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Item Transcriptomes of Electrophysiologically Recorded Dbx1-derived Respiratory Neurons of the preBötzinger Complex in Neonatal Mice(2022-02-01) Kallurkar, Prajkta S.; Picardo, Maria Cristina D.; Sugimura, Yae K.; Saha, Margaret; Conradi Smith, Gregory D.; Del Negro, Christopher ABreathing depends on interneurons in the preBötzinger complex (preBötC) derived from Dbx1-expressing precursors. Here we investigate whether rhythm- and pattern-generating functions reside in discrete classes of Dbx1 preBötC neurons. In a slice model of breathing with ~ 5 s cycle period, putatively rhythmogenic Type-1 Dbx1 preBötC neurons activate 100–300 ms prior to Type-2 neurons, putatively specialized for output pattern, and 300–500 ms prior to the inspiratory motor output. We sequenced Type-1 and Type-2 transcriptomes and identified differential expression of 123 genes including ionotropic receptors (Gria3, Gabra1) that may explain their preinspiratory activation profiles and Ca2+ signaling (Cracr2a, Sgk1) involved in inspiratory and sigh bursts. Surprisingly, neuropeptide receptors that influence breathing (e.g., µ-opioid and bombesin-like peptide receptors) were only sparsely expressed, which suggests that cognate peptides and opioid drugs exert their profound effects on a small fraction of the preBötC core. These data in the public domain help explain the neural origins of breathing.Item Generating a Close-to-Reality Synthetic Population of Ghana(2012-01-01) Frazier, Tyler; Alfons, AndreasThe purpose of this research is to generate a close-to-reality synthetic human population for use in a geosimulation of urban dynamics. Two commonly accepted approaches to generating synthetic human populations are Iterative Proportional Fitting (IPF) and Resampling with Replacement. While these methods are effective at reproducing one instance of the probability model describing the survey, it is an instance with extremely small variability amongst subgroups and is very unlikely to be the real population. IPF and Resampling with Replacement also rely on pure replication of units from the underlying sample which can increase unrealistic model behavior. In this work we present a sequential logic for estimating variables using multinomial logistic regressions and the conditional probabilities amongst each variable in order to generate combinations which were not represented in the original survey but are likely to occur in the real population. We also present a model based approach to imputing missing observation responses and apply the methodology to the Ghana Living Standard Survey 5 (GLSS5) in order to generate a comprehensive synthetic population for the Republic of Ghana, including such household and person variables as household size, tribal affiliation, educational attainment and annual income, amongst others. The R language and environment for statistical computing was used as well as the packages VIM and simPopulation in developing and executing the code. Contingency coefficients, cumulative distributions, mosaic plots, and box plots are presented for evaluation in order to demonstrate the effectiveness of the new method in its application to Ghana.Item Computational Algebra Applications in Reliability(IEEE, 1996-09-01) Hartless, G; Leemis, LawrenceReliability analysts are typically forced to choose between using an 'algorithmic programming language' or a 'reliability package' for analyzing their models and lifetime data. This paper shows that computational languages can be used to bridge the gap to combine the flexibility of a programming language with the ease of use of a package. Computational languages facilitate the development of new statistical techniques and are excellent teaching tools. This paper considers three diverse reliability problems that are handled easily with a computational algebra language: system reliability bounds; lifetime data analysis; and model selection.Item On the minimum of independent geometrically distributed random variables(Elsevier, 1995) Ciardo, Gianfranco; Leemis, Lawrence; Nicol, DavidThe expectations E[X(1)], E[Z(1)], and E[Y(1)] of the minimum of n independent geometric, modified geometric, or exponential random variables with matching expectations differ. We show how this is accounted for by stochastic variability and how E[X(1)]/E[Y(1)] equals the expected number of ties at the minimum for the geometric random variables. We then introduce the “shifted geometric distribution”, and show that there is a unique value of the shift for which the individual shifted geometric and exponential random variables match expectations both individually and in their minimums.Item Variate Generation for Nonhomogeneous Poisson Processes with Time Dependent Covariates(Taylor & Francis, 1993) Shih, Li-Hsing; Leemis, LawrenceAlgorithms are developed for generating a sequence of event times from a nonhomogeneous Poisson process that is influenced by the values of covariates that vary with time. Closed form expressions for random variate generation are shown for several baseline intensity and link functions. Two specific models linking the baseline process to the general model are considered: the accelerated time model and the proportional intensity model. In the accelerated time model, the cumulative intensity function of a nonhomogeneous Poisson process under covariate effects is [formula], where z is a covariate vector, ⋀0(t) is the baseline cumulative intensity function and ψ(z) is the link function. In the proportional intensity model, the cumulative intensity function of a nonhomogeneous Poisson process under covariate effects is [formula], where λ0(t) is the baseline intensity function.Item A Generalized Univariate Change-of-Variable Transformation Technique(INFORMS, 1997-08-01) Glen, Andrew G.; Leemis, Lawrence; Drew, John H.We present a generalized version of the univariate change-of-variable technique for transforming continuous random variables. Extending a theorem from Casella and Berger [1990. Statistical Inference, Wadsworth and Brooks/Cole, Inc., Pacific Grove, CA] for many-to-1 transformations, we consider more general univariate transformations. Specifically, the transformation can range from 1-to-1 to many-to-1 on various subsets of the support of the random variable of interest. We also present an implementation of the theorem in a computer algebra system that automates the technique. Some examples demonstrate the theorem's application.Item Computing the cumulative distribution function of the Kolmogorov–Smirnov statistic(2000-07-01) Drew, John H.; Glen, Andrew G.; Leemis, LawrenceWe present an algorithm for computing the cumulative distribution function of the Kolmogorov–Smirnov test statistic Dn in the all-parameters-known case. Birnbaum (1952, J. Amer. Statist. Assoc. 47, 425–441), gives an n-fold integral for the CDF of the test statistic which yields a function defined in a piecewise fashion, where each piece is a polynomial of degree n. Unfortunately, it is difficult to determine the appropriate limits of integration for computing these polynomials. Our algorithm performs the required integrations in a manner that avoids calculating the same integrals repeatedly, resulting in shorter computation time. It can be used to compute the entire CDF or just a portion of the CDF, which is more efficient for finding a critical value or a p-value associated with a hypothesis test. If the entire CDF is computed, it can be stored in memory so that various characteristics of the distribution of the test statistic (e.g., moments) can be calculated. To date, critical tables have been approximated by various techniques including asymptotic approximations, recursive formulas, and Monte Carlo simulation. Our approach yields exact critical values and significance levels. The algorithm has been implemented in a computer algebra system.Item Random Sampling(Lawrence M. Leemis, 2020-01-01) Leemis, LawrenceMathematical Statistics describes the mathematical underpinnings associated with the practice of statistics. The pre-requisite for this book is a calculus-based course in probability. Nearly 200 figures and dozens of Monte Carlo simulation experiments in R help develop the intuition behind the statistical methods. Real-world problems from a wide range of fields help the reader apply the statistical methods. Over 300 exercises are used to reinforce concepts and make this book appropriate for classroom use. The table of contents for this book is given below. 1. Random Sampling 2. Point Estimation 3. Interval Estimation 4. Hypothesis TestingItem Introducing R(Lawrence M. Leemis, 2022-01-01) Leemis, LawrenceR is an open source programming language and interactive programming environment that has become the software tool of choice in data analytics. Learning Base R provides an introduction to the language for those with and without prior programming experience. It introduces the key topics that you will need to begin analyzing data and programming in R. The focus here is on the R language rather than a particular application. Within the text, there are 200 exercises to assess your R skills.