433 research outputs found
Elements of Design for Containers and Solutions in the LinBox Library
We describe in this paper new design techniques used in the \cpp exact linear
algebra library \linbox, intended to make the library safer and easier to use,
while keeping it generic and efficient. First, we review the new simplified
structure for containers, based on our \emph{founding scope allocation} model.
We explain design choices and their impact on coding: unification of our matrix
classes, clearer model for matrices and submatrices, \etc Then we present a
variation of the \emph{strategy} design pattern that is comprised of a
controller--plugin system: the controller (solution) chooses among plug-ins
(algorithms) that always call back the controllers for subtasks. We give
examples using the solution \mul. Finally we present a benchmark architecture
that serves two purposes: Providing the user with easier ways to produce
graphs; Creating a framework for automatically tuning the library and
supporting regression testing.Comment: 8 pages, 4th International Congress on Mathematical Software, Seoul :
Korea, Republic Of (2014
Exact quantum query complexity of
In the exact quantum query model a successful algorithm must always output
the correct function value. We investigate the function that is true if exactly
or of the input bits given by an oracle are 1. We find an optimal
algorithm (for some cases), and a nontrivial general lower and upper bound on
the minimum number of queries to the black box.Comment: 19 pages, fixed some typos and constraint
High power impulse magnetron sputtering discharges: Instabilities and plasma self-organization
We report on instabilities in high power impulse magnetron sputtering plasmas which are likely to be of the generalized drift wave type. They are characterized by well defined regions of high and low plasma emissivity along the racetrack of the magnetron and cause periodic shifts in floating potential. The azimuthal mode number m depends on plasma current, plasma density, and gas pressure. The structures rotate in × direction at velocities of ∼10 km s−1 and frequencies up to 200 kHz. Collisions with residual gas atoms slow down the rotating wave, whereas increasing ionization degree of the gas and plasma conductivity speeds it up
Formation of molecular oxygen in ultracold O + OH reaction
We discuss the formation of molecular oxygen in ultracold collisions between
hydroxyl radicals and atomic oxygen. A time-independent quantum formalism based
on hyperspherical coordinates is employed for the calculations. Elastic,
inelastic and reactive cross sections as well as the vibrational and rotational
populations of the product O2 molecules are reported. A J-shifting
approximation is used to compute the rate coefficients. At temperatures T = 10
- 100 mK for which the OH molecules have been cooled and trapped
experimentally, the elastic and reactive rate coefficients are of comparable
magnitude, while at colder temperatures, T < 1 mK, the formation of molecular
oxygen becomes the dominant pathway. The validity of a classical capture model
to describe cold collisions of OH and O is also discussed. While very good
agreement is found between classical and quantum results at T=0.3 K, at higher
temperatures, the quantum calculations predict a larger rate coefficient than
the classical model, in agreement with experimental data for the O + OH
reaction. The zero-temperature limiting value of the rate coefficient is
predicted to be about 6.10^{-12} cm^3 molecule^{-1} s^{-1}, a value comparable
to that of barrierless alkali-metal atom - dimer systems and about a factor of
five larger than that of the tunneling dominated F + H2 reaction.Comment: 9 pages, 8 figure
On the expressive power of read-once determinants
We introduce and study the notion of read- projections of the determinant:
a polynomial is called a {\it read-
projection of determinant} if , where entries of matrix are
either field elements or variables such that each variable appears at most
times in . A monomial set is said to be expressible as read-
projection of determinant if there is a read- projection of determinant
such that the monomial set of is equal to . We obtain basic results
relating read- determinantal projections to the well-studied notion of
determinantal complexity. We show that for sufficiently large , the permanent polynomial and the elementary symmetric
polynomials of degree on variables for are
not expressible as read-once projection of determinant, whereas
and are expressible as read-once projections of determinant. We
also give examples of monomial sets which are not expressible as read-once
projections of determinant
On Tractable Exponential Sums
We consider the problem of evaluating certain exponential sums. These sums
take the form ,
where each x_i is summed over a ring Z_N, and f(x_1,...,x_n) is a multivariate
polynomial with integer coefficients. We show that the sum can be evaluated in
polynomial time in n and log N when f is a quadratic polynomial. This is true
even when the factorization of N is unknown. Previously, this was known for a
prime modulus N. On the other hand, for very specific families of polynomials
of degree \ge 3, we show the problem is #P-hard, even for any fixed prime or
prime power modulus. This leads to a complexity dichotomy theorem - a complete
classification of each problem to be either computable in polynomial time or
#P-hard - for a class of exponential sums. These sums arise in the
classifications of graph homomorphisms and some other counting CSP type
problems, and these results lead to complexity dichotomy theorems. For the
polynomial-time algorithm, Gauss sums form the basic building blocks. For the
hardness results, we prove group-theoretic necessary conditions for
tractability. These tests imply that the problem is #P-hard for even very
restricted families of simple cubic polynomials over fixed modulus N
Improved bounds for reduction to depth 4 and depth 3
Koiran showed that if a -variate polynomial of degree (with
) is computed by a circuit of size , then it is also computed by
a homogeneous circuit of depth four and of size
. Using this result, Gupta, Kamath, Kayal and
Saptharishi gave a upper bound for the
size of the smallest depth three circuit computing a -variate polynomial of
degree given by a circuit of size .
We improve here Koiran's bound. Indeed, we show that if we reduce an
arithmetic circuit to depth four, then the size becomes
. Mimicking Gupta, Kamath, Kayal and
Saptharishi's proof, it also implies the same upper bound for depth three
circuits.
This new bound is not far from optimal in the sense that Gupta, Kamath, Kayal
and Saptharishi also showed a lower bound for the size
of homogeneous depth four circuits such that gates at the bottom have fan-in at
most . Finally, we show that this last lower bound also holds if the
fan-in is at least
Ionization wave propagation on a micro cavity plasma array
Microcavity plasma arrays of inverse pyramidal cavities have been fabricated
in p-Si wafers. Each cavity acts as a microscopic dielectric barrier discharge.
Operated at atmospheric pressure in argon and excited with high voltage at
about 10 kHz, each cavity develops a localized microplasma. Experiments have
shown a strong interaction of individual cavities, leading to the propagation
of wave-like optical emission structures along the surface of the array. This
phenomenon is numerically investigated using computer simulation. The observed
ionization wave propagates with a speed of about 5 km/s, which agrees well the
experimental findings. It is found that the wave propagation is due to
sequential contributions of a drift of electrons followed by drift of ions
between cavities seeded by photoemission of electrons by the plasma in adjacent
cavities
Algorithms for zero-dimensional ideals using linear recurrent sequences
Inspired by Faug\`ere and Mou's sparse FGLM algorithm, we show how using
linear recurrent multi-dimensional sequences can allow one to perform
operations such as the primary decomposition of an ideal, by computing the
annihilator of one or several such sequences.Comment: LNCS, Computer Algebra in Scientific Computing CASC 201
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