Mathematics Commons^™

Two-Dimensional Magneto-Hydrodynamic System With Jump Processes: Well Posedness And Invariant Measures, Utpal Manna, Manil T Mohan

Communications on Stochastic Analysis

No abstract provided.

White Noise Representation Of Gaussian Random Fields, Zachary Gelbaum

Communications on Stochastic Analysis

No abstract provided.

A Graph-Theoretical Approach To The Selection Of The Minimum Tiling Path From A Physical Map, Serdar Bozdag

Mathematics, Statistics and Computer Science Faculty Research and Publications

The problem of computing the minimum tiling path (MTP) from a set of clones arranged in a physical map is a cornerstone of hierarchical (clone-by-clone) genome sequencing projects. We formulate this problem in a graph theoretical framework, and then solve by a combination of minimum hitting set and minimum spanning tree algorithms. The tool implementing this strategy, called FMTP, shows improved performance compared to the widely used software FPC. When we execute FMTP and FPC on the same physical map, the MTP produced by FMTP covers a higher portion of the genome, and uses a smaller number of clones. For …

Rattus Model Utilizing Selective Pulmonary Ischemia Induces Bronchiolitis Obliterans Organizing Pneumonia, John C. Densmore, Paul M. Jeziorczak, Anne V. Clough, Kirkwood A. Pritchard Jr, Breana Cummens, Meetha Medhora, Arjun Rao, Elizabeth R. Jacobs

Mathematics, Statistics and Computer Science Faculty Research and Publications

Bronchiolitis obliterans organizing pneumonia (BOOP), a morbid condition when associated with lung transplant and chronic lung disease, is believed to be a complication of ischemia. Our goal was to develop a simple and reliable model of lung ischemia in the Sprague-Dawley rat that would produce BOOP. Unilateral ischemia without airway occlusion was produced by an occlusive slipknot placed around the left main pulmonary artery. Studies were performed 7 days later. Relative pulmonary and systemic flow to each lung was measured by injection of technetium Tc 99m macroaggregated albumin. Histological sections were examined for structure and necrosis and scored for BOOP. …

On The Lp-Error Of Approximation Of Bivariate Functions By Harmonic Splines, Yuliya Babenko, Tatyana Leskevich

Faculty Articles

Interpolation by various types of splines is the standard procedure in many applications. In this paper we discuss harmonic spline “interpolation” (on the lines of a grid) as an alternative to polynomial spline interpolation (at vertices of a grid). We will discuss some advantages and drawbacks of this approach and present the asymptotics of the L_p-error for adaptive approximation by harmonic splines.

On The Quadratic Bundles Related To Hermitian Symmetric Spaces, Tihomir Valchev

Articles

We develop the direct scattering problem for quadratic bundles associated to Hermitian symmetric spaces. We adapt the dressing method for quadratic bundles which allows us to find special solutions to multicomponent derivative Schrodinger equation for instance. The latter is an infinite dimensional Hamiltonian system possessing infinite number of integrals of motion. We demonstrate how one can derive them by block diagonalization of the corresponding Lax pair.

Anterior Abdominal Stab Injury: A Comparison Of Self-Inflicted And Intentional Third-Party Stabbings, Aman Banerjee, Hannah Y. Zhou, Katherine B. Kelly, Bianca D. Downs, John J. Como, Jeffrey A. Claridge

Mathematics and Statistics Faculty Publications

Background: There is minimal literature comparing self-inflicted (SI) with non–self-inflicted (NSI) anterior abdominal stab wounds (AASW). Methods: Adult patients treated at a level 1 trauma center from 2006 through 2011 with an AASW were reviewed. Results: There were 215 patients with an AASW; 20% were SI. NSI patients had more nonabdominal injuries (47% vs 16%, P < .01) and disposition directly to the operating room (45% vs 26%, P = .02). Intra-abdominal injury rates were similar. One hundred twenty-eight patients had isolated AASWs; 28% were SI. SI patients had higher admission rates (86% vs 63%, P = .01). One hundred three patients had isolated stable/asymptomatic AASWs; 31% were SI. SI patients had more admissions (84% vs 52%, P < .01), had higher intensive care unit admission rates (23% vs 5%, P = .01), longer LOS (3.2 vs 1.4, P < .01), and higher hospital charges ($18,000 vs $11,000, P < .01). The rates of intra-abdominal injury were again similar. Conclusions: Controlling for extra-abdominal injuries, SI AASW patients have similar rates of intra-abdominal injury but use more resources.

Toric Complete Intersection Codes, Ivan Soprunov

Mathematics and Statistics Faculty Publications

In this paper we construct evaluation codes on zero-dimensional complete intersections in toric varieties and give lower bounds for their minimum distance. This generalizes the results of Gold–Little–Schenck and Ballico–Fontanari who considered evaluation codes on complete intersections in the projective space.

Mind The Gaps, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Ramsey Properties Of Countably Infinite Partial Orderings, Marcia J. Groszek

Dartmouth Scholarship

A partial ordering ℙ is chain-Ramsey if, for every natural number n and every coloring of the n-element chains from ℙ in finitely many colors, there is a monochromatic subordering ℚ isomorphic to ℙ. Chain-Ramsey partial orderings stratify naturally into levels. We show that a countably infinite partial ordering with finite levels is chain-Ramsey if and only if it is biembeddable with one of a canonical collection of examples constructed from certain edge-Ramsey families of finite bipartite graphs. A similar analysis applies to a large class of countably infinite partial orderings with infinite levels.

Isomorphisms Of Lattices Of Bures-Closed Bimodules Over Cartan Masas, Adam H. Fuller, David R. Pitts

Department of Mathematics: Faculty Publications

For i = 1; 2, let (Mi;Di) be pairs consisting of a Cartan MASA Di in a von Neumann algebra Mi, let atom(Di) be the set of atoms of Di, and let Si be the lattice of Bures-closed Di bimodules in Mi. We show that when Mi have separable preduals, there is a lattice isomorphism between S1 and S2 if and only if the sets

f(Q1;Q2) 2 atom(Di) atom(Di) : Q1MiQ2 6= (0)g

have the same cardinality. In particular, when Di is nonatomic, Si is isomorphic to the lattice of projections in L1([0; 1];m) where m is Lebesgue measure, regardless …

No Radial Excitations In Low Energy Qcd. Ii. The Shrinking Radius Of Hadrons, Tamar Friedmann

Mathematics Sciences: Faculty Publications

We discuss the implications of our prior results obtained in our companion paper (Eur. Phys. J. C (2013). doi:10.1140/epjc/s10052-013-2298-9). Inescapably, they lead to three laws governing the size of hadrons, including in particular protons and neutrons that make up the bulk of ordinary matter: (a) there are no radial excitations in low-energy QCD; (b) the size of a hadron is largest in its ground state; (c) the hadron’s size shrinks when its orbital excitation increases. The second and third laws follow from the first law. It follows that the path from confinement to asymptotic freedom is a Regge trajectory. It …

No Radial Excitations In Low Energy Qcd. I. Diquarks And Classification Of Mesons, Tamar Friedmann

Mathematics Sciences: Faculty Publications

We propose a new schematic model for mesons in which the building blocks are quarks and flavor-antisymmetric diquarks. The outcome is a new classification of the entire meson spectrum into quark–antiquark and diquark– antidiquark states which does not give rise to a radial quantum number: all mesons which have so far been believed to be radially excited are orbitally excited diquark–antidiquark states; similarly, there are no radially excited baryons. Further, mesons that were previously viewed as “exotic” are no longer exotic as they are now naturally integrated into the classification as diquark–antidiquark states. The classification also leads to the introduction …

How To Create A Jordan Algebra, Ian M. Anderson, Thomas J. Apedaile

How to... in 10 minutes or less

We show how to create a Jordan algebra in Maple using the commands AlgebraLibraryData and AlgebraData.

How To Create The Quaternion & Octonion Algebras, Ian M. Anderson, Thomas J. Apedaile

How to... in 10 minutes or less

We show how to create the quaternion and octonion algebras with the DifferentialGeometry software. For each algebra, there is a split-form also available.

The Ideal Free Strategy With Weak Allee Effect, Daniel Munther

Mathematics and Statistics Faculty Publications

This paper examines the interplay between optimal movement strategies and the weak Allee effect within the context of two competing species in a spatially heterogenous environment. When both species have the same populations dynamics, previous studies identified an ‘ideal free’ strategy which is able to exclude any other competitor playing a ‘non-ideal free’ strategy. We find that if the ideal free disperser is subject to a weak Allee effect, a competing species utilizing very weak or very strong advection will still be excluded despite having superior population dynamics. However, for intermediate advection rates, such a competitor can invade the ideal …

Usefulness Of Cardiac Biomarker Score For Risk Stratification In Stable Patients Undergoing Elective Cardiac Evaluation Across Glycemic Status, W.H. Wilson Tang, Naveed Iqbal, Yuping Wu, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Several clinically available cardiac biomarkers have established their prognostic value in patients with acute coronary syndromes. However, their relative prognostic significance in stable subjects has not been prospectively validated, either individually or in combination. The aim of this study was to evaluate the extent to which B-type natriuretic peptide, myeloperoxidase, and high-sensitivity C-reactive protein alone or together could be prognostic biomarkers in 3,635 consecutive stable patients without acute coronary syndrome who underwent elective diagnostic coronary angiography. After adjusting for traditional risk factors and renal function, each of the markers monitored was a significant predictor of incident major adverse cardiovascular events …

New Results For Oscillatory Behavior Of Even-Order Half-Linear Delay Differential Equations, Chenghui Zhang, Ravi P. Agarwal, Martin Bohner, Tongxing Li

Mathematics and Statistics Faculty Research & Creative Works

Some new oscillation results are presented that improve those reported in [C. Zhang, T. Li, B. Sun, and E. Thandapani, On the oscillation of higher-order half-linear delay differential equations, Appl. Math. Lett. 24 (2011) 1618-1621]. © 2012 Elsevier Ltd. All rights reserved.

Use Of Grothendieck Inequality In Interval Computations: Quadratic Terms Are Estimated Accurately Modulo A Constant Factor, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main problems of interval computations is to compute the range of a given function f over given intervals. For a linear function, we can feasibly estimate its range, but for quadratic (and for more complex) functions, the problem of computing the exact range is NP-hard. So, if we limit ourselves to feasible algorithms, we have to compute enclosures instead of the actual ranges. It is known that asymptotically the smallest possible excess width of these enclosures is O(Δ²), where Δ is the largest half-width of the input intervals. This asymptotics is attained for the Mean …

Checking Monotonicity Is Np-Hard Even For Cubic Polynomials, Andrzej Pownuk, Luc Longpre, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main problems of interval computations is to compute the range of a given function over given intervals. In general, this problem is computationally intractable (NP-hard) -- that is why we usually compute an enclosure and not the exact range. However, there are cases when it is possible to feasibly compute the exact range; one of these cases is when the function is monotonic with respect to each of its variables. The monotonicity assumption holds when the derivatives at a midpoint are different from 0 and the intervals are sufficiently narrow; because of this, monotonicity-based estimates are often …