunspot data set. In particular, we show that for K-step prediction, stochastic simulation is superior to simply iterating the predictor.

scholarly journals Determination of Optimal Shipping Quantity for Perishable Goods under Probabilistic Supply

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Si-Yeong Lim ◽  
Sun Hur
Keyword(s):  
Probability Distribution Function ◽  
Point Of View ◽  
Perishable Products ◽  
Limited Time ◽  
Operational Costs ◽  
Perishable Goods ◽  
Mean And Variance ◽  
Probabilistic Point ◽  
Optimal Quantity

The problems of shipping and transporting perishable goods are commonly considered in the literature as significant topics, but rarely did researchers adopt a probabilistic point of view in their models. It is common in SCM environments that the participating entities’ behaviors are random and unpredictable and so can only be modeled in a probabilistic way. In this paper, we consider the shipping problem of determining the optimal quantity of perishable products with a limited time to be stored in the warehouse. The optimal quantity minimizes the overall operational costs including those of inventory and shipping. We develop a mathematical model, from which the probability distribution function, mean, and variance of the length of the build-up period are derived and we establish a cost function for determining the optimal shipping value.

scholarly journals On Railroad Tank Car Puncture Performance: Part II — Estimating Metrics

2016 ◽  
Author(s):  
David Y. Jeong ◽  
Michael E. Carolan ◽  
Benjamin Perlman
Keyword(s):  
Structural Damage ◽  
Performance Metrics ◽  
Hazardous Materials ◽  
Point Of View ◽  
Structural Performance ◽  
Regulatory Agencies ◽  
Puncture Resistance ◽  
Mathematical Relationships ◽  
Design Factors ◽  
Probabilistic Point

This paper is the second in a two-part series on the puncture performance of railroad tank cars carrying hazardous materials in the event of an accident. Various metrics are often mentioned in the open literature to characterize the structural performance of tank cars under accident loading conditions. One of the consequences in terms of structural damage to the tank during accidents is puncture. This two-part series of papers focuses on four metrics to quantify the performance of tank cars against the threat of puncture: (1) speed, (2) force, (3) energy, and (4) conditional probability of release. In Part I, generalized tank car impact scenarios were illustrated. Particular focus is given to the generalized shell impact scenario because performance-based requirements for shell puncture resistance are being considered by the regulatory agencies in United States and Canada. Definitions for the four performance metrics were given. Physical and mathematical relationships among these metrics were outlined. Strengths and limitations of these performance metrics were discussed. In this paper (Part II), the multi-disciplinary approach to develop engineering tools to estimate the performance metrics is described. The complementary connection between testing and modeling is emphasized. Puncture performance metrics, which were estimated from other sources, are compared for different tank car designs. These comparisons are presented to interpret the metrics from a probabilistic point of view. In addition, sensitivity of the metrics to the operational and design factors is examined qualitatively.

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