FINITE PATTERN PROBLEMS RELATED TO LÜROTH EXPANSION

Let [Formula: see text] be a set of countable many functions, where every function [Formula: see text] satisfies [Formula: see text] and [Formula: see text] as [Formula: see text]. This paper studies the size of the set consisting of those numbers whose Lüroth digit sequence is strictly increasing and contains any finite pattern of [Formula: see text]. We prove that the Hausdorff dimension of such set is [Formula: see text] and give several applications.

0104 The Effect of Time, Sleep, and Wake on Motor Memory Consolidation: A Partial Replication of Walker, Et Al. (2002)

Introduction Findings from Walker, et al (2002) ‘Practice with Sleep Makes Perfect: Sleep-Dependent Motor Skill Learning’ demonstrate that performance on a widely used motor memory task (motor sequence task (MST)) benefits from a 12hr period of sleep (and not wake) even if the sleep period does not occur for approximately 12hrs after task acquisition, suggesting that sleep is crucial for motor memory consolidation. Using a larger sample, we attempted to replicate this finding, which is derived from Groups B & D from Walker et al (2002). Methods Participants (64 medical students: Age 21.2±0.8; N=33 females) were trained on the MST in the morning (10am; N=40) or evening (10pm; N=24) and then returned 12 and 24hrs later to be retested. The MST is a simple typing task that requires participants, at training, to type a 5-digit sequence (e.g., 4-1-3-2-4) as fast and accurately as possible over a series of 12 30-second trials with a 30-second break between each trial. At each retest, participants performed three 30-second trials. Results With 75% of the data collected we have found that when sleep follows training in the evening (first 12hr interval), the number of correctly typed sequences increased by 19.1% (cf. 20.5% in Walker (2002)). After a subsequent day of wake (second 12hr interval) performance increased by an additional 7.3% (cf. 2.0%). However, when a day of wake spanned the first 12hrs following training, performance increased by 14.5% (cf. 3.9%) followed by another 14.5% increase over the subsequent night (cf. 14.4%). Performance differences between sleep and wake participants were nonsignificant over the first 12hrs (p=0.38) and second 12hrs (p=0.49). Conclusion With most of data collection complete, our findings only partially replicate those of Walker et al (2002), and may draw into question the robustness of sleep for the processing motor memory. Support None

Intentionally fabricated autobiographical memories

Participants generated both autobiographical memories (AMs) that they believed to be true and intentionally fabricated autobiographical memories (IFAMs). Memories were constructed while a concurrent memory load (random 8-digit sequence) was held in mind or while there was no concurrent load. Amount and accuracy of recall of the concurrent memory load was reliably poorer following generation of IFAMs than following generation of AMs. There was no reliable effect of load on memory generation times; however, IFAMs always took longer to construct than AMs. Finally, replicating previous findings, fewer IFAMs had a field perspective than AMs, IFAMs were less vivid than AMs, and IFAMs contained more motion words (indicative of increased cognitive load). Taken together, these findings show a pattern of systematic differences that mark out IFAMs, and they also show that IFAMs can be identified indirectly by lowered performance on concurrent tasks that increase cognitive load.

Deleting digits

We consider here the positive integers with respect to their unique decimal expansions, where each n ∈ ℕ is given by for some non-negative integer k and digit sequence αkαk-1 … α0. With slight abuse of notation, we also use n to denote αkαk-1 … α0. For such sequences of digits (as well as for the numbers represented by the corresponding expansions) we write x ⊲ y if x is a subsequence of y, which means that either x = y or x can be obtained from y by deleting some digits of y. For example, 514 ⊲ 352148. The main problem is as follows: Given a set S ⊂ ℕ, find the smallest possible set M ⊂ S such that for all s ∈ S there exists m ∈ M with m ⊲ s.

ON POINTS WITH POSITIVE DENSITY OF THE DIGIT SEQUENCE IN INFINITE ITERATED FUNCTION SYSTEMS

Let $\{f_{n}\}_{n\geq 1}$ be an infinite iterated function system on $[0,1]$ and let $\unicode[STIX]{x1D6EC}$ be its attractor. Then, for any $x\in \unicode[STIX]{x1D6EC}$, it corresponds to a sequence of integers $\{a_{n}(x)\}_{n\geq 1}$, called the digit sequence of $x$, in the sense that $$\begin{eqnarray}x=\lim _{n\rightarrow \infty }f_{a_{1}(x)}\circ \cdots \circ f_{a_{n}(x)}(1).\end{eqnarray}$$ In this note, we investigate the size of the points whose digit sequences are strictly increasing and of upper Banach density one, which improves the work of Tong and Wang and Zhang and Cao.

Algorithm for Computing Attribute Reduction Based on Radix Sort of Optimized Linked List Structure

The attribute reduction algorithm of radix sort to integer digit sequence table is not ideal. In this paper, based on how integers is stored in computer memory, low and high storage mode is designed for the solving algorithm of U/C chain structure of a new reasonable optimization. The time complexity of the algorithm from O (K|C| |U|) is reduced to O (K|C| |U| log (|M|)). The efficiency of the algorithm is improved by 3.8%.