37 research outputs found
Turing machines can be efficiently simulated by the General Purpose Analog Computer
The Church-Turing thesis states that any sufficiently powerful computational
model which captures the notion of algorithm is computationally equivalent to
the Turing machine. This equivalence usually holds both at a computability
level and at a computational complexity level modulo polynomial reductions.
However, the situation is less clear in what concerns models of computation
using real numbers, and no analog of the Church-Turing thesis exists for this
case. Recently it was shown that some models of computation with real numbers
were equivalent from a computability perspective. In particular it was shown
that Shannon's General Purpose Analog Computer (GPAC) is equivalent to
Computable Analysis. However, little is known about what happens at a
computational complexity level. In this paper we shed some light on the
connections between this two models, from a computational complexity level, by
showing that, modulo polynomial reductions, computations of Turing machines can
be simulated by GPACs, without the need of using more (space) resources than
those used in the original Turing computation, as long as we are talking about
bounded computations. In other words, computations done by the GPAC are as
space-efficient as computations done in the context of Computable Analysis
The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation
In this paper we revisit one of the rst models of analog
computation, Shannon's General Purpose Analog Computer (GPAC).
The GPAC has often been argued to be weaker than computable analysis.
As main contribution, we show that if we change the notion of GPACcomputability
in a natural way, we compute exactly all real computable
functions (in the sense of computable analysis). Moreover, since GPACs
are equivalent to systems of polynomial di erential equations then we
show that all real computable functions can be de ned by such models
Solving analytic differential equations in polynomial time over unbounded domains
In this paper we consider the computational complexity of solving initial-value problems de ned with analytic ordinary diferential
equations (ODEs) over unbounded domains of Rn and Cn, under the Computable Analysis setting. We show that the solution can be computed in polynomial time over its maximal interval of de nition, provided it satis es a very generous bound on its growth, and that the function admits an analytic extension to the complex plane
Robust computations with dynamical systems
In this paper we discuss the computational power of Lipschitz
dynamical systems which are robust to in nitesimal perturbations.
Whereas the study in [1] was done only for not-so-natural systems from
a classical mathematical point of view (discontinuous di erential equation
systems, discontinuous piecewise a ne maps, or perturbed Turing
machines), we prove that the results presented there can be generalized
to Lipschitz and computable dynamical systems.
In other words, we prove that the perturbed reachability problem (i.e. the
reachability problem for systems which are subjected to in nitesimal perturbations)
is co-recursively enumerable for this kind of systems. Using
this result we show that if robustness to in nitesimal perturbations is
also required, the reachability problem becomes decidable. This result
can be interpreted in the following manner: undecidability of veri cation
doesn't hold for Lipschitz, computable and robust systems.
We also show that the perturbed reachability problem is co-r.e. complete
even for C1-systems
Economic efficiency and productivity of life-cycle beef cattle production systems in the South of Bahia
Estudaram-se a produtividade e a eficiência econômica de quatro sistemas de bovinos de corte, por meio de simulação, que diferiram quanto à taxa de natalidade (TN). A pesquisa foi realizada em uma fazenda de ciclo completo (SCC) com TN de 87%, e mais três sistemas simulados: -4TN com TN de 83%; -2TN com TN de 85%; e +2TN com TN de 89%. O SCC foi baseado em dados de um sistema de cria, recria e engorda com média de 3.453 cabeças, localizado no sul da Bahia, no período de janeiro de 2000 a dezembro de 2002. As TN foram ajustadas à demanda energética dos animais em cada sistema e à evolução do rebanho durante três anos. A quantidade de carne vendida foi de 149, 146, 144, 141 kg/ha/ano para -4TN, -2TN, SCC e +2TN, respectivamente. O lucro total acumulado, na mesma ordem de citação, foi de R737.526,16; R703.907,58. O retorno do capital investido acumulado foi de 7,8; 7,4; 7,3 e 7,0% para -4 TN, -2TN, SCC e +2TN, respectivamente. A variação da TN na atividade de cria, recria e engorda de bovinos alterou a produtividade e a eficiência econômica dos sistemas simulados. As respostas em produtividade e eficiência econômica diminuíram com o aumento da taxa de natalidade.Economic efficiency and productivity of life-cycle cattle raising systems were studied by simulations that differed in calving rates (CR). The study was conducted on a life-cycle cattle production system (SCC) with 87% CR, and three simulated systems: -4CR with 83% CR, -2CR with 85% CR, and +2CR with 89% CR. The SCC was based on data from a life-cycle cattle system of 3,453 animals in the South of Bahia State, from January 2000 to December 2002. CR was adjusted according to energy requirement and herd composition in SCC during three years. Meat amount sold was 149, 146, 144, and 141kg/ha/year for -4CR, -2CR, SCC, and +2CR, respectively. Accumulated profit and return on invested capital were R 737,526.16 and 7.4%; R 703,907.58 and 7.0% for -4CR, -2CR, SCC, and +2CR, respectively. Calving rate variation modified the economic efficiency and productivity of simulated production systems. Economic efficiency and productivity results decreased as calving rate increased
Bayesian joint estimation of non-Gaussianity and the power spectrum
We propose a rigorous, non-perturbative, Bayesian framework which enables one
jointly to test Gaussianity and estimate the power spectrum of CMB
anisotropies. It makes use of the Hilbert space of an harmonic oscillator to
set up an exact likelihood function, dependent on the power spectrum and on a
set of parameters , which are zero for Gaussian processes. The latter
can be expressed as series of cumulants; indeed they perturbatively reduce to
cumulants. However they have the advantage that their variation is essentially
unconstrained. Any truncation(i.e.: finite set of ) therefore still
produces a proper distribution - something which cannot be said of the only
other such tool on offer, the Edgeworth expansion. We apply our method to Very
Small Array (VSA) simulations based on signal Gaussianity, showing that our
algorithm is indeed not biased.Comment: 11pages, 4 figures, submitted to MNRA