Probability Commons^™

A Model For The Multi-Virus Contact Process, Xu Huang

Rose-Hulman Undergraduate Mathematics Journal

We study one specific version of the contact process on a graph. Here, we allow multiple infections carried by the nodes and include a probability of removing nodes in a graph. The removal probability is purely determined by the number of infections the node carries at the moment when it gets another infection. In this paper, we show that on any finite graph, any positive value of infection rate $\lambda$ will result in the death of the process almost surely. In the case of $d$-regular infinite trees, We also give a lower bound on the infection rate in order for …

Would You Choose The Same Nationality If You Were Born Again?, Keito Kono, Logan Bowerman

Harrisburg University Research Symposium: Highlighting Research, Innovation, & Creativity

Nationality is an important element in the formation of identity, but this brings up a question; that is whether people are proud of their nationality. Thus, we decided to investigate how many people would prefer to have the same nationality if they were born again. This survey is important because it could provide an opportunity to recognize people's interest in other countries and their patriotism

Reu-Deim Classification Of Hispanic Voters In Hispanic Groups Using Name And Zip Code Data In Palm Beach, Florida, Kamila Soto-Ortiz

Beyond: Undergraduate Research Journal

When it comes to registering to vote, Hispanic voters can only register as “Hispanic” in the “Race/Ethnicity” category, causing difficulties when analyzing voting trends amongst the Hispanic community. Upon the recent idea that not all Hispanic Groups vote the same, the goal is to create a model that can possibly identify a voter’s Hispanic Group with the information provided on the public Florida voter file. This is accomplished using name and zip code data for all voters in Palm Beach, Florida. This paper will explore the model implemented, its findings and limitations. Palm Beach, Florida, is met with low confidence …

Number Of Regions Created By Random Chords In The Circle, Shi Feng

Rose-Hulman Undergraduate Mathematics Journal

In this paper we discuss the number of regions in a unit circle after drawing n i.i.d. random chords in the circle according to a particular family of distribution. We find that as n goes to infinity, the distribution of the number of regions, properly shifted and scaled, converges to the standard normal distribution and the error can be bounded by Stein's method for proving Central Limit Theorem.

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 …

The "Benfordness" Of Bach Music, Chadrack Bantange, Darby Burgett, Luke Haws, Sybil Prince Nelson

Journal of Humanistic Mathematics

In this paper we analyze the distribution of musical note frequencies in Hertz to see whether they follow the logarithmic Benford distribution. Our results show that the music of Johann Sebastian Bach and Johann Christian Bach is Benford distributed while the computer-generated music is not. We also find that computer-generated music is statistically less Benford distributed than human- composed music.

Development And Testing Of A New Method For Velocity-Selecting White Dwarfs From Gaia By Galactic Population, Joseph Hammill

Doctoral Dissertations and Master's Theses

The detailed processes by which spiral galaxies form remains an open question in modern cosmology. Observations of the current configuration of spiral galaxies including the Milky Way reveal thin and thick disk and halo populations which must all be accounted for in formation theories and likely have distinct ages. Using the Milky Way as an example to probe this question, we are studying the formation history of these structures.

This work details our approach to age-dating the galaxy, velocity-selecting targets from a sample of white dwarfs from the Gaia DR3 catalog that have also been age-analysed using BASE-9. BASE-9 uses …

A Characterization Of Complex-Valued Random Variables With Rotationally-Invariant Moments, Michael L. Maiello

Rose-Hulman Undergraduate Mathematics Journal

A complex-valued random variable Z is rotationally invariant if the moments of Z are the same as the moments of W=e^{i*theta}Z. In the first part of the article, we characterize such random variables, in terms of "vanishing unbalanced moments," moment and cumulant generating functions, and polar decomposition. In the second part, we consider random variables whose moments are not necessarily finite, but which have a density. In this setting, we prove two characterizations that are equivalent to rotational invariance, one involving polar decomposition, and the other involving entropy. If a random variable has both a density and moments which determine …

(R2051) Analysis Of Map/Ph1, Ph2/2 Queueing Model With Working Breakdown, Repairs, Optional Service, And Balking, G. Ayyappan, G. Archana

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a classical queueing system with two types of heterogeneous servers has been considered. The Markovian Arrival Process (MAP) is used for the customer arrival, while phase type distribution (PH) is applicable for the offering of service to customers as well as the repair time of servers. Optional service are provided by the servers to the unsatisfied customers. The server-2 may get breakdown during the busy period of any type of service. Though the server- 2 got breakdown, server-2 has a capacity to provide the service at a slower rate to the current customer who is receiving service …

(R1975) Map/Ph(1), Ph(2)/2 Queue With Multiple Vacation, Optional Service, Consultations And Interruptions, G. Ayyappan, S. Sankeetha

Applications and Applied Mathematics: An International Journal (AAM)

Two types of services are explored in this paper: regular server and main server, both of which provide both regular and optional services. Customers arrive using the Markovian Arrival Process (MAP), and service time is allocated based on phase type. The regular server uses the main server as a resource. Customers’ service at the primary server is disrupted as a result. When the queue size is empty, the main server can take several vacations. This system has been represented as a QBD Process that investigates steady state with the use of matrix analytic techniques, employing finite-dimensional block matrices. Our model’s …

(R2027) A New Class Of Pareto Distribution: Estimation And Its Applications, Anitta Susan Aniyan, Dais George

Applications and Applied Mathematics: An International Journal (AAM)

The classical Pareto distribution is a positively skewed and right heavy-tailed lifetime distribution having a lot many applications in various fields of science and social science. In this work, via logarithmic trans-formed method, a new three parameter lifetime distribution, an extension of classical Pareto distribution is generated. The different structural properties of the new distribution are studied. The model parameters are estimated by the method of maximum likelihood and Bayesian procedure. When all the three parameters of the distribution are unknown, the Bayes estimators cannot be obtained in a closed form and hence, the Lindley’s approximation under squared error loss …

(R2053) Analysis Of Map/Ph/1 Queueing Model Subject To Two-Stage Vacation Policy With Imperfect Service, Setup Time, Breakdown, Delay Time, Phase Type Repair And Reneging Customer, N. Arulmozhi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study a continuous-time single server queueing system with an infinite system of capacity, a two-stage vacation policy with imperfect service, setup, breakdown, delay time, phase-type of repair and customer reneging. The Markovian Arrival Process is used for the arrival of a customer and the phase-type distribution is used when offering service. This encompasses the policy of two vacations: a single working vacation and multiple vacations. Using the Matrix-Analytic Method to approach the system generates an invariant probability vector for this model. Henceforth, the busy period, waiting time distribution and cost analysis are the additional findings. The …

Payments Data In Gambling Research, Kasra Ghaharian, Mana Azizsoltani

International Conference on Gambling & Risk Taking

A considerable body of gambling-related research has leveraged gamblers' behavioral tracking data to address a broad set of research questions. These data have typically comprised of gamblers' betting-related behaviors including, for example, the frequency and volume of betting. The analysis of gamblers' payment-related behavioral data is far less common, but provides a fruitful avenue gambling-related research.

In this presentation we discuss a selection of potential research opportunities that payments transaction data presents. We supplement this discussion with specific analyses that have been performed by our research group. We also discuss knowledge gaps and areas for future research.

A Game-Theoretic Analysis Of Baccara Chemin De Fer, Ii, Stewart N. Ethier, Jiyeon Lee

International Conference on Gambling & Risk Taking

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Tardys Quantifiers: Extracting Temporal And Reversible Dynamical Symmetries, Nhat Vu Minh Nguyen, Arjendu K. Pattanayak, Andres Aragoneses

2023 Symposium

One of the great challenges in complex and chaotic dynamics is to reveal the details of its underlying determinism. This can be manifest in the form of temporal correlations or structured patterns in the dynamics of a measurable variable. These temporal dynamical structures are sometimes a consequence of hidden global symmetries. Here we identify the temporal (approximate) symmetries of a semiconductor laser with external optical feedback, based on which we define the Temporal And Reversible DYnamical Symmetry (TARDYS) quantifiers to evaluate the relevance of specific temporal correlations in a time series. We show that these symmetries are also present in …

A Novel Family Of Chain Binomial Models To Investigate Correlated Vaccination And Infection Rates In Sveirs Epidemic Dynamics, Divine Wanduku

Biology and Medicine Through Mathematics Conference

No abstract provided.

Public Acceptance Of Guidance And Regulations For Space Flight Participation, Cory Trunkhill, Robert Joslin, Joseph Keebler

Journal of Aviation Technology and Engineering

Space flight participants are not professional astronauts and not subject to the rules and guidance covering space flight crewmembers. Ordinal logistic regression of survey data was utilized to explore public acceptance of current medical screening recommendations and regulations for safety risk and implied liability for civil space flight participation. Independent variables constituted participant demographic representations while dependent variables represented current Federal Aviation Administration guidance and regulations. Odds ratios were derived based on the demographic categories to interpret likelihood of acceptance for the criteria. Significant likely acceptance of guidance and regulations was found for five of twelve demographic variables influencing public …

Predicting High-Cap Tech Stock Polarity: A Combined Approach Using Support Vector Machines And Bidirectional Encoders From Transformers, Ian L. Grisham

Electronic Theses and Dissertations

The abundance, accessibility, and scale of data have engendered an era where machine learning can quickly and accurately solve complex problems, identify complicated patterns, and uncover intricate trends. One research area where many have applied these techniques is the stock market. Yet, financial domains are influenced by many factors and are notoriously difficult to predict due to their volatile and multivariate behavior. However, the literature indicates that public sentiment data may exhibit significant predictive qualities and improve a model’s ability to predict intricate trends. In this study, momentum SVM classification accuracy was compared between datasets that did and did not …

Mixing Measures For Trees Of Fixed Diameter, Ari Holcombe Pomerance

Mathematics, Statistics, and Computer Science Honors Projects

A mixing measure is the expected length of a random walk in a graph given a set of starting and stopping conditions. We determine the tree structures of order n with diameter d that minimize and maximize for a few mixing measures. We show that the maximizing tree is usually a broom graph or a double broom graph and that the minimizing tree is usually a seesaw graph or a double seesaw graph.

Large Deviations For Self Intersection Local Times Of Ornstein-Uhlenbeck Processes, Apostolos Gournaris

Doctoral Dissertations

In the area of large deviations, people concern about the asymptotic computation of small probabilities on an exponential scale. The general form of large deviations can be roughly described as: P{Yn ∈ A} ≈ exp{−bnI(A)} (n → ∞), for a random sequence {Yn}, a positive sequence bn with bn → ∞, and a coefficient I(A) ≥ 0. In applications, we often concern about the probability that the random variables take large values, that is we concern about the P{Yn ≥ λ}, where λ > 0. Here, we consider the Ornstein-Uhlenbeck process, study the properties of the local times and self intersection …