Probability Commons^™

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Ohio Recovery Housing: Resident Risk And Outcomes Assessment, Elyjiah Potter, Bivin Sadler

SMU Data Science Review

Addiction and substance abuse disorder is a significant problem in the United States. Over the past two decades, the United States has faced a boom in substance abuse, which has resulted in an increase in death and disruption of families across the nation. The State of Ohio has been particularly hard hit by the crisis, with overdose rates nearly doubling the national average. Established in the mid 1970’s Sober Living Housing is an alcohol and substance use recovery model emphasizing personal responsibility, sober living, and community support. This model has been adopted by the Ohio Recovery Housing organization, which seeks …

(R2060) An M/G/1 Retrial Queue With Recurrent Customers, General Retrial Times And Working Vacation, S. Pazhani Bala Murugan, A. Jeba Pauline Veronica

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we analyze an M/G/1 retrial queue with recurrent customers, general retrial times and working vacation. In this model, we use two types of customers. They are recurrent customers who rejoin the retrial queue after completion of their service and transit customers who leaves the system once their service complete. All the service times and retrial times for transit customers follows general distribution, retrial time for recurrent customers and working vacation time of the server are assumed to have an exponential distribution and also service time of the recurrent customers follows general distribution. We have used working vacation …

Exploration And Statistical Modeling Of Profit, Caleb Gibson

Undergraduate Honors Theses

For any company involved in sales, maximization of profit is the driving force that guides all decision-making. Many factors can influence how profitable a company can be, including external factors like changes in inflation or consumer demand or internal factors like pricing and product cost. Understanding specific trends in one's own internal data, a company can readily identify problem areas or potential growth opportunities to help increase profitability.

In this discussion, we use an extensive data set to examine how a company might analyze their own data to identify potential changes the company might investigate to drive better performance. Based …

Generalized Ratio-Product Cum Regression Variance Estimator In Two-Phase Sampling, Isah Muhammad

CBN Journal of Applied Statistics (JAS)

This study develops a flexible and efficient generalized ratio-product cum regression type estimator of population variance utilizing auxiliary variable in two-phase sampling that incorporates the properties of ratio-type and product-type estimators. The properties of the estimator were derived using first order approximation. The theoretical conditions under which the precision and the flexibility of the estimator is better than some classical estimators are also provided. Empirical evidence from five real datasets suggests that the proposed estimator outperforms the classical variance, ratio variance, product, and exponential ratio type estimators in terms of precision and efficiency. The estimator can be utilized to provide …

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

Stochastic Optimal Control Of Conditional Mckean-Vlasov Equations With Jump And Markovian Switching, Charles Samuel Conly Sharp

Theses and Dissertations

This thesis obtains a number of results in stochastic optimal control for conditional McKean-Vlasov equations with jump and Markovian switching. First, we prove the uniqueness of the solutions and derive a relevant version of Itô's formula. We provide the dynamic programming principle and prove the associated verification theorem. A stochastic maximum principle is established. Further, we derive the relationship between dynamic programming and the stochastic maximum principle. Additionally, we utilize our stochastic maximum principle result for a mean-variance portfolio selection problem.

Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury

Master's Theses

A central problem in neuroscience is to understand how memories are formed as a result of the activities of neurons. Valiant’s neuroidal model attempted to address this question by modeling the brain as a random graph and memories as subgraphs within that graph. However the question of memory capacity within that model has not been explored: how many memories can the brain hold? Valiant introduced the concept of interference between memories as the defining factor for capacity; excessive interference signals the model has reached capacity. Since then, exploration of capacity has been limited, but recent investigations have delved into the …

Langevin Dynamic Models For Smfret Dynamic Shift, David Frost, Keisha Cook Dr, Hugo Sanabria Dr

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Divisibility Probabilities For Products Of Randomly Chosen Integers, Noah Y. Fine

Rose-Hulman Undergraduate Mathematics Journal

We find a formula for the probability that the product of n positive integers, chosen at random, is divisible by some integer d. We do this via an inductive application of the Chinese Remainder Theorem, generating functions, and several other combinatorial arguments. Additionally, we apply this formula to find a unique, but slow, probabilistic primality test.

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 W. 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 …

(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 …

(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 …