In theory, it should be possible to infer realistic genetic networks from time series microarray data. In practice, however, network discovery has proved problematic. The three major challenges are: (1) inferring the network; (2) estimating the stability of the inferred network; and (3) making the network visually accessible to the user. Here we describe a method, tested on publicly available time series microarray data, which addresses these concerns. The inference of genetic networks from genome-wide experimental data is an important biological problem which has received much attention. Approaches to this problem have typically included application of clustering algorithms [6]; the use of Boolean networks [12, 1, 10]; the use of Bayesian networks [8, 11]; and the use of continuous models [21, 14, 19]. Overviews of the problem and general approaches to network inference can be found in [4, 3]. Our approach to network inference is similar to earlier methods in that we use both clustering and Boolean network inference. However, we have attempted to extend the process to better serve the end-user, the biologist. In particular, we have incorporated a system to assess the reliability of our network, and we have developed tools which allow interactive visualization of the proposed network.
This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been designed as a SPICE-compatible, high-performance analog circuit simulator capable of simulating electrical circuits at a variety of abstraction levels. Primarily, Xyce has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability the current state-of-the-art in the following areas: {sm_bullet} Capability to solve extremely large circuit problems by supporting large-scale parallel computing platforms (up to thousands of processors). Note that this includes support for most popular parallel and serial computers. {sm_bullet} Improved performance for all numerical kernels (e.g., time integrator, nonlinear and linear solvers) through state-of-the-art algorithms and novel techniques. {sm_bullet} Device models which are specifically tailored to meet Sandia's needs, including many radiation-aware devices. {sm_bullet} A client-server or multi-tiered operating model wherein the numerical kernel can operate independently of the graphical user interface (GUI). {sm_bullet} Object-oriented code design and implementation using modern coding practices that ensure that the Xyce Parallel Electronic Simulator will be maintainable and extensible far into the future. Xyce is a parallel code in the most general sense of the phrase - a message passing of computing platforms. These include serial, shared-memory and distributed-memory parallel implementation - which allows it to run efficiently on the widest possible number parallel as well as heterogeneous platforms. Careful attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows. One feature required by designers is the ability to add device models, many specific to the needs of Sandia, to the code. To this end, the device package in the Xyce These input formats include standard analytical models, behavioral models look-up Parallel Electronic Simulator is designed to support a variety of device model inputs. tables, and mesh-level PDE device models. Combined with this flexible interface is an architectural design that greatly simplifies the addition of circuit models. One of the most important feature of Xyce is in providing a platform for computational research and development aimed specifically at the needs of the Laboratory. With Xyce, Sandia now has an 'in-house' capability with which both new electrical (e.g., device model development) and algorithmic (e.g., faster time-integration methods) research and development can be performed. Ultimately, these capabilities are migrated to end users.
This document is a reference guide to the Xyce Parallel Electronic Simulator, and is a companion document to the Xyce Users' Guide. The focus of this document is (to the extent possible) exhaustively list device parameters, solver options, parser options, and other usage details of Xyce. This document is not intended to be a tutorial. Users who are new to circuit simulation are better served by the Xyce Users' Guide.
The surface micromachining processes used to manufacture MEMS devices and integrated circuits transpire at such small length scales and are sufficiently complex that a theoretical analysis of them is particularly inviting. Under development at Sandia National Laboratories (SNL) is Chemically Induced Surface Evolution with Level Sets (ChISELS), a level-set based feature-scale modeler of such processes. The theoretical models used, a description of the software and some example results are presented here. The focus to date has been of low-pressure and plasma enhanced chemical vapor deposition (low-pressure chemical vapor deposition, LPCVD and PECVD) processes. Both are employed in SNLs SUMMiT V technology. Examples of step coverage of SiO{sub 2} into a trench by each of the LPCVD and PECVD process are presented.
The diagonal-mass-matrix spectral element method has proven very successful in geophysical applications dominated by wave propagation. For these problems, the ability to run fully explicit time stepping schemes at relatively high order makes the method more competitive then finite element methods which require the inversion of a mass matrix. The method relies on Gauss-Lobatto points to be successful, since the grid points used are required to produce well conditioned polynomial interpolants, and be high quality 'Gauss-like' quadrature points that exactly integrate a space of polynomials of higher dimension than the number of quadrature points. These two requirements have traditionally limited the diagonal-mass-matrix spectral element method to use square or quadrilateral elements, where tensor products of Gauss-Lobatto points can be used. In non-tensor product domains such as the triangle, both optimal interpolation points and Gauss-like quadrature points are difficult to construct and there are few analytic results. To extend the diagonal-mass-matrix spectral element method to (for example) triangular elements, one must find appropriate points numerically. One successful approach has been to perform numerical searches for high quality interpolation points, as measured by the Lebesgue constant (Such as minimum energy electrostatic points and Fekete points). However, these points typically do not have any Gauss-like quadrature properties. In this work, we describe a new numerical method to look for Gauss-like quadrature points in the triangle, based on a previous algorithm for computing Fekete points. Performing a brute force search for such points is extremely difficult. A common strategy to increase the numerical efficiency of these searches is to reduce the number of unknowns by imposing symmetry conditions on the quadrature points. Motivated by spectral element methods, we propose a different way to reduce the number of unknowns: We look for quadrature formula that have the same number of points as the number of basis functions used in the spectral element method's transform algorithm. This is an important requirement if they are to be used in a diagonal-mass-matrix spectral element method. This restriction allows for the construction of cardinal functions (Lagrange interpolating polynomials). The ability to construct cardinal functions leads to a remarkable expression relating the variation in the quadrature weights to the variation in the quadrature points. This relation in turn leads to an analytical expression for the gradient of the quadrature error with respect to the quadrature points. Thus the quadrature weights have been completely removed from the optimization problem, and we can implement an exact steepest descent algorithm for driving the quadrature error to zero. Results from the algorithm will be presented for the triangle and the sphere.
Coupling between transient simulation codes of different fidelity can often be performed at the nonlinear solver level, if the time scales of the two codes are similar. A good example is electrical mixed-mode simulation, in which an analog circuit simulator is coupled to a PDE-based semiconductor device simulator. Semiconductor simulation problems, such as single-event upset (SEU), often require the fidelity of a mesh-based device simulator but are only meaningful when dynamically coupled with an external circuit. For such problems a mixed-level simulator is desirable, but the two types of simulation generally have different (somewhat conflicting) numerical requirements. To address these considerations, we have investigated variations of the two-level Newton algorithm, which preserves tight coupling between the circuit and the PDE device, while optimizing the numerics for both. The research was done within Xyce, a massively parallel electronic simulator under development at Sandia National Laboratories.
Dynamic memory management in C++ is one of the most common areas of difficulty and errors for amateur and expert C++ developers alike. The improper use of operator new and operator delete is arguably the most common cause of incorrect program behavior and segmentation faults in C++ programs. Here we introduce a templated concrete C++ class Teuchos::RefCountPtr<>, which is part of the Trilinos tools package Teuchos, that combines the concepts of smart pointers and reference counting to build a low-overhead but effective tool for simplifying dynamic memory management in C++. We discuss why the use of raw pointers for memory management, managed through explicit calls to operator new and operator delete, is so difficult to accomplish without making mistakes and how programs that use raw pointers for memory management can easily be modified to use RefCountPtr<>. In addition, explicit calls to operator delete is fragile and results in memory leaks in the presents of C++ exceptions. In its most basic usage, RefCountPtr<> automatically determines when operator delete should be called to free an object allocated with operator new and is not fragile in the presents of exceptions. The class also supports more sophisticated use cases as well. This document describes just the most basic usage of RefCountPtr<> to allow developers to get started using it right away. However, more detailed information on the design and advanced features of RefCountPtr<> is provided by the companion document 'Teuchos::RefCountPtr : The Trilinos Smart Reference-Counted Pointer Class for (Almost) Automatic Dynamic Memory Management in C++'.
The threat from biological weapons is assessed through both a comparative historical analysis of the patterns of biological weapons use and an assessment of the technological hurdles to proliferation and use that must be overcome. The history of biological weapons is studied to learn how agents have been acquired and what types of states and substate actors have used agents. Substate actors have generally been more willing than states to use pathogens and toxins and they have focused on those agents that are more readily available. There has been an increasing trend of bioterrorism incidents over the past century, but states and substate actors have struggled with one or more of the necessary technological steps. These steps include acquisition of a suitable agent, production of an appropriate quantity and form, and effective deployment. The technological hurdles associated with the steps present a real barrier to producing a high consequence event. However, the ever increasing technological sophistication of society continually lowers the barriers, resulting in a low but increasing probability of a high consequence bioterrorism event.
This document describes the main functionalities of the Amesos package, version 1.0. Amesos, available as part of Trilinos 4.0, provides an object-oriented interface to several serial and parallel sparse direct solvers libraries, for the solution of the linear systems of equations A X = B where A is a real sparse, distributed matrix, defined as an EpetraRowMatrix object, and X and B are defined as EpetraMultiVector objects. Amesos provides a common look-and-feel to several direct solvers, insulating the user from each package's details, such as matrix and vector formats, and data distribution.
The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries. The goal of the Trilinos Project is to develop parallel solver algorithms and libraries within an object-oriented software framework for the solution of large-scale, complex multiphysics engineering and scientific applications. The emphasis is on developing robust, scalable algorithms in a software framework, using abstract interfaces for flexible interoperability of components while providing a full-featured set of concrete classes that implement all the abstract interfaces. This document introduces the use of Trilinos, version 4.0. The presented material includes, among others, the definition of distributed matrices and vectors with Epetra, the iterative solution of linear systems with AztecOO, incomplete factorizations with IF-PACK, multilevel and domain decomposition preconditioners with ML, direct solution of linear system with Amesos, and iterative solution of nonlinear systems with NOX. The tutorial is a self-contained introduction, intended to help computational scientists effectively apply the appropriate Trilinos package to their applications. Basic examples are presented that are fit to be imitated. This document is a companion to the Trilinos User's Guide [20] and Trilinos Development Guides [21,22]. Please note that the documentation included in each of the Trilinos' packages is of fundamental importance.
ML is a multigrid preconditioning package intended to solve linear systems of equations Az = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package or to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the AZTEC 2.1 and AZTECOO iterative package [15]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and non-symmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.