Statistics and Probability Commons^™

Quantifying The Statistical Impact Of Grappa In Fcmri Data With A Real-Valued Isomorphism, Iain P. Bruce, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

The interpolation of missing spatial frequencies through the generalized auto-calibrating partially parallel acquisitions (GRAPPA) parallel magnetic resonance imaging (MRI) model implies a correlation is induced between the acquired and reconstructed frequency measurements. As the parallel image reconstruction algorithms in many medical MRI scanners are based on the GRAPPA model, this study aims to quantify the statistical implications that the GRAPPA model has in functional connectivity studies. The linear mathematical framework derived in the work of Rowe , 2007, is adapted to represent the complex-valued GRAPPA image reconstruction operation in terms of a real-valued isomorphism, and a statistical analysis is performed …

When Semi-Monotone Implies Monotone, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The basic theme of this talk is the extrinsic description of objects by means of morphisms. One way to do this is to say that all monomorphisms from the object are “special” in some way; the dual of this is to single out epimorphisms to the object.

A Statistical Fmri Model For Differential T2* Contrast Incorporating T1 And T2* Of Gray Matter, M. Muge Karaman, Iain P. Bruce, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Relaxation parameter estimation and brain activation detection are two main areas of study in magnetic resonance imaging (MRI) and functional magnetic resonance imaging (fMRI). Relaxation parameters can be used to distinguish voxels containing different types of tissue whereas activation determines voxels that are associated with neuronal activity. In fMRI, the standard practice has been to discard the first scans to avoid magnetic saturation effects. However, these first images have important information on the MR relaxivities for the type of tissue contained in voxels, which could provide pathological tissue discrimination. It is also well-known that the voxels located in gray matter …

Trivial Meet And Join Within The Lattice Of Monotone Triangles, John Engbers, Adam Hammett

Mathematics, Statistics and Computer Science Faculty Research and Publications

The lattice of monotone triangles (�_n, ≼) ordered by entry-wise comparisons is studied. Let τ_min denote the unique minimal element in this lattice, and τ_max the unique maximum. The number of r-tuples of monotone triangles (τ₁...,τ_r) with minimul infimum τ_min (maximul supremum τ_max, resp.) is shown to asymptotically approach r|�_n|^r-1 as n→ ∞. Thus, with high probability this even implies that one of the τ_i is τ_min (τ_max, resp.). Higher-order error terms are also discussed.

Master Regulators, Regulatory Networks, And Pathways Of Glioblastoma Subtypes, Serdar Bozdag, Aiguo Li, Mehmet Baysan, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Glioblastoma multiforme (GBM) is the most common malignant brain tumor. GBM samples are classified into subtypes based on their transcriptomic and epigenetic profiles. Despite numerous studies to better characterize GBM biology, a comprehensive study to identify GBM subtype-specific master regulators, gene regulatory networks, and pathways is missing. Here, we used FastMEDUSA to compute master regulators and gene regulatory networks for each GBM subtype. We also ran Gene Set Enrichment Analysis and Ingenuity Pathway Analysis on GBM expression dataset from The Cancer Genome Atlas Project to compute GBM- and GBM subtype-specific pathways. Our analysis was able to recover some of the …

Hp-Daemon: HIgh PErformance DIstributed ADaptive ENergy-Efficient MAtrix-MultiplicatiOn, Li Tan, Longxiang Chen, Zizhong Chen, Ziliang Zong, Rong Ge, Dong Li

Mathematics, Statistics and Computer Science Faculty Research and Publications

The demands of improving energy efficiency for high performance scientific applications arise crucially nowadays. Software-controlled hardware solutions directed by Dynamic Voltage and Frequency Scaling (DVFS) have shown their effectiveness extensively. Although DVFS is beneficial to green computing, introducing DVFS itself can incur non-negligible overhead, if there exist a large number of frequency switches issued by DVFS. In this paper, we propose a strategy to achieve the optimal energy savings for distributed matrix multiplication via algorithmically trading more computation and communication at a time adaptively with user-specified memory costs for less DVFS switches, which saves 7.5% more energy on average than …

Recurrence Relations For Moments Of Dual Generalized Order Statistics From Weibull Gamma Distribution And Its Characterizations, M. A. W. Mahmoud, Y. Abdel-Aty, N. M. Mohamed, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this paper, we establish explicit forms and new recurrence relations satisfied by the single and product moments of dual generalized order statistics from Weibull gamma distribution (WGD). The results include as particular cases the relations for moments of reversed order statistics and lower records. We present characterizations of WGD based on (i) recurrence relation for single moments, (ii) truncated moments of certain function of the variable and (iii) hazard function.

Indemics: An Interactive High-Performance Computing Framework For Data Intensive Epidemic Modeling, Keith R. Bisset, Jiangzhuo Chen, Suruchi Deodhar, Xizhou Feng, Yifei Ma, Madhav V. Marathe

Mathematics, Statistics and Computer Science Faculty Research and Publications

We describe the design and prototype implementation of Indemics (_Interactive; Epi_demic; _Simulation;)—a modeling environment utilizing high-performance computing technologies for supporting complex epidemic simulations. Indemics can support policy analysts and epidemiologists interested in planning and control of pandemics. Indemics goes beyond traditional epidemic simulations by providing a simple and powerful way to represent and analyze policy-based as well as individual-based adaptive interventions. Users can also stop the simulation at any point, assess the state of the simulated system, and add additional interventions. Indemics is available to end-users via a web-based interface.

Detailed performance analysis shows that Indemics greatly enhances the …

Efficient Detection Of Counterfeit Products In Large-Scale Rfid Systems Using Batch Authentication Protocols, Farzana Rahman, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

RFID technology facilitates processing of product information, making it a promising technology for anti-counterfeiting. However, in large-scale RFID applications, such as supply chain, retail industry, pharmaceutical industry, total tag estimation and tag authentication are two major research issues. Though there are per-tag authentication protocols and probabilistic approaches for total tag estimation in RFID systems, the RFID authentication protocols are mainly per-tag-based where the reader authenticates one tag at each time. For a batch of tags, current RFID systems have to identify them and then authenticate each tag sequentially, one at a time. This increases the protocol execution time due to …

Remarks On A Paper Of Lee And Lim, Gholamhossein Hamedani, Michael Slattery

Mathematics, Statistics and Computer Science Faculty Research and Publications

Lee and Lim (2009) state three characterizations of Loamax, exponential and power function distributions, the proofs of which, are based on the solutions of certain second order non-linear differential equations. For these characterizations, they make the following statement : "Therefore there exists a unique solution of the differential equation that satisfies the given initial conditions". Although the general solution of their first differential equation is easily obtainable, they do not obtain the general solutions of the other two differential equations to ensure their claim via initial conditions. In this very short report, we present the general solutions of these equations …

The Transmuted Marshall-Olkin Fréchet Distribution: Properties And Applications, Ahmed Z. Afify, Gholamhossein Hamedani, Indranil Ghosh, M. E. Mead

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper introduces a new four-parameter lifetime model, which extends the Marshall-Olkin Fréchet distribution introduced by Krishna et al. (2013), called the transmuted Marshall-Olkin Fréchet distribution. Various structural properties including ordinary and incomplete moments, quantile and generating function, Rényi and q-entropies and order statistics are derived. The maximum likelihood method is used to estimate the model parameters. We illustrate the superiority of the proposed distribution over other existing distributions in the literature in modeling two real life data sets.

Characterizations Of New Modified Weibull Distribution, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Several characterizations of a New Modified Weibull distribution, introduced by Doostmoradi et al. (2014), are presented. These characterizations are based on: (i) truncated moment of a function of the random variable; (ii) the hazard function; (iii) a single function of the random variable; (iv) truncated moment of certain function of the 1st order statistic.

Varieties Of P-Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The restriction semigroups, in both their one-sided and two-sided versions, have arisen in various fashions, meriting study for their own sake. From one historical perspective, as “weakly E-ample” semigroups, the definition revolves around a “designated set” of commuting idempotents, better thought of as projections. This class includes the inverse semigroups in a natural fashion. In a recent paper, the author introduced P-restriction semigroups in order to broaden the notion of “projection” (thereby encompassing the regular *-semigroups). That study is continued here from the varietal perspective introduced for restriction semigroups by V. Gould. The relationship between varieties of regular …

Using Intelligent Prefetching To Reduce The Energy Consumption Of A Large-Scale Storage System, Brian Romoser, Ziliang Zong, Ribel Fares, Joal Wood, Rong Ge

Mathematics, Statistics and Computer Science Faculty Research and Publications

Many high performance large-scale storage systems will experience significant workload increases as their user base and content availability grow over time. The U.S. Geological Survey (USGS) Earth Resources Observation and Science (EROS) center hosts one such system that has recently undergone a period of rapid growth as its user population grew nearly 400% in just about three years. When administrators of these massive storage systems face the challenge of meeting the demands of an ever increasing number of requests, the easiest solution is to integrate more advanced hardware to existing systems. However, additional investment in hardware may significantly increase the …

The Log-Beta Generalized Half-Normal Regression Model, Rodrigo R. Pescim, Edwin M. M. Ortega, Gauss M. Cordeiro, Clarice G. B. Demtrio, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a log-linear regression model based on the beta generalized half-normal distribution (Pescim et al., 2010). We formulate and develop a log-linear model using a new distribution so-called the log-beta generalized half normal distribution. We derive expansions for the cumulative distribution and density functions which do not depend on complicated functions. We obtain formal expressions for the moments and moment generating function. We characterize the proposed distribution using a simple relationship between two truncated moments. An advantage of the new distribution is that it includes as special sub-models classical distributions reported in the lifetime literature. We also show that …

Road Systems And Betweenness, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A road system is a collection of subsets of a set—the roads—such that every singleton subset is a road in the system and every doubleton subset is contained in a road. The induced ternary (betweenness) relation is defined by saying that a point c lies between points a and b if c is an element of every road that contains both a and b . Traditionally, betweenness relations have arisen from a plethora of other structures on a given set, reflecting intuitions that range from the order-theoretic to the geometric and topological. In this paper we initiate a study …

Progressive Reliability Method And Its Application To Offshore Mooring Systems, Mir Emad Mousavi, Paolo Gardoni, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

Assessing the reliability of complex systems (e.g. structures) is essential for a reliability-based optimal design that balances safety and costs of such systems. This paper proposes the Progressive Reliability Method (PRM) for the quantification of the reliability of complex systems. The proposed method is a closed-form solution for calculating the probability of failure. The new method is flexible to the definition of “failure” (i.e., can consider serviceability and ultimate-strength failures) and uses the rules of probability theory to estimate the failure probability of the system or its components. The method is first discussed in general and then illustrated in two …

Assessing Protein Conformational Sampling Methods Based On Bivariate Lag-Distributions Of Backbone Angles, Mehdi Maadooliat, Xin Gao, Jianhua Z. Huang

Mathematics, Statistics and Computer Science Faculty Research and Publications

Despite considerable progress in the past decades, protein structure prediction remains one of the major unsolved problems in computational biology. Angular-sampling-based methods have been extensively studied recently due to their ability to capture the continuous conformational space of protein structures. The literature has focused on using a variety of parametric models of the sequential dependencies between angle pairs along the protein chains. In this article, we present a thorough review of angular-sampling-based methods by assessing three main questions: What is the best distribution type to model the protein angles? What is a reasonable number of components in a mixture model …

Characterizations Of Distribution Of Ratio Of Rayleigh Random Variables, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the distribution of the ratio of two independent Rayleigh random variables are presented. These characterizations are based, on a truncated moment; on hazard function; and on certain functions of order statistics.

Bayesian Decision Theoretic Approach To Directional Multiple Hypotheses Problems, Naveen K. Bansal, Klaus J. Miescke

Mathematics, Statistics and Computer Science Faculty Research and Publications

A multiple hypothesis problem with directional alternatives is considered in a decision theoretic framework. Skewness in the alternatives is considered, and it is shown that this skewness permits the Bayes rules to possess certain advantages when one direction of the alternatives is more important or more probable than the other direction. Bayes rules subject to constraints on certain directional false discovery rates are obtained, and their performances are compared with a traditional FDR rule through simulation. We also analyzed a gene expression data using our methodology, and compare the results to that of a FDR method.

An Exploratory Study Of Pre-Service Middle School Teachers’ Knowledge Of Algebraic Thinking, Marta Magiera, Leigh A. Van Den Kieboom, John C. Moyer

Mathematics, Statistics and Computer Science Faculty Research and Publications

Using algebraic habits of mind as a framework, and focusing on thinking about functions and how they work, we examined the relationship between 18 pre-service middle school teachers’ ability to use the features of the algebraic thinking (AT) habit of mind “Building Rules to Represent Functions” and their ability to recognize and interpret the features of the same AT habit of mind in middle school students. We assessed the pre-service teachers’ own ability to use the AT habit of mind Building Rules to Represent Functions by examining their solutions to algebra-based tasks in a semester-long mathematics content course. We assessed …

An Investigation Of Teachers' Intentions And Reflections About Using Standards-Based And Traditional Textbooks In The Classroom, Bikai Nie, Tony Freedman, Stephen Hwang, Ning Wang, John Moyer, Jinfa Cai

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study analyzed teachers’ intentions for and reflections on their use of Standards-based [Connected Mathematics Program (CMP)] textbooks and traditional (non-CMP) mathematics textbooks to guide instruction. In this investigation of the interplay between textbooks and instruction, we focused on learning goals, instructional tasks, teachers’ anticipation of students’ difficulties, and their perceptions of students’ achievement of learning goals. All of these are aspects of teachers’ intentions and reflections that have proved fruitful in comparing the roles of the CMP and non-CMP mathematics textbooks in our Longitudinal Investigation of the Effect of Curriculum on Algebra Learning project. Whereas the cognitive level …

The Semigroups B2 And B0 Are Inherently Nonfinitely Based, As Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The five-element Brandt semigroup B₂ and its four-element subsemigroup B₀, obtained by omitting one nonidempotent, have played key roles in the study of varieties of semigroups. Regarded in that fashion, they have long been known to be finitely based. The semigroup B₂ carries the natural structure of an inverse semigroup. Regarded as such, in the signature {⋅, ^-1}, it is also finitely based. It is perhaps surprising, then, that in the intermediate signature of restriction semigroups — essentially, "forgetting" the inverse operation x ↦ x^-1 and retaining the induced operations x ↦ x^{+ …}

Sub-Independence: An Expository Perspective, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Limit theorems as well as other well-known results in probability and statistics are often based on the distribution of the sums of independent random variables. The concept of sub-independence, which is much weaker than that of independence, is shown to be sufficient to yield the conclusions of these theorems and results. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness.

Characterizations Of Distributions Of Ratio Of Certain Independent Random Variables, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the distributions of the ratio of two independent gamma and exponential random variables as well as that of two independent Weibull random variables are presented. These characterizations are based, on a simple relationship between two truncated moments ; on hazard function ; and on functions of order statistics.

On Generalized Gamma Convolution Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We present here characterizations of certain families of generalized gamma convolution distributions of L. Bondesson based on a simple relationship between two truncated moments. We also present a list of well-known random variables whose distributions or the distributions of certain functions of them belong to the class of generalized gamma convolutions.

The Pitman Inequality For Exchangeable Random Vectors, J. Behboodian, Naveen K. Bansal, Gholamhossein Hamedani, Hans Volkmer

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this short article the following inequality called the “Pitman inequality” is proved for the exchangeable random vector (X₁,X₂,…,X_n) without the assumption of continuity and symmetry for each component X_i:

P(|1n∑i=1nXi|≤|∑i=1nαiXi|)≥12 ,

where all αi≥0 are special weights with ∑i=1nαi=1.

Extremal H-Colorings Of Graphs With Fixed Minimum Degree, John Engbers

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, a homomorphism from G to H, or H-coloring of G, is a map from the vertices of G to the vertices of H that preserves adjacency. When H is composed of an edge with one looped endvertex, an H-coloring of G corresponds to an independent set in G. Galvin showed that, for sufficiently large n, the complete bipartite graph K_δ,n-δ is the n-vertex graph with minimum degree δ that has the largest number of independent sets.

In this paper, we begin the project of generalizing this …

Toward An Mhealth Intervention For Smoking Cessation, Golam Mushih Tanimul Ahsan, Ivor D. Addo, Sheikh Iqbal Ahamed, Daniel Petereit, Shalini Kanekar, Linda Burhansstipanov, Linda U. Krebs

Mathematics, Statistics and Computer Science Faculty Research and Publications

The prevalence of tobacco dependence in the United States (US) remains alarming. Invariably, smoke-related health problems are the leading preventable causes of death in the US. Research has shown that a culturally tailored cessation counseling program can help reduce smoking and other tobacco usage. In this paper, we present a mobile health (mHealth) solution that leverages the Short Message Service (SMS) or text messaging feature of mobile devices to motivate behavior change among tobacco users. Our approach implements the Theory of Planned Behavior (TPB) and a phase-based framework. We make contributions to improving previous mHealth intervention approaches by delivering personalized …

Characterizations Of Certain Recently Introduced Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the Beta Weibull Geometric distribution of Bidram et al. (2011), the New Generalized Exponential distribution of Bidram et al. (2012), and the Gamma Exponentiated Weibull distribution of Pinho et al. (2012) are presented. These characterizations are based on: (i) a simple relationship between two truncated moments (ii) certain functions of the nth order statistic, and (iii) certain functions of the 1st order statistics.