Data sets of very large linear feasibility problems solved by projection methods. (arXiv:1103.2952v1 [cs.MS])

Data sets of very large linear feasibility problems solved by projection methods. (arXiv:1103.2952v1 [cs.MS]): "

We give a link to a page on the Web on which we deposited a set of eight huge
Linear Programming (LP) problems for Intensity-Modulated Proton Therapy (IMPT)
treatment planning. These huge LP problems were employed in our recent research
and we were asked to make them public.

"

sin[n Delta t sin (n Delta t1)] as a source of unpredictable dynamics. (arXiv:1103.3160v1 [nlin.CD])

sin[n Delta t sin (n Delta t1)] as a source of unpredictable dynamics. (arXiv:1103.3160v1 [nlin.CD]): "

We investigate the ability of the function sin[n Delta t sin (n Delta t1)],
where n is an integer and growing number, to produce unpredictable sequences of
numbers. Classical mathematical tools for distinguishing periodic from chaotic
or random behaviour, such as sensitivity to the initial conditions, Fourier
analysis, and autocorrelation are used. Moreover, the function acos{sin[n Delta
t sin (n Delta t1)]}/pigreek is introduced to have an uniform density of
numbers in the interval [0,1], so it can be submitted to a battery of widely
used tests for random number generators. All these tools show that a proper
choice of Delta t and Delta t1, can produce a sequence of numbers behaving as
unpredictable dynamics.

"

PyDEC: Software and Algorithms for Discretization of Exterior Calculus. (arXiv:1103.3076v1 [cs.NA])

PyDEC: Software and Algorithms for Discretization of Exterior Calculus. (arXiv:1103.3076v1 [cs.NA]): "

This paper describes the algorithms, features and implementation of PyDEC, a
Python library for computations related to the Discretization of Exterior
Calculus (DEC). PyDEC facilitates inquiry into both physical problems on
manifolds as well as purely topological problems on abstract complexes. We
describe efficient algorithms for constructing the operators and objects that
arise in DEC and related topological problems. Our algorithms are formulated in
terms of high-level matrix operations which extend to arbitrary dimension. As a
result, our implementations map well to the facilities of numerical libraries
such as NumPy and SciPy. The availability of such libraries makes Python
suitable for prototyping numerical methods. We demonstrate how PyDEC is used to
solve physical and topological problems through several concise examples.

"

A study of the existing linear algebra libraries that you can use from C++ (Une \'etude des biblioth\`eques d'alg\`ebre lin\'eaire utilisables en C++). (arXiv:1103.3020v1 [cs.MS])

A study of the existing linear algebra libraries that you can use from C++ (Une \'etude des biblioth\`eques d'alg\`ebre lin\'eaire utilisables en C++). (arXiv:1103.3020v1 [cs.MS]): "

A study of the existing linear algebra libraries that you can use from C++

"

Quantum algorithm for the Boolean hidden shift problem. (arXiv:1103.3017v1 [quant-ph])

Quantum algorithm for the Boolean hidden shift problem. (arXiv:1103.3017v1 [quant-ph]): "

The hidden shift problem is a natural place to look for new separations
between classical and quantum models of computation. One advantage of this
problem is its flexibility, since it can be defined for a whole range of
functions and a whole range of underlying groups. In a way, this distinguishes
it from the hidden subgroup problem where more stringent requirements about the
existence of a periodic subgroup have to be made. And yet, the hidden shift
problem proves to be rich enough to capture interesting features of problems of
algebraic, geometric, and combinatorial flavor. We present a quantum algorithm
to identify the hidden shift for any Boolean function. Using Fourier analysis
for Boolean functions we relate the time and query complexity of the algorithm
to an intrinsic property of the function, namely its minimum influence. We show
that for randomly chosen functions the time complexity of the algorithm is
polynomial. Based on this we show an average case exponential separation
between classical and quantum time complexity. A perhaps interesting aspect of
this work is that, while the extremal case of the Boolean hidden shift problem
over so-called bent functions can be reduced to a hidden subgroup problem over
an abelian group, the more general case studied here does not seem to allow
such a reduction.

"

Fitzpatrick Algorithm for Multivariate Rational Interpolation. (arXiv:1103.3176v1 [math.NA])

Published with Blogger-droid v1.6.7

PyDEC: Software and Algorithms for Discretization of Exterior Calculus. (arXiv:1103.3076v1 [cs.NA])

Published with Blogger-droid v1.6.7