Digital Commons Network^™

On Pancyclic Representable Matroids, Brian Beavers, James Oxley

Faculty Publications

Bondy proved that an n-vertex simple Hamiltonian graph with at least n2/4 edges has cycles of every length unless it is isomorphic to Kn/2,n/2. This paper considers finding circuits of every size in GF(q)-representable matroids with large numbers of elements. A consequence of the main result is that a rank-r simple binary matroid with at least 2r-1 elements either has circuits of all sizes or is isomorphic to AG(r-1,2). © 2005 Elsevier B.V. All rights reserved.

Emma Spaulding Bryant: Civil War Bride, Carpetbagger's Wife, Ardent Feminist: Letters And Diaries, 1860-1900, Giselle Roberts

Civil War Book Review

Reconstructing female identity

Marriage wed Antebellum ideals and independence

Remarks On Monotone Control Systems With Multi-Valued Input-State Characteristics, Patrick De Leenheer, Michael Malisoff

Faculty Publications

We announce a new global small-gain theorem for feedback interconnections of monotone input-output systems with multi-valued input-state characteristics. This extends a small-gain theorem of Angeli and Sontag for monotone systems with singleton-valued characteristics. The proof of our theorem is based on Thieme's convergence theory for asymptotically autonomous systems. We also provide an illustrative example. © 2005 IEEE.

Host-Parasitoid Spatial Ecology: A Plea For A Landscape-Level Synthesis, James T. Cronin, John D. Reeve

Faculty Publications

A growing body of literature points to a large-scale research approach as essential for understanding population and community ecology. Many of our advances regarding the spatial ecology of predators and prey can be attributed to research with insect parasitoids and their hosts. In this review, we focus on the progress that has been made in the study of the movement and population dynamics of hosts and their parasitoids in heterogeneous landscapes, and how this research approach may be beneficial to pest management programs. To date, few studies have quantified prey and predator rates and ranges of dispersal and population dynamics …

New Symplectic 4-Manifolds With B+=1, Scott Baldridge

Faculty Publications

In 1995 Dusa McDuff and Dietmar Salamon conjectured the existence of symplectic 4-manifolds (X, ω) which satisfy b = 1, K = 0, K · ω > 0, and which fail to be of Lefschetz type. This is equivalent to finding a symplectic, homology T × S manifold with nontorsion canonical class and a cohomology ring which is not isomorphic to the cohomology ring of T × S . They needed such examples to complete a list of possible symplectic 4-manifolds with b = 1. In that same year Tian-Jun Li and Ai-ko Liu, working from a different point of view, …

Further Remarks On Strict Input-To-State Stable Lyapunov Functions For Time-Varying Systems, Michael Malisoff, Frédéric Mazenc

Faculty Publications

We study the stability properties of a class of time-varying non-linear systems. We assume that non-strict input-to-state stable (ISS) Lyapunov functions for our systems are given and posit a mild persistency of excitation condition on our given Lyapunov functions which guarantee the existence of strict ISS Lyapunov functions for our systems. Next, we provide simple direct constructions of explicit strict ISS Lyapunov functions for our systems by applying an integral smoothing method. We illustrate our constructions using a tracking problem for a rotating rigid body. © 2005 Elsevier Ltd. All rights reserved.

Lsu In The Eye Of The Storm: A University Model For Disaster Response, Renée Bacher, Teresa Devlin, Kristine Calongne, Joshua Duplechain, Stephanie Pertuit

LSU Press Published Books

No abstract provided.

Effective State Metamorphosis In Semi-Classical Loop Quantum Cosmology, Parampreet Singh

Faculty Publications

Modification to the behaviour of geometrical density at short scales is a key result of loop quantum cosmology, responsible for an interesting phenomenology in the very early universe. We demonstrate the way matter with arbitrary scale factor dependence in Hamiltonian incorporates this change in its effective dynamics in the loop-modified phase. For generic matter, the equation of state starts varying near a critical scale factor, becomes negative below it and violates the strong energy condition. This opens a new avenue to generalize various phenomenological applications in loop quantum cosmology. We show that different ways to define energy density may yield …

Semiclassical States, Effective Dynamics, And Classical Emergence In Loop Quantum Cosmology, Parampreet Singh, Kevin Vandersloot

Faculty Publications

We construct physical semiclassical states annihilated by the Hamiltonian constraint operator in the framework of loop quantum cosmology as a method of systematically determining the regime and validity of the semiclassical limit of the quantum theory. Our results indicate that the evolution can be effectively described using continuous classical equations of motion with nonperturbative corrections down to near the Planck scale below which the Universe can only be described by the discrete quantum constraint. These results, for the first time, provide concrete evidence of the emergence of classicality in loop quantum cosmology and also clearly demarcate the domain of validity …

The Effect Of Channel Length On The Residual Circulation In Tidally Dominated Channels, Chunyan Li, James O'Donnell

Faculty Publications

With an analytic model, this paper describes the subtidal circulation in tidally dominated channels of different lengths, with arbitrary lateral depth variations. The focus is on an important parameter associated with the reversal of the exchange flows. This parameter (δ) is defined as the ratio between the channel length and one-quarter of the tidal wavelength, which is determined by water depth and tidal frequency. In this study, a standard bottom drag coefficient, CD = 0.0025, is used. For a channel with δ smaller than 0.6-0.7 (short channels), the exchange flow at the open end has an inward transport in deep …

Army Of The Potomac Vol. Ii: Mcclellan Takes Command, September 1861-Februrary 1862, James D. Hardy

Civil War Book Review

Producing power

Army was built for a campaign, not a battle

Lincoln's Speeches Reconsidered, William D. Pederson

Civil War Book Review

Lincoln's lectures

Author calls for a closer critique

Search For Periodicities In The B8 Solar Neutrino Flux Measured By The Sudbury Neutrino Observatory, B. Aharmim, S. N. Ahmed, A. E. Anthony, E. W. Beier, A. Bellerive, M. Bergevin, S. D. Biller, M. G. Boulay, M. G. Bowler, Y. D. Chan, M. Chen, X. Chen, B. T. Cleveland, T. Costin, G. A. Cox, C. A. Currat, X. Dai, H. Deng, J. Detwiler, P. J. Doe, R. S. Dosanjh, G. Doucas, C. A. Duba, F. A. Duncan, M. Dunford, J. A. Dunmore, E. D. Earle, S. R. Elliott

Faculty Publications

A search has been made for sinusoidal periodic variations in the B8 solar neutrino flux using data collected by the Sudbury Neutrino Observatory over a 4-year time interval. The variation at a period of 1 yr is consistent with modulation of the B8 neutrino flux by the Earth's orbital eccentricity. No significant sinusoidal periodicities are found with periods between 1 d and 10 years with either an unbinned maximum likelihood analysis or a Lomb-Scargle periodogram analysis. The data are inconsistent with the hypothesis that the results of the recent analysis by Sturrock et al., based on elastic scattering events in …

Dynamical Evolution Of Quasicircular Binary Black Hole Data, Miguel Alcubierre, Bernd Brügmann, Peter Diener, F. Siddhartha Guzmán, Ian Hawke, Scott Hawley, Frank Herrmann, Michael Koppitz, Denis Pollney, Edward Seidel, Jonathan Thornburg

Faculty Publications

We study the fully nonlinear dynamical evolution of binary black hole data, whose orbital parameters are specified via the effective potential method for determining quasicircular orbits. The cases studied range from the Cook-Baumgarte innermost stable circular orbit (ISCO) to significantly beyond that separation. In all cases we find the black holes to coalesce (as determined by the appearance of a common apparent horizon) in less than half an orbital period. The results of the numerical simulations indicate that the initial holes are not actually in quasicircular orbits, but that they are in fact nearly plunging together. The dynamics of the …

The Structure Of Equivalent 3-Separations In A 3-Connected Matroid, Rhiannon Hall, James Oxley, Charles Semple

Faculty Publications

Let M be a matroid. When M is 2-connected, Cunningham and Edmonds gave a tree decomposition of M that displays all of its 2-separations. This result was extended by Oxley, Semple, and Whittle, who showed that, when M is 3-connected, there is a corresponding tree decomposition that displays all non-trivial 3-separations of M up to a certain natural equivalence. This equivalence is based on the notion of the full closure fcl(Y) of a set Y in M, which is obtained by beginning with Y and alternately applying the closure operators of M and M* until no new elements can be …

Gauss-Manin Connections For Arrangements, Iii Formal Connections, Daniel C. Cohen, Peter Orlik

Faculty Publications

We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a complex rank one local system. We define formal Gauss-Manin connection matrices in the Aomoto complex and prove that, for all arrangements and all local systems, these formal connection matrices specialize to Gauss-Manin connection matrices. © 2004 American Mathematical Society.

Enhancement Of Calcium-Dependent Afterpotentials In Oxytocin Neurons Of The Rat Supraoptic Nucleus During Lactation, Ryoichi Teruyama, William E. Armstrong

Faculty Publications

The firing pattern of oxytocin (OT) hormone synthesizing neurons changes dramatically immediately before each milk ejection, when a brief burst of action potentials is discharged. OT neurons possess intrinsic currents that would modulate this burst. Our previous studies showed the amplitude of the Ca2+-dependent afterhyperpolarization (AHP) following spike trains is significantly larger during lactation. In the present study we sought to determine which component of the AHP is enhanced, and whether the enhancement could be related to changes in whole-cell Ca2+ current or the Ca2+ transient in identified OT or vasopressin (VP) neurons during lactation. We confirmed, with whole-cell current-clamp …

Consistent Discretizations: The Gowdy Spacetimes, Rodolfo Gambini, Marcelo Ponce, Jorge Pullin

Faculty Publications

We apply the consistent discretization scheme to general relativity particularized to the Gowdy spacetimes. This is the first time the framework has been applied in detail in a nonlinear generally covariant gravitational situation with local degrees of freedom. We show that the scheme can be correctly used to numerically evolve the spacetimes. We show that the resulting numerical schemes are convergent and preserve approximately the constraints as expected. Given the numerical complexity of the method, further work will be needed to make it competitive with the usual free evolution methods currently in use in numerical relativity. © 2005 The American …

Mathematical Framework For Simulation Of Quantum Fields In Complex Interferometers Using The Two-Photon Formalism, Thomas Corbitt, Yanbei Chen, Nergis Mavalvala

Faculty Publications

We present a mathematical framework for simulation of optical fields in complex gravitational-wave interferometers. The simulation framework uses the two-photon formalism for optical fields and includes radiation pressure effects, an important addition required for simulating signal and noise fields in next-generation interferometers with high circulating power. We present a comparison of results from the simulation with analytical calculation and show that accurate agreement is achieved. © 2005 The American Physical Society.

On Atkin-Swinnerton-Dyer Congruence Relations, Wen Ching Winnie Li, Ling Long, Zifeng Yang

Faculty Publications

In this paper, we exhibit a noncongruence subgroup Γ whose space of weight 3 cusp forms S3(Γ) admits a basis satisfying the Atkin-Swinnerton-Dyer congruence relations with two weight 3 newforms for certain congruence subgroups. This gives a modularity interpretation of the motive attached to S3(Γ) by Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space. © 2004 Elsevier Inc. All rights reserved.

Early-Stage Folding In Proteins (In Silico) Sequence-To-Structure Relation, Michal Brylinski, Leszek Konieczny, Patryk Czerwonko, Wiktor Jurkowski, Irena Roterman

Faculty Publications

A sequence-to-structure library has been created based on the complete PDB database. The tetrapeptide was selected as a unit representing a well-defined structural motif. Seven structural forms were introduced for structure classification. The early-stage folding conformations were used as the objects for structure analysis and classification. The degree of determinability was estimated for the sequence-to-structure and structure-to-sequence relations. Probability calculus and informational entropy were applied for quantitative estimation of the mutual relation between them. The structural motifs representing different forms of loops and bends were found to favor particular sequences in structure-to-sequence analysis. © 2005 Hindawi Publishing Corporation.

Quantum Phase Transition In The U(3) Boson System, Feng Pan, Yu Zhang, Shuo Jin, J. P. Draayer, Mo Lin Ge, J. L. Birman

Faculty Publications

The quantum phase transitional behavior of the U(3) boson model is studied. Low-lying levels, overlaps of wavefunctions with those in the d-wave dominant and s- and d-wave mixed phases, as well as ground state occupation probabilities of s- and d-components are examined as functions of the control parameter and the number of particles. The results indicated that the s- and d-wave component change in the wavefunction possibly is a first order quantum phase transition in the large N limit. © 2005 Elsevier B.V. All rights reserved.

Groups Associated With Minimal Flows, J. D. Lawson, Amha T. Lisan

Faculty Publications

Let S be topological semigroup, we consider an appropriate semigroup compactification Ŝ of S. In this paper we study the connection between subgroups of a maximal group in a minimal left ideal of Ŝ, which arise as equivalence classes of some closed left congruence, and the minimal ow characterized by the left congruence. A particular topology is defined on a maximal group and it is shown that a closed subgroup under this topology is precisely the intersection of an equivalence class with the maximal group for some left congruence on Ŝ. © Mathematical Institute, Academy of Sciences of Czech Republic …

Time-Dependent Treatment Of A General Three-Level System, A. R.P. Rau, Weichang Zhao

Faculty Publications

Both unitary evolution and the effects of dissipation and decoherence for a general three-level system are of wide interest in quantum optics, molecular physics, and elsewhere. A previous paper presented a technique for solving the time-dependent operator equations involved but under certain restrictive conditions. We now extend our results to a general three-level system with arbitrary time-dependent Hamiltonians and Lindblad operators. Analytical handling of the SU(3) algebra of the eight operators involved leaves behind a set of coupled first-order differential equations for classical functions. Solution of this set gives a complete solution of the quantum problem, without having to invoke …

Fuse Measurements Of Far-Ultraviolet Extinction. I. Galactic Sight Lines, Ulysses J. Sofia, Michael J. Wolff, Brian Rachford, Karl D. Gordon, Geoffrey C. Clayton, Stefan I.B. Cartledge, Peter G. Martin, Bruce T. Draine, John S. Mathis, Theodore P. Snow, Douglas C.B. Whittet

Faculty Publications

We present extinction curves that include data down to far-ultraviolet wavelengths (FUV; 1050-1200 Å) for nine Galactic sight lines. The FUV extinction was measured using data from the Far Ultraviolet Spectroscopic Explorer. The sight lines were chosen for their unusual extinction properties in the infrared through the ultraviolet; that they probe a wide range of dust environments is evidenced by the large spread in their measured ratios of total to selective extinction, RV = 2.43-3.81. We find that extrapolation of the Fitzpatrick & Massa relationship from the ultraviolet appears to be a good predictor of the FUV extinction behavior. We …

Ensight, Jonathan Hefner

Honors Capstones

No abstract provided.

Dynamical Systems And The Logistic And Tent Maps, Kathleen Larkin Spires

Honors Capstones

No abstract provided.

On The Nature Of Connectivity Types, Miao Xu

Honors Capstones

No abstract provided.

Measure Extension Theorems For T0-Spaces, Klaus Keimel, Jimmie D. Lawson

Faculty Publications

The theme of this paper is the extension of continuous valuations on the lattice of open sets of a T0-space to Borel measures. A general extension principle is derived that provides a unified approach to a variety of extension theorems including valuations that are directed suprema of simple valuations, continuous valuations on locally compact sober spaces, and regular valuations on coherent sober spaces. © 2004 Elsevier B.V. All rights reserved.

Bounds And Extremal Configurations For The Torsional Rigidity Of Coated Fiber Reinforced Shafts, Robert Lipton, Tungyang Chen

Faculty Publications

In this paper we derive bounds on the torsional rigidity for coated fiber reinforced shafts. The bounds are used to assess the optimality or suboptimality of fiber reinforcement configurations. This investigation focuses on coated fiber reinforcements with circular cross section. It is shown how the effective antiplane shear modulus and torsional rigidity of each coated fiber are used to determine whether the configuration provides reinforcement above or below that of a homogeneous shaft containing no coated fibers. Simply connected shaft cross sections of arbitrary shape reinforced with any configuration of coated fibers are considered. Precise conditions on the effective antiplane …