Physical Sciences and Mathematics Commons^™

Improvement Of Ifng Elispot Performance Following Overnight Resting Of Frozen Pbmc Samples Confirmed Through Rigorous Statistical Analysis, Radleigh Santos, Alcinette Bunying, Nazila Sabri, John Yu, Anthony Gringeri, James Bender, Sylvia Janetzki, Clemencia Pinilla, Valeria A. Judkowski

Mathematics Faculty Articles

Immune monitoring of functional responses is a fundamental parameter to establish correlates of protection in clinical trials evaluating vaccines and therapies to boost antigen-specific responses. The IFNg ELISPOT assay is a well-standardized and validated method for the determination of functional IFNg-producing T-cells in peripheral blood mononuclear cells (PBMC); however, its performance greatly depends on the quality and integrity of the cryopreserved PBMC. Here, we investigate the effect of overnight (ON) resting of the PBMC on the detection of CD8-restricted peptide-specific responses by IFNg ELISPOT. The study used PBMC from healthy donors to evaluate the CD8 T-cell response to five pooled …

On Dual Toric Complete Intersection Codes, Pinar Celebi Demiraslan, Ivan Soprunov

Mathematics and Statistics Faculty Publications

In this paper we study duality for evaluation codes on intersections of ℓ hypersurfaces with given ℓ-dimensional Newton polytopes, so called toric complete intersection codes. In particular, we give a condition for such a code to be quasi-self-dual. In the case of it reduces to a combinatorial condition on the Newton polygons. This allows us to give an explicit construction of dual and quasi-self-dual toric complete intersection codes. We provide a list of examples over and an algorithm for producing them.

Cartan Subalgebras, Compact Roots And The Satake Diagram For Su(2, 2), Ian M. Anderson

Tutorials on... in 1 hour or less

In this worksheet we use the 15-dimensional real Lie algebra su(2, 2) to illustrate some important points regarding the general structure theory and classification of real semi-simple Lie algebras.

1. Recall that a real semi-simple Lie algebra g is called a compact Lie algebra if the Killing form is negative definite. The Lie algebra g is compact if and only if all the root vectors for any Cartan subalgebra are purely imaginary. However, if the root vectors are purely imaginary for some choice of Cartan subalgebra it is not necessarily true that the Lie algebra is compact.

2. A real …

Jordan Algebras And The Exceptional Lie Algebra F4, Ian M. Anderson

Tutorials on... in 1 hour or less

This worksheet analyzes the structure of the Jordan algebra J(3, O) and its split and exceptional versions. The algebra of derivations is related to the exceptional Lie algebra f4.

Linear Operators That Preserve Graphical Properties Of Matrices: Isolation Numbers, Leroy B. Beasley, Seok-Zun Song, Young Bae Jun

Mathematics and Statistics Faculty Publications

Let A be a Boolean {0, 1} matrix. The isolation number of A is the maximum number of ones in A such that no two are in any row or any column (that is they are independent), and no two are in a 2 × 2 submatrix of all ones. The isolation number of A is a lower bound on the Boolean rank of A. A linear operator on the set of m × n Boolean matrices is a mapping which is additive and maps the zero matrix, O, to itself. A mapping strongly preserves a set, S, if it …

Elliptic Curve Cryptography, Kerrie Pratt

Honors Program Theses and Projects

In the present day, security is essential for sending and receiving information. There are always stories about bank accounts being hacked, credit card numbers being stolen, and secret information being decoded. With the technology of the Internet age growing at a rapid pace, security is essential to keep privileged information safe. In order to ensure this information is kept private, so that information can be sent and received without being hacked and decoded, organizations employ different types of encryption. One of the current encoding systems is Elliptic Curve Cryptography (ECC). ECC uses elliptic curves over finite fields to send information …

Integrating Path-Dependent Functionals On Yeh-Wiener Space, Ian Pierce, David Skough

Department of Mathematics: Faculty Publications

Denote by Ca,b(Q) the generalized two-parameter Yeh-Wiener space with associated Gaussian measure. We investigate several scenarios in which integrals of functionals on this space can be reduced to integrals of related functionals over an appropriate single-parameter generalized Wiener space Cˆa,ˆb[0, T ]. This extends some interesting results of R. H. Cameron and D. A. Storvick.

Some Observations On Scientific Epistemology With Applications To Conflict Resolution And Constructive Controversy, Judith Puncochar, Don Faust

Other Presentations

An overview, by Judy and Don (published in 2013 in the BULLETIN OF SYMBOLIC LOGIC):

Explorationism is a perspective wherein all of our knowledge is (so far) less than certain, and naturally would come equipped with a base logic entailing machinery for representing and processing evidential knowledge. One such base logic is Evidence Logic, which strives to deal with the phenomenon of the gradational presence of both confirmatory and refutatory evidence. From this perspective, we will address questions surrounding sociological problem areas that we see as deeply infused with substantial epistemological factors. By defining a framework as any theory, …

On The Indispensable Premises Of The Indispensability Argument, Andrea Sereni, Marco Panza

MPP Published Research

We identify four different minimal versions of the indispensability argument, falling under four different varieties: an epistemic argument for semantic realism, an epistemic argument for platonism and a non-epistemic version of both. We argue that most current formulations of the argument can be reconstructed by building upon the suggested minimal versions. Part of our discussion relies on a clarification of the notion of (in)dispensability as relational in character. We then present some substantive consequences of our inquiry for the philosophical significance of the indispensability argument, the most relevant of which being that both naturalism and confirmational holism can be dispensed …

Computing Singular Values Of Large Matrices With An Inverse-Free Preconditioned Krylov Subspace Method, Qiao Liang, Qiang Ye

Mathematics Faculty Publications

We present an efficient algorithm for computing a few extreme singular values of a large sparse m×n matrix C. Our algorithm is based on reformulating the singular value problem as an eigenvalue problem for C^TC. To address the clustering of the singular values, we develop an inverse-free preconditioned Krylov subspace method to accelerate convergence. We consider preconditioning that is based on robust incomplete factorizations, and we discuss various implementation issues. Extensive numerical tests are presented to demonstrate efficiency and robustness of the new algorithm.

A Statistical Analysis Of The Role Of Critical-Thinking Games In College Students' Quantitative Reasoning, Melissa Radevicz

Honors Program Theses and Projects

Improving college students' quantitative reasoning is crucial to increase STEM-field retention rates. The National Survey of Student Engagement (NSSE), results indicate that "college students don't always get exposure to activities that develop [quantitative reasoning]" (Berrett & Sander, 2013). This study aimed to engage college students in quantitative reasoning through critical-thinking games. Phase 1, conducted in summer 2014 with a university research grant, involved a correlation analysis of the work of 133 college students enrolled in Elementary Statistics I, Chemical Principles II, Elements of Calculus, Pre-Calculus with Trigonometry, Multivariable Calculus, and Differential Equations. Participants held a variety of 39 different majors, …

Polynomials With Prescribed Bad Primes, David P. Roberts

Mathematics Publications

We tabulate polynomials in ℚ[t] with a given factorization partition, bad reduction entirely within a given set of primes, and satisfying auxiliary conditions associated to 0, 1, and ∞. We explain how these polynomials are of particular interest because of their role in the construction of nonsolvable number fields of arbitrarily large degree and bounded ramification.

Mixed Variational Formulation For The Wellposedness And Numerical Approximation Of A Pde Model Arising In A 3-D Fluid-Structure Interaction, George Avalos, Tom Clark

Faculty Work Comprehensive List

We present qualitative and numerical results on a partial differential equation (PDE) system which models a certain fluid-structure dynamics. Wellposedness is established by constructing for it a nonstandard semigroup generator representation; this representation is accomplished by an appropriate elimination of the pressure. This coupled PDE model involves the Stokes system which evolves on a three dimensional domain O coupled to a fourth order plate equation, possibly with rotational inertia parameter ρ>0. This plate PDE evolves on a flat portion Ω of the boundary of O. The coupling on Ω is implemented via the Dirichlet trace of the Stokes system …

Classical And Motivic Adams-Novikov Charts, Daniel C. Isaksen

Mathematics Research Reports

This document contains large-format Adams-Novikov charts that compute the classical 2-complete stable homotopy groups. The charts are essentially complete through the 59-stem. We believe that these are the most accurate and extensive charts of their kind. We also include a motivic Adams-Novikov E∞ chart.

Classical And Motivic Adams Charts, Daniel C. Isaksen

Mathematics Research Reports

This document contains large-format Adams charts that compute 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. The charts are essentially complete through the 59-stem and contain partial results to the 70-stem. In the classical context, we believe that these are the most accurate charts of their kind. We also include Adams charts for the motivic homotopy groups of the cofiber of τ.

Positive Solutions Of Boundary Value Dynamic Equations, Olusegun Michael Otunuga, Basant Karna, Bonita Lawrence

Mathematics Faculty Research

In this paper, we deal with the existence of a positive solution for 2^nd and 3^rd order boundary value problem by first defining their respective Green’s function. The Green’s function is used to derive the Green’s function for the 2nth and 3nth order boundary value problem, respectively, where n is a positive integer. The Green’s function is also used to derive conditions for positive solution of the 2nth and 3nth order eigen value differential equation, respectively.

Ogden College Of Science & Engineering Newsletter (Winter 2014), Cheryl Stevens, Dean

Ogden College of Science & Engineering Publications

No abstract provided.

A Database Of Number Fields, John W. Jones, David P. Roberts

Mathematics Publications

We describe an online database of number fields which accompanies this paper. The database centers on complete lists of number fields with prescribed invariants. Our description here focuses on summarizing tables and connections to theoretical issues of current interest.

Combinatorial Proofs Of Fibonomial Identities, Arthur Benjamin, Elizabeth Reiland

All HMC Faculty Publications and Research

We provide a list of simple looking identities that are still in need of combinatorial proof.

Connections Of Zero Curvature And Applications To Nonlinear Partial Differential Equations, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A general formulation of zero curvature connections in a principle bundle is presented and some applications are discussed. It is proved that a related connection based on a prolongation in an associated bundle remains zero curvature as well. It is also shown that the connection coefficients can be defined so that the partial differential equation to be studied appears as the curvature term in the structure equations. It is discussed how Lax pairs and Bäcklund tranformations can be formulated for such equations that occur as zero curvature terms.

Citizen Science Reveals Widespread Negative Effects Of Roads On Amphibian Distributions, Bradley J. Cosentino, David M. Marsh, Kara S. Jones, Joseph J. Apodaca, Christopher Bates, Jessica Beach, Karen H. Beard, Kelsie Becklin, Jane Margaret Bell, Christopher Crockett, George Fawson, Jennifer Fjelsted, Elizabeth A. Forys, Kristen S. Genet, Melanie Grover, Jaimie Holmes, Katherine Indeck, Nancy E. Karraker, Eran S. Kilpatrick, Tom A. Langen, Stephen G. Mugel, Alessandro Molina, James R. Vonesh, Ryan J. Weaver, Anisha Willey

Wildland Resources Faculty Publications

Landscape structure is important for shaping the abundance and distribution of amphibians, but prior studies of landscape effects have been species or ecosystem-specific. Using a large-scale, citizen science-generated database, we examined the effects of habitat composition, road disturbance, and habitat split (i.e. the isolation of wetland from forest by intervening land use) on the distribution and richness of frogs and toads in the eastern and central United States. Undergraduates from nine biology and environmental science courses collated occupancy data and characterized landscape structure at 1617 sampling locations from the North American Amphibian Monitoring Program. Our analysis revealed that anuran species …

Prognostic Value Of Elevated Serum Ceruloplasmin Levels In Patients With Heart Failure, Muhammad Hammadah, Yiying Fan, Yuping Wu, Stanley L. Hazen, W.H. Wilson Tang

Mathematics and Statistics Faculty Publications

Background: Ceruloplasmin (Cp) is a copper-binding acute-phase protein that is increased in inflammatory states and deficient in Wilson's disease. Recent studies demonstrate that increased levels of Cp are associated with increased risk of developing heart failure. Our objective was to test the hypothesis that serum Cp provides incremental and independent prediction of survival in stable patients with heart failure. Methods and Results: We measured serum Cp levels in 890 patients with stable heart failure undergoing elective cardiac evaluation that included coronary angiography. We examined the role of Cp levels in predicting survival over 5 years of follow-up. Mean Cp level …

Gradient-Based Compressive Sensing For Noise Image And Video Reconstruction, Huihuang Zhao, Yaonan Wang, Xiaojiang Peng, Zhijun Qiao

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this study, a fast gradient-based compressive sensing (FGB-CS) for noise image and video is proposed. Given a noise image or video, the authors first make it sparse by orthogonal transformation, and then reconstruct it by solving a convex optimisation problem with a novel gradient-based method. The main contribution is twofold. Firstly, they deal with the noise signal reconstruction as a convex minimisation problem, and propose a new compressive sensing based on gradient-based method for noise image and video. Secondly, to improve the computational efficiency of gradient-based compressive sensing, they formulate the convex optimisation of noise signal reconstruction under Lipschitz …

Enumeration Of Tilings Of Quartered Aztec Rectangles, Tri Lai

Department of Mathematics: Faculty Publications

We generalize a theorem of W. Jockusch and J. Propp on quartered Aztec diamonds by enumerating the tilings of quartered Aztec rectangles. We use subgraph replacement method to transform the dual graph of a quartered Aztec rectangle to the dual graph of a quartered lozenge hexagon, and then use Lindstr¨om-Gessel- Viennot methodology to find the number of tilings of a quartered lozenge hexagon.

Von Neumann Algebras And Extensions Of Inverse Semigroups, Allan P. Donsig, Adam H. Fuller, David R. Pitts

Department of Mathematics: Faculty Publications

In the 1970s, Feldman and Moore classified separably acting von Neumann algebras containing Cartan MASAs using measured equivalence re- lations and 2-cocycles on such equivalence relations. In this paper, we give a new classification in terms of extensions of inverse semigroups. Our approach is more algebraic in character and less point-based than that of Feldman-Moore. As an application, we give a restatement of the spectral theorem for bimodules in terms of subsets of inverse semigroups. We also show how our viewpoint leads naturally to a description of maximal subdiagonal algebras.

The Number Of Framings Of A Knot In A 3-Manifold, Patricia Cahn, Vladimir Chernov, Rustam Sadykov

Mathematics Sciences: Faculty Publications

In view of the self-linking invariant, the number |K| of framed knots in S3 with given underlying knot K is infinite. In fact, the second author previously defined affine self-linking invariants and used them to show that |K| is infinite for every knot in an orientable manifold unless the manifold contains a connected sum factor of S1 × S2; the knot K need not be zero-homologous and the manifold is not required to be compact. We show that when M is orientable, the number |K| is infinite unless K intersects a nonseparating sphere at exactly one point, in which case …

Quantum States Localized On Lagrangian Submanifolds, François Ziegler

Department of Mathematical Sciences Faculty Presentations

Let X be a symplectic manifold and Aut(L) the automorphism group of a Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M. Souriau in the 1990s, are certain positive-definite functions on Aut(L) or, less ambitiously, on any “large enough” subgroup G of Aut(L). This definition has two major drawbacks: when G = Aut(L) there are no known examples; and when G is a Lie subgroup the notion is far from selective enough. In this talk I’ll introduce the concept of a quantum state *localized at Y *, where Y is a coadjoint orbit of a subgroup …

Γ-Butyrobetaine Is A Proatherogenic Intermediate In Gut Microbial Metabolism Of L-Carnitine To Tmao, Robert A. Koeth, Bruce S. Levison, Miranda K. Culley, Jennifer A. Buffa, Zeneng Wang, Jill C. Gregory, Elin Org, Yuping Wu, Lin Li, Jonathan D. Smith, W.H. Wilson Tang, Joseph A. Didonato, Aldons J. Lusis, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

L-carnitine, a nutrient in red meat, was recently reported to accelerate atherosclerosis via a metaorganismal pathway involving gut microbial trimethylamine (TMA) formation and host hepatic conversion into trimethylamine-N-oxide (TMAO). Herein, we show that following L-carnitine ingestion, γ-butyrobetaine (γBB) is produced as an intermediary metabolite by gut microbes at a site anatomically proximal to and at a rate ∼1,000-fold higher than the formation of TMA. Moreover, we show that γBB is the major gut microbial metabolite formed from dietary L-carnitine in mice, is converted into TMA and TMAO in a gut microbiota-dependent manner (like dietary L-carnitine), and accelerates atherosclerosis. Gut microbial …

Prognostic Value Of Elevated Levels Of Intestinal Microbe-Generated Metabolite Trimethylamine-N-Oxide In Patients With Heart Failure: Refining The Gut Hypothesis, W.H. Wilson Tang, Zeneng Wang, Yiying Fan, Bruce Levison, Jennie E. Hazen, Lillian M. Donahue, Yuping Wu, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Background: Altered intestinal function is prevalent in patients with heart failure (HF), but its role in adverse outcomes is unclear. Objectives: This study investigated the potential pathophysiological contributions of intestinal microbiota in HF. Methods: We examined the relationship between fasting plasma trimethylamine-N-oxide (TMAO) and all-cause mortality over a 5-year follow-up in 720 patients with stable HF. Results:The median TMAO level was 5.0 μM, which was higher than in subjects without HF (3.5 μM; p < 0.001). There was modest but significant correlation between TMAO concentrations and B-type natriuretic peptide (BNP) levels (r = 0.23; p < 0.001). Higher plasma TMAO levels were associated with a 3.4-fold increased mortality risk. Following adjustments for traditional risk factors and BNP levels, elevated TMAO levels remained predictive of 5-year mortality risk (hazard ratio [HR]: 2.2; 95% CI: 1.42 to 3.43; p < 0.001), as well as following the addition of estimated glomerular filtration rate to the model (HR: 1.75; 95% CI: 1.07 to 2.86; p < 0.001). Conclusions: High TMAO levels were observed in patients with HF, and elevated TMAO levels portended higher long-term mortality risk independent of traditional risk factors and cardiorenal indexes.

A Potential Foundation For Emergent Space-Time, Kevin H. Knuth, Newshaw Bahreyni

Physics Faculty Scholarship

We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied on assumptions such as the existence of a 4-dimensional manifold, symmetries of space-time, or the constant speed of light, we demonstrate that these now familiar mathematics can be derived as the unique means to consistently quantify a network of events. This suggests that space-time need not be physical, but instead the mathematics of space and time emerges as the unique way in which an …