Digital Commons Network^™

Matrix-Model Description Of N = 2 Gauge Theories With Non-Hyperelliptic Seiberg-Witten Curves, Stephen G. Naculich, Howard J. Schnitzer, Niclas Wyllard

Physics Faculty Publications

Using matrix-model methods we study three different N=2 models: U(N)×U(N) with matter in the bifundamental representation, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric representation. We find that the (singular) cubic Seiberg-Witten curves (and associated Seiberg-Witten differentials) implied by the matrix models, although of a different form from the ones previously proposed using M-theory, can be transformed into the latter and are thus physically equivalent. We also calculate the one-instanton corrections to the gauge-coupling matrix using the perturbative expansion of the matrix model. For the U(N) theories with symmetric or antisymmetric matter we use …

Thompson's Group F Is Not Almost Convex, Sean Cleary, Jennifer Taback

Mathematics Faculty Publications

We show that Thompson's group F does not satisfy Cannon's almost convexity condition AC(n) for any positive integer n with respect to the standard generating set with two elements. To accomplish this, we construct a family of pairs of elements at distance n from the identity and distance 2 from each other, which are not connected by a path lying inside the n-ball of length less than k for increasingly large k. Our techniques rely upon Fordham's method for calculating the length of a word in F and upon an analysis of the generators' geometric actions on the tree pair …

Functions Of The Ectodomain And Cytoplasmic Tyrosine Phosphatase Domains Of Receptor Protein Tyrosine Phosphatase Dlar In Vivo, Neil X. Krueger, R. Sreekantha Reddy, Karl Johnson, Jack Bateman, Nancy Kaufmann, Daniella Scalice, David Van Vactor, Haruo Saito

Biology Faculty Publications

The receptor protein tyrosine phosphatase (PTPase) Dlar has an ectodomain consisting of three immunoglobulin (Ig)-like domains and nine fibronectin type III (FnIII) repeats and a cytoplasmic domain consisting of two PTPase domains, membrane-proximal PTP-D1 and C-terminal PTP-D2. A series of mutant Dlar transgenes were introduced into the Drosophila genome via P-element transformation and were then assayed for their capacity to rescue phenotypes caused by homozygous loss-of-function genotypes. The Ig-like domains, but not the FnIII domains, are essential for survival. Conversely, the FnIII domains, but not the Ig-like domains, are required during oogenesis, suggesting that different domains of the Dlar ectodomain …

Cubic Curves From Matrix Models And Generalized Konishi Anomalies, Stephen G. Naculich, Howard J. Schnitzer, Niclas Wyllard

Physics Faculty Publications

We study the matrix model/gauge theory connection for three different N =1 models: U(N) × U(N) with matter in bifundamental representations, U(N) with matter in the symmetric representation, and U (N) with matter in the antisymmetric representation. Using Ward identities, we explicitly show that the loop equations of the matrix models lead to cubic algebraic curves. We then establish the equivalence of the matrix model and gauge theory descriptions in two ways. First, we derive generalized Konishi anomaly equations in the gauge theories, showing that they are identical to the matrix-model equations. Second, we use a perturbative superspace analysis to …

Measurements And Models Of The Atmospheric Ar/N2 Ratio, Mark Battle, Michael Bender, Melissa B. Hendricks, David T. Ho, Robert Mika, Galen Mckinley, Song Miao Fan, Tegan Blaine, Ralph F. Keeling

Physics Faculty Publications

The Ar/N2 ratio of air measured at 6 globally distributed sites shows annual cycles with amplitudes of 12 to 37 parts in 106. Summertime maxima reflect the atmospheric Ar enrichment driven by seasonal warming and degassing of the oceans. Paired models of air-sea heat fluxes and atmospheric tracer transport predict seasonal cycles in the Ar/N2 ratio that agree with observations, within uncertainties.

Contingent Planning Under Uncertainty Via Stochastic Satisfiability, Stephen M. Majercik, Michael L. Littman

Computer Science Faculty Publications

We describe a new planning technique that efficiently solves probabilistic propositional contingent planning problems by converting them into instances of stochastic satisfiability (SSAT) and solving these problems instead. We make fundamental contributions in two areas: the solution of SSAT problems and the solution of stochastic planning problems. This is the first work extending the planning-as-satisfiability paradigm to stochastic domains. Our planner, ZANDER, can solve arbitrary, goal-oriented, finite-horizon partially observable Markov decision processes (POMDPs). An empirical study comparing ZANDER to seven other leading planners shows that its performance is competitive on a range of problems. © 2003 Elsevier Science B.V. All …

The N = 2 U(N) Gauge Theory Prepotential And Periods From A Perturbative Matrix Model Calculation, Stephen G. Naculich, Howard J. Schnitzer, Niclas Wyllard

Physics Faculty Publications

We perform a completely perturbative matrix model calculation of the physical low-energy quantities of the N = 2 U(N) gauge theory. Within the matrix model framework we propose a perturbative definition of the periods a i in terms of certain tadpole diagrams, and check our conjecture up to first order in the gauge theory instanton expansion. The prescription does not require knowledge of the Seiberg-0Witten differential or curve.We also compute the N = 2 prepotential F(a) perturbatively up to the first-instanton level, finding agreement with the known result. 2002 Elsevier Science B.V. All rights reserved.

Pp-Wave Limits And Orientifolds, Stephen G. Naculich, Howard J. Schnitzer, Niclas Wyllard

Physics Faculty Publications

We study the pp-wave limits of various elliptic models with orientifold planes and D7-branes, as well as the pp-wave limit of an orientifold of AdS5 × T11. Many of the limits contain both open and closed strings. We also present pp-wave limits of theories which give rise to a compact null direction and contain open strings. Maps between the string theory states and gauge theory operators are proposed. © 2002 Elsevier Science B.V. All rights reserved.

Bowdoin Orient V.132, No.1-24 (2002-2003), The Bowdoin Orient

The Bowdoin Orient 2000-2009

No abstract provided.

Resonance In The Menstrual Cycle: A New Model Of The Lh Surge, Mary Lou Zeeman, W. Weckesser, D. Gokhman

Mathematics Faculty Publications

In vertebrates, ovulation is triggered by a surge of LH from the pituitary. The precise mechanism by which rising oestradiol concentrations initiate the LH surge in the human menstrual cycle remains a fundamental open question of reproductive biology. It is well known that sampling of serum LH on a time scale of minutes reveals pulsatile release from the pituitary in response to pulses of gonadotrophin releasing hormone from the hypothalamus. The LH pulse frequency and amplitude vary considerably over the cycle, with the highest frequency and amplitude at the midcycle surge. Here a new mathematical model is presented of the …

Oakeshott, Berlin, And Liberalism, Paul Franco

Government Faculty Publications

This article compares the political philosophies of Michael Oakeshott and Isaiah Berlin, probably the two most important political philosophers in postwar Britain, who, strangely, had very little to do with one another during their illustrious careers. The article focuses on their respective critiques of rationalism and theories of liberal pluralism, arguing that Oakeshott provides the more consistent and philosophically satisfying account in both instances.

The Disembodied Spirit, Bowdoin College. Museum Of Art

Museum of Art Exhibition Catalogues

Exhibition catalog: Bowdoin College Museum of Art, Sept. 25-Dec. 7, 2003; Kemper Museum of Contemporary Art (Kansas City, Mo.), Mar. 5-May 23, 2004; Austin (Texas) Museum of Art, Sept. 11-Nov. 28, 2004

Includes essays by Tom Gunning and Pamela Thurschwell.

Beyond Thirst: The Dimensions Of Drink, Bowdoin College. Museum Of Art, Caitlin M. Nelson, Christine L. Paglia

Museum of Art Exhibition Catalogues

"This brochure accompanies an exhibition of the same name at the Bowdoin College Museum of Art from April 17 through June 15, 2003"--Page 2 of cover

Bowdoin College Catalogue (2002-2003), Bowdoin College

Bowdoin College Catalogues, Course Guides, and Academic Handbooks

No abstract provided.

General Relativistic Magnetohydrodynamics For The Numerical Construction Of Dynamical Spacetimes, T.W. Baumgarte, S.L. Shapiro

Physics Faculty Publications

No abstract provided.

Effects Of Differential Rotation On The Maximum Mass Of Neutron Stars, N.D. Lyford, T.W. Baumgarte, S.L. Shapiro

Physics Faculty Publications

No abstract provided.

Matrix Model Approach To The N = 2 U (N) Gauge Theory With Matter In The Fundamental Representation, Stephen G. Naculich, Howard J. Schnitzer, Niclas Wyllard

Physics Faculty Publications

We use matrix model technology to study the N = 2 U (N) gauge theory with Nf massive hypennultiplets in the fundamental representation. We perform a completely perturbative calculation of the periods ai and the prepotential F(a) up to the first instanton level, finding agreement with previous results in the literature. We also derive the Seiberg-Witten curve and differential from the large-M solution of the matrix model. We show that the two cases Nf < N and N ≤ Nf < 2N can be treated simultaneously. © SISSA/ISAS 2003.

The Large-Scale Geometry Of Some Metabelian Groups, Jennifer Taback, Kevin Whyte

Mathematics Faculty Publications

No abstract provided.

From Local To Global Behavior In Competitive Lotka-Volterra Systems, E. C. Zeeman, M. L. Zeeman

Mathematics Faculty Publications

In this paper we exploit the linear, quadratic, monotone and geometric structures of competitive Lotka-Volterra systems of arbitrary dimension to give geometric, algebraic and computational hypotheses for ruling out nontrivial recurrence. We thus deduce the global dynamics of a system from its local dynamics. The geometric hypotheses rely on the introduction of a split Liapunov function. We show that if a system has a fixed point p ∈ int R+n and the carrying simplex of the system lies to one side of its tangent hyperplane at p, then there is no nontrivial recurrence, and the global dynamics are known. We …

Collapse Of A Magnetized Star To A Black Hole, T.W. Baumgarte, S.L. Shapiro

Physics Faculty Publications

No abstract provided.

One-Armed Spiral Instability In Differentially Rotating Stars, M. Saijo, T.W. Baumgarte, S.L. Shapiro

Physics Faculty Publications

No abstract provided.