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- Mathematics, Statistics and Computer Science Faculty Research and Publications (315)
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Articles 1 - 30 of 338
Full-Text Articles in Physical Sciences and Mathematics
Enhancing Motor Imagery Decoding Via Transfer Learning, Olawunmi George, Sarthak Dabas, Abdur Sikder, Roger Smith, Praveen Madiraju, Nasim Yahyasoltani, Sheikh Iqbal Ahamed
Enhancing Motor Imagery Decoding Via Transfer Learning, Olawunmi George, Sarthak Dabas, Abdur Sikder, Roger Smith, Praveen Madiraju, Nasim Yahyasoltani, Sheikh Iqbal Ahamed
Computer Science Faculty Research and Publications
Motor imagery (MI) is arguably one of the most common brain–computer interface (BCI) paradigms. The decoding process, in many cases, involves the use of small amounts of data gathered over a period. The decoding performance might therefore be limited, due to the size of available data. Also, the non-stationarity of signals across sessions and subjects can pose a challenge to effective decoding. To solve these challenges, transfer learning is proposed as the suitable approach, which could yield optimal performance even with small amounts of data and handle the non-stationarity of signals with adaptation. It has been applied across domains and …
Gray Counters For Non-Volatile Memories, Arockia David Roy Kulandai, John Rose, Thomas Schwarz
Gray Counters For Non-Volatile Memories, Arockia David Roy Kulandai, John Rose, Thomas Schwarz
Computer Science Faculty Research and Publications
New technologies for non-volatile memories combine the speed and byte addressability of current memory technologies with the low cost, density, and non-volatility of current storage technologies. They use energy only when writing or reading data. While some newer technologies have practically unlimited endurance, others, such as Phase Change Memory do not. However, this limited endurance surpasses that of solid state drives by several orders of magnitude. They can be integrated into the current memory storage hierarchy as a replacement for DRAM. To manage limited endurance, age-based wear leveling divides the memory into pages and counts the number of writes to …
Emerging Technologies, Evolving Threats: Next-Generation Security Challenges, Tamara Bonaci, Katina Michael, Pablo Rivas, Lindsay J. Roberston, Michael Zimmer
Emerging Technologies, Evolving Threats: Next-Generation Security Challenges, Tamara Bonaci, Katina Michael, Pablo Rivas, Lindsay J. Roberston, Michael Zimmer
Computer Science Faculty Research and Publications
Security is a fundamental human requirement. We desire the security of our person against injury, security of our capability to provide for our families, security of income linked to needs (food, water, clothing, and shelter), and much more. Most also hope for security of a way of life that is fulfilling and pleasant and peaceful [1] . In 2003, Alkire [2] defined “human security” as: “[t]he objective … to safeguard the vital core of all human lives from critical pervasive threats, in a way that is consistent with long-term human fulfillment.” Today most of the world’s population is highly dependent, …
Data Augmentation Strategies For Eeg-Based Motor Imagery Decoding, Olawunmi George, Roger Smith, Praveen Madiraju, Nasim Yahyasoltani, Sheikh Iqbal Ahamed
Data Augmentation Strategies For Eeg-Based Motor Imagery Decoding, Olawunmi George, Roger Smith, Praveen Madiraju, Nasim Yahyasoltani, Sheikh Iqbal Ahamed
Computer Science Faculty Research and Publications
The wide use of motor imagery as a paradigm for brain-computer interfacing (BCI) points to its characteristic ability to generate discriminatory signals for communication and control. In recent times, deep learning techniques have increasingly been explored, in motor imagery decoding. While deep learning techniques are promising, a major challenge limiting their wide adoption is the amount of data available for decoding. To combat this challenge, data augmentation can be performed, to enhance decoding performance. In this study, we performed data augmentation by synthesizing motor imagery (MI) electroencephalography (EEG) trials, following six approaches. Data generated using these methods were evaluated based …
Context-Aware Graph-Based Self-Supervised Learning Of Whole Slide Images, Milam Aryal, Nasim Yahyasoltani
Context-Aware Graph-Based Self-Supervised Learning Of Whole Slide Images, Milam Aryal, Nasim Yahyasoltani
Computer Science Faculty Research and Publications
The gigapixel resolution of a single whole slide image (WSI), and the lack of huge annotated datasets needed for computational pathology, makes cancer diagnosis and grading with WSIs a challenging task. Moreover, downsampling of WSIs might result in loss of information critical for cancer diagnosis. Motivated by the fact that context such as topological structures in the tumor environment may contain critical information in cancer grading and diagnosis, a novel two-stage learning approach is proposed. Self-supervised learning is applied to improve training through unlabled data and graph convolutional network (GCN) is deployed to incorporate context from tumor and surrounding tissues. …
A Novel Framework For Mixed Reality–Based Control Of Collaborative Robot: Development Study, Md. Tanzil Shahria, Md. Samiul Haque Sunny, Md. Ishrak Islam Zarif, Md. Mahafuzur Rahaman Khan, Preet Parag Modi, Sheikh Iqbal Ahamed, Mohammad H. Rahman
A Novel Framework For Mixed Reality–Based Control Of Collaborative Robot: Development Study, Md. Tanzil Shahria, Md. Samiul Haque Sunny, Md. Ishrak Islam Zarif, Md. Mahafuzur Rahaman Khan, Preet Parag Modi, Sheikh Iqbal Ahamed, Mohammad H. Rahman
Computer Science Faculty Research and Publications
Background:
Applications of robotics in daily life are becoming essential by creating new possibilities in different fields, especially in the collaborative environment. The potentials of collaborative robots are tremendous as they can work in the same workspace as humans. A framework employing a top-notch technology for collaborative robots will surely be worthwhile for further research.
Objective:
This study aims to present the development of a novel framework for the collaborative robot using mixed reality.
Methods:
The framework uses Unity and Unity Hub as a cross-platform gaming engine and project management tool to design the mixed reality interface and digital twin. …
Guest Editorial: Introduction To Aoir 2021 Papers On Emerging Ethical Practices And Platform Challenges, Michael Zimmer
Guest Editorial: Introduction To Aoir 2021 Papers On Emerging Ethical Practices And Platform Challenges, Michael Zimmer
Computer Science Faculty Research and Publications
No abstract provided.
Privacy Concerns With Using Public Data For Suicide Risk Prediction Algorithms: A Public Opinion Survey Of Contextual Appropriateness, Michael Zimmer, Sarah Logan
Privacy Concerns With Using Public Data For Suicide Risk Prediction Algorithms: A Public Opinion Survey Of Contextual Appropriateness, Michael Zimmer, Sarah Logan
Computer Science Faculty Research and Publications
Purpose
Existing algorithms for predicting suicide risk rely solely on data from electronic health records, but such models could be improved through the incorporation of publicly available socioeconomic data – such as financial, legal, life event and sociodemographic data. The purpose of this study is to understand the complex ethical and privacy implications of incorporating sociodemographic data within the health context. This paper presents results from a survey exploring what the general public’s knowledge and concerns are about such publicly available data and the appropriateness of using it in suicide risk prediction algorithms.
Design/methodology/approach
A survey was developed to measure …
Accelerating Spatial Autocorrelation Computation With Parallelization, Vectorization And Memory Access Optimization, Anmol Paudel, Satish Puri
Accelerating Spatial Autocorrelation Computation With Parallelization, Vectorization And Memory Access Optimization, Anmol Paudel, Satish Puri
Computer Science Faculty Research and Publications
No abstract provided.
Workers’ Attitudes Toward Increased Surveillance During And After The Covid-19 Pandemic, Jessica Vitak, Michael Zimmer
Workers’ Attitudes Toward Increased Surveillance During And After The Covid-19 Pandemic, Jessica Vitak, Michael Zimmer
Computer Science Faculty Research and Publications
Amid the Covid-19 pandemic, the transition of many offices to remote work has led to new ways for employers to track workers’ movements, behavior, and productivity. Through their SSRC-funded research, Jessica Vitak and Michael Zimmer surveyed remote workers in the US about perceptions of current workplace monitoring practices. They argue that worker concerns about reductions in privacy and independence at work might have negative outcomes on worker productivity, satisfaction, and well-being.
Needles In A Haystack: How Pooling Can Control Error Rates In Noisy Tests, Arockia David Roy Kulandai, J. Stella, John Rose, Thomas Schwarz
Needles In A Haystack: How Pooling Can Control Error Rates In Noisy Tests, Arockia David Roy Kulandai, J. Stella, John Rose, Thomas Schwarz
Computer Science Faculty Research and Publications
Testing many individuals for a reasonably rare condition using imperfect, time consuming, and expensive tests can be facilitated by pooling. Pooling groups samples from different individuals that are then tested for the existence of a pathogen. An individual is diagnosed as a carrier if a threshold of the tests to which the individual contributed samples is positive. Our assumptions dictate a testing strategy that is not adaptive, with the exception of retesting positively diagnosed persons individually. Pooling is a standard proposal to stretch the supply of test kits. We show that it can also be used to control the false …
Comparing Generic And Community-Situated Crowdsourcing For Data Validation In The Context Of Recovery From Substance Use Disorders, Sabirat Rubya, Joseph Numainville, Svetlana Yarosh
Comparing Generic And Community-Situated Crowdsourcing For Data Validation In The Context Of Recovery From Substance Use Disorders, Sabirat Rubya, Joseph Numainville, Svetlana Yarosh
Computer Science Faculty Research and Publications
Targeting the right group of workers for crowdsourcing often achieves better quality results. One unique example of targeted crowdsourcing is seeking community-situated workers whose familiarity with the background and the norms of a particular group can help produce better outcome or accuracy. These community-situated crowd workers can be recruited in different ways from generic online crowdsourcing platforms or from online recovery communities. We evaluate three different approaches to recruit generic and community-situated crowd in terms of the time and the cost of recruitment, and the accuracy of task completion. We consider the context of Alcoholics Anonymous (AA), the largest peer …
Efficient Filters For Geometric Intersection Computations Using Gpu, Yiming Liu, Satish Puri
Efficient Filters For Geometric Intersection Computations Using Gpu, Yiming Liu, Satish Puri
Computer Science Faculty Research and Publications
Geometric intersection algorithms are fundamental in spatial analysis in Geographic Information System (GIS). Applying high performance computing to perform geometric intersection on huge amount of spatial data to get real-time results is necessary. Given two input geometries (polygon or polyline) of a candidate pair, we introduce a new two-step geospatial filter that first creates sketches of the geometries and uses it to detect workload and then refines the sketches by the common areas of sketches to decrease the overall computations in the refine phase. We call this filter PolySketch-based CMBR (PSCMBR) filter. We show the application of this filter in …
On Continuous Images Of Ultra-Arcs, Paul Bankston
On Continuous Images Of Ultra-Arcs, Paul Bankston
Mathematics, Statistics and Computer Science Faculty Research and Publications
Any space homeomorphic to one of the standard subcontinua of the Stone-Čech remainder of the real half-line is called an ultra-arc. Alternatively, an ultra-arc may be viewed as an ultracopower of the real unit interval via a free ultrafilter on a countable set. It is known that any continuum of weight is a continuous image of any ultra-arc; in this paper we address the problem of which continua are continuous images under special maps. Here are some of the results we present.
Functional Singular Spectrum Analysis And The Clustering Of Time-Dependent Data, Jordan Trinka
Functional Singular Spectrum Analysis And The Clustering Of Time-Dependent Data, Jordan Trinka
Mathematics, Statistics and Computer Science Student Research
The present work extends the application of the recently submitted functional singular spectrum analysis (FSSA) into the realm of structure level subsequence clustering. We begin with a comprehensive review of principal component analysis (PCA), functional principal component analysis (FPCA), singular spectrum analysis (SSA), and the recently submitted FSSA. We computationally show that the novel FSSA-FPCA hybrid clustering technique can be employed as an effective structure-based subsequence clustering method for call-center functional time series data where the method behaves as a dimension reduction technique for time-dependent data. Metrics, such as the F-ratio from k-means clustering, the w-correlation between reconstructed functional time …
Implementing Cybersecurity Into The Wisconsin K-12 Classroom, Dennis Brylow, Justin Wang, Debbie Perouli
Implementing Cybersecurity Into The Wisconsin K-12 Classroom, Dennis Brylow, Justin Wang, Debbie Perouli
Computer Science Faculty Research and Publications
Cybersecurity is a field that has seen its workforce demands rising steadily throughout the past decade. Although the Wisconsin Department of Administration has been actively encouraging collaboration efforts between the public and private sectors and promoting cybersecurity as a promising career path, the demand for cybersecurity professionals continues to be greater than the supply, which is a trend noticed also nationwide. The state of Wisconsin is facing several challenges in attempting to promote cybersecurity including limited security curricula resources, lack of programs and other initiatives that promote security principles, and lack of awareness of cybersecurity risks. In this paper, we …
Privacy, Michael Zimmer
Privacy, Michael Zimmer
Computer Science Faculty Research and Publications
Privacy is a difficult concept to singularly define. Its meaning, value, and level of protection vary across cultures and have evolved continuously over time. Yet, from an information policy and ethics perspective, privacy has had a central role to play throughout history, sparking considerable debate, and often rising in importance alongside technological development.
Mirdriver: A Tool To Infer Copy Number Derived Mirna-Gene Networks In Cancer, Banabithi Bose, Serdar Bozdag
Mirdriver: A Tool To Infer Copy Number Derived Mirna-Gene Networks In Cancer, Banabithi Bose, Serdar Bozdag
Computer Science Faculty Research and Publications
Copy number aberration events such as amplifications and deletions in chromosomal regions are prevalent in cancer patients. Frequently aberrated copy number regions include regulators such as microRNAs (miRNAs), which regulate downstream target genes that involve in the important biological processes in tumorigenesis and proliferation. Many previous studies explored the miRNA-gene interaction networks but copy number-derived miRNA regulations are limited. Identifying copy number-derived miRNA-target gene regulatory interactions in cancer could shed some light on biological mechanisms in tumor initiation and progression. In the present study, we developed a computational pipeline, called miRDriver which is based on the hypothesis that copy number …
Phenogeneranker: A Tool For Gene Prioritization Using Complete Multiplex Heterogeneous Networks, Cagatay Dursun, Naoki Shimoyama, Mary Shimoyama, Michael Schläppi, Serdar Bozdag
Phenogeneranker: A Tool For Gene Prioritization Using Complete Multiplex Heterogeneous Networks, Cagatay Dursun, Naoki Shimoyama, Mary Shimoyama, Michael Schläppi, Serdar Bozdag
Computer Science Faculty Research and Publications
Uncovering genotype-phenotype relationships is a fundamental challenge in genomics. Gene prioritization is an important step for this endeavor to make a short manageable list from a list of thousands of genes coming from high-throughput studies. Network propagation methods are promising and state of the art methods for gene prioritization based on the premise that functionally-related genes tend to be close to each other in the biological networks.
In this study, we present PhenoGeneRanker, an improved version of a recently developed network propagation method called Random Walk with Restart on Multiplex Heterogeneous Networks (RWR-MH). PhenoGeneRanker allows multi-layer gene and disease networks. …
Analyzing Happiness: Investigation On Happy Moments Using A Bag-Of-Words Approach And Related Ethical Discussions, Riddhiman Adib, Eyad Aldawood, Nathan Lang, Nina Lasswell, Shion Guha
Analyzing Happiness: Investigation On Happy Moments Using A Bag-Of-Words Approach And Related Ethical Discussions, Riddhiman Adib, Eyad Aldawood, Nathan Lang, Nina Lasswell, Shion Guha
Computer Science Faculty Research and Publications
In this research paper, we analyzed what moments and activities make people happy, based on a collection of happy moments. We are focusing on specific happy moments from a collection of text responses that people have shared through the crowd-sourcing platform: Amazon Mechanical Turk (MTurk). Using crowd-sourcing to collect our data allows us to advance our understanding of the cause of happiness, by focusing on words and real human experiences. Workers of MTurk were asked to reflect on what makes them happy in a given period and share three specific moments in complete sentences. Through text-based analysis, we will look …
Exploring The Impact Of (Not) Changing Default Settings In Algorithmic Crime Mapping - A Case Study Of Milwaukee, Wisconsin, Md Romael Haque, Katy Weathington, Shion Guha
Exploring The Impact Of (Not) Changing Default Settings In Algorithmic Crime Mapping - A Case Study Of Milwaukee, Wisconsin, Md Romael Haque, Katy Weathington, Shion Guha
Computer Science Faculty Research and Publications
Policing decisions, allocations and outcomes are determined by mapping historical crime data geo-spatially using popular algorithms. In this extended abstract, we present early results from a mixed-methods study of the practices, policies, and perceptions of algorithmic crime mapping in the city of Milwaukee, Wisconsin. We investigate this differential by visualizing potential demographic biases from publicly available crime data over 12 years (2005-2016) and conducting semi-structured interviews of 19 city stakeholders and provide future research directions from this study.
Characterizations Of Certain Recently Introduced Discrete Distributions, Gholamhossein G. Hamedani
Characterizations Of Certain Recently Introduced Discrete Distributions, Gholamhossein G. Hamedani
Mathematics, Statistics and Computer Science Faculty Research and Publications
Characterizations of certain recently introduced discrete distributions are presented to complete, in some way, the works cited in the References.
Nonparametric Collective Spectral Density Estimation With An Application To Clustering The Brain Signals, Mehdi Maadooliat, Ying Sun, Tianbo Chen
Nonparametric Collective Spectral Density Estimation With An Application To Clustering The Brain Signals, Mehdi Maadooliat, Ying Sun, Tianbo Chen
Mathematics, Statistics and Computer Science Faculty Research and Publications
In this paper, we develop a method for the simultaneous estimation of spectral density functions (SDFs) for a collection of stationary time series that share some common features. Due to the similarities among the SDFs, the log‐SDF can be represented using a common set of basis functions. The basis shared by the collection of the log‐SDFs is estimated as a low‐dimensional manifold of a large space spanned by a prespecified rich basis. A collective estimation approach pools information and borrows strength across the SDFs to achieve better estimation efficiency. Moreover, each estimated spectral density has a concise representation using the …
Smartphone-Based Prenatal Education For Parents With Preterm Birth Risk Factors, U. Olivia Kim, K. Barnekow, Sheikh Iqbal Ahamed, S. Dreier, C. Jones, M. Taylor, Md Kamrul Hasan, M. A. Basir
Smartphone-Based Prenatal Education For Parents With Preterm Birth Risk Factors, U. Olivia Kim, K. Barnekow, Sheikh Iqbal Ahamed, S. Dreier, C. Jones, M. Taylor, Md Kamrul Hasan, M. A. Basir
Mathematics, Statistics and Computer Science Faculty Research and Publications
Objective
To develop an educational mobile application (app) for expectant parents diagnosed with risk factors for premature birth.
Methods
Parent and medical advisory panels delineated the vision for the app. The app helps prepare for preterm birth. For pilot testing, obstetricians offered the app between 18–22 weeks gestational age to English speaking parents with risk factors for preterm birth. After 4 weeks of use, each participant completed a questionnaire. The software tracked topics accessed and duration of use.
Results
For pilot testing, 31 participants were recruited and 28 completed the questionnaire. After app utilization, participants reported heightened awareness of preterm …
Semicontinuity Of Betweenness Functions, Paul Bankston, Aisling Mccluskey, Richard J. Smith
Semicontinuity Of Betweenness Functions, Paul Bankston, Aisling Mccluskey, Richard J. Smith
Mathematics, Statistics and Computer Science Faculty Research and Publications
A ternary relational structure〈X,[⋅,⋅,⋅]〉, interpreting a notion of betweenness, gives rise to the family of intervals, with interval [a,b] being defined as the set of elements of X between a and b. Under very reasonable circumstances, X is also equipped with some topological structure, in such a way that each interval is a closed nonempty subset of X. The question then arises as to the continuity behavior—within the hyperspace context—of the betweenness function {x,y}↦[x,y]. We investigate two broad scenarios: the first involves metric spaces and Menger's betweenness interpretation; the second deals with continua and the subcontinuum interpretation.
The Transmuted Geometric-Quadratic Hazard Rate Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad
The Transmuted Geometric-Quadratic Hazard Rate Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad
Mathematics, Statistics and Computer Science Faculty Research and Publications
We propose a five parameter transmuted geometric quadratic hazard rate (TG-QHR) distribution derived from mixture of quadratic hazard rate (QHR), geometric and transmuted distributions via the application of transmuted geometric-G (TG-G) family of Afify et al.(Pak J Statist 32(2), 139-160, 2016). Some of its structural properties are studied. Moments, incomplete moments, inequality measures, residual life functions and some other properties are theoretically taken up. The TG-QHR distribution is characterized via different techniques. Estimates of the parameters for TG-QHR distribution are obtained using maximum likelihood method. The simulation studies are performed on the basis of graphical results to illustrate the performance …
Empirical Bayesian Approach To Testing Multiple Hypotheses With Separate Priors For Left And Right Alternatives, Naveen K. Bansal, Mehdi Maadooliat, Steven J. Schrodi
Empirical Bayesian Approach To Testing Multiple Hypotheses With Separate Priors For Left And Right Alternatives, Naveen K. Bansal, Mehdi Maadooliat, Steven J. Schrodi
Mathematics, Statistics and Computer Science Faculty Research and Publications
We consider a multiple hypotheses problem with directional alternatives in a decision theoretic framework. We obtain an empirical Bayes rule subject to a constraint on mixed directional false discovery rate (mdFDR≤α) under the semiparametric setting where the distribution of the test statistic is parametric, but the prior distribution is nonparametric. We proposed separate priors for the left tail and right tail alternatives as it may be required for many applications. The proposed Bayes rule is compared through simulation against rules proposed by Benjamini and Yekutieli and Efron. We illustrate the proposed methodology for two sets of …
Cancerin: A Computational Pipeline To Infer Cancer-Associated Cerna Interaction Networks, Duc Do, Serdar Bozdag
Cancerin: A Computational Pipeline To Infer Cancer-Associated Cerna Interaction Networks, Duc Do, Serdar Bozdag
Mathematics, Statistics and Computer Science Faculty Research and Publications
MicroRNAs (miRNAs) inhibit expression of target genes by binding to their RNA transcripts. It has been recently shown that RNA transcripts targeted by the same miRNA could “compete” for the miRNA molecules and thereby indirectly regulate each other. Experimental evidence has suggested that the aberration of such miRNA-mediated interaction between RNAs—called competing endogenous RNA (ceRNA) interaction—can play important roles in tumorigenesis. Given the difficulty of deciphering context-specific miRNA binding, and the existence of various gene regulatory factors such as DNA methylation and copy number alteration, inferring context-specific ceRNA interactions accurately is a computationally challenging task. Here we propose a computational …
Reality Versus Grant Application Research “Plans”, Linda Burhansstipanov, Linda U. Krebs, Daniel Petereit, Mark Dignan, Sheikh Iqbal Ahamed, Michele Sargent, Krisin Cina, Kimberly Crawford, Doris Thibeault, Simone Bordeaux, Shalini Kanekar, Golam Mushih Tanimul Ahsan, Drew Williams, Ivor D. Addo
Reality Versus Grant Application Research “Plans”, Linda Burhansstipanov, Linda U. Krebs, Daniel Petereit, Mark Dignan, Sheikh Iqbal Ahamed, Michele Sargent, Krisin Cina, Kimberly Crawford, Doris Thibeault, Simone Bordeaux, Shalini Kanekar, Golam Mushih Tanimul Ahsan, Drew Williams, Ivor D. Addo
Mathematics, Statistics and Computer Science Faculty Research and Publications
This article describes the implementation of the American Indian mHealth Smoking Dependence Study focusing on the differences between what was written in the grant application compared to what happened in reality. The study was designed to evaluate a multicomponent intervention involving 256 participants randomly assigned to one of 15 groups. Participants received either a minimal or an intense level of four intervention components: (1) nicotine replacement therapy, (2) precessation counseling, (3) cessation counseling, and (4) mHealth text messaging. The project team met via biweekly webinars as well as one to two in-person meetings per year throughout the study. The project …
A Note On Sum, Difference, Product And Ratio Of Kumaraswamy Random Variables, Avishek Mallick, Indranil Ghosh, Gholamhossein G. Hamedani
A Note On Sum, Difference, Product And Ratio Of Kumaraswamy Random Variables, Avishek Mallick, Indranil Ghosh, Gholamhossein G. Hamedani
Mathematics, Statistics and Computer Science Faculty Research and Publications
Explicit expressions for the densities of S = X1 + X2 , D = X1 − X2 , P = X1X2 and R= X1/X2 are derived when X1 and X2 are independent or sub-independent Kumaraswamy random variables. The expressions appear to involve the incomplete gamma functions. Some possible real life scenarios are mentioned in which such quantities might be of interest.