23,818 research outputs found
Enumeration and Decidable Properties of Automatic Sequences
We show that various aspects of k-automatic sequences -- such as having an
unbordered factor of length n -- are both decidable and effectively enumerable.
As a consequence it follows that many related sequences are either k-automatic
or k-regular. These include many sequences previously studied in the
literature, such as the recurrence function, the appearance function, and the
repetitivity index. We also give some new characterizations of the class of
k-regular sequences. Many results extend to other sequences defined in terms of
Pisot numeration systems
The effect of internal pipe wall roughness on the accuracy of clamp-on ultrasonic flow meters
Clamp-on transit-time ultrasonic flowmeters (UFMs) suffer from poor accuracy compared with spool-piece UFMs due to uncertainties that result from the in-field installation process. One of the important sources of uncertainties is internal pipe wall roughness which affects the flow profile and also causes significant scattering of ultrasound. This paper purely focuses on the parametric study to quantify the uncertainties (related to internal pipe wall roughness) induced by scattering of ultrasound and it shows that these effects are large even without taking into account the associated flow disturbances. The flowmeter signals for a reference clamp-on flowmeter setup were simulated using 2-D finite element analysis including simplifying assumptions (to simulate the effect of flow) that were deemed appropriate. The validity of the simulations was indirectly verified by carrying out experiments with different separation distances between ultrasonic probes. The error predicted by the simulations and the experimentally observed errors were in good agreement. Then, this simulation method was applied on pipe walls with rough internal surfaces. For ultrasonic waves at 1 MHz, it was found that compared with smooth pipes, pipes with only a moderately rough internal surface (with 0.2-mm rms and 5-mm correlation length) can exhibit systematic errors of 2 in the flow velocity measurement. This demonstrates that pipe internal surface roughness is a very important factor that limits the accuracy of clamp on UFMs
Accurate reconstruction of insertion-deletion histories by statistical phylogenetics
The Multiple Sequence Alignment (MSA) is a computational abstraction that
represents a partial summary either of indel history, or of structural
similarity. Taking the former view (indel history), it is possible to use
formal automata theory to generalize the phylogenetic likelihood framework for
finite substitution models (Dayhoff's probability matrices and Felsenstein's
pruning algorithm) to arbitrary-length sequences. In this paper, we report
results of a simulation-based benchmark of several methods for reconstruction
of indel history. The methods tested include a relatively new algorithm for
statistical marginalization of MSAs that sums over a stochastically-sampled
ensemble of the most probable evolutionary histories. For mammalian
evolutionary parameters on several different trees, the single most likely
history sampled by our algorithm appears less biased than histories
reconstructed by other MSA methods. The algorithm can also be used for
alignment-free inference, where the MSA is explicitly summed out of the
analysis. As an illustration of our method, we discuss reconstruction of the
evolutionary histories of human protein-coding genes.Comment: 28 pages, 15 figures. arXiv admin note: text overlap with
arXiv:1103.434
Muscle force is determined also by muscle relative position: isolated effects
Effects on force of changes of the position of extensor digitorum longus muscle (EDL) relative to surrounding tissues were investigated in rat. Connective tissue at the muscle bellies of tibialis anterior (TA), extensor hallucis longus (EHL) and EDL was left intact, to allow myofascial force transmission. The position of EDL muscle was altered, without changing EDL muscle–tendon complex length, and force exerted at proximal and distal tendons of EDL as well as summed force exerted at the distal tendons of TA and EHL muscles (TA+EHL) were measured. Proximal and distal EDL forces as well as distal TA+EHL force changed significantly on repositioning EDL muscle.\ud
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These muscle position–force characteristics were assessed at two EDL lengths and two TA+EHL lengths. It was shown that changes of muscle force with length changes of a muscle is the result of the length changes per se, as well as of changes of relative position of parts of the muscle. It is concluded that in addition to length, muscle position relative to its surroundings co-determines isometric muscle force.\ud
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Keywords: Intermuscular and extramuscular connective tissue; Myofascial force transmission; Rat m. extensor digitorum longus (EDL); Sarcomere length; Muscle relative positio
Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability
Previously referred to as `miraculous' in the scientific literature because
of its powerful properties and its wide application as optimal solution to the
problem of induction/inference, (approximations to) Algorithmic Probability
(AP) and the associated Universal Distribution are (or should be) of the
greatest importance in science. Here we investigate the emergence, the rates of
emergence and convergence, and the Coding-theorem like behaviour of AP in
Turing-subuniversal models of computation. We investigate empirical
distributions of computing models in the Chomsky hierarchy. We introduce
measures of algorithmic probability and algorithmic complexity based upon
resource-bounded computation, in contrast to previously thoroughly investigated
distributions produced from the output distribution of Turing machines. This
approach allows for numerical approximations to algorithmic
(Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a
computational hierarchy. We demonstrate that all these estimations are
correlated in rank and that they converge both in rank and values as a function
of computational power, despite fundamental differences between computational
models. In the context of natural processes that operate below the Turing
universal level because of finite resources and physical degradation, the
investigation of natural biases stemming from algorithmic rules may shed light
on the distribution of outcomes. We show that up to 60\% of the
simplicity/complexity bias in distributions produced even by the weakest of the
computational models can be accounted for by Algorithmic Probability in its
approximation to the Universal Distribution.Comment: 27 pages main text, 39 pages including supplement. Online complexity
calculator: http://complexitycalculator.com
Propagation of weak shocks through a random medium
The propagation of weak shock waves (M_s = 1.007, 1.03 and 1.1) through a statistically uniform random medium has been investigated experimentally in a shock tube. The wave-from geometry, rise time and amplitude of initially plane shocks which have propagated through a random mixture of helium and refrigerant 12 are measured. The effect of shock propagation on the properties of the random medium is visualized with schlieren and shadow photography. The pressure histories of the distorted shock waves reflecting from a normal end wall are observed to be both peaked and rounded. In the rounded case the perturbed shock is found to be made up of a succession of weak, slightly curved fronts with a total effective rise time orders of magnitude greater than the classical Taylor thickness. The radius of curvature of the weakest shocks after propagating through the random medium is inferred from observations at two downstream stations to be about 7 times the integral scale of the gas inhomogeneities. It is concluded that the observed distortions of the wave fronts can best be explained in terms of random focusing and defocusing of the front by the inhomogeneities in the medium. A ray-tracing calculation has been used to interpret the experimental observations. It is found that geometrical considerations are sufficient to account for many of the effects observed on the shocks
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