scholarly journals LOGLOG counting for the estimation of IP traffic

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Olivier Gandouet ◽  
Alain Jean-Marie
Keyword(s):  
Synthetic Data ◽  
Space Complexity ◽  
International Audience ◽  
Mean And Variance ◽  
The Mean ◽  
Ip Packets

International audience In this paper, we discuss the problem of estimating the number of "elephants'' in a stream of IP packets. First, the problem is formulated in the context of multisets. Next, we explore some of the theoretical space complexity of this problem, and it is shown that it cannot be solved with less than $\Omega (n)$ units of memory in general, $n$ being the number of different elements in the multiset. Finally, we describe an algorithm, based on Durand-Flajolet's LOGLOG algorithm coupled with a thinning of the packet stream, which returns an estimator of the number of elephants using a small amount of memory. This algorithm allows a good estimation for particular families of random multiset. The mean and variance of this estimator are computed. The algorithm is then tested on synthetic data.

scholarly journals Heteroscedastic Ensemble Postprocessing

2014 ◽  
Vol 142 (9) ◽  
pp. 3484-3502 ◽  
Author(s):  
Elizabeth A. Satterfield ◽  
Craig H. Bishop
Keyword(s):  
Posterior Distribution ◽  
Synthetic Data ◽  
Error Variance ◽  
Sample Variance ◽  
Ensemble Prediction ◽  
Analytic Approximation ◽  
True Error ◽  
Ensemble Forecasts ◽  
Mean And Variance ◽  
The Mean

Ensemble variances provide a prediction of the flow-dependent error variance of the ensemble mean or, possibly, a high-resolution forecast. However, small ensemble size, unaccounted for model error, and imperfections in ensemble generation schemes cause the predictions of error variance to be imperfect. In previous work, the authors developed an analytic approximation to the posterior distribution of true error variances, given an imperfect ensemble prediction, based on parameters recovered from long archives of innovation and ensemble variance pairs. This paper shows how heteroscedastic postprocessing enables climatological information to be blended with ensemble forecast information when information about the distribution of true error variances given an ensemble sample variance is available. A hierarchy of postprocessing methods are described, each graded on the amount of information about the posterior distribution of error variances used in the postprocessing. These homoscedastic methods are used to assess the value of knowledge of the mean and variance of the posterior distribution of error variances to ensemble postprocessing and explore sensitivity to various parameter regimes. Testing was performed using both synthetic data and operational ensemble forecasts of a Gaussian-distributed variable, to provide a proof-of-concept demonstration in a semi-idealized framework. Rank frequency histograms, weather roulette, continuous ranked probability score, and spread-skill diagrams are used to quantify the value of information about the posterior distribution of error variances. It is found that ensemble postprocessing schemes that utilize the full distribution of error variances given the ensemble sample variance outperform those that do not.

A Method for Inferring Conditional Stochastic Failure Rates From the Time-History of Observed Failures

2011 ◽  
Author(s):  
David Thompson ◽  
Philippe Pe´bay
Keyword(s):  
First Principles ◽  
Synthetic Data ◽  
Time History ◽  
Random Variable ◽  
Cumulative Damage ◽  
Operating Conditions ◽  
Operating Condition ◽  
History Of ◽  
Mean And Variance ◽  
The Mean

Observed failures, rather than first principles, are used to estimate fatigue rates probabilistically conditioned on operating conditions. The method developed assumes that a normal random variable may be used to approximate the damage limit (remaining lifetime) of components subjected to cumulative damage and that when a component fails, its damage limit has vanished at a rate proportional to the amount of time spent at each operating condition experienced during its lifetime. By considering differences in cumulative damage between pairs of failed components, we obtain the relative rates at which damage is accumulated for each observed operating condition. When the differences in component lifetimes are dominated by variations in experienced conditions, it is possible to estimate absolute rates. Otherwise, variations in initial damage limits dominate and it is only possible to estimate the mean and variance of this distribution. We demonstrate the procedure on synthetic data, including a test for the dominant source of lifetime variations.

scholarly journals Enumeration of words by the sum of differences between adjacent letters

2009 ◽  
Vol Vol. 11 no. 1 (Combinatorics) ◽  
Author(s):  
Toufik Mansour
Keyword(s):  
Generating Function ◽  
Explicit Formulas ◽  
International Audience ◽  
Mean And Variance ◽  
The Mean

Combinatorics International audience We consider the sum u of differences between adjacent letters of a word of n letters, chosen uniformly at random from a given alphabet. This paper obtains the enumerating generating function for the number of such words with respect to the sum u, as well as explicit formulas for the mean and variance of u.

scholarly journals Weighted statistical binary patterns for facial feature representation

2021 ◽  
Author(s):  
Hung Phuoc Truong ◽  
Thanh Phuong Nguyen ◽  
Yong-Guk Kim
Keyword(s):  
Comprehensive Evaluation ◽  
Facial Feature ◽  
Input Image ◽  
Feature Representation ◽  
Illumination Variation ◽  
Straight Line ◽  
Mean And Variance ◽  
The Mean ◽  
Face Datasets ◽  
Degraded Images

AbstractWe present a novel framework for efficient and robust facial feature representation based upon Local Binary Pattern (LBP), called Weighted Statistical Binary Pattern, wherein the descriptors utilize the straight-line topology along with different directions. The input image is initially divided into mean and variance moments. A new variance moment, which contains distinctive facial features, is prepared by extracting root k-th. Then, when Sign and Magnitude components along four different directions using the mean moment are constructed, a weighting approach according to the new variance is applied to each component. Finally, the weighted histograms of Sign and Magnitude components are concatenated to build a novel histogram of Complementary LBP along with different directions. A comprehensive evaluation using six public face datasets suggests that the present framework outperforms the state-of-the-art methods and achieves 98.51% for ORL, 98.72% for YALE, 98.83% for Caltech, 99.52% for AR, 94.78% for FERET, and 99.07% for KDEF in terms of accuracy, respectively. The influence of color spaces and the issue of degraded images are also analyzed with our descriptors. Such a result with theoretical underpinning confirms that our descriptors are robust against noise, illumination variation, diverse facial expressions, and head poses.

scholarly journals Groups and Individuals: Optical Flow Patterns of Broiler Chicken Flocks Are Correlated with the Behavior of Individual Birds

Animals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 568
Author(s):  
Sabine G. Gebhardt-Henrich ◽  
Ariane Stratmann ◽  
Marian Stamp Dawkins
Keyword(s):  
Optical Flow ◽  
Broiler Chicken ◽  
Average Length ◽  
Flow Patterns ◽  
Group Level ◽  
Positive Correlation ◽  
Water Test ◽  
Mean And Variance ◽  
The Mean

Group level measures of welfare flocks have been criticized on the grounds that they give only average measures and overlook the welfare of individual animals. However, we here show that the group-level optical flow patterns made by broiler flocks can be used to deliver information not just about the flock averages but also about the proportion of individuals in different movement categories. Mean optical flow provides information about the average movement of the whole flock while the variance, skew and kurtosis quantify the variation between individuals. We correlated flock optical flow patterns with the behavior and welfare of a sample of 16 birds per flock in two runway tests and a water (latency-to-lie) test. In the runway tests, there was a positive correlation between the average time taken to complete the runway and the skew and kurtosis of optical flow on day 28 of flock life (on average slow individuals came from flocks with a high skew and kurtosis). In the water test, there was a positive correlation between the average length of time the birds remained standing and the mean and variance of flock optical flow (on average, the most mobile individuals came from flocks with the highest mean). Patterns at the flock level thus contain valuable information about the activity of different proportions of the individuals within a flock.

scholarly journals A New Model for the Stochastic Point Reactor: Development and Comparison with Available Models

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 955
Author(s):  
Alamir Elsayed ◽  
Mohamed El-Beltagy ◽  
Amnah Al-Juhani ◽  
Shorooq Al-Qahtani
Keyword(s):  
Kinetic Model ◽  
Differential Equations ◽  
Test Cases ◽  
System Of Differential Equations ◽  
Reactor Model ◽  
Time System ◽  
New Model ◽  
Reactor Dynamics ◽  
Mean And Variance ◽  
The Mean

The point kinetic model is a system of differential equations that enables analysis of reactor dynamics without the need to solve coupled space-time system of partial differential equations (PDEs). The random variations, especially during the startup and shutdown, may become severe and hence should be accounted for in the reactor model. There are two well-known stochastic models for the point reactor that can be used to estimate the mean and variance of the neutron and precursor populations. In this paper, we reintroduce a new stochastic model for the point reactor, which we named the Langevin point kinetic model (LPK). The new LPK model combines the advantages, accuracy, and efficiency of the available models. The derivation of the LPK model is outlined in detail, and many test cases are analyzed to investigate the new model compared with the results in the literature.

Sequential simultaneous estimation of the mean and variance: The rate of convergence

Metrika ◽  
1986 ◽  
Vol 33 (1) ◽  
pp. 291-297 ◽  
Author(s):  
N. Mukhopadhyay ◽  
G. Vik
Keyword(s):  
Rate Of Convergence ◽  
Simultaneous Estimation ◽  
Mean And Variance ◽  
The Mean

A model for random instantaneous growth on an interval

1991 ◽  
Vol 28 (3) ◽  
pp. 529-538
Author(s):  
M. P. Quine
Keyword(s):  
Asymptotic Normality ◽  
Instantaneous Growth ◽  
Mean And Variance ◽  
The Mean

Points arrive in succession on an interval and immediately ‘cover' a region of length ½ to each side (less if they are close to the boundary or to a covered part). The location of a new point is uniformly distributed on the uncovered parts. We study the mean and variance of the total number of points ever formed, in particular as a → 0, in which case we also establish asymptotic normality.

scholarly journals A comparison of two methods for predicting changes in the distribution of gene frequency when selection is applied repeatedly to a finite population

1969 ◽  
Vol 13 (2) ◽  
pp. 117-126 ◽  
Author(s):  
Derek J. Pike
Keyword(s):  
Iterative Procedure ◽  
Gene Frequency ◽  
Finite Population ◽  
Transition Matrices ◽  
Single Cycle ◽  
Gene Frequencies ◽  
Mean And Variance ◽  
The Mean ◽  
The One ◽  
Selection Of

Robertson (1960) used probability transition matrices to estimate changes in gene frequency when sampling and selection are applied to a finite population. Curnow & Baker (1968) used Kojima's (1961) approximate formulae for the mean and variance of the change in gene frequency from a single cycle of selection applied to a finite population to develop an iterative procedure for studying the effects of repeated cycles of selection and regeneration. To do this they assumed a beta distribution for the unfixed gene frequencies at each generation.These two methods are discussed and a result used in Kojima's paper is proved. A number of sets of calculations are carried out using both methods and the results are compared to assess the accuracy of Curnow & Baker's method in relation to Robertson's approach.It is found that the one real fault in the Curnow-Baker method is its tendency to fix too high a proportion of the genes, particularly when the initial gene frequency is near to a fixation point. This fault is largely overcome when more individuals are selected. For selection of eight or more individuals the Curnow-Baker method is very accurate and appreciably faster than the transition matrix method.

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