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2019

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Articles 2581 - 2610 of 15928

Full-Text Articles in Physical Sciences and Mathematics

Demonstration Of Visible And Near Infrared Raman Spectrometers And Improved Matched Filter Model For Analysis Of Combined Raman Signals, Alexander Matthew Atkinson Oct 2019

Demonstration Of Visible And Near Infrared Raman Spectrometers And Improved Matched Filter Model For Analysis Of Combined Raman Signals, Alexander Matthew Atkinson

Electrical & Computer Engineering Theses & Dissertations

Raman spectroscopy is a powerful analysis technique that has found applications in fields such as analytical chemistry, planetary sciences, and medical diagnostics. Recent studies have shown that analysis of Raman spectral profiles can be greatly assisted by use of computational models with achievements including high accuracy pure sample classification with imbalanced data sets and detection of ideal sample deviations for pharmaceutical quality control. The adoption of automated methods is a necessary step in streamlining the analysis process as Raman hardware becomes more advanced. Due to limits in the architectures of current machine learning based Raman classification models, transfer from pure …


Pulse Power Effects On Transient Plasma Ignition For Combustion, David Wayne Alderman Ii Oct 2019

Pulse Power Effects On Transient Plasma Ignition For Combustion, David Wayne Alderman Ii

Electrical & Computer Engineering Theses & Dissertations

Transient plasma ignition (TPI) uses highly non-equilibrium plasmas, driven by less than 100 nanosecond, high-voltage pulses, to initiate combustion. The effects of pulse repetition frequency (PRF) and ultrashort nanosecond rise times on TPI are investigated in this work using lean, stoichiometric, and rich air-fuel mixtures at atmospheric pressure. Experimental data show the transient plasmas driven by ultrashort rise time, high voltage pulses at high PRF’s enhance the combustion of lean or stoichiometric air-methane mixtures in a static chamber. In particular, increasing PRF enhances the combustion performance by means of reduced delay times independent of the equivalence ratio of the air-fuel …


Electrohydrodynamic Simulations Of The Deformation Of Liquid-Filled Capsules, Pai Song Oct 2019

Electrohydrodynamic Simulations Of The Deformation Of Liquid-Filled Capsules, Pai Song

Mathematics & Statistics Theses & Dissertations

A comprehensive two- and three-dimensional framework for the electrohydrodynamic simulation of deformable capsules is provided. The role of a direct current (DC) electric field on the deformation and orientation of a liquid-filled capsule is thoroughly considered numerically. This framework is based on lattice Boltzmann method for the fluid, finite element method for the membrane structure of the capsule, fast immersed interface method for the electric field and immersed boundary method being used to consider the fluid-structure-electric interaction. Under the effect of electric field, two different types of equilibrium states, prolate or oblate are obtained. The numerical algorithm is also applied …


Who, Where, And What To Wear?: Extracting Fashion Knowledge From Social Media, Yunshan Ma, Xun Yang, Lizi Liao, Yixin Cao, Tat-Seng Chua Oct 2019

Who, Where, And What To Wear?: Extracting Fashion Knowledge From Social Media, Yunshan Ma, Xun Yang, Lizi Liao, Yixin Cao, Tat-Seng Chua

Research Collection School Of Computing and Information Systems

Fashion knowledge helps people to dress properly and addresses not only physiological needs of users, but also the demands of social activities and conventions. It usually involves three mutually related aspects of: occasion, person and clothing. However, there are few works focusing on extracting such knowledge, which will greatly benefit many downstream applications, such as fashion recommendation. In this paper, we propose a novel method to automatically harvest fashion knowledge from social media. We unify three tasks of occasion, person and clothing discovery from multiple modalities of images, texts and metadata. For person detection and analysis, we use the off-the-shelf …


Deep Hashing By Discriminating Hard Examples, Cheng Yan, Guansong Pang, Xiao Bai, Chunhua Shen, Jun Zhou, Edwin Hancock Oct 2019

Deep Hashing By Discriminating Hard Examples, Cheng Yan, Guansong Pang, Xiao Bai, Chunhua Shen, Jun Zhou, Edwin Hancock

Research Collection School Of Computing and Information Systems

This paper tackles a rarely explored but critical problem within learning to hash, i.e., to learn hash codes that effectively discriminate hard similar and dissimilar examples, to empower large-scale image retrieval. Hard similar examples refer to image pairs from the same semantic class that demonstrate some shared appearance but have different fine-grained appearance. Hard dissimilar examples are image pairs that come from different semantic classes but exhibit similar appearance. These hard examples generally have a small distance due to the shared appearance. Therefore, effective encoding of the hard examples can well discriminate the relevant images within a small Hamming distance, …


End-To-End Deep Reinforcement Learning For Multi-Agent Collaborative Exploration, Zichen Chen, Budhitama Subagdja, Ah-Hwee Tan Oct 2019

End-To-End Deep Reinforcement Learning For Multi-Agent Collaborative Exploration, Zichen Chen, Budhitama Subagdja, Ah-Hwee Tan

Research Collection School Of Computing and Information Systems

Exploring an unknown environment by multiple autonomous robots is a major challenge in robotics domains. As multiple robots are assigned to explore different locations, they may interfere each other making the overall tasks less efficient. In this paper, we present a new model called CNN-based Multi-agent Proximal Policy Optimization (CMAPPO) to multi-agent exploration wherein the agents learn the effective strategy to allocate and explore the environment using a new deep reinforcement learning architecture. The model combines convolutional neural network to process multi-channel visual inputs, curriculum-based learning, and PPO algorithm for motivation based reinforcement learning. Evaluations show that the proposed method …


Multi-Agent Collaborative Exploration Through Graph-Based Deep Reinforcement Learning, Tianze Luo, Budhitama Subagdja, Ah-Hwee Tan, Ah-Hwee Tan Oct 2019

Multi-Agent Collaborative Exploration Through Graph-Based Deep Reinforcement Learning, Tianze Luo, Budhitama Subagdja, Ah-Hwee Tan, Ah-Hwee Tan

Research Collection School Of Computing and Information Systems

Autonomous exploration by a single or multiple agents in an unknown environment leads to various applications in automation, such as cleaning, search and rescue, etc. Traditional methods normally take frontier locations and segmented regions of the environment into account to efficiently allocate target locations to different agents to visit. They may employ ad hoc solutions to allocate the task to the agents, but the allocation may not be efficient. In the literature, few studies focused on enhancing the traditional methods by applying machine learning models for agent performance improvement. In this paper, we propose a graph-based deep reinforcement learning approach …


Mixed-Dish Recognition With Contextual Relation Networks, Lixi Deng, Jingjing Chen, Qianru Sun, Xiangnan He, Sheng Tang, Zhaoyan Ming, Yongdong Zhang, Tat-Seng Chua Oct 2019

Mixed-Dish Recognition With Contextual Relation Networks, Lixi Deng, Jingjing Chen, Qianru Sun, Xiangnan He, Sheng Tang, Zhaoyan Ming, Yongdong Zhang, Tat-Seng Chua

Research Collection School Of Computing and Information Systems

Mixed dish is a food category that contains different dishes mixed in one plate, and is popular in Eastern and Southeast Asia. Recognizing individual dishes in a mixed dish image is important for health related applications, e.g. calculating the nutrition values. However, most existing methods that focus on single dish classification are not applicable to mixed-dish recognition. The new challenge in recognizing mixed-dish images are the complex ingredient combination and severe overlap among different dishes. In order to tackle these problems, we propose a novel approach called contextual relation networks (CR-Nets) that encodes the implicit and explicit contextual relations among …


Cognitive And Social Interaction Analysis In Graduate Discussion Forums, Mallika Gokarn Nitin, Swapna Gottipati, Venky Shankararaman Oct 2019

Cognitive And Social Interaction Analysis In Graduate Discussion Forums, Mallika Gokarn Nitin, Swapna Gottipati, Venky Shankararaman

Research Collection School Of Computing and Information Systems

Discussion forums play a key role in building knowledge repositories in an education institute. Asynchronous discussion forums enable part-time graduate professionals to have a better learning experience. This paper reports how a carefully curated discussion forum enhances the cognitive and social interactions among students in a graduate information systems course. In particular, we analyse the cognitive and social interactions and their impact on the student grades. To our surprise, the graduate students with their limited time resources, have higher order cognitive contributions and reasonable amount of social posts. We present the discussion forum design, cognitive and social behaviour analysis, grade …


On Analysing Supply And Demand In Labor Markets: Framework, Model And System, Hendrik Santoso Sugiarto, Ee-Peng Lim, Ngak Leng Sim Oct 2019

On Analysing Supply And Demand In Labor Markets: Framework, Model And System, Hendrik Santoso Sugiarto, Ee-Peng Lim, Ngak Leng Sim

Research Collection School Of Computing and Information Systems

The labor market refers to the market between job seekers and employers. As much of job seeking and talent hiring activities are now performed online, a large amount of job posting and application data have been collected and can be re-purposed for labor market analysis. In the labor market, both supply and demand are the key factors in determining an appropriate salary for both job applicants and employers in the market. However, it is challenging to discover the supply and demand for any labor market. In this paper, we propose a novel framework to built a labor market model using …


Smartbfa: A Passive Crowdsourcing System For Point-To-Point Barrier-Free Access, Mohammed Nazir Kamaldin, Susan Kee, Songwei Kong, Chengkai Lee, Huiguang Liang, Alisha Saini, Hwee-Pink Tan, Hwee Xian Tan Oct 2019

Smartbfa: A Passive Crowdsourcing System For Point-To-Point Barrier-Free Access, Mohammed Nazir Kamaldin, Susan Kee, Songwei Kong, Chengkai Lee, Huiguang Liang, Alisha Saini, Hwee-Pink Tan, Hwee Xian Tan

Research Collection School Of Computing and Information Systems

At the Bloomberg Live `Sooner Than You Think' forum [1] held in Singapore in 2018, nearly 75% of delegates picked inclusiveness to be the key measure of success for a smart city. An inclusive smart city is a citizen-centered approach that extends the experiences provided by smart city solutions to all citizens, including seniors and persons with disabilities (PwDs).Despite existing regulations on barrier-free accessibility for buildings and public infrastructure, pedestrian infrastructure is generally still inaccessible to PwDs in many parts of the world. In this paper, we present SmartBFA (Smart Mobility and Accessibility for Barrier Free Access) - a publicly-funded …


Tighter Security Proofs For Post-Quantum Key Encapsulation Mechanism In The Multi-Challenge Setting, Zhengyu Zhang, Puwen Wei, Haiyang Xue Oct 2019

Tighter Security Proofs For Post-Quantum Key Encapsulation Mechanism In The Multi-Challenge Setting, Zhengyu Zhang, Puwen Wei, Haiyang Xue

Research Collection School Of Computing and Information Systems

Due to the threat posed by quantum computers, a series of works investigate the security of cryptographic schemes in the quantum-accessible random oracle model (QROM) where the adversary can query the random oracle in superposition. In this paper, we present tighter security proofs of a generic transformations for key encapsulation mechanism (KEM) in the QROM in the multi-challenge setting, where the reduction loss is independent of the number of challenge ciphertexts. In particular, we introduce the notion of multi-challenge OW-CPA (mOW-CPA) security, which captures the one-wayness of the underlying public key encryption (PKE) under chosen plaintext attack in the multi-challenge …


Towards Generating Transformation Rules Without Examples For Android Api Replacement, Ferdian Thung, Hong Jin Kang, Lingxiao Jiang, David Lo Oct 2019

Towards Generating Transformation Rules Without Examples For Android Api Replacement, Ferdian Thung, Hong Jin Kang, Lingxiao Jiang, David Lo

Research Collection School Of Computing and Information Systems

Deprecation of APIs in software libraries is common when library maintainers make changes to a library and will no longer support certain APIs in the future. When deprecation occurs, developers whose programs depend on the APIs need to replace the usages of the deprecated APIs sooner or later. Often times, software documentation specifies which new APIs the developers should use in place of a deprecated API. However, replacing the usages of a deprecated API remains a challenge since developers may not know exactly how to use the new APIs. The developers would first need to understand the API changes before …


Bakken Flares And Satellite Images, University Of North Dakota. Energy And Environmental Research Center, Xiaodong Zhang Oct 2019

Bakken Flares And Satellite Images, University Of North Dakota. Energy And Environmental Research Center, Xiaodong Zhang

EERC Brochures and Fact Sheets

Fact sheet refuting a magazine article about Bakken gas flares and satellite images. Includes research into gas flares and satellite images by the University of North Dakota and the Energy & Environmental Research Center.


Effects Of Solvent Used For Fabrication On Drug Loading And Release Kinetics Of Electrosprayed Temozolomide-Loaded Plga Microparticles For The Treatment Of Glioblastoma, Daniel A. Rodriguez De Anda, Nareg Ohannesian, Karen S. Martirosyan, Sue Anne Chew Oct 2019

Effects Of Solvent Used For Fabrication On Drug Loading And Release Kinetics Of Electrosprayed Temozolomide-Loaded Plga Microparticles For The Treatment Of Glioblastoma, Daniel A. Rodriguez De Anda, Nareg Ohannesian, Karen S. Martirosyan, Sue Anne Chew

Physics and Astronomy Faculty Publications and Presentations

Glioblastoma multiforme (GBM) is the most common and invasive form of malignant brain tumors and despite advances in surgery, radiotherapy, and chemotherapy, the survival of patients with GBM still remains poor. Temozolomide (TMZ) is the chemotherapy drug that is most commonly given orally after surgical resection of these tumors. In this study, the effects of solvents (i.e., dichloromethane and acetonitrile) used for the fabrication of electrosprayed TMZ-loaded poly(lactic-co-glycolic acid) (PLGA) on drug loading, loading efficiency, drug release kinetics, surface morphology, and particle size were investigated. The results from this study demonstrated that by using a larger volume of a solvent …


Estimating The Angular Power Spectrum Of The Gravitational-Wave Background In The Presence Of Shot Noise, Alexander C. Jenkins, Joseph D. Romano, Mairi Sakellariadou Oct 2019

Estimating The Angular Power Spectrum Of The Gravitational-Wave Background In The Presence Of Shot Noise, Alexander C. Jenkins, Joseph D. Romano, Mairi Sakellariadou

Physics and Astronomy Faculty Publications and Presentations

There has been much recent interest in studying anisotropies in the astrophysical gravitational-wave (GW) background, as these could provide us with interesting new information about galaxy clustering and large-scale structure. However, this information is obscured by shot noise, caused by the finite number of GW sources that contribute to the background at any given time. We develop a new method for estimating the angular spectrum of anisotropies, based on the principle of combining statistically-independent data segments. We show that this gives an unbiased estimate of the true, astrophysical spectrum, removing the offset due to shot noise power, and that …


Characterization Of Argon And Ar/Cl2 Plasmas Used For The Processing Of Niobium Superconducting Radio-Frequency Cavities, Jeremy J. Peshl Oct 2019

Characterization Of Argon And Ar/Cl2 Plasmas Used For The Processing Of Niobium Superconducting Radio-Frequency Cavities, Jeremy J. Peshl

Physics Theses & Dissertations

The plasma processing of superconducting radio-frequency (SRF) cavities has shown significant promise as a complementary or possible replacement for the current wet etch processes. Empirical relationships between the user-controlled external parameters and the effectiveness of Reactive Ion Etching (RIE) for the removal of surface layers of bulk niobium have been previously established. However, a lack of a physical description of the etching discharge, particularly as the external parameters are varied, limits the development of this technology. A full understanding of how these external parameters affect both the amount of material removed and the physical properties of the plasma would aid …


Exercises Integrating High School Mathematics With Robot Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal Oct 2019

Exercises Integrating High School Mathematics With Robot Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal

Computer Science: Faculty Publications and Other Works

This paper presents progress in developing exercises for high school students incorporating level-appropriate mathematics into robotics activities. We assume mathematical foundations ranging from algebra to precalculus, whereas most prior work on integrating mathematics into robotics uses only very elementary mathematical reasoning or, at the other extreme, is comprised of technical papers or books using calculus and other advanced mathematics. The exercises suggested are relevant to any differerential-drive robot, which is an appropriate model for many different varieties of educational robots. They guide students towards comparing a variety of natural navigational strategies making use of typical movement primitives. The exercises align …


Soul Of Cafecs, Lucia Dettori, Steven Mcgee, Ron Greenberg, Dale Reed, Don Yanek, Andrew Rasmussen Oct 2019

Soul Of Cafecs, Lucia Dettori, Steven Mcgee, Ron Greenberg, Dale Reed, Don Yanek, Andrew Rasmussen

Computer Science: Faculty Publications and Other Works

No abstract provided.


Interaction Of A Platinum Triamine Complex Having A Seven-Membered Chelate Ring With N-Acetyl-Lmethionine And Guanosine 5'-Monophosphate, Jae Ko Oct 2019

Interaction Of A Platinum Triamine Complex Having A Seven-Membered Chelate Ring With N-Acetyl-Lmethionine And Guanosine 5'-Monophosphate, Jae Ko

Masters Theses & Specialist Projects

In the 1960s, Rosenberg and his colleagues confirmed the anti-cancer activity of cisplatin. Although cisplatin was capable of killing testicular cancer cells there were also serious side effects. It was necessary to find alternate ways of overcoming side effects, and soon many researchers have discovered novel platinum compounds that show similar reactivity. Recently, replacing one chloride group to a heterocyclic amine group showed significant cytotoxicity with a different binding activity than cisplatin. Previously in our lab, [Pt(Me5dien)(NO3)]+ and [Pt(Et2dien)Cl]+ have been synthesized and reacted with NAcetyl- L-methionine (N-AcMet) and Guanosine 5’-monophosphate (5’-GMP) showed unusual reactivity. Unlike most previously studied platinum …


Leaving Ligand Effects On Reactivity And Solubility Of Monofunctional Platinum(Ii) Anticancer Complexes, Heidi Linn Hruska Millay Oct 2019

Leaving Ligand Effects On Reactivity And Solubility Of Monofunctional Platinum(Ii) Anticancer Complexes, Heidi Linn Hruska Millay

Masters Theses & Specialist Projects

Monofunctional platinum(II) complexes, such as phenanthriplatin and pyriplatin, have notably different characteristics from the bifunctional anticancer complexes, such as cisplatin and oxaliplatin, which have detrimental toxicities and resistance associated with them. The unique properties of the monofunctional complexes may be exploited to target cancer cells without producing the toxic side effects associated with the current FDA-approved platinum-based anticancer drugs. To advance the understanding of these monofunctional platinum(II) complexes, this study replaced the chloride leaving ligand with an acetate group, which should increase solubility and alter the rate of reactivity with key amino acid and nucleotide targets. Phenanthriplatin and pyriplatin compounds …


Development Of An Autonomous Aerial Toolset For Agricultural Applications, Terrance Life Oct 2019

Development Of An Autonomous Aerial Toolset For Agricultural Applications, Terrance Life

Mahurin Honors College Capstone Experience/Thesis Projects

According to the United Nations, the world population is expected to grow from its current 7 billion to 9.7 billion by the year 2050. During this time, global food demand is also expected to increase by between 59% and 98% due to the population increase, accompanied by an increasing demand for protein due to a rising standard of living throughout developing countries. [1] Meeting this increase in required food production using present agricultural practices would necessitate a similar increase in farmland; a resource which does not exist in abundance. Therefore, in order to meet growing food demands, new methods will …


Evaluation Of Reasons That May Affect Whether Academically Capable Females Choose To Major In Stem, Kerri Alexander Adkins Oct 2019

Evaluation Of Reasons That May Affect Whether Academically Capable Females Choose To Major In Stem, Kerri Alexander Adkins

Dissertations

The purpose of this research was to study the reasons why academically capable females choose to pursue majors in STEM (science, technology, engineering, and math) fields. A mixed-methods approach using focus groups and a survey were used. Data were gathered from the focus group sessions and used to develop the survey that was then validated and checked for reliability. After some edits, the survey was administered to female freshmen attending Western Kentucky University. Unfortunately, all female students who completed the survey except one indicated they were pursuing STEM majors.

The results from this study suggest that the reasons surrounding the …


A Comparative Study Of Recommendation Systems, Ashwini Lokesh Oct 2019

A Comparative Study Of Recommendation Systems, Ashwini Lokesh

Masters Theses & Specialist Projects

Recommendation Systems or Recommender Systems have become widely popular due to surge of information at present time and consumer centric environment. Researchers have looked into a wide range of recommendation systems leveraging a wide range of algorithms. This study investigates three popular recommendation systems in existence, Collaborative Filtering, Content-Based Filtering, and Hybrid recommendation system. The famous MovieLens dataset was utilized for the purpose of this study. The evaluation looked into both quantitative and qualitative aspects of the recommendation systems. We found that from both the perspectives, the hybrid recommendation system performs comparatively better than standalone Collaborative Filtering or Content-Based Filtering …


Controllability And Observability Of Linear Nabla Discrete Fractional Systems, Tilekbek Zhoroev Oct 2019

Controllability And Observability Of Linear Nabla Discrete Fractional Systems, Tilekbek Zhoroev

Masters Theses & Specialist Projects

The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of the sequential fractional difference equations. In Chapter 4, we …


Byu’S Connection To The Development Of Optical Memory: Innovation Takes Multiple Disciplines, Dan Broadbent Oct 2019

Byu’S Connection To The Development Of Optical Memory: Innovation Takes Multiple Disciplines, Dan Broadbent

Faculty Publications

Optical memory technology is a way to store information using lasers and is used in videodiscs, CDs, DVDs, Blu-rays, M-Discs, etc. This technology was developed in Torrance, California in the 1970s by a team lead by Kent D. Broadbent, who graduated from BYU with a degree in Physics in 1949.

This display showcases the technology and those involved in its development.


One Story, Told Week By Week: Episodic Podcast Storytelling And The Habitat, Charlotte De Beauvoir Sep 2019

One Story, Told Week By Week: Episodic Podcast Storytelling And The Habitat, Charlotte De Beauvoir

RadioDoc Review

The rise and success of podcasting introduced episodic storytelling in the world of non-fiction sound narrative. Delivering a story in different entries is very different from producing a one-off piece. What concrete implications does this have for the narrative? And what keeps an audience listening to a podcast, episode through episode? This article offers some answers to these questions via a case study of The Habitat, a 2018 podcast by the American network Gimlet.


Identifying Relationships Of Interest In Complex Environments By Using Channel Theory, Andreas Bildstein, Junkang Feng Sep 2019

Identifying Relationships Of Interest In Complex Environments By Using Channel Theory, Andreas Bildstein, Junkang Feng

Communications of the IIMA

Complex environments show a high degree of dynamics caused by vital interactions between objects within those environments and alterations through which the set of objects and their characteristics within those environments go over time. Within this work, we show that we can tame the level of complexity in dynamic environments by identifying relationships of interest between objects in such environments. To this end, we apply the theory of Information Flow, also known as Channel Theory, to the application area of smart manufacturing. We enhance the way how the Channel Theory has been applied so far by using an …


Synthesis And Evaluation Of Novel Silica Hydride-Based Stationary Phases For Bioanalytical Applications Sep 2019

Synthesis And Evaluation Of Novel Silica Hydride-Based Stationary Phases For Bioanalytical Applications

Seiichiro Watanabe

Most HPLC columns are packed with silanol (Si-OH)-rich type-B silica that often
participates in undesired electrostatic interactions with sample solutes and produces a poor analyte peak shape. These silanols are also known to facilitate the surface hydration required for HILIC mode to retain polar analytes. However, the hydrated surface composition can easily fluctuate, which results in poor reproducibility and requires a lengthy equilibration step. In this study, four novel stationary phases have been developed by using the TYPE-CTM silica material, in which up to 95% of the surface silanols have been replaced with Si-H group. One of the advantages of …


Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model, Olusegun M. Otunuga Sep 2019

Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model, Olusegun M. Otunuga

Olusegun Michael Otunuga

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to …