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- Stochastic analysis (2)
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Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
Dynamic Influence Diagram-Based Deep Reinforcement Learning Framework And Application For Decision Support For Operators In Control Rooms, Joseph Mietkiewicz, Ammar N. Abbas, Chidera Winifred Amazu, Anders L. Madsen, Gabriele Baldissone
Dynamic Influence Diagram-Based Deep Reinforcement Learning Framework And Application For Decision Support For Operators In Control Rooms, Joseph Mietkiewicz, Ammar N. Abbas, Chidera Winifred Amazu, Anders L. Madsen, Gabriele Baldissone
Articles
In today’s complex industrial environment, operators are often faced with challenging situations that require quick and accurate decision-making. The human-machine interface (HMI) can display too much information, leading to information overload and potentially compromising the operator’s ability to respond effectively. To address this challenge, decision support models are needed to assist operators in identifying and responding to potential safety incidents. In this paper, we present an experiment to evaluate the effectiveness of a recommendation system in addressing the challenge of information overload. The case study focuses on a formaldehyde production simulator and examines the performance of an improved Human-Machine Interface …
Probability Models With Discrete And Continuous Parts, James E. Marengo, David L. Farnsworth
Probability Models With Discrete And Continuous Parts, James E. Marengo, David L. Farnsworth
Articles
In mathematical statistics courses, students learn that the quadratic function E ((X – x )-squared) is minimized when x is the mean of the random variable X, and that the graphs of this function for any two distributions of X are simply translates of each other. We focus on the problem of minimizing the function defined by y ( x) = E ( IX – xI-squared ) in the context of mixtures of probability distributions of the discrete, absolutely continuous, and singular continuous types. This problem is important, for example, in Bayesian statistics, when one attempts to compute the decision …
Probability Models And Compounding, David L. Farnsworth, James E. Marengo
Probability Models And Compounding, David L. Farnsworth, James E. Marengo
Articles
We present the case that the ideas contained in a particular sequence of formulas are important in probability and statistics. The synthesis offered by the concepts in the sequence can be very valuable. Facility with this sequence and its underpinnings should be in the skill set of anyone who uses or studies probability or statistics. For illustrative purposes, we give applications to mixture distributions and Bayesian analyses.
A Geometric Derivation Of The Irwin-Hall Distribution, James E. Marengo, Lucas Stefanic, David L. Farnsworth
A Geometric Derivation Of The Irwin-Hall Distribution, James E. Marengo, Lucas Stefanic, David L. Farnsworth
Articles
The Irwin-Hall distribution is the distribution of the sum of a finite number of independent identically distributed uniform random variables on the unit interval. Many applications arise since round-off errors have a transformed Irwin-Hall distribution and the distribution supplies spline approximations to normal distributions. We review some of the distribution’s history. The present derivation is very transparent, since it is geometric and explicitly uses the inclusion-exclusion principle. In certain special cases, the derivation can be extended to linear combinations of independent uniform random variables on other intervals of finite length.The derivation adds to the literature about methodologies for finding distributions …
The Conditional Poisson Process And The Erlang And Negative Binomial Distributions, Anurag Agarwal, Peter Bajorski, David L. Farnsworth, James E. Marengo, Wei Qian
The Conditional Poisson Process And The Erlang And Negative Binomial Distributions, Anurag Agarwal, Peter Bajorski, David L. Farnsworth, James E. Marengo, Wei Qian
Articles
It is a well known fact that for the hierarchical model of a Poisson random variable Y whose mean has an Erlang distribution, the unconditional distribution of Y is negative binomial. However, the proofs in the literature provide no intuitive understanding as to why this result should be true. It is the purpose of this manuscript to give a new proof of this result which provides such an understanding. The memoryless property of the exponential distribution allows one to conclude that the events in two independent Poisson processes may be regarded as Bernoulli trials, and this fact is used to …
Stochastic Hybrid Embodied Co2-Eq Analysis: An Application To The Irish Apartment Building Sector, Adolf Acquaye, Aidan Duffy, Biswajit Basu
Stochastic Hybrid Embodied Co2-Eq Analysis: An Application To The Irish Apartment Building Sector, Adolf Acquaye, Aidan Duffy, Biswajit Basu
Articles
Although embodiedCO2-eq analysis has seen recent developments as evident in the establishment of the ISO14040 and 14044 LCA standards, it is recognized that due to weaknesses in gathering data on product-related emissions,embodiedCO2-eq values are probabilistic. This paper presents a stochastic analysis of hybrid embodied CO2-eq in buildings to account for this weakness in traditional methods and, by way of example, applies it to an Irish construction-sector case study. Using seven apartment buildings, 70,000 results are simulated with Monte Carlo analysis and used to derive probabilistic and cumulative embodied CO2-eq intensity distributions for apartment buildings in Ireland. A Wakeby distribution with …
Embodied Emissions Abatement: A Policy Assessment Using Stochastic Analysis, Adolf Acquaye, Aidan Duffy, Biswajit Basu
Embodied Emissions Abatement: A Policy Assessment Using Stochastic Analysis, Adolf Acquaye, Aidan Duffy, Biswajit Basu
Articles
Policymakers traditionally focus on regulating operational energy use in buildings, ignoring other life cycle components such as embodied energy even though this may account for a significant portion of life cycle emissions. Data relating to embodied energy and emissions in buildings is limited. However, stochastic techniques can be used to estimate the distribution of such emissions from buildings. This helps policymakers identify which instruments are appropriate for achieving emissions reductions. A primary aim of this paper is to demonstrate this approach using a sample of apartment buildings in Ireland. A Monte-Carlo simulation suggests that the average probability distribution of embodied …
Fractional Anisotropic Diffusion For Noise Reduction In Magnetic Resonance Images, Jonathan Blackledge, Matthew Blackledge
Fractional Anisotropic Diffusion For Noise Reduction In Magnetic Resonance Images, Jonathan Blackledge, Matthew Blackledge
Articles
We extend the method of anisotropic diffusion for noise reduction in digital images to the case when the diffusion processes are non-Gaussian and Levy distributed. This yields a fractional diffusion equation characterised by the Levy index. A solution to this equation is considered and a numerical algorithm developed. The algorithm is then applied as a case study to the problem of reducing noise in magnetic resonance imaging. The focus of this study is on diffusion weighted images which have low signal-to-noise ratios.
Encryption Using Deterministic Chaos, Jonathan Blackledge, Nikolai Ptitsyn
Encryption Using Deterministic Chaos, Jonathan Blackledge, Nikolai Ptitsyn
Articles
The concepts of randomness, unpredictability, complexity and entropy form the basis of modern cryptography and a cryptosystem can be interpreted as the design of a key-dependent bijective transformation that is unpredictable to an observer for a given computational resource. For any cryptosystem, including a Pseudo-Random Number Generator (PRNG), encryption algorithm or a key exchange scheme, for example, a cryptanalyst has access to the time series of a dynamic system and knows the PRNG function (the algorithm that is assumed to be based on some iterative process) which is taken to be in the public domain by virtue of the Kerchhoff-Shannon …
Shadow Casting Phenomena At Newgrange, Frank Prendergast
Shadow Casting Phenomena At Newgrange, Frank Prendergast
Articles
A digital model of the Newgrange passage tomb and surrounding ring of monoliths known as the Great Circle is used to investigate sunrise shadow casting phenomena at the monument. Diurnal variation in shadow directions and lengths are analysed for their potential use in the Bronze Age to indicate the passage of seasonal time. Computer-aided simulations are developed from a photogrammetric survey to accurately show how three of the largest monoliths, located closest to the tomb entrance and archaeologically coded GC1, GC-1 and GC-2, cast their shadows onto the vertical face of the entrance kerbstone, coded K1. The phenomena occur at …