Analysis of Finite Buffer Queue: Maximum Entropy Probability Distribution With Shifted Fractional Geometric and Arithmetic Means

We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times. Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations of the dependence of the number of losses on the average batch size, buffer size, system load, autocorrelation structure, and time.

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Maximum-Entropy Probability Distribution of Free-Surface Elevations of Wind-Generated Coastal Waves

Coastal Engineering 2000 ◽

10.1061/40549(276)89 ◽

2001 ◽

Cited By ~ 1

Author(s):

Witold Cieślikiewicz

Keyword(s):

Free Surface ◽

Probability Distribution ◽

Maximum Entropy ◽

Coastal Waves

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INDEPENDENCE IN COMPLETE AND INCOMPLETE CAUSAL NETWORKS UNDER MAXIMUM ENTROPY

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488508005571 ◽

2008 ◽

Vol 16 (05) ◽

pp. 699-713 ◽

Cited By ~ 1

Author(s):

MICHAEL J. MARKHAM

Keyword(s):

Expert System ◽

Probability Distribution ◽

Maximum Entropy ◽

Linear Constraints ◽

Causal Network ◽

Missing Information ◽

Causal Networks ◽

Small Set

In an expert system having a consistent set of linear constraints it is known that the Method of Tribus may be used to determine a probability distribution which exhibits maximised entropy. The method is extended here to include independence constraints (Accommodation). The paper proceeds to discusses this extension, and its limitations, then goes on to advance a technique for determining a small set of independencies which can be added to the linear constraints required in a particular representation of an expert system called a causal network, so that the Maximum Entropy and Causal Networks methodologies give matching distributions (Emulation). This technique may also be applied in cases where no initial independencies are given and the linear constraints are incomplete, in order to provide an optimal ME fill-in for the missing information.

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Field-theoretic density estimation for biological sequence space with applications to 5′ splice site diversity and aneuploidy in cancer

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.2025782118 ◽

2021 ◽

Vol 118 (40) ◽

pp. e2025782118

Author(s):

Wei-Chia Chen ◽

Juannan Zhou ◽

Jason M. Sheltzer ◽

Justin B. Kinney ◽

David M. McCandlish

Keyword(s):

Probability Distribution ◽

Maximum Entropy ◽

Density Estimation ◽

Sequence Space ◽

Chromosomal Abnormalities ◽

Fundamental Problem ◽

Probability Distributions ◽

Biological Sequence ◽

Point Estimates ◽

Site Diversity

Density estimation in sequence space is a fundamental problem in machine learning that is also of great importance in computational biology. Due to the discrete nature and large dimensionality of sequence space, how best to estimate such probability distributions from a sample of observed sequences remains unclear. One common strategy for addressing this problem is to estimate the probability distribution using maximum entropy (i.e., calculating point estimates for some set of correlations based on the observed sequences and predicting the probability distribution that is as uniform as possible while still matching these point estimates). Building on recent advances in Bayesian field-theoretic density estimation, we present a generalization of this maximum entropy approach that provides greater expressivity in regions of sequence space where data are plentiful while still maintaining a conservative maximum entropy character in regions of sequence space where data are sparse or absent. In particular, we define a family of priors for probability distributions over sequence space with a single hyperparameter that controls the expected magnitude of higher-order correlations. This family of priors then results in a corresponding one-dimensional family of maximum a posteriori estimates that interpolate smoothly between the maximum entropy estimate and the observed sample frequencies. To demonstrate the power of this method, we use it to explore the high-dimensional geometry of the distribution of 5′ splice sites found in the human genome and to understand patterns of chromosomal abnormalities across human cancers.

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On Applying Evolutionary Computation Methods to Optimization of Vacation Cycle Costs in Finite-Buffer Queue

Artificial Intelligence and Soft Computing - Lecture Notes in Computer Science ◽

10.1007/978-3-319-07173-2_41 ◽

2014 ◽

pp. 480-491 ◽

Cited By ~ 21

Author(s):

Marcin Woźniak ◽

Wojciech M. Kempa ◽

Marcin Gabryel ◽

Robert K. Nowicki ◽

Zhifei Shao

Keyword(s):

Evolutionary Computation ◽

Finite Buffer ◽

Finite Buffer Queue

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Non-parametric Bayesian density estimation for biological sequence space with applications to pre-mRNA splicing and the karyotypic diversity of human cancer

10.1101/2020.11.25.399253 ◽

2020 ◽

Author(s):

Wei-Chia Chen ◽

Juannan Zhou ◽

Jason M Sheltzer ◽

Justin B Kinney ◽

David M McCandlish

Keyword(s):

Probability Distribution ◽

Maximum Entropy ◽

Density Estimation ◽

Cancer Progression ◽

Sequence Space ◽

Chromosomal Abnormalities ◽

Fundamental Problem ◽

Human Cancer ◽

Probability Distributions ◽

Point Estimates

AbstractDensity estimation in sequence space is a fundamental problem in machine learning that is of great importance in computational biology. Due to the discrete nature and large dimensionality of sequence space, how best to estimate such probability distributions from a sample of observed sequences remains unclear. One common strategy for addressing this problem is to estimate the probability distribution using maximum entropy, i.e. calculating point estimates for some set of correlations based on the observed sequences and predicting the probability distribution that is as uniform as possible while still matching these point estimates. Building on recent advances in Bayesian field-theoretic density estimation, we present a generalization of this maximum entropy approach that provides greater expressivity in regions of sequence space where data is plentiful while still maintaining a conservative maximum entropy char-acter in regions of sequence space where data is sparse or absent. In particular, we define a family of priors for probability distributions over sequence space with a single hyper-parameter that controls the expected magnitude of higher-order correlations. This family of priors then results in a corresponding one-dimensional family of maximum a posteriori estimates that interpolate smoothly between the maximum entropy estimate and the observed sample frequencies. To demonstrate the power of this method, we use it to explore the high-dimensional geometry of the distribution of 5′ splice sites found in the human genome and to understand the accumulation of chromosomal abnormalities during cancer progression.

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