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Euler-Richardson method preconditioned by weakly stochastic matrix algebras: a potential contribution to Pagerank computation

Tue, 2017-08-01 11:22

Let S be a column stochastic matrix with at least one full row. Then S describes a Pagerank-like random walk since the computation of the Perron vector x of S can be tackled by solving a suitable M-matrix linear system Mx = y, where M = I − τ A, A is a column stochastic matrix and τ is a positive coefficient smaller than one. The Pagerank centrality index on graphs is a relevant example where these two formulations appear. Previous investigations have shown that the Euler- Richardson (ER) method can be considered in order to approach the Pagerank computation problem by means of preconditioning strategies. In this work, it is observed indeed that the classical power method can be embedded into the ER scheme, through a suitable simple preconditioner. Therefore, a new preconditioner is proposed based on fast Householder transformations and the concept of low complexity weakly stochastic algebras, which gives rise to an effective alternative to the power method for large-scale sparse problems. Detailed mathematical reasonings for this choice are given and the convergence properties discussed. Numerical tests performed on real-world datasets are presented, showing the advantages given by the use of the proposed Householder-Richardson method.

Decomposition of approaches of a general linear model with fixed parameters

Fri, 2017-07-21 09:08

The well-known ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) under linear regression models can be represented by certain closed-form formulas composed by the given matrices and their generalized inverses in the models. This paper provides a general algebraic approach to relationships between OLSEs and BLUEs of the whole and partial mean parameter vectors in a constrained general linear model (CGLM) with fixed parameters by using a variety of matrix analysis tools on generalized inverses of matrices and matrix rank formulas. In particular, it establishes a variety of necessary and sufficient conditions for OLSEs to be BLUEs under a CGLM, which include many reasonable statistical interpretations on the equalities of OLSEs and BLUEs of parameter space in the CGLM. The whole work shows how to effectively establish matrix equalities composed by matrices and their generalized inverses and how to use them when characterizing performances of estimators of parameter spaces in linear models under most general assumptions.

Inverses of bicyclic graphs

Fri, 2017-07-21 09:08

A graph G is said to be nonsingular (resp., singular) if its adjacency matrix A(G) is nonsingular (resp., singular). The inverse of a nonsingular graph G is the unique weighted graph whose adjacency matrix is similar to the inverse of the adjacency matrix A(G) via a diagonal matrix of ±1s. Consider connected bipartite graphs with unique perfect matchings such that the graph obtained by contracting all matching edges is also bipartite. In [C.D. Godsil. Inverses of trees. Combinatorica, 5(1):33–39, 1985.], Godsil proved that such graphs are invertible. He posed the question of characterizing the bipartite graphs with unique perfect matchings possessing inverses. In this article, Godsil’s question for the class of bicyclic graphs is answered.

Curriculum Alignment and Science and Engineering Practices in the Classroom

Fri, 2017-07-14 12:57

The release of the Next Generation Science Standards (NGSS) in 2013 introduced educators to the three dimensions of science literacy, which are the (a) Disciplinary Core Ideas (DCIs), (b) Cross-Cutting Concepts (CCCs), and the (c) Science and Engineering Practices (SEPs). For educators to address all three dimensions, they must analyze not only the expected content, but also how that content is presented and connected. Curriculum mapping is a tool developed in 1980 that can be used to analyze curricular alignment. This project focused on the creation of rubrics to analyze and evaluate the use of SEPs in conjunction with curriculum maps in the 6-8 grade band.

Conceptual Change Theory’s Potential to Support Collaborative Environmental Problem Solving: Analogous Values and Convergent Properties

Fri, 2017-07-14 12:57

Contemporary understanding of our nervous system supports the contention that environment is inexorably linked to learning; that all experiences are learning experiences and all learning is experiential (Gooding & Metz, 2011; Hayward, 2012; Wilson, 1999). Public education systems in the US grew to accommodate cultural developments and were not designed to implement experiential education (Bishop & Scott, 1998; Dewey, 1915; Hayward, 2012). Ecologists and sociologists agree that global population growth and development are pushing our society to a precipice where traditional methods of production, valuation, and resource management become inadequate (IPCC, 2014; Proctor, Smith, & Wallace, 2013; Steffen & McNeill, 2007; Tietenberg & Lewis, 2012). Respected analysts from multiple disciplines have consistently expressed a need to update our system to one in which public good and sustainable development are guiding principles (Morton, 2012; Proctor, Smith, & Wallace, 2013; Steffen & McNeill, 2007; White, 1967). A populace that is informed and able to engage in collaborative environmental problem solving will foster this transition (Daniels & Walker, 2001; Hayward, 2012).

The objective of this study is to provide a synthesis of theoretical and experimental support for the claim that students who practice cooperative science learning through the Conceptual Change Model (CCM) may be better prepared to address environmental issues as collaborative citizens. Learning activities based on the CCM of knowledge acquisition developed by Schmidt, Saigo, and Stepans (2001) are analogous to effective collaborative environmental problem solving processes put forth by Daniels and Walker in Working through environmental conflict: The collaborative learning approach (2001). Some theorists recommend that methods be augmented with cultural knowledge to extend connection to place (Sinatra, 2005; Zhou, 2012). Based on the results of this academic investigation, I conclude the use of CCM to be potentially effective in encouraging development of skills common to environmental problem solving. I propose a commitment to creating lifelong learners adept at integrative collaboration be adopted as a universal goal of public education. Meaningful experiential learning can incorporate critical thinking and cooperative problem solving while accommodating individual cognitive ecologies.

Eventual Cone Invariance

Fri, 2017-07-07 10:59

Eventually nonnegative matrices are square matrices whose powers become and remain (entrywise) nonnegative. Using classical Perron-Frobenius theory for cone preserving maps, this notion is generalized to matrices whose powers eventually leave a proper cone K ⊂ R^n invariant, that is, A^mK ⊆ K for all sufficiently large m. Also studied are the related notions of eventual cone invariance by the matrix exponential, as well as other generalizations of M-matrix and dynamical system notions.

Optimal dual fusion frames for probabilistic erasures

Fri, 2017-07-07 10:59

For any fixed fusion frame, its optimal dual fusion frames for reconstruction is studied in case of erasures of subspaces. It is considered that a probability distribution of erasure of subspaces is given and that a blind reconstruction procedure is used, where the erased data are set to zero. It is proved that there are always optimal duals. Sufficient conditions for the canonical dual fusion frame being either the unique optimal dual, a non-unique optimal dual, or a non optimal dual, are obtained. The reconstruction error is analyzed, using the optimal duals in the probability model considered here and using the optimal duals in a non-probability model.

Quantifying the Impact of Population Size on Natural Selection Across the Genome

Wed, 2017-06-28 05:25

In a world of rapid anthropogenic change understanding factors influencing the pace with which a population can respond to natural selection has become a necessity for conservation. Often when considering risk of extinction we take population size into account. However, understanding evolutionary implications of that population size may also be important. Most mechanisms involved in evolution act within a population, such as selection, mutation, migration, and genetic drift. Notably, these processes are not static across species or populations and are often influenced by dynamic aspects such as population size. By comparing among groups that naturally show difference in population size we can better understand the impacts of population size pressures on genetic diversity and the effectiveness of natural selection. In this comparative study of five co-distributed Alaskan mammals—Collared Pikas, Hoary Marmots, Brown Lemmings, Artic Ground Squirrels, and Singing Voles—we tested whether population size influences the ability of a population to respond to selection using genomic data and predictive simulations. Our results show species with larger population sizes display more genomic variation, suggesting that selection may be working more effectively in larger populations. Meanwhile, smaller populations are more likely to lose advantageous loci by chance alone. In conclusion, evolution is not a static process, but rather, as we found, selection response is dynamic in relation to population size.

Likelihood of Bystander Intervention as a Function of a Social Norms

Wed, 2017-06-28 05:25

Bystander intervention is the decision of a third party to take action in a perceived, ongoing, or completed sexual assault to assist the victim. The primary goal of bystander intervention is to prevent sexual victimization before it is perpetrated. Research demonstrates how perceptions of community expectations can alter rape myth acceptance (RMA). RMA can be malleable if the community’s perception of RMA is higher or lower, at least temporarily. RMA can function as a social norm. This study evaluates the degree to which an individual’s perceptions of community support influences willingness to intervene in potential assault situations. It is expected that individuals’ perceptions of bystander behavior as normative will increase self-reported willingness to intervene, and perceptions of such behavior as uncommon, will decrease one’s intent to intervene. Participants (N=81) filled out two surveys assessing willingness to help and efficacy to help in a hypothetical sexual assault situation. Participants were randomly assigned to one of three groups: control group, low community support, or high community support. Trends in bystander efficacy demonstrated that higher levels of perceived community support lead to higher self-reported efficacy. This also held true for lower levels. Readiness to help was divided into three subscales (action, responsibility, and no awareness). The different conditions had no effect on action. Trends indicate feelings of responsibility and need for awareness in the two experimental groups.

Fabrication and Mechanical Characterization of Thiol-ene Polymers and Thiol-acrylate Liquid Crystal Elastomers

Wed, 2017-06-28 05:25

This study’s purpose was to synthesize and program thiol-acrylate and thiol-ene based polymeric materials. A Michael addition of dithiol and tetrathiol monomers with a diacrylate mesogen is the single crosslinking mechanism to form a polydomain. A room-temperature-nematic exhibiting local mesogenic alignment, termed polydomain. A strained polydomain with up to 45 mol% excess acrylate composition, allows photocrosslinking reaction forming monodomain elastomers. These polydomain and monodomain stages largely depend on the effects of increment in crosslink density, showing independent mechanical properties. To study mechanical behavior of polydomain and monodomain samples, dynamic mechanical analysis (DMA) was used to investigate linear viscoelastic region, glass transition temperature, isotropic transition temperature and thermal actuation properties. The amount of acrylate associated in LCEs changed mechanical properties of both polydomain and monodomain elastomers. Polydomain samples exhibited reduced transition temperatures, storage modulus, and high strain-to-failure with increased acrylate as a result of reduced crosslink density. Whereas, monodomain have higher transition temperatures, storage modulus, and reducing strain-to-failure with increased acrylate due to increased crosslink density. A tetrathiol monomer with triene is sole crosslinking mechanism to form radical thiol-ene network polymer. The evolution of mechanical properties is analyzed as a function of UV exposure, where ultraviolet light initiates radical reaction. Thiol-ene polymers were successfully prepared through photochemical reaction with up to 80 mol% excess thiol (relative to acrylate) to form glassy polymer networks with chemically function surfaces. DMA was used to investigate the viscoelastic region and glass transition temperature. Increased thiol concentration resulted in reduced glass transition temperature.

Fabrication and Mechanical Characterization of Thiol-ene Polymers and Thiol-acrylate Liquid Crystal Elastomers

Wed, 2017-06-28 05:25

This study’s purpose was to synthesize and program thiol-acrylate and thiol-ene based polymeric materials. A Michael addition of dithiol and tetrathiol monomers with a diacrylate mesogen is the single crosslinking mechanism to form a polydomain. A room-temperature-nematic exhibiting local mesogenic alignment, termed polydomain. A strained polydomain with up to 45 mol% excess acrylate composition, allows photocrosslinking reaction forming monodomain elastomers. These polydomain and monodomain stages largely depend on the effects of increment in crosslink density, showing independent mechanical properties. To study mechanical behavior of polydomain and monodomain samples, dynamic mechanical analysis (DMA) was used to investigate linear viscoelastic region, glass transition temperature, isotropic transition temperature and thermal actuation properties. The amount of acrylate associated in LCEs changed mechanical properties of both polydomain and monodomain elastomers. Polydomain samples exhibited reduced transition temperatures, storage modulus, and high strain-to-failure with increased acrylate as a result of reduced crosslink density. Whereas, monodomain have higher transition temperatures, storage modulus, and reducing strain-to-failure with increased acrylate due to increased crosslink density. A tetrathiol monomer with triene is sole crosslinking mechanism to form radical thiol-ene network polymer. The evolution of mechanical properties is analyzed as a function of UV exposure, where ultraviolet light initiates radical reaction. Thiol-ene polymers were successfully prepared through photochemical reaction with up to 80 mol% excess thiol (relative to acrylate) to form glassy polymer networks with chemically function surfaces. DMA was used to investigate the viscoelastic region and glass transition temperature. Increased thiol concentration resulted in reduced glass transition temperature.

MouseVision

Wed, 2017-06-28 05:25

MouseVision is a project that combines optical tracking and speech recognition software to create a mouse that does not rely on the use of arms and legs. It utilizes the openCV API to find an initial point to track and creates a point vector. Then it detects changes in the point vector to create a corresponding change in the mouse position on screen. It combines this aspect with the CMU Sphinx speech recognition library to perform clicks when the end user says “left click” or “right click”. The goal of this project was to make an interface that used cost-effective hardware, such as a webcam and microphone, to allow someone who is quadriplegic, or otherwise physically limited, to operate a mouse cursor. The project is considered successful, because a person without any arms at all is able to do basic computer tasks, such as play chess, using the MouseVision software.

Assessment of Cardiac Function in Mice Chronically Exposed to Volatile Organic Compounds

Wed, 2017-06-28 05:25

Atmospheric air pollutants, including Volatile Organic Compounds such as acrolein and polyvinyl chloride (VOC), have been linked to increased cardiovascular and metabolic dysfunction. This is of particular interest in Wyoming, where industrial mining may increase exposure to VOC. This project is part of a recently begun two-year collaboration with Dr. Jun Ren (UW Pharmacy School), to examine the relationship between VOC exposure and cardio-metabolic syndrome. We hypothesize that chronic (6-12 week) exposure to aerosolized VOC will result in cardiac dysfunction in mice. Mice will be exposed to VOC in Dr. Ren’s lab, transported to our lab, and subjected to pressure-volume loop analysis of cardiac function (PV). PV is the most comprehensive technique to measure cardiac function, including beat-by-beat determination of: cardiac output, heart rate, stroke volume, preload, afterload, and a load-independent measure of contractility. A PV transducer is inserted into the left ventricle (LV) via the carotid artery, and baseline loops are generated in real time. Inferior vena cava occlusions are performed to assess contractility over a range of end-diastolic volumes. Finally, two calibrations are necessary: 1) hypertonic saline calibration, to subtract parallel conductance (conductance due to cardiac muscle rather than ventricular volume), and 2) cuvette calibration, to convert conductance to volume. PV experiments for this project will begin in Fall 2017.

Attitudes Towards Autism in Healthcare and in Society

Wed, 2017-06-28 05:25

Autism did not appear as its own diagnosis in the Diagnostic and Statistical Manual (DSM) until the third edition in 1980 (Davis, pg 461). In 2014, the Center for Disease Control and Prevention (CDC) reported that autism diagnosis rates were 1 in 110 and stated the high prevalence as “an urgent public health concern” (McGuire, pg 55). This declaration lead to autism being described as an epidemic, which then lead to a widespread sense of fear (McGuire, pg 56). Disability studies scholars take a different approach when looking at autism and disabilities in general. The two main views of disabilities discussed by disability studies scholars are the medical and the social model. The medical model views disability as something that needs to be fixed or cured and as a person-centered problem. The social model views disability as something that is socially constructed (Davis, pg 462). In today’s health care, most health professionals view disabilities through the individual model. This takes the medical model to a new level and labels a disability as a tragedy. Disability studies scholars find this to be a nonproductive method of approaching disabilities (Durell). Because of this, a lot of medical students report discomfort when working with disabilities (Symons). Specifically, the field of occupational therapy (OT) is based on a client-centered practice philosophy. It has been argued that embracing disability studies and the viewpoints of disabled people could truly benefit the client-centered practice approach that is utilized by OTs (McCormack, page 2).

Attitudes Towards Autism in Healthcare and in Society

Wed, 2017-06-28 05:25

Autism did not appear as its own diagnosis in the Diagnostic and Statistical Manual (DSM) until the third edition in 1980 (Davis, pg 461). In 2014, the Center for Disease Control and Prevention (CDC) reported that autism diagnosis rates were 1 in 110 and stated the high prevalence as “an urgent public health concern” (McGuire, pg 55). This declaration lead to autism being described as an epidemic, which then lead to a widespread sense of fear (McGuire, pg 56). Disability studies scholars take a different approach when looking at autism and disabilities in general. The two main views of disabilities discussed by disability studies scholars are the medical and the social model. The medical model views disability as something that needs to be fixed or cured and as a person-centered problem. The social model views disability as something that is socially constructed (Davis, pg 462). In today’s health care, most health professionals view disabilities through the individual model. This takes the medical model to a new level and labels a disability as a tragedy. Disability studies scholars find this to be a nonproductive method of approaching disabilities (Durell). Because of this, a lot of medical students report discomfort when working with disabilities (Symons). Specifically, the field of occupational therapy (OT) is based on a client-centered practice philosophy. It has been argued that embracing disability studies and the viewpoints of disabled people could truly benefit the client-centered practice approach that is utilized by OTs (McCormack, page 2).

3D World for Reddit

Wed, 2017-06-28 05:25

Reddit describes itself as “the front page of the Internet.” It is a popular website that aims to help connect people and discover new things. Anybody can join this website, or anonymously browse its more than one million subreddits (discussion boards). The website is designed in a simple fashion; when logged in, users can customize their view, but it is generally laid out as a simple forum website. Our group aims to visually represent the existing Reddit community and give Reddit users a new and fun way to discover content on Reddit. Using the Unity game development engine, we have created a real-time 3D world for Reddit. Subreddits are represented as buildings within a city, and threads are represented as pictures within the building. From this 3D world, users can interact with subreddits and threads by viewing or commenting on them.

How Clinicians Report Discussing Self-Monitoring with Type 2 Diabetes Mellitus Patients

Wed, 2017-06-28 05:25

Patient self-monitoring is critical to diabetes self-management. With no detailed approach to discussing self-monitoring by the American Diabetes Association we examined how clinicians report discussing self-monitoring with patients. Semi-structured interviews were conducted and three key questions followed from the research question. Analysis included transcripts and debriefing notes. A constant-comparison approach with category coding and thematic representation was used. How the clinicians discuss self-monitoring relates to their perceptions of: (1) the clinician-patient relationship, (2) needs beyond diabetes, and (3) perceived benefits of self-monitoring. Participants revealed a continuum of relational approaches from “partnership” with the goal to achieve patient independence on one end to benevolent paternalism wherein the clinician “keep[s] people safe”, “make[s] slow fixes” and who, in a perfect world would like to “free” patients from insulin and self-monitoring requirements. Different needs of patients were reported to affect self-monitoring efforts and many benefits of self-monitoring were identified. While some clinicians take a partnering approach, others reported this possibility only in “the perfect world” due to patients’ struggles and obstacles outside of the clinician’s control. It’s not clear how the approaches to discussing self-monitoring relate to the clinician-patient relationship, patients’ needs or the benefits of self-monitoring. How clinicians talk about self-monitoring within the clinician-patient relationship may influence diabetes outcomes. Future research is needed to address the variety and severity of patients’ needs and to include the patient perspective.

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