Understanding diffusion in alumina is along-standing challenge in ceramic science. The present article applies a novel combination of metadynamics and kinetic Monte Carlo simulation approaches to the investigation of oxygen vacancy diffusion in alumina. Three classes of diffusive jumps with different activation energies were identified, the resulting diffusion coefficient being best fitted by an Arrhenius equation having apre-exponential factor of 7.88 x 10*-2 m*2s*-1 and anactivation energy of 510.83 kJ mol*1. This activation energy is very close to values for the most pure aluminas studied experimentally (activation energy 531 kJ mol*-1). The good agreement indicates that the dominating atomic-scale diffusion mechanism in alumina is vacancy diffusion.
lunes, 28 de septiembre de 2009
Oxygen vacancy diffusion in alumina: Newatomistic simulation methods applied to an old problem
Understanding diffusion in alumina is along-standing challenge in ceramic science. The present article applies a novel combination of metadynamics and kinetic Monte Carlo simulation approaches to the investigation of oxygen vacancy diffusion in alumina. Three classes of diffusive jumps with different activation energies were identified, the resulting diffusion coefficient being best fitted by an Arrhenius equation having apre-exponential factor of 7.88 x 10*-2 m*2s*-1 and anactivation energy of 510.83 kJ mol*1. This activation energy is very close to values for the most pure aluminas studied experimentally (activation energy 531 kJ mol*-1). The good agreement indicates that the dominating atomic-scale diffusion mechanism in alumina is vacancy diffusion.
Quantum Adiabatic Algorithms, Small Gaps, and Different Paths. (arXiv:0909.4766v1 [quant-ph])
We construct a set of instances of 3SAT which are not solved efficiently
using the simplest quantum adiabatic algorithm. These instances are obtained by
picking random clauses all consistent with two disparate planted solutions and
then penalizing one of them with a single additional clause. We argue that by
randomly modifying the beginning Hamiltonian, one obtains (with substantial
probability) an adiabatic path that removes this difficulty. This suggests that
the quantum adiabatic algorithm should in general be run on each instance with
many different random paths leading to the problem Hamiltonian. We do not know
whether this trick will help for a random instance of 3SAT (as opposed to an
instance from the particular set we consider), especially if the instance has
an exponential number of disparate assignments that violate few clauses. We use
a continuous imaginary time Quantum Monte Carlo algorithm in a novel way to
numerically investigate the ground state as well as the first excited state of
our system. Our arguments are supplemented by Quantum Monte Carlo data from
simulations with up to 150 spins.
viernes, 25 de septiembre de 2009
Fixed point and Bregman iterative methods for matrix rank minimization
Abstract The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing
and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear norm minimization.
Although the latter can be cast as a semidefinite programming problem, such an approach is computationally expensive to solve
when the matrices are large. In this paper, we propose fixed point and Bregman iterative algorithms for solving the nuclear
norm minimization problem and prove convergence of the first of these algorithms. By using a homotopy approach together with
an approximate singular value decomposition procedure, we get a very fast, robust and powerful algorithm, which we call FPCA
(Fixed Point Continuation with Approximate SVD), that can solve very large matrix rank minimization problems (the code can
be downloaded from http://www.columbia.edu/~sm2756/FPCA.htm for non-commercial use). Our numerical results on randomly generated and real matrix completion problems demonstrate that
this algorithm is much faster and provides much better recoverability than semidefinite programming solvers such as SDPT3.
For example, our algorithm can recover 1000 × 1000 matrices of rank 50 with a relative error of 10−5 in about 3 min by sampling only 20% of the elements. We know of no other method that achieves as good recoverability. Numerical
experiments on online recommendation, DNA microarray data set and image inpainting problems demonstrate the effectiveness
of our algorithms.
and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear norm minimization.
Although the latter can be cast as a semidefinite programming problem, such an approach is computationally expensive to solve
when the matrices are large. In this paper, we propose fixed point and Bregman iterative algorithms for solving the nuclear
norm minimization problem and prove convergence of the first of these algorithms. By using a homotopy approach together with
an approximate singular value decomposition procedure, we get a very fast, robust and powerful algorithm, which we call FPCA
(Fixed Point Continuation with Approximate SVD), that can solve very large matrix rank minimization problems (the code can
be downloaded from http://www.columbia.edu/~sm2756/FPCA.htm for non-commercial use). Our numerical results on randomly generated and real matrix completion problems demonstrate that
this algorithm is much faster and provides much better recoverability than semidefinite programming solvers such as SDPT3.
For example, our algorithm can recover 1000 × 1000 matrices of rank 50 with a relative error of 10−5 in about 3 min by sampling only 20% of the elements. We know of no other method that achieves as good recoverability. Numerical
experiments on online recommendation, DNA microarray data set and image inpainting problems demonstrate the effectiveness
of our algorithms.
- Content Type Journal Article
- Category Full Length Paper
- DOI 10.1007/s10107-009-0306-5
- Authors
- Shiqian Ma, Columbia University Department of Industrial Engineering and Operations Research New York NY 10027 USA
- Donald Goldfarb, Columbia University Department of Industrial Engineering and Operations Research New York NY 10027 USA
- Lifeng Chen, Columbia University Department of Industrial Engineering and Operations Research New York NY 10027 USA
- Journal Mathematical Programming
- Online ISSN 1436-4646
- Print ISSN 0025-5610
jueves, 24 de septiembre de 2009
Hilbert scales and Sobolev spaces defined by associated Legendre functions. (arXiv:0909.4266v1 [math.CA])
In this paper we study the Hilbert scales defined by the associated Legendre
functions for arbitrary integer values of the parameter. This problem is
equivalent to study the left-definite spectral theory associated to the
modified Legendre equation. We give several characterizations of the spaces as
weighted Sobolev spaces and prove identities among the spaces corresponding to
lower regularity index.
A Numerical Algorithm for Zero Counting. II: Distance to Ill-posedness and Smoothed Analysis. (arXiv:0909.4101v1 [cs.NA])
We show a Condition Number Theorem for the condition number of zero counting
for real polynomial systems. That is, we show that this condition number equals
the inverse of the normalized distance to the set of ill-posed systems (i.e.,
those having multiple real zeros). As a consequence, a smoothed analysis of
this condition number follows.
Numerical simulations of interfaces in relativistic hydrodynamics. (arXiv:0909.4217v1 [gr-qc])
We consider models of relativistic matter containing sharp interfaces across
which the matter model changes. These models will be relevant for neutron stars
with crusts, phase transitions, or for viscous boundaries where the length
scale is too short to be modelled smoothly. In particular we look at numerical
techniques that allow us to evolve stable interfaces, for the interfaces to
merge, and for strong waves and shocks to interact with the interfaces. We test
these techniques for ideal hydrodynamics in special and general relativity for
simple equations of state, finding that simple level set-based methods extend
well to relativistic hydrodynamics.
miércoles, 23 de septiembre de 2009
Euler integration over definable functions. (arXiv:0909.4054v1 [math.GN])
We extend the theory of Euler integration from the class of constructible
functions to that of "tame" real-valued functions (definable with respect to an
o-minimal structure). The corresponding integral operator has some unusual
defects (it is not a linear operator); however, it has a compelling
Morse-theoretic interpretation. In addition, we show that it is an appropriate
setting in which to do numerical analysis of Euler integrals, with applications
to incomplete and uncertain data in sensor networks.
martes, 22 de septiembre de 2009
A trillion triangles: New computer methods reveal secrets of ancient math problem
Mathematicians from North America, Europe, Australia, and South America have resolved the first one trillion cases of an ancient mathematics problem. The advance was made possible by a clever technique for multiplying large numbers. The numbers involved are so enormous that if their digits were written out by hand they would stretch to the moon and back. The biggest challenge was that these numbers could not even fit into the main memory of the available computers, so the researchers had to make extensive use of the computers' hard drives.
Finite Section Method for a Banach Algebra of Convolution Type Operators on $L^p(mathbb{R})$ with Symbols Generated by $PC$ and $SO$. (arXiv:0909.3821v1 [math.FA])
We prove the applicability of the finite section method to an arbitrary
operator in the Banach algebra generated by the operators of multiplication by
piecewise continuous functions and the convolution operators with symbols in
the algebra generated by piecewise continuous and slowly oscillating Fourier
multipliers on $L^p(mathbb{R})$, $1<p<infty$.
A Spectral Method for the Eigenvalue Problem for Elliptic Equations. (arXiv:0909.3607v1 [math.NA])
Let $Omega$ be an open, simply connected, and bounded region in
$mathbb{R}^{d}$, $dgeq2$, and assume its boundary $partialOmega$ is smooth.
Consider solving the eigenvalue problem $Lu=lambda u$ for an elliptic partial
differential operator $L$ over $Omega$ with zero values for either Dirichlet
or Neumann boundary conditions. We propose, analyze, and illustrate a 'spectral
method' for solving numerically such an eigenvalue problem. This is an
extension of the methods presented earlier in [5],[6].
lunes, 21 de septiembre de 2009
Mathematics, Recursion, and Universals in Human Languages. (arXiv:0909.3591v1 [cs.CL])
There are many scientific problems generated by the multiple and conflicting
alternative definitions of linguistic recursion and human recursive processing
that exist in the literature. The purpose of this article is to make available
to the linguistic community the standard mathematical definition of recursion
and to apply it to discuss linguistic recursion. As a byproduct, we obtain an
insight into certain "soft universals" of human languages, which are related to
cognitive constructs necessary to implement mathematical reasoning, i.e.
mathematical model theory.
domingo, 20 de septiembre de 2009
Finite element error estimates for 3D exterior incompressible flow with nonzero velocity at infinity
Abstract We consider a stationary incompressible Navier–Stokes flow in a 3D exterior domain, with nonzero velocity at infinity. In
order to approximate this flow, we use the stabilized P1–P1 finite element method proposed by Rebollo (Numer Math 79:283–319,
1998). Following an approach by Guirguis and Gunzburger (Model Math Anal Numer 21:445–464, 1987), we apply this method to
the Navier–Stokes system with Oseen term in a truncated exterior domain, under a pointwise boundary condition on the artificial
boundary. This leads to a discrete problem whose solution approximates the exterior flow, as is shown by error estimates.
order to approximate this flow, we use the stabilized P1–P1 finite element method proposed by Rebollo (Numer Math 79:283–319,
1998). Following an approach by Guirguis and Gunzburger (Model Math Anal Numer 21:445–464, 1987), we apply this method to
the Navier–Stokes system with Oseen term in a truncated exterior domain, under a pointwise boundary condition on the artificial
boundary. This leads to a discrete problem whose solution approximates the exterior flow, as is shown by error estimates.
- Content Type Journal Article
- DOI 10.1007/s00211-009-0253-3
- Authors
- Paul Deuring, Univ Lille Nord de France 59000 Lille France
- Journal Numerische Mathematik
- Online ISSN 0945-3245
- Print ISSN 0029-599X
Birkhoff normal form for splitting methods applied to semilinear Hamiltonian PDEs. Part I. Finite-dimensional discretization
Abstract We consider discretized Hamiltonian PDEs associated with a Hamiltonian function that can be split into a linear unbounded operator and a regular
nonlinear part. We consider splitting methods associated with this decomposition. Using a finite-dimensional Birkhoff normal
form result, we show the almost preservation of the actions of the numerical solution associated with the splitting method over arbitrary long time and for asymptotically large level
of space approximation, provided the Sobolev norm of the initial data is small enough. This result holds under generic non-resonance conditions on the frequencies of the linear operator and on the step size. We apply these results to nonlinear
Schrödinger equations as well as the nonlinear wave equation.
nonlinear part. We consider splitting methods associated with this decomposition. Using a finite-dimensional Birkhoff normal
form result, we show the almost preservation of the actions of the numerical solution associated with the splitting method over arbitrary long time and for asymptotically large level
of space approximation, provided the Sobolev norm of the initial data is small enough. This result holds under generic non-resonance conditions on the frequencies of the linear operator and on the step size. We apply these results to nonlinear
Schrödinger equations as well as the nonlinear wave equation.
- Content Type Journal Article
- DOI 10.1007/s00211-009-0258-y
- Authors
- Erwan Faou, INRIA and Ecole Normale Supérieure de Cachan, Bretagne Avenue Robert Schumann 35170 Bruz France
- Benoît Grébert, Université de Nantes Laboratoire de Mathématiques Jean Leray 2 rue de la Houssinière 44322 Nantes France
- Eric Paturel, Université de Nantes Laboratoire de Mathématiques Jean Leray 2 rue de la Houssinière 44322 Nantes France
- Journal Numerische Mathematik
- Online ISSN 0945-3245
- Print ISSN 0029-599X
A finite element method for surface PDEs: matrix properties
Abstract We consider a recently introduced new finite element approach for the discretization of elliptic partial differential equations
on surfaces. The main idea of this method is to use finite element spaces that are induced by triangulations of an “outer”
domain to discretize the partial differential equation on the surface. The method is particularly suitable for problems in
which there is a coupling with a problem in an outer domain that contains the surface, for example, two-phase flow problems.
It has been proved that the method has optimal order of convergence both in the H
1 and in the L
2-norm. In this paper, we address linear algebra aspects of this new finite element method. In particular the conditioning
of the mass and stiffness matrix is investigated. For the two-dimensional case we present an analysis which proves that the
(effective) spectral condition number of the diagonally scaled mass matrix and the diagonally scaled stiffness matrix behaves
like h
−3| ln h| and h
−2| ln h|, respectively, where h is the mesh size of the outer triangulation.
on surfaces. The main idea of this method is to use finite element spaces that are induced by triangulations of an “outer”
domain to discretize the partial differential equation on the surface. The method is particularly suitable for problems in
which there is a coupling with a problem in an outer domain that contains the surface, for example, two-phase flow problems.
It has been proved that the method has optimal order of convergence both in the H
1 and in the L
2-norm. In this paper, we address linear algebra aspects of this new finite element method. In particular the conditioning
of the mass and stiffness matrix is investigated. For the two-dimensional case we present an analysis which proves that the
(effective) spectral condition number of the diagonally scaled mass matrix and the diagonally scaled stiffness matrix behaves
like h
−3| ln h| and h
−2| ln h|, respectively, where h is the mesh size of the outer triangulation.
- Content Type Journal Article
- DOI 10.1007/s00211-009-0260-4
- Authors
- Maxim A. Olshanskii, Moscow State M.V. Lomonosov University Department of Mechanics and Mathematics 119899 Moscow Russia
- Arnold Reusken, RWTH-Aachen University Institut für Geometrie und Praktische Mathematik 52056 Aachen Germany
- Journal Numerische Mathematik
- Online ISSN 0945-3245
- Print ISSN 0029-599X
Continuous two-step Runge–Kutta methods for ordinary differential equations
Abstract New classes of continuous two-step Runge-Kutta methods for the numerical solution of ordinary differential equations are derived.
These methods are developed imposing some interpolation and collocation conditions, in order to obtain desirable stability
properties such as A-stability and L-stability. Particular structures of the stability polynomial are also investigated.
These methods are developed imposing some interpolation and collocation conditions, in order to obtain desirable stability
properties such as A-stability and L-stability. Particular structures of the stability polynomial are also investigated.
- Content Type Journal Article
- Category Original Paper
- DOI 10.1007/s11075-009-9329-5
- Authors
- Raffaele D’Ambrosio, Universitá degli Studi di Salerno Dipartimento di Matematica e Informatica Fisciano (SA) 84084 Italy
- Zdzislaw Jackiewicz, Arizona State University Department of Mathematics and Statistics Tempe AZ 85287 USA
- Journal Numerical Algorithms
- Online ISSN 1572-9265
- Print ISSN 1017-1398
jueves, 17 de septiembre de 2009
New Algorithms for Approximate Nash Equilibria in Bimatrix Games
We consider the problem of computing additively approximate Nash equilibria in noncooperative two-player games. We provide a new polynomial time algorithm that achieves an approximation guarantee of 0.36392. We first provide a simpler algorithm, that achieves a 0.38197-approximation, which is exactly the same factor as the algorithm of Daskalakis, Mehta and Papadimitriou.This algorithm is then tuned, improving the approximation error to 0.36392. Our method is relatively fast and simple, as it requires solving only one linear program and it is based on using the solution of an auxiliary zero-sum game as a starting point. Finally we also exhibit a simple reduction that allows us to compute approximate equilibria for multi-player games by using algorithms for two-player games.
miércoles, 16 de septiembre de 2009
A posteriori error analysis of nonconforming finite volume elements for general second-order elliptic PDEs
In this article, we study the a posteriori H1 and L2 error estimates for Crouzeix-Raviart nonconforming finite volume element discretization of general second-order elliptic problems in [Ropf]2. The error estimators yield global upper and local lower bounds. Finally, numerical experiments are performed to illustrate the theoretical findings. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2009
Bernstein Ritz-Galerkin method for solving an initial-boundary value problem that combines Neumann and integral condition for the wave equation
In this article, the Ritz-Galerkin method in Bernstein polynomial basis is implemented to give an approximate solution of a hyperbolic partial differential equation with an integral condition. We will deal here with a type of nonlocal boundary value problem, that is, the solution of a hyperbolic partial differential equation with a nonlocal boundary specification. The nonlocal conditions arise mainly when the data on the boundary cannot be measured directly. The properties of Bernstein polynomial and Ritz-Galerkin method are first presented, then Ritz-Galerkin method is used to reduce the given hyperbolic partial differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique presented in this article. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2009
Finite volume simulation of waves formed by sliding masses
We numerically study a relatively simple two-dimensional (2D) model for landslide-generated nonlinear surface water waves. The landslides are modeled as rigid and impervious bodies translating on a flat or an inclined bottom. The water motion is assumed to be properly modeled by the 2D nonlinear system of shallow water equations. The resulting 2D system is numerically solved by means of a conservative well-balanced high-resolution finite volume upwind scheme esspecially adapted to treat advancing wet/dry fronts over irregular topography. Numerical results for 1D and 2D benchmark cases include comparisons with analytical or asymptotic solutions as well as comparisons with experimental data. The numerical investigation reveals that although the presented model has certain limitations, it appears to be able to model important aspects and the most significant characteristics of wave formation and propagation in their initial generation stage, namely, the waves moving toward the shore, the subsequent run-up and run-down, the waves propagating toward deep water, as well as the shape and arrival time of these waves. Copyright © 2009 John Wiley & Sons, Ltd.
Implicit time integration of hyperbolic conservation laws via discontinuous Galerkin methods
A high-order, matrix-free implicit method has been developed for the transient solutions of hyperbolic conservation laws. The discontinuous Galerkin method is applied for temporal discretization. This method has the advantage that its discretization error is [Oscr]([Delta]t2p+1) when a polynomial basis of degree p is used for time discretization. The nonlinear system of equations from the implicit time discretization is solved at each time step using a nonlinear Krylov subspace projection method. The system of linear equations is solved by the generalized minimum residual algorithm with a lower-upper symmetric Gauss-Seidel preconditioner. The numerical results from the inviscid Burgers' equation indicate that the implicit method is several times faster in performance relative to explicit integration by the total variation diminishing Runge-Kutta method of order 3. The forward Euler method requires a time step proportional to the square of the spatial step for stability with equations such as Burgers' equation (J. Sci. Comput. 2001; 16:173-261). It would, hence, be much less efficient than other explicit methods, for example, Cockburn and Shu (Math. Comput. 1989; 52:411-435), which would only require a time step proportional to the spatial step. Copyright © 2009 John Wiley & Sons, Ltd.
Five-point positive meshless scheme for hyperbolic conservation laws
We consider a five-point positive meshless collocation method for the numerical solutions of transport process described by hyperbolic conservation laws. This positive meshless method uses the five-point scheme approximation for derivatives, and an artificial dissipation term to ensure the positivity of coefficients. The numerical examples confirm the good performance of the present five-point positive meshless scheme. Copyright © 2009 John Wiley & Sons, Ltd.
martes, 15 de septiembre de 2009
Discontinuous Galerkin methods for the Navier-Stokes equations using solenoidal approximations
An interior penalty method and a compact discontinuous Galerkin method are proposed and compared for the solution of the steady incompressible Navier-Stokes equations. Both compact formulations can be easily applied using high-order piecewise divergence-free approximations, leading to two uncoupled problems: one associated with velocity and hybrid pressure, and the other one only concerned with the computation of pressures in the elements interior. Numerical examples compare the efficiency and the accuracy of both proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.
Three-dimensional simulation of planar contraction viscoelastic flow by penalty finite element method
The planar contraction flow is a benchmark problem for the numerical investigation of viscoelastic flow. The mathematical model of three-dimensional viscoelastic fluids flow is established and the numerical simulation of its planar contraction flow is conducted by using the penalty finite element method with a differential Phan-Thien-Tanner constitutive model. The discrete elastic viscous split stress formulation in cooperating with the inconsistent streamline upwind scheme is employed to improve the computation stability. The distributions of velocity and stress obtained by simulation are compared with that of Quinzani's experimental results detected by laser-doppler velocimetry and flow-induced birefringence technologies. It shows that the numerical results agree well with the experimental results. The numerical methods proposed in the study can be well used to predict complex flow patterns of viscoelastic fluids. Copyright © 2009 John Wiley & Sons, Ltd.
jueves, 10 de septiembre de 2009
Numerical solution of a parabolic transmission problem
In this paper we investigate an initial boundary-value problem for a one-dimensional parabolic equation in two disconnected intervals. A finite-difference scheme approximating this problem is proposed and analysed. An estimate of the convergence rate, compatible with the smoothness of the input data (up to a logarithmic factor of the mesh size), is obtained.
Clase de Compiladores
Alumnos
El profesor de Compiladores ha hecho llegar la siguiente información para la clase de mañana Viernes 11 de Septiembre.
la razon posible suspension de clases y el aviso oficial seria durante la mañana de mañana lo cual a nosotros no afecta, por lo cual lo mejor es suspender las clases, pero se les pide enviar un correo a orojaslcc [at] gmail [dot] com,con datos, nombre completo rut y correo...., para inscribirlos a la plataforma moodle de compiladores y mantener contacto por esa plataforma...
Se agradece hacer llegar este aviso la resto de sus compañeros.
Saludos.
El profesor de Compiladores ha hecho llegar la siguiente información para la clase de mañana Viernes 11 de Septiembre.
la razon posible suspension de clases y el aviso oficial seria durante la mañana de mañana lo cual a nosotros no afecta, por lo cual lo mejor es suspender las clases, pero se les pide enviar un correo a orojaslcc [at] gmail [dot] com,con datos, nombre completo rut y correo...., para inscribirlos a la plataforma moodle de compiladores y mantener contacto por esa plataforma...
Se agradece hacer llegar este aviso la resto de sus compañeros.
Saludos.
miércoles, 9 de septiembre de 2009
Analog control of open quantum systems under arbitrary decoherence. (arXiv:0909.1680v1 [quant-ph])
We derive and investigate a general non-Markovian equation for the
time-dependence of a Hamiltonian that maximizes the fidelity of a desired
quantum gate on any finite-dimensional quantum system in the presence of
arbitrary bath and noise sources. The method is illustrated for a single-qubit
gate implemented on a three-level system.
Anyonic Topological Quantum Computation and the Virtual Braid Group. (arXiv:0909.1672v1 [quant-ph])
We introduce a recoupling theory for virtual braided trees. This recoupling
theory can be utilized to incorporate swap gates into anyonic models of quantum
computation.
Entanglement of graph states up to 8 qubits. (arXiv:0909.1603v1 [quant-ph])
The entanglement of graph states up to eight qubits is calculated in the
regime of iteration calculation. The entanglement measures could be the
relative entropy of entanglement, the logarithmic robustness or the geometric
measure. All 146 local inequivalent graphs are classified as three categories:
the 2-colorable graphs, the non 2-colorable graphs with identical upper LOCC
entanglement bound and lower bipartite entanglement bound, the non 2-colorable
graphs with unequal bounds. The last may displays non-integer entanglement. The
precision of iteration calculation of the entanglement is less than $10^{-14}$.
Computation and Dynamics: Classical and Quantum. (arXiv:0909.1594v1 [quant-ph])
We discuss classical and quantum computations in terms of corresponding
Hamiltonian dynamics. This allows us to introduce quantum computations which
involve parallel processing of both: the data and programme instructions. Using
mixed quantum-classical dynamics we look for a full cost of computations on
quantum computers with classical terminals.
Real time plasma equilibrium reconstruction in a Tokamak. (arXiv:0909.1646v1 [math.NA])
The problem of equilibrium of a plasma in a Tokamak is a free boundary
problemdescribed by the Grad-Shafranov equation in axisymmetric configurations.
The right hand side of this equation is a non linear source, which represents
the toroidal component of the plasma current density. This paper deals with the
real time identification of this non linear source from experimental
measurements. The proposed method is based on a fixed point algorithm, a finite
element resolution, a reduced basis method and a least-square optimization
formulation.
RIOT: I/O-Efficient Numerical Computing without SQL. (arXiv:0909.1766v1 [cs.DB])
R is a numerical computing environment that is widely popular for statistical
data analysis. Like many such environments, R performs poorly for large
datasets whose sizes exceed that of physical memory. We present our vision of
RIOT (R with I/O Transparency), a system that makes R programs I/O-efficient in
a way transparent to the users. We describe our experience with RIOT-DB, an
initial prototype that uses a relational database system as a backend. Despite
the overhead and inadequacy of generic database systems in handling array data
and numerical computation, RIOT-DB significantly outperforms R in many
large-data scenarios, thanks to a suite of high-level, inter-operation
optimizations that integrate seamlessly into R. While many techniques in RIOT
are inspired by databases (and, for RIOT-DB, realized by a database system),
RIOT users are insulated from anything database related. Compared with previous
approaches that require users to learn new languages and rewrite their programs
to interface with a database, RIOT will, we believe, be easier to adopt by the
majority of the R users.
Proposed Quantum Computer Consists of Billions of Electron Spins
(PhysOrg.com) -- While researchers have already demonstrated the building blocks for few-bit quantum computers, scaling these systems up to large quantum computers remains a challenge. One of the biggest problems is developing physical systems that can reliably store thousands of qubits, and enabling bits and pairs to be addressed individually for gate operations.
martes, 8 de septiembre de 2009
Numerical analysis of the planewave discretization of orbital-free and Kohn-Sham models Part I: The Thomas-Fermi-von Weizacker model. (arXiv:0909.1464v1 [math.NA])
We provide {it a priori} error estimates for the spectral and pseudospectral
Fourier (also called planewave) discretizations of the periodic
Thomas-Fermi-von Weizs"acker (TFW) model and of the Kohn-Sham model, within
the local density approximation (LDA). These models allow to compute
approximations of the ground state energy and density of molecular systems in
the condensed phase. The TFW model is stricly convex with respect to the
electronic density, and allows for a comprehensive analysis (Part I). This is
not the case for the Kohn-Sham LDA model, for which the uniqueness of the
ground state electronic density is not guaranteed. Under a coercivity
assumption on the second order optimality condition, we prove in Part II that
for large enough energy cut-offs, the discretized Kohn-Sham LDA problem has a
minimizer in the vicinity of any Kohn-Sham ground state, and that this
minimizer is unique up to unitary transform. We then derive optimal {it a
priori} error estimates for both the spectral and the pseudospectral
discretization methods.
Ayudantia 08092009 - Juego de vida de Conway 23/3
Un applet donde se implementa el Juego de Vida de Conway y otros mas...
link applet --- http://www.ibiblio.org/lifepatterns/
Codigo Fuente del Juego de Vida de Conway
codigo fuente 23/3 ---- http://adrigm.es/2008/12/otra-version-del-juego-de-la-vida/
Paper de 1970 con la definición de los primeros patrones
articulo original Conway --- http://www.ibiblio.org/lifepatterns/october1970.html
Investigador, Matematico, Programador, encontro los primeros patrones de crecimiento indefinido
Bill Gosper --- http://es.wikipedia.org/wiki/Bill_Gosper
Tarea: Implementar un Autómata Celular equivalente a una Máquina Universal de Turing (Turing-Completo) que genere números primos. En las proximas ayudantías se darán los detalles de la tarea, forma de entrega y los plazos.
link applet --- http://www.ibiblio.org/
Codigo Fuente del Juego de Vida de Conway
codigo fuente 23/3 ---- http://adrigm.es/2008/12/otra-
Paper de 1970 con la definición de los primeros patrones
articulo original Conway --- http://www.ibiblio.org/
Investigador, Matematico, Programador, encontro los primeros patrones de crecimiento indefinido
Bill Gosper --- http://es.wikipedia.org/wiki/
Tarea: Implementar un Autómata Celular equivalente a una Máquina Universal de Turing (Turing-Completo) que genere números primos. En las proximas ayudantías se darán los detalles de la tarea, forma de entrega y los plazos.
lunes, 7 de septiembre de 2009
Shore-MT: a scalable storage manager for the multicore era
Database storage managers have long been able to efficiently handle multiple concurrent requests. Until recently, however, a computer contained only a few single-core CPUs, and therefore only a few transactions could simultaneously access the storage manager's internal structures. This allowed storage managers to use non-scalable approaches without any penalty. With the arrival of multicore chips, however, this situation is rapidly changing. More and more threads can run in parallel, stressing the internal scalability of the storage manager. Systems optimized for high performance at a limited number of cores are not assured similarly high performance at a higher core count, because unanticipated scalability obstacles arise. We benchmark four popular open-source storage managers (Shore, BerkeleyDB, MySQL, and PostgreSQL) on a modern multicore machine, and find that they all suffer in terms of scalability. We briefly examine the bottlenecks in the various storage engines. We then present Shore-MT, a multithreaded and highly scalable version of Shore which we developed by identifying and successively removing internal bottlenecks. When compared to other DBMS, Shore-MT exhibits superior scalability and 2-4 times higher absolute throughput than its peers. We also show that designers should favor scalability to single-thread performance, and highlight important principles for writing scalable storage engines, illustrated with real examples from the development of Shore-MT.
The Fiscal Politics of Big Governments: Do Coalitions Matter?
This paper uses a closed voting rule to explain how gradual changes in the socio-economic structure of developed societies shift political coalitions and lead to rapid expansions of transfer programs. Equilibria in a lifecycle economy with three homogeneous groups of voters (retirees, skilled young workers, unskilled young workers) have three properties. One, if income inequality is sufficiently high, unskilled workers and retirees will form a dominant coalition which raises both intragenerational and intergenerational transfers. Two, when capital is abundant relative to labor, government transfers will be strictly intergenerational. Three, all transfers increase when the voting franchise is extended to less affluent individuals.
Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay
Sufficient conditions for permanence of a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay x˙1(t)=x1(t)[r1(t)−a11(t)x1(t−τ(t))−a12(t)x2(t)/(m2+x12(t))], x˙2(t)=x2(t)[r2(t)−a21(t)x2(t)/x1(t)], are obtained, where x1(t) and x2(t) stand for the density of the prey and the predator, respectively, and m≠0 is a constant. τ(t)≥0 stands for the time delays due to negative feedback of the prey population.
Existence and Uniqueness of Periodic Solutions of Mixed Monotone Functional Differential Equations
This paper deals with the existence and uniqueness of periodic solutions for the first-order functional differential equation y′(t)=−a(t)y(t)+f1(t,y(t−τ(t)))+f2(t,y(t−τ(t))) with periodic coefficients and delays. We choose the mixed monotone operator theory to approach
our problem because such methods, besides providing the usual existence results, may also sometimes provide uniqueness as well as additional numerical schemes for the computation of solutions.
Experimental EPR-Steering of Bell-local States. (arXiv:0909.0805v1 [quant-ph])
Entanglement is the defining feature of quantum mechanics, and understanding
the phenomenon is essential at the foundational level and for future progress
in quantum technology. The concept of steering was introduced in 1935 by
Schr"odinger as a generalization of the Einstein-Podolsky-Rosen (EPR) paradox.
Surprisingly, it has only recently been formalized as a quantum information
task with arbitrary bipartite states and measurements, for which the existence
of entanglement is necessary but not sufficient. Previous experiments in this
area have been restricted to the approach of Reid [PRA 40, 913], which followed
the original EPR argument in considering only two different measurement
settings per side. Here we implement more than two settings so as to be able to
demonstrate experimentally, for the first time, that EPR-steering occurs for
mixed entangled states that are Bell-local (that is, which cannot possibly
demonstrate Bell-nonlocality). Unlike the case of Bell inequalities, increasing
the number of measurement settings beyond two--we use up to six--dramatically
increases the robustness of the EPR-steering phenomenon to noise.
Quantum-circuit guide to optical and atomic interferometry. (arXiv:0909.0803v1 [quant-ph])
Atomic (qubit) and optical or microwave (modal) phase-estimation protocols
are placed on the same footing in terms of quantum-circuit diagrams. Circuit
equivalences are used to demonstrate the equivalence of protocols that achieve
the Heisenberg limit by employing entangled superpositions of Fock states, such
as N00N states. The key equivalences are those that disentangle a circuit so
that phase information is written exclusively on a mode or modes or on a qubit.
The Fock-state-superposition phase-estimation circuits are converted to use
entangled coherent-state superpositions; the resulting protocols are more
amenable to realization in the lab, particularly in a qubit/cavity setting at
microwave frequencies.
Chirped-pulse interferometry with finite frequency correlations. (arXiv:0909.0796v1 [quant-ph])
Chirped-pulse interferometry is a new interferometric technique encapsulating
the advantages of the quantum Hong-Ou-Mandel interferometer without the
drawbacks of using entangled photons. Both interferometers can exhibit
even-order dispersion cancellation which allows high resolution optical delay
measurements even in thick optical samples. In the present work, we show that
finite frequency correlations in chirped-pulse interferometry and
Hong-Ou-Mandel interferometry limit the degree of dispersion cancellation. Our
results are important considerations in designing practical devices based on
these technologies.
Classical analogues of two-photon quantum interference. (arXiv:0909.0792v1 [quant-ph])
Chirped-pulse interferometry (CPI) captures the metrological advantages of
quantum Hong-Ou-Mandel (HOM) interferometry in a completely classical system.
Modified HOM interferometers are the basis for a number of seminal
quantum-interference effects. Here, the corresponding modifications to CPI
allow for the first observation of classical analogues to the HOM peak and
quantum beating. They also allow a new classical technique for generating phase
super-resolution exhibiting a coherence length dramatically longer than that of
the laser light, analogous to increased two-photon coherence lengths in
entangled states.
"Quantum-optical coherence tomography" with classical light. (arXiv:0909.0791v1 [quant-ph])
Quantum-optical coherence tomography (Q-OCT) is an interferometric technique
for axial imaging offering several advantages over conventional methods.
Chirped-pulse interferometry (CPI) was recently demonstrated to exhibit all of
the benefits of the quantum interferometer upon which Q-OCT is based. Here we
use CPI to measure axial interferograms to profile a sample accruing the
important benefits of Q-OCT, including automatic dispersion cancellation, but
with 10 million times higher signal. Our technique solves the artifact problem
in Q-OCT and highlights the power of classical correlation in optical imaging.
Experimental violation of Svetlichny's inequality. (arXiv:0909.0789v1 [quant-ph])
It is well known that quantum mechanics is incompatible with local realistic
theories. Svetlichny showed, through the development of a Bell-like inequality,
that quantum mechanics is also incompatible with a restricted class of nonlocal
realistic theories for three particles where any two-body nonlocal correlations
are allowed [Phys. Rev. D 35, 3066 (1987)]. In the present work, we
experimentally generate three-photon GHZ states to test Svetlichny's
inequality. Our states are fully characterized by quantum state tomography
using an overcomplete set of measurements and have a fidelity of (84+/-1)% with
the target state. We measure a convincing, 3.6 std., violation of Svetlichny's
inequality and rule out this class of restricted nonlocal realistic models.
Topological Order Following a Quantum Quench. (arXiv:0909.0752v1 [quant-ph])
We determine the conditions under which topological order survives a rapid
quench. Specifically, we consider the case where a quantum spin system is
prepared in the ground state of the Toric Code Model and, after the quench, it
evolves with a Hamiltonian that does not support topological order. We provide
analytical results supported by numerical evidence for a variety of quench
Hamiltonians. The robustness of topological order under non-equilibrium
situations is tested by studying the topological entropy and a novel dynamical
measure, which makes use of the Ulhmann fidelity between partial density
matrices obtained from different topological sectors.
A new exoplanet to test tide theories
Almost 400 extrasolar planets have been found to date (see Physics Today, May 2009, page 46), but a new planet reported by Coel Hellier (Keele University) and colleagues stands out. Like many exoplanets, theirs, dubbed WASP-18b, is massive (10 times the mass of Jupiter) and has a small orbital radius (only 1/50th of Earth's). But its orbital period of only 0.94 day is the shortest for any "hot Jupiter" yet observed. Moreover, its large mass and small orbit are predicted to cause the strongest tidal interactions of any known star–planet system. According to current theory, the tidal bulge that the planet raises on its host star exerts a torque that will drain angular momentum from the planet and cause it to spiral inward. (For more on tidal interactions, see Physics Today, August 2009, page 11.) If the star's tidal dissipation rate is comparable to what's been measured for binary stars and for the gas giants in our own solar system, the infall will be quick: WASP-18b has less than a million years left in a lifetime, estimated from the age of its host star, of about a billion years. Over the next decade, WASP-18b's death spiral should produce a measurable shift in the planet's observed transit time. The absence of tidal decay—a notable possibility, given the rarity of finding a planet so close to the end of its life—would constitute direct evidence for a different class of tidal interactions in the host star and provide new constraints on models of stellar interiors. (C. Hellier et al., Nature 460, 1098, 2009.)—Richard J. Fitzgerald
High-Dimensional Non-Linear Variable Selection through Hierarchical Kernel Learning. (arXiv:0909.0844v1 [cs.LG])
We consider the problem of high-dimensional non-linear variable selection for
supervised learning. Our approach is based on performing linear selection among
exponentially many appropriately defined positive definite kernels that
characterize non-linear interactions between the original variables. To select
efficiently from these many kernels, we use the natural hierarchical structure
of the problem to extend the multiple kernel learning framework to kernels that
can be embedded in a directed acyclic graph; we show that it is then possible
to perform kernel selection through a graph-adapted sparsity-inducing norm, in
polynomial time in the number of selected kernels. Moreover, we study the
consistency of variable selection in high-dimensional settings, showing that
under certain assumptions, our regularization framework allows a number of
irrelevant variables which is exponential in the number of observations. Our
simulations on synthetic datasets and datasets from the UCI repository show
state-of-the-art predictive performance for non-linear regression problems.
Ternary Codes Associated with O^-(2n,q) and Power Moments of Kloosterman Sums with Square Arguments. (arXiv:0909.0811v1 [math.NT])
In this paper, we construct three ternary linear codes associated with the
orthogonal group O^-(2,q) and the special orthogonal groups SO^-(2,q) and
SO^-(4,q). Here q is a power of three. Then we obtain recursive formulas for
the power moments of Kloosterman sums with square arguments and for the even
power moments of those in terms of the frequencies of weights in the codes.
This is done via Pless power moment identity and by utilizing the explicit
expressions of "Gauss sums" for the orthogonal and special orthogonal groups
O^-(2n,q) and SO^-(2n,q).
An Infinite Family of Recursive Formulas Generating Power Moments of Kloosterman Sums with Trace One Arguments: O(2n+1,2^r) Case. (arXiv:0909.0809v1 [math.NT])
In this paper, we construct an infinite family of binary linear codes
associated with double cosets with respect to certain maximal parabolic
subgroup of the orthogonal group O(2n+1,q). Here q is a power of two. Then we
obtain an infinite family of recursive formulas generating the odd power
moments of Kloosterman sums with trace one arguments in terms of the
frequencies of weights in the codes associated with those double cosets in
O(2n+1,q) and in the codes associated with similar double cosets in the
symplectic group Sp(2n,q). This is done via Pless power moment identity and by
utilizing the explicit expressions of exponential sums over those double cosets
related to the evaluations of "Gauss sums" for the orthogonal group O(2n+1,q).
SKorean TV giants tout differing technologies
The world's top two makers of flat-panel televisions are stressing the energy-saving virtues of different display technologies in their race to dominate a huge global market.
West Coast fishermen embark on new wave of fishing
(AP) -- The West Coast groundfish fleet has struggled to stay afloat during major cutbacks to reverse long-standing problems with overfishing and to protect the seafloor from damage caused by bottom trawling gear.
Suscribirse a:
Entradas (Atom)