A Poset Connected to Artin Monoids of Simply Laced Type

Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W-orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representatons of the corresponding Artin group A. The poset generalizes many properties of the usual order on positive roots of W given by height. In this paper, a linear representation of the positive monoid of A is defined by use of the poset

Research program of the Geodynamics Branch

This report is the Fourth Annual Summary of the Research Program of the Geodynamics Branch. The branch is located within the Laboratory for Terrestrial Physics of the Space and Earth Sciences Directorate of the Goddard Space Flight Center. The research activities of the branch staff cover a broad spectrum of geoscience disciplines including: tectonophysics, space geodesy, geopotential field modeling, and dynamic oceanography. The NASA programs which are supported by the work described in this document include the Geodynamics and Ocean Programs, the Crustal Dynamics Project and the proposed Ocean Topography Experiment (TOPEX). The reports highlight the investigations conducted by the Geodynamics Branch staff during calendar year 1985. The individual papers are grouped into chapters on Crustal Movements and Solid Earth Dynamics, Gravity Field Modeling and Sensing Techniques, and Sea Surface Topography. Further information on the activities of the branch or the particular research efforts described herein can be obtained through the branch office or from individual staff members

Elevated fetal steroidogenic activity in autism

Autism affects males more than females, giving rise to the idea that the influence of steroid hormones on early fetal brain development may be one important early biological risk factor. Utilizing the Danish Historic Birth Cohort and Danish Psychiatric Central Register, we identified all amniotic fluid samples of males born between 1993 and 1999 who later received ICD-10 (International Classification of Diseases, 10th Revision) diagnoses of autism, Asperger syndrome or PDD-NOS (pervasive developmental disorder not otherwise specified) (n=128) compared with matched typically developing controls. Concentration levels of Δ4 sex steroids (progesterone, 17α-hydroxy-progesterone, androstenedione and testosterone) and cortisol were measured with liquid chromatography tandem mass spectrometry. All hormones were positively associated with each other and principal component analysis confirmed that one generalized latent steroidogenic factor was driving much of the variation in the data. The autism group showed elevations across all hormones on this latent generalized steroidogenic factor (Cohen's d=0.37, P=0.0009) and this elevation was uniform across ICD-10 diagnostic label. These results provide the first direct evidence of elevated fetal steroidogenic activity in autism. Such elevations may be important as epigenetic fetal programming mechanisms and may interact with other important pathophysiological factors in autism

BMW algebras of simply laced type

It is known that the recently discovered representations of the Artin groups of type A_n, the braid groups, can be constructed via BMW algebras. We introduce similar algebras of type D_n and E_n which also lead to the newly found faithful representations of the Artin groups of the corresponding types. We establish finite dimensionality of these algebras. Moreover, they have ideals I_1 and I_2 with I_2 contained in I_1 such that the quotient with respect to I_1 is the Hecke algebra and I_1/I_2 is a module for the corresponding Artin group generalizing the Lawrence-Krammer representation. Finally we give conjectures on the structure, the dimension and parabolic subalgebras of the BMW algebra, as well as on a generalization of deformations to Brauer algebras for simply laced spherical type other than A_n.Comment: 39 page

Amplitudes Fitted to Experimental Data and to Roy's Equations

The scalar-isoscalar, scalar-isotensor and vector-isovector pi-pi amplitudes are fitted simultaneously to experimental data and to Roy's equations. The resulting amplitudes are compared with those fitted only to experimental data. No additional constraints for the pi-pi threshold behaviour of the amplitudes are imposed. Threshold parameters are calculated for the amplitudes in the three waves. Spectrum of scalar mesons below 1.8 GeV is found from the analysis of the analytical structure of the fitted amplitudes.Comment: 3 pages, 1 figure. Talk given at MESON 2004: 8th International Workshop on Meson Production, Properties and Interactions, Cracow, Poland, 4-8 Jun 2004. Submitted to Int.J.Mod.Phys.

On Markovian solutions to Markov Chain BSDEs

We study (backward) stochastic differential equations with noise coming from a finite state Markov chain. We show that, for the solutions of these equations to be `Markovian', in the sense that they are deterministic functions of the state of the underlying chain, the integrand must be of a specific form. This allows us to connect these equations to coupled systems of ODEs, and hence to give fast numerical methods for the evaluation of Markov-Chain BSDEs

Improving the Functional Control of Aged Ferroelectrics using Insights from Atomistic Modelling

We provide a fundamental insight into the microscopic mechanisms of the ageing processes. Using large scale molecular dynamics simulations of the prototypical ferroelectric material PbTiO3, we demonstrate that the experimentally observed ageing phenomena can be reproduced from intrinsic interactions of defect-dipoles related to dopant-vacancy associates, even in the absence of extrinsic effects. We show that variation of the dopant concentration modifies the material's hysteretic response. We identify a universal method to reduce loss and tune the electromechanical properties of inexpensive ceramics for efficient technologies.Comment: 6 pages, 3 figure

Chiral Corrections to Lattice Calculations of Charge Radii

Logarithmic divergences in pion and proton charge radii associated with chiral loops are investigated to assess systematic uncertainties in current lattice determinations of charge radii. The chiral corrections offer a possible solution to the long standing problem of why present lattice calculations yield proton and pion radii which are similar in size.Comment: PostScript file only. Ten pages. Figures included. U. of MD Preprint #92-19

Low Energy Theorems For Nucleon-Nucleon Scattering

Low energy theorems are derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading order in an expansion in which both $m_\pi$ and $1/a$ (where $a$ is the scattering length) are treated as small mass scales. Comparisons with phase shift data, however, reveal a pattern of gross violations of the theorems for all coefficients in both the $^1S_0$ and $^3S_1$ channels. Analogous theorems are developed for the energy dependence $\epsilon$ parameter which describes $^3S_1 - ^3D_1$ mixing. These theorems are also violated. These failures strongly suggest that the physical value of $m_\pi$ is too large for the chiral expansion to be valid in this context. Comparisons of $m_\pi$ with phenomenological scales known to arise in the two-nucleon problem support this conjecture.Comment: 12 pages, 1 figure, 1 table; appendix added to discuss behavior in chiral limit; minor revisions including revised figure reference to recent work adde