Mathematics
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Item Student Choice Among Large Group, Small Group, and Individual Learning Environments in a Community College Mathematics Mini-Course(1986) Baldwin, Eldon C.; Davidson, Neil; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, MD)This study describes the development and implementation of a model for accommodation of preferences for alternative instructional environments. The study was stimulated by the existence of alternative instructional modes, and the absence of a procedure for accommodation of individual student differences which utilized these alternative modes. The Choice Model evolved during a series of pilot studies employing three instructional modes; individual (JM), small group (SGM), and large group (LGM). Three instructors were each given autonomy in designing one learning environment, each utilizing her/his preferred instructional mode. One section of a mathematics course was scheduled for one hundred students. On the first day the class was divided alphabetically into three orientation groups, each assigned to a separate class room. During the first week, the instructors described their respective environments to each group, using video taped illustrations from a previous semester. Environmental preferences were then assessed using take-home student questionnaires. In the final pilot, fifty-five students were oriented to all three environments. Each student was then assigned to his/her preferred learning environment. The distribution of environmental preferences was 24% for IM, 44% for SGM, and 33% for LGM. The following student characteristics were also investigated: 1)sex, 2)age, 3)academic background, 4)mathematics achievement, 5)mathematics attitude, 6)mathematics interest, 7)self-concept, 8)communication apprehension. and 9)interpersonal relations orientation. This investigation revealed several suggestive preference patterns: 1)Females and students with weak academic backgrounds tended to prefer the SGM environment. 2)Students with higher levels of communication apprehension tended to avoid the SGM environment. 3)New college students and students with negative mathematics attitudes tended to avoid the IM environment. 4)Students with higher grades in high school tended to prefer the LGM environment. Student preferences were successfully accommodated, and student evaluations of the Choice Model were generally positive. The literature suggests that opportunities to experience choice in education tend to enhance student growth and development; adaptation and institutionalization of the Model were addressed from this perspective. Additional studies with larger samples were recommended to further investigate environmental preferences with respect t o student and instructor characteristics of gender, age, race, socioeconomic background, academic background, and learning style.Item Better Metrics to Automatically Predict the Quality of a Text Summary(MDPI, 2012-09-26) Rankel, Peter A.; Conroy, John M.; Schlesinger, Judith D.In this paper we demonstrate a family of metrics for estimating the quality of a text summary relative to one or more human-generated summaries. The improved metrics are based on features automatically computed from the summaries to measure content and linguistic quality. The features are combined using one of three methods—robust regression, non-negative least squares, or canonical correlation, an eigenvalue method. The new metrics significantly outperform the previous standard for automatic text summarization evaluation, ROUGE.Item Complexity-Regularized Regression for Serially-Correlated Residuals with Applications to Stock Market Data(MDPI, 2014-12-23) Darmon, David; Girvan, MichelleA popular approach in the investigation of the short-term behavior of a non-stationary time series is to assume that the time series decomposes additively into a long-term trend and short-term fluctuations. A first step towards investigating the short-term behavior requires estimation of the trend, typically via smoothing in the time domain. We propose a method for time-domain smoothing, called complexity-regularized regression (CRR). This method extends recent work, which infers a regression function that makes residuals from a model “look random”. Our approach operationalizes non-randomness in the residuals by applying ideas from computational mechanics, in particular the statistical complexity of the residual process. The method is compared to generalized cross-validation (GCV), a standard approach for inferring regression functions, and shown to outperform GCV when the error terms are serially correlated. Regression under serially-correlated residuals has applications to time series analysis, where the residuals may represent short timescale activity. We apply CRR to a time series drawn from the Dow Jones Industrial Average and examine how both the long-term and short-term behavior of the market have changed over time.Item The Effect of Behavioral Objectives on Measures of Learning and Forgetting on High School Algebra(1972) Loh, Elwood Lockert; Walbesser, Henry H.; Mathematics and Education; Digital Repository at the University of Maryland; University of Maryland (College Park, MD)During the past decade, the number of educators who advocate the use of behavioral objectives in education has increased. The increase in the number of advocates of behavioral objectives has been followed by an increasing awareness of the need for empirical research to give credence to such a viewpoint. At present, there is not a substantial number of research studies in which behavioral objectives have been used as a manipulated variable. In previously reported learning studies in which behavioral objectives have been used as an experimental variable, measures of learning and measures of forgetting have been derived from achievement scores. The results obtained in the learning studies have not been singular in support of the use of behavioral objectives, however, the results obtained in forgetting studies have consistently supported their use. This two part study investigated the effect of presenting behavioral objectives to students during the initial phase of a learning program. There were six criterion variables observed: index of learning, rate of learning, index of forgetting, rate of forgetting, index of retention, and index of efficiency. Two 2-year algebra one classes with a total of 52 students were randomly partitioned into two treatment groups for the learning phase of the study. The classes were further randomly partitioned into three retention groups for the forgetting phase of the study. The instructional materials were programmed within the framework of a learning hierarchy. The use of the learning hierarchy facilitated the use of a procedure for separating behaviors not yet possessed by a student from behaviors previously acquired. This was accomplished by presenting students with preassessment tasks prior to instruction for a behavior in the learning hierarchy. If the subject's response to the preassessment task indicated that he possessed the behavior, instruction was not given for that behavior. If the response indicated that the subject had not previously acquired the behavior, instruction was presented. The measures of the time needed to acquire the behavior were subsequently used to compute the six experimental measures. Three retention periods of 7 calendar days, 14 calendar days, and 15 to 21 calendar days were used for the forgetting phase of the study. The results of the three retention periods were pooled for the two forgetting measures, the index of retention, and the index of efficiency. The data collected in the study were analyzed by six separate tests using a one-way analysis of variance. A 0.05 level of significance was used for each of the six tests. The following results were obtained: 1. The index of learning for students who were informed of behavioral objectives during the initial phases of the learning program was not greater than the index of learning for students who were not so informed. 2. The rate of learning for students who were informed of behavioral objectives during the initial phases of the learning program was not greater than the rate of learning for students who were not so informed. 3. The index of forgetting for students who were informed of behavioral objectives during the initial phases of the learning program was not less than the index of forgetting for students who were not so informed. 4. The rate of forgetting for students who were informed of behavioral objectives during the initial phases of the learning program was not less than the rate of forgetting for students who were not so informed. 5. The index of retention for students who were informed of behavioral objectives during the initial phases of the learning program was not greater than the index of retention for students who were not so informed. 6. The index of efficiency for students who were informed of behavioral objectives during the initial phases of the learning program was not greater than the index of efficiency for students who were not so informed. It was concluded that the results of the study do not support the use of behavioral objectives as a procedure for improving either measures of learning or measures of forgetting which are functions of the time needed to reach criterion in a learning program using programmed instruction for teaching an algebraic topic to below average mathematics students in senior high school. It was recommended that further research is needed to determine a reliable and valid procedure for measuring learning and forgetting. It was also recommended that alternatives to programmed instruction be considered for learning and forgetting studies.Item A Modern Overview of Local Sections of Flows(1990) Colston, Helen Marie; Markley, Nelson; Mathematics; University of Maryland (College Park, Md); Digital Repository at the University of MarylandThis paper examines local cross sections of a continuous flow on a locally compact metric space. Sane of the history of the study of local cross sections is reviewed, with particular attention given to H. Whitney's work. The paper presents a modern proof that local cross sections always exist at noncritical points of a flow. Whitney is the primary source for the key idea in the existence proof; he also gave characterizations of local cross sections on 2- and 3-dimensional manifolds. We show various topological properties of local cross sections, the most important one being that local cross sections on the same orbit are locally homeomorphic. A new elementary proof using the Jordan Curve Theorem shows that when a flow is given on a 2-manifold, a local cross section will be an arc. Whitney is cited for a similar result on 3-maniforlds. Finally, the so-called "dob=bone" space of R. Bing is used to construct a flow on a 4-manifold with a point at which every local cross section is not homeomorphic to a 3-dimensional disk.Item Some Solutions to Overdetermined Boundary Value Problems on Subdomains of Spheres(1990) Karlovitz, Max A.; Berenstein, Carlos; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)For n an open domain contained in a Riemannian manifold M, various researchers have considered the problem of finding functions u : Ω → R which satisfy overdetermined boundary value problems such as Δu + αu = 0 in Ω and u = 0 and ∂u/∂n = constant on ∂Ω. (Here Δ is the Laplace-Beltrami operator on M.) Their results demonstrate the relative difficulty of finding such solutions. It has been shown for various choices of M (e.g., M = R^n or S+n) that the only domains Ω with ∂Ω connected and sufficiently regular which admit solutions to problems such as the one above are metric balls (see, e.g., [Be1] or [Se]) . The first result of this thesis is a set of domains contained in S^n which are not metric balls but which do admit solutions to various overdetermined boundary value problems. In the case of the problem stated above, solutions are found for infinitely many choices of α. It is observed that the solutions found are isoparametric functions. (A function g is isoparametric if ~g and the le ngth of the gradient of g are both functions of g, see [Ca].) In some cases, it is shown that these functions are restrictions of spherical eigenfunctions. In some cases, they are not. Next, for these same domains, an original choice of variables is developed under which the Laplace operator can be separated. This separation of variables is used to find a complete set of Dirichlet eigenfunctions for the domains. Initial sequences of Dirichlet eigenvalues for some of the domains are computed numerically. Finally, some comments are made about the connection between solutions to overdetermined problems and isoparametric functions.Item Submaximal Function Algebras(1971) Van Meter, Garrett Oliver II; Gulick, Denny; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Let X be a compact Hausdorff space. A function algebra on X is a complex Banach subalgebra of C(X) which separates the points of X and contains the constants. Moreover, a function algebra on X is maximal if it is contained properly in no proper subalgebra of C(X). We mention that maximal function algebras are large enough to have a goodly amount of structure. In order that we be able to state the ideas and results simply let us assume that for each algebra A the underlying space X is so adjusted that A contains no non-trivial ideals of C(X). Generally if A is a maximal function algebra on X, then the topological dimension of X is at most one. The idea of this thesis is to extend the notion of maximal function algebra so that on the one hand features of maximal algebras would be retained, while on the other hand the topological dimension of the underlying space could be forced to be arbitrarily large. Thus our introduction of the notion of submaximal function algebra. We prove that all maximal algebras are submaximal. A submaximal, non-maximal algebra is A(Tn), the completion of the polynomials in n-complex variables on the unit n-torus in Cn. However, if A is submaximal on X, then each proper function algebra between A and C(X) is contained in a proper maximal function algebra on X. Moreover, we show by example that the converse to this last statement is false. If A is a submaximal function algebra on X, then every point in X has a compact neighborhood in X such that the algebra of restrictions of functions in A is dense in the continuous functions on the neighborhood. This is the (natural) analogue of the "pervasive" property of maximal function algebras. It turns out that maximal function algebras are antisymmetric, which means that they contain no non-constant real-valued functions. This is not true in general for submaximal function algebras. However, if we render the antisymmetric property in the following way, then it holds true for submaximal algebras: if the real-valued continuous functions f1,...,fn on X along with A together generate a dense subalgebra of C(X), then the continuous real-valued functions h1,...,hn on X and A together generate a dense subalgebra of C(X), provided only that each hj is sufficiently close to fj. In addition, we show that if A is submaximal on X, then there are always exist finitely many real-valued continuous functions on X which together with A generate a dense subalgebra of C(X). Finally we discuss tensor products of submaximal algebras. In particular, we prove that under certain restrictions, the tensor product of two submaximal algebras is submaximal.Item Completions(1964) Nielsen, Robert Maurice; Brace, John W.; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)This paper presents a new approach to the theory of completions. The treatment is based on the concept of convergence on filters and related topologies. For a given uniform Hausdorff space Xu and a collection S of Cauchy filters in Xu, the basic result is the construction of a uniform Hausdorff space. Xu having the properties that Xu is isomorphic to a dense subspace of Xu and every filter in S converges to a point in S. As a special case, the completion of Xu of Xu is obtained. The construction is so given as to prove the existence of the space Xu. The technique involves embedding the object X to be "completed" in a space of functions F which has as its domain a space of continuous functions C(X) defined on X. The procedure is analogous to the process of taking the bidual E" of a locally convex topological vector space. Indeed, E" is obtained as a special case. In the absence of sufficient structure on X, the Xu is obtained as the closure of X in F. In a locally convex space or an abelian topological group having enough character to separate points, Xu is obtained as a bidual or a second character group of the object X.Item Detection of co-eluted peptides using database search methods(Springer Nature, 2008-07-02) Alves, Gelio; Ogurtsov, Aleksey Y; Kwok, Siwei; Wu, Wells W; Wang, Guanghui; Shen, Rong-Fong; Yu, Yi-KuoCurrent experimental techniques, especially those applying liquid chromatography mass spectrometry, have made high-throughput proteomic studies possible. The increase in throughput however also raises concerns on the accuracy of identification or quantification. Most experimental procedures select in a given MS scan only a few relatively most intense parent ions, each to be fragmented (MS2) separately, and most other minor co-eluted peptides that have similar chromatographic retention times are ignored and their information lost. We have computationally investigated the possibility of enhancing the information retrieval during a given LC/MS experiment by selecting the two or three most intense parent ions for simultaneous fragmentation. A set of spectra is created via superimposing a number of MS2 spectra, each can be identified by all search methods tested with high confidence, to mimick the spectra of co-eluted peptides. The generated convoluted spectra were used to evaluate the capability of several database search methods – SEQUEST, Mascot, X!Tandem, OMSSA, and RAId_DbS – in identifying true peptides from superimposed spectra of co-eluted peptides. We show that using these simulated spectra, all the database search methods will gain eventually in the number of true peptides identified by using the compound spectra of co-eluted peptides. Reviewed by Vlad Petyuk (nominated by Arcady Mushegian), King Jordan and Shamil Sunyaev. For the full reviews, please go to the Reviewers' comments section.Item Simultaneous transcriptional profiling of Leishmania major and its murine macrophage host cell reveals insights into host-pathogen interactions(Springer Nature, 2015-12-29) Dillon, Laura A. L.; Suresh, Rahul; Okrah, Kwame; Corrada Bravo, Hector; Mosser, David M.; El-Sayed, Najib M.Parasites of the genus Leishmania are the causative agents of leishmaniasis, a group of diseases that range in manifestations from skin lesions to fatal visceral disease. The life cycle of Leishmania parasites is split between its insect vector and its mammalian host, where it resides primarily inside of macrophages. Once intracellular, Leishmania parasites must evade or deactivate the host's innate and adaptive immune responses in order to survive and replicate. We performed transcriptome profiling using RNA-seq to simultaneously identify global changes in murine macrophage and L. major gene expression as the parasite entered and persisted within murine macrophages during the first 72 h of an infection. Differential gene expression, pathway, and gene ontology analyses enabled us to identify modulations in host and parasite responses during an infection. The most substantial and dynamic gene expression responses by both macrophage and parasite were observed during early infection. Murine genes related to both pro- and anti-inflammatory immune responses and glycolysis were substantially upregulated and genes related to lipid metabolism, biogenesis, and Fc gamma receptor-mediated phagocytosis were downregulated. Upregulated parasite genes included those aimed at mitigating the effects of an oxidative response by the host immune system while downregulated genes were related to translation, cell signaling, fatty acid biosynthesis, and flagellum structure. The gene expression patterns identified in this work yield signatures that characterize multiple developmental stages of L. major parasites and the coordinated response of Leishmania-infected macrophages in the real-time setting of a dual biological system. This comprehensive dataset offers a clearer and more sensitive picture of the interplay between host and parasite during intracellular infection, providing additional insights into how pathogens are able to evade host defenses and modulate the biological functions of the cell in order to survive in the mammalian environment.