B-Coloring Of Regular Graphs, 2011 Illinois Wesleyan University

#### B-Coloring Of Regular Graphs, Taole Zhu, Josh Brown-Kramer, Faculty Advisor

*John Wesley Powell Student Research Conference*

No abstract provided.

Golden Apple Award For Excellence In Teaching, 2011 Providence College

#### Golden Apple Award For Excellence In Teaching, Anthony Rodriguez

*Anthony M. Rodriguez*

No abstract provided.

Axiomatic Foundations Of Mathematics, 2011 Stephen F Austin State University

#### Axiomatic Foundations Of Mathematics, Ryan Melton

*Undergraduate Research Conference*

No abstract provided.

Gut Flora Metabolism Of Phosphatidylcholine Promotes Cardiovascular Disease, 2011 Cleveland Clinic

#### Gut Flora Metabolism Of Phosphatidylcholine Promotes Cardiovascular Disease, Zeneng Wang, Elizabeth Klipfell, Brian J. Bennett, Robert Koeth, Bruce S. Levison, Brandon Dugar, Ariel E. Feldstein, Earl B. Britt, Xiaoming Fu, Yoo Mi Chung, Yuping Wu, Phil Schauer, Jonathan D. Smith, Hooman Allayee, W.H. Wilson Tang, Joseph A. Didonato, Aldons J. Lusis, Stanley L. Hazen

*Mathematics Faculty Publications*

Metabolomics studies hold promise for the discovery of pathways linked to disease processes. Cardiovascular disease (CVD) represents the leading cause of death and morbidity worldwide. Here we used a metabolomics approach to generate unbiased small-molecule metabolic profiles in plasma that predict risk for CVD. Three metabolites of the dietary lipid phosphatidylcholine—choline, trimethylamine N-oxide (TMAO) and betaine—were identified and then shown to predict risk for CVD in an independent large clinical cohort. Dietary supplementation of mice with choline, TMAO or betaine promoted upregulation of multiple macrophage scavenger receptors linked to atherosclerosis, and supplementation with choline or TMAO promoted atherosclerosis ...

Efficient First Order Methods For Linear Composite Regularizers, 2011 University of Chicago

#### Efficient First Order Methods For Linear Composite Regularizers, Andreas Argyriou, Charles A. Micchelli, Massimiliano Pontil, Lixin Shen, Yuesheng Xu

*Mathematics - Faculty Scholarship*

A wide class of regularization problems in machine learning and statistics employ a regularization term which is obtained by composing a simple convex function omega with a linear transformation. This setting includes Group Lasso methods, the Fused Lasso and other total variation methods, multi-task learning methods and many more. In this paper, we present a general approach for computing the proximity operator of this class of regularizers, under the assumption that the proximity operator of the function \omega is known in advance. Our approach builds on a recent line of research on optimal first order optimization methods and uses fixed ...

Wavelet-Based Analysis Of Neutron-Induced Photon Spectral Data, 2011 Western Kentucky University

#### Wavelet-Based Analysis Of Neutron-Induced Photon Spectral Data, Bruce Kessler, Alexander Barzilov, Phillip Womble

*Mathematics Faculty Publications*

Neutron-based methods of non-destructive inter- rogation of objects for the purpose of their characterization are well-established techniques, employed in the field of bulk material analysis, contraband detection, unexploded ordnance, etc. The characteristic gamma rays produced in nuclear reactions initiated by neutrons in the volume of the irradiated object (inelastic neutron scattering, thermal neutron capture, and activation) are used for the elemental identification. In many real-world applications, an automated spectral analysis is needed, and many algorithms are used for that purpose. The Applied Physics Institute at Western Kentucky University has recently started to employ a mathematical spectrum analysis technique based on ...

Wavelet-Based Analysis Of Neutron-Induced Photon Spectral Data, 2011 Western Kentucky University

#### Wavelet-Based Analysis Of Neutron-Induced Photon Spectral Data, Bruce Kessler, Alexander Barzilov, Phillip Womble

*Bruce Kessler*

Neutron-based methods of non-destructive inter- rogation of objects for the purpose of their characterization are well-established techniques, employed in the field of bulk material analysis, contraband detection, unexploded ordnance, etc. The characteristic gamma rays produced in nuclear reactions initiated by neutrons in the volume of the irradiated object (inelastic neutron scattering, thermal neutron capture, and activation) are used for the elemental identification. In many real-world applications, an automated spectral analysis is needed, and many algorithms are used for that purpose. The Applied Physics Institute at Western Kentucky University has recently started to employ a mathematical spectrum analysis technique based on ...

Tunable Vibrational Band Gaps In One-Dimensional Diatomic Granular Crystals With Three-Particle Unit Cells, 2011 UMASS, Amherst

#### Tunable Vibrational Band Gaps In One-Dimensional Diatomic Granular Crystals With Three-Particle Unit Cells, N. Boechler, J. Yang, G. Theocharis, Panos Kevrekidis, C. Daraio

*Panos Kevrekidis*

We investigate the tunable vibration filtering properties of statically compressed one-dimensional diatomic granular crystals composed of arrays of stainless steel spheres and cylinders interacting via Hertzian contact. The arrays consist of periodically repeated three-particle unit cells (sphere-cylinder-sphere) in which the length of the cylinder is varied systematically. We investigate the response of these granular crystals, given small amplitude dynamic displacements relative to those due to the static compression, and characterize their linear frequency spectrum. We find good agreement between theoretical dispersion relation analysis (for infinite systems), state-space analysis (for finite systems), and experiments. We report the observation of three distinct ...

Stable Generalized Finite Element Method (Sgfem), 2011 University of Texas at Austin

#### Stable Generalized Finite Element Method (Sgfem), I. Babuska, U. Banerjee

*Mathematics - Faculty Scholarship*

The Generalized Finite Element Method (GFEM) is a Partition of Unity Method (PUM), where the trial space of standard Finite Element Method (FEM) is augmented with non-polynomial shape functions with compact support. These shape functions, which are also known as the enrichments, mimic the local behavior of the unknown solution of the underlying variational problem. GFEM has been successfully used to solve a variety of problems with complicated features and microstructure. However, the stiffness matrix of GFEM is badly conditioned (much worse compared to the standard FEM) and there could be a severe loss of accuracy in the computed solution ...

Algebraic Properties Of A Family Of Generalized Laguerre Polynomials, 2011 University of Massachusetts - Amherst

#### Algebraic Properties Of A Family Of Generalized Laguerre Polynomials, F Hajir

*Farshid Hajir*

We study the algebraic properties of Generalized Laguerre Polynomials for negative integral values of the parameter. For integers r,n≥0 , we conjecture that L(−1−n−r)n(x)=∑nj=0(n−j+rn−j)xj/j! is a \Q -irreducible polynomial whose Galois group contains the alternating group on n letters. That this is so for r=n was conjectured in the 1950's by Grosswald and proven recently by Filaseta and Trifonov. It follows from recent work of Hajir and Wong that the conjecture is true when r is large with respect to n≥5 . Here we ...

Specializations Of One-Parameter Families Of Polynomials, 2011 University of Massachusetts - Amherst

#### Specializations Of One-Parameter Families Of Polynomials, F Hajir, S Wong

*Farshid Hajir*

Let K be a number field, and suppose λ(x,t)∈K[x,t] is irreducible over K(t). Using algebraic geometry and group theory, we describe conditions under which the K-exceptional set of λ, i.e. the set of α∈K for which the specialized polynomial λ(x,α) is K-reducible, is finite. We give three applications of the methods we develop. First, we show that for any fixed n≥10, all but finitely many K-specializations of the degree n generalized Laguerre polynomial L n (t) (x) are K-irreducible and have Galois group S n . Second, we study specializations ...

On The Galois Group Of Generalized Laguerre Polynomials, 2011 University of Massachusetts - Amherst

#### On The Galois Group Of Generalized Laguerre Polynomials, F Hajir

*Farshid Hajir*

Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be “large.” For a fixed α∈ℚ-ℤ <0 , Filaseta and Lam have shown that the nth degree Generalized Laguerre Polynomial L n (α) (x)=∑ j=0 n n+α n-j(-x) j /j! is irreducible for all large enough n. We use our criterion to show that, under these conditions, the Galois group of L n (α) (x) is either the alternating or symmetric group on n letters, generalizing results of Schur for α=0,1,±1 2,-1-n.

Finitely Ramified Iterated Extensions, 2011 University of Massachusetts - Amherst

#### Finitely Ramified Iterated Extensions, W Aitken, F Hajir, C Maire

*Farshid Hajir*

Let K be a number field, t a parameter, F = K(t), and φ(x)∈ K [x] a polynomial of degree d ≥ 2. The polynomial Φn(x,t) = φ^n (x) − t ∈ F[x], where φ^ n = φ ^ φ ^ … ^ φ is the n-fold iterate of φ, is irreducible over F; we give a formula for its discriminant. Let F be the field obtained by adjoining to F all roots (in a fixed ) of Φn(x,t) for all n ≥ 1; its Galois group Gal(Fφ/F) is the iterated monodromy group of φ. The iterated extension Fφ is finitely ramified ...

Modular Forms And Elliptic Curves Over The Field Of Fifth Roots Of Unity, 2011 University of Massachusetts - Amherst

#### Modular Forms And Elliptic Curves Over The Field Of Fifth Roots Of Unity, Pe Gunnells, F Hajir, Dan Yasaki

*Farshid Hajir*

Let F be the cyclotomic field of fifth roots of unity. We computationally investigate modularity of elliptic curves over F

On The Locus Of Hodge Classes, 2011 University of Massachusetts - Amherst

#### On The Locus Of Hodge Classes, E Cattani, P Deligne, A Kaplan

*Eduardo Cattani*

Let S be a nonsingular complex algebraic variety and V a polarized variation of Hodge structure of weight 2p with polarization form Q. Given an integer K, let S(K) be the space of pairs (s, u) with s ∈ S, u ∈ Vs integral of type (p, p), and Q(u, u) ≤ K. We show in Theorem 1.1 that S(K) is an algebraic variety, finite over S. When V is the local system H2p (Xs, Z)/torsion associated with a family of nonsingular projective varieties parametrized by S, the result implies that the locus where a given integral class ...

Frobenius Modules And Hodge Asymptotics, 2011 University of Massachusetts - Amherst

#### Frobenius Modules And Hodge Asymptotics, E Cattani, J Fernandez

*Eduardo Cattani*

We exhibit a direct correspondence between the potential defining the H1,1 small quantum module structure on the cohomology of a Calabi-Yau manifold and the asymptotic data of the A-model variation of Hodge structure. This is done in the abstract context of polarized variations of Hodge structure and Frobenius modules.

Complete Intersections In Toric Ideals, 2011 University of Massachusetts - Amherst

#### Complete Intersections In Toric Ideals, E Cattani, R Curran, A Dickenstein

*Eduardo Cattani*

We present examples that show that in dimension higher than one or codimension higher than two, there exist toric ideals such that no binomial ideal contained in and of the same dimension is a complete intersection. This result has important implications in sparse elimination theory and in the study of the Horn system of partial differential equations.

Asymptotic Hodge Theory And Quantum Products, 2011 University of Massachusetts - Amherst

#### Asymptotic Hodge Theory And Quantum Products, E Cattani, Javier Fernandez

*Eduardo Cattani*

Assuming suitable convergence properties for the Gromov-Witten potential of a Calabi-Yau manifold $X$ one may construct a polarized variation of Hodge structure over the complexified K\"ahler cone of $X$. In this paper we show that, in the case of fourfolds, there is a correspondence between ``quantum potentials'' and polarized variations of Hodge structures that degenerate to a maximally unipotent boundary point. Under this correspondence, the WDVV equations are seen to be equivalent to the Griffiths' trasversality property of a variation of Hodge structure.

Binomial Residues, 2011 University of Massachusetts - Amherst

#### Binomial Residues, E Cattani, A Dickenstein, B Sturmfels

*Eduardo Cattani*

A binomial residue is a rational function defined by a hypergeometric integral whose kernel is singular along binomial divisors. Binomial residues provide an integral representation for rational solutions of A-hypergeometric systems of Lawrence type. The space of binomial residues of a given degree, modulo those which are polynomial in some variable, has dimension equal to the Euler characteristic of the matroid associated with A.

Mixed Lefschetz Theorems And Hodge-Riemann Bilinear Relations, 2011 University of Massachusetts - Amherst

#### Mixed Lefschetz Theorems And Hodge-Riemann Bilinear Relations, E Cattani

*Eduardo Cattani*

The Hard Lefschetz Theorem (HLT) and the Hodge–Riemann bilinear relations (HRR) hold in various contexts: they impose restrictions on the cohomology algebra of a smooth compact Kähler manifold; they restrict the local monodromy of a polarized variation of Hodge structure; they impose conditions on the f-vectors of convex polytopes. While the statements of these theorems depend on the choice of a Kähler class, or its analog, there is usually a cone of possible choices. It is then natural to ask whether the HLT and HRR remain true in a mixed context. In this note, we present a unified approach ...