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Abstract We show that a computable function $f:\mathbb R\rightarrow \mathbb R$ has Luzin’s property (N) if and only if it reflects $\Pi ^1_1$ -randomness, if and only if it reflects $\Delta ^1_1({\mathcal {O}})$ -randomness, and if and only if it reflects ${\mathcal {O}}$ -Kurtz randomness, but reflecting Martin–Löf randomness or weak-2-randomness does not suffice. Here a function f is said to reflect a randomness notion R if whenever $f(x)$ is R -random, then x is R -random as well. If additionally f is known to have bounded variation, then we show f has Luzin’s (N) if and only if it reflects weak-2-randomness, and if and only if it reflects $\emptyset '$ -Kurtz randomness. This links classical real analysis with algorithmic randomness.
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I investigate the trade-off between regularity and randomness in Bridget Riley's early Op art, focusing on White Discs 2 (1964) and Fragment 6/9 (1965). I build on this to investigate the trade-off more generally. I analyse these two works and undertake three experimental investigations based on my observations. I first consider different types of randomness and the effect they have on the generated artwork. I then look at whether the introduction of randomness can be left to the computer or needs the artist's direction. For best aesthetic effect, there is some evidence that the choices made are not truly random. Finally, I consider how much randomness needs to be added to a regular pattern in order to produce a work that balances regularity and randomness in an aesthetically pleasing way. There is evidence that around two-thirds of the pattern needs to be retained.
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We show that a computable function $f:\mathbb R\rightarrow\mathbb R$ has Luzin's property (N) if and only if it reflects $\Pi^1_1$-randomnes, if and only if it reflects $\Delta^1_1(\mathcal O)$-randomness, and if and only if it reflects $\mathcal O$-Kurtz randomness, but reflecting Martin-L\"of randomness or weak-2-randomness does not suffice. Here a function $f$ is said to reflect a randomness notion $R$ if whenever $f(x)$ is $R$-random, then $x$ is $R$-random as well. If additionally $f$ is known to have bounded variation, then we show $f$ has Luzin's (N) if and only if it reflects weak-2-randomness, and if and only if it reflects $\emptyset'$-Kurtz randomness. This links classical real analysis with algorithmic randomness.
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Abstract We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Löf randomness.
Randomness tests
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Abstract In a number of studies, tendencies toward nonrepetition in judgments of randomness of visually presented sequences of events have been attributed to a biased concept of randomness. The present study proposed that such bias is due to “bottom-up” visual processes rather than a concept of randomness. Experiment 1 showed that judgments of randomness were less biased when repetitions were made less conspicuous by increasing the distance between adjacent items. Experiment 2 produced comparable results for increasing dissimilarity of categorically identical items. A third experiment showed that the bias in the judgment task was not related to a more direct measure of knowledge of random processes, the assignment of probabilities of repetition to imagined random sequences. The results supported the view that judgments of randomness are determined to a high degree by the conspicuousness of repetitions and are independent of the concept of randomness.
Repetition (rhetorical device)
Random sequence
Degree (music)
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Randomness tests
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This paper describes the development of a real-time path planner for off-road vehicles using a simulator. The general idea with the presented system is to extend a standard path-tracking algorithm with a simulator that, in real-time, tries to predict collisions in a window forward in time. If a collision is predicted, the vehicle is stopped and a path-search phase is initiated. Variants of the original path are generated and simulated until a feasible path is found. The real vehicle then continues, now tracking the replanned path.
Tracking (education)
Any-angle path planning
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Oblivious RAM (ORAM) is a technique to prevent not only the data but also their access pattern from being observed. Path ORAM is a recently proposed ORAM protocol, whose safety relies on the derived access pattern being observed as a sequence of accesses to random paths. In this paper, we analyze the effect of pseudorandom number generators (PRNGs) on the randomness of the derived path sequence. Our evaluation showed that, even with weak PRNGs that fail some of the diehard tests, the derived path sequences passed more tests. These results may open a new way to a light-weight implementation of Path ORAM.
Sequence (biology)
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This work starts from definition of randomness, the results of algorithmic randomness are analyzed from the perspective of application. Then, the source and nature of randomness is explored, and the relationship between infinity and randomness is found. The properties of randomness are summarized from the perspective of interaction between systems, that is, the set composed of sequences generated by randomness has the property of asymptotic completeness. Finally, the importance of randomness in AI research is emphasized.
Completeness (order theory)
Infinity
Randomness tests
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