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 R$780.695,42; R$737.526,16; R$727.031,52 e R$703.907,58. 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$780,695.42 and 7.8$ 737,526.16 and 7.4%; R$727,031.52 and 7.3$ 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 $\alpha_i$, 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 $\alpha_i$) 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