On Some Unexplored Properties and Computational Aspects of Arithmetic Mean and Median

2013 ◽  
Author(s):  
Sudhanshu K. Mishra
Keyword(s):  
Arithmetic Mean ◽  
Computational Aspects

On Statistics of Log-Ratio of Arithmetic Mean to Geometric Mean for Nakagami-m Fading Power

2012 ◽  
Vol E95-B (2) ◽  
pp. 647-650
Author(s):  
Ning WANG ◽  
Julian CHENG ◽  
Chintha TELLAMBURA
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Log Ratio

Some aspects of familiarization with binomial coefficients

2019 ◽  
pp. 49-53
Author(s):  
Abdulkarim Magomedov ◽  
S.A. Lavrenchenko
Keyword(s):  
Elementary Mathematics ◽  
Binomial Coefficients ◽  
Computational Aspects

New laconic proofs of two classical statements of combinatorics are proposed, computational aspects of binomial coefficients are considered, and examples of their application to problems of elementary mathematics are given.

Optimization of Regional Water Quality Monitoring Strategies

1987 ◽  
Vol 19 (5-6) ◽  
pp. 721-727 ◽  
Author(s):  
J. Pintér ◽  
L. Somlyódy
Keyword(s):  
Water Quality ◽  
Water Quality Management ◽  
Water Quality Monitoring ◽  
Primary Objective ◽  
Lake Balaton ◽  
Monitoring Networks ◽  
Monitoring Strategies ◽  
Time Period ◽  
Computational Aspects ◽  
Indicator Model

A conceptual framework is presented for optimizing the operation of regional monitoring networks which assist water quality management. The primary objective of the studied network is to determine the annual nutrient load carried into a lake by its tributaries. Following the description of the basic (single time–period, single water quality indicator) model, several extension possibilities and computational aspects are highlighted. The suggested methodology is illustrated by a numerical example, concerning the surveillance system on the tributaries of Lake Balaton (Hungary).

scholarly journals A Deterministic Rapid Intensification Aid

2011 ◽  
Vol 26 (4) ◽  
pp. 579-585 ◽  
Author(s):  
Charles R. Sampson ◽  
John Kaplan ◽  
John A. Knaff ◽  
Mark DeMaria ◽  
Chris A. Sisko
Keyword(s):  
Real Time ◽  
Arithmetic Mean ◽  
Forecast Errors ◽  
Rapid Intensification ◽  
Intensity Forecast ◽  
Probability Threshold ◽  
Forecast Time ◽  
National Hurricane Center ◽  
Made In

Abstract Rapid intensification (RI) is difficult to forecast, but some progress has been made in developing probabilistic guidance for predicting these events. One such method is the RI index. The RI index is a probabilistic text product available to National Hurricane Center (NHC) forecasters in real time. The RI index gives the probabilities of three intensification rates [25, 30, and 35 kt (24 h)−1; or 12.9, 15.4, and 18.0 m s−1 (24 h)−1] for the 24-h period commencing at the initial forecast time. In this study the authors attempt to develop a deterministic intensity forecast aid from the RI index and, then, implement it as part of a consensus intensity forecast (arithmetic mean of several deterministic intensity forecasts used in operations) that has been shown to generally have lower mean forecast errors than any of its members. The RI aid is constructed using the highest available RI index intensification rate available for probabilities at or above a given probability (i.e., a probability threshold). Results indicate that the higher the probability threshold is, the better the RI aid performs. The RI aid appears to outperform the consensus aids at about the 50% probability threshold. The RI aid also improves forecast errors of operational consensus aids starting with a probability threshold of 30% and reduces negative biases in the forecasts. The authors suggest a 40% threshold for producing the RI aid initially. The 40% threshold is available for approximately 8% of all verifying forecasts, produces approximately 4% reduction in mean forecast errors for the intensity consensus aids, and corrects the negative biases by approximately 15%–20%. In operations, the threshold could be moved up to maximize gains in skill (reducing availability) or moved down to maximize availability (reducing gains in skill).

scholarly journals Computational aspects of the weak micro‐periodicity saddle point problem

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Ritukesh Bharali ◽  
Fredrik Larsson ◽  
Ralf Jänicke
Keyword(s):  
Saddle Point ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Computational Aspects

scholarly journals Stochastic Order and Generalized Weighted Mean Invariance

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 662
Author(s):  
Mateu Sbert ◽  
Jordi Poch ◽  
Shuning Chen ◽  
Víctor Elvira
Keyword(s):  
Monte Carlo ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Arithmetic Mean ◽  
Stochastic Orders ◽  
Arithmetic Means ◽  
Increasing Convex Order ◽  
Monte Carlo Techniques ◽  
Multiple Importance Sampling ◽  
Invariance Properties

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

Query Games in Databases

2021 ◽  
Vol 50 (1) ◽  
pp. 78-85
Author(s):  
Ester Livshits ◽  
Leopoldo Bertossi ◽  
Benny Kimelfeld ◽  
Moshe Sebag
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
The Shapley Value ◽  
Computational Aspects ◽  
Aggregate Query ◽  
Boolean Query

Database tuples can be seen as players in the game of jointly realizing the answer to a query. Some tuples may contribute more than others to the outcome, which can be a binary value in the case of a Boolean query, a number for a numerical aggregate query, and so on. To quantify the contributions of tuples, we use the Shapley value that was introduced in cooperative game theory and has found applications in a plethora of domains. Specifically, the Shapley value of an individual tuple quantifies its contribution to the query. We investigate the applicability of the Shapley value in this setting, as well as the computational aspects of its calculation in terms of complexity, algorithms, and approximation.

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