Zero-Temperature Dynamics of Ising Spin Systems Following a Deep Quench: Results and Open Problems

We consider zero-temperature, stochastic Ising models with nearest-neighbor interactions and an initial spin configuration chosen from a symmetric Bernoulli distribution (corresponding physically to a deep quench). Whether a final state exists, i.e., whether each spin flips only finitely many times as time goes to infinity (for almost every initial spin configuration and realization of the dynamics), or if not, whether every spin - or only a fraction strictly less than one - flips infinitely often, depends on the nature of the couplings, the dimension, and the lattice type. We review results, examine open questions, and discuss related topics.Comment: 10 pages (LaTeX); to appear in Physica

Developing collaborative partnerships with culturally and linguistically diverse families during the IEP process

Family participation in the special education process has been federally mandated for 40 years, and educators recognize that effective collaboration with their students’ families leads to improved academic and social outcomes for students. However, while some family-school relationships are positive and collaborative, many are not, particularly for culturally and linguistically diverse (CLD) families. This article provides practice guidelines based in research for teachers who seek to improve their practices when working with CLD families who have children served by special education

Simulation of airborne electromagnetic measurements in three dimensional environments

A 3-D frequency domain EM modeling code has been implemented for helicopter electromagnetic (HEM) simulations. A vector Helmholtz formulation for the electric fields is employed to avoid problems associated with the first order Maxwell`s equations numerically decoupling in the air. Additional stability is introduced by formulating the problem in terms of the scattered electric fields which replaces an impressed dipole source with an equivalent source that possesses a much smoother spatial dependence and is easier to model. In older to compute this equivalent source, a primary field arising from dipole sources in a whole space must be calculated where ever the conductivity is different than that of the background. The Helmholtz equation is approximated using finite differences on a staggered grid. After finite differencing, a complex-symmetric matrix system of equations is assembled and preconditioned using Jacobi scaling before it is solved using the quasi-minimum residual (QMR) method. In order to both speed up the solution and allow for larger, more realistic models to be simulated, the scheme has been modified to run on massively parallel architectures. The solution has been compared against other I-D and 3-D numerical models and is found to produce results in good agreement. The versatility of the scheme is demonstrated by simulating a survey over a salt water intrusion zone in the Florida Everglades

3D electromagnetic inversion for environmental site characterization

A 3-D non-linear electromagnetic inversion scheme has been developed to produce images of subsurface conductivity structure from electromagnetic geophysical data. The solution is obtained by successive linearized model updates where full forward modeling is employed at each iteration to compute model sensitivities and predicted data. Regularization is applied to the problem to provide stability. Because the inverse part of the problem requires the solution of 10`s to 100`s of thousands of unknowns, and because each inverse iteration requires many forward models to be computed, the code has been implemented on massively parallel computer platforms. The use of the inversion code to image environmental sites is demonstrated on a data set collected with the Apex Parametrics {open_quote}MaxMin I-8S{close_quote} over a section of stacked barrels and metal filled boxes at the Idaho National Laboratory`s {open_quote}Cold Test Pit{close_quote}. The MaxMin is a loop-loop frequency domain system which operates from 440 Hz up to 56 kHz using various coil separations; for this survey coil separations of 15, 30 and 60 feet were employed. The out-of phase data are shown to be of very good quality while the in-phase are rather noisy due to slight mispositioning errors, which cause improper cancellation of the primary free space field in the receiver. Weighting the data appropriately by the estimated noise and applying the inversion scheme is demonstrated to better define the structure of the pit. In addition, comparisons are given for single coil separations and multiple separations to show the benefits of using multiple offset data

Image Appraisal for 2D and 3D Electromagnetic Inversion

Linearized methods are presented for appraising image resolution and parameter accuracy in images generated with two and three dimensional non-linear electromagnetic inversion schemes. When direct matrix inversion is employed, the model resolution and posterior model covariance matrices can be directly calculated. A method to examine how the horizontal and vertical resolution varies spatially within the electromagnetic property image is developed by examining the columns of the model resolution matrix. Plotting the square root of the diagonal of the model covariance matrix yields an estimate of how errors in the inversion process such as data noise and incorrect a priori assumptions about the imaged model map into parameter error. This type of image is shown to be useful in analyzing spatial variations in the image sensitivity to the data. A method is analyzed for statistically estimating the model covariance matrix when the conjugate gradient method is employed rather than a direct inversion technique (for example in 3D inversion). A method for calculating individual columns of the model resolution matrix using the conjugate gradient method is also developed. Examples of the image analysis techniques are provided on 2D and 3D synthetic cross well EM data sets, as well as a field data set collected at the Lost Hills Oil Field in Central California

Time efficient 3-D electromagnetic modeling on massively parallel computers

A numerical modeling algorithm has been developed to simulate the electromagnetic response of a three dimensional earth to a dipole source for frequencies ranging from 100 to 100MHz. The numerical problem is formulated in terms of a frequency domain--modified vector Helmholtz equation for the scattered electric fields. The resulting differential equation is approximated using a staggered finite difference grid which results in a linear system of equations for which the matrix is sparse and complex symmetric. The system of equations is solved using a preconditioned quasi-minimum-residual method. Dirichlet boundary conditions are employed at the edges of the mesh by setting the tangential electric fields equal to zero. At frequencies less than 1MHz, normal grid stretching is employed to mitigate unwanted reflections off the grid boundaries. For frequencies greater than this, absorbing boundary conditions must be employed by making the stretching parameters of the modified vector Helmholtz equation complex which introduces loss at the boundaries. To allow for faster calculation of realistic models, the original serial version of the code has been modified to run on a massively parallel architecture. This modification involves three distinct tasks; (1) mapping the finite difference stencil to a processor stencil which allows for the necessary information to be exchanged between processors that contain adjacent nodes in the model, (2) determining the most efficient method to input the model which is accomplished by dividing the input into ``global`` and ``local`` data and then reading the two sets in differently, and (3) deciding how to output the data which is an inherently nonparallel process

Why social networks are different from other types of networks

We argue that social networks differ from most other types of networks, including technological and biological networks, in two important ways. First, they have non-trivial clustering or network transitivity, and second, they show positive correlations, also called assortative mixing, between the degrees of adjacent vertices. Social networks are often divided into groups or communities, and it has recently been suggested that this division could account for the observed clustering. We demonstrate that group structure in networks can also account for degree correlations. We show using a simple model that we should expect assortative mixing in such networks whenever there is variation in the sizes of the groups and that the predicted level of assortative mixing compares well with that observed in real-world networks.Comment: 9 pages, 2 figure

Thermodynamics and Universality for Mean Field Quantum Spin Glasses

We study aspects of the thermodynamics of quantum versions of spin glasses. By means of the Lie-Trotter formula for exponential sums of operators, we adapt methods used to analyze classical spin glass models to answer analogous questions about quantum models.Comment: 17 page

Can we avoid high coupling?

It is considered good software design practice to organize source code into modules and to favour within-module connections (cohesion) over between-module connections (coupling), leading to the oft-repeated maxim "low coupling/high cohesion". Prior research into network theory and its application to software systems has found evidence that many important properties in real software systems exhibit approximately scale-free structure, including coupling; researchers have claimed that such scale-free structures are ubiquitous. This implies that high coupling must be unavoidable, statistically speaking, apparently contradicting standard ideas about software structure. We present a model that leads to the simple predictions that approximately scale-free structures ought to arise both for between-module connectivity and overall connectivity, and not as the result of poor design or optimization shortcuts. These predictions are borne out by our large-scale empirical study. Hence we conclude that high coupling is not avoidable--and that this is in fact quite reasonable